Liquid Interfaces in Chemical, Biological, and Pharmaceutical Applications (Surfactant Science Series)

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ISBN: 0-8247-0457-6 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-261-8482; fax: 41-61-261-8896 World Wide Web http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright # 2001 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced on transmitted in any form or by any means, electronic or mechanical, including photocopying, microﬁlming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA

Preface

Boundary membranes play a key role in the cells of all contemporary organisms, and simple models of membrane function are therefore of considerable interest. The interface of two immiscible liquids has been widely used for this purpose. For example, the fundamental processes of photosynthesis, biocatalysis, membrane fusion and interactions of cells, ion pumping, and electron transport have all been investigated in such interfacial systems. Processes occurring at the interface between two immiscible liquids present a challenge of great interest because heterogeneous structures of this kind are frequently encountered in Nature. In particular, the electrical double layer at the oil–water interface occurs in a heterogeneous interfacial region that separates different bulk regions of conductive polarized media with a spatial separation of charges. The electrical double layer at the interface between two immiscible liquids determines the kinetics of charge transfer across the phase boundaries, stability and electrokinetic properties of lyophobic colloids, mechanisms of phase transfer or interfacial catalysis, charge separation in biological energy transduction, and heterogeneous enzymatic catalysis. The elucidation of the structure of the interface between two immiscible liquids and the mechanism of charge separation is a fundamental problem of modern chemistry and chemical technology. The interface between two immiscible electrolyte solutions can be either polarizable or nonpolarizable, depending on its permeability to charged particles in the system. If the interface is impermeable to charged particles or the transfer between the phases is difﬁcult, it is called polarizable. A completely nonpolarizable interface containing at least one common ion can pass a high current in either direction without giving rise to a deviation of the interfacial potential difference from the equilibrium value. Although in practice we encounter neither ideally polarizable nor completely nonpolarizable interfaces, under certain conditions the properties of some interfaces are close to ideal. Since any interface is permeable to ions to some extent, only an approximation of the limiting version of a polarizable interface can be realized experimentally. Michael Faraday ﬁrst studied electron transfer reactions at oil–water interfaces to prepare colloidal metals by reducing metal salts at the ether–water or carbon disulﬁde– water interfaces. As the ﬁeld progressed after Faraday’s pioneering observations, it iii

iv

Preface

became clear that vectorial charge transfer at the interface between two dielectric media is an important stage in many bioelectrochemical processes such as those mediated by energy-transducing membranes. Studies have been made on redox and hydrolysis reactions catalyzed by enzymes, photosynthetic pigments, metal complexes of porphyrins, bacteria, and submitochondrial particles, as well as in systems with an extended surface—in microemulsions, vesicles, and reversed micelles. Naturally immobilized enzymes and pigments embedded in a hydrophilic-hydrophobic interface have properties similar to their functional state in a membrane. For instance, certain enzymes can be highly active at the interface but virtually inactive in a homogeneous medium. The interface between two immiscible liquids with immobilized photosynthetic pigments can serve as a convenient model for investigating photoprocesses that are accompanied by spatial separation of charges. The efﬁciency of charge separation deﬁnes the quantum yield of any photochemical reaction. Heterogeneous sytems will be most effective in this regard, where the oxidants and the reductants are either in different phases or sterically separated. Different solubilities of the substrates and reaction products in the two phases of heterogeneous systems can alter the redox potential of reactants, making it possible to carry out reactions that cannot be performed in a homogeneous phase. Elucidation of photosynthetic mechanisms is also signiﬁcant in designing artiﬁcial systems for solar energy utilization. The quantum yield of the photocatalytic reaction depends ﬁrst of all on the efﬁciency of the photochemical charge separation. The most effective system should be a heterogeneous system in which the oxidant and the reductant are either in different phases or sterically separated. The difference in solubilities of the substrates and reaction products in both phases of such a heterogeneous structure as the octane–water interface can shift the reaction equilibrium. The redox potential scale is thereby altered, making it possible to carry out reactions that cannot be performed in a homogeneous phase. Extraction of the reaction products and adsorption of the reaction components determine high catalytic properties of the interface between two immiscible liquids, recognized recently as interfacial catalysis. Chemical models of photosynthesis have been used to investigate two types of reactions: photosynthesis and photocatalysis. In photosynthetic processes the standard Gibbs free energy of the reaction is positive, and solar energy is utilized to perform work. In photocatalytic processes the free energy is negative and solar energy is used to overcome the activation barrier. The processes of life have been found to generate electric ﬁelds in every organism that has been examined with suitable and sufﬁciently sensitive measuring techniques. The electrochemical conduction of electrochemical excitation over specialized structures must be regarded as one of the most universal properties of living organisms. It arose at the early stages of evolution in connection with the need for transmission of a signal about an external inﬂuence from one part of a biological system to another. Clearly, then, the chemical and physical properties of liquid interfaces represent a signiﬁcant interdisciplinary research area for a broad range of investigators, such as those who have contributed to this book. The chapters are organized into three parts. The ﬁrst deals with the chemical and physical structure of oil–water interfaces and membrane surfaces. Eighteen chapters present discussion of interfacial potentials, ion solvation, electrostatic instabilities in double layers, theory of adsorption, nonlinear optics, interfacial kinetics, microstructure effects, ultramicroelectrode techniques, catalysis, and extraction. The second part, on biological applications of interfacial phenomena, has ten chapters that deal successively with protein encapsulation, membranes, effects of phospholi-

Preface

v

pids, biocatalysis, oscillation of membrane potentials, and fundamentals of interfacial electrochemical phenomena in green plants. The ﬁnal part, on pharmaceutical applications, consists of ﬁve chapters and includes topics such as drugs at liquid interfaces, NMR studies, and drugs and gene delivery. We thank the authors for the time they spent on this project and for teaching us about their work. Alexander G. Volkov

Contents

Preface iii Contributors Part I.

xi

Chemistry at Liquid Interfaces

1.

Interfacial Potentials and Cells Zbigniew Koczorowski

1

2.

Ion Solvation and Resolvation 23 Toshiyuki Osakai and Kuniyoshi Ebina

3.

Electroelastic Instabilities in Double Layers and Membranes Michael B. Partenskii and Peter C. Jordan

4.

The GvdW Theory: A Density Functional Theory of Adsorption, Surface Tension, and Screening 83 Sture Nordholm and Robert Penfold

5.

Adsorption at Polarized Liquid–Liquid Interfaces Takashi Kakiuchi

6.

Nonlinear Optics at Liquid–Liquid Interfaces Pierre-Francois Brevet

7.

The Lattice-Gas and Other Simple Models for Liquid–Liquid Interfaces Wolfgang Schmickler

8.

Dynamic Aspects of Heterogeneous Electron-Transfer Reactions at Liquid–Liquid Interfaces 179 David J. Fermı´n and Riikka Lahtinen

9.

Dynamic Behaviors of Molecules at Liquid–Liquid Interfaces Using the TimeResolved Quasi-Elastic Laser Scattering Method 229 Isao Tsuyumoto and Tsuguo Sawada

51

105

123 153

vii

viii

Contents

10.

Microstructure Effects on Transport in Reverse Microemulsions 241 John Texter

11.

Investigation of Oil–Water Interfaces by Spectroscopic Methods. Relations with Rheological Properties of Multiphasic Systems 257 Eric Dufour, C. Lopez, and S. Herbert

12.

Scanning Electrochemical Microscopy as a Local Probe of Chemical Processes at Liquid Interfaces 283 Anna L. Barker, Christopher J. Slevin, Patrick R. Unwin, and Jie Zhang

13.

Hydrodynamic Techniques for Investigating Reaction Kinetics at Liquid–Liquid Interfaces: Historical Overview and Recent Developments 325 Christopher J. Slevin, Patrick R. Unwin, and Jie Zhang

14.

Catalytic Effect of the Liquid–Liquid Interface in Solvent Extraction Kinetics Hitoshi Watarai

15.

Voltammetry at Micro-ITIES 373 Biao Liu and Michael V. Mirkin

16.

Dynamics of Polar Solvent Motion at Liquid Interfaces Nancy E. Levinger and Ruth E. Riter

17.

Capacitance and Surface Tension Measurements of Liquid–Liquid Interfaces Zdeneˇk Samec

18.

Liquid Membrane Ion-Selective Electrodes: Response Mechanisms Studied by Optical Second Harmonic Generation and Photoswitchable Ionophores as a Molecular Probe 439 Yoshio Umezawa

Part II.

399

Liquid Interfaces in Biological Applications

19.

Water-in-Oil Microemulsions: Protein Encapsulation and Release Douglas G. Hayes

20.

Biomimetic Charge Transfers Through Artiﬁcial Membranes 487 Sorin Kihara, Hiroyuki Ohde, Kohji Maeda, Yumi Yoshida, and Osamu Shirai

21.

DNA-Modiﬁed Electrodes. Molecular Recognition of DNA and Biosensor Applications 515 Koji Nakano

22.

Phospholipids at Liquid–Liquid Interfaces and Their Effect on Charge Transfer 533 Lasse Murtoma¨ki, Jose´ A. Manzanares, Salvador Mafe´, and Kyo¨sti Kontturi

23.

Biocatalysis in Liquid–Liquid Biphasic Media: Coupled Mass Transfer and Chemical Reactions 553 Mohamed Gargouri

24.

Design of Biocompatible Ion Sensors Keiichi Kimura

585

355

469

415

Contents

ix

25.

The Oscillation of Membrane Potential or Membrane Current Kohji Maeda and Sorin Kihara

26.

Selective Ion Transfer of Alkali and Alkaline Earth Metal Ions Facilitated by Naphtho-15-Crown-5 Across Liquid–Liquid Interfaces and a Bilayer Lipid Membrane 629 Hidekazu Doe

27.

Langmuir and Langmuir–Blodgett Films of Chlorophyll a and Photosystem II Complex 641 Roger M. Leblanc and Veeranjaneyulu Konka

28.

Interfacial Electrical Phenomena in Green Plants: Action Potentials Alexander G. Volkov and John Mwesigwa

Part III.

609

649

Pharmaceutical Applications: Drugs at Liquid Interfaces

29.

Voltammetric Study of Drugs at Liquid–Liquid Interfaces Mitsugi Senda, Yuko Kubota, and Hajime Katano

30.

Electrical Potential Oscillation Across a Water–Oil–Water Liquid Membrane in the Presence of Drugs 699 Kensuke Arai and Fumiyo Kusu

31.

Transfer Mechanisms and Lipophilicity of Ionizable Drugs Fre´de´ric Reymond

32.

NMR Studies on Lipid Bilayer Interfaces Coupled with Anesthetics and Endocrine Disruptors 775 Emiko Okamura and Masaru Nakahara

33.

Lipid Bilayers in Cells: Implications in Drug and Gene Delivery T. Marjukka Suhonen, Pekka Suhonen, and Arto Urtti

Index

845

683

729

807

Contributors

Kensuke Arai Department of Analytical Chemistry, Tokyo University of Pharmacy and Life Science, Tokyo, Japan Anna L. Barker

Department of Chemistry, University of Warwick, Coventry, England

Pierre-Francois Brevet Laboratoire d’Electrochimie, De´partement de Chimie, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, Switzerland Hidekazu Doe

Department of Chemistry, Osaka City University, Osaka, Japan

Eric Dufour De´partement Qualite´ et Economie Alimentaires, ENITA ClermontFerrand, Lempdes, France Kuniyoshi Ebina Kobe, Japan

Division of Sciences for Natural Environment, Kobe University,

David J. Fermı´n Laboratoire d’Electrochimie, De´partement de Chimie, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, Switzerland Mohamed Gargouri Department of Biological and Chemical Engineering, National Institute for Applied Science and Technology, Tunis, Tunisia Douglas G. Hayes Department of Chemical and Materials Engineering, University of Alabama in Huntsville, Huntsville, Alabama S. Herbert

INRA-LEIMA, Nantes, France

Peter C. Jordan Massachusetts

Department

of

Chemistry,

Brandeis

University,

Waltham,

Takashi Kakiuchi Department of Energy and Hydrocarbon Chemistry, Kyoto University, Kyoto, Japan Hajime Katano Sorin Kihara

Department of Bioscience, Fukui Prefectural University, Fukui, Japan Department of Chemistry, Kyoto Institute of Technology, Kyoto, Japan xi

xii

Contributors

Keiichi Kimura Department of Applied Chemistry, Faculty of Systems Engineering, Wakayama University, Wakayama, Japan Zbigniew Koczorowski Poland

Department of Chemistry, University of Warsaw, Warsaw,

Veeranjaneyulu Konka Florida

Department of Chemistry, University of Miami, Coral Gables,

Kyo¨sti Kontturi Department of Chemical Technology, Helsinki University of Technology, Espoo, Finland Yuko Kubota

Department of Bioscience, Fukui Prefectural University, Fukui, Japan

Fumiyo Kusu Department of Analytical Chemistry, Tokyo University of Pharmacy and Life Science, Tokyo, Japan Riikka Lahtinen Laboratory of Physical Chemistry and Electrochemistry, Department of Chemical Technology, Helsinki University of Technology, Espoo, Finland Roger M. Leblanc Florida

Department of Chemistry, University of Miami, Coral Gables,

Nancy E. Levinger Colorado

Department of Chemistry, Colorado State University, Fort Collins,

Biao Liu Department of Chemistry and Biochemistry, City University of New York, Queens College, Flushing, New York C. Lopez

INRA-LEIMA, Nantes, France

Kohji Maeda

Department of Chemistry, Kyoto Institute of Technology, Kyoto, Japan

Salvador Mafe´ Valencia, Spain

Department of Thermodynamics, University of Valencia, Burjasot,

Jose´ A. Manzanares Department of Thermodynamics, University of Valencia, Burjasot, Valencia, Spain Michael V. Mirkin Department of Chemistry and Biochemistry, City University of New York, Queens College, Flushing, New York Lasse Murtoma¨ki Department of Chemical Technology, Helsinki University of Technology, Espoo, Finland John Mwesigwa

Department of Chemistry, Oakwood College, Huntsville, Alabama

Masaru Nakahara

Institute for Chemical Research, Kyoto University, Kyoto, Japan

Koji Nakano Department of Chemical Systems and Engineering, Kyushu University, Fukuoka, Japan Sture Nordholm

Department of Chemistry, Go¨teborg University, Go¨teborg, Sweden

Hiroyuki Ohde Japan

Department of Chemistry, Kyoto Institute of Technology, Kyoto,

Emiko Okamura Toshiyuki Osakai

Institute for Chemical Research, Kyoto University, Kyoto, Japan Department of Chemistry, Kobe University, Kobe, Japan

Contributors

xiii

Michael B. Partenskii Massachusetts

Department of Chemistry, Brandeis University, Waltham,

Robert Penfold Food Materials Science Division, Institute of Food Research, Norwich, England Fre´de´ric Reymond Laboratoire d’Electrochimie, De´partement de Chimie, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, Switzerland Ruth E. Riter

Department of Chemistry, Agnes Scott College, Decatur, Georgia

Zdeneˇk Samec J. Heyrovsky´ Institute of Physical Chemistry, Academy of Sciences of The Czech Republic, Prague, Czech Republic Tsuguo Sawada Tokyo, Japan

Department of Advanced Materials Science, University of Tokyo,

Wolfgang Schmickler Germany Mitsugi Senda

Department of Electrochemistry, University of Ulm, Ulm,

Department of Bioscience, Fukui Prefectural University, Fukui, Japan

Osamu Shirai Department of Nuclear Energy System, Japan Atomic Energy Research Institute, Ibaraki, Japan Christopher J. Slevin Department of Chemistry, University of Warwick, Coventry, England Pekka Suhonen Finland

Department of Pharmaceutics, University of Kuopio, Kuopio,

T. Marjukka Suhonen Finland John Texter

Department of Pharmaceutics, University of Kuopio, Kuopio,

Strider Research Corporation, Rochester, New York

Isao Tsuyumoto Department of Environmental Systems Engineering, Kanazawa Institute of Technology, Ishikawa, Japan Yoshio Umezawa

Department of Chemistry, University of Tokyo, Tokyo, Japan

Patrick R. Unwin England Arto Urtti

Department of Chemistry, University of Warwick, Coventry,

Department of Pharmaceutics, University of Kuopio, Kuopio, Finland

Alexander G. Volkov Alabama Hitoshi Watarai Yumi Yoshida Jie Zhang

Department of Chemistry, Oakwood College, Huntsville,

Department of Chemistry, Osaka University, Osaka, Japan Department of Chemistry, Kyoto Institute of Technology, Kyoto, Japan

Department of Chemistry, University of Warwick, Coventry, England

Current afﬁliation: DiagnoSwiss, Monthey, Switzerland.

1 Interfacial Potentials and Cells ZBIGNIEW KOCZOROWSKI Warsaw, Poland

I.

Department of Chemistry, University of Warsaw,

INTRODUCTION

Liquid surfaces and liquid–liquid interfaces are very common and have tremendous signiﬁcance in the real world. Especially important are the interfaces between two immiscible liquid electrolyte solutions (acronym ITIES), which occur in tissues and cells of all living organisms. The usual presence of aqueous electrolyte solution as one phase of ITIES is the main reason for the electrochemical nature of such interfaces. Every liquid interface is usually electriﬁed by ion separation, dipole orientation, or both (Section II). It is convenient to distinguish two groups of immiscible liquid– liquid interfaces: water–polar solvent, such as nitrobenzene and 1,2-dichloroethane, and water–nonpolar solvent, e.g., octane or decane interfaces. For the second group it is impossible to investigate the interphase electrochemical equilibria and the Galvani potentials, whereas it is normal practice for the ﬁrst group (Section III). On the other hand, these systems are very important as parts of the voltaic cells. They make it possible to measure the surface potential differences and the adsorption potentials (Section IV). Electrochemical studies of liquid–liquid interfaces brought very signiﬁcant advances during the last quarter of the 20th century. Traditional electrochemical experiments and theoretical approaches of interfacial chemistry have contributed much to our present understanding of the phenomena occurring at the ITIES. The fast development of this discipline has been documented in many review articles. Among them should be mentioned some reviews published during the last several years [1–16]. The brief history of achievements, and references to them, can be found in a number of papers [1,3,4,8,11,17,18]. Liquid–liquid interfaces occur as macro- and also as micro- and nanoheterogenous systems (termed small systems), described in colloidal chemistry as, e.g., miscelles, vesicles, and microemulsions [14,19] (see also Section V). Up to now, fast progress concerns mainly the macrosystems (> 100 m), including all types of natural and artiﬁcial membranes.

1

2

II.

Koczorowski

ELECTRIFIED LIQUID–LIQUID INTERFACES AND THEIR ELECTRICAL POTENTIALS

At a phase boundary (or interface) the molecular species experience anisotropic forces, which vary with the distance from the interface. This causes a net orientation of solvent and other molecular dipoles and a net excess of ions near the phase boundary, on both sides of the solution. The term ‘‘electriﬁed’’ interface means that there occur differences in potential, charge densities, dipole moments, and electric currents. The system and terminology of the thermodynamic and electrical interfacial potentials, recommended for description of all electriﬁed phases and interfaces [18,20,21], is also very useful for the liquid–liquid boundaries [3,8,14,15–17,22–35], e.g., at the interfaces of two immiscible electrolyte solutions: water (w), and an organic solvent (s). The presence of an electrical potential drop, i.e., interfacial potential, across the boundary between two dissimilar phases, as well as at their surfaces exposed to a neutral gas phase, is the most characteristic feature of every interface and surface electriﬁed due to the ion separation and dipole orientation. This charge separation is usually described as the formation of the ionic and dipolar double layers. The main interfacial potential is the Galvani potential (termed also by Trasatti the operative potential), ws ’, which is the difference of inner potentials ’2 and ’s of both phases. It is a function only of the chemical nature of the contacting phases in the equilibrium, but it is not a measurable quantity. In the equilibrium state, the electrochemical potentials of each i ion, present simultaneously in both phases are identical: wi ¼ si

ð1Þ

Using the deﬁnition of the electrochemical potential this can be rewritten in the following forms: ws ’ ¼ ’w ’s ¼ ð1=zi FÞws i

ð2Þ

s s 0;w þ RT ln awi þ zi F’w ¼ 0;s i i þ RT ln ai þ zi F’

ð3Þ

w s where i0;w , 0;s i stand for standard chemical potentials of ions, ai and ai represent their activities in both phases, and R, F, and T have their usual meanings, namely the gas constant, Faraday constant, and temperature (K). From Eq. (3) one can derive the dependence of the Nernst dependence of the Galvani potential at the single interface.

ws ’ ¼ ’w ’s ¼ ws ’0i þ

RT asi ln zi F awi

ð4Þ

It follows from Eq. (4) that the Galvani potential can be calculated from the values of the standard potential and the activity of any ion participating in the equilibrium distribution. The standard Galvani potential is deﬁned as follows: ws ’0i ¼ sw G0i =zi F

ð5Þ

This dependence is fundamental for electrochemistry, but its key role for liquid–liquid interfaces was ﬁrst recognized by Koryta [1–5,35]. The standard transfer energy of an ion 0;ws , denoted in abbreviated form from the aqueous phase to the nonaqueous phase, Gtr;i w 0 by the symbol s Gi is the difference of standard chemical potential of standard chemical potentials of the ions, i.e., of the standard Gibbs energies of solvation in both phases,

Interfacial Potentials and Cells

ws G0i ¼ 0;w i0;s i

3

ð6Þ

Equation (4) can be rewritten in the form: ws ’ ¼ ws ’0i þ

RT is csi ln zi F iw cwi

ð7Þ

where sw and iw represent the activity coefﬁcients. Besides the Galvani potential, another important interfacial potential is the Volta potential, ws , sometimes called the contact potential. ws is the difference of the outer potentials of the phases, which are in electrochemical equilibrium with regard to the charged species, i.e., ions or electrons. As for any two-phase electrochemical system, including the w/s system, it may be characterized by the commonly known relation: ws ¼ zi Fðwi wi Þ

ð8Þ

s where M i and i are the real potentials of the charged species i, deﬁned as the sum of its chemical potential and the electrical term containing the surface potential of the phase, e.g., for the solution:

si ¼ si þ zi Fs

ð9Þ

The electrical potentials assumed to exist at liquid–liquid interfaces, including inert gas or liquid dielectric environments are presented in Fig. 1. Equations (1) and (2) together with ws ¼ 2s ’ 2s

ð10Þ

make it possible to ﬁnd some important electrochemical information. The Volta potential, in contradiction to the Galvani potential, has the advantage of being measurable but also the disadvantage that it is not determined only by the chemical nature of the phases which create the interface, but also by the state at their surfaces, represented by the surface potentials, Eqs. (8) and (9). In principle, the distribution of ions and dipoles at the w/s interface is different from that at the free w and s surfaces. Therefore, the Galvani potential may be also written, in the absence of speciﬁc adsorption, as the sum of the charge and dipole components [15,20– 22]: ws ’ ¼ gws ðionÞ þ gws ðdipÞ

FIG. 1 The electric potentials assumed to exist at liquid–liquid interfaces.

ð11Þ

4

Koczorowski

Usually gws ðionÞ 6¼ 2s and gws ðdipÞ 6¼ ws . This is caused by mutual inﬂuence of the contacting phases on the orientation of dipolar molecules in the interfacial zone. The situation that no charge transfer across the interface occurs is named the ideal polarized or blocked interface. Such interfaces do not permit, due to thermodynamic or kinetic reasons, either electron or ion transfer. They possess Galvani potentials ﬁxed by the electrolyte and charge. Of course, the ideal polarizable interface is practically a limiting case of the interfaces with charge transfer, because any interface is always permeable to ions to some extent. Therefore, only an approximation of the ideal polarizable interface can be realized experimentally (Section III.D). If the interface is in the zero charge state, named also the point of zero charge (pzc), the Galvani potential should be equal to the dipolar term [19–21]: ws ’ðpzcÞ ¼ ws gðdipÞ

ð12Þ

The speciﬁc adsorption, which in the case of ITIES is usually the adsorption of ionic pairs [8], contributes to the Galvani potential, as well as changes the zero charge of this interface. The surface potential of a liquid solvent s, s , is deﬁned as the difference of electrical potentials across the interface between this solvent and the gas phase, with the assumption that the outer potential of the solvent is zero [21,22]. The potential s of pure molecular liquid arises from a preferred orientation of the solvent dipoles in the free surface zone. At the surface of solution the electric ﬁeld responsible for the surface potential may arise from a preferred orientation of the solvent and solute dipoles, and from the ionic double layer (Section IV). The potential s , as the difference of electrical potential across the interface between the phase and gas, is not measurable. But its relative changes caused by the change of solution composition can be determined using the proper voltaic cells (see Section IV). The name ‘‘surface potential’’ is unfortunately also often used for the description the ionic double layer potential (i.e., the ionic part of the Galvani potential) at the interfaces of membranes, microemulsion droplets and micelles, measured usually by the acid–base indicator technique (Section V).

III.

LIQUID GALVANIC CELLS AND THE GALVANI POTENTIALS

The interface separating two immiscible electrolyte solutions, e.g., one aqueous and the other based on a polar organic solvent, may be reversible with respect to one or many ions simultaneously, and also to electrons. Works by Nernst constitute a fundamental contribution to the electrochemical analysis of the phase equilibrium between two immiscible electrolyte solutions [1–3]. According to these works, in the above system electrical potentials originate from the difference of distribution coefﬁcients of ions of the electrolyte present in the both phases. Nernst’s approach was supported by Verwey and Niessen’s interpretation [23], and by the experiments of Randles and Karpfen [24], and others, cited in Ref. 3. These authors, and in particular Davies and Rideal [17] consolidated the description of Galvani potential in the case of the 1 : 1 electrolyte distribution. As mentioned in the Introduction, in the discussion of liquid electrochemical cells it is necessary to distinguish two groups of immiscible liquid–liquid interfaces: water–polar organic solvent, e.g., nitrobenzene, and water–nonpolar organic solvent (water–oil or water–hydrocarbon), e.g., octane type systems. It is schematically presented as

Interfacial Potentials and Cells

5

j j

polar solvent (s) þ ions

water (w) þ ions

ws ’ SCHEME 1 and j j

nonpolar solvent (ns) + ions

water (w) + ions

w=ns SCHEME 2 The main difference is the presence of a dissociated electrolyte in the organic phase of the ﬁrst group in contradiction to the second. As clearly shown by Davies and Rideal [17], this decides about the character of the interfacial potential to be measured. If the organic phase constitutes the solution of the dissociated electrolyte, the ionic double layer is created there, and the Galvani potential changes may be measured. In the opposite case, the voltaic cell allows one to measure the surface potential changes (see Section IV). Of course, in liquid galvanic cells only the water–polar solvent interfaces can be investigated. A.

Galvani Potential and Ionic Distribution Equilibria

Le Hung presented a general theoretical approach for calculating the Galvani potential ws ’ at the interface of two immiscible electrolyte solutions, e.g., aqueous (w) and organic solvent (s) [25]. Le Hung’s approach allows the calculation of ws ’ when the initial concentration (ci ), activity coefﬁcients (i ) and standard energies of transfer of ions (ws G0i ) are known in both solutions. According to Le Hung, one deals, in general, with a system composed of two liquid immiscible phases containing Iizi ions; this can be described as follows: w

j

s

Iizi

j

Iizi

Vw

$ SCHEME 3

Vs

where zi represents the charge of the Iizi ion, and Vw and Vs are the volumes of phases w and s, respectively. In the equilibrium state the electrochemical potentials of each ion are the same in both phases, and the equations (1) to (7) are fulﬁlled. It is apparent from the mass conservation law that: Vw cwi þ Vs csi ¼ mi

ð13Þ

where mi represents the number of moles of condition of electroneutrality is still valid: j X 1

zi cwi ¼ 0

j X 1

zi csi ¼ 0

j X

Iizi

ions in both phases. For these phases the

zi mi ¼ 0

ð14Þ

1

Using Eqs. (7), (13), and (14), Le Hung derived the general dependence describing the difference of Galvani potentials between the phases w and s:

6

Koczorowski j X 1

iw zi F w w 0 ’ s ’i Vw þ Vs s exp ¼0 zm m i RT s i

ð15Þ

or in the form: h X

zi ci0;w

i

V w zF 1 þ s is exp i ws ’ ws ’0i þ RT V w i þ

j X

zi ci0;s

h

Vw iw zi F w w 0 ’ s ’i 1þ ¼0 exp RT s Vs is

ð16Þ

Ions having initial concentrations, i.e., not equilibrium conditions, c0;w and ci0;s , marked i with indices from 1 to h and from h to j, occur in the phases w and s, respectively. When 0;s w 0 w the values of zi , Vw , Vs , iw , is , c0;w i , ci , s ’i , and T are known, one can ﬁnd s ’. The convenient form of Hung’s equation is the dependence [14] h X i¼1

h X zi ciw;0 rzi cis;0 ¼0 w s þ 1 þ rði =i Þ i¼1 1 þ rðiw =is Þei

ð17Þ

where r ¼ V s =V w

ð18Þ

ei ¼ exp ðzi F=RTÞðws ’eq ws ’0i Þ

ð19Þ

and

The above equation allows the calculation of Galvani potentials at the interfaces of immiscible electrolyte solutions in the presence of any number of ions with any valence, also including the cases of association or complexing in one of the phases. Makrlik [26] described the cases of association and formation of complexes with participation of one of the ions but in both phases. In a later work [27] Le Hung extended his approach and also considered any mutual interaction of ions and molecules present in both phases. Buck and Vanysek performed the detailed analysis of various practical cases, including membrane equilibria, of multi-ion distribution potential equations [28,29]. The few cases of Le Hung’s equation, for practically important and simple systems, are discussed below.

B.

Distribution Potentials for Binary Electrolytes

In the case of an electrolyte of the type Mm Xx , in the state distribution equilibrium, i.e., for the system: w

j

s

Mm Xx Vw

$ j

Mm X x Vs

SCHEME 4 Eq. (16) can be written as follows:

Interfacial Potentials and Cells

w M zM þ F w þ w 0 s ’ s ’ðM þ Þ Vw þ Vs s exp Zm ; mM þ RT M þ Xw ZX F w w 0 s ’ s ’ðX Þ Vw þ Vs s exp ¼0 þ ZX mX RT X

7

ð20Þ

From Eqs. (14) and (20) one can obtain: ws ’0 ¼

zM þ ws ’0M þ zX ws ’0X RT s þ Xw ln M þ w s ðzX þ zM þ ÞF M zX þ zM þ þ X

ð21Þ

When the distribution equilibrium refers to the 1 : 1 valent electrolyte, e.g., MX, where zX ¼ 1, i.e., for the system j $

w MþX

s MþX

SCHEME 5 Vw ¼ Vs Eq. (21) appears in the form: ws ’ðMXÞ ¼

s w ws ’0ðM þ Þ þ ws ’0ðX Þ RT M þ ln w Xs þ 2F M þ X 2

ð22Þ

The above dependence, which has been known for a long time, can be directly derived from Eq. (3) and the electroneutrality conditions of Eq. (14) which for that case are in the form: RT s ln aM þ =awM þ F RT lnðasX =awX Þ ws ’ ¼ ws ’0 ðX Þ F ws ’ ¼ ws ’0 ðM þ Þ þ

ð23Þ ð24Þ

and csM þ cwX ¼1 cwM þ csX

ð25Þ

The formal Galvani potential, described by Eq. (22), practically does not depend on the concentration of ions of the electrolyte MX. Since the term containing the activity coefﬁcients of ions in both solutions is, as experimentally shown, equal to zero it may be neglected. This results predominantly from the cross-symmetry of this term and is even more evident when the ion activity coefﬁcients are replaced by their mean values. A decrease of the difference in the activity coefﬁcients in both phase is, in addition, favored by partial hydration of the ions in the organic phase [31–33]. Thus, a liquid interface is practically characterized by the standard Galvani potential, usually known as the distribution potential. For symmetrical electrolytes, of, e.g., type 1 : 1, such a liquid–liquid interface, in equilibrium, is described by the standard Galvani potential, usually called the distribution potential. This very important quantity can be expressed in the three equivalent forms, i.e., using the ionic standard potentials, or standard Gibbs energies of transfer, and employing the limiting ionic partition coefﬁcients [3]:

8

Koczorowski

ws ’ðMXÞ ¼ 12 ws ’0 M þ þ ws ’0 ðX Þ

ð26Þ

ws ’0 ðMXÞ ¼

1 w 0 G þ ws G0X 2F s M

ð27Þ

ws ’0 ðMXÞ ¼

RT Bws;0 ðM þ Þ ln s;0 2F Bw ðX Þ

ð28Þ

It is obvious from Eq. (21) that Eqs. (22), (26), (27), and (28) apply to all symmetrical electrolytes, i.e., to electrolytes dissociating into the same number of cations and anions. According to Eq. (26), which directly ensues from Eq. (22), the distribution potential is the arithmetic mean of the Galvani potentials of cations and anions. These potentials are the ionic constituents of the distribution potential, and in fact, according to Eq. (5) they can be considered as electrical representations of the ionic transfer energies Gi , or limiting distribution coefﬁcients of the ions, Bi [3]. Here, the reader is referred to the following equations: þ Fws ’0 ðM þ Þ ¼ ws G0M þ ¼ RT ln Bs;0 w ðM Þ

ð29Þ

Fws ’0 ðX Þ ¼ ws G0X ¼ RT ln Bws;0 ðX Þ

ð30Þ

It is noteworthy [3,31] that for the case where þ w;0 1 Bw;0 M ¼ Bs ðX Þ s

ð31Þ

it appears that ws ’0 ðMXÞ ¼ ws ’0 ðM þ Þ ¼ ws ’0 ðX Þ

ð32Þ

Equation (31) is true only when standard chemical potentials, i.e., chemical solvation energies, of cations and anions are identical in both phases. Indeed, this occurs when two solutions in the same solvent are separated by a membrane. Hence, the Donnan equilibrium expressed in the form of Eq. (32) can be considered as a particular case of the Nernst distribution equilibrium. The distribution coefﬁcients or distribution constants of the ions, Bws;0 ðM þ Þ and Bws;0 ðX Þ, are related to the extraction constant KMX and to the distribution coefﬁcient of the B0MX electrolyte in the manner described below [24]. The standard distribution constant describing the equilibrium in the system M þ ðwÞ þ X ðwÞ

$ SCHEME 6

M þ ðsÞ þ X ðsÞ

can be expressed, in the equilibrium state, as follows: as þ asX 0 ¼ exp G0MX =RT ¼ M KMX awM þ awX

ð33Þ

Expressing the distribution constant in terms of the mean electrolyte activities one obtains: s a KMX ¼ ð34Þ aw From the above dependence, and from the deﬁnition of the limiting or activity distribution coefﬁcient of electrolyte, i.e., from the equation: Bs;0 wðMXÞ ¼

as aw

ð35Þ

Interfacial Potentials and Cells

9

a relationship between the above-mentioned functions is as follows: h i1=2 1=2 s;0 s;0 Bs;0 wðMXÞ ¼ KMX ¼ BwðM þ Þ BwðX Þ

ð36Þ

The transfer energies and distribution coefﬁcients refer to two mutually saturated, i.e., in a sense, mixed solvents. It should be noted that this is a case where, under conditions of distribution equilibrium, the quantities in question can be experimentally measured; this would not be possible with mutually miscible solvents [34]. C.

Interfaces Reversible with Respect to Single Ions

The interface between w and s containing electrolytes of the MX1 and MX2 type, respectively, and represented in the form: w

j

s

M þ X1

j

M þ X2

SCHEME 7 constitutes an interface reversible with regard to the common cation M þ under the following conditions [1–3]: sw G0X1 0 sw G0X2 0

ð37Þ

sw G0X2 < sw G0M þ < sw G0X1 It is obvious from the above conditions that the transfer of strongly hydrophylic X1 anions from phase w to s and of strongly hydrophobic X2 anions from phase s to w is much more difﬁcult compared to the transfer of the common hydrophylic–hydrophobic M þ cations. In the equilibrium state, the Galvani potential is deﬁned in terms of the Nernst equation (4): ws ’ ¼ ws ’ðM þ Þ ¼ ws ’0ðM þ Þ þ

RT awM þ ln s F aM þ

ð38Þ

When the concentration of M þ ions is the same in both phases of the system of Scheme 7, the interface is characterized by the formal Galvani potential of the M þ ions, i.e. by the equation: ws ’fðM þ Þ ¼ ws ’0ðM þ Þ þ

w RT M þ ln s F M þ

ð39Þ

Equations (38) and (39) have been known and used for a long time as special relations describing Haber’s ion-selective systems. D.

Liquid Galvanic Cells

Measurement of electrical potential differences requires a complete electrical circuit, i.e., the electrochemical cell. An electrochemical galvanic cell consisting of all conducting phases, and among them at least one interface separating two immiscible electrolyte solutions is called for short a liquid galvanic cell. In contrast, the system composed of con-

10

Koczorowski

ducting, condensed phases in series, with a gas gap or dielectric liquid phase is called a liquid voltaic cell (see Section IV). It is known [3] that galvanic liquid cells, being in the state of complete equilibrium, i.e. containing reversible electrodes in both phases, cannot constitute any subject of research interest, because according to the second law of thermodynamics such systems would have a zero or constant value of EMF. Therefore, the application of salt bridges, providing practically constant or negligible diffusion potentials, constitutes a nonthermodynamic procedure usually necessary in many electrochemical experiments. Also in the case of investigation of interfaces between immiscible electrolyte solutions only a liquid galvanic cell with transport allows the characterization of the interface. Practically all liquid cells with reversible interfacial equilibria examined can be considered as liquid galvanic cells of the Nernst, Haber, or intermediate type [3]. Usually, a dashed vertical bar (j) is used to represent the junction between liquids. A double dashed vertical bar (k) represents a liquid junction in which the diffusion potential has been assumed to be eliminated. Galvanic cells of the Nerst type are also termed cells with ‘‘dissolution membranes’’ or ‘‘solvent type membranes’’ [3]. Such systems are deﬁned by the distribution equilibria in which all ions, present in aqueous and in organic solvents, participate (Section III.A). The general examples of the liquid concentration and chemical galvanic cells of this type are presented in the form of Schemes 8 and 9. The concentration cells of the Nernst type can be represented in the form of the scheme

SCE

k

aqueous

j organic

j aqueous

k

k k

solution M þ A ; c1

j solution j M þ A

j solution j M þ A ; c2

k k

j j

j j

k k

k k

Bc1 Bc2 ðc1 6¼ c2 Þ

SCE

SCHEME 8 where the completely dissociated MA electrolyte, with the distribution coefﬁcient B (concentrations c1 6¼ c2 ), generates an EMF practically equal to the diffusion potential in the organic phase. As predicted by Nernst, independently of concentration, the distribution potentials of both liquid interfaces should be identical (Section III.B). In the above scheme SCE represents a saturated calomel electrode. Chemical cells of the Nernst type can be represented by the following scheme:

SCE

k

aqueous

j organic

j aqueous

k

k k

solution M þ A ; c1

j solution j M þ A M þ L

j solution j M þ L ; c2

k k

j

j

k

k

Bc1 Bc2

SCE

SCHEME 9 In such cells, aqueous solutions contain electrolytes with a common cation M þ . The EMF of this cell is equal to the difference of distribution potentials of both electrolytes and to the diffusion potential in the organic phase. Under appropriate conditions the EMF depends only on the difference of distribution potentials. It should be noted that cells of this type can also contain many and various ions in both phases.

Interfacial Potentials and Cells

11

Liquid cells containing an ion exchanger in the organic phase, e.g., a salt with a highly hydrophobic anion or cation Rþ , could be considered [3] as concentration cells:

SCE

k k

aqueous solution

j organic j solution

k k

MþX ; c1

j j

j aqueous k j solution k

Rþ X c1 c2

j j

MþX ; c2

k k

SCE

SCHEME 10 or as chemical cells:

SCE

k

aqueous

j organic

j aqueous k

k k

solution MþX ;

j solution j Rþ X

j solution j M þ L

k k

k

c1

j

j

k

c2

SCE

SCHEME 11 There are large cations in these cells, e.g., tetra-alkylammonium cations in the organic phase; and the interfacial ion exchange involves only so-called critical ions, here X and L . M þ ions are practically not transferred through the organic phase. Both liquid interfaces are reversible with respect to the appropriate anion, X or L . EMF is, in practice, also inﬂuenced by the diffusion potential in the organic phase, and in the case of cells of the type in Scheme 11 – by the difference of standard transfer energies of both ions (Section III.A) Cells of the type in Scheme 10 represent the simplest case of an ion-selective liquid cell; its EMF is often called a membrane, or monoionic, potential [3]. The ﬁrst term is too narrow due to the fact that the membrane potential corresponds to the behavior of a number of cells, including those of Schemes 8 to 11, and to the cells with solid membranes and with Donnan equilibrium. Cells of the type in Scheme 11 represent the simplest case of cells with a bi-ionic potential [3]. Hence, in the case of a larger number of ions transferred through the organic phase a multi- or polyionic potential should be considered. Liquid ion-selective electrodes operate on the basis of cells of the type in Scheme 10; their selectivity can be examined with the use of Scheme 11 and polyionic cells. In modern investigations of the electrochemical properties of immiscible electrolyte solutions mixed cells are used, i.e., cells containing one interface, e.g., that under investigation – Nernstian or polarizable, and a second reference interface of the Haber types (Scheme 7 or 10). The system usually in the form shown below: w TBAþ Cl

j j

n TBA TPhB

0:01 M

j SCHEME 12

0:01 M

þ

is a typical reference interface commonly used in the above investigations. It follows from Le Hung’s analysis [25] that in the presence of tetrabutylammonium chloride in water and tetraphenylborate (TBATPhB) in nitrobenzene (or 1,2-dichloroethane), the interface appears to be reversible with respect to TBAþ ions.

12

Koczorowski

Interfaces of the type in Scheme 8 are used as liquid ion-selective electrodes. It is apparent that they constitute a special case of distribution systems reversible in regard to two or more ions. Here, Le Hung’s equation, (16) and (17), allows quantitative evaluation of the inﬂuence of the presence of other ions on the selectivity of these systems. E.

Polarizable Interfaces

The interface between an aqueous solution containing a strongly hydrophilic electrolyte, e.g., LiCl, and a nitrobenzene solution containing a strongly hydrophobic salt, e.g., tetrabutylammonium tetraphenylborate (TBATPhB), schematically shown below: j j

w LiCl

n TBATPhB

SCHEME 13 constitutes a very important system in studies of immiscible electrolyte solutions. Since the distribution coefﬁcients of the above electrolytes can be deﬁned by the inequalities [1,2] Bn;0 w ðLiClÞ 1

and

Bwn;0 ðTBATPhBÞ 1

ð40Þ

the interface of Scheme 13, in certain potential limits, behaves nearly as ideally polarizable (see Section II). The degree of polarizability of system can be found from the data calculated by Le Hung [25] with the use of Eqs. (16) and (17). In the equilibrium state of the interphase between the solutions of 0.05 M LiCl in water and 0.05 M TBATPhB in nitrobenzene, the concentrations of Liþ and Cl in the organic phase lower than 107 M, and the concentrations of TBAþ and TPhB in the aqueous phase are about 3 107 M each [3]. These concentrations are too low to establish permanent reversible equilibria. They are, however, signiﬁcantly higher compared to those of the components present in the mercury–aqueous KF solution system [20]. A detailed analysis of this behavior, as well as its analogy to the mercury–KF solution system, can be found in several papers [1–3,8,14]. The ions of both electrolytes, existing in the system of Scheme 13, are practically present only in one of the phases, respectively. This allows them to function as supporting electrolytes in both solvents. Hence, the above system is necessary to study electrical double layer structure, zero-charge potentials and the kinetics of ion and electron reactions at interface between immiscible electrolyte solutions. F. Redox Systems Heterogeneous electron reactions at liquid–liquid interfaces occur in many chemical and biological systems. The interfaces between two immiscible solutions in water–nitrobenzene and water–1,2-dichloroethane are broadly used for modeling studies of kinetics of electron transfer between redox couples present in both media. The basic scheme of such a reaction is Oxw1 þ Red2s

$ SCHEME 14

Red1w þ Oxs2

Red and Ox represent the components at the redox couples. Usually, the reactant in aqueous phase was the ½FeðCNÞ6 3=4 couple, and various couples in the organic phase

Interfacial Potentials and Cells

13

[30–35]. The Nernst equation for the electrochemical equilibrium of the type in Scheme 14 [30] is ws ¼ E2s;0 E1w;0 þ ws ’0Hþ þ ðRT=nFÞ ln

asox2 awRed1 asRed2 awox1

ð41Þ

where E1s;0 and E2w;0 are standard redox potentials of both couples related to the standard Hþ =H2 reference electrode in the respective phases, ws ’0H þ is the standard proton transfer potential, and n is the number of electrons transferred in th reaction of Scheme 14. Equation (41) is valid if none of the ionic components are transferable across the interface, and the only common charged components are electrons. However, some the redox species are necessarily charged components, and counterions of redox couples also exist in the two phases. All of these ionic components can essentially distribute over the two phases, depending on its w0 ’0i value. In this case, the equilibrium point is affected by the partition of ionic components and the value of the mixed Galvani potential occurs (see Section III.G). It is determined by two physically different system properties. The presence of supporting electrolytes also inﬂuences the point of equilibrium through the redistribution of constituent ions. This special type of mixed potential is important not only for deﬁning the initial state of the electrochemical studies of electron transfer reactions but also for understanding other phenomena which involve free-energy coupling of electron and ion transfer reactions, e.g., energy transfer in biological systems and redox-reaction-driven uphill transport of ions across a liquid membrane [14,33,36,37]. A method of calculating equilibrium conditions for electron and ion transfer coupling has been proposed [14,31].

G.

Common Properties of ITIES

The investigations of interfacial phenomena of immiscible electrolyte solutions are very important from the theoretical point of view. They provide convenient approaches to the determination of various physciochemical parameters, such as transfer and solvation energy of ions, partition and diffusion coefﬁcients, as well as interfacial potentials [1– 7,12–17]. Of course, it should be remembered that at equilibrium, either in the presence or absence of an electrolyte, the solvents forming the discussed system are saturated in each other. Therefore, these two phases, in a sense, constitute two mixed solvents. The electrochemisty of ITIES is developing mainly on the basis of the studies of the water–nitrobenzene and water-1,2-dichloroethane interfaces. The polarizability ranges of these interfaces in the presence of typical electrolytes (Scheme 13) are about 0.30 V. Extension of these ranges has been achieved using other organic ions or/and solvents [2,8]. For example, TBAþ ions may be substituted by tetraphenylarsonium crystal violet cations and TPhB ions by dicarbollyl cobaltate (III) anions [1,2]. Standard ionic potentials ws ’0 can be calculated from the ionic distribution coefﬁcients or transfer energies; see Eq. (30). In order to perform such calculations, an appropriate nonthermodynamic assumption that allows division of the B0ðMXÞ or G electrolyte function into ionic constituents has to be made. At the present time, the assumption about the equality of the transfer energies of tetraphenylarsonium cations (TPhAsþ ) and tetraphenylborate anions (TPhB ) is considered as most appropriate [2,36]. It can be presented in the following form: 0 1 2 G ðTphAsTPhBÞ

¼ G0 ðTPhAsþ Þ ¼ G0 ðTPhB Þ

ð42Þ

14

Koczorowski

Another proposed procedure of ﬁnding the ionic data is the application of a special salt bridge, which provides practically constant or negligible liquid junction potentials. The water–nitrobenzene system, containing tetraethylammonium picrate (TEAPi) in the partition equilibrium state, has been proposed as a convenient liquid junction bridge for the liquid voltaic and galvanic cells. The distribution potential of this system, and the diffusion potential at the contact of nitrobenezene with many organic solvents, are close to zero [3,38–40]. The cell containing TEAPi–bridge can be represented by the following scheme: k SCE

w

k k

j

k

s

j MX

j

n

k MX

j

w

j

k SCHEME 15

TEAPi j

k k

TEAPi

SCE

k

Alternatively, it has been found that the Galvani potential of zero charge, in the absence of speciﬁc adsorption, equals zero. This means that there is no speciﬁc orientation of the molecules of both solvents, and the dipolar part of the Galvani potential, Eq. (12), is zero [8,22,41]. The observed discrepancies between the results of various measurements in different ITIES systems have been mainly caused by the speciﬁc adsorption [8]. Recently, the analysis of thermodynamic and free charge potentials at ITIES was performed by Volkov [42]. The ionic potentials ws ’0i can be experimentally determined either with the use of galvanic cells containing interfaces of the type in Scheme 7 or electroanalytically, using for instance, polarography, voltammetry, or chronopotentiometry. The values of ws G0i and ws ’0i , obtained with the use of electrochemical methods for the water–1,2-dichloroethane, water–dichloromethane, water–acetophenone, water–methyl-isobutyl ketone, o-nitrotoluene, and chloroform systems, and recently for 2-heptanone and 2-octanone [43] systems, have been published. These data are listed in many papers [1–10,14,37]. The most probable values for a few ions in water–nitrobenzene and water–1,2-dichloroethane systems are presented in Table 1. It is worthwhile mentioning that the interfacial potential created at the liquid–liquid interface is governed by single ionic or redox equilibrium only in the simple cases. The presence of various, often two, interfacial processes is a source of the steady-state potential, named also the mixed or the rest potential. Its value is situated between the two equilibrium potentials, near that one which corresponds to the higher exchange current

TABLE 1 The Recommended Standard Potentials of Ions in Water– Nitrobenzene (w/n) and Water–1,2-Dichloroethane (w/d) Systems [44] ws ’0 (mV) Ion Pi ClO 4 Me4 Nþ Et4 Nþ Bu4 Nþ Ph4 Asþ

w/n

w/d

38 95 30 66 275 375

57 170 160 19 225 365

Interfacial Potentials and Cells

15

density. The modern theory of liquid membrane ion-selective electrodes and their selectivity coefﬁcients has been developed on the basis of the concept of mixed potentials [45–47]. The closeness of the values of the equilibrium and mixed state potentials, as well as the shape of the time-dependence of interfacial potential [48] during the ion partition process, are the reasons that sometimes it is difﬁcult to ﬁnd whether the examined system is in equilibrium or in the stationary state. As was observed and described by the theoretical model, after the ﬁst several seconds, changes of potential occurring during the ion partition process become very slow [48]. It was shown that during the process, the ion ﬁrst is transferred by a very fast interfacial step (the time of the ‘‘local interfacial equilibrium’’ formation [29]), followed by a mixed transfer–diffusion stage, and ﬁnally moved by slow diffusion.

IV.

LIQUID VOLTAIC CELLS

Liquid voltaic cells are systems composed of conducting, condensed phases in series, with a thin gap containing gas or liquid dielectric (e.g., decane) situated between two condensed phases. The liquid voltaic cells contain at least one liquid surface [2,15]. Due to the presence of a dielectric, special techniques for the investigation of voltaic cells are necessary. Usually, it is the dynamic condenser method, named also the vibrating plate method, the vibrating condenser method, or Kelvin–Zisman probe. In this method, the capacity of the condenser created by the investigated surface and the plate (vibrating plate), is continuously modulated by periodical vibration of the plate. The a.c. output is then ampliﬁed, and fed back to the condenser to obtain null-balance operation [49,50]. Recently, scanning Kelvin probes and microprobes, as high-resolution surface analysis devices, have been developed. They allow one to investigate the lateral distribution of the work functions of the surfaces of various phases, including the determination of the potential proﬁles of metals and semiconductors under very thin ﬁlms of electrolytic solution, and also of the surface potential map of various polymer- and biomembranes [50–56]. The lateral resolution and the sensitivity are in the 100 nm and 1 mV ranges, respectively [54]. A.

Volta Potentials of ITIES

The liquid voltaic cell type ref

k k

w

el:

k

MþX

j j j gas j j

j

s MþX

j j

w

j MþX

k ref: j k j Ek ¼ ws k el:

j

SCHEME 16 contains the interface created at the contact of an aqueous and organic solutions of electrolyte MX being in the partition equilibrium. The compensating voltage, Ek , from a potentiometer is adjusted until the electric ﬁeld strength in the gas space between the two condensed phases is zero. This state means that the Volta potential is zero, and simultaneously that the compensating voltage equals the sum of all Galvani potentials existing in the system plus the difference of surface potentials (instead of Galvani potential) between the liquid phases, which contact the gas space. The application of two identical reference electrodes and the elimination of the liquid junction potentials by proper salt bridges (k),

16

Koczorowski

removes their contributions to the compensation potential. Using Eq. (3), after simple rearrangement we have [15]: E ¼ sw ðMXÞ

ð43Þ

Thus, the Volta potential may be operationally deﬁned as the compensating voltage of the cell of Scheme 16. However, it should be stressed that the compensating voltage of a voltaic cell is not always the direct measure of the Volta potential. The appropriate mutual arrangement of phases, as well as application of reversible electrodes or salt bridges in the systems, allows measurement of not only the Volta potential but also the surface and the Galvani potentials. These possibilities are schematically illustrated by [15] k

w

j gas

j

s

j

w

k

Ek ¼ ws

j

s

k

Ek ¼ ws

k

Ek ¼ ws ’

SCHEME 17 k

w

j gas

j

s SCHEME 18

k

w

j gas

j

w SCHEME 19

Practically, the Volta potential at the water–nonaqueous solvent interface, sw , is measured as the difference in the compensating voltages of the cells of Schemes 20 and 21 [57–59]. The vibrating plate is the mediatory electrode for both cells: s M

Vib:pl

gas Mþ þ X

j

w

j j Mþ þ X

SCE M; E20

SCHEME 20 M

Vib:pl

w

j j

Mþ þ X SCHEME 21

j

gas

2w ðMXÞ ¼ E20 E21

SCE

M; E21

ð44Þ

The reliability of the experimental ws ðMXÞ values was checked for systems containing nitrobenzene [57,58], nitromethane and 1,2-dichloroethane [59] as organic solvent, by comparing the differences in these values for various pairs of salts with the differences in the Galvani potentials, ws ’ðMXÞ for the same pairs [3]. The differences should be the same. The ws ’ or ws data can be used for the estimation of ion solvation energies in the water saturated solvent. The results are reliable if the inﬂuence of the electrolyte MX on the surface potential of solvent in the investigated concentration range, is negligibly small. The liquid–liquid partition systems discussed above are in fact very similar to various membrane-type interfaces and may serve as a model for them. A good example is, for instance, the distribution of a dissociated salt between aqueous solution and a permeable organic polymer [60].

Interfacial Potentials and Cells

B.

17

Adsorption Potentials of Dipolar Compounds

The adsorption of the dipolar organic compound B on the water surface can take place as the result of either spreading B from the appropriate solution over water, i.e. formation of a Langmuir monolayer, or expelling the molecules of the considered compound from the bulk aqueous solution, i.e. formation a Gibbs layer or monolayer [6,11,15,17,18]. The ﬁrst way is used for relatively large, amphipathic molecules, i.e., molecules composed of hydrophobic parts, most commonly a ﬂexible hydrocarbon chain, with the number of carbon atoms in the chain greater than ten. There is also a large number of such compounds, including molecules of biological interest, with aromatic hydrophobic groups. The total number of the adsorbed B molecules per, e.g., 1 m2 of the surface, NB , may be easily evaluated from the amount of the spread compound B. The second way is common for molecules easily soluble in water, and is called the adsorption from solution. Surface tension measurements make it possible to calculate, from the Gibbs isotherm, the surface excess of substance B, which is a relative quantity. Replacement of gas by the nonpolar, e.g., hydrocarbon phase (or oil phase) is used to modify the interactions between molecules in a spread ﬁlm of investigated longchain substances [6,15,17,18]. The nonpolar solvent–water interface possesses the advantage over that between gas and water, that the cohesion (i.e., interactions between adsorbed molecules due to dipole and van der Waals forces) is negligible. Thus, at the oil–water interfaces behavior of adsorbates is much closer to ideal, but quantitative interpretation may be uncertain, in particular for the higher chains which are predominantly dissolved in the oil phase to an unknown activity. Adsorption of dipolar substances at the w/a and w/o interfaces changes surface tension and modiﬁes the surface potential of water [15]: ref: k el:

k k

w

w

k

MX þ B

k k

gas MþX

ref: Ek ¼ w el:

SCHEME 22 As seen in this sketch, the change of compensation voltage E, due to adsorption is the surface potential difference, usually called shortly surface potential, or better the adsorption potential E ¼ w ¼ w W þB

ð45Þ

The experimental investigation of w may be performed directly as presented in the cell of Scheme 22, or by using two measuring cells (Schemes 23 and 24). In the ﬁrst case, the voltaic cell with differential ionizing probe or jet method can be used. In the second case, the ionizing probe or vibrating plate method are applied (see Section IV). These probes are two versions of so-called air electrodes, which mediate in the measurement of voltaic cells. The air electrode, e.g., vibrating plate, creates in fact the two following cells:

18

Koczorowski

w M

Vib:pl

gas

Ref:el

M; E23

Ref:el

M; E24

MX SCHEME 23 w M

Vib:pl

gas MX þ B SCHEME 24

and E ¼ E23 E24 ¼ w

ð46Þ

The presence of supporting electrolyte MX in the aqueous phases secures the stability of the measurements. However, MX must not adsorb at the surface to avoid an inﬂuence on w potential. It is common in the literature to link w with the properties of the neutral adsorbate by means of the Helmholtz equation [6,11,15,17,18] w ¼ NB P? B =0

ð47Þ

where 0 and are the electrical permittivity of vacuum, and the relative permittivity of the interfacial region, respectively, and p? B is the normal component of the molecular dipole moment of the substance B. Either from the known value NB , or from the slope of the experimental relationship of w vs. NB , the quantity p ¼ p? B =0

ð48Þ

can be derived. It may be treated as the apparent surface dipole moment of the adsorbate. The effect of an electric ﬁeld on the surface tension and surface excess of adsorbed solutes can be calculated from the experimental data of adsorption potential, using Maxwell relations found from a thermodynamic analysis of the Volta potential [61]. It is known that the p values derived from experimental w data, e.g., for insoluble monolayers, with the assumption e ¼ 1 are substantially different from the dipole moment for the same molecule in the bulk of the solution [17]. The reasons offered to explain this difference are manifold e.g. (1) inappropriate value of e, (2) reorientation of water molecules around the adsorbate, and (3) lateral interaction between adsorbed molecules in the monolayer. The various models of p have been described in a number of papers [61–67]. The very popular applications of the adsorption potential measurements are those dealing with the surface potential changes at the water–air and water–hydrocarbon interfaces when a monolayer ﬁlm is formed by an adsorbed substance. Phospholipid monolayers, for instance, formed at such interfaces have been extensively used to study the surface properties of the monolayers, which are expected to represent, to some extent, the surface properties of bilayers, and biological, as well as various artiﬁcial membranes. An interest in a number of applications of the ordered thin organic ﬁlms, e.g., Langmuir– Blodgett layers, dominated the insoluble monolayer research activity during the last decade. Equations (47) and (48) concern the case of neutral adsorbates, where there is no ionic double layer to contribute to the surface potential. In the case of charged, i.e., ionic adsorbates the measured potential w consists of two terms. The ﬁrst term is due to dipoles oriented at the interface, which may be described by the above formulas, and the

Interfacial Potentials and Cells

19

second term presents the potential of the ionic double layer at the interface from aqueous side w ¼ p=AB þ gw ðionÞ

ð49Þ

w

where g (ion) is the electrical potential drop between the ﬁlm of adsorbed long-chain ions and the bulk of aqueous solution. AB is the reciprocal value of NB and expresses the surface area per ion. The physical meaning of the gw (ion) potential depends on the accepted model of ionic double layer. The proposed models correspond to the Gouy–Chapman diffuse layer, with or without allowance for the Stern modiﬁcation and/or the penetration of small counterions above the plane of the ionic heads of the adsorbed large ions [17,18]. The presence of adsorbed Langmuir monolayers may induce very high changes of the surface potential of water. For example, w shifts attaining ca. 0:9 (hexadecylamine hydrochloride), and ca. þ1:0 V (perﬂuorodecanoic acid) have been observed [68]. Studies of the adsorption of surface active electrolytes at the oil–water interface provide a convenient method for testing electrical double layer theory and for determining the state of water and ions in the neighborhood of an interface. The change in the surface amount of the large ions modiﬁes the surface charge density. For instance, the surface ionic area of 100 A2 per ion corresponds to 16 ; C=cm2 . The measurement of the concentration dependence of the changes of surface potential were also applied to ﬁnd the critical concentration of formation of the micellar solution [18]. The possibility of determination of the difference of surface potentials of solvents, see Scheme 18, among others, has been used for the investigation of ws between mutually saturated water and organic solvent: namely nitrobenzene [57,58], nitroethane and 1,2-dichloroethane (DCE) [59], and isobutyl methyl ketone (IB) [69]. The results show a very strong inﬂuence of the added organic solvent on the surface potential of water, while the presence of water in the nonaqueous phase has practically no effect on its s potential. The information resulting from the surface potential measurements may also be used in the analysis of the interfacial structure of liquid–liquid interfaces and their dipole and zero-charge potentials [3,15,22].

V.

SMALL LIQUID–LIQUID INTERFACES

The microheterogenous and nanoheterogenous (mesoscopic) liquid–liquid systems may be concisely called the small systems. They comprise the micro- and nanodomains, described in colloidal chemistry as a variety of structures, e.g., micelles, rods, disks, vesicles, microemulsions, monolayers, and Langmuir–Blodgett layers [6,17–19,70]. The properties of these systems depend strongly on the interfacial potentials created at the interface. They arise from oriented molecular dipoles, from ionization of the surfactant hydrophylic groups, and from the partition and adsorption of ions presented in the environment. Unfortunately, we do not have microinterface voltmeters, and we can use only indirect methods like various chemical probes and electrokinetic methods. These methods make it possible to estimate only part of the Galvani potential, denoted here ws ’ . The common method of estimation of the interfacial potential in microheterogeneous systems is to use pH indicators adsorbed at for instance charged micelles. The ‘‘local interfacial’’ proton activity is related to the bulk activity and to an interfacial potential by Boltzmann’s law according to the equation [17,70–72]

20

Koczorowski

pHa ¼ pH0a ðws ’ F=2:3RT Þ

ð50Þ

Changes of pH are about 3 pH units to the alkaline side for adsorbed acids and to the acidic side for adsorbed amines have been reported [17]. However, the equilibrium of the indicator adsorbed at an interface may also be affected by a lower dielectric constant as compared to bulk water. Therefore, it is better to use instead pH, the ‘‘interfacial’’ and ‘‘bulk’’ pK values in Eq. (50). The concept of the use at pH indicators for the evaluation of ws ’ is also basis of other methods, like spinlabeled EPR, optical and electrochemical probes [19,70]. The results of the determination of the ws ’ by means of these methods may be loaded with an error of up to 50 mV [19]. For some the potentials determined by these methods, ws ’ values are in a good agreement with the electrokinetic (zeta) potentials found using microelectrophoresis [73]. It is proof that, for small systems, there is lack of methods for ﬁnding the complete value of ws ’. Fortunately the microinterfaces between two immiscible electrolytes seem to be a very useful experimental model of small liquid–liquid systems. The formation and investigation of the micro-ITIES is continuously perfected [74–76]. The smallest diameter so far achieved was 5 m. The main utilization of micro-ITIES is developed, in parallel with application of ultramicroelectrodes. Kakiuchi performed a very important analysis of the distribution potential in the small systems [14,31]. Using the general Le Hung approach, he discussed the behavior of ws ’eq at its extreme, when r ! 0 or 1. When all ions are initially dissolved only in the w phase, Eq. (17) takes a simple form: X

zi ciw;0

Y

1 þ rðjw =js Þej ¼ 0

ð51Þ

j6¼i

i

where j 6¼ k under the product means that the product is taken over all ionic species except i. It can be further simpliﬁed when r ! 0: X i

" zi ciw;0

X

jw =js

# ej ¼ 0

ð52Þ

j6¼i

Using the equation, very strong concentration effects in small systems have been calculated. For instance, if the macroaqueous phase contains 1 M NaCl and 1 M NaTPB, the concentration of this electrolyte in the micro-organic phase at partition equilibrium is 1390 M [14]! This approach is valid if the phases in small systems are thick enough (> 1 m), in comparison to the Debye screening length, to fulﬁll the electroneutrality conditions.

ACKNOWLEDGMENT The author is pleased to acknowledge the ﬁnancial support from the Polish Committee on Scientiﬁc Research (BST-623/19/99).

Interfacial Potentials and Cells

21

REFERENCES 1. 2. 3.

4.

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.

P. Vanysek, Lecture Notes in Electrochemistry, vol. 39, Springer-Verlag, New York, 1985, pp. 1–106. J. Koryta. Electrochim. Acta 32:419 (1987). Z. Koczorowski, in The Interface Structure and Electrochemical Processes at the Boundary Between Two Immiscible Liquids (V. E. Kazarinov, ed.), Springer-Verlag, Berlin–Heidelberg, 1987, pp. 143–178. L. I. Boguslavsky and A. G. Volkov, in The Interface Structure and Electrochemical Processes at the Boundary Between Two Immiscible Liquids (V. E. Kazarinov, ed.), Springer-Verlag, Berlin–Heidelberg, 1987, pp. 77–106. Z. Samec. Chem Rev. 88:617 (1988) K. S. Birdi, Lipid and Biopolymer Monolayer at Liquid Interface, Plenum Press, New York– London, 1988, chaps. 4 and 5. V. S. Martin and A. Volkov. J. Colloid Interface Sci. 131:382 (1989). H. H. Girault and D. Schiffrin, in Electroanalytical Chemistry (A. J. Bard, ed.), vol. 15, Marcel Dekker, New York, 1989, pp. 1–144. V. S. Markin and A. G. Volkov. Adv. Colloid Interface Sci. 31:111 (1990). M. Senda, T. Kakiuchi, and T. Osakai. Electrochim. Acta 36:253 (1991). A. Ulman, An Introduction to Ultrathin Organic Films: from Langmuir–Blodgett to SelfAssembly, Academic Press, Boston, 1991. P. Vanysek, in Electrochemistry and Dispersions (R. M. Mackay and T. Texter, eds.), VCH Publishers, New York, 1992, pp. 71–84. H. H. Girault, in Modern Aspects of Electrochemistry (J. O’M. Bockris, B. E. Conway, and R. E. White, eds.), No. 25, 1993, pp. 1–62. T. Kakiuchi, in Liquid–Liquid Interfaces: Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, 1996, pp. 1–18. Z. Koczorowski, in Liquid–Liquid Interfaces. Theory and Methods (A. G. Volkov and D. Deamer, eds.), CRC Press, Boca Raton, 1996, pp. 19–37. A. G. Volkov, D. W. Deamer, D. L. Tanelian, and V. S. Markin, Liquid Interfaces in Chemistry and Biology, Wiley-Interscience, New York, 1998, pp. 130–319. T. Davies and E. K. Rideal, Interfacial Phenomena, Academic Press, New York, 1963, chaps. 2–6. J. Llopis, in Modern Aspects of Electrochemistry (J. O’M. Bockris and B. E. Conway, eds.), No. 6, Plenum Press, New York, 1971, pp. 91–159. N. A. Kotov and M. G. Kuzmin, in Liquid–Liquid Interfaces. Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, 1996, pp. 213–224. R Parsons, in Modern Aspects of Electrochemistry (J. O’M. Bockris and B. M. Conway, eds.), Butterworths, London, 1954, vol. 1, chap. 3. S. Trasatii and R. Parson. Pure Appl. Chem. 58:1251 (1986). Z. Koczorowski. J. Electroanal. Chem. 190:257 (1985). E. J. V. Verwey and K. F. Niessen. Phil. Mag. 28:435(1939). F. M. Karpfen and J. E. B. Randles. Trans. Faraday Soc. 49:823 (1953). L. Q. Hung. J. Electroanal. Chem. 149:1 (1985). E. Makrlik. Electrochim. Acta 28:573 (1995). L. Q. Hung. J. Electroanal. Chem. 149:1 (1985). R. P. Buck and P. Vanysek. J. Electroanal. Chem. 292:73 (1990). P. Vanysek and R. P. Buck. J. Electroanal. Chem. 297:19 (1991). Z. Samec. J. Electroanal. Chem. 99:197 (1979). T. Kakiuchi. Electrochim. Acta. 40:2999 (1995). A. G. Volkov, M. I. Gugeshashvili, and A. W. Deamer. Electrochim. Acta 40:2849 (1995). V. J. Cunnane, G. Geblewicz, and D. Schiffrin. Electrochim Acta 40:3005 (1995). V. J. Cunnane and L. Murtomaki, in Liquid–Liquid Interfaces. Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, 1996, pp. 401–416.

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35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73 74. 75. 76.

A. G. Volkov and A. W. Deamer. Progr. Colloid Polym. Sci. 103:21 (1997). O. Popovych and R. G. Bates. Crit. Revs. Anal. Chem. 1:73 (1970). J. Koryta, P. Vanysek, and M Brezina. J. Electroanal. Chem. 75:211 (1977). Z. Koczorowski. J. Electroanal. Chem. 127:11 (1981). Z. Koczorowski and G. Geblewicz. J. Electroanal. Chem. 152:55 (1983). G. Geblewicz and Z. Koczorowski. J. Electroanal. Chem. 158:37 (1983). H. H. Girault and D. Schiffrin. Electrochim. Acta 31:1341 (1986). A. G. Volkov. Langmuir 12:3315 (1996). Y. Cheng and D. J. Schiffrin. J. Electroanal. Chem. 429:37 (1997). T. Wandlowski, V. Marecek, and Z. Samec. Electrochim. Acta 15:1173 (1990). T. Kakiuchi and M. Senda. Bull. Chem. Soc. Jpn. 57:1801 (1984). S. Kihara and Z. Yoshida. Talanta 31:789 (1984). T. Kakiuchi, I. Obi, and M. Senda. Bull. Chem. Soc. Jpn. 57:1636 (1985). C. A. Chang, E. Wang, Z. Pang. J. Electroanal. Chem. 266:143 (1989). W. A. Zisman. Rev. Sci. Instrum. 3:367 (1932). J. M. Palau and J. Bonnet. J. Phys. E: Sci. Instrum. 21:674 (1988). M. Fujihira and K. Hirosuke. Thin Solid Films 242:163 (1994). M. T. Nguyen, K. K. Kanazawa, P. Brock, and A. F. Diaz. Langmuir 10:597 (1994). I. D. Baikie, P. J. S. Smith, D. M. Portﬁeld, and P. J. Estrup. Rev. Sci. Instrum. 70:1842 (1999). W. Nabhan, B. Equer, A. Broniatowski, and G. De Rosny. Rev. Sci. Instrum. 68:3108 (1997). E. Moons, A. Goossens, and T. Savenije. J. Phys. Chem. B 101:8492 (1997). I. Frateur, E. Bayet, M. Keddam, and B. Tribollet. Electrochem. Commun. 1:336 (1999). Z. Koczorowski and I Zago´rska. J. Electroanal. Chem. 159:183 (1983). I. Zago´rska and Z. Koczorowski. J. Electroanal. Chem. 204:273 (1986). I. Zago´rska, Z. Koczorowski, and I. Paleska. J. Electroanal. Chem. 282:51 (1990). K Doblhofer and M. Cappadonia. Colloids Surfaces 41:211 (1989). A. N. Frumkin, B. B. Damaskin, and A. A. Survila. J. Electroanal. Chem. 16:493 (1968). B. B. Damaskin, A. N. Frumkin, and A. Chizhov. J. Electroanal. Chem. 28:93 (1970). R. J. Demchak and T. Fort Jr. J. Colloid Interface Sci. 46:191 (1974). V. Vogel and D. Mo¨bius. J. Colloid Interface Sci. 126:408 (1988). O. N. Oliveira Jr, A. Riul, and L. G. F. Fereira. Thin Solid Films 242:239 (1994). Z. Koczorowski, S. Kurowski, and S. Trasatti. J. Electroanal. Chem. 329:25 (1992). P. Nikitas and A. Pappa-Louisi. J. Electroanal. Chem. 385:257 (1995). A. N. Frumkin, X. A. Jofa, and M. A. Gerovich. Zh. Fiz. Khim. 30:1456 (1956). Z. Koczorowski, I. Zago´rska, and A. Kalin´ska. Electrochim. Acta 34:1857 (1989). R. B. Gennis, Biomembranes, Springer-Verlag, New York, 1989, pp. 235–269. M. S. Fernandez and P. Fromherz. J. Chem. Phys. 81:1755 (1977). C. J. Drummond, F. Grieser, and T. W. Healy. J. Am. Chem. Soc. 92:2604 (1988). A. M. Carmona-Ribeiro and B. R. Midmore. J. Phys. Chem. 96:3542 (1992). G. Taylor and H. H. Girault. J. Electroanal. Chem. 208:179 (1986). P. Vanysek. Electrochim. Acta 40:2841 (1995). V. J. Cunnane, D. J. Schiffrin, and D. E. Williams. Electrochim. Acta 40:2943 (1995).

2 Ion Solvation and Resolvation TOSHIYUKI OSAKAI

Department of Chemistry, Kobe University, Kobe, Japan

KUNIYOSHI EBINA Division of Sciences for Natural Environment, Kobe University, Kobe, Japan

I.

INTRODUCTION

Much attention has been directed since olden times towards ion solvation, which is a key concept for understanding various chemical processes with electrolyte solutions. In 1920, a theoretical equation of ion solvation energy (G0s ) was ﬁrst proposed by Born [1], who considered the ion as a hard sphere of a given radius (r) immersed in a continuous medium of constant permittivity (), and then deﬁned G0s as the electrostatic energy for charging the ion up to ze (z, the charge number of the ion; e, the elementary charge): N z2 e2 1 1 G0s ðBornÞ ¼ A ð1Þ 80 r where NA is the Avogadro constant, and 0 the permittivity of vacuum. Since the term ‘‘1’’ in the parentheses of the RHS of Eq. (1) is 1/[the relative permittivity of vacuum (¼ 1, by deﬁnition)], G0s (Born) can also be regarded as the electrostatic energy required for the transfer of the ion from vacuum to the medium having the permittivity of . Accordingly, the Gibbs free energy of ion transfer (G0;O!W ), i.e., the resolvation energy for the tr transfer of an ion from one medium (e.g., organic solvent, O) to another (e.g., water, W) can be expressed as N A z2 e2 1 1 0;O!W ðBornÞ ¼ Gtr ð2Þ 80 r O W where O and W are the relative permittivities of O and W, respectively. The Born equation thus derived is based on very simple assumptions that the ion is a sphere and that the solvents are homogeneous dielectrics. In practice, however, ions have certain chemical characters, and solvents consist of molecules of given sizes, which show various chemical properties. In the simple Born model, such chemical properties of ions as well as solvents are not taken into account. Such defects of the simple Born model have been well known for at least 60 years and some attempts have been made to modify this model. On the other hand, there has been another approach that focuses on short-range interactions of an ion with solvent molecules. The purpose of this chapter is to discuss mainly recent development in the theory of ion solvation energy. Because we allowed much space for introducing our new, non23

24

Osakai and Ebina

Bornian theory of the Gibbs free energy of ion resolvation, a vast amount of work dealing with ion solvation and resolvation could not fully be reviewed. The reader is referred to some books [2–5] and review articles [6–10] for a general survey.

II.

MODIFICATIONS OF THE BORN MODEL

The defects of the Born equation [1] may be put into two categories; one is for large ions and the other for small ions. The defect for large ions is concerned with the fact that the Born equation does not take account of the energy of the formation of a cavity for introducing an ion into the solvent. This energy, which corresponds to the so-called ‘‘solvophobic’’ interaction, is more noticeable for large ions. Consequently, a modiﬁcation has generally been made by adding a nonelectrostatic term, G0s ðneÞ, to the Born equation: G0s ¼ G0s ðelÞ þ G0s ðneÞ

ð3Þ

where G0s ðel) is the electrostatic term which is given by the Born equation (or its modiﬁcations). As described by the previous authors [9], the division shown in Eq. (3) is somewhat arbitrary, because different effects may overlap. However, such a division is useful for evaluating the individual effects in a heuristic way. The evaluation of the nonelectrostatic term is usually empirical and multifarious. Based on a skillful argument, however, Volkov and coworkers [9,11,12] proposed that the nonelectrostatic term of the ion transfer energy, G0;O!W (ne), should be expressed by a tr semiempirical equation called the Uhlig equation [13], which is given by 0;O!W Gtr ðneÞ ¼ 4NA r2 O;W

ð4Þ

when the surface tension at the boundary of organic solvent (O) with air is smaller than that of water (W) with air. In this formula, the difference in the energies for forming a surface around an ion in O and in W is to be evaluated simply by using the interfacial tension (O;W ) between the two phases. The Uhlig formula is shown to be valid for O;W > 10 mN m1 and r > 0:2 nm [9]. The other defect of the Born equation is for relatively small ions and is concerned with the change in the solvent structure around an ion when it is inserted in the solvent; this change is caused by the high electric ﬁeld formed by the ion. Many attempts have been made since long ago to mitigate this defect by modifying the Born equation in various ways: (1) by correcting the ionic radii (for example, see Ref. 14), (2) by taking account of the effect of dielectric saturation (i.e., the lowering of the permittivity of solvents adjacent to an ion due to the high electric ﬁeld) [9,11,12,15–17], or (3) by doing both (1) and (2) [18]. In modiﬁcation (1), a constant value (r) is added to the crystal ionic radius (r), and the value of r þ r is used in place of r in Eq. (1). By using the values of r þ r (dependent on the ionic valence) determined empirically, fairly good agreement was obtained between experimental and theoretical values for the ion hydration energy. An example [14] is shown in Fig. 1. The solid lines in the ﬁgure represent the plots obtained by using the crystal ionic radii for r in the Born equation. It should be noted that the plots for the cations showed a curved line inconsistent with the Born equation [See Eq. (1) again]. However, adding a constant rð¼ 0:85 A˚) to the crystal ionic radius for all the cations could make the curved line straight, as shown by a dashed line. But, the physical meaning

Ion Solvation and Resolvation

25

FIG. 1 Modiﬁcation of the Born equation by correcting ionic radii. Solid curves for crystal radii, dotted for corrected radii (for cations, r ¼ 0:85 A˚; for anions, r ¼ 0:1 A˚). (From Ref. 14. Copyright 1939 the American Institute of Physics.)

of r still remains obscure. Such a modiﬁcation seems unable to come to the essential solution to this problem. The modiﬁcation by method 2 is more acceptable. Although several types of modiﬁcations have been reported, Abraham and Liszi [15] proposed one of the simplest and well-known modiﬁcations. Figure 2(b) shows the proposed ‘‘one-layer’’ model. In this model, an ion of radius r and charge ze is surrounded by a local solvent layer of thickness (b r) and dielectric constant 1 , immersed in the bulk solvent of dielectric constant b . The thickness (b r) of the solvent layer is taken as the solvent radius, and its dielectric constant 1 is supposed to become considerably lower than that of the bulk solvent owing to dielectric saturation. The electrostatic term of the ion solvation energy is then given by G0s ðelÞ

N z2 e2 ¼ A 80 r

1 1 1 1 1 1 þ 1 1 r b b b

ð5Þ

On the assumption that 2 ¼ 2, the theoretical values of the ion solvation energy were shown to agree well with the experimental values for univalent cations and anions in various solvents (e.g., 1,1- and 1,2-dichloroethane, tetrahydrofuran, 1,2-dimethoxyethane, ammonia, acetone, acetonitrile, nitromethane, 1-propanol, ethanol, methanol, and water). Abraham et al. [16,17] proposed an extended model in which the local solvent layer was further divided into two layers of different dielectric constants. The nonlocal electrostatic theory [9,11,12] was also presented, in which the permittivity of a medium was assumed to change continuously with the electric ﬁeld around an ion. Combined with the abovementioned Uhlig formula, it was successfully employed to elucidate the ion transfer energy at the nitrobenzene–water and 1,2-dichloroethane–water interfaces. It should be noted that in the modiﬁed Born equation of Eq. (5), the value of 1 ð¼ 2Þ is extremely small compared with that of b ð¼ 78:54 for water). In the Born equation as well as its modiﬁcations, the reciprocal of the permittivity (1=) crucially determines the magnitude of the ion solvation energy. As b > 10 (i.e., 1=b < 0:1) for most polar sol-

26

Osakai and Ebina

FIG. 2 (a) The Born model [1]. (b) The one-layer model proposed by Abraham and Liszi [15]. (From Ref. 10. Copyright the Japan Society for Analytical Chemistry.)

vents, we see how great the modiﬁcation is when we set 1 ¼ 2 (i.e., 1=1 ¼ 0:5). It seems far beyond the ‘‘modiﬁcation.’’ What does the assumption ‘‘1 ¼ 2’’ really mean? Since the permittivity reﬂects the extent of the rotational ﬂuctuation of molecular dipoles of the solvent, the low permittivity means that the solvent molecules are strongly restricted in their movements in the vicinity of the ion which has the high electric ﬁeld at the surface. This suggests that the short-range ion–solvent interactions, including such chemical interactions as hydrogen bonds, should play the most signiﬁcant role in the ion solvation energy. As mentioned above, the Born equation is essentially based on the long-range ion–solvent interaction. Ironically enough, however, its modiﬁcations insist on the importance of the short-range interactions rather than the long-range ones.

III.

EMPIRICAL APPROACHES TO SHORT-RANGE INTERACTIONS

In the Born equation, the ion–solvent interaction energy is determined only by one physical parameter of the solvent, i.e., the dielectric constant. However, since actual ion– solvent interactions include ‘‘speciﬁc’’ interactions such as the charge-transfer interaction or hydrogen bonds, it is natural to think that the Born equation should be insufﬁcient. It is well known that the difference in the behavior of an ion in different solvents is not often elucidated in terms of the dielectric constant. Since around 1950, in studies of solvent effects for organic reactions, empirical solvent parameters have been used; these parameters represent the capabilities of solvents for the solute–solvent interactions (especially Lewis acid–base interactions). Though the solute–solvent interactions should depend on the solute as well as on the solvent, the empirical solvent parameters are considered to be irrelevant to solutes; in other words, the use of only these parameters enables us to evaluate the solvation energies. Strictly

Ion Solvation and Resolvation

27

speaking, this is not correct. In practice, however, good correlations of the empirical parameters with the solvent effects have been seen in a number of systems (for reviews, see Refs. 19 and 20). The best-known solvent parameters are the donor number [21] and acceptor number [22] proposed by Gutmann and coworkers. The donor number (DN) for a donor solvent D is deﬁned as the positive value of the enthalpy difference H (kcal mol1 ) for the reaction of D with an acceptor-halide SbCl5 (D þ SbCl5 ! D SbCl5 ) in an inert medium such as 1,2-dichloroethane. DN is a fair measure for the donor properties of a solvent. The correlations of DN with the solvation energies are known to be good particularly for solvation of cations. A typical example [19] is shown in Fig. 3. The acceptor number (AN) for a solvent A is determined by comparing the electronpair accepting ability of the solvent with that of SbCl5 , from the oxygen atom of triethylphosphine oxide Et3 PO in 1,2-dichloroethane [22]. To put it concretely, the 31 P-NMR chemical shift of Et3 PO in solvent A, ðEt3 PO AÞ, which would reﬂect the electron density around the 31 P nucleus, was measured, and then its relative value against the chemical shift of Et3 PO SbCl5 in 1,2-dichloroethane was deﬁned as AN: AN ¼

ðEt3 PO AÞ 100 ðEt3 PO SbCl5 Þ

ð6Þ

AN is known to show good correlations with the solvation energies of anions. Also, AN has good correlations with other solvent parameters deﬁned in different reaction systems, e.g., Grunwald and Winstein’s Y-value [24], Kosower’s Z-value [25], Dimroth and Reichardt’s ET -value [26,27], etc. Taft et al. [28] proposed the solvatochromic parameters, , , and , which describe three solvent’s abilities, respectively, to stabilize a charge or a dipole by virtue of its dielectric effect, to donate a proton (or accept an electron pair), and to accept a proton (or donate an electron pair). It was shown that the AN for nonprotonic solvents correlates

FIG. 3 Correlation between the Gibbs free energy of transfer of Kþ from CH3 CN to a solvent and DN. The free energies of transfer were determined by EMF measurements [23] based on the assumption of negligible liquid junction in a cell: KðHgÞj0:01 M KClO4 (solvent) k0:1 M Et4 NPic ðCH3 CNÞk0:01 M KClO4 ðCH3 CNÞjKðHgÞ. NM: nitromethane; TMS: tetramethylene sulfonate; PDC: propanediol-1,2-carbonate; DMF: dimethylformamide; NMP; N-methyl-2-pyrrolidone, DMA: dimethylacetamide; DMSO: dimethyl sulfoxide; HMPA: hexamethylphosphoramide. (From Ref. 19. Copyright 1978 Plenum Press, New York.)

28

Osakai and Ebina

well with and for protonic solvents with a linear combination of and . It was therefore concluded that AN was, in fact, a combined measure of solvent polarity/polarizability and hydrogen bond donor ability. It was also shown that DN was linear to for oxygen bases and RCN nitrogen bases, though the correlation broke down for pyridine. In Taft et al.’s studies, the macroscopically deﬁned solvent parameters were analyzed at a molecular level; therefore their conclusions are full of interesting suggestions for the understanding of solute–solvent interactions.

IV.

A VOLTAMMETRIC STUDY WITH POLYANIONS

The above-mentioned solvent parameters are the solvent-side measures for describing the solute–solvent interactions. Accordingly, they are useful for predicting the effects observed when the solvent is changed, but inadequate when the solute is changed. On the other hand, the Born equation includes the parameters for both the solvent and solute (ion), i.e., the dielectric constant () as a solvent parameter and the ionic charge and radius (z and r) as ion parameters. This is an advantage of the Born equation and therefore the reason why the Born equation has been widely used for many years notwithstanding a lot of criticisms. However, in theoretical studies with the Born equation or its modiﬁcations, the r-dependence of the solvation energy was generally examined for the ions with the common zvalue; the dependence on the z-value has not been elucidated successfully. Previously, Osakai and coworkers [29–31] employed ion-transfer voltammetry to 0 determine the standard ion-transfer potentials (W O ) of heteropoly- and isopolyoxometalate anions (in short, polyanions) at the nitrobenzene (NB)/W and 1,2-dichloroethane 0 (1,2-DCE)/W interfaces; W O is directly related to the transfer energy by G0;O!W tr ð7Þ zF 0 0;O!W The values of W , obtained for the NB/W interface, are summarO as well as Gtr 0 ized in Table 1. As seen, the value of W O for the polyanions, so their transfer energies as well, depend only on the ionic size and charge. Thus there was no indication that the iontransfer potential (or the energy) was signiﬁcantly inﬂuenced by such ‘‘speciﬁc’’ solvation as due to electron localization in a polyanion. This seems to support the hypothesis that the surface charge of such a polyanion is nonlocalized. If we assume the polyanion to be a hard sphere with a uniform surface electric ﬁeld strength (E), then E is a function only of z and r: ze E¼ ð8Þ 40 r2 0 W O ¼

0 In order to clarify the role of the surface ﬁeld strength, we have plotted the values of W O

against E [see Fig. 4(A) [29]]. Surprisingly, all the data lie on a straight line despite the large differences in sizes, charges, and even structures, as seen in the ﬁgure. A similar linear plot was also obtained for the polyanion transfer at the 1,2-DCE/W interface [30]. Because polyanions are generally quite large, a contribution from the solvophobic interaction (i.e., the cavity formation energy) to its solvation energy should not be 0 neglected. Accordingly, from the observed W O -values, the contribution was subtracted with the help of the Uhlig equation [Eq. (4)]. Even after this subtraction, the linear 0 relationship still manifested itself in the resultant ‘‘electrostatic’’ term, W O ðelÞ 0;O!W ¼ ½Gtr ðelÞ=zF, as shown in Fig. 4(B) [33]. This excellent correlation strongly

Ion Solvation and Resolvation

29

0 0;O!W TABLE 1 Values of W of Polyanions for the NB/W System [29] and Their O and Gtr Values of r and E

No. 1 2 3 4 5 6 7 8 9

Polyanion ; -[XM12 O40 4 (X ¼ Si; Ge; M ¼ Mo; WÞ ; -½XM12 O40 3 (X ¼ P; As; M ¼ Mo; WÞ -½X2 Mo18 O62 6 ðX ¼ P; AsÞ -½S2 Mo18 O62 4 ½S2 VMo17 O62 5 ½P2 Mo18 O61 4 (containing P2 O4 7 Þ ½Mo6 O19 2 ½VMo5 O19 3 -½Mo8 O26 4

r (nm)

Ea (10 V m1 )

0 W O

(V)

0.56b

1:84

0:067 0:003

25.9

0.56b

1:38

0:248 0:004

71.8

0.648c

2:06

0:005 0:000

2.9

0.648c 0:648c 0.644c

1:37 1:72 1:39

0.269 0.085 0.239

103.8 41.0 92.2

0.437c 0.437c 0.485c

1:51 2:26 2:45

0.164 0:119 0:137

31.6 34:4 52:9

10

G0;O!W tr (kJ mol1 )

a

Calculated from Eq. (8). Literature value [32]. c Evaluated using the simple relation r ðnmÞ ¼ 0:164n1=3 (with n the number of oxygen atoms in the polyanion) [30]. Source: From Ref. 33. b

0 W FIG. 4 Plots of (A) W O and (B) O (el) of polyanions at the NB/W interface against E. (From Ref. 33. Copyright 1996 Elsevier Science B.V., Amsterdam.)

30

Osakai and Ebina

suggests that the surface ﬁeld strength E should play an important role in the resolvation energies of polyanions. 0 Then, what would the linear E-dependence of W O mean? If we suppose that the 0;O!W 0 Gtr for the polyanions is given by the Born equation, W O ðelÞ should be proportional to z=r [cf. Eqs. (2) and (7)]; this dependence would come from the overall inte0 gration of a function of the electric ﬁeld. In actuality, however, W O ðel) depends on the 2 value of E at the surface, which is proportional to z=r . This suggests that the shortrange ion–solvent interactions, rather than the Born-type long-range electrostatic interaction, play a major role in the z-dependence of the resolvation energy of polyanions. 0 Thus it is unsuitable to refer to W O ðelÞ as the ‘‘electrostatic’’ term. Instead, the term 0 will be referred to as the charge (z)-dependent term, being written as W O ðz-dep) [cf. Eq. (26)].

V.

A MODEL HAMILTONIAN APPROACH TO ION–SOLVENT INTERACTIONS

0 The authors [33] have elucidated the linear dependence of W O ðz-depÞ on E for the polyanions by a quantum chemical consideration. A model Hamiltonian approach to the charge transfer (CT) interaction between a polyanion and solvents has been made on the basis of the Mulliken’s CT complex theory [34]. Let us consider a case in which an ion (donor, Dz ) and a solvent (acceptor, A) form a CT complex. The ground state energy WN (see Fig. 5) can be obtained as a solution of the secular equation: W0 X W01 S01 X ð9Þ ¼0 W01 S01 X W1 X

where W0 is the energy in a no-bond state, j 0 i ¼ j ðDz AÞi, in which Dz and A come into contact without changing their electronic conﬁgurations; W1 is the energy in a dative state, j 1 i ¼ j ðDzþ1 A Þi, corresponding to the transfer of an electron from Dz to A; and W01 and S01 are deﬁned by W01 ¼ h 0 jHj 1 i (H being the Hamiltonian operator) and S01 ¼ h 0 j 1 i, respectively. The CT interaction energy W, i.e., the resonance energy in the ground state is given by W ¼ W0 WN

FIG. 5 The charge transfer between an ion (donor, Dz ) and a solvent (acceptor, A).

ð10Þ

Ion Solvation and Resolvation

31

In the previous paper [33], the effect of the ionic charge z on W was investigated for the CT interaction between a polyanion and water. The effect will come out through W1 and W01 . By using a simple model in which an electron in the surface atom of a polyanion is transferred to a solvent molecule, the effect of z on W through W1 is considered as follows: if the ionic radius r is much larger than the CT distance d and the radius of the surface atom rO , the z-dependence of W1 can be expressed in terms of the surface ﬁeld strength E of the polyanion as ed W1 W~ 1 þ E ð11Þ r where the E-independent term will be approximated as W~ 1 ¼ W0 þ Ip0 Ea ðAÞ

e2 40 r d

ð12Þ

with Ip0 being the ionization potential of the surface atom, Ea ðAÞ the electron afﬁnity of the solvent, and r the relative permittivity of the solvent in the ﬁrst solvation shell (being assumed to be equal to the optical permittivity, op ¼ 1:8 for water). The last term has been introduced as a correction factor for electrostatic effects of the liquid medium. Next, the effect of z on W through the transition matrix element W01 is considered as follows: for rigorous determination of W01 , all electrons in the system should be treated. However, for the sake of simplicity, we devote our attention only to the transferring electron; the other electrons would be regarded as forming the ‘‘effective’’ potential Veff ðxÞ for the transferring electron (x the coordinate of the electron given from the ion center). This enables us to reduce the many-body problem to a one-body problem: D E H one-body LUMO ð13Þ W01 HOMO D A where HOMO is the highest occupied molecular orbital (HOMO) of Dz , LUMO the lowest D A unoccupied molecular orbital (LUMO) of A, and H one-body the one-body Hamiltonian being given by H one-body ¼

h2 r2 þ Veff ðxÞ 82 m

ð14Þ

In order to give a concrete expression for Veff ðxÞ, a simple model has been assumed (see Fig. 6). In this model, it is postulated that an electron in the HOMO (essentially the 2p orbital) of the surface oxygen atom (Osurg ) of the polyanion partially transfers to the LUMO of water (the 4a1 molecular orbital). Then Veff ðxÞ can be expressed as Veff ðxÞ ¼ Vcharge-electron ðxÞ þ Vcharge-hole þ Vps ðxÞ

ð15Þ

where Vcharge-electron ðxÞ and Vcharge-hole represent potential energies ascribed to the Coulomb interactions between the ionic charge and the transferring electron and between the ionic charge and a positive hole formed on the Osurf atom, respectively, and where Vps ðxÞ is the pseudopotential, i.e., the effective potential formed by the nucleus of the Osurf atom and its electrons other than the transferring electron. Although it is difﬁcult to obtain an exact expression for Vps ðxÞ, its appropriate expression only in the overlapping region (shown in D in Fig. 6) will be necessary for evaluating the matrix element with Eq. (13). As seen in Fig. 6, the overlapping region located around the place where the electron density of the 2p (Osurf ) orbital is the highest. The pertinent potential around this place

32

Osakai and Ebina

FIG. 6 Quantum chemical model of the CT complex of a polyanion and water. (From Ref. 33. Copyright 1996 Elsevier Science B.V., Amsterdam.)

should be used; the Coulomb potential has been employed here, on assuming that a positive charge of 2 is located at the center of the Osurf atom. Thus, the corresponding jVps ðxÞj LUMO i can be calculated approximately. energy h HOMO D A Finally, under the condition that r rO , the z-dependence of W01 can be expressed as a function of E, as in the case of W1 [Eq. (11)]: W01 ¼ W~ 01 þ eE with

D E ¼ rO D ¼ rO HOMO j LUMO D A * + 2 D h HOMO 2 LUMO þ W~ 01 ¼ 2 r A D 8 m

ð16Þ

ð17Þ

HOMO Vps ðxÞ LUMO D A

E

ð18Þ

From the above analysis, it is found that both W1 and W01 are linear functions of the surface electric ﬁeld strength E, so that W obtained from Eq. (9) is also a function of E. The important point is that the z-dependence of the matrix element can be expressed only through E. By actually solving the secular equation (9), it has been found that the Edependence of W is well represented by a quadratic equation: W ¼ 0 þ 1 E þ 2 E 2

ð19Þ

It should be noted, however, that this equation represents the energy for a one-to-one ion– solvent interaction. When the ion is much larger than the solvent, it can be assumed that the number (N) of solvent molecules adjacent to the ion is proportional to the surface area of the ion: N ¼ 4r2 (where is the number of solvent molecules per unit surface area of the ion). Accordingly, the contribution of the CT interaction to the ion solvation energy G0s is given by

Ion Solvation and Resolvation

33

G0s ðCTÞ ¼ N W ¼ 0 þ 1 E þ 2 E 2

ð20Þ

with n ¼ 4r n ðn ¼ 1; 2; 3Þ; note that n is proportional to r . The contribution of is then given by the CT interaction to the ion-transfer energy G0;O!W tr 2

2

2 G0;O!W ðCTÞ Gs0;W ðCTÞ G0;O s ðCTÞ ¼ 0 þ 1 E þ 2 E tr

ð21Þ

O with n ¼ W n n . Here, the superscripts ‘‘W’’ and ‘‘O’’ refer to water and organic phases. Accordingly, the contribution of the CT interaction to the ion-transfer potential [being given by Eq. (7)] can be expressed as 0 1 þ 1 þ 2 E W O ðCTÞ ¼ 0 E

ð22Þ

O O with n ¼ ðW W n n Þ=0 which depends neither on z nor r. In view of the necessity of knowing an approximate value of the coefﬁcient 2 of the linear term in Eq. (22), we have (CT) consists of only the contribution from made a daring assumption that G0;O!W tr water, namely, G0;O!W ðCTÞ G0;W ðCTÞ. This leads to the following approximation: s tr 0 W 1 þ 1W þ 2W E W O ðCTÞ ¼ 0 E

ð23Þ

where nW ¼ W W n =0

ðn ¼ 1; 2; 3Þ 2W

ð24Þ

Thus the coefﬁcient can be evaluated from and The approximate value of W 18 2 ð¼ 9:4 10 molecules m ) is obtained from the density of bulk water by assuming that the thickness of the ﬁrst solvation shell equals the diameter (0.28 nm) of a water molecule, 22 ðeVÞ V2 m2 from the whereas the value of W 2 has been obtained to be 2:025 10 W estimation of the E-dependence of W. Finally, the coefﬁcient 2 has been evaluated to be 3:5 1011 m. This value is close to the experimental value of 2:85 1011 m, which 0 comes from the slope of the W O ðelÞ vs. E plot in Fig. 4(B). From this result, the authors [33] have concluded that the CT interaction plays a major role in the observed linear 0 W 0 dependence of W O ðelÞ or O ðz-depÞ on E, though this conclusion seems to be overstated to some extent.

VI.

W

W 2 .

SELECTIVE HYDRATION OF IONS IN ORGANIC SOLVENTS

0;O!W In almost all theoretical studies of Gtr , it is postulated or tacitly understood that when an ion is transferred across the O/W interface, it strips off solvated molecules completely, and hence the crystal ionic radius is usually employed for the calculation of . Although Abraham and Liszi [17], in considering the transfer between mutually G0;O!W tr saturated solvents, were aware of the effects of hydration of ions in organic solvents in which water is quite soluble (e.g., 1-octanol, 1-pentanol, and methylisobutyl ketone), they concluded that in solvents such as NB and1,2-DCE, the solubility of water is rather small and most ions in the water-saturated solvent exist as unhydrated entities. However, even a water-immiscible organic solvent such as NB dissolves a considerable amount of water (e.g., ca. 170 mM H2 O in NB). In such a medium, hydrophilic ions such as Liþ , Naþ , Ca2þ , Ba2þ , Cl , and Br are selectively solvated by water. This phenomenon has become apparent since at least 1968 by solvent extraction studies with the Karl–Fischer method [35–45]. Rais et al. [35] and Iwachido and coworkers [36–39] determined hydration numbers, i.e., the number of coextracted water molecules, for alkali and alkaline earth metal

34

Osakai and Ebina

ions in NB. Some inorganic anions (Cl , Br ,, I , SCN , ClO 4 , and NO3 ) have also been found to coextract water into NB [40–42]. Similar phenomena have further been observed in solvents other than NB (e.g., 1,1- and 1,2-dichloroethane, 4-methyl-2-pentanone, chloroform, NB–benzene mixtures) [42–45]. If these observations are valid, we should reconsider the previous theories of G0;O!W in which the hydration of ions in O is not tr properly taken into account. From this point of view, Osakai et al. [46] reafﬁrmed the coextraction of water into NB for a variety of common ions and determined their accurate hydration numbers in NB. In the previous study [46], various kinds of cations and anions (listed in Table 2) were extracted from water to NB using several extractants: tetraphenylborate (TPB ) and dipicrylaminate (DPA ) for the cations; n-Bu4 Nþ , n-Pen4 Nþ , n-Hep4 Nþ , and tris(1,10phenanthroline)iron(II) ([Fe(phen)3 2þ Þ for the anions. The increase in the water concentration in the NB phase, ½H2 O, with extraction of an ion was evaluated as a function of equilibrium concentration of the ion in NB. A typical example, obtained in the DPA

TABLE 2 at 25 C

Numbers (n) of Coextracted Water Molecules in NB and Radii (rh ) of Hydrated Ions n

Cation Liþ Naþ Kþ Rbþ Csþ Ca2þ Ba2þ Me4 Nþ Et4 Nþ n-Bu4 Nþ Ph4 Asþ

TPB system 6.3 4.0

15 10 0 0 ( 0[42])

DPA system 5.7 (4.2[35]; 5.5[36]) 3.6 (3.6[35]; 3.5[36]) 1.0 (1.0[35]; 1.3[36]) 0.7 (0[35]; 0.7[36]) 0.4 (0[35]; 0.7[36]) 12 (13[36]) 11 (9.4[36]) 0 0 0

av

rh (nm)

ra (nm)

6:0 0:4 3:8 0:3 1.0 0.7 0.4 14 2 11 1 0 00 0 0

0.351 0.307 0.220 0.212 0.206 0.467 0.435

0.073 0.116 0.152 0.166 0.181 0.114 0.149 0.279 0.337 0.413 0.426

n

Anion Cl Br I SCN ClO 4 NO 3 TPB a

n-Bu4 Nþ system

2.1 (1.8[43]) 0.9 1.1 0.3 ( 1:4½42Þ 0ð 0[42])

n-Pen4 Nþ system 4.0 (3.3[43]) 2.1 0.8 1.1 0.2 0

n-Hep4 Nþ system

2.0 1.0 1.0 0.2 0

½FeðphenÞ3 2þ system —b (5.5[41]) 1.0c (2.1[41]) 1.1c (1.9[41]) 0.1c (0.64[41]) 1.7c 0c

av 4.0 2:1 0:1 0:9 0:1 1:1 0:1 0:2 0:1 1.7 0

rh (nm)

ra (nm)

0.322 0.276 0.248 0.260 0.244 0.267

0.167 0.182 0.206 0.213 0.236 0.189 0.421

Crystal (or bare) ionic radii (see Table 3). No reliable value could be obtained due to extremely low extractability (the distribution ratio D < 0:03). c Corrected for the contribution (n ¼ 0:3) from ½FeðphenÞ3 2þ . Source: From Ref. 46. b

Ion Solvation and Resolvation

35

system, is shown in Fig. 7. The hydrophobic organic cations (Me4 Nþ , Et4 Nþ , and TPAsþ ) showed no increase in water concentration, indicating that these cations as well as DPA had no ability to transport water to NB. In contrast, hydrophilic metal ions showed a distinguishing increase. The slope of each linear plot should correspond to the number (n) of water molecules coextracted to NB with a metal ion, which are listed in Table 2 together with those determined in other systems. As seen in the table, for both cations and anions, the n values determined were only slightly dependent on the nature of extractant (i.e., coion). This implies that ion-pair formation in NB is of less signiﬁcance or that the ions are almost dissociated. Thus accurate numbers of water molecules, being certainly associated with individual ions, could be determined. Based on these measurements, a new model of the transfer of hydrophilic ions across the O/W interface was proposed (see Fig. 8). In this model, the hydrophilic ion transfers from W to O with some water molecules associated with the ion. A typical example in Fig. 8 shows that a sodium ion transfers across the NB/W interface with four water molecules. of such a hydrophilic ion, therefore, the transferring In theoretical treatment of G0;O!W tr species should be regarded as the ‘‘hydrated’’ ion. In accordance, the radii (rh Þ of hydrated ions in NB were estimated from the hydration numbers (n) and crystal ionic radii (r) by rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 3 3 n þ r3 ð25Þ rh ¼ 4 d where d is the density of water in the hydration shell (here, the value of d is assumed to be the same as that of bulk water, i.e., 3:33 1028 molecule m3 ). The estimated values of rh are also shown in Table 2. As seen in Table 2, the order of the magnitude of rh for alkali metal ions is the reverse of that of the magnitude of r. This means that a more hydrophilic ion has a larger rh . However, this fact does contradict the expectation from Bornian electrostatic theories. As can be seen in the Born equation [Eq. (2)], it is expected that the larger the radius an ion 0;O!W has, the more positive the Gtr value the ion has, that is, the more hydrophobic it

FIG. 7 Plots of the increase of water concentration in NB (½H2 OÞ with extraction of cations with DPA against the equilibrium cation concentration in NB. Each value in the parentheses shows the number (n) of coextracted water molecules per ion. (From Ref. 46. Copyright 1997 American Chemical Society.)

36

Osakai and Ebina

FIG. 8 Proposed model of the transfer of a hydrophilic ion across the O/W interface. The illustration shows the transfer of Naþ from W to NB as a typical example. (From Ref. 46. Copyright 1997 American Chemical Society.)

becomes. This would show that Liþ , as an example, is more hydrophobic than Csþ , but this is of course not the case. Thus, if hydrated radii of ions are used, Bornian electrostatic solvation models are invalid. Then we made a new approach that recognizes short-range interactions of a 0;O!W for hydrophilic ions could be hydrated ion with solvents. By this approach, Gtr elucidated on the basis of the proposed model in Fig. 8 (see Section VII). A similar model for some hydrophilic ions, was also employed by Sa´nchez et al. [47] to elucidate G0;O!W tr but using a Bornian electrostatic theory. Recently, the abilities of primary to tertiary alkylammonium ions with Me, Et, and n-Bu groups to transport water to NB have been studied [48]. As the result of careful consideration of the ion-pair formation, it has been shown that the hydration numbers (nh ) of the ammonium ions in NB, being little affected by the alkyl chain length, are simply dependent on the class of the ammonium ion: nh ¼ 1:64, 1.04, 0.66, respectively, for the primary, secondary, and tertiary ammonium ions.

VII. A.

NON-BORNIAN THEORY OF THE RESOLVATION ENERGY OF IONS Theoretical Model

Based on the above-mentioned experimental and theoretical ﬁndings, we have proposed a new, non-Bornian theory of G0;O!W of ions [49]. In this theory, it is assumed that a tr hydrophilic ion which is selectively hydrated in organic solvent transfers across the O/W interface as the hydrated ion, and a hydrophobic ion which is not hydrated in the O phase transfers as a bare ion, as depicted in Fig. 9. In a conventional manner we divide G0;O!W into two terms: tr 0;O!W 0;O!W Gtr ¼ Gtr ðz-indepÞ þ G0;O!W ðz-depÞ tr

ðz-indepÞ G0;O!W tr

ð26Þ

is the charge-independent term corresponding to the solvophowhere bic interaction or the energy of the formation of a cavity in solvents, and G0;O!W ðz-depÞ tr is the charge-dependent term, which has so far been considered mainly as describing

Ion Solvation and Resolvation

37

FIG. 9 Proposed model of the transfer of (a) a hydrophilic ion and (b) a hydrophobic ion across the O/W interface. (From Ref. 49. Copyright 1998 American Chemical Society.)

electrostatic (i.e., long-range) ion–solvent interaction, but is here treated as describing speciﬁc (short-range) interactions. ðz-indepÞ, we employed the Uhlig formula [Eq. (4)]. For the evaluation of G0;O!W tr This formula may be applicable to the NB/W interface (O;W ¼ 25:2 mN m1 [50]) and to all ions studied (see Table 3), which include the ‘‘hydrated’’ ions with a hydrated radius rh ð¼ rÞ larger than 0.20 nm as well as the ‘‘unhydrated’’ ions of r > 0:23 nm. 0;O!W ðz-dep) in Eq. (26) is here assumed to be govThe charge-dependent term Gtr erned by short-range ion–solvent interactions. The long-range interactions of an ion with the solvents in the second and further solvation shells are ignored in the present theory. Because the short-range (i.e., chemical) interactions recognize some overlap of the electron orbitals of the ion and the solvent molecule in its immediate vicinity, they should be explained on quantum chemical considerations. In ab initio molecular orbital studies [58], the self-consistent-ﬁeld (SCF) energy of the ion–molecule interaction, USCF , is partitioned into several terms including Coulomb (COU), polarization (POL), charge-transfer (CT), and exchange (EX) terms: USCF ¼ UCOU þ UPOL þ UCT þ UEX

ð27Þ

The ﬁrst two terms UCOU and UPOL correspond to the empirical energy of ion–dipole and ion–induced dipole interactions, being given by UCOU ¼ Ehcos i

ð28Þ

1 UPOL ¼ E 2 2

ð29Þ

and

where and are the dipole moment and electronic polarizability of the solvent molecule, respectively, is the angle between the dipole axis and the line connecting the point dipole and point charge, h i indicates the ensemble average, and E is the ‘‘effective’’ electrical ﬁeld strength, which can be approximated by the surface ﬁeld strength of the ion given by Eq. (8), when r is much larger than the radius of the dipole (i.e., solvent molecule).

38

Osakai and Ebina

TABLE 3 Charge Numbers and Radii of Ions and Their Hydration Numbers and Hydrated Radii in NB at 25 C Ion Hydrated cations Liþ Naþ Kþ Rbþ Csþ Ca2þ Ba2þ Nonhydrated cations Me4 Nþ Et4 Nþ n-Pr4 Nþ n-Bu4 Nþ Ph4 Asþ ðTPAsþ Þ ½NiðbpyÞ3 2þ ½NiðphenÞ3 2þ ½FeðphenÞ3 2þ Hydrated anions Cl Br I SCN NO 3 Nonhydrated anions ClO 4 IO 4 2,4-dinitrophenol 2,4,6-trinitrophenol Ph4 B ðTPB Þ Polyanions ; -½XM12 O40 4 ; -½XM12 O40 3 -½X2 Mo18 O62 6 -½S2 Mo18 O62 4 ½S2 VMo17 O62 5 ½P2 Mo18 O61 4 ½Mo6 O19 2 ½VMo5 O19 3 -½Mo8 O26 4

z

ra (nm)

nb

rh c (nm)

1 1 1 1 1 2 2

0.073 0.116 0.152 0.166 0.181 0.114 0.149

6.0 3.8 1.0 0.7 0.4 14 11

0.351 0.307 0.220 0.212 0.206 0.467 0.435

1 1 1 1 1 2 2 2

0.279d 0.337d 0.379d 0.413d 0.416f 0.527g 0.544g 0.541g

0 0 0e 0 0 0e 0e e 0 (0.3)

1 1 1 1 1

0.167 0.182 0.206 0.213h 0.189i

4.0 2.1 0.9 1.1 1.7

1 1 1 1 1

0.236i 0.249i 0.315j 0.332j 0.421f

0e (0.2) 0e 0e 0e 0

4 3 6 4 5 4 2 3 4

0.56k 0.56k 0.648k 0.648k 0.648k 0.644k 0.437k 0.437k 0.485k

0e 0e 0e 0e 0e 0e 0e 0e 0e

0.322 0.276 0.248 0.260 0.267

Ion Solvation and Resolvation

39

The third term, UCT , in Eq. (27) is due to the partial electron transfer between an ion and solvents in its immediate vicinity. The model Hamiltonian approach [33], described in Section V, has shown that UCT ð¼ W in Ref. 33) per primary solvent molecule, for an ion such as the polyanion, can also be expressed as a function of E, approximately a quadratic equation: UCT ¼ 0 1 E 2 E 2

ð30Þ

The coefﬁcients 0 , 1 , and 2 (denoted as 0 , 1 , and 2 in Ref. 33) are inﬂuenced by various molecular properties of the solvent and an ion, including their electron-donating or accepting abilities. Hence, these coefﬁcients are speciﬁc to the ion. Nevertheless, they may be considered as common to a family of ions such as the polyanions whose surface atoms, directly interacting with solvents, are oxygens. This is the case for ‘‘hydrated’’ cations or anions whose surfaces are composed of some water molecules that interact with outer water molecules in the W phase or with organic solvents in the O phase. The remaining term, UEX , in Eq. (27) represents the nonclassical repulsion term, being inherently independent of E. By summarizing the above argument, we conclude that the short-range interaction energy, USR ð¼ USCF Þ, can be given by a quadratic function of E: USR ¼ A BE CE 2

ð31Þ

A ¼ 0 þ UEX

ð32Þ

B ¼ Ehcos i þ 1 C ¼ þ 2 2

ð33Þ

with

ð34Þ

The validity of Eq. (31) has been conﬁrmed by an approach from redox potentials of heteropoly oxometalate anions as well [59]. In Eq. (31) we should note that USR represents the interaction energy per primary solvent molecule. Then the number of solvent molecules that can be interact directly with an ion in phase S ð¼ O or W) is denoted as N S . Accordingly, the contribution of the shortof the ion phase S (i.e., transfer range interactions to the solvation energy G0;vac!S tr energy from vacuum) is given from Eq. (31) as

Footnotes to Table 3 a Shannon’s crystal ionic radii [51], except where otherwise noted. b Ref. 46. c Estimated by Eq. (25). d van der Waals radii calculated from the partial molar ionic volumes [52]. e Assumed. f Ref. 6. g van der Waals radii calculated from the partial molar ionic volumes [53,54]. h Ref. 55. i Thermochemical radii [56]. j From van der Waals volumes calculated from atomic increments [57]. k See Table 1. Source: From Ref. 49.

40

Osakai and Ebina

G0;vac!S ðSRÞ ¼ N S USR ¼ AS N S BS N S E C S N S E 2 tr

ð35Þ

where the superscript S of A, B, and C represents the S phase. Because the transfer energy G0;O!W is the difference between G0;S s ’s in O and W, the contribution of short-range tr can be expressed as interactions to G0;O!W tr 0;O!W ðSRÞ ¼ 1 2 E 3 E 2 Gtr

ð36Þ

1 ¼ A W N W A O N O

ð37Þ

2 ¼ BW N W BO N O

ð38Þ

3 ¼ C W N W C O N O

ð39Þ

with

0;O!W (SR) Gtr

is given approximately by a quadratic equation of E. The In this manner coefﬁcients 1 , 2 , and 3 are related to various molecular properties of the ion and solvents [see Eqs. (32)–(34) and Eqs. (37)–(39)]. To estimate theoretically these coefﬁcients using an appropriate model may not be impossible, but rather difﬁcult at the present stage, because there is insufﬁcient information on the above-mentioned molecular properties (in particular, the charge-transfer properties). Consequently, coefﬁcients 1 , 2 , and 3 in Eq. (36) have been determined empirically, as shown below. B.

Experimental Data

In the present analyses [49], 34 ions are classiﬁed into ﬁve groups: (1) hydrated cations, (2) nonhydrated cations, (3) hydrated anions, (4) nonhydrated anions, and (5) polyanions. Here, the term ‘‘hydrated’’ or ‘‘nonhydrated’’ means that the ion is associated with some water molecules in the O phase or not, respectively. 1. Ionic Radii All ions studied are assumed to be spherical, and radii (r) of the bare ions are listed in Table 3. Unless otherwise noted, authorized values of crystal ionic radii or van der Waals radii are adopted [51–57]. 2. Hydration Numbers of Ions in NB The numbers (n) of coextracted water molecules shown in Table 3 are from Table 2 [46]. In the case of n-Pr4 Nþ , metal complex cations, larger anions of r > 0:23 nm, and polyanions, it is assumed that n ¼ 0. Although the n value of ½FeðphenÞ3 2þ or ClO 4 was reported to be as small as 0.3 or 0.2 [46], these ions have been classiﬁed as ‘‘nonhydrated’’ (i.e., n ¼ 0) so that comparatively better results may be obtained. In Table 3 are also shown the hydrated radii (rh ) which are evaluated with n and r by Eq. (25). A good correlation of rh with the Stokes radius [60] (rs ) has been observed for hydrated cations (alkali and alkaline earth metal ions) [46]: rh ðnmÞ ¼ 1:310 rs ðnmÞ þ 0:055

ðR ¼ 0:997Þ

ð40Þ

In this equation and the following remarks, R shows the correlation coefﬁcient. For the prediction of G0;O!W of a hydrophilic ion whose n value is unknown, it is tr desirable that the n value can be obtained with r and z only. Since the interactions of a small ion with water molecules in the hydration shell may be mostly electrostatic, the

Ion Solvation and Resolvation

41

dependence of n on (z=r) has been investigated for hydrophilic cations and anions. As a result, it has been found that the plots of n against (z=r) lie on a quadratic curve: For cations: ðR ¼ 0:966Þ n ¼ 0:566 þ 0:0091ðz=rÞ þ 0:04745ðz=rÞ2 For anions: n ¼ 5:844 þ 3:775ðz=rÞ þ 0:5661ðz=rÞ2 ðR ¼ 0:930Þ

ð41Þ ð42Þ

where r is in nanometers. Equations (41) and (42) are applicable in the range of ðz=rÞ > 5 and ðz=rÞ < 4, respectively. Using these equations, we can predict, though somewhat roughly, the n value of a hydrophilic ion. Regarding the cations, however, their n values could be obtained more accurately from the Stokes radii by using the relations of Eqs. (25) and (40). 3.

Gibbs Energies of Transfer of Ions

0;O!W In 1977 Koryta et al. [61] reported the Gtr values of several common ions at the NB/W interface, which were calculated from the extraction data using an extra thermodynamic assumption. Afterward, a newly developed electrochemical technique (so-called ion-transfer voltammetry) with a polarizable O/W interface was employed to determine G0trO!W for a variety of ions [33,62–71]. In Table 4 the reliable values of G0;O!W tr are compiled. Regarding the ions whose G0;O!W values are available for both electrotr chemical and extraction measurements, the electrochemical data, which seem to be more accurate, have been chosen preferentially. For several ions, somewhat different G0;O!W tr values from electrochemical measurements have been reported, as also seen in the database provided by Girault on a website [72]. In this study, however, we have carefully chosen reliable values for the respective ions, which were determined under well-deﬁned conditions (reference electrodes, solution compositions, etc.).

C.

Data Analyses

1.

Calculation of Cavity Formation Energies

Using the Uhlig formula [Eq. (4)] the values of G0;O!W (z-indep) have been obtained tr from ionic radii, as shown in Table 4. For the hydrated cations and anions, their hydrated 0;O!W (zradii (rh Þ have been employed for r in Eq. (4). Table 4 also shows the values of Gtr 0;O!W (z-indep) from the total G0;O!W dep) which have been obtained by subtracting Gtr tr [see Eq. (26)]. 2. Regression Analyses for Hydrated Ions Unless noted otherwise, it has been assumed that the number of the solvent molecules N S (S ¼ O or W) that can interact directly with a hydrated ion in phase S is equal to the hydration number: NO ¼ NW ¼ n

ð43Þ

For Ca2þ and Ba2þ , whose n values are larger than 10, however, it is thought that some hydrated water molecules not only in the ﬁrst hydration shell but also in the second hydration shell are cotransferred into NB. Accordingly, it can be supposed that some water molecules in the ﬁrst hydration shell (i.e., in the vicinity of the ion) are covered with the second hydration shell, so that they cannot be associated with outer solvent

42

Osakai and Ebina

TABLE 4 Standard Gibbs Energies of Transfer of Ions from NB to W and Their ChargeIndependent and Charge-Dependent Components at 25 C

Ion Hydrated cations Liþ Naþ Kþ Rbþ Csþ Ca2þ Ba2þ Nonhydrated cations Me4 Nþ Et4 Nþ n-Pr4 Nþ n-Bu4 Nþ Ph4 Asþ ðTPAsþ Þ ½NiðbpyÞ3 2þ ½NiðphenÞ3 2þ ½FeðphenÞ3 2þ Hydrated anions Cl Br I SCN NO 3 Nonhydrated anions ClO 4 IO 4 2,4-dinitrophenol 2,4,6-trinitrophenol Ph4 B ðTPB Þ Polyanions ; -½XM12 O40 4 ; -½XM12 O40 3 -½X2 Mo18 O62 6 -½S2 Mo18 O62 4 ½S2 VMo17 O62 5 ½P2 Mo18 O61 4 ½Mo6 O19 2 ½VMo5 O19 3 -½Mo8 O26 4

G0;O!W tr (kJ mol1 )

G0;O!W (z-indep)a tr (kJ mol1 )

G0;O!W (z-dep)b tr (kJ mol1 )

38:2c;d 34:2c;d 23:5c;d 19:4c;d 15:4c;d 67:3d;e 61:8d;e

23.6 17.9 9.2 8.6 8.1 41.6 36.0

61:8 52:1 32:7 28:0 23:5 108:9 97:8

3:4c;d 5.3f 16:4g 26:5h 35:9c;d 30:5i 41:3i 44:0j

14.8 21.7 27.4 32.5 34.6 53.0 56.4 55.8

18:2 16:4 11:0 6:0 1.3 22:5 15:1 11:8

38:2k 27:8l 18:4l 15:8l 25:2l

19.8 14.6 11.7 12.9 13.5

58:0 42:4 30:1 28:7 38:7

7:9l 6m 5:7n 6:7n 35:9d

10.6 11.8 18.9 21.0 33.8

18:5 17:8 24:6 14:3 2.1

25:9o 71.8o 2:9o 103:8o 41:0o 92:2o 31:6o 34:4o 52:9o

59.8 59.8 80.1 80.1 80.1 79.1 36.4 36:4 44.9

33:9 12.0 77:2 23.7 39:1 13.1 4:8 70:8 97:8

Ion Solvation and Resolvation

43

molecules (W or NB). Such an effect is here called ‘‘shielding.’’ In these cases, N S cannot be equated simply to n and should be reduced to some extent. It has been found that for the above two cations, the subtraction of 4 from the net n values may lead to the best result in the following regression analysis. If we suppose that G0trO!W (z-dep) for the hydrated ions is ruled out by short-range interactions, a combination of Eqs. (36)–(39) and Eq. (43) yields G0trO!W ðz-depÞ=n ¼ A BE CE 2

ð44Þ

with A ¼ A A , B ¼ B B , and C ¼ C C . In Fig. 10 the values of G0;O!W (z-dep)=n for the hydrated cations (*) and anions (*) are plotted against E, tr being calculated by Eq. (8) with r ¼ rh . Note that the plots of Ca2þ and Ba2þ have been compensated for the ‘‘shielding’’ effect: the symbols () in Fig. 10 represent the plots with the net values of n ð¼ 14 or 11 for Ca2þ or Ba2þ , respectively). 0;O!W (z-dep) per hydrated water As seen in Fig. 10, in accordance with Eq. (44), Gtr becomes progressively greater as E is enhanced. Since the contribution from the interaction in W to G0;O!W (z-dep) is probably more signiﬁcant than that from the interaction tr in NB, the dependences shown in Fig. 10 seem to suggest that the hydrogen bonds, which are formed around a hydrated ion in W and which must be broken in its transfer to NB, are strengthened by the surface ﬁeld of the hydrated ion. The solid lines in Fig. 10 represent the quadratic curves obtained in regression analyses. W

O

W

O

W

O

For hydrated cations: G0;O!W ðz-depÞ=n ¼ 8:90 þ 4:506E 4:853E 2 tr For hydrated anions: G0;O!W ðz-depÞ=n ¼ 50:17 52:51E 19:33E 2 tr where

0;O!W (z-dep) Gtr

is in kJ mol

1

10

ðR ¼ 0:931Þ ðR ¼ 0:999Þ

ð45Þ ð46Þ

1

and E is in 10 V m .

3. Regression Analyses for Nonhydrated Ions As for the nonhydrated ions including the polyanions, it has been assumed that N S is proportional to the surface area of the ion:

Footnotes to Table 4 a Evaluated using Eq. (4) (note that r ¼ rh for the hydrated ions). b 0;O!W 0;O!W G0;O!W (z-depÞ ¼ Gtr Gtr (z-indep). tr c Ref. 61. d Determined using extraction data; the other values were determined by electrochemical measurements. e Ref. 62. f Ref. 63. The value is revised by employing Me4 Nþ as an internal reference in the place of n-Bu4 Nþ . g Unpublished data obtained by means of the former electrochemical technique [64]. h Ref. 65. i Ref. 66. j Ref. 67. k Ref. 68. l Ref. 69. m Ref. 70. n Ref. 71. o Calculated from the standard ion-transfer potentials compiled previously [33]. Source: From Ref. 49.

44

Osakai and Ebina

FIG. 10 Plots of G0;O!W (z-depÞ=n against E (with r ¼ rh ) for hydrated cations (*) and anions tr (*). Note that the n values for the plots of Ca2þ and Ba2þ have been corrected for the ‘‘shielding’’ effect (see text) by subtracting 4 from their net values of n; () represents the plots with the net values. Solid lines show the regression curves [Eqs. (45) and (46)]. (From Ref. 49. Copyright 1998 American Chemical Society.)

N S ¼ 4r2 S

ð47Þ

where is the number of solvent molecules per unit surface area of the ion in phase S (z-dep) is ruled only by short-range ð¼ O or W). We have also assumed that G0;O!W tr interactions in the same manner as the hydrated ions and then have obtained from Eqs. (36)–(39) and Eq. (47): S

0;O!W ðz-depÞ=ð4r2 Þ ¼ A 0 B 0 E C 0 E 2 Gtr 0

0

ð48Þ 0

with A ¼ A A , B ¼ B B , and C ¼ C C . (z-dep)/(4r2 ) have been plotted In accordance with Eq. (48), the values of G0;O!W tr against E in Fig. 11. The respective plots for the three ion groups have been found to lie on a single quadratic curve. W W

O O

W W

O O

W W

For nonhydrated cations: G0;O!W ðz-depÞ=ð4r2 Þ ¼ 28:19 43:08E þ 9:582E 2 tr For nonhydrated anions: G0;O!W ðz-depÞ=ð4r2 Þ ¼ 33:04 þ 47:53E þ 9:518E 2 tr For polyanions: G0;O!W ðz-depÞ=ð4r2 Þ ¼ 13:40 7:685E 11:08E 2 tr 0;O!W (z-dep) Gtr

1

10

O O

ðR ¼ 0:987Þ

ð49Þ

ðR ¼ 0:967Þ

ð50Þ

ðR ¼ 0:989Þ

ð51Þ

1

is in kJ mol , r in nm, and E in 10 V m . It is noteworthy that where the plots of the polyanions with a wide variety of charges (z ¼ 2 to 6) lie on a single curve. 4. Total Gibbs Energies of Transfer of Ions 0;O!W The values of Gtr have been calculated using the Uhlig formula [Eq. (4)] for the charge-independent part and the empirical equations [Eqs. (45), (46), (49), (50), and (51)] 0;O!W for the charge-dependent part. Table 5 gives the calculated values of Gtr for 34 ions, and the values are compared in Fig. 12 with the observed values shown in Table 4. As seen

Ion Solvation and Resolvation

45

FIG. 11 Plots of G0trO!W (z-depÞ=ð4r2 Þ against E for nonhydrated cations (~) and anions (~) and polyanions (&). Solid lines show the regression curves [Eqs. (49), (50), and (51)]. (From Ref. 49. Copyright 1998 American Chemical Society.)

FIG. 12 Comparison of the calculated and observed values of G0trO!W for 34 ions: (*) hydrated cations, (*) hydrated anions, (~) nonhydrated cations, (~) nonhydrated anions, and (&) polyanions. (From Ref. 49. Copyright 1998 American Chemical Society.)

46 TABLE 5

Osakai and Ebina Calculations of Standard Gibbs Energies of Transfer of Ions from NB to W (25 C)

Ion Hydrated cations Liþ Naþ Kþ Rbþ Csþ Ca2þ Ba2þ Nonhydrated cations Me4 Nþ Et4 Nþ n-Pr4 Nþ n-Bu4 Nþ Ph4 Asþ ðTPAsþ Þ ½NiðbpyÞ3 2þ ½NiðphenÞ3 2þ ½FeðphenÞ3 2þ Hydrated anions Cl Br I SCN NO 3 Nonhydrated anions ClO 4 IO 4 2,4-dinitrophenol 2,4,6-trinitrophenol Ph4 B ðTPB Þ Polyanions ; -½XM12 O40 4 ; -½XM12 O40 3 -½X2 Mo18 O62 6 -½S2 Mo18 O62 4 ½S2 VMo17 O62 5 ½P2 Mo18 O61 4 ½Mo6 O19 2 ½VMo5 O19 3 -½Mo8 O26 4 a

Ea (10 V m1 ) 10

(z-dep)b G0;O!W tr (kJ mol1 )

(calc)c G0;O!W tr (kJ mol1 )

61:5 50:9 38:3 30:7 19:6 114:1 93:1

37:9 33:0 29:0 22:1 11:5 72:5 57:1

ðþ0:3Þe ðþ1:2Þ ð5:5Þ ð2:7Þ ðþ3:9Þ ð5:2) ðþ4:7Þ

18:3 15:7 9:7 2:9 0.1 21:6 17:3 18:1

3:5 5.9 17.7 29.6 34.7 31.4 39.1 37.7

ð0:1Þ ðþ0:6Þ ðþ1:3Þ ðþ3:1Þ ð1:2Þ (þ0:9Þ (2:2) (6:3)

64:1 45:9 31:8 30:9 42:7

44:3 31:3 20:1 18:0 29:2

ð0:3Þ ðþ1:5Þ ðþ0:2Þ ð0:1Þ ð1:3Þ

2:59 2:32 1:45 1:31 0:81

18:4 20:3 19:8 17:7 1.6

7:7 8:9 0:9 3.3 35.4

ðþ1:4Þ ð2:4Þ ðþ4:8Þ ð3:4Þ ð0:5Þ

1:84 1:38 2:06 1:37 1:71 1:39 1:51 2:26 2:45

38:8 11.7 93:3 16.3 31:6 14.1 0:5 62:2 101:1

21.0 71.5 13:3 96.4 48.5 93.2 35.9 25:7 56:3

(4:9) ð0:3Þ ð16:2Þ ð7:4Þ ðþ7:5Þ ðþ1:0Þ ðþ4:3Þ ðþ8:7Þ (3:4)

1.17 1.53 2.97 3.19 3.38 1.32 1.52

(27.0)d (10.7) (6.23) (5.23) (4.39) (22.2) (13.0)

1.85 1.27 1.00 0.84 0.79 1.04 0.97 0.98 1:39 1:89 2:35 2:13 2:03

ð5:16Þd ð4:35Þ ð3:39Þ ð3:17Þ ð4:03)

Evaluated from Eq. (8). For the hydrated ions, their hydrated radii were employed for the value of r. Calculated using Eqs. (45), (49), (46), (50), and (51) for hydrated cations, nonhydrated cations, hydrated anions, nonhydrated anions, and polyanions, respectively. c 0;O!W Obtained by adding the calculated values of G0;O!W (z-dep) to the values of Gtr (z-indep) in Table 4. tr d The values in parentheses are surface ﬁeld strengths of the bare ions. e The values in parentheses show the deviations from the observed values. Source: From Ref. 49. b

Ion Solvation and Resolvation

47

from the ﬁgure, satisfactory agreement has been observed (R ¼ 0:994; standard deviation, 0 0;O!W by Eq. (7), the correSD ¼ 4:63 kJ mol1 ). Also, for the W O being related to Gtr lation of the calculated and observed values has been found to be very good (R ¼ 0:995; SD ¼ 0:023 V). D.

Predictions

0 (and W Based on the proposed theory, the values of G0;O!W O ) have been predicted for tr þ 2þ 2þ 2þ 2þ 3þ hydrophilic ions (NH4 , Mg , Sr , Ni , Fe ; Fe , ClO3 , BrO 3 , CN , IO3 , HCO3 , 0;O!W values have been reported, but their hydration numbers are NO2 , OH ), whose Gtr unknown. In the predictions, the ﬁrst decision on whether the ion is hydrated in NB is made by means of ðz=rÞ; as described above, if ðz=rÞ > 5 (r in nm) for a cation or ðz=rÞ < 4 for an anion (except polyanions), the ion should be hydrated in NB to a certain extent. For these hydrated ions, the hydration number and the hydrated radius are evaluated. 0;O!W Then the charge-independent and -dependent terms of Gtr are calculated using the Uhlig formula and the empirical equation, respectively. Finally, the summation of the two . terms yields the total value of G0;O!W tr (z-dep) for highly hydrated cations (Mg2þ , Sr2þ , Ni2þ , In the calculation of G0;O!W tr 2þ 3þ Fe , Fe ) with n > 10, the values of n for use in Eq. (45) have been corrected for the ‘‘shielding’’ effect, on the assumption that the corrected value of n is proportional to the surface area of the hydrated ion:

ncorr ¼ f ð4r2 Þ

ð52Þ

The factor f has been determined to be 42.05 by a regression analysis, so that the ncorr values of Ca2þ and Ba2þ may be approximated to n 4 (see above). Although the results of the predictions (see Table 5 in Ref. 49) are not shown here, it has been found that the proposed theory is promising not only for an understanding of but also for its prediction. G0;O!W tr E.

Discussion

In the proposed theory, short-range ion–solvent interaction energies are formulated as Eq. (31). the coefﬁcients A, B, and C in the quadratic equation are related to coefﬁcients 1 , [Eq. (36)]. The above-mentioned regression 2 , and 3 in the formula for G0;O!W tr analyses have clearly shown that these coefﬁcients are common to a family of ions. This suggests that the surface chemical constitution of an ion should play a major role in its short-range interactions with solvents. For hydrated ions, their surfaces are composed of water molecules, which may prevent the inner ion from interacting directly with outer solvent molecules. Accordingly, the quantum chemical properties of the inner ion hardly inﬂuence direct interactions of the hydrated ion with solvents. The inner ion may function only as the origin of the surface electrical ﬁeld of the hydrated ion, which should affect the short-range interaction energy, as shown in Eq. (31). As for the nonhydrated cations studied, their surfaces are mainly composed of C–H atomic groups, while the ﬁve nonhydrated anions, being forced to be classiﬁed into one group, have miscellaneous surfaces. As also described above, the surfaces of the polyanions are composed of oxygens without exception. Thus Eq. (31) turns out to be quite promising for an understanding of G0;O!W for ions with the common surface. tr The coefﬁcients in Eq. (44) or (48) coming from those in Eq. (31) have been determined empirically in the present study. As shown above, these coefﬁcients are related to

48

Osakai and Ebina

some molecular properties of the ion and the solvent. However, it seems premature to discuss these relations quantitatively, because the coefﬁcients would be heavily affected by 0;O!W . It is desired to collect accurate and reliable values of the experimental errors in Gtr 0;O!W Gtr for many other kinds of ions. In the present non-Bornian theory it should be noted again that the long-range electrostatic interactions of an ion with solvents in the second and further solvation shells are ignored. However, the electrostatic energies should contribute to a considerable extent to the solvation energies of ions in each phase. Nevertheless, the proposed equations for G0;O!W , in which short-range interactions are only considered, have been found to be tr ﬁtted very well to the experimental data. This may be understood by recognizing that is the difference in the solvation energy between the two phases. It is most G0;O!W tr probable that the long-range electrostatic solvation energies in the respective phases are 0;O!W for the most part canceled in Gtr . This will result in the predominant contribution of 0;O!W . Thus, our daring ignoring of the long-range electroshort-range interactions to Gtr than Bornian electrostatic models. static energies have given a better account of G0;O!W tr

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M. Born. Z. Phys. 1: 45 (1920). Y. Marcus, Ion Solvation, Wiley, Chichester, 1985. Y. Marcus, Ion Properties, Marcel Dekker, New York, 1997. R. R. Dogonadze, E. Ka´lma´n, A. A. Kornyshev, and J. Ulstrup (eds.), The Chemical Physics of Solvation: Part A, Theory of Solvation, Elsevier, Amsterdam, 1985. P. Politzer and J. S. Murray (eds.), Quantitative Treatments of Solute/Solvent Interactions, Elsevier, Amsterdam, 1994. Y. Marcus. Rev. Anal. Chem. 5:53 (1980). Y. Marcus. Pure Appl. Chem. 62:899 (1990). Y. Marcus, in Liquid–Liquid Interfaces: Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, 1996, pp. 39–61. V. S. Markin and A. G. Volkov. Electrochim. Acta 34:93 (1989). T. Osakai and K. Ebina. Bunseki 1998:589 (1998) (in Japanese). A. A. Kornyshev and A. G. Volkov. J. Electroanal. Chem. 180:363 (1984). A. A. Kornyshev, in Ref. 4, pp. 77–118. H. H. Uhlig. J. Phys. Chem. 41:1215 (1937). W. M. Latimer, K. S. Pitzer, and C. M. Slansky. J. Chem. Phys. 7:108 (1939). M. H. Abraham and J. Liszi. J. Chem. Soc. Faraday Trans. 1 74:1604; 2858 (1978). M. H. Abraham, J. Liszi, and L. Me´sza´ros. J. Chem. Phys. 70:2491 (1979). M. H. Abraham and J. Liszi. J. Inorg. Nucl. Chem. 43:143 (1981). Y. Marcus. J. Chem. Soc. Faraday Trans. 87:2995 (1991). V. Gutmann, The Donor–Acceptor Approach to Molecular Interactions, Plenum Press, New York, 1978. K. Burger, Solvation, Ionic and Complex Formation Reactions in Non-Aqueous Solvents: Experimental Methods for Their Investigation, Akade´miai Kiado´, Budapest, 1983. V. Gutmann and E. Wychera. Inorg. Nucl. Chem. Lett. 2:257 (1966). U. Mayer, V. Gutmann, and W. Gerger. Monatsch. Chem. 106:1235 (1975). D. A. Owensby, A. J. Parker, and J. W. Diggle. J. Am. Chem. Soc. 96:2682 (1974). E. Grunwald and S. Winstein. J. Am. Chem. Soc. 70:846 (1948). E. M. Kosower. An Introduction to Physical Organic Chemistry, Wiley, New York, 1968, p. 259. K. Dimroth, C. Reichardt, T. Siepmann, and F. Bohlmann. Liebigs Ann. Chem. 661:1 (1963). C. Reichardt. Angew. Chem. Int. Ed. Engl. 4:29 (1965).

Ion Solvation and Resolvation

49

28. R. W. Taft, N. J. Pienta, M. J. Kamlet, and E. M. Arnett. J. Org. Chem. 46:661 (1981). 29. T. Osakai, H. Katano, K. Maeda, S. Himeno, and A. Saito. Bull. Chem. Soc. Jpn. 66:1111 (1993) and references therein. 30. T. Osakai, S. Himeno, A. Saito, K. Maeda, and H. Katano. J. Electroanal. Chem. 360:299 (1993). 31. T. Osakai, S. Himeno, and A. Saito. Bunseki Kagaku 43:1 (1994) (in Japanese with English abstract). 32. T. Kurucsev, A. M. Sargeson, and B. O. West. J. Phys. Chem. 61:1567 (1957). 33. T. Osakai and K. Ebina. J. Electroanal. Chem. 412:1 (1996). 34. R. S. Mulliken. J. Am. Chem. Soc. 74:811 (1952). 35. J. Rais, M. Kyrs˘ , and M. Pivon˘kova´. J. Inorg. Nucl. Chem. 30:611 (1968). 36. S. Motomizu, K. Toˆei, and T. Iwachido. Bull. Chem. Soc. Jpn. 42:1006 (1969). 37. M. Kawasaki, K. Toˆei, and T. Iwachido. Chem. Lett. 417 (1972). 38. T. Iwachido, M. Minami, A. Sadakane, and K. Toˆei. Chem. Lett. 1511 (1977). 39. T. Iwachido, M. Minami, M. Kimura, A. Sadakane, M. Kawasaki, and K. Toˆei. Bull. Chem. Soc. Jpn. 53:703 (1980). 40. Y. Yamamoto, T. Tarumoto, and T. Tarui. Chem. Lett. 459 (1972). 41. Y. Yamamoto, T. Tarumoto, and T. Tarui. Bull. Chem. Soc. Jpn. 46:1466 (1973). 42. T. Kenjo and R. M. Diamond. J. Phys. Chem. 76:2454 (1972). 43. T. Kenjo and R. M. Diamond. J. Inorg. Nucl. Chem. 36:183 (1974). 44. S. Kusakabe, M. Shinoda, and K. Kusafuka. Bull. Chem. Soc. Jpn. 62:333 (1989). 45. S. Kusakabe and M. Arai. Bull. Chem. Soc. Jpn. 69:581 (1996). 46. T. Osakai, A. Ogata, and K. Ebina. J. Phys. Chem. B. 101:8341 (1997). 47. C. Sa´nchez, E. Leiva, S. A. Dassie, and A. M. Baruzzi. Bull. Chem. Soc. Jpn. 71:549 (1998). 48. A. Ogata, Y. Tsujino, and T. Osakai. Phys. Chem. Chem. Phys. 2:247 (2000). 49. T. Osakai and K. Ebina. J. Phys. Chem. B 102:5691 (1998). 50. T. Kakiuchi, M. Nakanishi, and M. Senda. Bull. Chem. Soc. Jpn. 61:1845 (1988). 51. R. D. Shannon. Acta Cryst. A32:751 (1976). 52. E. J. King. J. Phys. Chem. 74:4590 (1970). 53. H. Yokoyama, K. Shinozaki, S. Hattori, F. Miyazaki. and M. Goto. J. Mol. Lig. 65/66:357 (1995). 54. H. Yokoyama, K. Shinozaki, S. Hattori, and F. Miyazaki. Bull. Chem. Soc. Jpn. 70:2357 (1997). 55. H. D. B. Jenkins and K. P. Thakur. J. Chem. Educ. 56:576 (1979). 56. Y. Marcus, in Ref. 2, pp. 46–47; for IO 4 , see A. F. Kapustinskii. Quat. Rev. 10:283 (1956). 57. J. T. Edward. J. Chem. Educ. 47:261 (1970). 58. A. Karpfen and P. Schuster, in Ref. 4, pp. 265–312. 59. T. Osakai, K. Maeda, K. Ebina, H. Hayamizu, M. Hoshino, K. Muto, and S. Himeno. Bull. Chem. Soc. Jpn. 70:2473 (1997). 60. E. R. Nightingale, Jr. J Phys. Chem. 63:1381 (1959). 61. J. Koryta, P. Vanysek, and M. Br˘ ezina. J. Electroanal. Chem. 75:211 (1977). 62. V. Marec˘ek and Z. Samec. Anal. Chim. Acta 151:265 (1983). 63. T. Osakai, T. Kakutani, Y. Nishiwaki, and M. Senda. Bunseki Kagaku 32:E81 (1983). 64. T. Kakutani, T. Osakai, and M. Senda. Bull. Chem. Soc. Jpn. 56:991 (1983). 65. Z. Samec, V. Marec˘ek, and D. Homolka. Faraday Discuss. Chem. Soc. 77:197 (1984). 66. D. Homolka and H. Wendt. Ber. Bunsen-Ges. Phys. Chem. 89:1075 (1985). 67. T. Kakutani, Y. Nishiwaki, and M. Senda. Bunseki Kagaku 33:E175 (1984). 68. B. Hundhammer and S. Wilke. J. Electroanal. Chem. 266:133 (1989). 69. T. Osakai and K. Muto. Anal. Sci. 14:157 (1998). 70. S. Kihara, M. Suzuki, K. Maeda, K. Ogura, and M. Matsui. J. Electroanal. Chem. 210:147 (1986). 71. T. Ohkouchi, T. Kakutani, and M. Senda. Bioelectrochem. Bioenerg. 25:81 (1991). 72. http://dcwww.epﬂ.ch/cgi-bin/LE/DB/InterrDB.pl.

3 Electroelastic Instabilities in Double Layers and Membranes MICHAEL B. PARTENSKII and PETER C. JORDAN Department of Chemistry, Brandeis University, Waltham, Massachusetts

I.

INTRODUCTION

Electrical double layers and membranes have certain common features. Both are quasitwo-dimensional structures. In both, variation of applied voltage inﬂuences the distribution of charge as well as the structural parameters (effective thickness). And in both cases coupling between the electric ﬁeld and these parameters can lead to instabilities and phase transitions. These instabilities may be described and understood using an electroelastic metaphor ﬁrst introduced in 1973 by Crowley [1] in relation to membrane breakdown (‘‘electroporation’’). Although this model failed to quantitatively describe the onset of instability at small voltage with little deformation, it generated signiﬁcant interest in studies of the electroelasticity of membranes. In some aspects, the electrical response of membranes is similar to the action of an external pressure (such as osmotic stress). But it also has features with no direct analogy to mechanical effects, such as speciﬁc interaction of an applied voltage with surface undulations which can cause instabilities in membranes. Similar phenomena appear equally important in the behavior of electrochemical interfaces where electrical stress affects structural parameters of electrical double layers. These are most closely related to the question of whether, for electrical double layers, it is possible for the differential capacitance, C, to be negative. It has been shown that the prediction of C < 0 in some models of double layers has a direct analogy in the behavior of the elastic capacitors. And, as in membranes, it is also related to possible instabilities and interfacial phase transitions at the interfaces. This chapter is devoted to the behavior of double layers and inclusion-free membranes. Section II treats two simple models, the ‘‘elastic dimer’’ and the ‘‘elastic capacitor.’’ They help to demonstrate the origin of electroelastic instabilities. Section III considers electrochemical interfaces. We discuss theoretical predictions of negative capacitance and how they may be related to reality. For this purpose we introduce three sorts of electrical control and show that this anomaly is most likely to arise in models which assume that the charge density on the electrode is uniform and can be controlled. This ‘‘control’’ is a convenient theoretical construct, but in real applications only the total charge or the applied voltage can be ﬁxed. We then show that predictions of C < 0 under control may indicate that in reality the symmetry breaks. Such interfaces undergo a transition to a nonuniform state; the initial uniformity assumption is erroneous. Most 51

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of this discussion is couched in terms of the electroelastic analogy. Section IV describes electroelastic phenomena in inclusion free membranes with possible relation to instabilities. We ﬁrst treat the Crowley model (a rigid interface). We then consider the ‘‘hydrodynamic,’’ ‘‘electroporative,’’ and ‘‘smectic bilayer’’ perspectives on the initiation of an electroelastic instability. Finally, we describe some attempts to modify the smectic model to account for the basic experimental observation: membrane rupture occurs at low voltages with little electrostriction. These are based on the idea that nonlocality of the elastic moduli softens the symmetrical modes thus enhancing thickness ﬂuctuations at short wavelengths. Possible consequences of this hypothesis for different membrane properties are discussed.

II.

ELECTROELASTIC INSTABILITIES. SIMPLE EXAMPLES

A.

Charges on a Spring (Elastic Dimer)

The nature of the instabilities related to coupling of electrical and elastic degrees of freedom can be illustrated by a very simple example. Consider two charges, q and q, separated by a spring. The corresponding Hamiltonian is H¼

q2 þ E0 ðlÞ 40 l

ð1Þ

where E0 is the bond energy. In an harmonic approximation we write E0 ¼

K ðl l0 Þ2 2

ð2Þ

where K is a ‘‘spring constant,’’ l is the distance between charges, and l0 is the length of the isolated spring. For the sake of convenience we use dimensionless units W¼

H Kl02

q Q ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 40 Kl03

z¼

l l0

ð3Þ

so that W ¼

Q2 1 þ ð1 zÞ2 2 z

ð4Þ

Global behavior of the system is determined by a single parameter, the reduced charge Q; relative distance z is the internal variable, deﬁned by the equilibrium condition @W ¼0 @z

which follows from

@H ¼0 @l

ð5Þ

Before proceeding further we analyze the behavior of the system by viewing its energy surface WðQ; zÞ (Fig. 1). At short distances, z ! 0, the elastic force cannot compete with the electrostatic attraction and W ! 1 for any Q 6¼ 0. For sufﬁciently smallp jQj a local ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ minimum 0 < z 1 exists. It disappears when Q reaches its critical value Qc ¼ 4=27 and z has contracted to zc ¼ 2=3. Both Qc and zc can be deﬁned by solving Eq. (5) together with the marginal equilibrium condition. As we see, ‘‘molecular equilibrium’’ at ﬁnite z, if its exists, is always local, while globally, charges are stable only in direct contact (the collapsed state). In reality, however, additional short-range repulsion would prevent the system from collapsing. Figure 2 incorporates this additional interaction. We see that the

Electroelastic Instabilities

FIG. 1 Energy of elastically coupled charges.

FIG. 2 Energy of elastically coupled charges with an additional short-range repulsion term.

53

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Partenskii and Jordan

‘‘molecule’’ becomes bistable, and Qc now corresponds to charge at which the barrier between the two minima disappears. B.

Elastic Capacitors

Our elastic molecule illustrates the onset of instability. However, conditions when charges can be smoothly controlled by the observer are hard to achieve. In applications and studies of interfacial phenomena the controlled electrical variable is usually a voltage V across the interfaces rather than charges involved in their polarization. The distributions of charges composing electrical double layers of different origin can be approximated by ‘‘interfacial capacitors.’’ As we will see in Section III, the distributions of charges are ﬂexible and strongly affected by the applied voltage. As a result, not only the charge q on the ‘‘plates’’ of interfacial capacitors, but also the effective ‘‘gap’’ between the plates depends on V. This naturally leads to ‘‘relaxing gap’’ capacitors, which in many cases can be described as ‘‘elastic capacitors’’ (ECs). The energy of an EC under ﬁxed voltage is [2] H ¼ H0 ðq; lÞ qV

ð6Þ

where H0 ðq; lÞ ¼

q2 l þ AE0 ðlÞ 20 A

ð7Þ

is the energy of isolated capacitor with charge q, A is the surface area of its ‘‘plates,’’ and l are the effective dielectric constant and the gap width respectively, and E0 is the elastic energy per unit area. The contribution qV in Eq. (6) is responsible for charge exchange between the potentiostat (battery) and the capacitor. The equilibrium conditions @H ¼0 @l

@H ¼0 @q

@2 H >0 @2 l

ð8Þ ð9Þ

deﬁne the equilibrium gap lðVÞ and equilibrium charge qðVÞ. Notice that Eq. (7) assumes that charge distributions are uniform. The validity of this assumption will be discussed in Section III. In the uniform case all properties can be equally well described by the surface charge density q ð10Þ ¼ A In equilibrium, as follows from Eqs. (7) and (8) 2 @E þ 0¼0 20 @l

ð11Þ

l ¼V 0

ð12Þ

Equation (12) leads directly to an expression of H through V and l: ! 0 V 2 þ E0 ðlÞ A H¼ 2l

ð13Þ

Electroelastic Instabilities

55

Equation (13) becomes equivalent to Eq. (1) if q2 is replaced by V 2 =2. In the units of Eq. (3), introducing the dimensionless voltage, V ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Kl03 =0

ð14Þ

and using Eq. (2), we have H¼

2 1 þ ð1 zÞ2 2z 2

ð15Þ

From the previous analysis it follows that the harmonic elastic capacitor collapses when approaches its critical value rﬃﬃﬃ 2 2 and zc ¼ 2=3 ð16Þ c ¼ 3 3 C.

General Observations

Several questions must be addressed with respect to the simple examples just outlined. Despite their formal similarity, it is important to keep in mind that the ﬁrst instability describes an isolated system, where charge is a controlled variable. In contrast, the EC as introduced becomes unstable only in contact with a potentiostat (battery), when V is ﬁxed and charge can change. Thus, the collapse of an EC leads to inﬁnite growth of q 1=l, accompanied by electric current from a battery to the EC. If isolated, the EC remains stable for all values of q corresponding to l > 0, as can be seen from Eq. (7). The major difference from the elastic dimer is that electrical energy of an isolated EC is positive and ﬁnite for all q and l while for the dimer it goes to 1 when l ! 0. In the next section we reexamine this result and show that the uniformity assumption for the charge distribution across the plates of a capacitor can fail, and this can inﬂuence the stability condition for an isolated EC. Another observation should be made with respect to the term ‘‘elastic’’ in describing interfacial capacitors. It was originally introduced by Crowley [1] for membranes and reﬂects the compressibility of lipid layers which behave in some respects like an elastic ﬁlm. Its relation to electrochemical interfaces is less obvious. Consider an interface between a metal electrode and an electrolyte. As we will see in Section III, the effective gap of the interfacial capacitor is the distance between the centers of mass of the electronic, ‘‘e,’’ and ionic, ‘‘i,’’ charge density distributions ne;i : l ¼ x i xe Ð þ1 xe;i ¼

1

ð17Þ ni;e ðxÞx dx e;i

ð18Þ

where e ¼ i ¼ , the surface density of electron charge. Both distributions depend on (and V) and l usually changes with charging. Consequently, the interface may be represented as a ‘‘relaxing gap’’ capacitor. Consider a hypothetical attempt to alter the equilibrium electron and ion density proﬁles, causing the displacement of xe and xi from their equilibrium positions. The corresponding increase in free energy can be expressed through the effective restoring force opposing the variation of l from its equilibrium value. In turn, the restoring force can usually be expressed in terms of an effective elastic constant. This is where the analogy with the EC comes into play.

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The ‘‘elasticity’’ can be related to very different contributions to the energy of the interface. It includes classical and nonclassical (exchange, correlation) electrostatic interactions in ion–electron systems, entropic effects, Lennard–Jones and van der Waals-type interactions between solvent molecules and electrode, etc. Therefore, use of the macroscopic term should not hide its relation to ‘‘microscopic’’ reality. On the other hand, microscopic behavior could be much richer than the predictions of such simpliﬁed electroelastic models. Some of these differences will be discussed below.

III.

NEGATIVE DIFFERENTIAL CAPACITANCE AND ELECTRICAL DOUBLE LAYER STABILITY

A.

Historical Review

The traditional treatment of a double layer at electrode–electrolyte interfaces is based on its separation into two series contributions: the compact (‘‘Helmholtz’’) layer and the diffusive (‘‘dif’’) layer, so that the inverse capacitance is 1 1 1 Cdl ¼ CH þ Cdif

ð19Þ

Both terms affect whether the double layer capacitance can become negative. 1. ‘‘Molecular Capacitor’’ (MC) and the Cooper–Harrison Catastrophe The problem of negative capacitance ﬁrst arose in theoretical studies of CH based on socalled ‘‘molecular models.’’ Molecular or ‘‘dipolar capacitor’’ models treat the layer of water molecules adjacent to a metal electrode as a lattice of point or ﬁnite-size dipoles [3,4]. Many studies have focused on the response of such a layer to electrode charging and comparison with the measurements of the compact layer capacitance, CH ðÞ using the technique suggested by Grahame [5,6]. Much of this work has been inspired by the ‘‘Cooper–Harrison (CH) catastrophe,’’ the prediction of negative CH ðÞ in molecular models of the compact layer. Here we only brieﬂy discuss the origin of this anomaly (see Ref. 7 for more details and references). (a) General Characteristics of an MC. Consider the isolated MC with a charge density on its plates. Focusing on the capacitance C (the index ‘‘H’’ is omitted), we ﬁrst introduce the potential drop across the MC as

¼ F0 d þ d

ð20Þ

where* F0 ¼ 4

ð21Þ

is the external ﬁeld created by the plates of MC, and

d ¼ 4Px

Px ¼ Ns hpx i

ð22Þ

in which hpx i is the average normal-to-plane projection of the dipolar moment, and Ns is the number of dipoles per unit area. Using the deﬁnition of differential capacitance (per unit area),

* Unlike the rest of the chapter, here we adopt Gaussian electrostatic units which are typically used in the literature devoted to molecular capacitors and double layer theory.

Electroelastic Instabilities

C¼

d

d

57

ð23Þ

we ﬁnd 1 ¼ 4ðd 4 Þ 4C

ð24Þ

where ¼ Ns

dhpx i dF0

ð25Þ

is the susceptibility of the dipolar lattice. It follows from Eq. (24) that if it were possible that d=4

ð26Þ

then it would be possible for C to become negative. (b) The MC in a Mean Field Approximation (MFA). In the majority of papers including the original CH paper [8], the MC was treated in Ising-type n-state models with dipoles perpendicular to the plates: px ¼ psx where the vector sx is limited to equally spaced values between 1 and 1. We consider the simplest ‘‘spin 1/2’’ model n ¼ 2 (Fig. 3), a choice justiﬁed by the fact that the appearance of the CH catastrophe is independent of n. The local ﬁeld acting on a speciﬁc dipole in a lattice is F ¼ F0 þ Fd þ F 0

ð27Þ

0

where the ﬁeld F describes interaction between a dipole and its own images. Interaction with this ﬁeld does not depend on the dipolar orientation and can be omitted [7]. The ﬁeld Fd created by the rest of the dipolar lattice has been a subject of considerable controversy. Following most authors, we restrict analysis to the MFA assuming that all dipoles except one have moments equal to their mean value hpx i. Then, Fd ¼

nL Jhsx i p

ð28Þ

where J ¼ p2 =a3 is the interaction energy between antiparallel nearest neighbors, a is the lattice constant, and nL is the effective number of nearest neighbors. For a bare lattice where dipolar ﬁelds are not shielded by the plates of capacitor, nL equals X 3 n0L ¼ a3 r1i ð29Þ i

is 9 and 11 for square and hexagonal lattices respectively. Focusing on the CH catastrophe we notice from Eq. (26) that the most ‘‘dangerous’’ point is where is largest. In the MC models considered this obviously corresponds to ¼ 0; increasing orients dipoles and makes them less susceptible to variation of the n0L

FIG. 3 Molecular capacitor in ‘‘spin 1/2’’ model.

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Partenskii and Jordan

external ﬁeld (in the limit ! 1 the lattice is totally frozen and ! 0). In this ‘‘zero charge’’ point for ‘‘spin 1/2’’ [8] we have ¼

Ja3 Ns kT þ JnL

ð30Þ

from which is clear that two factors oppose the orientation of dipoles in the MC: temperature and dipolar interactions. The latter occurs because in the Ising model considered, the interaction energy between two lattice dipoles is minimal when dipoles are opposed. Equation (30) emphasizes the importance of the effective number of nearest neighbors; with p, Ns , and T ﬁxed, the susceptibility becomes larger for smaller nL . (c) Effective Number of Nearest Neighbors and the CH Catastrophe. It follows from Eqs. (30) and (26) that C becomes negative if nL <

4a3 Ns kT J d

ð31Þ

pﬃﬃﬃ For a hexagonal lattice, Nshex ¼ 2= 3a2 ; choosing for water dipoles at room temperature J 2kT [3], and assuming a ¼ d, this leads (see Ref. 3) to nhex L < 14:2

ð32Þ

As mentioned before, for a bare lattice nhex L 11. CH made the apparently reasonable assumption that screening of the dipolar ﬁeld by the conductive plates of the MC should below this value, thus insuring that Eq. (32) is satisﬁed, leading to the decrease nhex L catastrophe. (d) Summation Over the Dipolar Images and Resolution of the CH Catastrophe. To account for the screening of the dipolar lattice by the plates of the MC it is convenient to use the method of images. Every original dipole in this approach creates an inﬁnite chain of similarly oriented image dipoles, with period d. As a result, calculation of local ﬁelds in MFA requires summation over the inﬁnite lattice of equal dipoles, hpx i, excluding the images corresponding to the ‘‘original’’ dipole. Due to the conditional convergence of the corresponding series* [9], the result depends on the order in which the sums are calculated. This ambiguity is the cause of the CH catastrophe. Two ways of carrying out the summation have been discussed [10]. 1.

2.

The ‘‘chain’’ (or c-) approach starts with the chain of dipoles normal to the original plane, including an original dipole located in a lattice site and the inﬁnite set of its images. The ﬁeld of each chain decays exponentially with distance , much faster than the 1=3 law corresponding to the bare lattice. It leads to a decrease in the effective number of nearest neighbors and seemingly gives rise to the CH catastrophe. It also seems to justify a suggestion that if the lattice constant a is large enough, the CH catastrophe becomes inevitable [11]. The ‘‘plane’’ (p-) approach starts with the inﬁnite plane of dipoles, with further summation over the inﬁnite stack of these planes (including the original lattice and all its images). As a result,

* The dipolar contributions to the local ﬁeld diverges if the terms are replaced by their absolute values.

Electroelastic Instabilities

F pl ¼ F ch þ Fu

59

Fu ¼

d d

ð33Þ

Surprisingly, in addition to the ‘‘chain’’ contribution, F ch , the local ﬁeld calculated in the p-approach also contains the uniform part, Fu ¼ 4Px =d. This last term noticeably increases the effective number of nearest neighbors so that the CH catastrophe disappears. But does the catastrophe really exist in the chain approach? To underline the problem we used the word ‘‘seemingly’’ with respect to the appearance of the CH anomaly. We now consider this more carefully. Notice that in the chain summation each dipole is treated as if it were inserted between the inﬁnite plates of capacitor. No matter how many dipoles we have, they do not affect the potential drop across the gap of the MC. It can only mean that the average polarization, Px , in Eqs. (20) and (22) equals zero. In its turn, Px is proportional to Ns Ad =A, where A and Ad are the areas of the plate and of the dipolar array respectively. This means that the chain approach is valid when Ad =A ! 0. In other words, even for the inﬁnitely large dipolar lattice, its size is inﬁnitesimally small in comparison to A. Since in this picture Px ! 0, according to Eq. (24) the capacitance C ! 4=d > 0 and the CH catastrophe disappears. The p-approach corresponds to Ad =A ! 1 with both A and Ad ! 1. In this case the CH catastrophe disappears because of the uniform contribution which increases the effective number of nearest neighbors. In other words, both summation procedures are valid.* They describe different physical situations. In the c-summation the size of the dipolar array is much smaller than the size of the capacitor, while in the p-approach both are equal. One can imagine an inﬁnite number of different summation orders corresponding to different relations between A and Ad , leading to results between the p- and c-limits. To solve the problem unambiguously, one must consider a ﬁnite dipolar lattice between ﬁnite plates, which requires accounting for edge effects and makes the whole problem much more complicated. (e) Conclusion, and a Further Question. We have seen that the CH catastrophe arises as a result of inconsistencies in the treatment of the electric ﬁeld and the potential in the molecular capacitor. Were they analyzed consistently, then, at least in the framework of Ising models and the MFA, a catastrophe would not appear and the capacitance of an MC would always be positive. But another question arises. Does this imply that the capacitance of a double layer can never become negative? Before addressing this question we will analyze some other occurrences of the C < 0 problem in the theory of electriﬁed interfaces. 2.

Diffuse Electron and Ionic Distributions in a Double Layer and the Problem of C < 0 Statistical mechanical and microscopic theories of the double layer have often been intensively reviewed. Our focus is only on features related to the problem of negative C.

* The following example helps in visualization of the difference between the two ways of summation. Consider the potential difference ðL; RÞ ¼ ðLÞ ðLÞ between points L and L on the axis of a uniform dipolar disk (where Px is the surface dipole moment density) in the limit of inﬁnite R and L. Since ðL; RÞ ¼ 4Px ½1 L2 =ðL2 þ R2 Þ, limR!1 limL!1 ðL; RÞ ¼ 0, while limL!1 limR!1 ðL; RÞ ¼ 4Px . The ﬁrst result obviously corresponds to the c-approach, while the second one corresponds to the p-approach.

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(a) Diffuse Models of Ionic Distributions in Electrolytes. The ﬁrst model of the diffuse ionic distribution in electrolytes was developed by Gouy and Chapman (GC) many years ago. In this and similar ‘‘local models’’ the charge density is considered to be a local function of the potential ðxÞ, nlocal ðxÞ ¼ f ½ ðxÞ

ð34Þ

In such models capacitance can never become negative [12]. The GC model for a 1 : 1 electrolyte is illustrative: Cdif ¼ aðb þ 2 Þ

ð35Þ

where a and b are positive and depend on temperature, ionic concentration, and bulk dielectric constant. However, the question of C < 0 inevitably emerges in theoretical studies of the diffuse layer that go beyond the local approach (see, e.g., Refs. 13–18). This anomaly is related to some speciﬁc properties of ionic distributions. (b) Properties of the Ionic Distribution Which Can Cause a Capacitance Anomaly. Let us examine the features of an ionic distribution that can lead to Cdif < 0. Quite generally, the potential drop across the double layer, ð1Þ ð1Þ (where x ¼ 1 and x ¼ 1 correspond to the bulk electrode and electrolyte respectively) can be represented as ¼ 4 ½xi ðÞ xe ðÞ 4Px

ð36Þ

Then, using Eq. (23) we ﬁnd 1 dl dPx ¼ lðÞ þ 4C d d

ð37Þ

where the effective gap of the interfacial capacitor, l, is deﬁned by Eq. (17). Focusing on the effect of the ionic distribution, we consider the so-called primitive model where ions occupy a region of uniform dielectric constant . In addition we temporarily ignore the diffuseness of the electronic distribution (the perfect conductor model) assuming xe ¼ const: ¼ 0. Then for the diffuse layer capacitance ð1 ð 1 @ 1 ð0Þ ð38Þ ¼ n ðxÞx dx n ðxÞx dx=

4Cdif ðÞ @ 0 0 Here we assume ð1Þ ¼ 0 and choose > 0. It is now clear that differential capacitance becomes negative at some value of if the centroid of the ionic distribution induced by a small variation becomes negative. Given that ions do not penetrate the region x < 0, this can only happen if nðxÞ is a nonmonotonic function of variable polarity. However, the total electrolyte charge density, nðxÞ, is not necessarily oscillating, and it can even be monotonic. Figures 4–6 illustrate the various possibilities. nðxÞ represents a nonmonotonous charge density corresponding to some variation of . It is a function constructed to reﬂect two features of the ionic shielding of the electrode charge. Ð1 1. Neutrality condition (required): 0 nðxÞ dx ¼ . 2. ‘‘Charge condensation’’ near the electrode (quite a typical feature, which is necessary but not sufﬁcient for attaining C < 0): charging is accompanied by increased charge density near the electrode at the expense of some depletion in the tail regions of the ionic distribution. Figure 4 depicts a generalized Raleigh [19] model originally designed to explain extremely high values of interfacial capacitance in contacts of metals and solid electrolytes, silver-ion conductors (such as AgCl). This is a two-layer model satisfying conditions 1 and

Electroelastic Instabilities

61

FIG. 4 Induced potential drop ðxÞ in the Raleigh model of the ionic distribution. k ¼ 0:2 (curve 1), 0.33 (curve 2), and 0.4 (curve 3). Gray area shows the Raleigh distribution of the induced charge with a ¼ 0:3 nm and k ¼ 0:33 (see text) which corresponds to curve 2. The total induced charge is normalized

2. Charge densities in the layers are n1 at x < a and kn1 at a < x < 2a; the layer thickness a and the dimensionless constant k < 1 are the parameters of the model. Using this to mimic the distribution induced by , we ﬁnd that n1 ¼ =að1 kÞ. The center of mass of this distribution is ¼ xRaleigh i

n1 a2 að1 3kÞ ð1 3kÞ ¼ 2 1k

ð39Þ

xi becomes negative for k > 1=3. Figure 4 demonstrates that C becomes negative when xi is negative. This transition is obvious from the behavior of ðxÞ [see Eq. (38)]. For curve 1 (k ¼ 0:2) the additional barrier ð0Þ ð 0:75Þ has a ‘‘normal’’ positive sign; for curve 2 (k ¼ 1=3) this barrier disappears, and for curve 3 ðk ¼ 0:4) it becomes negative ( 0:5). Figure 5 presents a more realistic picture where nðxÞ is continuous. QðxÞ is the total ionic charge accumulated between x ¼ 0 and the point x:

FIG. 5 Model-induced charge density proﬁle nðxÞ (curve 1), QðxÞ (curve 2), and ðxÞ (curve 3) in the diffuse layer ( ¼ 0:2, dimensionless units).

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Partenskii and Jordan

QðxÞ ¼

ðx

nðx 0 Þ dx 0

0

and ðxÞ ¼ 4½ þ QðxÞx þ

ðx

x 0 nðx 0 Þ dx 0

ð40Þ

0

It demonstrates an important feature promoting negative C: ‘‘overshielding’’ of the electrode charge in the adjacent region of electrolyte. This is the cause of depletion in the more distant parts of the double layer causing effective displacement of the charge centroid towards the electrode.* Figure 6 demonstrates the possibility that if the initial potential proﬁle 0 ðxÞ corresponding to some 0 is monotonic (GC-type), then a small additional nonmonotonic variation in ðxÞ arising from the additional charge density of Fig. 5 and leading to C < 0 may still leave the total potential proﬁle ðxÞ monotonic. The same is true for the total charge density nðxÞ. This speculation mimics the results of numerical experiments described in Refs. 17 and 18. The same can be true for charge density proﬁles. It demonstrates that charge density oscillations are neither necessary nor sufﬁcient to give rise to negative C. 3. Negative Capacitance in Primitive Models of Electrolyte A possible reason that the problem of C < 0 did not receive much attention was the assertion [15] (BLH) that such an anomaly was forbidden. The proof was based on the statistical mechanical analysis of the primitive model of electrolytes between two oppositely charged planes, and . It was noticed in Ref. 10 that the BLH analysis missed a very simple contribution to the Hamiltonian, direct interaction between the charged walls, 2L 2 (L is the distance between the walls). With proper choice of the Hamiltonian the condition on the capacitance would be C > 2=L. It simply means that due to ionic shielding of the electric ﬁeld, the capacitance exceeded its ‘‘geometrical’’ value corresponding to the electrolyte-free dielectric gap.

FIG. 6 Potential proﬁle for 0 (curve 1) and 0 þ (curve 2).

* Such a behavior can represent, for instance, condensation near an electrode of a monotonous charge density n ðxÞ following a variation of [18].

Electroelastic Instabilities

63

This analysis has been developed further [20–22]. At the same time attention focused on the analogous anomaly in the theory and simulations of the double layer [17,18]. Progress was, however, slightly misdirected by the assertion [21] that there are no restrictions on the sign of C, regardless of the model considered or the choice of experimental conditions. In what follows we will show that there are severe restrictions strongly limiting the possibility of capacitance anomalies. But here we only stress that it has never been proven that negative capacitance is forbidden for any model of an electrolyte at a uniformly charged interface. 4. Contribution of Metal Electrons and the Negative Capacitance Problem In the early 1980s it became clear that metal electrons play an important role in the electrical response at metal–electrolyte interfaces. Different aspects have been extensively reviewed [23–27]. Here we only brieﬂy discuss the problem of negative capacitance, and how it arose in these studies. Although it was clear that separation of an interface into ‘‘surface’’ and ‘‘bulk’’ components as in Eq. (19) is artiﬁcial and must disappear in a consistent microscopic analysis, electronic effects were initially discussed in terms of a ‘‘compact layer’’ and its capacitance CH . It was apparent early on that the electrons strongly inﬂuence double layer properties [28–33]. In traditional models of an electriﬁed interface, metal electrons are artiﬁcially localized within the electrode. This leads to misinterpretation of the electronic inﬂuences on the compact layer. CH in those models would always be smaller than its ‘‘ideal conductor’’ limit (with electrode charge spread over an inﬁnitesimally thin region at the electrode surface x ¼ 0) IC ¼ H ð41Þ 4CH xH where xH is the effective width of the compact layer, and H is the effective permittivity. Self-consistent analysis of electronic effects altered this simple view substantially. By analogy to Eqs. (36) and (37), compact layer capacitance in the simplest model, accounting only for electronic effects, is now deﬁned by 1 dx ¼ xH xe e 4CH d

ð42Þ

It was ﬁrst noticed in Ref. 31 that at moderate negative the condition xe

dxe xH d

ð43Þ

may be fulﬁlled for contacts of metals with solid electrolytes (silver-ion conductors), so that CH ðÞ can become negative. Similar anomalies have been found in contacts of metals with solvents [34,35], results which have not been easily accepted. Moreover, in some calculations they have been carefully avoided, partially in the belief that they are prohibited by the BLH theorem (for a discussion see Refs. 7 and 36). 5.

Electroelastic Models. Proof that Negative Capacitance is Admissible for Uniformly Charged Interface Models Elastic capacitors (Section II) are very useful as ‘‘electromechanical’’ analogs of microscopic interfacial capacitors [22,31,34]. But most importantly, they demonstrate that nega-

64

Partenskii and Jordan

tive capacitance can coexist with interfacial equilibrium and stability as long as the total charge is ﬁxed and the charge density is kept uniform. Under these conditions, corresponding to so-called -control [37], the elastic capacitor is described by the Hamiltonian, Eq. (7). In dimensionless units this becomes 1 W ¼ s2 z þ ð1 zÞ2 2

ð44Þ

where s ¼ ð4=kl0 Þ2 , the dimensionless charge density. Other units are the same as in Eq. (3). From the equilibrium conditions for ﬁxed s it follows that [37]: zðsÞ ¼ 1

s2 2

vðsÞ ¼ s

s2 3

3 C 1 ¼ 1 s2 2

ð45Þ

and C1 0 for jsj > s0 ¼ ð2=3Þ1=2 . At the same time, @2 W=@l 2 ¼ 1 > 0, and in this region the system is stable. Thus capacitance under -control can be negative. And as this is possible for one simple model, it should also be possible for some other models obeying the same conditions of -control.

B.

The Sign of C and Different Types of Electrical Control

In the analysis of molecular capacitors, the diffuse layer and elastic capacitors, we have always assumed that the electrode charge density could be controlled. Under such conditions it is generally possible for C to become negative while the system remains stable. For example, contraction of the gap z in an elastic capacitor proceeds smoothly with growing until the plates come in contact, while C becomes negative for z < 2=3. At the same time, as shown in Section II for an EC connected to a battery, the EC collapses after z 0:6 is reached. How can these seemingly contradictory results be reconciled? And how can -control be related to reality? Is C < 0 observable? These questions are addressed in this section. 1. Three Types of Control (a) -Control. In the vast majority of studies in double layer theory, the charge density is considered an independent control variable. This forms the framework where the question of negative C originated. But this assumption must be treated very carefully. In practice there is no way to control . Therefore, -control is a purely theoretical construct. It works perfectly well only if an interface ‘‘chooses’’ to remain uniform.* (b) Isolated Capacitor, q-Control. In real experiments with ‘‘ideally polarizable’’{ interfaces there are basically two options: either the cell is isolated, or it is connected to a potentiostat (battery). For an isolated capacitor the total charge on the electrode is ﬁxed (‘‘q-control’’). If the system remains uniform, then - and q-controls are equivalent, being deﬁned by Eq. (10). However, when for any reason a uniform distribution becomes unstable, then only q-control is a valid description of the isolated interface.

* We are not describing microscopic structural nonuniformity, which is discussed in another chapter of this book, and assume that the electrode surface is uniform. { We exclude situations where there is electric current across the interface which would cause some additional complications.

Electroelastic Instabilities

65

(c) Global System, -Control. Now consider a cell connected to a battery. Usually, the subsystem is immersed between two metal electrodes. Here electrical control of the cell is maintained via the electronic subsystems of the electrodes [38]. The real controlled variable is the difference between the electrochemical potentials of electrons of both electrodes, 1 and 2 . To avoid the complexities due to contact phenomena (‘‘Volta potential’’) we assume both electrodes are made of the same metal and therefore have the same chemical potentials (Fermi energies). The difference between chemical potentials equals the voltage:

¼

1 2 e

ð46Þ

In this case the voltage across the interface is the actual controlled variable and we deal with -control. 2.

Stability Conditions

(a) C is Nonnegative Under -Control. The transition from an isolated to a global system is accompanied by transformation of the Hamiltonian [see Eq. (6)]: H ¼ H0 q

ð47Þ

It is generally true (for a discussion see Ref. 39) that for Hamiltonians of the form H ¼ H0 XF the susceptibility is 2 1 ðX hXiÞ 0 @X=@F ¼ kT

ð48Þ

ð49Þ

where h i denotes a statistical average with the Hamiltonian, Eq. (48). The transition from isolated ðH0 Þ to global ðHÞ belongs to this class [see Eq. (6)], which is why capacitance under -control is deﬁned as 2 @hi A ¼ ð hiÞ C¼ ð50Þ @

kT [40–43] and is strictly nonnegative. (b) Isolated Capacitor. Suppose now that the charge q is ﬁxed. As mentioned, if could be kept uniform, then C can unconditionally become negative. The elastic capacitors we have studied are examples of systems for which - and q-controls are equivalent. Indeed, with plates rigid, any nonuniform redistribution of charge density can only increase the EC’s energy, and therefore cannot become stable. It would be different if the plates of an EC were somewhat deformable. Transition to a nonuniform state could then occur due to coupling between the electrical and ‘‘elastic’’ degrees of freedom. In reality, the electronic and ionic ‘‘plates’’ of an interfacial capacitor are never absolutely rigid. Therefore, a uniform distribution should always be tested with respect to its stability under some nonuniform perturbations. Recently [7] we constructed an example showing that interfacial ﬂexibility can cause instability of the uniform state. Two elastic capacitors, C1 and C2 , were connected in parallel. The total charge was ﬁxed, but it was allowed to redistribute between C1 and C2 . It was shown that if the interface was absolutely ‘‘soft’’, i.e., contraction of the two gaps was not coupled, the uniform distribution became unstable at precisely the point where the dimensionless charge density s reached the critical value, s0 ¼ ð2=3Þ1=2 . In other words, the uniform distribution became unstable at the point where, under control, C 1

66

Partenskii and Jordan

would have changed sign, so that the region with C < 0 is unacceptable for such interfaces. If, however, the Ci are coupled by a spring, then the stability region expands towards larger . We can also use another argument similar to one suggested by Nikitas [44]. Consider a small area of the interface. Given that this area is much smaller than the total area of contact, we may consider the rest of the interface a potentiostat which keeps the potential in the chosen area ﬁxed. Then, the selected area can be considered under -control and its local capacitance cannot be negative. Therefore, the selected area is likely to undergo a transition simultaneously accepting some charge from the rest of the interface. As this reasoning can be applied to any area of the interface, it strongly suggests that in the isolated system, the uniform state becomes unstable in a region where -control predicts C < 0. C.

Summary

The question of the allowed sign of C was and remains a topic of discussion with signiﬁcant contradictions. We suggest here that a major reason for these contradictions is that theoretical calculations for electriﬁed interfaces are more easily carried out assuming a uniform electrode charge. Most studies have used this condition and, on some occasions, the restriction of -control took its toll. And those were exactly the situations where negative capacitance was predicted. The conviction that C should be strictly positive was so compelling that it has been typically believed to also apply under -control conditions (see Refs. 7 and 36 for a review). In some other cases, confusion was caused by an opposite extreme, dropping the restrictions on C < 0 even for -control. The discussion in Refs. 17 and 18 is illustrative. Torrie [17] presented very important results for grand canonical Monte Carlo simulations of an electrical double layer in 2 : 1 electrolytes. Those results provide very convincing evidence that C < 0 can occur under control. However, instead of analyzing the consequences of this fact for real systems, the author simply quotes the statement [21] that sign of C is not restricted, even for -control. Reliance on this result (see a critique in Ref. 22) simply ignored the problem and discouraged closer study of this system. Similarly, Wei et al. [18] made analogous predictions of C < 0 using hypernettedchain theory and incorporating molecular polarizability. However, the discussion was again restricted to the plausibility of negative C under -control. We suggest that results yielding C < 0 under -control have considerable importance, even though this type of control is unrealistic. They provide an important indication that in a system studied under q-control there is a range of where the plane uniform state is unstable, and the system undergoes a transition to a nonuniform state with charge density varying along the plane of electrode. Therefore, a computational paradigm could be formulated as follows: ‘‘If C becomes negative under -control, study the stability of this state towards ‘charge density’ perturbations. It is very possible that a phase transition to a nonuniform state appears.’’ The same system treated under -control becomes unstable in the vicinity of c (which corresponds to C ! 1) and can also undergo a phase transition (see Refs. 7 and 24 for discussion). But, unlike the isolated system under q-control, it can acquire some additional charge from the battery, so that the initial and ﬁnal states would correspond to different values of q. The relation of transitions under q- and -control is another prospective area of research.

Electroelastic Instabilities

IV.

67

ELECTROELASTIC INTERACTIONS, STABILITY, AND BREAKDOWN IN MEMBRANES

Study of the mechanisms of membranes’ interaction with electric ﬁelds and the consequences for membrane stability and electroporation are very important both for better understanding of membranes’ properties and for different applications involving electrical manipulation of their behavior [45–48]. By controlling the electrical setup it is possible to inﬂuence transmembrane permeability and thus gain some control over processes such as targeted drug delivery, DNA transport into cells, etc. This is also important for development of ‘‘bioelectrochemical’’ sensors, where membranes are in contact with electrodes and applied voltage is used for monitoring changes caused by the interaction with the environment [49–52]. A.

Some Perspectives on Membrane Instability

1.

Crowley’s Model

The ﬁrst model of membrane electroporation was suggested by Crowley [1]. In Crowley’s model the membrane is viewed as the isotropic elastic material. The necessary background for understanding its voltage-induced instability was discussed in Section II. Crowley’s approximation for the elasticity energy term in Eq. (7) is E0 ðhÞ ¼ Bh0 z½lnðzÞ 1 ¼ Ez½lnðzÞ 1

ð51Þ

where h ¼ hðÞ is the local thickness of the membrane ( is a two-dimensional radius vector in the membrane plane), h0 is its unperturbed value, B and E are the Young’s and ‘‘stretching’’ moduli, respectively. Using Eq. (51) with Eqs. (7) and (8), we ﬁnd a relation between the membrane ‘‘contraction’’ factor, z ¼ h=h0 (h is the equilibrium thickness) and the voltage V [53]: E lnðzÞ ¼ pE h0

ð52Þ

where pE ðV; hÞ ¼

m 0 V 2 2h2

ð53Þ

is the electrical pressure as a function of the applied voltage and membrane thickness, and m is the membrane dielectric constant. sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ 2Eh0 1 ð54Þ ln V ¼ z z m 0 The critical membrane contraction can be derived in the manner outlined in Section II: zc ¼ expð0:5Þ 0:61

ð55Þ

which corresponds to critical membrane thinning 39%. The corresponding critical voltage, derived from Eq. (54), is sﬃﬃﬃﬃﬃﬃﬃﬃ Eh0 ð56Þ Vc 0:61 0 Equation (55) illustrates the major shortcoming of the original electroelastic model; it predicts membrane thinning of almost 40%, a result vastly different from the experimental

68

Partenskii and Jordan

ﬁnding that critical thinning never exceeds 2–3%. The computed critical voltage Vc equals 3:4 V and 5:9 V for representative ‘‘soft’’ [stearoyloleoylphosphatidyl-choline (SOPC)] and rigid [SOPC-cholesterol]) (SOPC:CHOL, 1 : 1)] membranes respectively (see Table 1 for the membrane parameters). Experimentally, the characteristic critical voltage Vexper depends on the duration of the applied electrical pulse. For brief pulses, 0:01 0:1 S, Vexper 1 V, and for longer ones ( 1 S) Vexper < 0:5 V. As a result, both the extent of the membrane contraction and the breakdown voltage predicted by Crowley’s model greatly exceed the experimental values.*

2. Hydrodynamic Models An alternative description of membrane stability has been based on hydrodynamic models, originally developed for liquid ﬁlms in various environments [54–56]. Rupture of the ﬁlm was rationalized by the instability of symmetrical ‘‘squeezing modes’’ (SQM) related to the thickness ﬂuctuations. In the simplest form it can be described by a condition [54] ðd 2 Vdis =dh2 Þ0 < 22 =a2 where Vdis is the interaction contribution related to the ‘‘disjoining pressure,’’y is the surface tension and a is the characteristic size of the ﬁlm. At the critical ﬁlm thickness h0 , deﬁned by this condition, the free energy cost of ﬂuctuation due to the disjoining pressure is negative and overwhelms the positive contribution due to the surface tension at the wavelength ¼ a. When this happens, there is ﬂow in the ﬁlm from the thinner to the thicker regions leading to spontaneous growth of interfacial perturbations [57]. Similar instability is caused by the electrostatic attraction due to the applied voltage [56]. Subsequently the hydrodynamic approach was extended to viscoelastic ﬁlms apparently designed to imitate membranes (see Refs. 58–60, and references therein). A number of studies [58, 61–64] concluded that the SQM could be unstable in such models at small voltages with low associated thinning, consistent with the experimental results. However, as has been shown [60, 65–67], the viscoelastic models leading to instability of the SQM did not account for the elastic force normal to the membrane plane which opposes thickness

TABLE 1 Elastic Parameters for Representative Soft (SOPC) and Rigid (SOPC : CHOL, 1 : 1) Membranes (Parameters E, Kc , and H0 are Taken from Refs. 117–119, , k1 and r1 from Ref. 53) Membrane ‘‘Soft’’ ‘‘Rigid’’

E (N/m)

Kc (J)

h0 (nm)

k1

r1

0.002 0.006

0:9 1017 2:4 1017

2.8 3.4

0.014 0.0087

0.1 0.1

0.06 0.04

* The values of stretching constant E that Crowley quoted in his original paper were substantially underestimated. As a result, his estimates of Vc were in better agreement with experiment. However, zc did not depend on E and reached the same subnormal value. It must be noted that critical thinning 1 zc almost universally reaches 30–40% for various models of the elastic energy [7]. y Disjoining pressure was attributed in Ref. 54 to the combined effect of van der Waals attraction and long-range electrostatic repulsion between similarly charged membrane surfaces.

Electroelastic Instabilities

69

ﬂuctuations. The most obvious manifestation of this neglect is the prediction of zero breakdown voltage for vanishing surface tension [61]. Thus, this approach is more appropriate for liquid systems where thickness ﬂuctuations arise from redistribution of molecules between surface and inner regions of the ﬁlm. In addition, this model is also descriptive of ‘‘colored’’ lipid ﬁlms. But it is hardly appropriate for lipid bilayers where steric interaction between the hydrocarbon tails of lipid molecules provides the quasielastic force opposing the thickness ﬂuctuations, a force which stabilizes the bilayer. After the viscoelastic model is modiﬁed to account for this force [66], the original Crowley model problem recurs; breakdown requires extensive thinning (see reference 32 in Partenskii et al. [53]). 3. The Pore Formation Model The most developed and widely used approach to electroporation and membrane rupture views pore formation as a result of large nonlinear ﬂuctuations, rather than loss of stability for small (linear) ﬂuctuations. This theory of electroporation has been intensively reviewed [68–70], and we will discuss it only brieﬂy. The approach is similar to the theory of crystal defect formation or to the phenomenology of nucleation in ﬁrst-order phase transitions. The idea of applying this approach to pore formation in bimolecular free ﬁlms can be traced back to the work of Deryagin and Gutop [71]. It was extended to describe spontaneous rupture of lipid bilayers [72,73] and electroporation [74] (see also Ref. 70 and references therein). The energy of the membrane with a virtual water-ﬁlled pore of a radius r subject to an applied voltage V is [70,74] Wp ¼ 2r r2 0:5 CV 2 r2

ð57Þ

where is the energy per unit length along the circumference needed to form the pore, is the energy per unit area of the ﬂat, pore-free membrane, and p 1 C0 ð58Þ C ¼ m is the approximate change of the capacitance due to the presence of the pore; C0 is the capacitance per unit area of a pore-free membrane, p and m are the permittivity of water inside the pore and of the membrane respectively. The critical pore radius, rc , and critical barrier, Wp , are both deﬁned by minimizing Eq. (57) with respect to r: rc ¼

þ 0:5C V 2

Wp;c ¼

2 þ 0:5C V 2

ð59Þ

As has been described in Ref. 70, this approach can reasonably account for membrane electroporation, reversible and irreversible. On the other hand, a theory of the processes leading to formation of the initial (hydrophobic) pores has not yet been developed. Existing approaches to the description of the probability of pore formation, in addition to the barrier parameters , , and some others (accounting, e.g., for the possible dependence of on r), also involve parameters such as the ‘‘diffusion constant in r-space,’’ Dp , or the ‘‘attempt rate density,’’ 0 . These parameters are hard to establish from ﬁrst principles. For instance, the rate of critical pore appearance, c , is described in Ref. 75 through an Arrhenius equation: c ¼ 0 Vm expðWp;c =kTÞ where Vm is the total volume of the membrane. Nucleation of a hydrophobic pore requires cooperative motion of 8 lipid molecules and 8–10 water molecules. Given that lipid

70

Partenskii and Jordan

molecules are not rigid, the corresponding entropy contribution (or the ‘‘attempt rate’’ density 0 ) is hard to quantify with precision. Estimates [75] of 0 are very approximate and vary over 9–10 orders of magnitude. Estimates of Wp;c vary from 30 to 50 kT. It is basically assumed [75] that the uncertainty in 0 is balanced by the uncertainty in the barrier, so that taken together they result in a reasonable concentration of pores. These assumptions are difﬁcult to verify. Another concern is related to the fact that this approach ignores the role of membrane undulations. These are known to be important in membranes’ macroscopic behavior (stretching diagram, adhesion, capacitance) and as they noticeably interact with the electric ﬁeld, they are likely to also contribute in the processes related to electroporation. At least one such relation is well known: at small surface tension the bending modes of membrane undulations become unstable at low voltages. In the next section we describe the membrane undulations and present a hypothesis as to their role in membrane instability. B.

The Smectic Bilayer Model (SBM) in an Electric Field

The most successful continuum description of membrane elasticity, dynamics, and thermodynamics is based on the smectic bilayer model (for examples of different versions and applications of this approach see Ref. 76–82 and references therein). We introduce this model in conjunction with the question of membrane undulations. 1. Membrane Undulations in the SBM Let U þ ðÞ and U ðÞ be z-components of the displacement of the upper (þ) and lower () membrane surfaces; is a two-dimensional radius vector in the XY plane. We express these as U ¼ u0 þ u

ð60Þ

where u0 is the displacement caused by external forces (such as electrical or mechanical stress) while u describes a nonuniform ﬂuctuation of the membrane surface. For further analysis we decompose membrane ﬂuctuations into a Fourier series, X u ðÞ ¼ u ðqÞ expðiqÞ ð61Þ q

(a) Elastic energy. We now treat separately the peristaltic (symmetrical, s-) and bending (antisymmetrical, a-) modes of membrane undulations, uþ s ¼ us ¼ u

uþ a ¼ ua ¼ u

ð62Þ

The elastic energy (per unit area) consists of three contributions [78–80]: 1.

Compression (stretching) energy, W1 , for which we choose Crowley’s form, Eq. (51). For small undulations this becomes W1 ¼

E ðz zÞ2 2h20 z

ð63Þ

with z z ¼ uþ u : 2. Splay (‘‘bending’’ or ‘‘curvature’’) deﬁned by a splay constant K1 , or by a curvature elastic modulus Kc ¼ K1 h [76],

Electroelastic Instabilities

W2 ¼

3.

71

Kc 2 2 ðr uÞ 2 ?

ð64Þ

where r? ¼ @=@ is the gradient operator in the plane of the membrane. Surface tension contribution deﬁned by a stress applied to a membrane, typically expressed as [77] W3 ¼ ðr? uÞ2 =2 þ 2 =2E

ð65Þ

where the ﬁrst contribution is related to undulations and the second to elastic stretching.* (b) Interaction with the Electric Field. In most studies of the effect of an applied voltage on membranes, the model of ideal conductor ( ¼ 1) is used for the surrounding solvent. Then the membrane surface can be considered an equipotential. The solution of the Laplace equation leads to following results for the electrostatic energies of membrane undulations [56,78,88]: ( Welectr ¼ 2qjuq j pE 2

tanhðqh=2Þ

ða-modeÞ

cothðqh=2Þ

ðs-modeÞ

ð66Þ

The ‘‘ideal conductor’’ model does not account for diffuseness of the ionic distribution in the electrolyte and the corresponding ‘‘spreading’’ of the electric ﬁeld with a potential drop outside the membrane. To account approximately for these effects we apply Poisson–Boltzmann theory. The results for the modes’ energies can be summarized as follows [89]: W

s;a

¼ m þ s

B2 F 2 a0 a1 h þ a0 Bs;a þ s;a s;a 2q

!

2 2 2 þ q2 2 c0 þ 2c0 c1 þ c0 Ds;a þ Ds;a 2 4

!

ð67Þ

where

* The origin of the ‘‘surface tension’’ in membranes recently became a subject of intensive discussion (see, e.g., Refs. 83–87, and references therein). To outline the problem, we note that thermodynamic ‘‘surface tension’’ in liquids is a result of molecular exchange between surface and inner volumes when a new surface is created. The corresponding free energy contribution is a result of the different surroundings of a molecule in the bulk and on the surface. In isolated bilayers, however, such exchange is impossible. Area (projected) can only change due to unfolding the bilayer’s undulations and elastically stretching the bilayer. The tension at equilibrium is zero. However, the situation can be different if area can grow due to molecular exchange with an environment. Such a situation can occur, for instance, in experiments with black lipid ﬁlms, where exchange between the bilayer and the rim is possible.

72

Partenskii and Jordan

Bs;a ¼ a0 r a1 ¼ s;a

ðr 1Þ þ s;a

Ds;a ¼

Fs;a =q þ 1 1=r s;a

a0 ¼

r 1þ

r c 2 B þ Ds;a ð þ Þ ð ÞDs;a þ Bs;a c1 ¼ 0 s;a 2ð1 þ Þ 2ð1 þ Þ 4 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ r ¼ m =s ¼ 1 þ rFs;a =q ¼ 2 þ q 2 ¼ rh=2

and Fs ¼ tanhðqh=2Þ

Fa ¼ cothðqh=2Þ

lD1 is the reciprocal Debye length and s is the dielectric constant of the solvent. Through most of what follows we use the ideal conductor approximation, Eq. (66). Ionic effects will be considered in Section IV.D. 2. Dispersion Equations Using Eqs. (61) and (54), and combining Eqs. (63), (64), and (65), we ﬁnd ws;a ¼

Ejuq j2 fs;a ðx; zÞ h20

ð68Þ

1 xz fs ðx; zÞ ¼ þ b1 x2 þ b2 x4 þ x lnðzÞ coth z 2 xz fa ðx; zÞ ¼ x2 þ x4 þ x lnðzÞ tanh 2

ð69Þ ð70Þ

where ¼

Kc 4Eh20

¼

4E

x ¼ qh0

ð71Þ

The dimensionless constants b1 and b2 were introduced by Leikin [78]; they account for the fact that contributions from each monolayer to the bending modulus and the surface tension can differ for the two modes considered. Such effects are probably small so that b1 b2 1 [78]. We note that the electrical potential enters Eqs. (69) and (70) only through the parameter z. 3. Instability of Membrane Undulations Under an Applied Voltage (a) Bending Modes. In some sense, the bending modes of membrane undulations at long wavelengths (small x) are similar to those in simple ﬂuids. The curvature contribution is x4 and can be neglected in this limit, while the stretching moduli (another important peculiarity of the double layers) does not manifest itself in bending. As a result, the stability condition for a-modes is similar to results for free liquid ﬁlms (see, e.g., Refs. 56,65). It can be derived from Eq. (70). In the limit of small x where the membrane is especially ‘‘soft’’ and the instability is most likely to occur, fa ðx; zÞ x2 ð þ z lnðzÞ=2Þ The bending mode is stable if

ð72Þ

Electroelastic Instabilities

1 þ z lnðzÞ > 0 2

73

ð73Þ

For the physical interesting region, z 1, we ﬁnd z > 1 2. Combining the last condition with Eq. (52) and using Eq. (71) we ﬁnd that the a-mode becomes unstable at sﬃﬃﬃﬃﬃﬃﬃﬃﬃ h0 a V Vc

ð74Þ m 0 It follows from Eqs. (73) and (74) that the only stabilizing force for a-modes at long is the membrane tension, and critical voltage vanishes as ! 0. In experiments with black lipid membranes the surface tension arises from the contact of the bilayer with the bulk phase contained in the surrounding rim and is typically 0:002 N=m. Then choosing h0 3 109 m, we ﬁnd Vca 0:6 V. Experimentally, the characteristic critical voltage Vexper depends on the duration of the applied electrical pulse. For brief pulses, 0:01 0:1 s, Vexper 1 V, and for longer ones ( 1 sÞ Vexper 0:5 V [90]. Further increase of leads to even smaller Vexper [see Refs. 70 and 91 for liquid membranes and Ref. 92 for bilayers with inclusions (ﬂuid mosaic cell membranes) and references therein]. Thus the onset of BM instability is likely related to the long pulse instability. The increase of the electroporation threshold [91] is also in qualitative agreement with Eq. (74). The long- instability of bending modes does not lead directly to formation of pores because it does not affect the internal structure of the membrane. But it can possibly lead to ripping the membrane off the rim and resulting‘‘permeabilization.’’ From our viewpoint, neglect of such an instability is one of the shortcomings of the pore formation models (see the previous discussion). (b) Squeezing Modes. We now analyze Eq. (69). In the limit x ! 0, fs ! 1 þ 2 lnðzÞ. As a result, the condition of instability, fs ¼ 0, leads to Crowley’s results, Eqs. (55) and (56), derived for a plane membrane. Some softening of this condition can be expected at x 6¼ 0 because the stabilization due to electric ﬁeld grows with x [the function x cothðxz=2Þ in Eq. (69) is essentially a linearly increasing function of x for x 1]. Indeed, instability is ﬁrst lost at ﬁnite (for SOPC it corresponds to x 1:25 [53]). However, the corresponding reduction of Vc and zc is insigniﬁcant (for instance, Vc drops by only 5 mV [53]). C.

Nonlocal Model of Membrane Instability

It follows from previous discussion that the destabilizing electrostatic contribution grows in absolute value with x (with increasing ). But the inﬂuence of the nonuniform electrical force is overwhelmed by the stabilizing bending and stretching contributions. As a result, the traditional smectic model cannot explain how a small transmembrane voltage can lead to membrane breakdown. The obvious solution is to abandon this approach and to develop an alternative, such as the ‘‘pore formation model.’’ However, as we noticed before, this approach postulates rather than proves the appearance of hydrophobic pores. Another option is to try to modify the smectic model in order to account for the lowvoltage, low-thinning instability. It was suggested in Ref. 53 that the instability could be explained as due to s-modes if (1) the membrane moduli depended on the wavelength of ﬂuctuations, and (2) this dependence resulted in substantial softening of s-modes at short . Condition (1) is quite common and normally is described as ‘‘nonlocality.’’ In general, nonlocality of constitutive equations means that forces acting at a point r and conjugate to a ﬂuctuating variable s, depend not only on the value sðrÞ at r, but also on its behavior in

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more distant regions. This leads directly to a two-point integral for the energy W so that (in an harmonic approximation) ð ð75Þ W ¼ Kðr; r 0 ÞsðrÞsðr 0 Þ dr dr 0 where, depending on the property considered, the kernel Kðr; r 0 Þ depends on a nonlocal susceptibility or a nonlocal modulus. For instance, in nonlocal electrostatics, the role of K is played by ðr; r 0 Þ, the nonlocal dielectric constant, while electric ﬁeld strength, EðrÞ, corresponds to sðrÞ [93–95]. In nonlocal elastic theory K is the elastic modulus Dðr; r 0 Þ and s describes displacements uðrÞ [93,96]. The local limit in a uniform systemÐcorresponds to Kðr; r 0 Þ ¼ K ðr r 0 Þ where ðrÞ is a delta-function in which case W ¼ K s2 ðrÞ dr. As long as K is a function of r r 0 (the uniformity condition), the Fourier transform of Eq. (75) is X KðqÞjsq j2 ð76Þ W¼ q

Ð where KðqÞ ¼ expðiqrÞKðrÞ dr. Thus, nonlocality can be either described through the spatial dependence of the generalized susceptibility, Kðr; r 0 Þ, or through the dependence of its Fourier transform on wave vector q. Condition (2) is also quite common. For instance, in crystals it results in a reduced sound velocity, vs ðqÞ when q approaches a boundary of the Brillouin zone [93,96], a direct result of the periodicity of a crystal lattice. In addition, interaction between modes can lead to creation of ‘‘soft mode’’ with q 6¼ 0 and corresponding structural transitions [97,98]. The importance of nonlocality at ﬂuid interfaces and the corresponding softening of surface modes has been demonstrated recently, both theoretically [99] and experimentally [100]. In a phenomenological treatment [53] the parameters describing the nonlocal softening of the s-mode were chosen to ﬁt the conditions that the membrane becomes unstable at voltages corresponding to low thinning, z < 3% It was also assumed that at long (small x) the mode energy approaches Eq. (69). Two approximations for the mode energies in the short- limit were suggested in Ref. 53; their effects on membrane undulations are almost identical. Here we use only one of them (see also Refs. 89,101): fsNL ðx; zÞ ¼ ½1 tðxÞ4 ðk1 þ r1 x4 Þ þ tðxÞ4 fs ðx; zÞ

ð77Þ

where tðxÞ ¼

expðsaÞ þ 1 exp½sða xÞ þ 1

ð78Þ

The parameters a and s were chosen to satisfy the conditions that the transition to the short- behavior occurs at 1:5h0 and that it is steep enough so that by ð2 3Þh0 the long- limit is quite reliable. Given that membrane thinning does not exceed 2–3%, the model parameters r1 and k1 have been selected so that the s-mode energy approaches 0 as z ! zcr ¼ 0:97. In addition, it was required that the corresponding critical wavelength, cr is of the order of h0 . This procedure is illustrated in Fig. 7. The thick curve corresponds to V ¼ 0. The thinner curve illustrates the case where the applied voltage leads to instability at cr ðx 2Þ. The membrane parameters for the local and nonlocal approximations are presented in Table 1.

Electroelastic Instabilities

75

FIG. 7 Nonlocal (dimensionless) energy fsNL ðx; zÞ of the s-mode for the transitional and short- regions at V ¼ 0 ðz ¼ 1, upper curve) and V ¼ 1:3 V (z ¼ 0:97, lower curve). (Reprinted from Ref. 53, by permission, Journal of Chemical Physics.)

D.

Elastic Nonlocality and Equilibrium Membrane Properties

It the previous section we suggested a possibility of effective softening of the s-mode as a mechanism leading to membrane breakdown. However, this phenomenological assumption requires microscopic justiﬁcation. But before proceeding further, it is important to check if this assumption is consistent with the description of such equilibrium membrane properties as the membrane stretching diagram, thickness ﬂuctuations, and the low-voltage membrane capacitance. These properties are well described in the local approximation and introduction of nonlocality should lead to similar predictions. 1. Membrane Stretching Diagram and Thickness Fluctuations It is well known that surface undulations strongly inﬂuence the stretching diagram of membranes. They are responsible for the ‘‘entropic’’ behavior, the extremely steep increase of projected area A? at small tensions. In the analysis of these phenomena based on the local model the contribution of the s-modes to A? can be neglected as it is strongly reduced due to the high values of membrane stretching constant, E. As a result, the major contribution comes from the soft long- bending modes [76]. However, the assumption of softening of the symmetrical modes made in the nonlocal model may enhance their contribution to the projected area at short and thus alter the stretching diagram. Such a possibility has been analyzed in Ref. 53. Analysis very similar to that of Ref. 77 leads to the following expression for the fractional variation ¼ A? =A of the projected area: ¼

kT 16Eh20

ð xmax xmin

x3

1 1 þ dx f2 ðx; zÞ fa ðx; zÞ

ð79Þ

Stretching diagrams calculated in local (L) [Eqs (69) and (70)] and nonlocal (NL) [with Eq. (77) instead of Eq. (69)] approximations are contrasted in Fig. 8. It can be seen from Fig. 8 that nonlocal results are in good agreement with the local approximation and, consequently, with experiment. At small tensions ( 2 104 N=m) the slope of the stretching diagram is very steep. This domain corresponds to the ‘‘nonelastic’’ or ‘‘entropic’’ region of membrane stretching. For 0ð3 4Þ103 N=m the slope is practically constant. In the intermediate region there is a sharp transition between these two regimes. Unlike local calculations, nonlocal results depend on the choice of min (or

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FIG. 8 Stretching diagram for soft (S) and rigid (R) membranes for (a) min ¼ 1:5 nm and (b) min ¼ 1:2 nm. ‘‘L’’ corresponds to the local model, while ‘‘NL’’ describes the nonlocal calculations (see text). The parameters of Table 1 are used (1 dyne=cm ¼ 103 N=m). (Reprinted from Ref. 53, by permission, Journal of Chemical Physics.)

xmax ). As a result, for the cut-off min 1 nm, close to the size of the lipid headgroups, the differences may reach 10–15%, being more signiﬁcant for soft membranes. However, as noted in Ref. 53, this discrepancy might be an artifact due to the same expression, 1 A? ðqÞ ¼ A½quðqÞ2 2

ð80Þ

being used for the mode contributions in the variation of the projected area. In fact, this expression is based on the assumption that there is tilting of the lipids such that headgroups are always aligned parallel to the membrane–water interface, which is only valid at long . At short wavelengths, 1:0–2.0 nm, this condition is harder to achieve and up and down displacements of the lipids, which may consume less projected area than the parallel alignment, are the natural ones. In other words, Eq. (80) should be modiﬁed to account for the short dispersion of the projected area. Effectively, it is equivalent to an increase of min . The value 1:5–2.0 nm is a reasonable limit for the validity of the macroscopic expression, Eq. (80). Membrane thickness ﬂuctuations were initially discussed in the local approach by Hladky and Gruen (HG) [102] in conjunction with their possible effect on membrane capacitance. They are directly related to the spectrum of s-modes: ð 2 kT xmax x dx ð81Þ ðh h0 Þ ¼ 2E xmin fs ðx; zÞ In Ref. 53 these calculations were reproduced using the nonlocal approach. Following HG, the results were contrasted for two cutoffs, min ¼ 1 nm and min ¼ 10 nm. The nonlocal results for RMS thickness ﬂuctuations h~ ¼ hðh h0 Þ2 i1=2 are comparable in magnitude, but slightly smaller than those found by HG. However, the nonlocal model predicts that the ﬂuctuation spectrum should peak at wavelengths 2–5 nm. Thus a

Electroelastic Instabilities

77

valuable test of the nonlocal hypothesis can come from investigating this range of ﬂuctuations, either by means of molecular dynamics simulation or directly, by soft x-ray scattering from real membranes. 2.

Effect of Undulations on Membrane Capacitance

Initially the effect of applied voltage on membrane capacitance was attributed to the uniform electrostriction, in the manner of the elastic capacitor model [1,103]. The effect of undulations was ﬁrst considered by Leikin [78]. In Ref. 89 the combined effect of undulations and uniform compression is studied, including the possible inﬂuence of nonlocality. The differential capacitance Cd is presented as C d ¼ C0d þ Cud where C0d

@h ¼ m2 0 h V @V h

ð82Þ ! ð83Þ

is the capacitance of the uniform membrane compressed by the electric ﬁeld and " # ð kT X xmax 1 @2 fl ðx; zÞ @fl ðx; zÞ2 d Cu ¼ fl ðx; zÞ dx @V Ah20 l¼s;a xmin fl ðx; zÞ2 @V 2

ð84Þ

is the contribution from undulations. At comparatively small voltages (91 V) it is sufﬁcient to use the approximation h h0 ð1 bV 2 Þ b¼ m 0 ð85Þ 2Eh0 which follows from Eq. (52). The differential capacitance can be expressed as C d ðVÞ C d ð0Þð1 þ V 2 Þ where C d ð0Þ corresponds to V ¼ 0 and parameter characterizes the effect of voltage. To compare with experiment, the integral membrane capacitance C must be deﬁned. It is [89] 2 CðVÞ ¼ Cð0Þ 1 þ V 3 The results are presented in Table 2. TABLE 2 Voltage Variation Factor as a Function of Tension () for the Uniform Membrane, and with Undulation Included in both Local (L) and Nonlocal (NL) Approximations, for Soft/ Rigid Membranes in the Metallic Approximation, Eq. (66) ð103 N=mÞ 2 3 4 5 10

Uniform

Undulations (L)

Undulations (NL)

0.016/0.005 0.016/0.005 0.016/0.005

0.024/0.007 0.021/0.006 0.020/0.005 0.020/0.005 0.017/0.005

0.028/0.008 0.023/0.007 0.021/0.006 0.020/0.006 0.018/0.005

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In addition, the effect of ionic screening was analyzed [89] using Eqs. (67). The ionic concentrations considered (1.0 M, 0.1 M, 0.01 M) correspond to Debye lengths lD ¼ 0:3; 1 and 3 nm. The results for lD ¼ 3 nm, the most dilute electrolyte, where ionic screening is least effective, are presented in Table 3. The results can be summarized as follows: 1.

2.

3. 4.

The nonlocal results for CðVÞ are consistent with local calculations. Introducing softening of the s-modes at short only changes the undulative contribution to C by 10–15%. Electrostriction dominates the voltage dependence of membrane capacitance. However, at low tensions (94 103 N=m) the contribution of undulations is also important. The latter is in good agreement with the results of [78] if the same membrane parameters are chosen. At higher tension undulations are damped and their role becomes less signiﬁcant. In rigid membranes is small; however, the relative undulatory contribution is still signiﬁcant. Ionic screening has only a minor effect on the voltage dependence of the capacitance for the ionic strengths considered, 0:01 M.

Results at 0:002–0.004 N/m are found to be in good qualitative agreement with the ‘‘short pulse’’ experiments [104] with exper ranging from 0.018 to 0.036. E.

Summary

We have shown that postulating short- softening of the s-modes of membrane undulations, which can explain the low-voltage low-thinning instability, is consistent with observed equilibrium properties of membranes. This ﬁnding supports the hypothesis but obviously does not prove it. Although partially hidden in averaged thermodynamic properties such as the stretching diagram or the voltage dependence of capacitance, nonlocality can play a more important role when the inﬂuence of short-scale perturbations is signiﬁcant. It can have a direct relation to the anomalous roughness of a membrane surface suggested to account for the discrepancy between calculations of the adhesion energy based on the Young equation and on the conventional (local) theory of entropic forces between the membranes [105]. Mode softening could be a reason for this roughness and for the corresponding hidden projected area [105]. This suggestion complements the hypothesis of special types of structural defects (hats and saddles) [106]. It may also be related to the ﬁnding of ‘‘remarkable out-of-plane vibrational motion’’ of lipid molecules [107] which can contribute strongly to short-range repulsive forces between membranes [108]. Another group of phenomena where short- behavior could be important is related to peptide insertion into membranes. TABLE 3 Effect of Ionic screening on the Capacitance at V ¼ 0, Cð0Þ, and on the Factor , Describing the Voltage Dependence of C, for Two Tensions, 1 ¼ 0:002 and 2 ¼ 0:01 N/m, for the Representative Soft Membranes (SOPC)

‘‘Metallic,’’ Eq. (66) lD ¼ 3 nm, Eq. (67)

C(0) (F/m)

ð1 Þ

ð2 Þ

6:4 103 5:9 103

0.028 0.028

0.018 0.017

Electroelastic Instabilities

79

Typically, the insertion induces sharp variation of the membrane proﬁle at the distances 0.5–1.0 nm from the membrane–peptide interface [79–82]. The steepness of this perturbation indicates that the short- behavior of membrane moduli must be important in the estimates of the elastic energy. In addition, a peptide inserted in a membrane almost certainly perturbs the membrane’s elastic moduli in the immediate vicinity of the inclusion. Both these effects, membrane nonlocality and nonuniform modiﬁcation of elastic properties by insertions, might play an important role in resolving the contradiction between the local calculations [80] and the experimental data for the mean lifetime of a gramicidin channel [81,109,110].* In our approach to membrane breakdown we have only taken preliminary steps. Among the phenomena still to be understood is the combined effect of electrical and mechanical stress. From the ‘‘undulational’’ point of view it is not clear how mechanical tension, which suppresses the undulations, can enhance the approach to membrane instability. Notice that pore formation models, where the release of mechanical and electrical energy is considered a driving force for the transition, provide a natural explanation for these effects [70]. The linear approach requires some modiﬁcation to describe such phenomena. One suggestion is that membrane moduli should depend on both electrical and mechanical stress, which would cause an additional mode softening [111]. We hope that combining this effect with nonlocality will be illuminating. Further progress in understanding membrane instability and nonlocality requires development of microscopic theory and modeling. Analysis of membrane thickness ﬂuctuations derived from molecular dynamics simulations can serve such a purpose. A possible difﬁculty with such analysis must be mentioned. In a natural environment isolated membranes assume a stressless state. However, MD modeling requires imposition of special boundary conditions corresponding to a stressed state of the membrane (see Refs. 84,87,112). This stress can interfere with the ﬂuctuations of membrane shape and thickness, an effect that must be accounted for in analyzing data extracted from computer experiments. Other possible direct probes are optical experiments similar to studies [113] of vesicles but expanded towards shorter (20–30 A˚). Alternatively neutron spin-echo studies of stacked bilayer arrays, which can probe the 10–30 A˚ range [114], might possibly be applicable here. Finally, the x-ray grazing-incidence technique has been shown to be a powerful tool for studying short wavelength ﬂuctuations at ﬂuid interfaces [100]. The application of this technique to the investigation of membrane surface ﬂuctuations can reasonably be expected in the near future [115,116].

ACKNOWLEDGMENT This work was supported by a grant from the National Institutes of Health, GM-28643.

* An assumption that continuum parameters are inappropriate at the short length scale was introduced in Ref. 109.

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88. D. Andelman, in Handbook of Biological Physics (R. Lipowsky and E. Sackmann, eds.), vol. 1, Elsevier Science, Washington, D.C., 1995, pp. 603–642. 89. M. Partensky and P. Jordan. Mol. Phys. 98:193 (2000). 90. R. Benz and U. Zimmermann. Biochim. Biophys. Acta 597:637 (1980). 91. G. Troiano, L. Tung, V. Sharma, and K. Stebe. Biophys. J. 75:880 (1998). 92. J. Akinlaja and F. Sachs. Biophys. J. 75:247 (1998). 93. W. Harrison, Solid State Theory, Sinauer Associates, Sunderland, MA, 1984. 94. A. Kornyshev, in Chemical Physics of Solvation (R. Dogonadze, E. Kalman, A. Kornyshev, and J. Ulstrup, eds.), vol. C, Elsevier, Amsterdam, 1985, ch. 6. 95. P. Bopp, A. Kornyshev, and G. Sutmann. J. Chem. Phys. 109:1939 (1998). 96. N. Ashcroft and N. Mermin, Solid State Physics, Holt, Rinehart and Winston, New York, 1977. 97. M. Kaplan and B. Vekhter, Cooperative Phenomena in Jahn–Teller Crystals, Plenum Press, New York, 1995. 98. B. Strukov and A. Levaniuk, Ferroelectric Phenomena in Crystals: Physical Foundations, Springer, Berlin, New York, 1998. 99. K. Mecke and S. Dietrich. Phys. Rev. E59:6766 (1999). 100. C. Fradin, A. Braslau, D. Luzet, D. Smilgies, M. Alba, N. Boudet, K. Mecke, and J. Daillant. Nature 403:871 (2000) 101. M. Partenskii and P. Jordan. Biophys. J. A54 (1999). 102. S. Hladky and D. Gruen. Biophys. J. 38:251 (1982). 103. S. White and T. Thompson. Biochim. Biophys. Acta 323:7 (1973). 104. O. Alvarez and R. Latorre. Biophys. J. 21:1 (1978) 105. W. Helfrich, in Handbook of Biological Physics. (R. Lipowsky and E. Sackmann, eds.), vol. 1, Elsevier Science, New York, 1995, pp. 691–721. 106. W. Helfrich. Liq. Crys. 5:1647 (1989). 107. E. Sackmann, in Handbook of Biological Physics (R. Lipowsky and E. Sackmann, eds.), vol. 1, Elsevier Science, Washington, DC, 1995, pp. 213–304. 108. J. N. Israelachvili and H. Wennerstroem. Langmuir 6:873 (1990). 109. C. Nielsen, M. Goulian, and O. Andersen. Biophys. J. 74:1966 (1998). 110. J. A. Lundbæk and O. Andersen. Biophys. 76:889 (1999). 111. V. Dorman, M. Partenskii, and P. Jordan. Biophys J. 72:A69 (1997). 112. R. Goetz and R. Lipowsky. J. Chem. Phys. 108:7397 (1998). 113. H. Engelhart, H. Duwe, and E. Sackmann. J. Phys. Lett. 46:395 (1985). 114. W. Pfeifer, S. Konig, L. J. F., T. Bayerl, D. Richter, and E. Sackmann. Europhys. Lett. 23:457 (1993). 115. C. Fradin, D. Luzet, A. Braslau, M. Alba, F. Muller, J. Daillant, J. Petit, and F. Rieutord. Langmuir 14:7327 (1998). 116. L. Perino-Gallice, B. Amalric, E. A. Braslau, T. Charitat, J. Daillant, G. Fragneto, and F. Graner, Colloids and Polymers (2000) (submitted). 117. D. Needham and R. M. Hochmuth. Biophys. J. 55:1001 (1989). 118. D. Needham and R. Nunn. Biophys. J. 58:997 (1990). 119. E. A. Evans and W. Rawicz. Phys. Rev. Lett. 64:2094 (1990).

4 The GvdW Theory: A Density Functional Theory of Adsorption, Surface Tension, and Screening STURE NORDHOLM Department of Chemistry, Go¨teborg University, Go¨teborg, Sweden ROBERT PENFOLD Food Materials Science Division, Institute of Food Research, Norwich, England

I.

INTRODUCTION

The debt owed to J. van der Waals for revealing the essence of ﬂuid behavior in his famous analysis of the binding energy and excluded volume mechanisms [1,2] is widely recognized as enormous. Less known is the fact that van der Waals also extended his theory to nonuniform ﬂuids [3]. This work was a beginning of the development of so-called density functional theories which have only recently gained prominence in both quantum chemistry [4,5] and statistical mechanics [6,7]. Here we shall review the origin of the generalized van der Waals (GvdW) theory with the aim to show that the remarkable accuracy of simple mechanistic analysis applies also to a wide range of nonuniform ﬂuid phenomena such as adsorption, surface tension, and electrolyte screening. Thus the traditional equation of state of van der Waals as well as the Debye–Hu¨ckel and Poisson–Boltzmann theories of electrolyte screening are simple special cases of the GvdW theory which unify and considerably extend these well-known traditional approximations to account, in particular, for nonlocal entropy and short-range packing structure. The key idea of the GvdW theory is a greatly simpliﬁed treatment of correlations in the ﬂuid. Note that if there were no interactions then the ideal gas partition function would be a sum over all possible conﬁgurations of the ﬂuid. In a realistic interacting ﬂuid these conﬁgurations would occur with a weighting factor for each. This weighting factor would reﬂect the potential energy VðRÞ associated with the conﬁguration R through the Boltzmann factor exp½VðRÞ. This innocent-looking weighting factor introduces enormous complexity which will continue to be the subject of analysis and approximation in liquid state theory for all the foreseeable future. van der Waals introduced the idea that for bulk ﬂuids the weighting factor be allowed only two possible values, 0 or 1. In this way the ensemble of conﬁgurations and weights was dramatically simpliﬁed. The conﬁgurations which showed overlap between hard repulsive parts of the pair potentials acting between the particles were simply eliminated by the so-called ‘‘excluded volume effect.’’ The average potential energy was then calculated by the mean ﬁeld approximation, i.e., over the truncated but otherwise unweighted ensemble of conﬁgurations. In this way entropy, internal energy, and free energy could be obtained by greatly simpliﬁed calculations. 83

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This approach certainly does not always yield thermodynamic properties of high accuracy. It is, however, uniquely well suited to the treatment of simple ﬂuids. We shall see that it works very well for Lennard–Jones models of simple ﬂuids which have quite shortrange interactions. It also works very well, in principle better, for primitive models of electrolyte solutions. We are able by this GvdW theory to resolve both short-range packing structure at hard walls and long-range screening mechanisms in electrolyte solutions. We feel therefore that this theory should be of great utility in the ﬁeld of electrochemistry where both short-range ﬂuid properties and long-range electrolyte screening mechanisms meet and mingle. Perhaps the greatest advantage of the theory is that it retains great simplicity, while offering generality and numerical efﬁciency through the variational nature of the density functional formulation. Thus, it need not remain in the hands of a few specialists but will, hopefully, be useful for nearly any practitioner of chemistry.

II.

THE VAN DER WAALS LEGACY: GENERALIZED

Every chemist knows the van der Waals equation of state, P¼

kB T a 2 v v0 v

ð1Þ

In it the pressure P is found in terms of temperature T and volume per particle v. The interactions enter through two parameters: v0 , the excluded volume per particle, and a, the binding energy per particle at unity density in a bulk ﬂuid. The equation of state arose as an extension of the ideal gas law, P¼

kB T v

ð2Þ

It was assumed that the volume V was reduced by the presence of ‘‘other particles’’ to the free volume V Nv0 where N is the number of particles. In arriving at the binding energy effect the mean ﬁeld approximation was used, which says that the soft (negative) part of the pair potential was sampled in an uncorrelated manner as if the system was an ideal gas. The corresponding free energy per particle in the bulk ﬂuid is n ð3Þ f ¼ 3kB T ln þ kB T ln kB T an 1 nv0 where is the thermal wavelength which does not depend on volume and n is the particle density N=V. The third term on the RHS, kB T, is the so-called communal entropy term which reﬂects the large density ﬂuctuations in the bulk ideal gas. If we instead restrict the ideal gas particles to singly occupied cells, each of volume v ¼ V=N, then the communal entropy term disappears and we get n fc ¼ kB T ln an ð4Þ 1 nv0 Here we have limited ourselves to the conﬁgurational free energy per particle fc , i.e., we have omitted the kinetic part which in classical statistical mechanics just yields the ﬁrst term 3kB T ln . The ﬁrst minor generalization of van der Waals’ original derivation is the omission of the communal entropy. We will be dealing with interacting, often dense, ﬂuids which do not display the same density ﬂuctuations as do the corresponding ideal gases.

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Thus we prefer to make the cell model our reference for density ﬂuctuations. Density ﬂuctuations are thereby truncated but in a well-deﬁned way open to correction. The second generalization is the reinterpretation of the excluded volume per particle v0 . Realizing that only binary collisions are likely in a low-density gas, van der Waals suggested the value 2 3 =2 for hard spheres of diameter and for particles which were modeled as hard spheres with attractive tails. Thus, for the Lennard–Jones ﬂuid where the pair potential actually is " # 12 6 ð5Þ

ðrÞ ¼ 4 12 6 r r the interaction is typically approximated as a hard sphere potential for r < . The estimate of van der Waals is chosen to give the correct second virial coefﬁcient B2 ðTÞ at low densities. At higher densities the excluded volume per particle decreases due to the overlap of excluded volume spheres centered on each particle. Thus the effective excluded volume v0 is density dependent and it decreases monotonically with density. If we are to treat a wide range of ﬂuid densities it is then better to determine a constant excluded volume v0 in the high-density limit. In fact, in the simplest form of GvdW theory denoted GvdW(S) [8], v0 is taken to be 3 to give the pressure divergence at the close packing limit in the simple cubic crystal structure. We shall use the Lennard–Jones ﬂuid as the illustrative example as we review the GvdW theory. In the GvdW(S) theory the equation of state is just like the vdW equation of state above with the parameters given by v0 ¼ 3 and a ¼ 16 3 =9. This equation of state works moderately well. However, we do not wish to deal only with bulk thermodynamic properties. We wish to treat surface tension and adsorption, screening phenomena in electrolyte solutions, etc. To do this we need a free energy density functional, i.e., an expression for the conﬁgurational free energy as a function of the particle density which is now considered to be a function of position. If all particle–particle interactions were local in the ﬂuid then the functional would have been of the form ð ð ð6Þ Fc ¼ drnðrÞfc ðnðrÞÞ þ drnðrÞVext ðrÞ where fc ðnÞ is the free energy per particle in the corresponding bulk ﬂuid. Here Vext ðrÞ is an external potential. This type of fully local potential has some limited use, e.g., to consider adsorption in a slowly varying external potential. It fails, however, to describe the most important phenomena such as surface tension and adsorption at most types of interfaces. These phenomena reﬂect in a fundamental way the nonlocal interactions in the ﬂuid. The most obvious nonlocality of the free energy arises due to the range of the attractive or soft interactions represented by the second term in the equation of state, a=v2 . The corresponding potential energy can be obtained by the functional ð ð 1 drnðrÞ dr 0 nðr 0 Þ s ðr; r 0 Þ EV ¼ ð7Þ 2 Here s is the soft and normally attractive part of the pair potential. This simple bilinear form of functional lacks correlation effects except that which is introduced by the truncation of the integral at the onset of the inner hard part of the potential. We are then using an extended form of the mean ﬁeld approximation as did van der Waals in his original

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work. We can now write down the ﬁrst truly useful free energy density functional in the form ð ð ð ð nðrÞ 1 drnðrÞ dr 0 nðr 0 Þ s ðr; r 0 Þ þ drVext ðrÞ þ ð8Þ Fc ¼ kB T drnðrÞ ln 1 nðrÞv0 2 This type of functional, which we refer to as ‘‘coarse-grained,’’ can be used to calculate both surface tension and adsorption isotherms to quite good accuracy for many ﬂuids and interfaces. It can also be used for screening problems in the theory of electrolytes. We shall illustrate the applicability of the GvdW(S) functional above by considering the case of gas–liquid surface tension for the Lennard–Jones ﬂuid. This will also introduce the variational principle by which equilibrium properties are most efﬁciently found in a density functional theory. Suppose we assume the proﬁle to be of step function shape, i.e., changing abruptly from liquid to gas density at a plane. In this case the binding energy integrals in EV can be done analytically and we get for the surface tension [9] ¼

3 4 27 ðnl ng Þ2 ¼ aðnl ng Þ2 4 64

ð9Þ

This expression is not particularly accurate, as shown in Fig. 1, but it tells a large part of the story of surface tension. It arises predominantly due to the loss of binding energy of the liquid-phase particles at the interface. It is roughly proportional to the product of the binding energy constant a and the range of the attractions . It is also in this approximation proportional to the square of the density difference nl ng . We shall see, however, that this proportionality is more nearly to the fourth power of the density difference. A more accurate result can be obtained by allowing the density proﬁle at the interface to relax. The optimal proﬁle is the one which minimizes the free energy. The surface tension is computed by ﬁrst calculating the free energy for the interface (over a sufﬁciently wide slice of the liquid and gas phases) and then subtracting the corresponding free energy obtained from the fully local functional. The fully optimized proﬁle can be obtained by iteratively reﬁning it point by point to yield the best possible shape, i.e., that corresponding to the lowest free energy. More conveniently, and very nearly as accurately, we can

FIG. 1 The calculated surface tension of an argon ﬂuid represented as a Lennard–Jones ﬂuid is shown as a function of temperature. The GvdW(HS-B2 )-functional is used in all cases. The ﬁlled squares correspond to step function proﬁle and local entropy, the ﬁlled circles to tanh proﬁle with local entropy, and the open circles to tanh proﬁle with nonlocal entropy. The latter data are in good agreement with experiment.

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choose a plausible proﬁle shape with a width parameter and then ﬁnd the optimal value. A favored proﬁle shape is the tanh proﬁle, n l ng nðxÞ ¼ ng þ ð10Þ 1 þ expðxÞ The corresponding result for the surface tension [9] provides quite reasonable accuracy for a Lennard–Jones ﬂuid or an inert gas ﬂuid, except helium which displays large quantum effects. Thus we can conclude that the leading mechanisms of surface tension in a simple ﬂuid is the loss of binding energy of the liquid phase at the gas–liquid interface and the second most important mechanism is likely to be the adsorption–depletion at the interface which creates a molecularly smooth density proﬁle instead of an abrupt step in the density. The next most important mechanism affecting the surface tension at a single component simple ﬂuid gas–liquid interface is, we believe, associated with the nonlocality of the repulsive interactions. To account for this mechanism, observe that it enters by way of the excluded volume effect. In the coarse-grained GvdW(S) theory above, the free volume factor ðrÞ is given by ðrÞ ¼ 1 nðrÞ 3

ð11Þ

for a Lennard–Jones ﬂuid. The role of the density in this expression is to describe the number of other particles within repulsive range. If the particle density is varying signiﬁcantly on the length scale then the local particle density nðrÞ should clearly be replaced by some nonlocal average. The natural domain for such an average is the sphere of radius , the range of the hard repulsion, centered on the location of our test particle at r. Thus, we get in the so-called ‘‘ﬁne-grained’’ GvdW(S) theory [10] ðrÞ ¼ 1 n ðrÞ 3 where n ðrÞ is the coarse-grained particle density deﬁned by ð 3 dsn ðsÞ n ðrÞ ¼ 4 3 jrsj<

ð12Þ

ð13Þ

This is clearly only the simplest of possible nonlocal density averages which accounts for the range of the repulsion. Within the GvdW theory we have adhered to this simplest form which works very well as it stands. There are, however, a number of different suggestions available in the density functional literature which arise from matching the GvdW approach to the modern liquid state theory based on pair-correlation analysis. The functionals obtained this way are generally referred to as ‘‘weighted-density functionals’’ [6,7]. As can be seen in Fig. 1 the nonlocal entropy in the form of a nonlocal excluded volume effect systematically reduces the surfaces tension of a Lennard–Jones or inert gas ﬂuid and brings the GvdW result close to corresponding simulation or experimental results. One can understand this in terms of the easing of excluded volume constraints on the dominant liquid phase close the interface. The nonlocal entropy also brings the possibility of describing the characteristic packing structure of a simple ﬂuid around one of its own particles or at a hard wall. In the ‘‘ﬁne-grained’’ GvdW theory (because it distinguishes between the ﬁne-grained particle density nðrÞ and the coarse grained n ðrÞ entering the free volume factor) these ubiquitous oscillations can be understood as a consequence of the ‘‘overlapping excluded volume’’ mechanism. At a hard wall the excluded volume spheres of neighboring hard spheres are partially buried in the already excluded volume associated with the wall [10–12]. This provides excess free volume for the rest of the ﬂuid and thereby attracts the ﬁrst shell of particles towards the wall. They then

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make up a structured wall for a second layer to be attracted to, thus forming another wall attracting a third layer, and so on. In order to accurately describe such oscillations, which have been the center of attention of modern liquid state theory, two major requirements need be fulﬁlled. The ﬁrst has already been discussed above, i.e., the need to accurately resolve the nonlocal interactions, in particular the repulsive interactions. The second is the need to accurately resolve the mechanisms of the equation of state of the bulk ﬂuid. Thus we need a mechanistically accurate bulk equation of state in order to create a free energy functional which can accurately resolve nonuniform ﬂuid phenomena related to the nonlocality of interactions. So far we have only discussed the original van der Waals form of equation of state and its slight modiﬁcation by choosing a high-density estimate for the excluded volume, v0 ¼ 3 for a ﬂuid with effective hard sphere diameter , instead of the low-density estimate v0 ¼ 2 3 =3 suggested by van der Waals. These two estimates really suggest that the excluded volume per particle is density dependent. Several different forms of equations of state have been developed within the GvdW effort which account for this density dependence of the excluded volume [13,14]. Here we shall describe only one simple extension of this type which nevertheless produces substantial improvements in the treatment of surface tension. We call it the GvdW(HS-B2 ) equation of state [14] because it is designed to reproduce the hard sphere second virial coefﬁcient B2 in the low-density limit while retaining close packing at the simple cubic limiting density of n ¼ 3 . Its form is as follows:

2 1 3 k T a B k T 3 P¼ B 3 2 v v

ð14Þ

Here the correction to obtain the exact hard sphere B2 is added linearly while at high density v0 acts nonlinearly and deﬁnes the close-packing limit. The corresponding free energy density functional is nðrÞ 2 3 1 n ðrÞ þ Fc ¼ kB T drnðrÞ ln 3 1 nðrÞ 3 Z ð ð 1 drnðrÞ dr 0 nðr 0 Þ s ðr; r 0 Þ þ drVext ðrÞ þ 2 ð

ð15Þ

This functional gives a good account of both the equation of state and the surface tension of a Lennard–Jones ﬂuid. The surface tension is shown in Fig. 1. The critical parameters obtained from the equation of state are shown in Table 1.

TABLE 1 Critical Parameters for the Lennard–Jones Model are Given in Reduced Units such that ¼ 1 and ¼ 1 Source GvdW(HS-B2 ) Simulation Argon (experiment)

Pc

nc

Tc

0.156 0.13–0.17 0.116

0.333 0.32–0.36 0.316

1.25 1.32–1.36 1.26

The simulation results have been extracted from the literature: see, e.g., B. Smit. J. Chem. Phys. 96:8639 (1992).

The GvdW Theory

III.

89

SURFACE TENSION IN MIXTURES

The GvdW theory has been applied also to mixtures of Lennard–Jones ﬂuids [15,16]. The extension to mixtures is straightforward with respect to the binding energy and interaction with an external ﬁeld but not quite so straightforward with respect to the excluded volume effect. The GvdW(S) theory produces for a mixture of c components an equation of state of the form P¼

c c X c X X aij kB T v v0i i¼1 j¼1 v2i i¼1 i

ð16Þ

Here we have taken the pair potential acting between particles of species i and j, respectively, to be ! ij12 ij6

sij ðrÞ ¼ 4ij 12 6 ð17Þ r r The choice of appropriate potential parameters to use in the study of a certain mixture can be a signiﬁcant problem. Traditionally the Lorentz–Berthelot rules, 1 ij ¼ ðii þ jj Þ 2 pﬃﬃﬃﬃﬃﬃﬃﬃﬃ ij ¼ ii jj

ð18Þ ð19Þ

are frequently used to allow between-species Lennard–Jones potentials to be found from within-species potentials which are better known. The former (Lorentz) rule is generally found adequate but the latter (Berthelot) rule is often found to overestimate the strength of between species attraction. Thus one often introduces a correction factor kij pﬃﬃﬃﬃﬃﬃﬃﬃﬃ ij ¼ kij ii jj ð20Þ where kij is typically 0.95 or so, i.e., a little below unity. The form of the free volume factor ðrÞ is so far generally taken to be i ðrÞ ¼ 1

c X

n i ðrÞii3

ð21Þ

i¼1

This form is particularly simple, since ðrÞ is independent of the type of species i. It behaves as if each particle excluded a volume equal to the smallest cube into which its effective hard sphere shape could be placed. The alternative form i ðrÞ ¼ 1

c X

n i ðrÞij3

ð22Þ

i¼1

may seem more realistic, since it refers the excluded volume to the type of particle. Thus a large particle will be more squeezed by its neighbors than a small particle. Reasonable as this may sound, it also brings some less physical features, such as total exclusion of large particles from a solvent of small particles still not at close packing. As a result the former linear mixture rule for the free volume factor has most often been preferred in the GvdW applications. In the GvdW(HS-B2 ) form of the theory the correction term brings in the binary type of excluded volume mixing rule. The free energy density functional becomes

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Fc ¼ kB T

c ð X i¼1

"

# ! c X ni ðrÞ 2 3 3 P jj nj ðrÞ drni ðrÞ ln þ 3 ij 1 cj¼1 nj ðrÞjj3 j¼1

ð c X c ð 1X þ drni ðrÞ dsnj ðsÞ sij ðjr sjÞ 2 i¼1 j¼1

ð23Þ

The corresponding GvdW(S) functional is obtained by dropping the second term in the square brackets of the entropy part of the functional above. The minimization of this functional presents a problem which for many component mixtures can be quite timeconsuming if the truly optimal form of the interface and free energy is to be found. One may use an iterative method of solution much like the famous scheme used to solve for the Hartree–Fock wave function in electronic structure calculations [4]. An alternative, much to be preferred when sufﬁciently accurate, is to use a simple parametrized form for the particle densities through the interface and then determine the optimal values of these parameters. The simplest possible scheme is, of course, to take the proﬁle to be a step function, ni ðxÞ ¼ nli

for x < 0

¼ ngi

for x 0

ð24Þ

This will be the form of the proﬁle if we used a fully local free energy density functional in our calculation. In the case of the HS-B2 -approximation the fully local functional would be " # ! c ð c X X ni ðrÞ 2 3 3 P jj nj ðrÞ drni ðrÞ ln þ Fc;loc ¼ kB T 3 ij 1 cj¼1 nj ðrÞjj3 i¼1 j¼1 ð25Þ ð c X c c ð X X drni ðrÞVext ðrÞ aij drni ðrÞnj ðrÞ þ i¼1 j¼1

i¼1

Note that the external ﬁeld Vext vanishes in the normal surface tension calculation. In the fully local approximation there is no surface tension. Thus we can obtain the surface tension associated with a planar interface of area A by the expression ð26Þ ¼ Fc ðn1;opt ; . . . ; nc;opt Þ Fc;loc ðn1;B ; . . . ; nc;B Þ =A Here n1;opt ; . . . ; nc;opt are the correct particle densities obtained by optimizing the nonlocal free energy, while n1;B ; . . . ; nc;B imply that bulk particle densities have been used on both sides of a step function interface. The main problem is to ﬁnd the free energy of the real interface with nonlocal energetic and entropic effects. For a general multicomponent interface the minimization of the nonlocal HS-B2 -functional is a nontrivial numerical problem. Fortunately, the variational nature of the problem lends itself to a stepwise solution where simple parametrization of the density proﬁles through the interface upon integration of the functional yields the free energy as a function of the parameters. In fact, if we take the proﬁle to be a step function as in the case of local free energy then with local entropy we get the result ¼

c X c 27 X a ðn nig Þðnjl njg Þ 64 i¼1 j¼1 ij il

ð27Þ

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91

which is the simplest estimate of the surface tension of a mixture. It will be an overestimate, since nonlocal entropy, smooth interfacial proﬁles and adsorption to the interface are all surface-tension-reducing mechanisms. In order to approach the true surface tension but keep the calculation simple we can use an extension to mixtures of the tanh proﬁle applied with great success to single component ﬂuids. It may seem then that we could take each component to be of tanh shape but this will not be recommended here. It turns out that it is better to take the total particle density ntot and the mole fraction of each component xi ðzÞ ¼ ni ðzÞ=ntot ðzÞ to be of tanh shape, i.e., ntot;l ntot;g 1 þ expðzÞ xi;l xi;g xi ðzÞ ¼ xi;g þ 1 þ expðzÞ

ð28Þ

ntot ðzÞ ¼ ntot;g þ

i ¼ 1; . . . ; c

ð29Þ

The reason for this is subtle and subject to veriﬁcation in speciﬁc cases but related to the more fundamental nature of relative concentrations than component particle densities in mixtures. If we use this tanhðn; xÞ scheme then we ﬁnd, for example, that the volatile component will naturally show adsorption to the interface. This is illustrated in Fig. 2. A study of the surface tension of Lennard–Jones mixtures has recently been completed [17]. Very good agreement was obtained in comparison with both experiment and simulation. In Fig. 3 we show results obtained by this tanhðn; xÞ scheme for an Ar– methane mixture in comparison with simulation. We note that if we make the comparison at the same reduced temperature T ¼ T=Tc , then there is quite reasonable agreement with the surface tension obtained by simulation. The slight but signiﬁcant deviation between the critical temperatures in the simulation and in the HS-B2 approximation will otherwise give rise to a similar deviation in surface tension. In the study of the Ar–Kr mixture we found that neither the simulation nor the GvdW theory appear to be able to reproduce a slight dip in the surface tension below linear interpolation as a function of composition unless it is assumed that the Berthelot rule should be corrected by a factor slightly less than unity, i.e., 0.97 in the case of the GvdW theory, which lowers the surface tension most for

FIG. 2 The tanhðn; xÞ proﬁles for a liquid–gas interface in a binary mixture are illustrated. The full and dashed lines correspond to mole fractions x1 ðzÞ and x2 ðzÞ, while dash–dotted and dotted lines correspond to particle densities n1 ðzÞ and n2 ðzÞ of a nonvolatile (1) and volatile (2) component. Note that there is adsorption of the volatile component to the interface.

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FIG. 3 The calculated surface tension of an argon–methane mixture as function of composition (mole fraction of argon) is shown as open circles in comparison with corresponding simulation results obtained by Mecke, Winkelmann, and Fischer [J. Chem. Phys. 110:1188 (1999)]. The GvdW(HS-B2 ) functional was used with tanhðn; xÞ proﬁles.

x ¼ 0:5 or so. Such corrections are commonly found in many other applications of the Lorentz–Berthelot mixing rules.

IV.

GVDW THEORY OF ELECTROLYTE SOLUTIONS

Electrolyte solutions have a theoretical description which is quite distinct from that of Lennard–Jones ﬂuids. The reason is that the latter are short-range simple ﬂuids for which the virial equation of state provides a good description of the onset of nonideality. The ionic interactions are long-range and as a consequence electrolyte solutions are predominantly correlated ﬂuids for which the virial equation of state is inapplicable. The second virial coefﬁcient is not deﬁnable for the Coulomb interaction, since its falloff with 1=r gives it essentially inﬁnite range. Instead the electrolyte solutions are governed by the screening mechanism which neutralizes every charge by adsorption of counterions and desorption of coions. The screening mechanism is a correlation mechanism. Thus the GvdW theory in its very simplest form fails to capture the essence of a bulk electrolyte solution. Let us consider ﬁrst the primitive restricted model of an electrolyte solution wherein the ions are hard spheres of equal size in which are embedded charges q1 and q2 , respectively, and the solvent is accounted for only by a relative dielectric permittivity . If we were to apply the HS-B2 -functional to the bulk electrolyte solution in this model we would simply end up with a hard sphere ﬂuid, since the uncorrelated motion of counterions and coions would leave the charge density ðrÞ equal to zero everywhere around any one of the ions. Thus the mean-ﬁeld approximation, which ignores correlations among the ions and therefore neglects charge screening, is not appropriate for bulk electrolytes. It may seem that the prospects are bleak for the GvdW approach to electrolytes but, in fact, the reverse is the case. We need only follow Debye and Hu¨ckel [18] into their analysis of the screening mechanism, almost as successful as the van der Waals analysis of short-range ﬂuids, to see that the mean-ﬁeld approximation can be applied to the correlation mechanism with great advantage. In fact, we can then add ﬁnite ion size effects to the analysis and thereby unify these two most successful traditional theories.

The GvdW Theory

A.

93

Recovering the Poisson–Boltzmann Equation

The GvdW density functional for a binary primitive electrolyte with the hard sphere diameters set to zero will have the form ð Fðn1 ; n2 Þ ¼ kB T dr½n1 ðrÞ ln n1 ðrÞ þ n2 ðrÞ ln n2 ðrÞ ð30Þ ð ð ð 1 1 þ drðrÞ dsðsÞ þ drext ðrÞðrÞ 2 40 jr sj Here the charge density is deﬁned as ðrÞ ¼ q1 n1 ðrÞ þ q2 n2 ðrÞ

ð31Þ

and ext is an external electric ﬁeld which is to be screened. This functional can be minimized by the Lagrange multiplier method which readily yields the result n1 ðrÞ ¼ n1B expðq1 ðrÞ=kB T Þ n2 ðrÞ ¼ n2B expðq2 ðrÞ=kB T Þ

ð32Þ

The electrostatic ﬁeld is now the sum of the external ﬁeld ext and an internal ﬁeld created by the ions, ð 1 ð33Þ ðrÞ ¼ ext ðrÞ þ dsðsÞ 40 jr sj Recalling now the Poisson equation relating a charge density and a corresponding ﬁeld we get r2 ðrÞ ¼ ðrÞ=0

ð34Þ

in the part of space where the ions make up the only charges. Finally, inserting the results for the ion densities in ðrÞ on the right we get r2 ðrÞ ¼

1 ½q n expðq1 ðrÞ=kB T Þ þ q2 n2B expðq2 ðrÞ=kB T Þ 0 1 1B

ð35Þ

This is the famous Poisson–Boltzmann equation. B.

. . . and the Debye–Hu¨ckel Theory

In their analysis of electrolyte screening Debye and Hu¨ckel assumed that the screening mechanism was weak, i.e., qi ðrÞ=kB T 1 ð36Þ for all ions i and positions r. Then the exponentials in the Poisson–Boltzmann equation can be expanded as expðqi ðrÞ=kB T Þ ’ 1 qi ðrÞ=kB T and the Poisson–Boltzmann equation takes the form " # 1 q21 n1B þ q22 n2B 2 r ðrÞ ¼ ðrÞ 0 kB T Deﬁning the inverse screening length 0 by

ð37Þ

ð38Þ

94

Nordholm and Penfold

20 ¼¼

q21 n1B þ q22 n2B 0 kB T

ð39Þ

we have r2 ðrÞ ¼ 20 ðrÞ

ð40Þ

which is the basic equation of the Debye–Hu¨ckel theory of electrolyte screening. C.

Hole-Corrected Debye–Hu¨ckel Theory

We have seen above that GvdW theory yields Poisson–Boltzmann and Debye–Hu¨ckel theory by neglect of ion size and excluded volume effects. Let us now consider how such effects might be brought into a corrected form of Debye–Hu¨ckel theory. We note that the ion size enters in two fundamentally different ways: (1) reducing the entropy by the introduction of excluded volume and (2) altering the electrostatic energy by keeping the ions from approaching closer than the relevant hard sphere diameter ij . We shall show ﬁrst that if we retain the restricted primitive model and take the charges to be symmetrical, q1 ¼ q2 , then the excluded volume effect vanishes in the linearized Debye–Hu¨ckel limit. This follows by reformulating the free energy in terms of total ion density nðrÞ ¼ n1 ðrÞ þ n2 ðrÞ and charge density ðrÞ ¼ q1 n1 ðrÞ þ q2 n2 ðrÞ, which in the symmetrical case is equal to q½n1 ðrÞ n2 ðrÞ. In the linearized theory ðrÞ is decoupled from nðrÞ, since a linear response to an electric ﬁeld will preserve nðrÞ, changing the ion densities in opposite directions to the same extent. Thus the excluded volume effect is absent. This is a great simpliﬁcation and undoubtedly a reason for the considerable success of the simple Debye–Hu¨ckel theory. 1. Local Hole Correction of the Electrostatic Energy While the excluded volume effect does not affect the screening mechanism in the linearized theory for symmetrical primitive electrolyte models, there is still an effect on the electrostatic energy. Note that in the Poisson–Boltzmann or Debye–Hu¨ckel theories the ions are point particles without size. The Coulomb integrals do not account for the truncation at r ¼ which is essential in the van der Waals calculation of binding energy. Putting this truncation in the Coulomb integrals turns out to be a nontrivial task so we shall approach it stepwise by ﬁrst considering a local approximation [19] which is justiﬁed if 0 1, i.e., if the Debye length 1=0 is much greater than the ion size . In this limit the charge density ðrÞ is essentially constant on the length scale of and the hole correction to the electrostatic energy can be approximated as ð ð ð ð 1 1 1 1 2 drðrÞ dr ðrÞ ’ dsðsÞ ds 2 4 2 4 jr sj jr sj 0 0 s< s< ð41Þ ð 2 2 ¼ dr ðrÞ 40 This is the electrostatic energy arising from ions approaching within of each other. When subtracted from the free energy functional above the corrected Debye–Hu¨ckel equation becomes r2 ðrÞ ¼ 2 ðrÞ with deﬁned by

ð42Þ

The GvdW Theory

95

2 ¼ 20 = 1 20 2 =2

ð43Þ

Thus we have found that the screening should be moreqefﬁcient than in the Debye–Hu¨ckel ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ theory. The Debye length 1= is shorter by the factor 1 20 2 =2 due to the hard sphere holes cut in the Coulomb integrals which reduce the repulsion associated with counterion accumulation. A comparison with Monte Carlo simulation results [20] bears out this view of the ion size effect [19]. 2.

Nonlocal Hole Correction of the Electrostatic Energy: CDH Theory

The hole correction of the electrostatic energy is a nonlocal mechanism just like the excluded volume effect in the GvdW theory of simple ﬂuids. We shall now consider the charge density around a hard sphere ion in an electrolyte solution still represented in the symmetrical primitive model. In order to account for this fact in the simplest way we shall assume that the charge density i ðrÞ around an ion of type i maintains its simple exponential form as obtained in the usual Debye–Hu¨ckel theory, i.e., 8 2 q i < 1 exp½ðr Þ r > 4ð1 þ Þ r ð44Þ i ðrÞ ¼ : 0 r The -value is, however, now to be determined by minimizing the free energy including nonlocal corrections of the electrostatic energy. The integrals required are elementary but large in number and one obtains ﬁnally a free energy Fc;i ðÞ ¼ TS0 þ

kB T 3 qi ½2 þ 3 þ expðÞ 2 16nB ð1 þ Þ 160 ð1 þ Þ2

ð45Þ

wherein the ﬁrst term is a background free energy of the bulk electrolyte solution, the second term is related to the cost in entropy to create an exponential screening charge density, and the third term is the electrostatic energy. The total particle density is denoted nB , i.e., nB ¼ n1B þ n2B . The minimization yields a -value, which in turn allows the internal electrostatic energy to be calculated, and by Debye charging over coupling parameter one can readily obtain the osmotic coefﬁcient ,

¼ P=nB kB T ¼ ðPð ¼ 0Þ þ PÞ=nB kB T and the activity coefﬁcient deﬁned by the relation X X ln ¼ xi ln i ¼ xi ði ð ¼ 0Þ þ Di Þ=kB T i

ð46Þ

ð47Þ

i

Here i ð ¼ 0Þ is the change in chemical potential of an ion of type i due to its hard sphere size and Di is the corresponding change due to its electrostatic interactions. The results are compared with Monte Carlo results for 1-1 or 2-2 salt solutions by Van Megen and Snook [20] in Figs. 4–9 and discussed in the original publication [21]. We note that the 1-1 data are very well reproduced up to more than 2M solutions. The 2-2 results show signiﬁcant deviations due mainly to a nonlinear response to strong electrostatic coupling but the trends and magnitudes are well reproduced. The upturn in osmotic pressure and activity are related mainly to the hard sphere excluded volume effect which in these calculations by both the DH and the CDH theories was accounted for by the GvdW(I) equation of state for hard spheres which yields

96

Nordholm and Penfold

FIG. 4 The calculated internal energy of a 1-1 salt (line) is compared with the corresponding simulation results (open circles) obtained by Van Megen and Snook (Ref. 20). The Debye–Hu¨ckel (DH, dashed line) and corrected Debye–Hu¨ckel (CDH, full line) theory were used together with a GvdW(I) treatment of the uncharged hard-sphere mixture. The ion diameter was 4.25 A˚, the temperature was 298 K and the dielectric constant was 78.36.

FIG. 5 As in Fig. 4 but the osmotic coefﬁcient is shown.

The GvdW Theory

FIG. 6 As in Fig. 4 but the logarithm of the mean activity coefﬁcient is shown.

FIG. 7 As in Fig. 4 but the internal energy of a 2-2 salt is shown.

97

98

Nordholm and Penfold

FIG. 8 As in Fig. 4 but the osmotic coefﬁcient of a 2-2 salt is shown.

FIG. 9 As in Fig. 4 but the logarithm of the mean activity coefﬁcient for a 2-2 salt is shown.

The GvdW Theory

99

X

2 lnð1 niB 3 Þ ln niB Fc ð ¼ 0Þ ¼ kB T Ni 3 i " # 2 nB 3 Pð ¼ 0Þ ¼ nB kB T 1 þ 3 1 nB 3 " # 2 nB 3 3 k T lnð1 nB Þ 1 ð ¼ 0Þ ¼ 3 B 1 nB 3

ð48Þ ð49Þ

ð50Þ

Thus we can see that a combination of van der Waals treatment of hard sphere excluded volume and Debye–Hu¨ckel treatment of screening with a minor generalization to account for hole correction of electrostatic interactions yields quite accurate bulk thermodynamic data for symmetrical salt solutions. 3. Hole Correction of the Debye–Hu¨ckel Coion Density Proﬁle: The DHH Theory So far in our revision of the Debye–Hu¨ckel theory we have focused our attention on the truncation of Coulomb integrals due to hard sphere holes formed around the ions. The corresponding corrections have redeﬁned the inverse Debye length but not altered the exponential form of the charge density. Now we shall take note of the fact that the exponential form of the charge density cannot be maintained at high -values, since this would imply a negative coion density for small separations. Recall that in the linear theory for symmetrical primitive electrolyte models we have ðrÞ ¼ q1 n1 ðrÞ þ q2 n2 ðrÞ ¼ q½n1 ðrÞ n2 ðrÞ and, if the central ion is of type 1 and q1 ¼ q > 0, then 8 2 1 exp½ðr Þ < n 1 ðrÞ ¼ n 1B 1B 2q 8ð1 þ Þ r n1 ðrÞ ¼ : 0

ð51Þ

r>

ð52Þ

r

Now we see that if is large enough and small enough then n1 ðrÞ will become negative for small r before the truncation arises at r ¼ . This is, of course, impossible and we must either abandon the use of the linearized DH (Debye–Hu¨ckel) approach altogether or eliminate the negative portion of the coion density proﬁle. It turns out that nature, as usual, is benign and allows us to retain the simple DH form of proﬁle and still get good accuracy for many strongly coupled electrolytes as long as we remove the unphysical negative particle densities [22]. A particularly illustrative case is offered by the so-called one-component plasma (OCP) model wherein one component is made up of charged point particles and the other is a uniform neutralizing background charge density. The Debye–Hu¨ckel theory now leads to the charge density ðrÞ ¼

q20 1 expðrÞ 4 r

ð53Þ

which will always produce an unphysical ion density nðrÞ ¼ nB

20 1 expð0 rÞ 4 r

for sufﬁciently small r. Here the DH -value is given by

ð54Þ

100

Nordholm and Penfold

20 ¼

nB q2 3 ¼ 2 0 kB T a

ð55Þ

where a ¼ ð3=4nB Þ1=3 and the coupling strength is deﬁned as q2 =ð40 kB TaÞ. The DH theory then leads to the result for the electrostatic potential energy per ion u u^ ¼

u ð3Þ3=2 ¼ kB T 6

ð56Þ

the electrostatic contribution to the free energy 2 ð3Þ f^ ¼ F=NkB T ¼ u^ ¼ 3 9

3=2

ð57Þ

and the osmotic coefﬁcient

0 ¼

P 1 ð3Þ3=2 ¼ 1 þ u^ ¼ 1 nB kB T 3 18

ð58Þ

The accuracy of the DH results for u^ , f^, and 0 is good for low coupling strength, < 1, but for higher coupling strength the errors become very large. By correcting the ion density so that it vanishes rather than going negative for small r while maintaining full neutralization, i.e., 8

< n 1 h exp½ ðr hÞ r>h B 0 r nðrÞ ¼ ð59Þ : 0 r h we get a greatly improved representation of the screening and the thermodynamic properties. The hole can be found to have the size h given by 1=3 i ! 1 1 h 1 þ ð3Þ3=2 1 ¼ ð60Þ h¼ 0 0 where we have introduced the auxiliary variable ! ¼ ð1 þ ð3Þ3=2 Þ1=3 . The thermodynamic properties can then be readily found to be 1 u^ ¼ ð!2 1Þ 4 " ! # 2 1 ! þ ! þ 1 2 ! 1 2 f^ ¼ ! 1 ln þ pﬃﬃﬃ arctan pﬃﬃﬃ 4 3 3 3ð! þ 1Þ

¼1

1 2 ð! 1Þ 12

ð61Þ ð62Þ ð63Þ

The results of the simple DHH theory outlined here are shown compared with DH results and corresponding Monte Carlo results in Figs. 10–12. Clearly, the major error of the DH theory has been accounted for. The OCP model is greatly idealized but the same hole correction method can be applied to more realistic electrolyte models. In a series of articles the DHH theory has been applied to a one-component plasma composed of charged hard spheres [23], to local correlation correction of the screening of macroions by counterions [24], and to the generation of correlated free energy density functionals for electrolyte solutions [25,26]. The extensive results obtained bear out the hopeful view of the DHH approximation provided by the OCP results shown here. It is noteworthy that in

The GvdW Theory

101

FIG. 10 The calculated internal energy of a one-component plasma as a function of coupling strength is compared with corresponding simulation results (open circles) by Brush, Sahlin, and Teller (J. Chem. Phys. 45:2102 (1966). The Debye–Hu¨ckel (DH) and hole-corrected Debye– Hu¨ckel (DHH) theories were used with results as shown (indicated lines).

FIG. 11 As in Fig. 10 but the osmotic coefﬁcient is shown.

102

Nordholm and Penfold

FIG. 12

As in Fig. 10 but the reduced free energy is shown.

the case of hard sphere ions the electrostatic hole is at high coion density and weak coupling preempted by the hard sphere hole. The latter were accounted for in the CDH theory above as a general reduction of Coulomb interactions due to hard sphere exclusion. The DHH theory brings in electrostatic hole formation between ions of the same charge. In both cases we have applied simple correlation mechanisms in the spirit of the original van der Waals analysis which applies, with some generalization, as well to electrolytes as to simple ﬂuids.

V.

CONCLUSION

Our review of the generalized van der Waals theory has taken us from the simple cubic equation of state, which is known to all chemists, to the surface tension problem, which can be regarded as the most important nonuniform ﬂuid property, to the electrolyte screening mechanism in salt solutions. Along this route we went from bulk behavior through the interfacial properties to the correlation dominated Coulomb ﬂuids retaining the simple physical van der Waals approach to ﬂuids. We thereby hope to have demonstrated that this analysis combining volume exclusion correlations with mean-ﬁeld neglect of correlations is capable of very fruitful generalization and extension to widespread phenomena and very useful accuracy. Thus we have found within the conﬁnes of the variational formulation of the GvdW theory not only the traditional van der Waals theory but also the Poisson–Boltzmann and Debye–Hu¨ckel theories and all the applications of these theories to ﬂuids of both short range and long range interactions. Bulk thermodynamic properties, adsorption, surface tension and screening phenomena can be simply and efﬁciently addressed. A key role in the efﬁciency is played by the variational density functional approach which permits simple parametrized density proﬁles to be used. This is particularly well illustrated by the tanh proﬁles in the surface tension applications and

The GvdW Theory

103

by the use of Debye–Hu¨ckel charge densities with optimized -values in the electrolyte applications. Electrochemistry is, with its combination of simple ﬂuids and ions, a natural area of application for the GvdW theory. Here there is an obvious need to understand both the short-range ﬂuids, the long-range electrolyte solutions and their properties in bulk and at interfaces. We hope this review can provide a useful tool for electrochemists and many others with communal interests and stimulate further progress in a ﬁeld rich in ﬂuid phenomena and mechanisms.

ACKNOWLEDGMENT We would like to thank S. Sarman for help in the preparation of this review and the Swedish Natural Science Research Council for ﬁnancial support.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

J. D. van der Waals, Dissertation, Leiden, 1873. A. Ya. Kipnis, B. E. Yavelov, and J. S. Rowlinson, Van der Waals and Molecular Science, Clarendon Press, Oxford, 1996. J. D. van der Waals. Z. Phys. Chem. (Leipzig) 13:657 (1894). R. G. Parr and W. Yang, Density-Functional Methods of Atoms and Molecules, Oxford University Press, New York, 1989. A. D. Becke. J. Chem. Phys. 88:1053 (1988); ibid. 98:5648 (1993). P. Tarazona. Mol. Phys. 52:81 (1984); Phys. Rev. A 31:2672 (1985). W. A. Curtin and N. W. Ashcroft. Phys. Rev. A 32:2909 (1985). S. Nordholm and A. D. J. Haymet. Aust. J. Chem. 30:2013 (1980). S. Nordholm and J. Gibson. Aust. J. Chem. 34:2263 (1981). S. Nordholm, M. Johnson, and B. C. Freasier. Aust. J. Chem. 33:2139 (1980). B. C. Freasier, C. E. Woodward, and S. Nordholm. J. Chem. Phys. 90:5657 (1989). S. Nordholm and R. Penfold. J. Chem. Phys. 96:3022 (1992). M. A. Hooper and S. Nordholm. Aust. J. Chem. 34:1809 (1981). S. Abbas and S. Nordholm. J. Colloid Interface Sci. 166:481 (1994). S. Nordholm, P. R. Harrowell, and K. Cheung. Aust. J. Chem. 35:247 (1982). P. R. Harrowell and S. Nordholm. Aust. J. Chem. 35:673 (1982). H. Greberg, G. Paolini, J. Satherley, R. Penfold, and S. Nordholm. J. Colloid Interface Sci. (submitted). P. Debye and E. Hu¨ckel. Phys. Z. 24:185 (1923). S. Nordholm. J. Chem. Phys. 78:5759 (1983). W. Van Megen and I. Snook. Mol. Phys. 39:1043 (1980). S. Nordholm. Aust. J. Chem. 37:1 (1984). S. Nordholm. Chem. Phys. Lett. 105:302 (1984). R. Penfold, S. Nordholm, B Jo¨nsson, and C. E. Woodward. J. Chem. Phys. 92:1915 (1990). R. Penfold, S. Nordholm, B. Jo¨nsson, and C. E. Woodward. J. Chem. Phys. 95:2055 (1991). R. Penfold and S. Nordholm. J. Chem. Phys. 96:3102 (1992). R. Penfold, B. Jo¨nsson, S. Nordholm, and N. Nichols. Phys. Rev. E (to appear).

5 Adsorption at Polarized Liquid^Liquid Interfaces TAKASHI KAKIUCHI Department of Energy and Hydrocarbon Chemistry, Kyoto University, Kyoto, Japan

I.

INTRODUCTION

Adsorption is the term used to describe the state of a system, composed of two phases in contact, in which the concentration of a certain substance is enriched or depleted at the interface where the phases meet, e.g., air–water, liquid–liquid, solid–liquid, or solid–solid interfaces. So far as our life is concerned, liquid interfaces are much more important than other interfaces. First, the sum of the areas of various liquid interfaces relevant to us would deﬁnitely be much larger than that of other types of interfaces, as can be envisaged by thinking of various membranes in biological cells. Second, liquid interfaces, in particular, liquid–liquid interfaces are replenishable and adaptive to their environment down to the nanometer scale. This ﬂexibility is indispensable in developing biological functions as well as in homeostasis. Furthermore, the fact that the facile mass transfer is possible on both sides of the liquid–liquid interface between the two solution phases of different solvation characters allows intricate designing of chemical reactions unique to biological systems. Recent advances in biochemistry and molecular biology have elucidated numerous intriguing mechanisms of speciﬁc recognition of molecules and its functioning in biological systems, e.g., antigen–antibody interactions and various receptors on cell membranes which can be energized in response to even a single molecule [1,2]. The concept of adsorption thus seems to have been replaced by more speciﬁc interactions between physiologically active molecules and their speciﬁc receptors, which may be better described by intermolecular interactions than surface phenomena. The term adsorption tacitly assumes the averaging of intermolecular interactions over a certain ensemble in a heterogeneous environment, as does the concept of ‘‘interface’’ which implies a boundary between the two statistically meaningful and macroscopically distinguishable phases. Adsorption is thus a macroscopic concept in that the interaction between adsorbate molecules and a heterogeneous environment created by a large number of other molecules and atoms plays a decisive role. All speciﬁc interactions between physiologically active molecules and its receptors actually take place in such many-body environments. The physicochemical properties of liquid interfaces are therefore worth paying continuing and increasing attention in biochemistry, biophysics, and pharmacological science. 105

106

Kakiuchi

The appreciation of the importance of adsorption phenomena at liquid interfaces is probably as old as human history, since it is easily recognized in many facets of everyday life. It is not surprising that liquid interfaces have been a favorite subject of scientiﬁc interest since as early as the eighteenth century [3,4]. From an experimental point of view, one obvious virtue of the liquid interfaces for studying adsorption phenomena is that we can use surface tension or interfacial tension for thermodynamic analysis of the surface properties. The interfacial tension is related to the adsorbed amount of surface active substances through the Gibbs adsorption equation, X i di at T; P ¼ const: ð1Þ d ¼ i

where is the interfacial tension, i is the relative surface excess of the component i, and i is the chemical potential of i in the adjacent solution phase. Thanks to its ﬂuid character, the interfacial tension can be accurately determined using a variety of methods. The measurement of the interfacial tension at the solid surface is, on the contrary, not straightforward, because of the contribution of the strain term to the deformation of the interface [5]. X d ¼ i di þ ð gÞ de at T; P ¼ const: ð2Þ i

where g is the stress and e is the equilibrium strain, both of which are tensor quantities. The development of thermodynamic analysis of solid surfaces lagged behind the study of liquid surfaces by about a century due to these stress and strain terms [5]. The meaning of experimentally obtained macroscopic properties is still a subject of discussion, especially in relation to microscopic information about the interface in the atomic or molecular scale now compiled [6,7]. The availability of thermodynamically reliable quantities at liquid interfaces is advantageous as a reference in examining data obtained by other surface speciﬁc techniques. The model-independent solid information about thermodynamics of adsorption can be used as a norm in microscopic interpretation and understanding of currently available surface speciﬁc experimental techniques and theoretical approaches such as molecular dynamics simulations. This chapter will focus on the adsorption at the polarized liquid– liquid interfaces, which enable us to externally control the phase-boundary potential, providing an additional degree of freedom in studying the adsorption of electriﬁed interfaces. A main emphasis will be on some aspects that have not been fully dealt with in previous reviews and monographs [8–21].

II.

THERMODYNAMIC REFLECTIONS ON LIQUID–LIQUID INTERFACES

Thermodynamics of adsorption at liquid interfaces has been well established [22–24]. Of particular interest in view of biochemical and pharmaceutical applications is the adsorption of ionic substances, as many of biologically active compounds are ionic under the physiological conditions. For studying the adsorption of ionic components at the liquid– liquid interface, the polarized liquid–liquid interface is advantageous in that the adsorption of ionic components can be examined by strictly controlling the electrical state of the interface, which is in contrast to the adsorption studies at the air–water or nonpolar oil– water interfaces [25].

Adsorption at Polarized Liquid–Liquid Interfaces

A.

107

Thermodynamics of Electrocapillarity

Every interface is more or less electrically charged, unless special care is exercised experimentally [26]. The energy of the system containing the interface hence depends on its electrical state. The thermodynamics of interfaces that explicitly takes account of the contribution of the phase-boundary potential is called the thermodynamics of electrocapillarity [27]. Thermodynamic treatments of the electrocapillary phenomena at the electrode–solution interface have been generalized to the polarized as well as nonpolarized liquid–liquid interface by Kakiuchi [28] and further by Markin and Volkov [29]. We summarize the essential idea of the electrocapillary equation, so far as it will be required in the following. The electrocapillary equation for a polarized liquid–liquid interface has the form X d ¼ qW dE þ i0 di at T; P ¼ const: ð3Þ i

where qW is the excess surface charge density on the aqueous side of the interface, E is the phase-boundary potential referred to the potential of the oil phase and is measured using appropriate reference electrodes, each of which reversibly responds to the activity of an ionic species in the corresponding phase, and i0 is the relative surface excess of a component i. The sum is taken over all chemical potentials, in both phases, which are independently altered. In the case of polarized interface where no ionic species are in common to both phases, E can be changed independently keeping the chemical composition of the two phases constant. If the system contains at least one common ionic species, E becomes dependent on the composition of ionic species in the system, i.e., nonpolarized interface. One important advantage of the polarized interface is that one can determine the relative surface excess of an ionic species whose counterions are reversible to a reference electrode. The adsorption properties of an ionic component, e.g., ionic surfactant, can thus be studied independently, i.e., without being disturbed by the presence of counterionic species, unlike the case of ionic surfactant adsorption at nonpolar oil–water and air–water interfaces [25]. The merits of the polarized interface are not available at nonpolarized liquid–liquid interfaces, because of the dependency of the phase-boundary potential on the solution composition.

B.

Surface Excess

The meaning of the surface excess is illustrated in Fig. 1, in which the solid line represents the actual concentration proﬁle of an adsorbate i, when the bulk concentration of i in the phase ( ¼ O or W) is ci . The hatched area corresponds to be the surface excess of i, i . This quantity depends on the location of the dividing surface. On the other hand, the experimentally accessible quantity should not depend on the location of the artiﬁcially introduced dividing surface. The relative surface excess, which is independent of the location of the dividing surface, is deﬁned by relativizing it with respect to those of certain reference components. In oil–water interfaces, the mutual solubility of solvents can be signiﬁcant. The relative surface excess in Eq. (3) is then related to the surface excesses through W i0 ¼ i JxO i Kxi

for the component i which itself is miscible between the two phases, and

ð4Þ

108

Kakiuchi

FIG. 1 An illustration of the meaning of surface excess.

j0 ¼ j KxW j

ð5Þ

j0 ¼ j JxO j

ð6Þ

or

for the component j which is present only in W [Eq. (5)] or O [Eq. (6)], where J¼

W l 00 xW l 0 l 0 xl 00 O O W xW l 0 xl 00 xl 0 xl 00

ð7Þ

K¼

O l 0 xO l 00 l 00 xl 0 O O W xW l 0 xl 00 xl 0 xl 00

ð8Þ

and the subscripts l 0 and l 00 designate the solvent species. Thermodynamically available is the relative surface excess deﬁned by one of Eqs. (4)–(6). The necessity of this relativization comes from the Gibbs–Duhem equation, which imposes the restriction of the change in chemical potentials in one phase. When a component of interest is considerably surface active, its adsorbed amount is high even when its bulk concentration is low. The second terms on the right-hand side of Eqs. (4)–(6) are then small and the relative surface excesses are simply taken as the surface excesses, which, in turn, may be seen as the surface concentration. For example, dilauroylphosphatidylcholine forms a saturated monolayer in the liquid-expanded state at the nitrobenzene–water interface when its concentration in nitrobenzene is 105 mol dm3 [30]. Then the experimentally obtained value, 1:76 1010 mol cm2 , can be considered to be the surface concentration. The second terms on the right-hand side of Eqs. (4)–(6), however, are not always negligible. The negative adsorption, i.e., the depletion, of nonsurface active ions is associated with the contribution of the second term, making the value on the left-hand side negative [31]. In this case, the interfacial tension at the potential of zero charge, pzc,

Adsorption at Polarized Liquid–Liquid Interfaces

109

increases with the increase in the chemical potential of a salt composed of nonspeciﬁcally adsorbed ions. The magnitude of the increase can be estimated through Eq. (3) ð ln a2 pzc ¼ 2RT i0 dðln aÞ ð9Þ ln a1

where a is the mean ionic activity of the ion i. The increase in surface tension is observed also at the air–electrolyte solution interface [32].

C.

Adsorption Isotherms

In its broad sense, an adsorption isotherm is an experimental or theoretical functional relationship between the adsorbed amount of a component and its amount in the bulk phase adjacent to the interface. Usually, the adsorption isotherm of a component i has the form Bi ci ¼ f ð i Þ

ð10Þ

where Bi is the adsorption coefﬁcient of i for the adsorption from the phase ð ¼ O or W), ci is the concentration of i, and f ð i Þ is the fugacity of i at the interface and is a certain function of the surface coverage of i, i . Bi is related to the standard adsorption free energy of adsorption of i from the phase through G;0 ads;i ¼ RT ln Bi . The standard ;0 3 1 states for this Gads;i are a unit concentration (mol dm , mol kg , etc.) of i in the phase referred to the inﬁnite dilution and i ¼ 1 in the adsorbed state. Most frequently found to experimentally describe observed adsorption isotherms are the Langmuir adsorption isotherm, f ð i Þ ¼

i 1 i

ð11Þ

and the Frumkin isotherm, f ð i Þ ¼

i expð2a i Þ 1 i

ð12Þ

where a is the interaction parameter, which represents the intermolecular interaction between adsorbed molecules and is negative in the case of the presence of repulsion and is positive in the case of attraction. However, care must be exercised in interpreting the physical meaning of the parameters obtained from ﬁtting experimental data to those isotherms, because theoretically distant adsorption isotherms can be phenomenologically very similar. One can further elaborate a model to have a concrete form of f ð i Þ, depending on which aspect of the adsorption one wants to describe more precisely, e.g., a more rigorous treatment of intermolecular interactions between adsorbed species, the activity instead of the concentration of adsorbates, the competitive adsorption of multiple species, or the difference in the size of the molecule between the solvent and the adsorbate. An extension that may be particularly pertinent to liquid interfaces has been made by Markin and Volkov, who allowed for the replacement of solvent molecules and adsorbate molecules based on the surface solution model [33,34]. Their isotherm, the amphiphilic isotherm takes the form

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Kakiuchi

BxrA ¼

½ p ðp 1Þ p1 expð2a Þ pp ð1 Þp

ð13Þ

where xA is the mole fraction of the adsorbate A, r is the number of aggregates of surfactant at the interface and p is the number of solvent molecules replaced by one surfactant molecule. One may further generalize this amphiphilic isotherm to accommodate the difference in the size of two solvent species or to use higher approximations to allow for the intermolecular interactions. The adsorption free energy and other parameters may be determined, provided that a proper adsorption isotherm is identiﬁed and is ﬁtted to experimental data. However, it is usually difﬁcult to unequivocally choose an appropriate isotherm; an experimental isotherm may well be ﬁtted to a multitude of theoretical isotherms having several adjustable parameters. If the adsorption isotherm at a very small surface coverage is accessible experimentally, the adsorption free energy can be determined from the limiting slope of the isotherm, as all isotherms reduce to Henry’s law when ! 0: Bi ci ¼ i

ð14Þ

Experimentally, may not be directly available. Then, Henry’s law of the form 0

Bi ci ¼ i

ð15Þ 0

is more practical. The standard state of for the adsorption free energy, RT ln Bi , is then i ¼ 1, instead of i ¼ 1. D.

Adsorption and Partitioning of Ionic Components in Liquid–Liquid Two-Phase Systems

1. Correlation Between Adsorption and Partition In the case of the adsorption at a liquid–liquid interface, the adsorption is possible from both sides of the interface and hence the adsorption of an adsorbate at the interface is not independent of its partitioning between the two phases. This link between the adsorption and partition is unique to liquid–liquid interfaces and is of particular importance in the case of the adsorption of ionic components, since both adsorption and partition of ionic components strongly depend on the phase-boundary potential [23]. Suppose that an ionic component i is in a distribution equilibrium between an oil phase O and an aqueous phase W and also adsorbs at the interface between O and W. At equilibrium, the condition of distribution equilibrium is W O i ¼ i

ð16Þ

If the adsorption equilibrium is also established, S O i ¼ i

ð17Þ

S W i ¼ i

ð18Þ

and

where S stands for the interface. Hence, Eqs. (16), (17), and (18) are not independent of each other. This means that the adsorption free energies of i vary with the phase-boundary potential, since from Eq. (16) the Nernst equation holds for ion partitioning,

Adsorption at Polarized Liquid–Liquid Interfaces W W O ¼ O i þ

RT cO ln i zi F cW i

111

ð19Þ

where W O is the phase-boundary potential, that is, the difference in the inner potentials in O and W, W O [35]. W O i is the standard ion-transfer potential of ion i, which is related to the standard free energy of the transfer of ion i from O to W through [8] GO!W; ¼ zi FW O i tr;i

Remembering Eq. (10), from Eqs. (17)–(19), we obtain W O;0 W GW;0 ads;i Gads;i ¼ zi F O O i

ð20Þ

ð21Þ

where G;0 ads;i is the standard adsorption free energy for the adsorption of i from the phase ( ¼ W or O). Figure 2 illustrates that the change in the phase-boundary potential is O;0 proportioned to GW;0 ads;i and Gads;i with a coefﬁcient . The difference in the adsorption at the O/W interface of a substance from O and from W expresses the hydrophilic– lipophilic balance (HLB) of the substance and should be related to the HLB used for predicting the type of emulsion [36]. Equation (21) and hence Eq. (19), show how the HLB of an ionic component varies with the phase-boundary potential (cf. Fig. 2). In other words, the right-hand side of Eq. (21) deﬁnes the electrochemical HLB for this twophase system. O;0 When the two adsorption free energies is equal, e.g., GW;0 ads;i ¼ Gads;i ; W W O balance ¼ O i

ð22Þ

Thus, the HLB of an ionic surface-active substance is balanced at the standard ion-trans fer potential. This is simply a reinterpretation of the deﬁnition of W O i , but is a very important relation, which is valid no matter what the actual form of the adsorption

FIG. 2 A schematic representation of the relationship between adsorption free energy for the adsorption from the phase ( ¼ O or W), G;0 ads;i , and the phase and phase-boundary potential, O;0 ;0 W;0 ;0; ;0; W is G;0 O , where Gads;i ¼ Gads;i þ RT y, Gads;i ¼ Gads;i RTð1 Þy, Gads;i ads;i at

W W W W O ¼ O i , and y ¼ ðz; F=RTÞ½O O i :

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Kakiuchi

isotherm is. The intrinsic surface activity of a series of ionic surfactants at the liquid–liquid W ;0; interface should be deﬁned in two ways. One is the values of G;0 ads;i at O i , Gads;i . ;0 The other is Gads;i at the potential of zero charge (PZC), where no direct electrostatic effect is expected. The former reﬂects the afﬁnity to the interfacial region when the driving forces toward the interface from W and from O are balanced, notwithstanding that the surface activity at W O i is exhibited under the inﬂuence of the phase-boundary potential W as O i is usually different from the PZC. G;0 ads;i values at the PZC are, however, useful in comparing the ‘‘intrinsic’’ or ‘‘chemical’’ surface activities of ionic compounds. 2. Effect of Phase-Boundary Potential on Adsorption Free Energy In the case of the adsorption of ions, the adsorption free energy is proportional to the excess surface charge density [37], or the phase-boundary potential, W O . The latter proportionality stems from the experimental linear relationship between qW and W O

[31]. On the other hand, the adsorption free energy is quadratically dependent on W O

in the case of the adsorption of neutral compounds [38]. It seems that within the experimentally available range of the potential window, ca. 300 mV the linear term prevails in the adsorption of ionic surfactants [39,40]. Therefore, W O; W GO;0 ads;i ¼ Gads;i þ zi F O O i

ð23Þ

where is the constant that does not vary with W O . From Eqs. (16–18) and (23), we can derive for GW;0 ads;i W W;0; W GW;0 ads;i ¼ Gads;i zi Fð1 Þ O O i

ð24Þ

In Eqs. (23) and (24), 0 1, because otherwise they contradict with the Nernst equaW;0 tion, which is a thermodynamic requirement. Thus GO;0 rds;i and Gads;i vary with the phase-boundary potential oppositely, as illustrated in Fig. 3. The parallelism between W the above dependence of G;0 ads;i on O and the Butler–Volmer relationship in electron

FIG. 3 An illustration of the change in adsorption free energy with phase-boundary potential.

Adsorption at Polarized Liquid–Liquid Interfaces

113

transfer reactions or ion transfer reactions [19] illustrates the simplest way of dividing the electrochemical driving force into two complementary and counteracting subprocesses. 3.

Dependence of Adsorptivity on Phase-Boundary Potential

We have seen that when a cationic (anionic) surfactant adsorbs from W, GW;0 ads;i becomes increasingly negative (positive) with the positive (negative) shift of W O , leading to the stronger adsorption from the W (O) side of the interface. However, simultaneously, the bulk concentration of the cationic (anionic) surfactant in W becomes extremely small as the positive (negative) shift of W O . It is therefore interesting to examine the dependence of adsorptivity, that is, the product of the adsorption coefﬁcient and the concentration [cf. Eq. (10)], on the phase-boundary potential [73]. We consider an oil–water two-phase system, which contains an ionic surfactant i. If we vary the phase-boundary potential either by externally applying the voltage using two electrodes or by adjusting the solution composition of potential determining ions, the concentration of i in each phase varies accordingly, keeping the total amount of i in the system, mi , constant. The condition of the latter is O O V W cW i þ V ci ¼ m i

ð25Þ

where V is the volume of the phase . By combining this equation with Eqs. (10) and (23), we obtain for the adsorption from the O phase, B i mi ¼ f ð Þ

ð26Þ

where B is the adsorption coefﬁcient at W O i . The only potential-dependent term, , is given by

i ¼

eð1 Þy 1 þ rey

ð27Þ

zi F W O W O i RT

ð28Þ

where y¼

and r is V O =V W . Figure 4 illustrates the dependence of i on W O for the case when r ¼ 1 at several different values of i [Fig. 4(a)] and when i ¼ 0:5 and at several different values of r [Fig. 4(b)]. From Fig. 4(a), one can see that i takes a maximum around y ¼ 0, i.e., W O i . The volume ratio affects strongly the value of i as shown in Fig. 4(b), which is ascribed to the dependence of the equilibrium concentration on r through Eq. (25). This simple example illustrates the necessity of taking into account the variation of the phase-boundary potential, and hence the adsorption of i, when one tries to measure the adsorption properties of a certain ionic species in the oil–water two-phase systems by changing the concentration of i in one of the phases. A similar situation exists also in voltammetric measurements of the transfer of surface-active ions across the polarized O/W interface. In this case, the timevarying thickness of the diffusion layers plays the role of the ﬁxed volume in the above partition example. The adsorption of surface-active ions is hence expected to reach a maximum around the half-wave potential of the ion transfer.

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Kakiuchi

FIG. 4 (a) Dependence of i on W O at r ¼ 1 when i ¼ 0:1 (curve 1), 0.3 (curve 2), 0.5 (curve 3), 0.7 (curve 4), and 0.9 (curve 5). (b) Dependence of i on W O at i ¼ 0:5 and when r ¼ 0:01 (curve 1), 0.1 (curve 2), 1 (curve 3), 10 (curve 4), and 100 (curve 5).

III.

INTERPHASE INTERACTIONS AT LIQUID–LIQUID INTERFACES

One notable feature of the liquid–liquid interface is that molecules in one phase can interact at the interface with other molecules dissolved in the other phase. This subject has not been treated in depth in previous review articles on electrochemical studies of liquid–liquid interfaces. A.

Interfacial Tension Measurements

Electrocapillary curves, i.e., the interfacial tension vs. the applied potential curves are well known for the mercury–solution interface and have been utilized also for interpreting the

Adsorption at Polarized Liquid–Liquid Interfaces

115

surface properties of nonmetallic electriﬁed interfaces, e.g., colloid surfaces, although the mercury–solution interface is considerably different from oil–solution interfaces. The establishment of the polarized oil–water interfaces has widened the applicability of the concept of electrocapillarity and has elucidated new electrochemical aspects of oil–water interfaces [19]. A ﬁrst attempt to analyze the double layer structure at the polarized nitrobenzene– water interface was made by Kakiuchi and Senda based on the electrocapillary curves and the Gouy–Chapman theory [31]. It was shown that the thermodynamic study of the ion adsorption is possible using the framework of the approach developed in studying the mercury–solution interface. The main conclusion was that the modiﬁed Verway–Niessen model [41] of the electrical double layer, i.e., the ion free inner layer is interposed between two diffuse double layers which are well described by the Gouy–Chapman theory. They later applied the same approach for studying the adsorption of ionic and nonionic surfactants at the nitrobenzene–water interface. Figure 5 shows the electrocapillary curves when hexadecyltrimethylammonium ions (HTMAþ ) are present in the nitrobenzene phase. Interestingly, the interfacial tension decreased only when the potential E EPZC is negative. In other words, HTMAþ ions adsorb at the interface only when W O is negative and

> 0. Even in the absence of externally applied potential, are not surface active when W O

0:4 V, depending on the ionic the distribution potential can vary between 0:4 W O

FIG. 5 Electrocapillary curves for the interface between aqueous solution of 0.05 mol dm3 LiCl and nitrobenzene solution of 0:1 x mol dm3 tetrapentylammonium tetraphenylborate þ x mol dm3 hexadecyltrimethylammonium tetraphenylborate at 25 C: x ¼ 0 (*), 0.005 (~), 0.02 (&), 0.05 (*), and 0.1 (~). (From Ref. 39, reproduced by permission. The Chemical Society of Japan.)

116

Kakiuchi

species involved [42]. The observed marked dependence of the surface activity on W O

may therefore be of considerable importance in understanding the surface activity of ionic components in actual systems, e.g., microemulsion and vesicles. The interaction between the adsorbed molecules and a chemical species present in the opposite side of the interface is clearly seen in the effect of the counterion species on the HTMAþ adsorption. Electrocapillary curves in Fig. 6 show that the interfacial tension at a given potential in the presence of the HTMAþ ion adsorption depends on the anionic species in the aqueous side of the interface and decreases in the order, F , Cl , and Br [40]. By changing the counterions from F to Cl or Br , the adsorption free energy of HTMAþ increase by 1.2 or 4.6 kJ mol1 . This greater effect of Br ions is in harmony with the results obtained at the air–water interface [43]. We note that this effect of the counterion species from the opposite side of the interface does not necessarily mean the interfacial ion-pair formation, which seems to suppose the presence of salt formation at the boundary layer [44–46]. A thermodynamic criterion of the interfacial ion-pair formation has been discussed in detail [40]. Another interesting example of the interaction of adsorbates with ions belonging to the opposite side of the interface is the adsorption of nonionic surfactants having an oligo(ethylene glycol) unit as a hydrophilic group. Figure 7 shows the electrocapillary curves for the adsorption of tetra(ethylene glycol) mono-n-dodecyl ether (C12E4) at the nitrobenzene–water interface [47]. Unlike ionic surfactants, the interfacial tension is lowered over the entire range of the potential window. However, the adsorbed amount of this

FIG. 6 Comparison of electrocapillary curves for the interface between nitrobenzene solution of 0.1 mol dm3 hexadecyltrimethylammonium tetraphenylborate and aqueous solution of 0.05 mol dm3 LiF (*), LiCl (~), and LiBr (&). (From Ref. 40, reproduced by permission. The Chemical Society of Japan.)

Adsorption at Polarized Liquid–Liquid Interfaces

117

FIG. 7 Electrocapillary curves at 25 C for the interface between nitrobenzene solution of 0.1 mol dm3 tetrapentylammonium tetraphenylborate and aqueous solution of 0.5 mol dm3 LiCl in the presence of x mmol dm3 C12E4: x ¼ 0 (curve 1), 1 (curve 2), 2 (curve 3), 5 (curve 4), 7 (curve 5), 10 (curve 6), 15 (curve 7), 20 (curve 8), 30 (curve 9), 40 (curve 10), 50 (curve 11), 70 (curve 12), 80 (curve 13), and 100 (curve 14). (From Ref. 47, reproduced by permission. The Chemical Society of Japan.)

surfactant shows a pronounced dependence on the phase-boundary potential as shown in Fig. 8. This dependence is caused by the interaction of the tetraethylene glycol unit of adsorbed C12E4 from the nitrobenzene side with Liþ ions at the interface. As W O is made more positive, the surface concentration of Liþ ions in the aqueous solution side of the interface increases, which favors the interaction of the tetraethylene glycol unit and Liþ ions. By using the Gouy–Chapman theory for the dependence of the surface concentration of Liþ ions, the observed dependence of the adsorption of C12E4 is satisfactorily explained [48]. Recent studies of complex formation reactions between calix[4]arene in 1,2-dichroloethane and divalent cations in water using a pendant drop method [49] and a Langmuir–Blodgett monolayers [50] have shown the importance of the surface process in the heterogeneous environment. Since poly(oxyethylene)-type nonionic surfactants have a capability of facilitating the transfer of cations [51,52], the above interphase complexation may be seen as an example of precomplex formation before the bulk transfer of ions, which is seen when W O

is sufﬁciently positive. The presence of such precomplex formation at the interface, which is detectable voltammetrically [53], may have signiﬁcance in the rate of complex formation and the selectivity in the bulk facilitated transfer. B.

Electrochemical Techniques

Among a few electrochemical techniques available for studying the adsorption, the AC impedance technique has been most widely employed. Its high sensitivity to the physico-

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Kakiuchi

FIG. 8 Dependence of the adsorbed amount of C12E4 on the applied potential. Concentration of C12E4 in nitrobenzene is 50 (curve 1), 20 (curve 2), 10 (curve 3), and 5 (curve 4) mmol dm3 . (From Ref. 47, reproduced by permission. The Chemical Society of Japan.)

chemical state of the liquid–liquid interface in addition to its ease of measurements, makes the double layer capacitance a particularly attractive probe for studying the adsorption at polarized liquid–liquid interfaces. The capacitance measurements have been employed for studying the adsorption of phospholipids [54–54] and other surfactants [57] at the polarized oil–water interface. The capacitance is sensitive enough to detect the phase transition of adsorbed phospholipid monolayers [58,59]. Cyclic voltammetry can also be employed to assess the magnitude of double layer capacitance [60]. Potential-step measurements using a micropipet have been used for evaluating the capacitance of and the transfer across a phospholipid monolayer [61]. Phospholipids are adsorbed at the nitrobenzene–water interface from the nitrobenzene solution side. The interaction of adsorbed dipalmitoylphosphatidylserine and Ca2þ or Mg2þ causes a dramatic effect in the state of the monolayer; the critical concentration was found to be 2 mmol dm3 for both Ca2þ and Mr2þ ions to cause the phase transition of the monolayer from a liquid-expanded to a condensed state, demonstrating the importance of the interphase electrostatic interactions [56]. This phase transition caused by the interphase interaction was utilized for detecting the interfacial enzymatic hydrolysis of phosphatidylcholine monolayer by phospholipase D at the nitrobenzene–water interface, using the fact that adsorbed phosphatidates, a product of hydrolysis, form a solid monolayer in the presence of divalent cations in W [62,63]. Interfacial hydrolysis itself is a good example of the interphase reaction, or a liquid–liquid two-phase biocatalysis, where the heterogeneous environment created by the interface plays a signiﬁcant role in characterizing the chemical processes. For example, the effect of the surface charge density on the rate of hydrolysis has been quantitatively estimated [63,64].

Adsorption at Polarized Liquid–Liquid Interfaces

IV.

119

CONCLUSIONS

The interphase interactions inferred from macroscopic approaches introduced above have raised many intriguing questions, which wait microscopic interpretation and evidence at a molecular level. Among several possible techniques, e.g., FT-IR, x-ray and neutron scattering, surface second-harmonic generation and sum-frequency generation are promising [65–68] and have already provided valuable information about molecular orientation at liquid–liquid interfaces [69–72]. Such microscopic studies and theoretical modeling in parallel with thermodynamic approaches will allow us to have an integrated view and understanding of interfacial properties and processes at liquid–liquid interfaces.

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T. Kondo and T. Kakiuchi. Bioelectrochem. Bioenerg. 34:93 (1994). T. Kondo and T. Kakiuchi. Bioelectrochem. Bioenerg. 36:53 (1995). K. B. Eisenthal. Acc. Chem. Res. 26:636 (1993). R. M. Corn and D. A. Higgins. Chem. Rev. 94:107 (1994). P. F. Brevet and H. H. Girault, in Liquid–Liquid Interfaces: Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, 1996, p. 103. P. F. Brevet. Surface Second Harmonic Generation, Press Polytech. Univ. Romandes, Lausanne, 1997. D. A. Higgins and R. M. Corn. J. Phys. Chem. 97:489 (1993). J. C. Conboy and G. L. Richmond. J. Phys. Chem. B. 101:983 (1997). R. A. Walker, J. A. Gruetzmacher, and G. L. Richmond. J. Am. Chem. Soc. 120:6991 (1998). P. B. Miranda and Y. R. Shen. J. Phys. Chem. B. 103:3293 (1999). T. Kakiuchi, in preparation.

6 Nonlinear Optics at Liquid^Liquid Interfaces PIERRE-FRANCOIS BREVET Laboratoire d’Electrochimie, De´partement de Chimie, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, Switzerland

I.

INTRODUCTION

Processes at interfaces are ubiquitous in nature. They occur in respiration or photosynthesis reactions, for example, and one of the elementary steps in these mechanisms often involves the transfer of charged species across the interface. As a result, any experimental studies attached to the investigation of these transfer reactions entail the development of a surface sensitive technique. For charged species transfer reactions, the methodology of choice has long been derived from standard electrochemistry, since the transfer of a charged particle across an interface gives rise to a current which is amenable to detection by conventional electrochemical techniques [1]. The ﬁeld of liquid–liquid electrochemistry has greatly beneﬁted from these general ideas [2–4]. A major drawback of this approach, though, is that the distinction between the different transferring species is not an easy matter. This is an important problem in many aspects relevant to biological processes, as the transfer of an electron across the interface is often coupled to the simultaneous transfer of an ion. More selective techniques have been devised, and the most successful rely on spectroscopy principles. Indeed, the signature of a transferring species may be obtained from its absorption or emission spectrum and therefore UV-visible absorption and ﬂuorescence spectroscopy have been employed extensively [5–10]. The use of other techniques like resonance Raman spectroscopy has also been reported [11,12]. Nevertheless, linear optical techniques have no intrinsic surface speciﬁcity and therefore require an optimized optical conﬁguration to gain surface speciﬁcity. The geometry of choice in this case is the total internal reﬂection (TIR) geometry whereby the light impinges onto the interface from the medium of highest refractive index n1 , usually the organic phase, with an angle of incidence larger than the critical angle given by arcsinðn2 =n1 Þ. The electromagnetic wave present in the low-index phase (index n2 ) is thus an evanescent wave for which the penetration depth is only of the order of 100 nm. This depth is only a fraction of the diffusion layer in mass transport limited processes but is still far greater than the Debye screening length and therefore precludes any studies addressing the problem of adsorption or double layer effects at interfaces. This is clearly a major limitation, circumvented only on rare occasions [13,14]. This problem has led to the development of nonlinear optical techniques that do have a much more reduced probing depth at the interface owing to symmetry rules. The simplest nonlinear techniques are the three wave mixing techniques, namely sum 123

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frequency and difference frequency generation (respectively SFG and DFG) whereby two fundamental photons of frequency !1 and !2 are converted into one photon at the frequency !1 þ !2 in SFG or !1 !2 in DFG [15]. In the simple case where a single fundamental frequency is used, two photons at the frequency ! are converted into one photon at the frequency 2!. The technique is called second harmonic generation (SHG) and is probably the one that is the most widely used because of the simplicity of the experimental arrangement. Although originally applied in surface science to study molecular adsorption on clean surfaces under high-vacuum conditions, the ﬁeld has rapidly expanded to other domains [16,17]. The ﬁrst study of liquid–liquid interfaces has been reported by S. G. Grubb et al. in 1988 for the orientation of compounds at the water–carbon tetrachloride interface [18]. Subsequently, the structure and the dynamics of liquid interfaces have been the focus of interest and the problem of charge transfer reactions across the polarized liquid–liquid interfaces has only been addressed recently [19,20]. The present review intends to cover the work reported on nonlinear optics at liquid– liquid interface since the ﬁrst report of S. G. Grubb et al. [18]. The theoretical aspects of nonlinear optics are ﬁrst introduced in Section II. The experimental results covering the molecular structure of liquid interfaces are presented in Section III, followed by a section devoted to the dynamics and the reactivity at these interfaces. Section V focuses on new aspects where spherical interfaces with radii of curvature of the order of the wavelength of light are investigated. Section VI presents the ﬁeld of SFG.

II.

THEORETICAL APPROACHES

A.

General Theoretical Framework

The problem is restricted in this section to SHG only and hence to a single monochromatic electromagnetic wave impinging at the interface between two dielectric media. This is the general framework describing SHG at both air–liquid and liquid–liquid interfaces. The light source is taken as a well-deﬁned monochromatic harmonic plane wave and is characterized by its wave vector kð!Þ and its electric ﬁeld vector Eð!Þ. On impinging at the interface between the two media from medium 1, the wave is refracted into medium 2 and reﬂected back into medium 1 according to the usual laws of linear optics (see Fig. 1) [21]. In particular, the Snell–Descartes law holds for the angles of incidence, reﬂection, and refraction at the fundamental frequency. The fundamental electromagnetic wave induces a polarization wave in the medium while traveling, as a result of the action of the electric ﬁeld Eð!Þ on all the particles constituting the dielectric medium. At optical frequencies ranging between 1013 and 1015 Hz, only the electronic motion is of interest and the polarization is reduced to its electronic part. In most cases, one can assume that the polarization oscillates at the exciting frequency. However, for large ﬁeld amplitudes, one has to include the nonlinear components oscillating at harmonic frequencies owing to the nonlinear response of the electrons of the material to the excitation ﬁeld. The ﬁrst-order nonlinear contribution varies quadratically with the excitation ﬁeld and therefore contains a contribution oscillating at the second harmonic frequency of the exciting ﬁeld. Introducing the electronic susceptibility tensor ð2Þ ð2!; !; !Þ characterizing the materials, this component is given by [15,22]: P NL ð2!Þ ¼ 0 K ð2Þ ð2!; !; !Þð2Þ ð2!; !; !Þ : Eð!ÞEð!Þ

ð1Þ

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FIG. 1 Geometry for the SHG process at the interface between two centrosymmetrical materials. The nonlinear polarization is a sheet of polarization in the plane of the interface located at the origin of the Z axis.

where 0 is the vacuum permittivity. The quantity K ð2Þ ð2!; !; !Þ arises from the deﬁnition of the polarization and accounts in particular for the degeneration of the fundamental electric ﬁeld. For SHG, K ð2Þ ð2!; !; !Þ ¼ 1=4, but for SFG, K ð2Þ ð2!; !; !Þ ¼ 1=2 [22,23]. Solving the wave equation in the medium, it appears that the component of the nonlinear polarization as given in Eq. (1) acts as a source for an electromagnetic wave propagating at twice the fundamental frequency within the medium. The properties of the nonlinear polarization source induced in the medium are found in the susceptibility tensor ð2Þ ð2!; !; !Þ that possesses the symmetry properties of the material it describes. In particular, for liquids, the susceptibility tensor possesses the property of inversion symmetry. This symmetry operation transforms the co-ordinates (x; y; z) of any point in the medium into the co-ordinates (x; y; z). As a result, dropping the frequency dependencies for clarity, the nonlinear polarization is transformed as: P NL ¼ 0 K ð2Þ ð2Þ EE ¼ 0 K ð2Þ ð2Þ ðEÞðEÞ ¼ P NL

ð2Þ

using the inversion symmetry operation on the vectors, a relationship only fulﬁlled if the susceptibility tensor ð2Þ ð2!; !; !Þ vanishes altogether. This property for the susceptibility tensor describing liquids is the origin of the surface speciﬁcity of the SHG process at the interface between two centrosymmetrical media [24–26]. For liquids, the susceptibility tensor vanishes except at interfaces where the inversion symmetry operation transforms any point in Liquid 1 into a point in Liquid 2. The nonvanishing surface tensor, written as ð2Þ S ð2!; !; !Þ with a subscript, still possesses the remaining symmetry properties of the interface and in particular the isotropy within the surface plane. As a result, from the ð2Þ initial 27 S;IJK components, only four survive, three only being independent: ð2Þ ð2Þ ð2Þ ð2Þ , and S;ZZZ , the normal to the interface being taken along the S;XZX ¼ S;XXZ , S;ZXX ^ ^ Z axis with the X axis in the interface plane. The surface nonlinear polarization P NL S ð2!Þ is localized at the interface and is usually described as a nonlinear polarization sheet. This approximation holds because the thickness corresponding to the physical region of the

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interface where the bulk properties of one liquid change to the bulk properties of the other liquid is much smaller than the wavelength of light. Within this formalism, the problem can be treated with the help of the laws of linear optics yielding for the SH intensity I SHG [15,22,27,28]: qﬃﬃﬃﬃﬃﬃﬃ Re 2! 1 !2 SHG 2 ! 2 ¼ ð3Þ I 2 jj ðI Þ 80 c3 2 pﬃﬃﬃﬃ!ﬃpﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2! 2! Re 1 m cos m where !1 and 2! 1 are the relative optical dielectric constants of Liquid 1 at the fundamental and the harmonic frequency, and I ! is the fundamental wave intensity. 2! m is the optical dielectric constant of the interfacial region, which may be taken as the average of the constant of both adjacent liquid phases [29,30]. The factor is given by:

ð2Þ ð2Þ ð2Þ 2 sin 2 sin þ a2 S;XZX þ a3 ð2Þ þ a ¼ a1 S;XZX 4 S;ZZZ cos cos S;ZXX ð4Þ 2 þ a5 ð2Þ sin cos S;ZXX where the coefﬁcients ai , i ¼ 1; . . . ; 5 contain all the geometrical parameters and the optical linear dielectric constants [22]. and are respectively the fundamental and the harmonic light polarization angle. For example, with ¼ 0 the fundamental wave is ppolarized, whereas with ¼ 90 the fundamental wave is s-polarized. Equations (3) and (4) fully express the output SH intensity in terms of the linear and the nonlinear properties of the interface and the geometrical angles. They are the basic equations for the analysis of the data obtained from SHG experiments. Equations (3) and (4) give the SH intensity obtained in reﬂection mode. Although this is usually the most convenient experimental arrangement, the interfacial nonlinear polarization radiates both in the upward and the downward direction and therefore a transmitted wave does also emerge from Liquid 2, allowing a detection in transmission mode (see Fig. 1) [2]. A feature of interest is the possibility of obtaining the condition of total internal reﬂection (TIR). Under this condition, the fundamental beam impinges on the interface from the liquid with the highest index of refraction yielding a SH intensity enhancement of more than a hundred times. Two TIR angles exist, given by the following relationships: n!1 sin 1! ¼ n!2

and

n!1 sin 1! ¼ n2! 2

ð5Þ

nji

is the optical index of medium i at frequency j, derived from the generalized where Snell–Descartes law [31]. B.

The Case of Pure Solvents

The theoretical framework developed above is valid in the electric dipole approximation. In this context, it is assumed that the nonlinear polarization P NL S ð2!Þ is reduced to the electric dipole contribution as given in Eq. (1). This assumption is only valid if the surface susceptibility tensor ð2Þ ð2!; !; !Þ is large enough to dwarf the contribution from higher orders of the multipole expansion like the electric quadrupole contribution and is therefore the simplest approximation for the nonlinear polarization. At pure solvent interfaces, this may not be the case, since the nonlinear optical activity of solvent molecules like water, 1,2-dichloroethane (DCE), alcohols, or alkanes is rather low. The magnitude of the molecular hyperpolarizability of water, measured by DC electric ﬁeld induced second harmonic

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generation (EFISH), has been found to be about 0:56 1031 esu [32,33], that of 1,2dichloroethane to be about 0:42 1030 esu, and of nitrobenzene 2:3 1030 esu [34]. Conversely, the magnitude of the molecular hyperpolarizability of very efﬁcient nonlinear optical compounds may reach values in excess of 1000 1030 esu, as for donor–acceptor polyenes [35]. Hence Eq. (1) fails to fully describe the nonlinear polarization of neat liquid interfaces and higher orders of the multipole expansion have to be introduced [22,27,36,37]. This problem severely hinders the surface speciﬁcity of the SHG process, since the next contribution to take into account is the electric quadrupole contribution, neglecting any effects of magnetic origin. The nonlinear polarization is then given by: NL P NL ð2!Þ ¼ P NL DE ð2!Þ þ P QE ð2!Þ

ð6Þ

where the electric quadrupole term is given by [22,27,38]: P NL QE ð2!Þ ¼ r Qð2!Þ

ð7Þ

The electric quadrupole Qð2!Þ involves both the gradient of the electromagnetic incident electric ﬁeld Eð!Þ and the gradient of the electric quadrupole susceptibility tensor ð2Þ Q ð2!; !; !Þ. This problem is nonetheless solved by the mere addition of supplementary terms in the surface susceptibility tensor. As a result, the surface susceptibility tensor becomes an effective tensor instead of a purely surface speciﬁc one [27,38]: ð2Þ ð2Þ ð2Þ eff ;XZX ¼ S;XZX þ rQ;XZXZ ð2Þ ð2Þ ð2Þ eff ;ZXX ¼ S;ZXX þ rQ;ZZXX þ fg;ZXX

ð8Þ

ð2Þ ð2Þ ð2Þ eff ;ZZZ ¼ S;ZZZ þ rQ;ZZZZ þ fg;ZZZ

Interestingly, the contributions from the gradient of the electromagnetic ﬁeld across the interface, fg;ZXX and fg;ZZZ , which scale with the mismatch in the optical dielectric constants of the media forming the interface [37], only appear in the susceptibility tensor ð2Þ components ð2Þ eff ;ZXX and eff ;ZZZ . Therefore, these contributions may be rejected with a proper selection of the light polarization of the SH wave. Indeed, with ¼ 90 , the SH wave is s-polarized and only depends on the susceptibility tensor element ð2Þ eff ;XZX . Nevertheless, the contribution from the gradient of the electric quadrupole susceptibility tensor is still measured with the surface contribution. As mentioned above, the major drawback of this situation is the loss of the surface speciﬁcity of the technique because the gradient of the electromagnetic ﬁeld extends over the scale of a wavelength on both sides of the interface. This problem can turn out to be a severe impediment at air–liquid interfaces where the electromagnetic ﬁeld gradients are large, owing to the optical dielectric constant mismatch between air and liquids. This has been clearly emphasized at the air–water interface, whereas at liquid–liquid interfaces, the ﬁeld gradients are much smaller owing to the better matching of the optical dielectric constants. The loss of surface speciﬁcity at the latter interfaces is not as dramatic [39]. Absolute magnitudes for the effective susceptibility tensor have been reported for several interfaces and show a rather large spread (see Table 1) [40]. The air–water interface ð2Þ has a susceptibility value of 6:04 1018 esu for the eff ;XZX susceptibility component [26,40,41]. This large magnitude arises from the overwhelming contribution of the electric quadrupole contribution, the gradient of the electromagnetic ﬁeld in particular. The same observation can be made for the air–alcohol interfaces although some surface speciﬁcity may be obtained when the s-polarized output SHG signal is collected. Conversely, liquid– liquid interfaces present much more reduced values, in particular the water–DCE inter-

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TABLE 1 Absolute Magnitude of the Nonvanishing Susceptibility Tensor Component at Several Air–Liquid and Liquid–Liquid Interfaces [40]. All units are in esu but Transformation into SI Units is Obtained Using the Relationship 1 esu ¼ 3:72 1021 C3 m3 J2 1018 ð2Þ eff ;XZX

Interface Air–water Air–octanol Water–octanol Water–hexane Water–DCE

6.04 4.11 2.46 0.095 0.55

1018 ð2Þ eff ; ZXX 3.38 3.01 2.43 0.104 0.60

1018 ð2Þ eff ; ZZZ 12.58 11.89 7.39 0.39 1.88

ð2Þ face, with a magnitude of 0:5 1018 esu only for the eff ;XZX component, or the water– alkane interface [39]. This is in line with the picture of water molecules lying rather ﬂat at the interface with the dipole moment oriented parallel to the interface [42,43]. Surprisingly, water–alcohol interfaces yield absolute magnitude similar to the air–alcohol ones; see the case of octanol in Table 1, for example. This feature may stem from a strong surface contribution originating from the molecular alignment at the interface subsequent to the interaction of the polar hydroxyl headgroup of the alcohol with water molecules [40].

C.

The Molecular Description

If the electric dipole contribution dominates in the total SH response, the macroscopic response can be related to the presence of optically nonlinear active compounds at the interface. In this case, the susceptibility tensor is the sum of the contribution of each single molecule, all of them coherently radiating. For a collection of compounds, it yields: ð2Þ S ¼

X

NS;i hT i i i

ð9Þ

i

where NS;i is the number of molecules of type i per unit surface and i the hyperpolarizability tensor of a single molecule. The transformation tensor T i links the macroscopic surface susceptibility tensor to the molecular hyperpolarizability tensor. The brackets therefore emphasize that an ensemble average must be performed over all the possible molecular conﬁgurations of a molecule sitting at the interface (see Fig. 2). As expected, the quantity hT i i vanishes if the averaging is performed over all the possible orientations, irrespective of the amphiphilic character of the moiety. This indicates that a nonoriented distribution of molecules at the interface does not lead to any SH signal as required by the rule of centrosymmetry. However, if a preferential orientation does exist owing to the amphiphilic character of the surface species, the quantity hT i i does not vanish. Complete expressions for the quantity hT i i have been given in the literature for many different systems [22,44]. In most experiments, the SH wavelength is tuned near an electronic resonance of the surface compounds, thereby reducing the number of nonvanishing elements of the hyperpolarizability tensor i . A resonance at the second harmonic frequency is usually preferred, since this conﬁguration avoids the spurious effects coming from one photon absorption process with the intense fundamental beam. A two-state model involving the ground and the ﬁrst excited electronic states S0 and S1 is then adequate to

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FIG. 2 Molecular orientation angles at liquid interfaces for rodlike molecules. The out-of-plane motion is a rotation away from the OZ axis, whereas the in-plane motion is performed with the (OX, OY) plane.

describe the nonlinear optical activity of the molecule, the tensor elements ð2Þ ijk taking the following form [45]: ð2Þ ijk ¼ "

e3 ð0Þ g ð0Þ e 2 2h

# ri rj rk !2eg þ 2!2 þ ri rj rk þ rk rj !2eg !2 ½!2eg !2 ½!2eg 4!2

ð10Þ

ð0Þ where ð0Þ g and e are the ground and the excited state population respectively, !eg is the transition frequency between the ground and the excited state, ri is the transition moment along the molecular axis i and ri is the change in the dipole moment along the axis i ð2Þ is obtained when both the transiundergone during the transition. The maximum of ijk tion moment and the change in dipole during the transition are maximized. This explains why compounds undergoing large charge transfer during the transition from the ground to the excited state are good candidates as nonlinear optical probes. If the transition moment and the change in dipole occur along the same axis of the molecule, only one tensor element dominates, the expression of which is: ð2Þ;NR þ ð2Þ zzz ¼ zzz

!2eg

A 4!2 4i!

ð11Þ

where A is a constant and the width of the resonance. The hyperpolarizability element is the sum of a resonant and a nonresonant contribution. As a consequence, the set of equations (9) can be vastly reduced for a single component monolayer at the interface, namely: ð2Þ 2 ð2Þ 20 ð2Þ S;XZX ¼ 20 S;ZXX ¼ Ns hcos sin i zzz 3 ð2Þ 0 ð2Þ S;ZZZ ¼ Ns hcos i zzz

if random distributions are assumed for the two other and equations set, the orientational parameter D given by:

ð12Þ Euler angles. From this

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D¼

hcos3 i hcos i

ð13Þ

is usually extracted but the knowledge of a distribution function has to be assumed beforehand to get the angle of orientation. Although a Gaussian distribution function would be more adequate, albeit with the disadvantage of introducing as an extra parameter the width of the distribution, a Dirac distribution function is often used. This implies the assumption of an inﬁnitely sharp distribution for the molecular angle . In absence of a distribution of angles determined by an independent method, the angle of orientation must only be used as a convenient parameter to describe the interface angular distribution [46,47]. Before closing this section, it is worth mentioning that the hyperpolarizability tensors are complex quantities usually given in the old cgs system of units of esu (electrostatic units). The transformation into the International System is readily obtained with the relationship: ð2Þ ðSIÞ ¼ 3:71 1021 ð2Þ ðesuÞ

ð14Þ

where the SI units are C3 m3 J3 . D.

Polarized Interfaces

The case of polarized interfaces is usually described within the context of the metal– electrolyte interface where the metal charge dependence of the SH intensity is dramatic because of the strong interfacial electric ﬁeld present at the interface [16]. It has long been a real challenge at the polarized liquid–liquid interface but has, however, been observed at charged air–water interfaces [48]. At polarized interfaces, the static DC electric ﬁeld established across the interface couples to the electromagnetic ﬁeld impinging onto the surface. This process is described with the following nonlinear polarization: 1 P ð2Þ ð2!Þ ¼ 0 K ð3Þ ð3Þ ð2!; !; !; 0ÞEð!ÞEð!ÞEð0Þ 6

ð15Þ

with K ð3Þ ¼ 1=4. Although it is a third-order nonlinear optical process mixing four waves, the nonlinear polarization only oscillates at the harmonic frequency owing to the coupling to a static electric ﬁeld. Because the magnitude of the third-order susceptibility tensor ð3Þ ð2!; !; !; 0Þ is much smaller than the magnitude of the second-order susceptibility tensor ð2Þ ð2!; !; !Þ, coupling to strong electric ﬁelds only gives rise to a nonnegligible contribution. This is the reason why the observation of this DC-ﬁeld-induced SHG contribution has been mainly restricted to the metal–electrolyte interface. As opposed to second-order nonlinear processes, this contribution does not possess the symmetry cancellation in media with inversion symmetry and therefore the surface speciﬁcity of this contribution ﬁnds its origin in the conﬁnement to the region where the static electric ﬁeld is nonvanishing. This means that, in principle, this contribution extends over the whole double layer region. E.

Circular Dichroism

In order to describe the problems of the nonlinear optical response from biological systems, the question of chirality must be addressed. Linear circular dichroism (CD) has been investigated extensively for biological compounds and a wealth of data are available on

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this topic [49]. Inversely, in nonlinear optics, this problem has been barely touched on and only few reports have appeared so far [50,51]. The surface susceptibility tensor of a chiral surface possesses different symmetry properties as compared to the surface susceptibility tensor of an isotropic surface. The main difference for a chiral surface arises from the axes OX and the OY, the two axes in the plane of the surface, which are no longer indistinguishable. The nonvanishing elements of the susceptibility tensor are then [52]: ð2Þ ð2Þ ð2Þ ð2Þ S;XZX ¼ S;XXZ ¼ S;YYZ ¼ S;YYZ ð2Þ ð2Þ S;ZXX ¼ S;ZYY

ð2Þ S;ZZZ

ð16Þ

ð2Þ ð2Þ ð2Þ ð2Þ S;XYZ ¼ S;XZY ¼ S;YXZ ¼ S;YZX

Only for achiral surfaces does the last tensor element vanish altogether. Equation (4) retains a similar form but now accommodates a new tensor element. To date, very few experimental works have been reported on chiral surfaces, although the nonlinear effects are expected to be rather large [51].

III.

MOLECULAR STRUCTURE

A.

Surface Coverage

The SH signal directly scales as the square of the surface concentration of the optically active compounds, as deduced from Eqs. (3), (4), and (9). Hence, the SHG technique can be used as a determination of the surface coverage. Unfortunately, it is very difﬁcult to obtain an absolute calibration of the SH intensity and therefore to determine the absolute number for the surface density of molecules at the interface. This determination also entails the separate measurement of the hyperpolarizability tensor i , another difﬁcult task because of local ﬁelds effects as the coverage increases [53]. However, with a proper normalization of the SH intensity with the one obtained at full monolayer coverage, the adsorption isotherm can still be extracted through the square root of the SH intensity. Such a procedure has been followed at the polarized water–DCE interface, for example, see Fig. 3 in the case of 2-(n-octadecylamino)-naphthalene-6-sulfonate (ONS) [54]. The surface coverage takes the form:

a G0Ads zbF w c o ð17Þ þ ln ¼ ln i 1 RT RT asol RT where ai and asol are respectively the solute and the solvent bulk activities and G0Ads is the Gibbs energy of adsorption. The electrostatic contribution to the adsorption energy has been made explicit and a plot of ln½ =ð1 Þ with the applied potential wo across the interface yields the value of b, the extent of the potential drop actually felt by the adsorbing species. This introduces a discussion on the molecular arrangement of the monolayer at the interface and in particular on the exact location of the plane of adsorption [54]. In the case of ONS, the adsorption was taking place from the organic phase and the polar head of ONS species was found to signiﬁcantly protrude into the aqueous phase. The last term in Eq. (17) accounts for the intermolecular interactions within the monolayer through the Frumkin parameter c.

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FIG. 3 Adsorption isotherm of ONS at the polarized water–DCE interface: (square) experimental, (dotted) Langmuir isotherm, and (solid) Frumkin isotherm. (From Ref. 55, copyright American Chemical Society.)

The relationship between the square root of the SH intensity and the surface coverage of the surface active species only holds provided the bare interface does not give rise to any signiﬁcant background SH signal. If this assumption is not true, interference between the signal from the background and the monolayer occurs, yielding a perturbed isotherm at low coverage. This has been clearly demonstrated at the quartz–air interface for the adsorption of rhodamine 110 in the case of a destructive interference [55]. Nevertheless, with compounds of very high hyperpolarizability like the donor–acceptor polyenes for example, fractions of monolayers as low as 0.001% should readily be detected. Another source for erroneous conclusions is the possibility of intralayer rearrangements or reorientation processes leading to a change in the susceptibility tensor element while the surface density of the active compounds remains unchanged. This has been observed at the air–water interface for a monolayer of the protein glucose oxidase (GOx) [56]. A change of the polarization conﬁguration is usually enough to disentangle adsorption from intralayer rearrangement processes. Besides these effects, interfacial measurements have demonstrated the ability of the nonlinear technique to investigate biological membranes. Polypeptides have also received attention. Clear evidence for coadsorption as the result of multipoint electrostatic interaction has been observed for the synthetic poly-L-glutamic acid polypeptide [57].

B.

Molecular Orientation

One question addressed in the literature is the relationship between the angle of orientation of the adsorbed species within the monolayer and their amphiphilic character. The case of surfactants like fatty acids or phospholipids is deferred until Section VI, since the technique of choice is SFG in order to perform a surface vibrational study. Phenol deri-

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vatives have been extensively studied at the air–water interface and a light polarization analysis shows a preferential orientation [47,58–61]. The angle of orientation has been related to the surface activity of the moiety for a series of simple phenol derivatives, namely p-nitrophenol, phenol, and p-propylphenol. At full monolayer coverage, for a hydrophilic substituent as in the case of p-nitrophenol, the molecule is shown to lie with a rather ﬂat position at the air–water interface and to take a position more perpendicular to the interface as the substituent’s hydrophobicity is increased. Hence phenol was shown to take a position more tilted towards the surface normal and p-propylphenol to take an even straighter position. Furthermore, the effect of the change of the polarity of the nonpolar solvent, hexane replacing air, was shown to screen these hydrophilic–hydrophobic interactions with the aqueous surface yielding an identical orientation for all compounds [47]. These results are in line with molecular dynamics calculations [62,63]. One major assumption at the basis of these works is the absolute orientation of the moiety at the interface, whether pointing up with the hydroxyl group in the aqueous phase or down. For the phenol derivatives, the hydroxyl group was always assumed to point into the aqueous phase. However, only absolute phase measurements can yield such a determination, an experiment realized through interference between the SH signal from the monolayer and a quartz reference [64]. In a recent experimental work, the reference was obtained from another compound coadsorbed at the interface with the molecule of interest [65]. Other classes of compounds investigated include the rhodamine and the eosin dye families involving a xanthene ring. With rhodamine 6G for example, two different resonant conﬁgurations were used: either resonant with the fundamental wave or with the harmonic wave [66,67]. The orientation of the long axis of the xanthene ring was found to be oriented with an angle of about 55 with the surface plane. The role of the carboxylic group in the process of adsorption at the hydrophilic air-fused silica surface was also emphasized. SHG has been used extensively for the determination of the structure of surfactant monolayers to address the question of the role of long-tail chains in intermolecular repulsion interactions. The orientation of the surfactants was thus monitored for soluble and insoluble naphthalene sulfonate derivatives, with an alkyl chain containing respectively 6 and 18 carbon atoms. They were shown to exhibit a similar angle of orientation irrespective of the surface coverage and to present an identical surface density at full monolayer coverage. This results supports the view that a soluble surfactant forms a saturated monolayer by adsorption very much identical in its structure to an insoluble monolayer formed by the spreading of the compound on the surface [68]. Reorientation as a function of surface coverage is usually very weak but was nevertheless observed for dodecylnaphthalene sulfonate or 1-(3 0 ; 5 0 -di-t-butyl)phenyl-3-glycero-rac-glycerin at the air–water interface [69,70]. The kinetics of adsorption, phase transition from the liquid expanded to the liquid condensed state, and surface diffusion were also observed [43,71–76]. Finally, it is worth adding that very small molecules are amenable to detection at interfaces. This has been proven for compounds like SO2 at the air–water interface or for the more environmentally relevant stratospheric ozone reaction products like HOCl at the surface of ice [77,78]. C.

Interfacial Solvation

The heterogeneity of the solvent at the interface introduces another degree of complexity in the problem. Molecular dynamics calculations have been able to give a molecular picture of the interfacial solvation of adsorbates but experiments have long been a chal-

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lenge [79]. The problem has though recently been addressed by SHG with the recording of surface SHG spectra and the comparison with the corresponding UV-visible bulk phase spectra. The maximum of the nonlinear and the linear optical spectra usually differ but the exact location of the resonance must be carefully extracted from the nonlinear optical measurements because of the contribution of the nonresonant term in the hyperpolarizability tensor, see Eq. (11) [80]. The general scheme underlying the experimental approach is to extend the polarity scale of homogeneous media to interfacial regions with the use of an appropriate molecular probe. The compound usually taken as the reference compound is 4-(2,4,6-triphenylpyridinium)-2,6-diphenylphenoxide, ET ð30Þ, which belongs to the family of the betaine dyes. It possesses a large solvatochromic shift and this shift, when renormalized on a general solvent scale, deﬁnes the polarity of the medium. The solvatochromic shift of ET ð30Þ arises from the charge transfer band and is deﬁned as 0 for tetramethylsilane (TMS) and 1 for water [81]. The scale is deﬁned with the normalized parameter ETN ð30Þ as: ETN ð30Þ ¼

ET ðsolventÞ ET ðTMSÞ ET ðwaterÞ ET ðTMSÞ

ð18Þ

where ET (solvent) is the location of the charge transfer absorption band maximum. The air–water polarity thus has a polarity of 0.01 in this scale and the n-heptane–water interface 0.52, bulk phase n-heptane having itself a value of 0.01 on this polarity scale [30]. The ETN (30) scale was conﬁrmed with another compound, N,N-diethyl-p-nitroaniline (DEPNA), yielding a scale consistent with the ETN (30) one. In a rather general manner, the polarity of the interface is deduced from the average of the polarity Pi of the two adjacent bulk media: Pw=o ¼

Pw þ Po 2

ð19Þ

This indicates that the polarity of a medium is a long-range property that goes much further than the ﬁrst solvation shell and therefore involves the two adjacent bulk media properties. This result is, however, valid for compounds the solvation of which is not determined by speciﬁc interactions with the ﬁrst solvent shell, but rather by long-range forces like dipole interactions. The solvation of DEPNA was determined by molecular dynamics too and similar conclusions were drawn [82]. D.

Surface Equilibrium

As a consequence of the change of the polarity of the interface as compared to the bulk solution, chemical equilibrium may be shifted towards the reactants or the products if changes in the charges or the dipoles are involved. A thermodynamic cycle between the surface and the bulk phase can thus be deﬁned with the Gibbs energies of adsorption and the different equilibrium constants. The energy of adsorption contains two contributions, a chemical part G0Ads assumed unaffected by changes in the charge, and an electrostatic part WBorn the magnitude of which, evaluated with the Born model [83,84], emphasizes the dependence of WBorn with the charge z. Hence, neutral species are much more favored at interfaces than charged species owing to the reduced polarity of water next to a hydrophobic wall. This observation is of great relevance in surface chemistry for the acid–base equilibrium for example. The protonation–deprotonation reaction will involve a change in the charge of the species and therefore a change in the surface equilibrium constant, assuming that the chemical term is constant. The pKaS observed at the interface is thus:

Nonlinear Optics at Liquid–Liquid Interfaces

pKaS ¼ pKa

1 ½WBorn ðAHÞ WBorn ðAÞ 2:3RT

135

ð20Þ

provided the proton equilibrium between the surface and the bulk phase follows a Boltzmann equilibrium: pHS ¼ pH

Fsb

2:3RT

ð21Þ

where sb is the potential drop between the bulk phase and the surface. In Eq. (20), WBorn ðAHÞ vanishes if the form AH is neutral. A surface equilibrium has been reported for several compounds at the air–water interface: anilinium, phenolates, hemicyanine, or eosin B and the observed shift of the surface pKaS is usually of several units [75,85–87]. For the equilibrium between p-nitrophenol and its anion, the surface pKaS is 7.9 as compared to a value of 7.15 in the bulk aqueous phase. Similarly, for the dye eosin B, which has two protonation sites and therefore presents a neutral acid, a singly charged and a doubly charged anionic form at the interface presents two surface pKaS of 4.0 and 4.2 at the air– water interface as compared to 2.2 and 3.7 in bulk aqueous solution. The location of the adsorption plane for the different forms at the interface was inferred from the different shift observed for the two equilibrium constants. The doubly charged form of eosin B was thus found to lie further into the aqueous phase as compared to the singly charged form. The case of 4-(4 0 -dodecyloxyazobenzene)-benzoic acid (DBA) has been studied at the water–DCE interface [88]. At liquid–liquid interfaces though, the problem is complicated by the possible transfer of species across the interface. The SH signal may be used as a surface titration tool (see Fig. 4). Yet, the midpoint of the titration curve is not the point where the surface concentrations of the acid and the base are equal. Indeed, a proper account of the ratio of the hyperpolarizability tensor of the two forms has to be taken and consequently the point of equal surface concentration may lie far away from the midpoint.

FIG. 4 SHG intensity from the dye eosin B adsorbed at the air–water interface as a function of the pH of the bulk aqueous solution. The aqueous dye concentration is 30 M and the fundamental wavelength is 532 nm.

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Different orientations for the protonated and deprotonated species as well as a change of the surface coverage with the bulk aqueous pH can further complicate the problem. Another determination of the surface equilibrium entails the use of the coupling of the DC electric ﬁeld present at charged interfaces with the electromagnetic ﬁeld, as described in the theoretical section. Integration of the nonlinear polarization over the whole double layer leads to the following expression of the effective susceptibility tensor: ð2Þ eff ¼ A þ B ð0Þ

ð22Þ

where the surface potential ð0Þ can be separately calculated from a Gouy–Chapman model. This method has been used for the determination of the surface pKaS of p-hexadecylaniline at the air–water interface, the surface pKaS of which was found to be 3.6 at the interface and 5.3 in the bulk aqueous phase. These results conﬁrm that neutral forms are favored at the interface [89]. E.

Polarized Interfaces

Interfaces between two immiscible electrolyte solutions (ITIES) have scarcely been investigated by nonlinear optics. Some literature is available on adsorption and orientation at ITIES and was covered in the sections above [54,88,90]. No reorientation of the adsorbates as a function of the applied potential was observed in the course of these experiments, a feature probably due to the weak interaction energy between the molecular dipole and the DC electric ﬁeld. The inﬂuence of the ion transfer reaction across the interface in the thermodynamic equilibrium between the bulk phases and the interface was, however, underlined [88]. At ITIES, the origin of the second harmonic signal may stem from the change in surface concentration of the active species with the externally applied potential or from the coupling of the DC electric ﬁeld with the electromagnetic ﬁelds. This matter is still a question of debate but in an attempt to address it, the SH intensity was measured at the water–DCE interface as a function of the applied potential in presence of the supporting electrolytes only [91]. The aqueous electrolyte was LiCl and different organic supporting electrolytes were used. In particular, the organic cation was either tetrabutylammonium (TBAþ ), which possesses only four alkyl chains and therefore has a weak hyperpolarizability tensor, or tetraphenylarsonium (TPhAsþ ) which has four phenyl rings and thus a much larger hyperpolarizability. The organic anion was tetraphenylborate (TPhB ). The SH response exhibited a parabolic shape similar to the one observed at the metal–electrolyte interface for TPhAsþ . However, for the cation TBAþ , the SH intensity vanished at the negative end of the potential window where the organic cation is accumulated at the interface. The authors were thus led to the conclusion that the SH signal ﬁnds its origin in the potential-dependent concentration of the organic supporting electrolytes. In all cases, the inﬂuence of the aqueous supporting electrolyte was negligible.

IV.

INTERFACIAL DYNAMICS AND REACTIVITY

A.

Interfacial Dynamics

Molecules adsorbed at interfaces are in constant motion, both from the point of view of their orientation and of the dynamic exchange with the bulk solution. The distribution of orientation angle is characterized by the parameter D, see Eq. (13), or the angle of orientation . Complete randomness for the angle , the angle of rotation around the principal

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molecular axis, is assumed hereafter. The two angles and deﬁne the in-plane and the out-of-plane motion of the molecule at the surface and are readily accessed by experiment. The anisotropy of the rotation motion of compounds at interfaces has been clearly evidenced in the case of the dye coumarin C314 [92]. The strategy operating to separate the two in-plane and out-of-plane motions relies on the selective preparation of the excitedstate distribution of molecules with a pump pulse of well-deﬁned state. Indeed, the perturbation of the initial distribution is produced by a pump pulse photoexciting the molecules form their ground state to their excited state. The probe pulse, which is actually performing the SHG process at the interface, subsequently samples the relaxing molecular distribution at ﬁxed time intervals. With the use of a selective excitation according to the polarization state of the pump pulse with respect to the polarization state of the probe pulse, the two motions have different weights and can be deconvoluted. One of the major caveats of these experiments is the clear separation of the orientation processes from other processes like radiative and nonradiative decays of the excited population. Population effects are usually observed a time scales of a few nanoseconds and correspond to processes like ﬂuorescence emission, for example. Orientation processes occur on the picosecond time scale. For coumarin C314, the out-of-plane motion was found to have a relaxation time of about 350 ps, whereas the in-plane motion had a relaxation time of about 600 ps. Such a difference was attributed to the restoring force acting on the molecules for the out-of-plane motion, whereas no such force is acting in the case of the inplane motion. The time scale of the two different motions reported for C314 at the air–water interface can also be compared to the rotation motion in the bulk phase. As has also been reported for rhodamine 6G at the same interface, the relaxation time is longer than the rotational diffusion time in bulk water at the interface for the out-of-plane motion [92,93]. These longer time scales are explained by rotational motions at the interface chieﬂy controlled by the friction on the aqueous side of the air–water interface. These results are at odds with the experimental ﬁndings observed for the dye eosin B at the same interface (see Fig. 5) [94]. The relaxation time of the out-of-plane motion of the doubly charged anionic form of this dye was observed after a complete randomization of the orientation distribution corresponding to the angle . The time scale at the interface was found to be 90 ps, a relaxation time much shorter than the one observed in the bulk aqueous phase at about 350 ps. This was explained by the reduced hydrogen bonding at the interface between the dye and the water molecules, owing to an increased competition with other water molecules. Population and orientation decays are not the fastest events in the dynamics of solutes at interfaces. Solvation processes indeed occur on the femtosecond time scale. In the ground state of a molecule, the electronic distribution, and therefore the charge distribution in the molecular volume, is such that a polar solvent is speciﬁcally oriented around the molecule in the bulk phase to minimize the energy of the state. In the excited state, the electronic distribution is often rearranged and this process may be quite extensive in a charge transfer excited state where the change in dipole moment from the ground to the excited state is rather large. As a result, the solvation properties of the excited state are the ones pertaining in the ground state, since the electronic excitation is a much faster event than the solvent reorganization. This conﬁguration is highly unfavorable. The solvent thus undergoes a reorganization in order to minimize the energy of the excited state. This feature, known as the Stoke shift, is usually observed through the time evolution of emission spectra [95]. At the interface, this effect is observed as a shift of the SH spectrum at early times subsequently to the photoexcitation. Conversely, and because this phenom-

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FIG. 5 Time-resolved SHG intensity from the doubly charged eosin B at the air–water interface after randomization of the orientation distribution. (a) Square root of the SH signal recorded for the s-polarized SHG output intensity and the fundamental beam 45 -polarized. (b) Square root of the SH signal recorded for the p-polarized SHG output intensity and the fundamental beam s-polarized. (From Ref. 96, copyright Elsevier Science BV.)

enon occurs on a fast time scale, the solvent reorganization process can be observed as the early time evolution of the SHG signal at a single frequency. This technique has been used at the air–water interface for coumarin C314, which possesses a large change in dipole during the excitation from the ground to the excited state. The time scale of the solvent reorganization was measured to be 790 fs, a value close to the longitudinal dielectric relaxation of bulk water, the value of which is only 590 fs [96]. This is attributed to the long-range effects of solvation and in particular of the solute–solvent interactions, in accordance with the polarity scale, which describes the similar long-range effects.

B.

Photoisomerization

The photoisomerization reaction gives a valuable tool to investigate the molecular friction at the interface. Depending on the exact location of the reaction path, whether predominantly in one or the other phase, the time scale of the rate of the reaction is severely modiﬁed. The photoisomerization reaction of the dyes malachite green and 3,3 0 -diethyloxadicarbocyanine iodide (DODCI) has been reported at several interfaces, the air–

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water and different alkane–water interfaces, to illustrate this phenomenon [97,98]. Malachite green is present at the interface with its phenyl ring protruding out of the aqueous phase, whereas the two dimethylaniline groups are anchored into the aqueous phase. The isomerization reaction rate is found insensitive to the phase adjacent to the aqueous phase, the relaxation rate being 3.5 ps at the air–water interface and 3.6 ps at the pentadecane–water interface. Both rates are slower than the rate in the bulk aqueous phase, i.e., 0.7 ps. They are also faster than the rate observed at the silica–water interface, which is 6.2 ps. Inversely, the isomerization rate of DODCI is measured to be 220 ps at the air–water interface, whereas it is 520 ps in the bulk phase water. These differences were attributed to the exact location of the path of the isomerization reaction. In the case of malachite green, the isomerization is thought to occur through rotation around the two carbophenyl bonds protruding into the aqueous phase without involving the phenyl group sticking into the other phase. As a result, the motion is slowed down because the molecular friction on the aqueous side of the interface is increased. For DODCI, the isomerization reaction is thought to occur through the one of the methylene bonds protruding out of the aqueous phase into the air. Thus, the two different behaviors of malachite green and DODCI may be reconciled by assuming that the isomerization path involves the part of the molecule in the aqueous phase for malachite green and the part in the air for DODCI at the air–water interface. This assumption implies that the inﬂuence of molecular friction on reaction rates at interfaces is path-dependent. On the aqueous side of the air–water interface, the molecular friction appears stronger than the bulk phase one. Photoisomerization was also reported at the water–DCE interface for the organic dye 4-(4 0 -dodecyloxyazobenzene)-benzoic acid (DBA) [99]. This dye is under the trans form in its ground state but can be converted into its cis isomer when illuminated with UV light. In the bulk DCE phase, the thermally driven back-conversion from the cis isomer to the trans isomer is rather slow as a result of the high energy barrier of nearly 100 kJ mol1 . At the water–DCE interface, the conversion from the trans to the cis isomer with UV light is also efﬁcient, however, no signiﬁcant thermally driven relaxation to the trans isomer is observed. This surprising result is attributed to intermolecular interactions within the dye monolayer at the interface, like hydrogen bonding through the azo nitrogens of the azobenzene DBA either with other DBA molecules or with the aqueous solvent. C.

Electron Transfer Reactions

Electron transfer reactions constitute an ubiquitous class of chemical reactions. This is particularly true in biological systems where these reactions often occur at interfaces, in photosynthesis for instance. It is therefore challenging to use the surface speciﬁcity and the time resolution of the SHG technique to investigate these processes. At liquid–liquid interfaces, these processes are mimicked through the following scheme: Dorg þ Aaq

hv D þ Aaq !Dþ org þ Aaq ! org SCHEME 1

where the two redox couples are located in the organic and the aqueous phase during the whole duration of the experiment. Hence, Scheme 1 describes a true heterogeneous electron transfer (ET) reaction across the interface. One of the major problems usually arising during this reaction scheme is the simultaneous transfer of one of the reactants or products across the interface as this process is difﬁcult to uncouple from the ET reaction. Several systems have been devised and one of the most efﬁcient ones so far is formed by zinc

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porphyrins located in the aqueous phase and ferrocene derivatives in the organic phase [100]. The SHG technique is an adequate technique to follow these ET reactions and the experiment has been performed on a system constituted by tris-(2,2 0 -bipyridinyl) ruthenium (II) RuðbpyÞ2þ 3 dissolved in the aqueous phase as the sensitizer and trans-1-ferrocenyl-2-(4-(trimethylammonio)phenyl)ethylene (1þ ) located in the organic phase as the donor species [101]. The RuðbpyÞ2þ 3 species were ﬁrst photoexcited by light at 488 nm and the time evolution of the donor 1þ at the water–DCE interface was followed by SHG (see Fig. 6). The heterogeneous ET reaction was clearly observed and its rate limited by the diffusion rate of the excited RuðbpyÞ2þ 3 species to the interface. This experiment clearly demonstrated the advantages of nonlinear optics over linear optical techniques like ﬂuorescence in total internal reﬂection (TIR) or transient absorption owing to its surface speciﬁcity [102,103].

D.

Ion Transfer Reactions

Charge transfer reactions at ITIES include both ET reactions and ion transfer (IT) reactions. One question that may be addressed by nonlinear optics is the problem of the surface excess concentration during the IT reaction. Preliminary experiments have been reported for the IT reaction of sodium assisted by the crown ether ligand 4-nitro-benzo-15crown-5 [104]. In the absence of sodium, the adsorption from the organic phase and the reorientation of the neutral crown ether at the interface has been observed. In the presence of the sodium ion, the problem is complicated by the complex formation between the crown ether and sodium. The SH response observed as a function of the applied potential clearly exhibited features related to the different steps in the mechanisms of the assisted ion transfer reaction although a clear relationship is difﬁcult to establish as the ion transfer itself may be convoluted with monolayer rearrangements like reorientation.

FIG. 6 SHG intensity as a function of time (ON) with and (OFF) without illumination of the interface by a probe UV pulse. The increased SHG intensity during illumination arises from the production of the species 1þ at the interface by photoinduced electron transfer, see text for more details. (From Ref. 103, copyright American Chemical Society.)

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Other studies involved the measurements of the SHG response from ion selective electrodes (ISE) [105,106] but one of the difﬁculties lies in the reabsorption of the SH signal generated at the interface in the bulk of one phase as the active species transfer.

V.

SHG FROM CENTROSYMMETRICAL PARTICLES

In the sections above, only inﬁnite planar interfaces between air and an aqueous phase or two immiscible liquids like water and DCE were considered. Reducing the question to this class of surfaces only would be a severe limitation in the scope of the review as more reports appear in the literature debating on the SH response from small centrosymmetrical particles [107–110]. It is the purpose of this section to discuss the SHG response from interfaces having a radius of curvature of the order of the wavelength of light. In the theoretical section above, the nonlinear polarization induced by the fundamental wave incident on a planar interface for a system made of two centrosymmetrical materials in contact was described. However, if one considers small spheres of a centrosymmetrical material embedded in another centrosymmetrical material, like bubbles of a liquid in another liquid, the nonlinear polarization at the interface of a single sphere is a spherical sheet instead of the planar one obtained at planar surfaces. When the radius of curvature is much smaller than the wavelength of light, the electric ﬁeld amplitude of the fundamental electromagnetic wave can be taken as constant over the whole sphere (see Fig. 7). Hence, one can always ﬁnd for any inﬁnitely small surface element of the surface

FIG. 7 Schematics of the SHG process at the surface of a sphere of a centrosymmetrical medium with a radius much smaller and of the order of the wavelength of light. The cancellation or the addition of the nonlinear polarization contribution is given explicitly and underlines the effect of the electromagnetic ﬁeld and the surface orientation.

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another inﬁnitely small surface element on the other side of the sphere with a corresponding nonlinear polarization of equal amplitude pointing in the opposite direction. The net result of this ﬁnding is that the overall surface nonlinear polarization of the particle vanishes altogether and no SHG signal may be observed from such a particle. This case would be observed for small nanoparticles the diameter of which is in the range of 1 to 20 nm. In fact, in the case of metallic nanoparticles, this case is nearly reached, although an SHG signal can still be collected from the contribution arising from the electromagnetic ﬁeld gradients [111–113]. Since all particles in the solution radiate at the harmonic frequency without any phase relationship, the SH signal collected from a monodispersed solution of particles is incoherent [114]. This process is known as hyper-Rayleigh scattering (HRS). For particles with a radius of curvature of the order of, or larger than, the wavelength of light, the incoming fundamental electric ﬁeld cannot be assumed constant over the particle diameter any longer. Hence, the compensation of the nonlinear polarization from two opposite surface elements is incomplete and an SHG signal from the particle is collected. This phase matching condition is given as [115]: ¼ 1 expðikLÞ

ð23Þ

where L is the coherence length and k ¼ k2! 2k! is the wave vector mismatch. The maximum SH intensity is therefore obtained when ¼ 2 or similarly for kL ¼ . This condition deﬁnes a coherence length of about a few microns. The problem of particles having a diameter of the order of the wavelength of light has been recently discussed for the dye malachite green adsorbed on polystyrene particles of about 1 m diameter [115]. The SH intensity was shown to depend on the square of the number of adsorbed malachite green molecules per particle, indicating that the adsorbed dye molecules of a single polystyrene particle were coherently radiating at the harmonic frequency. The SH intensity was, however, shown to depend linearly with the number density of the polystyrene particles, underlining a noncoherent SH generation from the assembly of particles. The most striking advantage of this conﬁguration is the possibility of investigating liposome bilayers and transport processes across these layers. Protein monolayers have already been investigated at planar surfaces [56] but liposome spherical bilayers are also accessible by nonlinear optics in bulk solution. The transport of the dye malachite green across a phospholipid bilayer membrane has thus been reported [116], the experiment relying on the adsorption of malachite green at the aqueous media–bilayer membrane on both the internal and the external side (see Fig. 8). Because the two sides of the membrane have an opposite orientation, the two opposite contributions of the nonlinear polarization are expected to cancel each other. As a result, the initial point of the experiment was obtained with the malachite green only adsorbed on the external membrane side of the dioleoylphosphatidylglycerol (DOPG) liposome bilayer by adding the dye after the liposome preparation. The transport of the dye across the membrane to the internal side was then followed through the loss of the SH signal as the internal side contribution to the signal increased, therefore compensating the external side contribution. The loss of the SHG intensity was occurring on time scales of about 100 s but the transport could be blocked for a bilayer of dipalmitoylphosphatidylglycerol (DPPG). The difference between DOPG and DPPG were interpreted in terms of the structure of the bilayer, DPPG being in a gel state where the restricted arrangement prevents the transport of the dye. These results undoubtedly will raise a strong interest in the biological sciences.

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FIG. 8 SHG intensity as a function of time for a solution of DOPG and DPPG liposomes in presence of the dye malachite green in the solution and adsorbed at the liposome surface. The effect of transport across the bilayer is observed through the decay of the SHG intensity at short times. (From Ref. 117, copyright Elsevier Science BV.)

VI.

SUM FREQUENCY GENERATION

A.

Theoretical Background

Equation (1) has been set above in the case of the SHG process. This process entails the mixing of two identical frequency electromagnetic waves and therefore constitutes a particular case of the general problem of the mixing of two different frequency waves. The general form of Eq. (1) is therefore [15,22]: P NL ð!3 Þ ¼ 0 K ð2Þ ð!3 ; !1 ; !2 Þð2Þ ð!3 ; !1 ; !2 Þ : Eð!1 ÞEð!2 Þ

ð24Þ

where we have either the condition !3 ¼ !1 þ !2 , the process known as sum frequency generation (SFG), or !3 ¼ !1 !2 , this process being known as difference frequency mixing (DFG). Although experiments may be readily performed with two visible frequencies, one interesting conﬁguration lies in the possibility of using one visible frequency and one infrared frequency, which can be tuned over vibrational resonances of the molecular adsorbates. In this case, a surface vibrational spectrum is recorded, the surface speciﬁcity arising from the three-wave mixing process. This possibility has been widely used in recent years to investigate surfactants and phospholipids at liquid interfaces [117]. These species are present at liquid surfaces in a wide range of phenomena but it was very difﬁcult to get a clear molecular picture of the interface. SFG IR Vis Generalization of the Snell–Descartes law yields nSFG ¼ nIR 1 w3 sin1 1 w1 sin 1 þ n1 Vis SFG w2 sin 1 deﬁning an outgoing SFG wave angle 1 close to the outgoing fundamental

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visible wave angle 1Vis . Similarly, the outgoing angle 1DFG is determined through the Vis IR IR w3 sin 1DFG ¼ nVis relation nDFG 1 1 w2 sin 1 n1 w1 sin 1 . With a collinear conﬁguration of the two incoming beams, the SFG wave has usually a smaller angle than the visible outgoing fundamental wave and the DFG one a larger angle, although the experimental apparatus requires a careful rejection of the fundamental waves. For this reason, the counterpropagating conﬁguration is sometimes preferred. The SFG intensity takes a form similar to the one given in Eq. (3), although the SFG intensity depends linearly on both fundamental wave intensities [22]. The hyperpolarizability tensor is obtained in a way similar to the case of SHG. However, the selection rules for an SFG resonance at the IR frequency implies that the vibrational mode is both IR and Raman active, as the SF hyperpolarizability tensor elements involve both an IR absorption and a Raman–anti-Stokes cross-section. Conversely, the DFG hyperpolarizability tensor elements involve an IR absorption and a Raman–Stokes cross-section. The hyperpolarizability tensor elements can be written in a rather compact form involving several vibrational excitations as [117]: X Aq ð2Þ ð2Þ ð25Þ S ¼ S;NR þ !IR !q þ iq q where the summation is made over the vibrational modes. The appearance of the nonresonant contribution ð2Þ S;NR in the hyperpolarizability tensor is the source for interference in the SFG spectra. Interestingly, Eq. (25) must be slightly modiﬁed for the case of DFG: X Aq ð2Þ ð2Þ ð26Þ S ¼ S;NR þ ! !q iq IR q this simple change in phase allowing one to disentangle the nonresonant from the resonant contribution if the SFG and the DFG spectra are collected [118]. B.

Vibrational Surface Spectrum of Solvents

The ﬁrst vibrational surface spectrum recorded was that of the CH stretch region of methanol at the air–methanol interface [119]. It yielded a molecular picture of the interface where the end CH3 group is pointing into the air in agreement with the theoretical predictions [120]. This work initiated the studies on the surface vibrational spectrum of water, since water surfaces represent by far the most widely used system. The spectral region of interest is the OH stretching region extending from 3000 cm1 to 3800 cm1 (see Fig. 9) [121]. Three vibrational modes dominate: the OH stretching mode at 3680 cm1 , the OH stretch at 3400 cm1 , and the OH stretch at 3200 cm1 . The ﬁrst mode characterizes the free OH bonds pointing out of the water phase. The second one corresponds to bonded O and H atoms within a disordered network, and therefore characterizes the waterlike structure, whereas the third one corresponds to the bonded O and H atoms in a more regular network hence characterizing the icelike structure. The relative magnitude of these modes is indicative of the hydrogen bonding network prevailing at the surface. It was deduced from different sets of experiments involving water–alcohol mixtures and temperature dependence measurements, that the water hydrogen bonding network resembles that of ice next to the interface [122]. The molecular network is formed at the interface by water molecules tetrahedrally coordinated through hydrogen bonds. In this structure, about 25% of the water molecules have a dangling OH bond protruding in the hydrophobic phase. This icelike network is, however, severely distorted, since the peak at 3400 cm1

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FIG. 9 Vibrational sum frequency spectrum in the OH mode region of the neat air–water interface at different temperature for the fundamental visible and infrared beams respectively s- and p-polarized and the SFG beam s-polarized. (From Ref. 120, copyright American Physical Society.)

characterizing liquid water is still rather large. A molecular dynamics study has led to similar surface vibrational spectra [123]. These results suggest that liquid surfaces are more ordered than their bulk phase, owing to the strong hydrogen bonding network. This has also been observed at air–alcohol surfaces [124] and also at the water–hexane [122] and the water–CCl4 interfaces [125]. In the CH2 stretching spectral region between 2800 cm1 and 3000 cm1 , information on the alkyl chain conformation can be inferred. For symmetry reasons, the CH2 stretching mode should not be nonlinear optically active in all-trans chains because of the cancellation of the contribution from CH2 groups on both sides of the alkyl chain. Hence, this mode is a nice tool to measure the extent of gauche defects in these chains. Experimentally, at the air–alcohol interface, the weak magnitude of the CH2 stretching mode indicated that the alkyl chains remain almost all-trans with very few gauche defects. The number of defects is rather insensitive to the length of alkyl chain. These results suggest that chain–chain interactions are highly effective in ordering the chains at the interface. At water–alkane interfaces a similar observation can be made, although an increase in the temperature introduces defects in the chain [126,127]. In fact, according to the weak magnitude of the CH3 antisymmetrical stretching mode, the alkyl chains are oriented perpendicular to the surface [126]. The molecular order at the interface can be severely disrupted as it has been demonstrated when methanol is added to an aqueous solution [122]. Inversely, adsorption can lead to an enhancement of the order as is the case

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with small additions of sulfuric acid at the air–water interface [128]. At high acid concentrations, the aqueous surface resembles that of sulfuric acid. Other mixtures have been studied, in particular glycerol–water [129], acetonitrile–water [130], and aqueous salt solutions [131]. C.

Surfactants and Phospholipids

Liquid interfaces have been also investigated in the presence of cationic and anionic surfactants. In the CH2 and the CH3 regions between 2800 and 3000 cm1 , information on the chain–chain interactions can be obtained, whereas in the OH region, information on the water hydrogen bonding network is obtained. The vibrational spectrum of pentadecanoic acid (PDA) at the air–water interface at full coverage for example is dominated by the CH3 symmetrical stretch and the CH3 Fermi resonance modes [127]. The absence of the CH2 modes clearly indicates the high degree of order of the alkyl chains, which take a predominantly all-trans conﬁguration. It also appears that as the surface coverage is reduced, the constraints are released and the number of gauche defects increases, as seen from the increase of the ratio of the intensity of the CH2 mode intensity to the CH3 mode intensity. Interestingly, the headgroup of the surfactant seems to play a nonnegligible role in the ordering process. For a polar cationic head, in the case of dodecylammonium chloride or dodecyltrimethylammonium chloride, the number of gauche defects was lower as compared to the case of sodium dodecylsulfate or sodium dodecylsulfonate for the same alkyl chain length [132]. This was explained in terms of the penetration depth of the polar cationic heads into the aqueous phase, the number of gauche defects being reduced as a result of the shorter length of the alkyl chain protruding outside the aqueous phase. The general picture emerging from these studies can be even more reﬁned if complementary information from other techniques like neutron reﬂection experiments are included [133]. In the spectral region of the OH modes, the structure of water itself is obtained in the presence of the surfactant monolayer. In the case of pentadecanoic acid at the air–water interface, the OH peak at 3200 cm1 was found to dominate over the one at 3450 cm1 , underlining the tetrahedral arrangement of the hydrogen bonding network of the water molecules in an icelike structure [127]. More strikingly, it has been possible to observe the orientation ﬂip of the water molecules with the sign of the surface charge introduced by the surfactants polar heads. A constructive interference in the region of 2970 cm1 between the CH3 Fermi resonance mode and the OH stretching mode lying at 3200 cm1 has been observed for the cationic surfactant dodecylammonium chloride. Conversely, a destructive interference between these two modes was reported for the anonic surfactant sodium dodecylsulfonate [134,135]. The interference arises from the reversal of the alignment direction of the water dipoles in the vicinity of the interface upon the change of the sign of the surface charge. With a cationic surfactant, the water molecules are preponderantly oriented with the oxygen pointing towards the surface, whereas in the presence of the anionic surfactant, the hydrogen atoms point towards the surface. At neutral surfaces, where a mixed monolayer of cationic and anionic surfactants was spread, the alignment of the water molecules was lost and the corresponding signal of the OH stretching mode at 3200 cm1 was negligible. One major interest in vibrational surface spectroscopy is the ability to directly probe lipid layers. Similarly to the previous case, the structure of the alkyl chains of phospholipids is readily determined from the ratio of the magnitude of the CH2 and CH3 symmetrical stretching modes [136,137]. At the D2 O–CCl4 interface, a layer of

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dilauroylphosphatidylcholine (DLPC) at a coverage of 50 A2 /molecule was found to possess a high degree of order (see Fig. 10) [138]. Indeed, the ratio of the two CH2 and CH3 symmetrical stretching modes indicated the dominance of the CH3 symmetrical stretching mode as a result of the cancellation of the contribution of the different CH2 groups along the chains. This is the result of nearly gauche defect free chains, indicative of high chain order. The alkyl chain of DLPC is 12 carbons long and these results were compared to longer alkyl chain length phosphatidylcholines, like dimyristoyl (DMPC), dipalmitoyl(DPPC), and distearoyl- (DSPC) phosphatidylcholines with alkyl chains 14, 16, and 18 carbons long, respectively. Surprisingly, it is observed that, at odds with the results obtained at the air–water interface, at the D2 O–CCl4 interface the longer the alkyl chain length is, the larger is the disorder [138]. A similar behavior has been observed at the solid–liquid interface [139]. The reason is that the organic solvent screens the chain– chain interactions leading to the reduction of the constraints within the chains. As opposed to the air–water interface, long alkyl chains at oil–water interfaces are more readily permeable to the organic solvent.

VII.

CONCLUSIONS

Liquid interfaces are widely found in nature as a substrate for chemical reactions. This is rather obvious in biology, but even in the diluted stratospheric conditions, many reactions occur at interfaces like the surface of ice crystallites. The number of techniques available to carry out these studies is, however, limited and this is particularly true in optics, since linear optical methods do not possess the ultimate molecular resolution. This resolution is inherent to nonlinear optical processes of even order. For liquid–liquid systems, optics turns out to be rather powerful owing to the possibility of nondestructively investigating buried interfaces. Furthermore, it appears that planar interfaces are not the only conﬁg-

FIG. 10 Vibrational sum frequency spectrum of saturated monolayers of dilauroyl- (DLPC), dimyristoyl- (DMPC), dipalmitoyl- (DPPC), and distearoyl-phosphatidylcholine (DSPC) at the D2 O–CCl4 interface at ambient temperature in the region of the methylene and methyl symmetrical stretches. (From Ref. 139, copyright American Chemical Society.)

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uration accessible to the experiment as recently demonstrated for spherical microscopic particles. The molecular resolution obtained by spectroscopy, combined with the surface speciﬁcity of nonlinear optics, has brought to light a detailed picture of interfaces in good agreement with the data obtained by other techniques like neutron reﬂection, for example, or calculations, molecular dynamics, or continuum models. One parameter of great interest has been the possibility of determining an angle of orientation for the compounds sitting at the interface. Unfortunately, information on the distribution function for this angle is difﬁcult to obtain by independent measurements. Nevertheless, this is of real interest for interfacial reactions involving light absorption like photosynthesis or interfacial ET reactions. This is probably the reason for the large predominance of reports appearing in the literature on this topic as compared to dynamics or reactivity at interfaces. The latter two ﬁelds will certainly emerge as two new directions as new laser sources with better time resolution appear on the market. SFG will certainly beneﬁt too from these technological advances as long wavelengths become easier to produce.

ACKNOWLEDGMENTS The author acknowledges the generous support of the Fond national Suisse and fruitful discussions at the Laboratoire d’Electrochimie of the Ecole Polytechnique Fe´de´rale de Lausanne with J. Rinuy, A. Piron, P. Galletto, D. J. Fermin, and H. H. Girault. The Laboratoire d’Electrochimie is part of the European Network on Training and Mobility of Researchers ‘‘Organization, Dynamics and Reactivity of Electriﬁed Liquid–Liquid Interfaces (ODRELLI).’’

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7 The Lattice-Gas and Other Simple Models for Liquid^Liquid Interfaces WOLFGANG SCHMICKLER Ulm, Ulm, Germany

I.

Department of Electrochemistry, University of

INTRODUCTION

The lattice gas has been used as a model for a variety of physical and chemical systems. Its application to simple mixtures is routinely treated in textbooks on statistical mechanics, so it is natural to use it as a starting point for the modeling of liquid–liquid interfaces. In the simplest case the system contains two kinds of solvent particles that occupy positions on a lattice, and with an appropriate choice of the interaction parameters it separates into two phases. This simple version is mainly of didactical value [1], since molecular dynamics allows the study of much more realistic models of the interface between two pure liquids [2,3]. However, even with the fastest computers available today, molecular dynamics is limited to comparatively small ensembles, too small to contain more than a few ions, so that the space-charge regions cannot be included. In contrast, Monte Carlo simulations for the lattice gas can be performed with 105 to 106 particles, so that modeling of the space charge poses no problem. In addition, analytical methods such as the quasichemical approximation allow the treatment of inﬁnite ensembles. Therefore the lattice-gas model has proved most useful for the study of those processes in which the ionic double layer plays a major role, and there are quite a few. So it has been used to investigate the interfacial capacity, electron and ion-transfer reactions, and even such complex processes as ion pairing and assisted ion transfer. Because of its simplicity we cannot expect this model to give quantitative results for particular systems, but it is ideally suited to qualitative investigations such as the prediction of trends and orders of magnitude for various effects. In the following we will review recent applications of the lattice-gas model to liquid– liquid interfaces. We will start by presenting the basics of the model and various ways of treating its statistical mechanics. Then we will present model calculations for interfacial properties and for electron- and ion-transfer reactions. It is one of the virtues of the latticegas model that it is sufﬁciently ﬂexible to serve as a framework for practically all processes at these interfaces. Of course, the lattice gas is not the only simple model that has been proposed for liquid–liquid interfaces. So we will conclude this review by a survey of several other models, which have usually been devised for certain aspects such as the interfacial capacity or ion transfer. Some of these models give a similar view of the interface, while others are radically different. 153

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THE BASICS OF THE LATTICE-GAS MODEL

All applications of the lattice-gas model to liquid–liquid interfaces have been based upon a three-dimensional, typically simple cubic lattice. Each lattice site is occupied by one of a variety of particles. In the simplest case the system contains two kinds of solvent molecules, and the interactions are restricted to nearest neighbors. If we label the two types of solvents molecules S1 and S2 , the interaction is speciﬁed by a symmetrical 2 2 matrix wij , where each element speciﬁes the interaction between two neighboring molecules of type Si and Sj . Whether the system separates into two phases or forms a homogeneous mixture, depends on the relative strength of the cross-interaction w12 with respect to the self-interaction terms w11 and w22 , which can be expressed through the combination: w ¼ w12 ðw11 þ w22 Þ=2

ð1Þ

If w=kT is large, the system separates into two phases: phase 1 contains mainly solvent molecules S1 and has only a low concentration of S2 , and phase 2 is mainly composed of S2 . If w is small, entropy wins and the systems forms one phase. Details will be discussed below. If the system separates, it can be extended to a model for the interface between two solutions by introducing ions. In the basic case the system contains a salt composed of cations K1þ and anions A 1 which is preferentially solvated by the solvent S1 , but badly solvable in solution 2, and a salt K2þ A 2 that is preferentially dissolved in solvent 2. This can be achieved by choosing suitable interaction parameters between the ions and the two solvents. In addition to the nearest-neighbor interaction, each ion experiences the electrostatic potential generated by the other ions. In the literature this has generally been equated with the macroscopic potential calculated from the Poisson–Boltzmann equation. This corresponds to a mean-ﬁeld approximation (vide infra), in which correlations between the ions are neglected. This approximation should be the better the low the concentrations of the ions.

III.

METHODS FOR TREATING THE LATTICE GAS

A.

The Mean-Field Approximation

The simplest treatment of the lattice-gas model is through the mean-ﬁeld or randommixing approximation, which is treated in a number of textbooks (see, e.g., Refs. 1 and 4). We give a short summary of its application to liquid–liquid interfaces, since it nicely illustrates under what conditions the phases separate. We consider a system composed of N1 solvent molecules S1 and N2 molecules S2 ; by Nij , i; j ¼ 1; 2 we denote the numbers of nearest-neighbor pairs fi; jg. The energy E of the mixture is then: E ¼ N11 w11 þ N22 w22 þ N12 w12

ð2Þ

The numbers of pairs are related to the numbers of molecules and the number m of nearest neighbours: mN1 ¼ 2N11 þ N12

ð3Þ

mN2 ¼ 2N22 þ N12

ð4Þ

The Lattice-Gas and Other Models

155

These relations can be used to introduce the quantities: E11 ¼ mN1 w11 =2

ð5Þ

E22 ¼ mN2 w22 =2

ð6Þ

and to rewrite the energy in the form: E ¼ E11 þ E22 þ N12 w

ð7Þ

where w has been deﬁned in the previous section. So far the treatment has been exact. The mean-ﬁeld approximation consists in assuming that the particles are randomly mixed, so that: N12 ¼ mNx1 x2

with

x1 ¼ N1 =N; x2 ¼ N2 =N

ð8Þ

where N is the total number of molecules, and the two mole fractions are related by x1 þ x2 ¼ 1. The Helmholtz free energy is obtained by adding the entropy term; this equals the Gibbs free energy, since the lattice is ﬁxed and does not change with pressure. Hence we obtain: G ¼ E11 þ E22 þ mNx1 x2 w þ NkT ðx1 ln x1 þ x2 ln x2 Þ

ð9Þ

The last two terms give the free energy of mixing, which we rewrite in the compact form: Gmix ¼ x1 ð1 x1 Þ þ x1 ln x1 þ ð1 x1 Þ lnð1 x1 Þ NkT

ð10Þ

where ¼ mw=kT. Figure 1 shows the Gibbs energy of mixing as a function of the composition x1 for various values of . All curves are symmetrical with respect to the line x1 ¼ 1=2. For > 2 the curve has a maximum at x1 ¼ 1=2 and two symmetrically placed minima. In this case the mixture will separate into two phases, each corresponding

FIG. 1 Gibbs energy of mixing as a function of the composition in the mean-ﬁeld approximation; the values of are from top to bottom: 3.0, 2.5, 2.0 (critical value), 1.0, 0.0, 0:5. (After Ref. 1 with permission from the author.)

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to a minimum. For < 2 there is only one minimum at x1 ¼ 1=2, and the mixture will not separate. While these results are qualitatively correct, in an exact treatment of the model the critical interaction is generally not at ¼ 2, but lies at a different value, which will depend on the geometry of the lattice and not only on the number of nearest neighbors. Also, this treatment says nothing about the structure of the interface. It can be extended by introducing gradient terms, which allow the calculation of density proﬁles for the two solvents [1,5]. Since there are more accurate methods available for this purpose we refer to the cited literature. B.

The Quasichemical Approximation

The mean-ﬁeld approximation neglects correlations between the particles and is therefore not very accurate. The quasichemical approximation improves upon this by accounting for the correlations between pairs of neighboring particles. We brieﬂy give the essence of this method, since it will be used in a few studies reported below. Detailed accounts can be found in the literature [6]. We consider the basic case in which the system is composed of two solvents. The formation of pairs (1,2) is supposed to be in equilibrium with pairs (1; 1) and (2; 2), and considered to be a reaction of the type: 2ð1; 2Þ Ð ð1; 1Þ þ ð2; 2Þ

ð11Þ

The equilibrium condition is expressed through the partition functions qij per pair of particles: q11 / expðw11 =kT Þ

q22 / expðw22 =kT Þ

q12 / 2 expðw12 =kT Þ

ð12Þ

all with the same proportionality constant; the extra factor of 2 in the last term is due to the twofold degeneracy. This gives: 1 N12 ¼ ðN11 N22 Þ1=2 expðw=kTÞ 2

ð13Þ

From this equation and Eqs. (2) and (4) the energy of the system can be obtained. The entropy is more difﬁcult to derive, and we refer to the literature [4,6]. Generally, the quasichemical gives better results than the mean-ﬁeld approximation, since it allows for local order. We note that for the three-dimensional lattice gas no exact analytical solution exists. C.

Monte Carlo Simulations

Monte Carlo simulations offer a convenient way of obtaining numerically exact results. If the short-range interactions are restricted to nearest neighbors, and the Coulomb interaction effected through the average macroscopic potential, quite large ensembles can be handled, and the incorporation of the space-charge regions poses no problems. The simulations are typically performed on a three-dimensional lattice, each site being numbered by a triple ðl; m; nÞ of integers. Let the region l < 0 be occupied by solution 1, l > 0 by solution 2. The simulations usually start with the particles pertaining to solution 1, i.e., the solvent S1 and, if present, the ions K1þ and A 1 , distributed randomly in l < 0; similarly, the particles of solution 2 are in the region l > 0. Equilibrium is attained through a Metropolis [7] algorithm, which can be implemented in the following way:

The Lattice-Gas and Other Models

157

During one Monte Carlo step each particle is sampled in turn; a nearest neighbor is chosen at random, and the energy E for an exchange of the two particles is calculated. If E < 0, the two particles are always exchanged. If E > 0, a random number r 2 ð0; 1Þ is chosen, and the exchange is effected if expðE=kTÞ > r. The ﬁrst N steps, with N being of the order of 104 –105 , are discarded, and in the subsequent steps the distributions of the particles and of the electrostatic potential, and other properties of the system are sampled. The interface can be charged by adding an excess number of cations to one phase, and an equal number of anions to the other phase. For certain purposes extra particles may be added to the basic setup. The Monte Carlo method is quite ﬂexible, and for reasonable ensemble sizes such as 100 20 20 particles, it is also quite fast, a typical run taking no more than a few hours on a decent computer.

IV.

RESULTS OF MODEL CALCULATIONS FOR THE LATTICE GAS

A.

Structure of the Interface

We ﬁrst consider the simplest system consisting of two pure, immiscible solvents. Within the lattice-gas model the energetics of the system on a particular lattice are governed by the single parameter w [see Eq. (1)], which determines the structure of the interface and the particle proﬁles. The results presented in this section are for a simple cubic lattice. Monte Carlo simulation shows [8] that at a given instance the interface is rough on a molecular scale (see Fig. 2); this agrees well with results from molecular-dynamics studies performed with more realistic models [2,3]. When the particle densities are averaged parallel to the interface, i.e., over n and m, and over time, one obtains one-dimensional particle proﬁles f1 ðlÞ and f2 ðlÞ ¼ 1 f1 ðlÞ for the two solvents S1 and S2 , which are conveniently normalized to unity for a lattice that is completely ﬁlled with one species. Figure 3 shows two examples for such proﬁles. Note that the two solvents are to some extent soluble in each other, so that there is always a ﬁnite concentration of solvent 1 in the phase

FIG. 2 Snapshot of the interface of a gas on a simple cubic lattice with dimensions 100 16 16 for w=kT ¼ 0:6; the average position of the interface is between l ¼ 50 and l ¼ 51.

158

Schmickler

FIG. 3 Fig. 2.

Density proﬁle f2 ðlÞ of the solvent S2 for two different values q=kT; other parameters as in

that consists mainly of solvent 2, and vice versa. The smaller w, the larger this solubility – remember that for sufﬁciently small values of w the two solvents mix completely. The width of the interface can be deﬁned by ﬁtting these proﬁles to a suitable function; a possible choice is: f ðxÞ ¼ fb þ

1 2fb ð1 þ tanhðx xs Þ=Þ 2

ð14Þ

where fb is the bulk concentration of solvent S1 in phase 1, xs is the position of the interface, and measures the width of the interface. There is a simple correlation between the width of the interface, the surface energy, and the miscibility of the solvents (see Table 1): the lower the surface energy, the wider is the interface, and the greater the miscibility of the solvents. This relation, which is intuitively expected, has also been observed in a density-functional study of an ensemble of dipoles [5], on which we will report below (see Section V.B). In the simple systems discussed so far the particle proﬁles are necessarily symmetrical with respect to the interface. This need no longer be the case for more complicated systems with several particles. As an example we show in Fig. 4 the particle proﬁles at the interface between an aqueous solution and a PVC-based membrane. B.

The Interfacial Capacity

The simplest model for the ionic distribution at liquid–liquid interfaces is the Verwey– Niessen model [10], which consists of two Gouy–Chapman space-charge layers back to TABLE 1 Interaction Parameter w, Decay Length (in Lattice Constants), and Bulk Composition fb for a Lattice Gas. Other System Parameters as in Fig. 2 w 0.5 0.6 0.7

fb

2.1 1.2 0.8

0.885 0.956 0.979

The Lattice-Gas and Other Models

159

FIG. 4 Particle proﬁle at the interface between an aqueous solution (open triangles) and a PVCbased membrane (full squares). Data taken from [9].

back. One would expect this model to work well at low ionic concentrations, however, there one often ﬁnds that the interfacial capacity is higher than that predicted by Verwey and Niessen. This is illustrated in Fig. 5, which shows the interfacial capacity at the potential of zero charge for several 10 mM solutions in contact with an aqueous solution. In contrast, at metal–solution interfaces the capacity is typically lower than predicted by the Gouy–Chapman theory.

FIG. 5 Comparison of the experimental capacity Cexp and the Verwey–Niessen capacity CVN at the potential of zero charge for 10 mM ionic solutions in various solvents. Details of these systems can be found in Ref. 11.

160

Schmickler

An explanation of this fact was offered by Pereira et al. [11] and by Huber et al. [12]: the overlap of the two solvents at the interface entails an overlap of the two space-charge regions. Thus the average separation between the opposing charges is reduced, and the capacity enhanced. Both groups performed explicit calculations; the former employed the quasichemical approximation, while the latter performed Monte Carlo simulations. To some extent these two techniques complement each other: the quasichemical approximation should be good at low electrolyte concentrations, while the Monte Carlo simulations, because of the ﬁnite ensemble size, are performed for more concentrated solutions. We ﬁrst summarize the work of Pereira et al. [11]. The authors assume that the distribution of the two solvents is ﬁxed, and given by: ( 1 12 expðx=Þ for x < 0 f1 ðxÞ ¼ ð15Þ 1 for x > 0 2 expðx=Þ where measures the width of the interface. The nearest-neighbor interactions of the ions with the solvents have to be chosen þ such that the ions K1þ and A 1 are preferentially solvated in solvent 1, K2 and A2 in solvent þ 2. The simplest choice is to set the interaction of K1 and A1 with S1 equal u, and with solvent S2 equal to u, where u < 0. Similarly, the interactions of K2þ and A 2 with S1 and S2 are u and u, respectively. Of course, nonsymmetrical choices are also possible, and are discussed in the original paper. The interaction parameter u determines the energy of transfer of the ion between the two pure solvents, which is 2mu. The energy of the cations K1þ can be written as: þ þ E1þ ¼ uN11 uN12

ð16Þ

where N1jþ ði ¼ 1; 2Þ denotes the number of pairs of ions K1þ and solvent molecules i. Within the quasichemical approximation the number of pairs can be expressed through the numbers N1þ of cations K1þ and solvent molecules N1 and N2 : þ N11 / N1þ N1 exp u

ð17Þ

þ N12 / N1þ N2 exp u

ð18Þ

with the same constant of proportionality. For low ionic concentrations: þ þ N11 þ N12 ¼ mN1þ

ð19Þ

From Eqs. (18) and (19) the numbers of pairs are easily calculated: þ N11 ¼ mN1þ þ ¼ mN1þ N12

f1

f1 e u u e þf

f1 e

f2 e u

2e

u

u

þ f2 e u

ð20Þ ð21Þ

where ¼ 1=kT. The electrochemical potential of the ion is obtained by taking the energy per particle, and by adding an entropy term and the electrostatic interaction per particle; for the entropy Pereira et al. take the expression for an ideal solution. This gives: ~ þ 1 ¼ mu

f1 e u f2 e u þ kT ln cþ 1 þ e0

f1 e u þ f2 e u

ð22Þ

where cþ 1 denotes the concentration, and the electrostatic potential. All ions are assumed to be monovalent. The distribution of the cation K1þ near the interface is obtained from

The Lattice-Gas and Other Models

161

the condition that its electrochemical potential must be the same as in the bulk of solvent S1 , where it has the value: ~ þ 1 ð1Þ ¼ mu þ kT ln c0 þ e0 ð1Þ

ð23Þ

A short calculation gives: þ cþ 1 ðxÞ ¼ c0 exp e0 ½ ðxÞ ð1Þ g1 ðxÞ

ð24Þ

where ðxÞ ¼ exp 2 mu gþ 1

f2 e u f1 e u þ f 2 e u

ð25Þ

Similar equations can be derived for the other ions. The charge density ðxÞ is then obtained by adding the charge densities pertaining to all four kinds of ions. Both ðxÞ and the electrostatic potential ðxÞ are calculated by solving the Poisson equation selfconsistently, and the particle distributions then follow by substituting ðxÞ into Eq. (25) and the respective equations for the other ions. As an example Fig. 6 shows the distribution of the ions for a potential difference of ¼ ð1Þ ð1Þ ¼ kT=e0 between the two bulk phases. In these calculations the dielectric constant was taken as ¼ 80 for both phases, and the bulk concentrations of all ions were assumed to be equal. This simpliﬁes the calculations, and the Debye length LD , which is the same for both solutions, can be used to scale the x axis. The most important feature of these distributions is the overlap of the space-charge regions at the interface, which is clearly visible in the ﬁgure.

FIG. 6 Normalized distribution cðxÞ=c0 of the ions for a potential drop of 0 =kT ¼ 1. The full lines give the distribution of the majority ions; in the region x < 0 these are the anions, in x > 0 these are the cations. The dashed lines give the distributions of the counterions. System parameters: m ¼ 4, u ¼ 3kT.

162

Schmickler

The charge density that is stored at the interface is obtained from the particle proﬁles: ð1 ð1 e0 cþ ðxÞ c ðxÞ ¼ e0 cþ ð26Þ ¼ 1 1 2 ðxÞ c2 ðxÞ 1

1

The interfacial capacity is then obtained by calculating the proﬁles for various potential drops and subsequent differentiation. Figure 7 shows several examples of capacity– potential characteristics for several widths of the interface. Obviously, the wider the interface, the higher the capacity. In all cases investigated it was higher than that calculated from the Verwey–Niessen model, in which: 1 e

CVN ¼ C0 cosh 0 2 4kT

(Verwey--Niessen)

ð27Þ

with C0 ¼ 0 =LD . In the ﬁgure, all capacities have been normalized by dividing through C0 . Huber et al. [12] investigated the same model by Monte Carlo simulations; however, they focused on a different aspect: the dependence of the interfacial capacity on the nature of the ions, which in this model is characterized by the interaction constant u. Samec et al. [13] have observed the following experimental trend: the wider the potential window in which no reactions take place, the lower the interfacial capacity. Since the width of the window is determined by the free energy of transfer of the ions, which is 2mu in this model, the capacity should be lower, the higher juj. In order to check this prediction, Huber et al. performed simulations on a lattice of dimensions 200 20 20; the lattice constant was taken as 4 A˚, and a dielectric constant of ¼ 80 was assumed throughout the system. Since a fair number of ions is needed to obtain good statistics, the ionic concentrations in this study are of the order of 0.1 M. Figure 8 shows the distribution of the ions K1þ and A 1 for two different values of the interactions constant u. The smaller juj, the lower is the repulsion of these ions from phase

FIG. 7 Normalized interfacial capacity versus the potential drop for various widths of the interface. (1) =LD ¼ 0:2; (2) =LD ¼ 0:1; (3) =LD ¼ 0:05; (4) Verwey–Niessen capacity.

The Lattice-Gas and Other Models

163

FIG. 8 Distribution of the cations Kþ 1 and anions A1 at the interface for an excess-charge density of 0.0225 C m2 ; the full symbols are for u ¼ 3kT, the open symbols for u ¼ 1kT. The Debye length was LD ¼ 13:9 A˚, the solvent interaction w ¼ 0:55kT. The lines are meant as guides for the eye.

2, and the larger is the overlap of the space-charge regions; this entails a higher capacity, as can be seen from Fig. 9. These capacity curves illustrate also another effect that becomes important at higher ionic concentrations: when the lattice spacing is of the same order of magnitude as the Debye length, the size of the ions can no longer be neglected, as is usually done in the quasichemical and similar approximations. This ﬁnite-size effect reduces the interfacial capacity; therefore, depending on the other system parameters, the capacity can be either higher or lower than predicted by the Verwey–Niessen model. Thermodynamics show that the surface tension becomes lower when the interface is charged; this should lead to a widening of the interface. This has indeed been observed by

FIG. 9 Interfacial capacity for various ion–solvent interactions. System parameters: (1) u ¼ 3kT, (2) u ¼ 2kT; (3) u ¼ 1kT. The crosses denote the Gouy–Chapman capacity. Other parameters as in Fig. 8.

164

Schmickler

TABLE 2 Interfacial Width for Various Energies of Transfer of the Ions; the Other Parameters Are the Same as in Fig. 8 u ðkTÞ 1 1 2 2 3 3

ðVÞ

(A˚)

0 0.091 0 0.1 0 0.1

7.03 8.85 7.03 7.42 7.03 7.16

Huber et al. [12] (see Table 2). Another way of explaining this effect is the following: when the interface is charged the ions experience a stronger ﬁeld that pulls them toward the other side. Thus they penetrate further into the other solution, and pull a few of their surrounding molecules with them. As expected, this effect is more marked when the free energy of transfer of the ions is small, because then the energy barrier at the interface is lower. C.

Interfacial Ion Pairing

As noted above, the capacity of liquid–liquid interfaces depends on the nature of the ions dissolved in the two adjoining phases. In some cases the capacity is related o the free energy of transfer of the ions involved, but in other cases quite strong dependencies are observed which can be explained by a tendency to form ion pairs at the interface. Evidence for this effect, which was ﬁrst discussed by Hajkova et al. [14], was obtained in a paper by Cheng et al. [15], who observed marked changes in the capacity when they varied the composition of the aqueous phase. Further examples were provided by Pereira et al. [16], who also performed explicit calculations for ion pairing based on the lattice-gas model. Indeed, ion pairing can be introduced quite easily into the lattice gas by letting one pair of ions pertaining to different phases, e.g., K1þ and A 2 , interact through an attractive potential v < 0. The resulting model can be treated within the quasichemical approximation [16] by calculating the number of pairs of K1þ and A 2 along the line of Eqs. (16) to (21), or by Monte Carlo simulations [17]. Both approaches give qualitatively quite similar results. We review the results of the simulations, which are more recent. Technically, these simulations are very similar to those of Huber et al. [12]; the major difference is the introduction of the attractive potential between the pairing ions. In addition, these authors introduce different dielectric constants 1 and 2 for the two solutions. Near the interface the dielectric constant varies locally according to the simple prescription: x ¼ 1 f1 ðxÞ þ 2 f2 ðxÞ

ð28Þ

In the simulation the values 1 ¼ 80 and 2 ¼ 10 were taken. When phase 1 is negatively charged, the ions K1þ and A 2 are repelled from the interface, and the particle distribution is the same as in the absence of ion pairing. However, when phase 1 is positively charged, these ions are driven towards the surface, where they may form pairs. Hence their concentration at the interface is enhanced (see Fig. 10). This effect is the larger, the higher the excess-charge density, since the probability of

The Lattice-Gas and Other Models

165

FIG. 10 Distribution of the ions Kþ 1 and A2 in the presence (full lines) and in the absence (dashed lines) of ion pairing. In the former case, the ionic interaction parameter was taken as v ¼ 9kT. The surface-charge density was taken as ¼ 2:34 C cm2 in phase 1.

ion pairing depends on the product of the concentrations of K1þ and A 2 , and hence roughly on the square of the excess charge. Ion pairing increases the charge that is stored at a given potential, and hence the interfacial capacity. The capacity characteristics in Fig. 11 show the asymmetry that is quite typical for ion pairing [15].

D.

Ion-Transfer Reactions

In Section IV.B the energy of an ion was calculated by a simple version of the quasichemical approximation. The same procedure can be used to calculate the potential of mean force pmf ðxÞ of an ion [18], which is the average potential that the ion experiences as a function of its position x in the direction perpendicular to the surface. This consists of two

FIG. 11 Interfacial capacity as a function of the total potential drop in the presence and in the absence (solid line) of ion pairing. Dotted line: v ¼ 9kT; dashed line: v ¼ 10kT.

166

Schmickler

components: the chemical part, which in the lattice-gas model is due to the interaction with the nearest neighbors, and the electrostatic part. From Eqs. (20) and (21) we obtain:

pmf ðxÞ ¼ mu

f1 e u f2 e u þ ze0 ðxÞ f1 e u þ f2 e u

ð29Þ

where the ﬁrst term is the chemical part; z is the charge number of the ion. The potential of mean force is similar to the electrochemical potential, but it does not depend on the concentration; it is the potential that a single ion experiences as it moves toward, and possibly across, the interface. In the two bulk phases the potential of mean force is constant, but it may vary near the interface. The difference in the bulk values of the chemical part is the free energy of transfer of the ion, which in our model is 2mu (we assume u < 0). Let us consider the situation in which the ion-transfer reaction is in equilibrium, and the concentration of the transferring ion is the same in both phases; the system is then at the standard equilibrium potential 00 . In this case the potential of mean force is the same in the bulk of both phases; the chemical and the electrostatic parts must balance: 0 ¼ 2mu

at equilibrium

ð30Þ

Both terms vary near the interface: the chemical term rises by an amount 2mu over a region of width 2, while the electrostatic term drops by the same amount over a region, whose width is given by the two Debye lengths. Figure 12 shows the case where the Debye lengths are the same in both phases. Unless the concentration of the background electrolyte is very high, LD > . Therefore the potential of mean force ﬁrst decreases as the ion moves from the bulk of phase 1 towards the interface, reaches a minimum, and rises rapidly in the region where the two solvents mix. It attains its maximum when the ion is mostly surrounded by solvent 2, and then decreases towards the bulk value. On application of an overpotential the free energy of the reaction is changed, and so is the potential of mean force. A positive overpotential lowers the maximum and deepens the minimum; the reverse is true for negative overpotentials (see Fig. 13). For very high overpotentials the two extrema disappear. Thus a very high positive overpoten-

FIG. 12 The potential of mean force for an ion-transfer reaction at equilibrium: (1) chemical term; (2) electrostatic term; (3) total potential. System parameters: u ¼ 0:5kT, n ¼ 4, =LD ¼ 0:1.

The Lattice-Gas and Other Models

167

FIG. 13 The potential of mean force for various overpotentials. (1) 0 ¼ 2kT; (2) 0 ¼ kT; (3) 0 ¼ 0; (4) 0 ¼ 2kT; (5) 0 ¼ 2kT. The system parameters are the same as in Fig. 12.

tial leads to a barrierless transition; in this case ion transport is likely to be rate determining. Conversely, at high negative overpotentials the transition occurs without activation. From the potential of mean force the rate constant can be calculated. We ﬁrst assume that transition-state theory is valid, and approximate the potential near the minimum and near the maximum by parabolas. The rate of escape of a particle from the well over the barrier is then [19]: ¼

! v vmin exp max 2 kT

ð31Þ

where ! is the frequency at the bottom of the well, and vmin and vmax are the values of the potential at the minimum and at the maximum, respectively. The reaction rate is given by the product of with the concentration cs of the ions in the bulk. The latter are in equilibrium with the well – otherwise the rate is determined by mass transport. Setting the chemical potential in the well equal to that in the bulk gives: rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2kT v cs ¼ c0 ð32Þ exp min 2 kT m! where c0 is the concentration in the bulk, and m the effective mass. The rate constant is then: rﬃﬃﬃﬃﬃﬃﬃﬃﬃ kT v v ð33Þ k¼ exp max k0 exp max 2m kT kT Both the frequency of the well and its depth cancel, so that the free energy of activation is determined by the height of the maximum in the potential of mean force. The height of this maximum varies with the applied overpotential (see Fig. 13). To a ﬁrst approximation this dependence is linear, and a Butler–Volmer type relation should hold over a limited range of potentials. Explicit model calculation gives transfer coefﬁcients between zero and unity; there is no reason why they should be close to 1=2. For large overpotentials the barrier disappears, and the rate will then be determined by ion transport.

168

Schmickler

If friction plays a role in the crossing of the energy barrier, the reaction is slower than predicted by transition-state theory. According to Kramers’ theory [20] the preexponential factor must then be replaced by: k00 ¼

k ; !b 0

with

¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ !2b þ 2 =2

ð34Þ

where k0 is the preexponential factor in the transition-state theory [see Eq. (33)], !b is the barrier frequency, and the coefﬁcient of friction on the barrier. In the overdamped case, when !b , the preexponential factor simpliﬁes to: k00 ¼

!b k 0

ð35Þ

The rate constant is then inversely proportional to the coefﬁcient of friction. Unfortunately, at the present time the experimental results for ion-transfer reactions are contradictory, so that it is not possible to verify the predictions of this model. Also, this model is only valid if the rate is determined by the ion-transfer step, and not by transport, and if the concentration of the supporting electrolyte is sufﬁciently low so that the extension of the space-charge regions is less than the width of the region where the two solvents mix. These conditions are not always fulﬁlled in experiments. The above model can be extended to assisted ion transfer, in which the ion forms a complex with a suitable ionophore. The various mechanisms for such reactions have been classiﬁed by Shao et al. [21] and reviewed by Girault [22]. Schmickler [23] has examined the case of transfer by interfacial complexation, which is marked by the following reaction sequence (see Fig. 14): The transferring ion moves from the bulk of solution 1 towards the interface with solution 2, in which it is poorly soluble. At the interface it reacts with an ionophore from solution 2, and then the complexed ion is transferred towards the bulk of solution 2. The reaction is again governed by the potentials of mean force for the participating particles. A typical situation is shown in Fig. 15: the reacting ion has a large energy of transfer from solution 1 to solution 2, so that the transfer of the uncomplexed ion is highly unfavorable. In contrast, the ionophore and the complexed ion are highly soluble in solution 2, but poorly soluble in solution 1. The most favorable reaction path is therefore along the potential of mean force of the ion towards the interface; there the ion reacts with

FIG. 14

Ion transfer assisted by interfacial complexation (schematic).

The Lattice-Gas and Other Models

169

FIG. 15 Potential of mean force for the ion, the ionphore, and the complexed ion [23]. The Debye lengths for the two solutions have been taken as LD ¼ 30 A˚, and width of the interface as 3 A˚. The absolute value of the free energy of transfer was taken as 6kT for all particles, and the potential drop across the interface as 0 ¼ 3kT.

the ionophore, and the complexed particle can then move with little or no energy of activation to the bulk of phase 2. The rate of the ion transfer is governed by the complexation reaction, whose rate constant should not depend on potential since it is a purely chemical reaction. However, the concentrations of the reactant change with potential. Typically, the ionophore is uncharged, so that a change in the potential drop affects only the concentration of the ions at the interface. If the thickness of the interface is neglected, the concentration of the ion at the interface is given by: 0 z s cs ¼ c0 exp ð36Þ kT where the potential s at the interface can, to a ﬁrst approximation, be calculated from the Verwey–Niessen theory. Explicit calculations within the lattice-gas model [23] show some quantitative corrections to these simple relations, but they also support the assertion that the change of the rate with potential is governed by changes in the ionic concentration at the interface.

E.

Electron-Transfer Reactions

Electron-transfer reactions at liquid–liquid interfaces have the form: ð2Þ ð1Þ ð2Þ Oxð1Þ 1 þ Red2 Ð Red1 þ Ox2

ð37Þ

where the subscript labels the chemical species, and the superscript indicates the solution in which it is situated. They are just a special case of electron transfer in solutions, and should therefore, to a ﬁrst approximation, obey the theories of Marcus [24] and Hush [25]. So the rate of electron transfer from a reduced species labeled , situated at r , and an oxidized species at r can be written in the form:

170

Schmickler

ðE FÞ2 r ¼ A r r exp s 4kT

ð38Þ

where the preexponential factor A depends on the electronic overlap, Es is the energy of reorganization, and F the reaction free energy. The latter contains a chemical and an electrostatic term: F ¼ F 0 0 ðz Þ ðz Þ ð39Þ and thus depends on the position of the reactants. In principle, the energy of reorganization could also vary with position, but this dependence is expected to be small [26]. The preexponential factor usually decays exponentially with the separation of the reactants: A ¼ B exp r r ð40Þ where the inverse decay length is of the order of 1 A˚1 . In order to obtain an expression for the rate constant, we introduce the normalized red ox red particle densities ox ðzÞ and ðzÞ, which obey the conditions ð1Þ ¼ ð1Þ ¼ 1. They are related to the potential of mean force through: ðzÞ ¼ exp

pmf ðzÞ kT

ð41Þ

and can therefore be calculated from the lattice-gas model. With the aid of these quantities the rate constant for electron transfer from solution 2 to solution 1 can be written in the form: ð ð red 0 0 ket ¼ B dz dr 0 ox ðzÞ ðz Þ exp ðjr r jÞ ð42Þ fEs F 0 þ e0 ½ ðzÞ ðz 0 Þg2 exp 4kT The integrals have to be performed over the region in which the two reactants do not overlap. Equation (42) can serve as a basis for the calculation of the reaction rate and of current–potential curves. However, some basic features can be obtained by simple considerations. The two reactants meet at the interface in the region where the two solvents mix. Typically, the width of this region will be much smaller than the Debye lengths of the two solutions. Therefore the potential drop between the two reactants is small, and does not change much with the total potential . So a change of affects mainly the concentration of the reactants at the interface, and not the driving force for the reaction [22,26]. In this respect electron-transfer reactions at liquid–liquid interfaces resemble those at the interface between a semiconductor and an electrolyte solution. If the variation of the reactants’ concentration at the interface is calculated from the Verwey–Niessen theory, the following expression for the transfer coefﬁcient results:

red ¼ zox 1 þ z2

þ coshð =2Þ zred 2 1 þ 2 þ 2 coshð =2Þ

with

¼

2 L1D 1 L2d

ð43Þ

red In the symmetrical case, where ¼ 1, this simpliﬁes to ¼ ðzox 1 z2 Þ=2, and the transfer coefﬁcient is independent of the potential. In the general case the transfer coefﬁcient varies, and Tafel plots are expected to exhibit some curvature. These considerations are borne out by explicit model calculations (see Fig. 16), which give results close to those predicted by simple application of the Verwey–Niessen

The Lattice-Gas and Other Models

171

FIG. 16 Current–potential curves for various charge numbers of the reactants. System parameters: red ox red for curves (1)–(3) Debye lengths L1 ¼ L2 ¼ 40 A˚, 1 ¼ 2 ; (1) zox 1 ¼ 1, z2 ¼ 1; (2) z1 ¼ 1, z2 ¼ 0; ox red ox red ˚ (3) z1 ¼ z2 ¼ 0; (4) L1 ¼ L2 ¼ 10 A, 1 ¼ 2 , z1 ¼ z2 ¼ 0.

model. The deviations are larger, the greater the width of the interface, the smaller the Debye lengths, and the larger the reactants. Experimental results for electron-transfer reactions are contradictory at the present time: investigations by Ding et al. [27] indicate that a change in the potential drop affects mainly the reactants’ concentration and only to a minor extent the driving force. This is in contrast to results by Tsionsky et al. [28] which suggest that only the driving force and not the concentration is changed. Very recently Liu and Mirkin [29] studied electron transfer from neutral zinc porphyrin molecules to an aqueous phase and found a potential-independent rate constant; this indicates that in this system neither the driving force nor the concentration for the neutral reactant is changed, which is in line with the model presented above. Perhaps this important issue will have been clariﬁed by the time this book appears.

V.

OTHER MODELS FOR LIQUID–LIQUID INTERFACES

So far, the lattice gas has been the only model that makes predictions both about structure and reactions at liquid–liquid interfaces. There are however, various other models for particular features of these interfaces. Some of them give similar, others give contradictory results. In the following, we brieﬂy review a few of these models. A.

The Modiﬁed Verwey–Niessen Model

The Gouy–Chapman theory for metal–solution interfaces predicts interfacial capacities which are too high for more concentrated electrolyte solutions. It has therefore been amended by introducing an ion-free layer, the so-called Helmholtz layer, in contract with the metal surface. Although the resulting model has been somewhat discredited [30], it has been transferred to liquid–liquid interfaces [31] by postulating a double layer of solvent molecules into which the ions cannot penetrate (see Fig. 17); this is known as the modiﬁed Verwey–Niessen model. Since the interfacial capacity of liquid–liquid interfaces is

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Schmickler

FIG. 17

The modiﬁed Verwey–Niessen model.

often higher than predicted by the simple Verwey–Niessen model, there is little reason to introduce such an ion-free layer; nevertheless, this model is still quite popular. In itself, the modiﬁed Verwey–Niessen model has little predictive value, since the properties of the dividing layer are not known, and its thickness and dielectric constant can be ﬁtted to any experimental data. It has been combined with the modiﬁed Poisson–Boltzmann theory [32], in particular with the version known as MPB4 [33,34]. However, even the combined model still has an adjustable parameter, so that its validity is difﬁcult to assess. B.

Density-Functional Theory

Density-functional theory is best known as the basis for electronic structure calculations. A variant of this theory can be used to calculate the structure of inhomogeneous ﬂuids [35]: the free energy of the ﬂuid is expressed as a functional of the density of the various components; a theorem asserts that this functional attains its minimum for the true density proﬁles. Henderson and Schmickler [5] applied this formalism to the interface between two liquids. They considered an ensemble containing two kinds of spherical molecules which interact through their dipole moments and through a Yukawa potential. The free energy for the homogeneous system was calculated from perturbation theory, and the phase diagram was determined. Whether a separation into two phases occurs or not depends on the system parameters. Roughly speaking, phase separation is favored when the two dipole moments differ greatly, and when the cross-interaction between different molecules is much smaller than the self-interaction between identical molecules. When the two phases separate the distribution of the solvent molecules is inhomogeneous at the interface; this gives rise to an additional contribution to the free energy, which Henderson and Schmickler treated in the square gradient approximation [36]. Using simple trial functions, they calculated the density proﬁles at the interface for a number of system parameters. The results show the same qualitative behavior as those obtained by Monte Carlo simulations for the lattice gas: the lower the interfacial tension, the wider is the interfacial region in which the two solvents mix (see Table 3). It would be desirable to extend this model to electrolyte solutions, but it is extremely difﬁcult to calculate a free-energy functional that accounts for the presence of ions. C.

Capillary Waves

Both the lattice-gas model and computer simulations predict that the interface is rough on a molecular scale. If this roughness is not too large, the interface can be represented by a

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173

TABLE 3 Interfacial Widths, Bulk Composition, and Interfacial Tension Es in erg cm2 at the Interface Between Two Dipolar Liquids [5]. x01 Denotes the Mole Fraction of Solvent Si in Phase i (A)

x01

x02

Es

3.24 5.23 7.40 13.80

1.00 0.96 0.91 0.85

1.00 0.96 0.92 0.84

153.0 44.0 20.0 6.5

function Sðx; yÞ at a particular moment of time. The two-dimensional Fourier components AðqÞ of this surface function are known as capillary waves; q is a two-dimensional wave vector. Thus, a rough surface can be considered as a superposition of capillary waves, which are present at all wavelengths. Of course, they cannot be observed as traveling waves, but only as a ﬂuctuating surface roughness. The energy stored in a capillary wave is proportional to the surface area it creates. This entails a prediction for the distribution of the amplitudes:

AðqÞA ðqÞ ¼

kT Es jqj2

ð44Þ

where the angular brackets denote thermal expectation values. This relation has indeed been observed in computer simulations of liquid–liquid interfaces [2,3]. The concepts of capillary waves and surface roughness can also be used to explain how the surface roughness increases the interfacial capacity beyond the Verwey–Niessen value. For this purpose Pecina and Badiali [37] have solved the linear Poisson–Boltzmann equation across the interface between two solutions with different dielectric constants and Debye lengths separated by a corrugated surface. A major difﬁculty is the boundary condition at the rough interface, which these authors handle by a perturbation expansion treating the roughness as a small parameter. Following Daikhin et al. [38], who had considered a similar problem for rough metal electrodes, Pecina and Badiali express the deviation from the Verwey–Niessen theory through a roughness function R~ ði ; i Þ, which depends on the dielectric constants of the two solutions and on their Debye inverse lengths i ¼ 1=Li . So the interfacial capacity per area is written as: C ¼ CVN R~ ði ; i Þ

ð45Þ

Obviously, if the two Debye lengths are much larger than the average height of the surface corrugation, the roughness plays no role, so that the roughness function tends to unity in that limit. On the other hand, when the two Debye lengths are much smaller than the corrugation – a case which should be difﬁcult to obtain in practice – the roughness function is the ratio of the geometrical area to the area of the ﬂat surface. As an illustration Pecina and Badiali consider a simple one-dimensional corrugation of the form: SðxÞ ¼ h cos kx

ð46Þ

Figure 18 shows the dependence of the roughness function on the two dimensionless parameters 1 h and 2 h. In accord with the limits considered above, the roughness function increases monotonically with both variables.

174

Schmickler

FIG. 18 Roughness function in dependence of the dimensionless parameters 1 h and 2 h. The dielectric constants have been taken as 1 ¼ 80, 2 ¼ 10. The ratio of the geometrical area to that of the ﬂat surface was taken as 1.62 [37].

Recently, these authors have treated speciﬁc adsorption at corrugated liquid–liquid interfaces [39]; however, because of the complicated mathematics involved this work does not fall under the heading ‘‘simple models.’’ Also, Urbakh et al. [40] have extended the results for the interfacial capacity to the nonlinear region. D.

Kakiuchi’s Model for Ion Transfer

In the lattice-gas model, as treated in Section IV.D above, ion transfer is viewed as an activated process. In an alternative view it is considered as a transport governed by the Nernst–Planck or the Langevin equation. These two models are not necessarily contradictive: for high ionic concentrations the space-charge regions and the interface have similar widths, and then the barrier for ion transfer may vanish. So the activated mechanism may operate at low and the transport mechanism at high ionic concentrations. Kakiuchi [41] has examined the transport mechanism in some detail. He considers the interface as a region of thickness in which friction is considerably larger than in the bulk. The transferring ion has different electrochemical potentials ~ i ði ¼ 1; 2Þ in the two bulk phases; as usual, they can be decomposed into their chemical and their electrostatic parts: ~ i ¼ i þ ze0 i , where z is the charge number of the ion. When the system is in equilibrium, and the concentration of the ion is the same in the two solutions, then the difference in the inner potential is given by: ¼ ð47Þ 1 2 =z0 where the superscript denotes the standard state. serves as the reference potential drop. When the actual potential drop differs from this value, the electrostatic driving force is given by: f ¼

ð48Þ

The drop in the electrochemical potential across the boundary layer is assumed to be linear, and the diffusion coefﬁcient D taken as constant. Following the work of

The Lattice-Gas and Other Models

175

FIG. 19 Normalized current density jn ¼ j=Dc1 as a function of the normalized driving force y according to Kakiuchi [41]. Full line: c2 ¼ c1 ; dashed line: c2 ¼ c1 =2; dotted line: c2 ¼ c1 =10:

Goldman [42], Kakiuchi derives the following approximate solution to the Nernst–Planck equation for the ion transport across the interface and the concomitant current density: D yey yey c c j ¼ zF ð49Þ sinh y 1 sinh y 2 where ci is the concentration of the ion in the indicated phase, and zF f ð50Þ 2RT is the normalized electrostatic driving force. The two terms in the square brackets in Eq. (49) denote the difference between a forward and a backward current. The current–potential relationship predicted by Eqs. (49) and (50) differs strongly from the Butler–Volmer law. For y 1 the current density is proportional to the electrostatic driving force. Further, the shape of the current–potential curves depends on the ratio c1 =c2 ; the curve is symmetrical only when the two bulk concentrations are equal (see Fig. 19), otherwise it can be quite unsymmetrical, so that the interface can have rectifying properties. Obviously, these current–potential curves are quite different from those obtained from the lattice-gas model. As we have noted in Section IV.D, there are no reliable experimental data for iontransfer reactions, so that a comparison with experiment is not possible at this time. y¼

VI.

CONCLUSIONS

The simple models that we have reviewed here help in visualizing the structure of liquid– liquid interfaces and the reactions that occur at them. In addition, they predict trends and orders of magnitudes. So far, the lattice gas has been unique in that it can serve as a unifying model for practically all processes at the interface. The other models that we have discussed aim to explain particular features. Several models are just different ways of representing the same physical phenomenon. For example, the lattice-gas model, capillary waves, and the density functional calculations presented above basically have the same view of the interface. However,

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other models are not compatible with each other; for example, the modiﬁed Verwey– Niessen theory cannot be reconciled with the lattice-gas model for the interfacial capacity. Unfortunately the development of models is hindered by a lack of reliable experimental data. For example, the rates of ion-transfer reactions measured at different times and by different groups vary widely. Also, it has been suggested that the high interfacial capacities that are measured in certain systems are an experimental artifact [13]. While this is frustrating for the researcher who wants to decide between competing models, it can also be viewed as a sign that the electrochemistry of liquid–liquid interfaces is an active ﬁeld, where fundamental issues are just being explored.

ACKNOWLEDGMENT Financial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

W. Schmickler, Interfacial Electrochemistry, Oxford University Press, Oxford, New York, 1996. I. Benjamin. Chem. Rev. 96:1449 (1996). I. Benjamin. Ann. Rev. Phys. Chem. 48:407 (1997). T. L. Hill, Introduction to Statistical Thermodynamics, Addison-Wesley, Reading, Mass., 1960. D. Henderson, and W. Schmickler. JCS Faraday 92:3839 (1996). R. H. Fowler and E. A. Guggenheim, Statistical Thermodynamics, Cambridge, 1939. N. Metropolis, A. W. Rosenbluth, A. H. Teller, and E. Teller. J. Chem. Phys. 21:1087 (1953). W. Schmickler, unpublished results. A. Vinze, G. Horvai, F. A. M. Leermaker, and J. M. H. M. Sheutjens. Sensors Actuators 18– 19:42 (1994). E. J. W. Verwey and K. F. Niessen. Philos. Mag. 28:435 (1939). C. M. Pereira, W. Schmickler, A. F. Silva, and M. J. Sousa. Chem. Phys. Lett. 268:13 (1997). T. Huber, O. Pecina, and W. Schmickler. J. Electroanal. Chem. 467:203 (1999). Z. Samec, A. Troja´nek, and J. Langmeier. J. Electroanal. Chem. 444:1 (1998). P. Hajkova, D. Homolka, V. Marecek, and Z. Samec. J. Electroanal. Chem. 151:277 (1983). Y. Cheng, V. J. Cunnane, D. J. Schiffrin, and L. Mutoma¨ki. J. Chem. Soc. Faraday Trans. 81:107 (1991). C. M. Pereira, W. Schmickler, F. Silva, and M. J. Sousa. J. Electroanal. Chem. 436:9 (1997). S. Frank and W. Schmickler, submitted to J. Electroanal. Chem. W. Schmickler. J. Electroanal. Chem. 426:5 (1997). R. Landauer and J. A. Swanson. Chem. Rev. 121:1668 (1961). H. A. Kramers. Physica 7:284 (1940). Y. Shao, M. Osborne, and H. Girault. J. Electroanal. Chem. 318:101 (1991). H. Girault, in Modern Aspects of Electrochemistry (J. O’M. Bockris, B. E. Conway, and R. E. White, eds.), vol. 25, Plenum Press, New York, 1993. W. Schmickler. J. Electroanal. Chem. 460:144 (1999). R. A. Marcus. J. Chem. Phys. 24:966 (1956). N. S. Hush. J. Chem. Phys. 28:962 (1958). W. Schmickler. J. Electroanal. Chem. 428:123 (1997). Z. Ding, D. J. Fermı´ n, P.-F. Brevet, and H. H. Girault. J. Electroanal. Chem. 458:139 (1998). M. Tsionsky, A. J. Bard, and M. V. Mirkin. J. Phys. Chem. 100:17881 (1996). B. Liu and M. V. Mirkin. J. Am. Chem. Soc. 121:8352 (1999).

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30. W. Schmickler. Chem. Rev. 96:3177 (1996). 31. P. Vanysek, Electrochemistry on Liquid–Liquid Interfaces, Lecture Notes in Chemistry, vol. 39, Springer, New York, 1985. 32. C. W. Outhwaite, L. B. Bhuyiyan, and S. Levine. J. Chem. Soc. Faraday Trans. II 76:1388 (1980). 33. Q. Cui, G. Zhu, and E. Wang. J. Electroanal. Chem. 372:15 (1994); 383:7 (1995). 34. T. Wandlowski, K. Holub, V. Marecek, and Z. Samec. Electrochim. Acta 40:2887 (1996). 35. D. Henderson (ed.), Fundamentals of Inhomogenous Fluids, Dekker, New York, 1992. 36. F. F. Abraham. J. Chem. Phys. 63:157 (1975). 37. O. Pecina and J. P. Badiali. Phys. Rev. E 58:6041 (1998). 38. L. I. Daikin, A. A. Kornyshev, and M. Urbakh. Phys. Rev. E 53:6192 (1996). 39. O. Pecina and J. P. Badiali. J. Electroanal. Chem. 475:46 (1999). 40. M. Urbakh, A. A. Kornyshev, and L. I. Daikin, submitted to J. Electroanal. Chem. 41. T. Kakiuchi. J. Electroanal. Chem. 322:55 (1992). 42. D. E. Goldman. J. Gen Physiol. 27:37 (1943)

8 Dynamic Aspects of Heterogeneous Electron-Transfer Reactions at Liquid^ Liquid Interfaces DAVID J. FERMI´N Laboratoire d’Electrochimie, De´partement de Chimie, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, Switzerland RIIKKA LAHTINEN Laboratory of Physical Chemistry and Electrochemistry, Department of Chemical Technology, Helsinki University of Technology, Espoo, Finland

I.

INTRODUCTION

The molecular nature of interfaces between two immiscible electrolyte solutions (ITIES) provides a well-deﬁned framework for fundamental studies of heterogeneous electrontransfer processes (ET). The potential impact of this topic has been recognized even before carrying out comprehensive work. Outstanding contributions by Samec [1], Kharkats and Volkov [2], and Marcus [3–6] delivered basic descriptions of the ET dynamics involving two redox couples separated by a polarized liquid–liquid junction. Further developments including lattice-gas [7] and molecular dynamics modeling [8,9] have complemented these initial steps. By contrast, experimental studies have been able to address electron-transfer kinetics across ITIES only in the last few years. Among these recent advances, photoinduced heterogeneous ET has provided some exciting insights into the elementary processes at dye-sensitized liquid–liquid interfaces. The present chapter reviews these contributions, not only highlighting the experimental aspects and establishing comparisons with existing ET models, but also analyzing new perspectives for areas of practical interest such as twophase catalysis and solar energy conversion.

II.

FUNDAMENTAL CHALLENGES SURROUNDING ELECTRON-TRANSFER REACTIONS

The interpretation of phenomenological electron-transfer kinetics in terms of fundamental models based on transition state theory [1,3–6,10] has been hindered by our primitive understanding of the interfacial structure and potential distribution across ITIES. The structure of ITIES was initially studied by electrochemical and thermodynamic analyses, and more recently by computer simulations and interfacial spectroscopy. Classical electrochemical analysis based on differential capacitance and surface tension measurements has been extensively discussed in the literature [11–18]. The picture that emerged from 179

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these studies described the interface as two diffuse layers separated by an ‘‘inner layer.’’ This approach, commonly referred to as the modiﬁed Verwey–Niessen model (MVN), has raised a great number of controversies, especially in connection to the nature of the ‘‘inner layer.’’ Molecular dynamics and Monte Carlo computer simulations have provided detailed microscopic pictures of liquid–liquid junctions [19–21]. One of the most interesting features underlined by these studies is that the interface is molecularly sharp, featuring ‘‘ﬁngering’’ phenomena between both solvents. At the picosecond time scale, this phenomenon introduces a degree of roughness to the junction within a region of 10 A˚. Time averaging of these events deﬁnes a region in which dielectric, solvation, and transport properties depend on the position along the axis perpendicular to the interface. However, it is not clear yet how these phenomena would affect the kinetics of charge transfer process. These theoretical calculations are based on a collection of a few hundred solvent molecules where no electrolyte species are taken into account. Considering that homogeneous and heterogeneous ion–ion interactions play important roles on interfacial processes, only limited comparison with experimental data can be performed. The lattice-gas model has proved to be a rather useful theoretical approach to the study of ionic interactions at liquid–liquid interfaces [7,22]. By contrast to quantitative molecular dynamics, where Newton’s equations of motion are solved for all particles in the system over a certain period of time, the lattice-gas model considers only interactions between nearest neighbors in a cubic lattice arrangement. Basic aspects regarding this type of calculation have been described in recent publications [22,23]. Ionic distributions in the absence [7,22] and presence of ion-pairing interaction [24–27] have been considered as a function of the Galvani potential difference. The potential dependence of the heterogeneous ET rate constant is one of the most important outputs of this work. Simulations suggested that if the Debye lengths in each electrolyte solution are larger than the width of the interface, the potential drop across the reactants is very small, therefore any potential perturbation will manifest itself by changes in the interfacial concentration of reactants [7]. From the experimental point of view, structural aspects have been addressed by interfacial spectroscopic methods such as neutron reﬂectivity [28–32] and quasielastic laser scattering [33–36]. The latter technique has provided valuable information on the frequency of capillary waves generated by thermal ﬂuctuations at the liquid–liquid junction. Although this technique has been employed for adsorption studies at nonpolarized interfaces, it is also expected to provide useful information on the interfacial structure during charge-transfer processes. Important advances have also emerged from nonlinear optics, in particular second harmonic generation (SHG). The noncentrosymmetrical nature of the liquid–liquid junctions allows SHG responses as well as sum frequency generation (SFG) signals from species at the interface, providing information on the excess concentration, molecular orientation, and structure. Basic aspects of these powerful techniques have been comprehensively described [37,38] and more recent contributions are reviewed in this book (Chapter 6). These spectroscopic and theoretical developments have stimulated the recent advances on electron-transfer dynamics at ITIES. In addition to the correlation between structure and dynamics of charge transfer, fundamental problems in connection with the energetics of ET reactions remain to be fully addressed. We shall consider these problems primarily before discussing kinetic aspects in full detail.

Dynamic Aspects of Electron-Transfer Reactions

A.

181

Energetics of ET and Photoinduced ET Reactions

From the thermodynamic point of view, the occurrence of a heterogeneous ET event at a liquid–liquid interface is determined not only by the relation of redox potentials between reactants in each phase, but also by the Galvani potential difference. Let us consider the general reaction, o w o Ow 1 þ R2 Ð R1 þ O2

ð1Þ

where the superscripts ‘‘w’’ and ‘‘o’’ correspond to the aqueous and organic phases. The Nernst equation associated with the equilibrium conditions is given by w o RT aO1 aR2 w 0 ln ð2Þ

¼

w o o et o nF aw R1 aO2 0 where the standard potential w o et is determined by 0 0;o 0;w w o et ¼ EO2=R2 EO1=R1

ð3Þ

In order to express the standard redox potentials of the two couples located in different 0;o can be expressed in terms of solvents on a same potential scale, e.g., SHE in water, EO2=R2 0;w the corresponding redox potential in water ðEO2=R2 Þ and the Gibbs energies of transfer of the species R2 and O2 , 0;o 0;w EO2=R2 ¼ EO2=R2 þ

G0;w!o G0;w!o R2 O2 nF

ð4Þ

So far, the experimentally obtained formal electron-transfer potentials have not been rationalized in terms of Eqs. (3) and(4). In view of the lack of a suitable redox reference for organic electrolytes, we have recently studied the oxidation of ferrocene (Fc) by the hexacyanoferrate redox couple at the water–1,2-dichloroethane (DCE) interface. Figure 1(a) displays a typical cyclic voltammogram recorded on a four-electrode potentiostat for the cell conﬁguration represented in Fig. 1(b). The Galvani potential scale was estimated considering the so-called TATB assumption [39,40]. Under this approximation the transfer potentials of several standard ions such as tetrapropylammonium (TPAþ ) and tetramethylammonium (TMAþ ) are documented (see database at www.epf.ch/le). Unless otherwise indicated, the convention adopted throughout this review deﬁnes positive currents to the transfer of positive charges from water to DCE. The voltammogram in Fig. 1(a) shows the electron-transfer signal in comparison with the transfer wave of TPAþ . From the difference in the half wave transfer potentials, it can be estimated that the formal electron0 transfer potential is w o et ¼ 0:160 0:010 V. Taking into account that the concentration of the hexacyanoferrate couple is in large excess with respect to ferrocene, the observed formal ET potential can be effectively expressed as ! RT FeðCNÞ3 w 00 0;DCE 0;w 6 ln o et ¼ EðFcþ =FcÞ EðFeðCNÞ3 =FeðCNÞ4 Þ ð5Þ 6 6 F FeðCNÞ4 6 Under similar conditions, the formal redox potential of the aqueous couple has been estimated as 0:358 0:005 ; V vs SHE. From Eq. (5), it is obtained that the formal 0 0 ;DCE redox potential of Fc in DCE is EFc þ =Fc ¼ 0:635 0:015 V vs SHE. The redox potential of Fc obtained from the cyclic voltammetry experiments at the water–DCE interface can be veriﬁed by evaluating the thermodynamic cycle given by Eq. (4). It follows that

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182

FIG. 1 (a) Cyclic voltammogram of the heterogeneous oxidation of ferrocene by the hexacyanoferrate redox couple at the water–DCE interface at 10 mV s1 . The convention adopted throughout the review deﬁnes positive currents as the transfer of a positive charge from water to DCE. (b) The composition of the cell schematically represented. BTPPA and TPBCl stand for bis(triphenylphosphoranylidene)-ammonium and tetrakis(4-chlorophenyl) borate respectively. The current was measured through two platinum counterelectrodes located in each phase. The surface area of the liquid– liquid junction was 1:53 cm2 . The cation tetrapropylammonium (TPAþ Þ was also present in the aqueous phase as a reference for the Galvani potential scale.

0

0 ;DCE o;w w 0 0;w!o EFc =F þ =Fc ¼ EðFcþ =FcÞ þ o Fcþ GFc

ð6Þ

corresponds to the Fc Gibbs energy of transfer from water where the parameter G0;w!o Fc 0 0 ;w to the DCE phase. An average value for the Fc redox potential of EFc þ =Fc ¼ 0:381 0:006 V was derived from voltammetry at ultramicroelectrodes [41], while the parameter ¼ 24:3 0:2 kJ mol1 has been estimated from extraction methods. The third G0;w!o Fc parameter required in Eq. (6) was obtained by monitoring the transfer of Fcþ accumulated during the oxidation of Fc by CuSO4 at the water–DCE interface. Figure 2 shows cyclic voltammograms featuring the 0transfers of Fcþ and the standard TMAþ , from which the 0 formal transfer potential w o Fcþ ¼ 0:005 0:010 V can0 be estimated. Introducing all these 0 ;DCE data into Eq. (6) gives a value of 0:638 0:020 V for EFc þ =Fc . It should be noticed that this analysis implicitly considered that the hydration energies of Fcþ , TMAþ , and TPAþ are not substantially affected by the difference in ionic strengths in the experiments of Figs. 1 and 2. Despite this simplifying assumption, the redox potentials for Fc calculated from both approaches are consistent within the error margins. A similar analysis can also be carried out by referring the potential scale to the potential of minimum differential capacitance curve. This potential is close to the potential of zero charge for interfaces where interfacial ion-pairing or speciﬁc adsorption phenomena are negligible. Hanzlı´ k et al. have obtained similar values for the same thermodynamic cycle [Eq. (4)] at the water– nitrobenzene interface [42].

Dynamic Aspects of Electron-Transfer Reactions

183

FIG. 2 Cyclic voltammogram of the ferricenium transfer across the water–DCE interface at 10 mV s1 . The electrochemical cell featured a similar arrangement to Fig. 1(b), but the organic phase contained 2 mM of ferrocene. Heterogeneous oxidation of Fc occurred in the presence of 0.2 mM CuSO4 in the aqueous phase. Supporting electrolytes were 10 mM Li2 SO4 and 10 mM BTPPATPBCl. The transfer of the standard tetramethylammonium (TMAþ ) under the same condition is also superimposed.

Semiquantitative relations between the redox scales in both electrolyte phases allow a clearer description of the energetics involved in ET reactions at ITIES. A graphic representation of the relations between redox potentials for various aqueous and organic phase couples is shown in Fig. 3. For instance, the interfacial oxidation of dimethylferrocene (DMFc) and the reduction of tetracyanoquinodimethane (TCNQ) by ferro/ferricyanide can take place within the ideally polarizable potential range, while the oxidation of TPBCl is outside the potential range. These considerations are consistent with the experimental studies reported by Ding et al. [43]. This kind of analysis is particularly relevant in studies of electron transfer rates as a function the Gibbs energy of electron transfer [44– 46]. Furthermore, it also allows comparisons between the Gibbs energy of electron transfer and the transfer of ionic species present at the liquid–liquid junctions. For a given relation of redox potentials and concentration ratio of electroactive species, the onset of the ET reaction is determined by the Galvani potential difference [see Eqs. (2) and (3)]. However, a special case can be envisaged when redox species are photoexcitable dyes adsorbed at the interface. Assuming that the excited-state lifetime is comparable to the characteristic time of ET, the faradaic reaction can be initiated by illumination of the interface. The redox potentials associated with the ground and triplet states of the water-soluble zinc tetra-N-methyl-4-pyridium porphyrin (ZnTMPyP4þ ) are schematically shown in Fig. 4(a) [47]. At externally polarized interfaces, the ET from Fc to the porphyrin species can proceed only via the excited state of the dye. This is the fundamental phenomenon behind the recent developments on dye-sensitized liquid–liquid interfaces [48–50]. As discussed in Section V of this review, ‘‘uphill’’ electron-transfer processes can take place between two redox species at the liquid–liquid interface mediated by the excited state of adsorbed dye species. The energetics involved in these types of photosynthetic processes are schematically illustrated in Fig. 4(b) [51]. In this mechanism, part of the incident photon energy is employed to compensate the negative Get . B.

General Overview on the Controlling Factors of ET Kinetics

Similarly to charge-transfer processes at solid–electrolyte interfaces, the ET rate for heterogeneous reactions at ITIES is determined by the ﬂux of reactants to the interface as well

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FIG. 3 Comparison of potential scales for redox species in aqueous and DCE phases versus SHE. Redox potentials in DCE were experimentally measured against the couple Fcþ =Fc. The formal redox potential of this couple in DCE was obtained by evaluating the parameters in the thermodynamic cycle given by Eq. (7).

as the dynamics of the ET step. Mass transport processes have been rigorously described for planar diffusion regimes [52–55], spherical diffusion at microinterfaces [56], and more recently for ‘‘approach curves’’ familiar from scanning electrochemical microscopy (SECM) [45,57] and microelectrochemical measurements at expanding droplets (MEMED) [58,59]. On the other hand, the kinetics of the ET step and its dependence on the Galvani potential difference remain largely controversial. We shall concentrate on the latter aspects throughout this review. As mentioned earlier, a good deal of these controversies are due to the primitive understanding of the double layer structure. Extending the formalism for ET in homogeneous phase, reactions at liquid–liquid interfaces can be described in terms of a series of elementary steps initiated by the approach of reactants to the interfacial region and the formation of the ET precursor complex [1,5,60],

Dynamic Aspects of Electron-Transfer Reactions

185

FIG. 4 (a) Latimer diagram of the water soluble zinc tetra-N-methyl-4-pyridium porphyrin (ZnTMPyP4þ ). (Reprinted with permission from Ref. 47.) (b) Schematic representation of a photosynthetic process based on porphyrin sensitized water–organic interface. Dotted line corresponds to the back electron-transfer process. (Reprinted from Ref. 51 with permission from Elsevier Science.)

o w o Ow 1 þ R2 Ð O1 jR2 w o o Ow 1 R2 Ð O1 R2 w o o O1 R2 Ð Rw 1 O2 O w o R1 O2 Ð Rw 1 O2 w o o Rw 1 O2 Ð R1 þ O2

Precursor complex formation

ð7Þ

Precursor reorganizations

ð8Þ

Electron transfer

ð9Þ

Successor reorganization

ð10Þ

Successor dissociation

ð11Þ

The ﬁrst controversial point in this mechanism is the nature of the reaction planes where the precursor formation and the ET reaction take place. Samec assumed that the ET step occurs across an ion-free layer composed of oriented solvent molecules [1]. By contrast, Girault and Schiffrin considered a mixed solvent region where electrochemical potentials are dependent on the position of the reactants at the interface [60]. From a general perspective, the phenomenological ET rate constant can be expressed in terms of ket ¼ Z expðGact =RTÞ

ð12Þ

where Z is a preexponential factor related to the position of the reactants at the interface, and the activation energy Gact is determined by the reorganization energy , the formal

Fermı´n and Lahtinen

186 0

Gibbs energy of electron transfer (Get0 Þ and the work terms for precursor formation (wp Þ and successor dissociation ðws Þ, !2 0 þ Get0 þ ws wp Gact ¼ wp þ ð13Þ 4 From classical transition state theory, the phenomenological rate constant of ET can be expressed as h

i a b exp z F

z F

=RT exp ðeFab Þ=RT ð14Þ ket ¼ kpzc O1 R2 w o et where e is the charge transferred in Eq. (9), and ‘‘a’’ and ‘‘b’’ correspond to the position of the reaction planes in the aqueous and organic phases along the axis perpendicular to the liquid–liquid boundary. The differences in the so-called ‘‘ion-free layer’’ and ‘‘mixed solvent layer’’ formalisms are translated in the physical meaning of the preexponential pzc parameter kpzc et . Samec deﬁned ket as the ‘‘true’’ forward heterogeneous ET rate constant at zero Galvani potential difference [1], kpzc et ¼ BVm d exp½=4RT

ð15Þ

where the parameter B is associated with the electronic overlap, Vm is the mean molar volume of reactants, d is the thickness of the inner layer and is the total reorganization energy. For the ‘‘mixed solvent layer formalism,’’ the preexponential parameter kpzc et was estimated by extension of the Newton and Sutin approach [61], 0 0 0 0 kpzc et ¼ R exp½=4RT exp wp =RT exp pzc wp ws þ eF O1 =R2 =RT ð16Þ w0p and w0s are the potential independent terms of wp and ws . is the effective electron hopping frequency, while R is the region where the electronic coupling between the reactants is substantial. It is evident that the validation of either approach is difﬁcult to address from the experimental point of view, especially considering that the potential dependencies are formally identical [Eq. (14)]. However, the most important conclusion up to this point is that the Galvani potential difference can affect the interfacial concentration of ionic reactants, bringing about changes in the observed ET rate. Alternatively, changes of the junction polarization can modify the potential drop between redox species, giving rise to variations on the free energy of ET. The mechanisms, in which the interfacial potential can operate on the observed ET rate, correspond to the so-called concentration polarization and Butler–Volmer behavior respectively. In subsequent works, Marcus developed his theory further in a series of papers providing expressions for the work terms, the reorganization energy and the macroscopic ET rate constants [3–6]. Assuming a sharp liquid–liquid boundary, the solution of the mean molar volume of reactants yields an expression for ket of the form ket ¼ 2ðaO1 þ aR2 ÞðRÞ3 expðGact =RT Þ

ð17Þ

where aO1 , aR2 , and correspond to the molecular radii of the reactant species and the transmission coefﬁcient respectively. As discussed in the next section, recent measurements of ket for reactions involving large driving forces provided a maximum value of the order of 102 M1 cm s1 [45]. This value is of the same order as the preexponential factor in Eq. (17), assuming R 0:1 nm and aO1 þ aR2 1 nm.

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In order to fully evaluate Eq. (17), expressions involving the outer-sphere reorganization term 0 , as well as the work terms, were also established [5], op ðeÞ2 1 1 ðeÞ2 1 1 ðeÞ2 Dop o Dw þ op op Dsw Dso 2aO1 Dop 2aR2 Dop 4d1 Dop w w ðDo þ Dw Þ o op Ds Ds ðeÞ2 Dop Dsw Dso w Do s o s ws op op Dw ðDo þ Dw Þ 4d2 Dop Dso ðDsw þ Dso Þ o ðDw þ Do Þ 2ðeÞ2 1 1 op Dsw þ Dso R Dop w þ Do ! ðzO1 Þ2 ðzR2 Þ2 Dso Dsw 2 zO1 zR2 þ wp ¼ s s s s R Dsw þ Dso 4d1 Dw 4d2 Do Do þ Dw 0 ¼

ð18Þ ð19Þ

where Ds and Dop are the static and optical dielectric constants for both media, d is the perpendicular distance from the ion center to the interfacial boundary, and R is the centerto-center distance between the reactant species. The expression for ws can be easily obtained by replacing the charges of the reactants by the corresponding values of the products. Initial comparisons of rate constants obtained from Eqs. (13) and (17–19), and from experimental studies based on cyclic voltammograms and impedance measurements give support to this approach [62,63]. However, one limitation is that the Galvani potential difference is not explicitly deﬁned in the expressions of the work terms. In that respect the analysis leading to Eqs. (14)–(16) provides a clearer description. The ‘‘ﬂat’’ interface model employed by Marcus does not seem to be in agreement with the ‘‘rough’’ picture obtained from molecular dynamics simulations [19,21,64–66]. Benjamin examined the main assumptions of work terms [Eq. (19)] and the reorganization energy [Eq. (18)] by MD simulations of the water–DCE junction [8,19]. It was found that the electric ﬁeld induced by both liquids underestimates the effect of water molecules and overestimates the effect of DCE molecules in the case of the continuum approach. However, the total ﬁeld as a function of the charge of the reactants is consistent in both analyses. In conclusion, the continuum model remains as a good approximation despite the crude description of the liquid-liquid boundary. The lattice-gas modeling by Schmickler also extended the Marcus approach to the work terms [7]. In this case, detailed analysis of particle distributions allowed estimations of ket without deﬁning a mean reaction volume. Furthermore, the study of particle distribution as a function of the interfacial potential provided an explicit description of the effect of the Galvani potential difference on the observed rate constant. As mentioned earlier, these calculations indicated that changes in the Galvani potential difference have a negligible effect on Gact as long as the separation between the redox centers is substantially shorter than the Debye lengths in each electrolyte phase. In this case, the potential dependence of ket will be only given by the ﬁrst exponential term in Eq. (14). However, as discussed throughout this chapter, experimental results provide clear evidence that concentration polarization effect is not the only factor involved in the behavior of ket as a function of the applied potential. The theoretical aspects highlighted in this section show that describing heterogeneous ET dynamics by the continuum model can be regarded as reasonable. In the next section, we shall discuss in detail the experimental advances and how some results cast doubts in the picture outlined so far.

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III.

ELECTRON-TRANSFER REACTION AT ITIES

Heterogeneous ET reactions have been consistently studied as a function of the bias potential applied through reference electrodes located at each electrolyte phase. This approach limits the potential range for ET studies to the region where the interface behaves as an ideally polarizable junction. On the other hand, recent developments have incorporated techniques based on the SECM concept, in which the Galvani potential difference is determined by the ratio of a common ion between the two liquid phases. Both approaches require appropriate experimental conditions in order to minimize competing processes, which can complicate the analysis of the heterogeneous ET responses. We shall review some experimental aspects concerning both types of approaches before considering the dynamics of ET reactions in detail. A.

Electron-Transfer Reactions at Externally Polarized Interfaces

Heterogeneous ET reactions at polarizable liquid–liquid interfaces have been mainly approached from current–potential relationships. In this respect, a rather important issue is to minimize the contribution of ion-transfer reactions to the current responses associated with the ET step. This requirement has been recognized by several authors [43,62,67–72]. Firstly, reactants and products should remain in their respective phases within the potential range where the ET process takes place. In addition to redox stability, the supporting electrolytes should also provide an appropriate potential window for the redox reaction. According to Eqs. (2) and (3), the redox potentials of the species involved in the ET should ‘‘match’’ in a way that the formal electron-transfer potential occurs within the potential window established by the transfer of the ionic species present at the liquid–liquid junction. The results shown in Figs. 1 and 2 provide an example of voltammetric ET responses when the above conditions are fulﬁlled. A difference of 0 w 0 approximately 150 mV is observed between w o et and o Fcþ . The organic solvent should feature a low solubility in water and a high dielectric constant. Numerous studies have been reported for liquid–liquid junctions involving DCE [43,62,70,71,73], nitrobenzene [67,68,74,75], and nitrophenyloctylether (NPOE) [56]. Various hydrophobic electrolytes have been employed in these solvents. Tetraphenylarsonium (TPAsþ Þ [[71,75,76], bis-triphenylphosphoranylidene (BTPPAþ ) [43,50], and hydrophobic tetra-arylammonium [77,78] are among the cations used in the organic phase. The choice for anions has been mostly restricted to borate derivatives, tetraphenylborate (TPB ) [70,79,80], tetrakis(4-chlorophenyl)borate (TPBCI ) [43,81,82], and tetrakis(penta-ﬂuoro)phenylborate (TPFB ) [49,83], as well as dicarbollylcobaltate [75]. The redox stability organic of phase cations is commonly very high in comparison to the anionic phenylborate derivatives. It has been proposed that Fcþ is reduced to Fc in DCE in the presence of TPB ðPh4 B Þ [71], 2Fcþ þ Ph4 B ! Ph2 þ Ph2 Bþ þ 2Fc

ð20Þ

This reaction has been associated with anomalous voltammetric responses during ET reactions in the presence of aqueous redox couples [71,84]. However, as indicated in Fig. 3, the redox potential of TPB is considerably more positive than Fc in DCE, therefore the reaction in Eq. (20) must involve a complex interfacial catalytic mechanism to indeed take place. On the other hand, Ding et al. have studied the oxidation of 1,1 dimethylferrocene (DMFc) and the reduction of TCNQ by FeðCNÞ36 =4 at the water–

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DCE interface in the presence of TPBCl [43,82]. The accumulation of products of the redox reactions were followed by spectrophotometry in situ, and quantitative relationships were obtained between the accumulation of products and the charge transfer across the interface. These results conﬁrmed the higher stability of this anion in comparison to TPB . It was also reported that the redox potential of TPBCl is 0.51 V more positive than 0;DCE EFc þ =Fc (see Fig. 3). However, the redox stability of the chlorinated derivative of tetraphenylborate is not sufﬁcient in the presence of highly reactive species such as photoexcited water-soluble porphyrins. Fermı´ n et al. have shown that TPBCl can be oxidized by adsorbed zinc tetrakis-(carboxyphenyl)porphyrin at the water–DCE interface under illumination [50]. Under these conditions, the fully ﬂuorinated derivative TPFB has proved to be extremely stable and consequently ideal for photoinduced ET studies [49,83]. Another anion which exhibits high redox stability is PF6 ; however, its solubility in the water phase restricts the positive end of the ideally polarizable window to w o < 0:2 V [85]. Requirements for redox potential matching and high transfer energy have limited the 3 =4 choice for the aqueous redox species to ½FeðCNÞ [43,56,62,63,70,71,74,76,81,82,86], 6 þ þ þ þ Fe2 =3 in the presence of citrate [71] or at low pH [87], Ce3 =4 and permanganate [80]. These redox couples have been employed for simple one-electron-transfer reactions involving ferrocene derivatives [43,56,67,68,71,74,80,82,84], TCNQ [43,63,76,80,82], lutetium diphthalocyanine LuðPCÞ2 [62,63], ruthenium bis(pyridine)(meso-tetraphenylporphyrinato) (RuðTPPÞðPyÞ2 Þ [70,76], and tetrathiafulvalene TTF [80,88]. Other interesting redox active species employed in the organic phase is the tetraoctylammonium tetrachloroaurate (TOAAuCl4 ). The interfacial reduction of the Au complex by ferrocyanide at the water–DCE junction leads to the formation of gold particles [89]. More recently, the nucleation of Pd particles has been reported from reduction of ammonium tetrachloropalladate in the aqueous phase by ferrocene derivatives in DCE [90,91]. In general, successful studies of heterogeneous ET have featured highly charged ionic species in the aqueous phase and rather hydrophobic couples in the organic electrolyte. Furthermore, high ionic strength and excess concentration of the redox couple in the aqueous phase are commonly part of the experimental practice followed in these studies. These two additional conditions minimize the partition of the organic redox couple by ‘‘salting out effect’’ and allow one to treat the electrochemical responses in terms of a pseudo-ﬁrst-order process (a constant composition approximation). Spectroscopic detection of ET products has also been employed for monitoring the progress of the reaction. Obviously, the essential requirement for this analysis is the stability of the spectroscopic probe. Compton and coworkers have developed a cell arrangement for in-situ EPR detection of the radical ions generated during the reduction of TCNQ, 2,3,5,6-tetrachloro-p-benzoquinone (TCBQ), 2,3,5,6-tetraﬂuoro-p-benzoquinone (TFBQ), and the oxidation of tetrathiafulvalene (TTF) in DCE [88,92]. It was conﬁrmed for all the organic redox species studied that the radical ion was stable in the organic phase in the presence of the electrolytes BTPPATPBCl, TPAsTPBCl, and TBAPF6 . These results were consistent with the spectrophotometric analysis of the TCNQ reduction reported by Ding et al. [43]. In this work, the accumulation of the radical TCNQ following the ET from ferrocyanide was followed by UV-visible reﬂectance in total internal reﬂection (TIR) according to the scheme in Fig. 5(a). The evolution of the absorption peaks associated with the radical anions in Fig. 5(b) is clearly observed at the onset of the ET potential range depicted in the cyclic voltammograms of Fig. 5(c). Furthermore, it is also shown that the differential cyclic voltabsorptograms at 650 nm shown in Fig. 5(d) are directly proportional to the voltammetric responses. The propor-

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FIG. 5 (a) Schematic diagram of the heterogeneous reduction of TCNQ by the hexacyanoferrate couple at water–DCE interface monitored by UV-visible spectroscopy in TIR. (b) Evolution of the absorption bands associated with the radical TCNQ as the Galvani potential difference is swept from 0.190 to 0.260 V, with a difference of 40 mV between each spectrum. (From Ref. 82, reproduced by permission of The Royal Society of Chemistry.) (c) Cyclic voltammograms corresponding to the same process at various scan rates. (d) Differential cyclic voltabsorptogram obtained in situ at 670 nm. The composition of the electrochemical cell is identical to that in Fig. 1(b), but with a 4 ratio 0.01 M/0.4 M FeðCNÞ3 in the aqueous phase and 6 104 M TCNQ in DCE. 6 =FeðCNÞ6 (Figures (c) and (d) were reprinted from Ref. 43 with permission from Elsevier Science.)

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191

tionality between the absorbance in TIR (ATIR Þ and the faradaic current (I f ) is given by [43] dATIR 2TCNQ f ¼ I dt FS cos

ð21Þ

where TCNQ and correspond to the molar absorption coefﬁcient of the product in the organic phase and the light incident angle, respectively. The satisfactory correlation between spectroscopic and electrochemical responses provides a suitable framework for the kinetic analysis of these systems. B.

‘‘Open-Circuit’’ Liquid–Liquid Junctions

Techniques based on the concept of scanning electrochemical microscopy (SECM) have provided valuable kinetic information for charge-transfer processes at ITIES [44,45,57,93,94]. These techniques allow the monitoring of concentration proﬁles of the ET products via an ultramicroelectrode (UME) approaching the liquid–liquid junction (Chapter 13). In this case, the Galvani potential difference can be controlled by the partition of a common ion between the electrolyte solutions. A variety of organic solvents has been studied, e.g., benzene, nitrobenzene, and DCE. The Galvani potential difference is generally controlled by the ratio of ClO 4 ions present in both phases. Similarly to experiments under potentiostatic conditions, success in the analysis of ET kinetics relies on the fact that neither products nor reactants can transfer across the interface. Various redox couples in the aqueous phase have been studied, including 3=4 3=4 2=3 3=2þ =2 , RuðCNÞ , MoðCNÞ , Fe , FeEDTA , IrCl , and CoðIIIÞ=ðIIÞ FeðCNÞ3=4 6 6 8 6 sepalchrate [44,45,95]. In the organic phase, zinc meso(tetraphenyl)porphyrin (ZnPor), TCNQ, Fc, and DMFc have been most frequently employed. The condition for redox potential matching is rather different for this approach in comparison to externally biased interfaces. In the case of SECM, one of the reactants is generated at the UME tip at some distance from the interface, therefore the ET driving force with respect to the redox species in the opposite phase could be extremely high. This condition allows a unique possibility of accessing rate constants in the inverted Marcus region [44,45] or studying electrogenerated chemiluminescence phenomena [96]. Another interesting approach to ET reactions at liquid–liquid interfaces has been recently introduced by Shi and Anson [77,78,97]. Thin organic electrolyte layers were suspended in dry and polished pyrolytic graphite electrodes, which were subsequently introduced in the aqueous electrolyte. The thin organic layer contains supporting electrolytes such as tetra-N-hexylammonium perchlorate (THAClO4 ) and various organic redox . The species, while the aqueous phase contained NaClO4 and the couple FeðCNÞ3=4 6 sequence of experiments displayed in Figs. 6(a) and 6(b) demonstrates that direct ET from the aqueous redox couple to the solid electrolyte does not take place in the presence of the thin organic layer. In the presence of only decamethylferrocene (DCMFc) in the organic layer, Fig. 6(c), a reversible voltammetric response is observed associated with the generation of DCMFcþ . Figure 6(d) illustrates an enhancement of the cathodic current when both redox couples are introduced in respective phases, indicating that DCMFc is heterogeneously oxidized by FeðCNÞ3 6 across the water–nitrobenzene interface and that the product accumulation is monitored at the solid electrode. Although this analysis was extended to large variety of redox couples, a major complication arises from the effective control of the Galvani potential difference across the liquid–liquid junction. For instance, the authors rationalized the dependence of the redox potentials for various couples in the

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FIG. 6 Cyclic voltammograms of 0.5 mM RuðNH3 Þ3þ 6 at a pyrolytic graphite electrode before (A) and after (B) depositing a thin layer of nitrobenzene containing 0.08 M tetraethylammonium perchlorate. Scan rate 5 mV s1 and S ¼ 5 mA. Cyclic voltammogram of 0.2 mM DCMFc in the nitrobenzene thin layer, S ¼ 2 A (C). Steady-state current as function of the applied potential of the graphite-modiﬁed electrode in the presence of 0.2 mM DCMFc and 2 mM RuðNH3 Þ3þ 6 , S ¼ 2 A (D). (Reprinted with permission from Ref. 97. Copyright 1999 American Chemical Society.)

organic layer with the concentration ratio of ClO 4 [97] via the relations established by Kakiuchi on partition equilibriums for large volume ratios [98]. However, a surprising 0 independence of the ET rate with the G0et , which is incompatible with Eqs. (13) and (14), casts some doubts on the potential distribution across these types of interfaces. C.

Dark Electron-Transfer Kinetics

Early studies of ET dynamics at externally biased interfaces were based on conventional cyclic voltammetry employing four-electrode potentiostats [62,67–70,79]. The formal pseudo-ﬁrst-order electron-transfer rate constants [ket ðcm s1 Þ were measured on the basis of the Nicholson method [99] and convolution potential sweep voltammetry [79,100] in the presence of an excess of one of the reactant species. The constant composition approximation allows expression of the ET rate constant with the same units as in heterogeneous reaction on solid electrodes. However, any comparison with the expression described in Section II.B requires the transformation to bimolecular units, i.e., M1 cm s1 . Values of ket of the order of 1–2 103 cm s1 (0.05 to 0.1 M1 cm s1 ) were reported for FeðCNÞ36 =4 in the aqueous phase and the redox species LuðPCÞ2 , SnðPCÞ2 , TCNQ, and RuTPPðPyÞ2 in DCE [62,70]. Despite the fact that large potential perturbations across the interface introduce interferences in kinetic analysis [101], these early estimations allowed some preliminary comparisons to established ET models in heterogeneous media. Nonfaradaic components associated with the uncompensated resistance between reference electrodes (Ru ) and the double layer capacitance (Cdl Þ can be accurately determined by AC impedance measurements. In this technique, a small AC potential perturbation is superimposed to the DC bias, and the resulting AC current is measured as a function of the frequency of modulation. The simplest circuit considered for a polarizable

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193

liquid–liquid interface is illustrated in Fig. 7 [101–103]. The impedance component associated with the transfer of the supporting electrolyte is represented by Zb , while the ET impedance element corresponds to Zf . From the equivalent circuit in Fig. 7, it follows that f the real ðYref Þ and imaginary ðYim Þ components of the faradaic admittance are given by Yref ¼ Yret Yreb

ð22Þ

f t b ¼ Yim Yim Yim

ð23Þ

where the superscripts ‘‘t’’ and ‘‘b’’ correspond to the admittance measured in the presence and absence of the redox couples respectively. Equations (22)–(23) allow a simple evaluation of the resistive and capacitive components of the faradaic impedance,

2 2 f f f f Yre þ Yim ð24Þ Zre ¼ Yre f Zim

¼

f Yim

2 2 f f Yre þ Yim

ð25Þ

f f and Zim as a function of the frequency of potential modulation (Randles’ Analysis of Zre plots) provides the phenomenological ET rate constant [63,74]. It should be noted that the f extrapolation of Zre at high frequency gives effectively the sum Rct þ Ru , where Rct is the charge transfer resistance,

Rct ¼

RT z2 F 2 Aket c

ð26Þ

determined by the pseudo-ﬁrst-order ket ðcm s1 ), the surface area A and the concentration of the limiting reactant c. The accurate determination of the uncompensated resistance is an essential condition for reliable determination of the ET rate constant. One of the ﬁrst analyses of ET kinetics based on AC impedance was reported by Chen et al. [74] from the oxidation of Fc by FeðCNÞ36 =4 at the water–nitrobenzene interface. Figure 8 contrasts the impedance responses in the complex plane in the presence and absence of Fc. These

FIG. 7 Simpliﬁed equivalent circuit for charge-transfer processes at externally biased ITIES. The parallel arrangement of double layer capacitance (Cdl ), impedance of base electrolyte transfer (Zb ) and electron-transfer impedance (Zf ) is coupled in series with the uncompensated resistance (Ru ) between the reference electrodes. (Reprinted from Ref. 74 with permission from Elsevier Science.)

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FIG. 8 Complex impedance plot associated with the heterogeneous oxidation of Fc by ferri/ferrocyanide at the water–nitrobenzene interface. The responses only in the presence of 0.1 M ferrocene (&) are contrasted with (&) those obtained upon addition of 1 mM K3 FeðCNÞ6 and 0.1 mM K4 FeðCNÞ6 . (Reprinted from Ref. 74 with permission from Elsevier Science.)

authors did not extent their analysis into the magnitude of ket ; however, it was indicated that the exchange current density obtained from Rct was exponentially dependent on the 0 Galvani potential difference as well as on Get0 [74]. Cheng and Schiffrin [63] employed this approach for the analysis of the systems involving FeðCNÞ36 =4 in the aqueous phase and LuðPCÞ2 , RuðTPPÞðPyÞ2 , and TCNQ in DCE. A major disadvantage of this technique is that the spectra are rather featureless and the frequency range is limited to less than 1 kHz. Calculation of the faradaic impedance via the analysis of the admittance [Eqs. (22)–(26)] in the range of 1 to 30 Hz provided rate constants within a 50 mV range of the formal ET potential. The potential dependence of ket will be discussed in the next section. The formal ET rate constants were roughly of the same order as in the previous reports [62,70], i.e., 1 to 5 103 cm s1 (0.05 to 0:1 M1 cm s1 ). Although these values were successfully interpreted in terms of the Marcus model for ﬂat interfaces [Eqs. (17)–(19)], it was realized that the continuum model for a ‘‘mixed solvent layer’’ also approaches these experimental values [3–6]. The accuracy of the AC-impedance analysis far exceeds the previous studies based on cyclic voltammetry. However, the limited frequency range available for liquid–liquid interfaces imposes severe restrictions for the deconvolution of the various responses associated with the elements in Fig. 7. An alternative approach was introduced by Ding et al.

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FIG. 9 Real component of the AC current (a) and imaginary part of the normalized potentialmodulated reﬂectance (b) for the TCNQ reduction by ferrocyanide at the water–DCE interface. Experimental conditions as in Fig. 5. The potential modulation was 30 mV rms at 3.2 Hz. (c) Optical Randles plot obtained from the frequency-dependent analysis of the PMR responses. (Reprinted from Ref. 43 with permission from Elsevier Science.)

[43] based on the frequency dependence of spectroscopic responses, commonly referred to as potential modulated reﬂectance spectroscopy (PMR) [104–109]. In this case, the interface is perturbed in an identical fashion to AC impedance, but the frequency-dependent reﬂectance in TIR is measured as opposite to the AC current (I~f ). In the conﬁguration described in Fig. 4, and for small potential amplitudes, the normalized AC reﬂectance [ðR=RÞAC ] is proportional to the frequency-dependent concentration of TCNQ at the interface. Following Eq. (21), it can be easily demonstrated that the optical responses are 90 out of phase with respect to the faradaic current [108,109]. FA cos I~f ¼ ðR=RÞAC i! 2TCNQ

ð27Þ

where ! corresponds to the angular frequency of potential modulation. The phase shift between the frequency-dependent optical and electrical responses is exempliﬁed in Fig. 9. The real component of the AC current during the reduction of TCNQ by ferrocyanide [Fig. 9(a)] exhibits the same potential dependence as the quadrature component of R=R [Fig. 9(b)]. The most relevant aspect of this approach is that the faradaic impedance is directly accessed from the optical responses. It follows from Eqs. (24), (25) and (27),

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Zre ¼

2TCNQ w !1 ðR=RÞim o 1 2 2 FS cos ’ ðR=RÞ þ ðR=RÞ re

Zim ¼

ð28aÞ

im

2TCNQ w !1 ðR=RÞre o 1 2 2 FS cos ’ ðR=RÞ þ ðR=RÞ re

ð28bÞ

im

where w o 1 corresponds to the amplitude of potential modulation. The second terms in Eqs. (28a) and (28b) were deﬁned as the optical impedance parameters Fre and Fim respectively. Similarly to the Randles method, the charge-transfer resistance Rct can be effectively estimated from extrapolation of Fre to high frequencies. Figure 9(c) illustrates a typical example obtained for the ferrocyanide–TCNQ system [43]. A further advantage of this technique is that the extrapolated value of the parameter Fre is proportional to Rct , i.e., independent of the uncompensated resistance. The formal pseudo-ﬁrst-order ET rate constant obtained from the optical analysis was largely consistent with the electrical impedance studies [63]. A further spectroscopic approach was employed in the work by Ding et al. [43], in which the absorption transient is recorded after a potential step. For the case of TCNQ, the absorption transient is given by ! 2TCNQ ½TCNQkf 2 t1=2 1 ð29Þ ATIR ¼ 2 cos ’ 1=2 where ¼

kf 1=2 DTCNQ

þ

kb 1=2 DTCNQ

ð30Þ

and the rate constants kf and kb stand for the forward and backward electron transfer. The rate constants obtained for the ferrocyanide–TCNQ system by chronoabsorptometry were consistent with the data derived from PMR. The combination of the two optical analyses allowed accessing ET rate constant values over a wider potential range than in the case of the electrical impedance analysis. This is a particularly relevant aspect for studies of the potential dependence of the interfacial ket . Initial analysis of ET kinetics under open circuit was performed at different experimental conditions than those described for externally biased interfaces [44,93,94]. Recent developments on SECM and MEMED (Chapters 12 and 13) have proved to monitor ET kinetics over a wide range of time scales. Barker et al. have extended the analysis of concentration proﬁles beyond the constant composition approximation [45] previously employed for SECM studies. For redox species exhibiting similar diffusion coefﬁcients, the constant composition approximation requires in excess of 15 to 20 times of the species which regenerates the probe at the liquid–liquid junction. However, extension of the analysis to a variety of concentration ratios allows measurements of very fast processes, which would otherwise appear as diffusion controlled. For instance, it was estimated that the bimolecular heterogeneous rate constant between the radical ZnTPPþ and FeðCNÞ4 6 approaches 55 M1 cm s1 at the water–benzene interface. This result remarkably contrasts with the 1:8 M1 cm s1 reported by Shi and Anson obtained for suspended thin organic electrolyte layers on graphite electrodes [97]. The recently developed MEMED technique provides accurate measurements for rather slow processes, beyond the range available for SECM [59]. In this approach, the liquid–liquid interface is an expanding droplet, and the concentration proﬁles of the redox

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species located in the static phase are monitored by a microelectrode as the drop expands. Contrary to the results obtained by Liu and Mirkin employing SECM [46], Unwin et al. successfully analyzed the ET kinetics between ferrocyanide and TCNQ at the water–DCE interface by MEMED [110]. The discrepancies between these two approaches may be connected to the reliability of SECM to measure rather slow charge-transfer kinetics. The dynamics of ET can also be severely affected by the addition of surfactants to the liquid–liquid junctions. The approach of redox species to the interfacial region can be effectively hindered by adsorbed surfactant molecules featuring phosphocholine heads [44,76,111], inducing a substantial decrease of ket . The extent of the ET blocking depends on the arrangement of the lipid layer, the structure of the surfactant, and the size of the redox species. Tsionsky et al. attempted to analyze the value of ket of the þ RuðCNÞ4 6 =ZnTPP system as a function of the length of the phospholipid hydrocarbon chain [44]. Although a decrease of the rate constant was evident with increasing number of methylene groups, the trend was complicated by variations on the properties of the lipid layer. For instance, the rate constant obtained for the C-10 chain was rather similar to that for C-20. This behavior was interpreted in terms of partial penetration of ZnTPPþ through the lipid layer, providing faster transfer kinetics than expected. Cheng and Schiffrin observed that ET involving ferri/ferrocyanide and RuðTPPÞðpyÞ2 and LuðPCÞ2 was inhibited by lecithin–cholesterol adsorbed at the water–DCE interface, although electron transfer to TCNQ was still measurable. This difference was rationalized in terms of the size of the redox species. While the Ru and Lu complexes are rather bulky, TCNQ is considerably smaller and therefore able to penetrate the lipid layer. Delville et al. demonstrated that the electronic structure of the phospholipid can also play a role on the ET dynamics [111]. In this work, it was shown that electrons are transferred faster through polyconjugated chains in comparison with saturated ones. D.

Butler–Volmer vs. Concentration Polarization

The potential dependence of the ET rate constant is one of the most controversial issues in this ﬁeld. By accessing the fraction of the Galvani potential difference operating on the ET step, also known as the transfer coefﬁcient , essential information on the potential distribution and structure of the interface can be obtained. As discussed in Section II.B, two mechanisms can contribute to the dependence of ket on w o : concentration polarization and changes in the free energy of ET (Butler–Volmer). While the latter is traditionally associated with metal–electrolyte interfaces, the former is commonly observed at semiconductor–electrolyte junctions where the density of charge carriers in the solid is ﬁnite. Lattice-gas modeling of the interface established that if the distance separating the redox couples is smaller than the Debye lengths at the interface, changes in w o will mostly affect the interfacial concentrations of the ionic species [7]. However, a great deal of the experimental studies have been carried out at rather high ionic strengths, where the Debye lengths could be rather short and different from the classical Gouy–Chapman expression. The theoretical approach by Samec based on the ion-free compact layer model established that the ‘‘true’’ apparent transfer coefﬁcient is obtained after correction for concentration polarization effect [1] [see Eq. (14)]. Subsequent studies by Samec and coworkers on the ferricyanide–Fc system provided values of smaller than the expected 0.5. Preliminary attempts to rationalize this behavior were based on deﬁning effective interfacial charges and separation distance between reactants [79]. The inconclusive trends reported in these studies were ascribed to complications arising from ion pairing of the ferro/ferricyanide ions. Later analysis of the same system appeared to show that ket is

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rather independent of the Galvani potential difference, and the observed dependence is mainly connected to concentration polarization [67]. The kinetic analysis by Cheng and Schiffrin of the TCNQ reduction by ferrocyanide arrived at a different conclusion [63]. In this case, the aqueous phase features a rather high ionic strength and an excess of the redox couple with respect to the organic phase. The cyclic voltammogram exhibited a peak-to-peak difference close to 59 mV as exempliﬁed in Fig. 5(c). The authors rationalized this behavior by considering the aqueous phase acting as a ‘‘metallic’’ electrode, under the assumption that the excess concentration of the aqueous redox couple remains unaffected by the Galvani potential difference. Impedance analysis following Eqs. (22)–(26) provided a potential dependence of the observed ket , which did not follow a pure Butler–Volmer behavior. The observed deviations were interpreted in terms of a perturbation of the local potential due to interfacial ion pairing of the ionic redox couple in the aqueous phase and the organic supporting electrolyte. This conclusion is not entirely consistent with the admittance analysis itself, as the ion-pairing excess charge would introduce an extra contribution to the total imaginary t admittance Yim which cannot be separated from the faradaic admittance by simple subb [Eq. (23)]. For instance, this excess charge traction of the base electrolyte response Yim would manifest itself as an increase of the differential capacitance with respect to theoretical values obtained in the absence of ion pairing [24,25,112]. The non-steady-state optical analysis introduced by Ding et al. also featured deviations from the Butler–Volmer behavior under identical conditions [43]. In this case, the large potential range accessible with these techniques allows measurements of the rate constant in the vicinity of the potential of zero charge (kpzc obs ). The potential dependence as obtained from the optical analysis of the of the ET rate constant normalized by kpzc obs TCNQ reduction by ferrocyanide is displayed in Fig. 10(a) [43]. This dependence was analyzed in terms of the preencounter equilibrium model associated with a ‘‘mixed-solvent layer’’ type of interfacial structure [see Eqs. (14) and (16)]. The experimental results were compared to the theoretical curve obtained from Eq. (14) assuming that the potential drop between the reaction planes (ab ) is zero. The potential drop in the aqueous side was estimated by the Gouy–Chapman model. The theoretical curve underestimates the experimental trend, and the difference can be associated with the third term in Eq. (14). Figure 10(b) shows the inner potential as a function of the Galvani potential difference assuming a value of 0.5 for the transfer coefﬁcient . From this analysis it is estimated that about 30% of the Galvani potential difference is developed between the redox reaction planes. It should be mentioned that these calculations are approximate, especially considering the primitive model employed for calculating ion distributions under high ionic strength. However, we believe that a more sophisticated model would not change substantially the physical aspects highlighted in this approach. The previous analysis indicates that although the voltammetric behavior suggests that the aqueous phase behaves as a ‘‘metal electrode’’ dipped into the organic phase, the interfacial concentration of the aqueous redox couple does exhibit a dependence on the Galvani potential difference. In this sense, it is not necessary to invoke potential perturbations due to interfacial ion pairing in order to account for deviations from the Butler– Volmer behavior [63]. This phenomenon has also been discarded in recent studies of the same system based on SECM [46]. In this work, the authors observed a potential independent ket for the reaction sequence, 3 RuðCNÞ4 6 !RuðCNÞ6 þ e

(at the microelectrode tip in water phase)

ð31Þ

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FIG. 10 Potential dependence of the electron-transfer rate constant (ket ) normalized to the value at the potential of zero charge (kpzc obs ) for the TCNQ reduction by hexacyanoferrate at the water–DCE interface. Full line was estimated from Eq. (14), assuming that the potential drop across the inner layer is negligible. Dependence of the potential drop across the ET reaction plane with the Galvani potential difference, as obtained from recalculation of the two trends in (a), assuming a transfer coefﬁcient of 0.5 (b). These results suggest that approximately 30% of the Galvani potential difference is developed between the reacting species under the experimental conditions deﬁned in Figs. 5 and 9. (Reprinted from Ref. 43 with permission from Elsevier Science.)

ket 4 þ RuðCNÞ3 6 ðwÞ þ ZnTPPðoÞ ! RuðCNÞ6 ðwÞ þ ZnTPP ðoÞ

(at ITIES)

ð32Þ

This result was taken as an experimental conﬁrmation of the model developed by Schmickler [7]. However, it appeared somehow contradictory with other results obtained with SECM. It was also suggested that concentration polarization phenomena occurring at the aqueous side are negligible as the whole potential drop is presumably developed in the benzene phase. This assumption can be qualitatively veriﬁed by evaluating a simpliﬁed expression for the potential distribution based on a back-to-back diffuse double layer [40,113], w w RT c 1 0 w ln 0 0

w ¼ 1=2o ð33Þ 2F c where and c correspond to the dielectric constant and concentration of the ionic species in the corresponding electrolyte solution. Taking an arbitrary value of 0.2 V for the Galvani potential difference w o , the potential developed in the aqueous side could range from 5 mV to 50 mV depending on the composition of the electrolyte in the organic phase. For the sake of comparison, this potential drop is similar to that observed for the

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water–DCE junction under the conditions described in Fig. 1 and Ref. [43]. Although a more thorough analysis would require an estimation of the Galvani potential difference, it is clear that the potential drop in the aqueous phase is not necessarily negligible and therefore concentration polarization effects for highly charged species such as RuðCNÞ3 6 should be considered. In other words, the weak increase of observed ket as

becomes more positive can be attributed to a combined depletion of RuðCNÞ3 the w o 6 and increase of the real heterogeneous ET rate constant. Similar SECM studies by Tsionsky et al. [44,93] revealed a strong potential dependence of ket , featuring an apparent transfer coefﬁcient of 0.5, for the system described in Eqs. (31) and (32). In this report, the feedback current was measured for the ZnTPP species instead of the aqueous redox couple. The value of was conﬁrmed over a potential range of 120 mV and various concentration of RuðCNÞ4 6 in the aqueous phase under the constant composition approximation. This behavior was rationalized in terms of conventional ET theories transposed to liquid–liquid junctions as initially postulated by Samec in 1979 [1]. The apparent value of was also taken as a criterion for neglecting concentration polarization phenomena. Furthermore, as the difference in the ET driving force was increased by changing the redox couple in the aqueous phase, the transfer coefﬁcient decreased until the ET kinetics was diffusion controlled [44]. These crucial experimental results provide a ﬁrst conﬁrmation of the ket dependence on the free energy of electron transfer [5]. A more spectacular demonstration was later reported by Barker et al., who extended the SECM analysis beyond the constant composition approximation obtaining kinetic responses on the inverted Marcus region [45]. Although the correlation between ket and the driving force determined by Eq. (14) has been conﬁrmed by various experimental approaches, the effect of the Galvani potential difference remains to be fully understood. The elegant theoretical description by Schmickler seems to be in conﬂict with a great deal of experimental results. Even clearer evidence of the ket dependence on w o has been presented by Fermı´ n et al. for photoinduced electron-transfer processes involving water-soluble porphyrins [50,83]. As discussed in the next section, the rationalization of the potential dependence of ket in these systems is complicated by perturbations of the interfacial potential associated with the speciﬁc adsorption of the ionic dye.

IV.

PHOTOINDUCED ET REACTIONS

Photoinduced ET at liquid–liquid interfaces has been widely recognized as a model system for natural photosynthesis and heterogeneous photocatalysis [114–119]. One of the key aspects of photochemical reactions in these systems is that the efﬁciency of product separation can be enhanced by differences in solvation energy, diminishing the probability of a back electron-transfer process (see Fig. 11). For instance, Brugger and Gra¨tzel reported that the efﬁciency of the photoreduction of the amphiphilic methyl viologen C14 V2þ by RuðbpyÞ2þ 3 is effectively enhanced in the presence of cationic micelles formed by cetyltrimethylammonium chloride [120]. Flash photolysis studies indicated that while the kinetics of the photoinduced reaction,

2þ þ RuðbpyÞ2þ ! RuðbpyÞ3þ 3 þ C14 V 3 þ C14 V

ð34Þ

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FIG. 11 General mechanism for the heterogeneous photoreduction of a species ‘‘Q’’ located in the organic phase by the water-soluble sensitizer ‘‘S.’’ The electron-transfer step is in competition with the decay of the excited state, while a second competition involved the separation of the geminate ion-pair and back electron transfer. The latter process can be further affected by the presence of a redox couple able to regenerate the initial ground of the dye. This process is commonly referred to as supersensitization. (Reprinted with permission from Ref. 166. Copyright 1999 American Chemical Society.)

remains unaffected by the presence of the cationic micelles, the rate of the back electron transfer þ 2þ ! RuðbpyÞ2þ RuðbpyÞ3þ 3 þ C14 V 3 þ C14 V

ð35Þ

was substantially decreased. These results suggest that the lower hydrophilicity of the radical C14 Vþ allows it to be trapped inside the micellar cage, avoiding back electron transfer by keeping away the oxidized dye by electrostatic repulsion. In a series of papers by Kotov and Kuzmin, the effect of polarizable liquid–liquid junctions on the separation of photoproducts was studied by photocurrent measurements [121–123]. The systems studied featured homogeneous quenching of protoporphyrin by quinone, and quinone by tetraphenylborate, as well as self-quenching of tetraphenylporphyrin in the organic phase. For all cases, charged photoproducts were generated and the transfer of these species across the liquid–liquid junction was followed by photocurrent measurements. The time scales of the photoresponses were in the range of fractions of a minute to minutes. Rather complex analysis was proposed in order to account for the various possible photoprocesses, including photo-oxidation of the organic supporting electrolyte. A comprehensive review of these works has been presented elsewhere [117]. As mentioned in previous sections, we shall concentrate on systems where photoactive species and redox quenchers are separated by the liquid–liquid junction. Although the distance separating the redox species effectively slows down the back electron transfer, it also brings about a decrease of the photoinduced ET reaction in comparison to homogeneous processes. As represented in Fig. 11, the overall efﬁciency of the photoreaction is initially determined by the ratio between ket and the rate of excited state decay (kd ). In this respect, vectorial ET can be enhanced by speciﬁc interaction of the reactants with the liquid–liquid junction, e.g., speciﬁc adsorption, self-assembling, and interfacial ion pairing. Considering the role of these interfacial interactions, ITIES can be regarded as a photochemical molecular device (PMD), i.e., an assembly of molecules capable of performing light-induced functions [124,125].

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A.

Recent Spectroscopic Studies on Photoinduced ET at Liquid–Liquid Interfaces

The elementary steps involved in photoinduced ET processes are schematically represented in Fig. 11. At the interfacial region, the electron-transfer step is in competition with the relaxation of the excited state. The intermediate species generated after the ET step can be associated with the geminate ion pair familiar from classical photochemistry. In the case of a heterogeneous photoreaction, the ET products are located in different electrolyte phases with their solvation shells. Subsequently, a new competition is developed between the separation of photoproducts and back electron transfer. Two ways can be envisaged for monitoring the dynamics of photoinduced reactions, (1) spectroscopic detection of reactants and/or products by time-resolved spectroscopy or (2) monitoring the ﬂux of charge transfer under potentiostatic conditions upon illumination (photocurrent measurements). The former approach is treated in this section. Corn and coworkers provided one of the ﬁrst spectroscopic evidences of photoinduced ET reactions at liquid–liquid interfaces employing optical second harmonic generation (SHG) [126]. The interfacial photochemical reaction involving RuðbpyÞ2þ 3 and the SHG probe trans-1-ferrocenyl-2-[4-(trimethylammonium)phenyl] ethylene was studied at the water–DCE interface. Experimental details and results have been reviewed in the chapter on nonlinear optics (Chapter 6). The photo-oxidation of the ferrocene unit in the surface active species introduces a strong change in the nonlinear optic parameters of the interface under illumination. The rise time and decay for the SHG signal upon a square-wave light perturbation were of the order of 10 to 20 s1 . The rather slow dynamic responses are not essentially related to the kinetics of charge transfer but to other processes such as diffusion of the excited state to the interface, lateral diffusion of the oxidized probe, and product desorption. A more direct approach to the photoinduced ET dynamics involves monitoring the lifetime of the excited state at the interface. By illuminating the interface in TIR from the electrolyte phase containing the quencher species, the generation of excited state is limited to the characteristic penetration depth given by the evanescent wave () [127], ¼

2

1 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 n1 sin ðn22 =n21 Þ

ð36Þ

where is the wavelength of illumination, is the incident angle, n1 and n2 correspond to the refractive indexes of the phase containing the dye and the light propagating phase respectively. For the water–DCE interface under illumination from the organic side in the visible range at higher than the critical angle (67:56 ), the penetration depth into the aqueous phase is of the order of 100 nm. In the presence of a dye species, the penetration depth is further reduced according to the Beer–Lambert expression, resulting in a distribution of the excited state c ðxÞ of the form c ðxÞt¼0 ¼ A expðxÞ

ð37Þ

where is the penetration depth of light into the aqueous phase corrected for dye absorption. Considering the diffusion controlled interfacial quenching of the excited state, it follows that the time dependent ﬂuorescence signal is proportional to

pﬃﬃﬃﬃﬃﬃ

pﬃﬃﬃﬃﬃﬃ A exp 2 Dt erfc Dt exp 2 Dt erfc Dt NðtÞ ¼ expðkd tÞ ð38Þ

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203

where the parameter includes the bimolecular rate constant of heterogeneous quenching kq . ¼

kq cq D

ð39Þ

kd and D correspond to the rate of decay and diffusion coefﬁcient of the excited state respectively, while cq is the bulk concentration of the quencher species. On the basis of Eqs. (36)–(39), the ﬂuorescence transients for two dyes with different excited-state lifetime are simulated in Fig. 12. A noticeable difference in the luminescent decay between the limits of inﬁnitely fast quenching and kq ¼ 0 is observed for Eu(III). The rate constant of excited-state decay for this cation is 104 s1 , which is approximately two orders of magnitude slower than for RuðbpyÞ2þ 3 . In the latter case, the decay of the luminescence is very similar for the inﬁnitely fast and inﬁnitely slow limits. Indeed, these simulations indicate that the dynamics of heterogeneous quenching at the liquid–liquid junction can be accessed by time-resolved spectroscopy only if the diffusion of the excited state can effectively compete with the relaxation process. The above analysis was entirely consistent with the experimental behavior observed for the systems Eu(III) and anthracene as well as RuðbpyÞ2þ 3 and TCNQ at the water–DCE interface [127]. The dependence of the rate of ﬂuorescent decay for Eu(III) on the anthra-

FIG. 12 Simulation of ﬂuorescent decays for dye species located in the aqueous phase following laser pulses in TIR from the water–DCE interface according to Eq. (38). A fast rate constant of excited state decay (106 s1 ) was assumed in (a). The results showed no difference between inﬁnitely fast or slow kinetics of quenching. On the other hand, a much slower rate of decay can be observed for other sensitizers like Eu3þ and porphyrin species. Under these conditions, heterogeneous quenching associated with the species Q can be readily observed as depicted in (b). (Reprinted with permission from Ref. 127. Copyright 1997 American Chemical Society.)

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cene concentration allowed estimations of the interfacial quenching rate constant of the order of 20 M1 cm s1 . The value of kq is of the same order as the maximum electron– transfer rate constant observed experimentally for the reduction of ZnTPPþ by FeðCNÞ4 6 at the water–benzene interface [45]. It is also close to the limit determined by Eq. (17) for separation between redox species over few nanometers. Although the latter reaction takes place in the dark, the large driving force involved (see redox potential diagram) may lie close to that expected for a photoinduced process. A rather important aspect that should be considered is that interfacial quenching of dyes does not necessarily imply an electron-transfer step. Indeed, many photochemical reactions involving anthracene occur via energy transfer rather than ET [128]. A way to discern between both kinds of mechanisms is via monitoring the accumulation of photoproducts at the interface. For instance, heterogeneous quenching of water-soluble porphyrins by TCNQ at the water–toluene interface showed a clear accumulation of the radical TCNQ under illumination [129]. This system was also analyzed within the framework of the excited-state diffusion model where time-resolved absorption of the porphyrin triplet state provided a quenching rate constant of the order of 92 M1 cm s1 .

B.

Photocurrent Responses Originating from Heterogeneous Quenching of Dyes

Under potentiostatic conditions, the perturbation of the charge across the interface associated with the photoinduced ET step is relaxed through the counterelectrodes located in each phase. In the absence of coupled ion-transfer reactions, the photocurrent responses are proportional to the ﬂux of charge associated with the heterogeneous quenching of the dye species. From the mechanism in Fig. 11, it is also observed that not only heterogeneous ET occurs via the dye-excited state, but also via back electron transfer involving the interfacial geminate ion pair. By contrast to time-resolved spectroscopy, photocurrent responses at well-deﬁned systems are a deﬁnitive evidence of heterogeneous photoinduced electron transfer. However, these measurements are carried out at time scales longer than fractions of milliseconds. This restriction is imposed by the time constant of charging the interfacial double layer (Ru Cdl Þ under potentiostatic conditions. The ﬁrst report on photocurrent measurements at liquid–liquid interfaces was published by Marecek et al. for the photoreduction of methylviologen in the aqueous phase by RuðbpyÞ2þ 3 located in the organic phase (DCE or benzonitrile) [48], 2þ þ RuðbpyÞ2þ ! RuðbpyÞ3þ ð40Þ 3 DCE þ MV 3 DCE þ MV water water The cationic dye was associated with the anion (7,8,9,10,11,12 Br6 -1-CB11 H6 Þ in order to dissolve it in the organic phase. The polarizable window available for photoinduced electron transfer in this system extended over 100 mV for the conditions speciﬁed in Fig. 13. The photocurrent responses were measured under chopped light and lock-in detection at 8.4 Hz. Figure 13(b) shows that some photoresponses occur only in the presence of the dye species, which the authors attributed to the transfer of RuðbpyÞ2þ 3 to the aqueous phase as a result of interfacial polarization induced by the chopped light [130]. Upon addition of MV2þ in the aqueous phase, an increase in the amplitude of the photocurrent is observed in conjunction to a slight change of phase shift. The authors proposed that these effects can be taken as an evidence for heterogeneous photoinduced ET. However, the analysis of curves 2 and 3 in Fig. 13(c) appears rather inconsistent with this idea. The ‘‘photoinduced’’ transfer of the cationic dye would involve a current

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FIG. 13 Cyclic voltammogram (a) and potential dependence of the photoresponses (b)–(c) to chopped illumination and lock-in detection associated with the photoreaction in Eq. (40). The CV shows that the polarizable window extended to less than 100 mV. The photocurrent measurements carried out were done in the presence (trace 3) and absence (trace 2) of the redox quencher in the organic phase. (Reprinted with permission from Ref. 48. Copyright 1989 American Chemical Society.)

response of opposite sign to the ET phenomenon; therefore it is difﬁcult to reconcile both faradaic processes with an increase of the photocurrent amplitude. Furthermore, if it is assumed that the ET is the predominant step, the phase shift should be approximately 180 with respect to the signal observed in the absence of MV2þ . Another point subject to criticism from this work is the apparent absence of DC photocurrents upon constant illumination. Although the responses in Fig. 13(c) appear effectively in phase at the chopping frequency, it is possible that slow photoinduced perturbation of accumulated charge at the interface can be connected with these photoresponses, e.g., photoionization of the dye [72]. In this respect, clearer evidence of photoinduced ET was introduced by Brown et al. for the reaction [49] 2þ 3þ RuðbpyÞ3 water þTCNQDCE ! RuðbpyÞ3 water þTCNQ ð41Þ DCE Within the potential range where RuðbpyÞ2þ 3 remains in the aqueous phase, photocurrent responses are clearly observed with a slow rising time of the order of 10 s as shown in Fig. 14(a). According to the convention employed by these authors, positive currents correspond to the transfer of a negative charge from water to DCE. No photoresponses were observed in the absence of either the dye in the aqueous phase or TCNQ in DCE. Further analysis of the interfacial behavior of the product TCNQ revealed that the ion transfer occurred outside of the polarizable window [cf. Fig. 14(d)], conﬁrming that these photoresponses are not affected by coupled ion-transfer processes. An earlier report also showed photoeffects for the photoreduction of the viologen C7 V2þ under similar conditions [131]. Although the reports by Brown et al. provided strong evidence of photoinduced heterogeneous ET responses [49], the rather slow rising times observed in the transients of Fig. 14(a) are difﬁcult to rationalize on the basis of the mechanism in Fig. 11. Another puzzling point is the potential dependence of the photocurrent obtained under chopped

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FIG. 14 On–off photocurrent responses (a) associated with the reaction in Eq. (41) at w o ¼ 0:225 V. In this ﬁgure, positive currents correspond to the transfer of a negative charge from water to DCE. The potential dependence of the photocurrent (b) was obtained under chopped illumination and lock-in detection. The maximum in the photocurrent–potential curve contrasts with the small changes in the dark current shown in (c). These responses are developed within the polarizable window described in (d). (From Ref. 49. Reproduced by permission of The Royal Society of Chemistry.)

illumination and lock-in detection exempliﬁed in Fig. 14(b). As the Galvani potential difference was swept negative, an increase of the photocurrent was detected in the region between 0:10 to 0:20 V. This behavior is consistent with kinetically controlled ET reaction from the aqueous to the organic phase. As the potential becomes more negative a decrease of the photocurrents is observed which is difﬁcult to analyze solely in terms of total amplitude. In principle, the attenuation of the photocurrent can be associated with a decrease of the interfacial concentration of the cationic dye. Another possibility is that as the interfacial capacitance increases steeply in this region, therefore increasing the attenuation of the photocurrent due to the slow dynamics of double layer charging–discharging [132]. In order to explore these phenomena, a full analysis of the photocurrent amplitude and phase shift at various chopping frequencies is required. This type of analysis will be discussed in the next section. More recently, a series of papers based on photocurrent responses involving water soluble porphyrin species has allowed to address the various aspects involved in the mechanism of Fig. 11 [50,73,83]. Photocurrent transients at the water–DCE interface in the presence of zinc tetrakis(carboxyphenyl) porphyrin (ZnTPPC4 ) and Fc under monochromatic light are shown in Fig. 15 at various Galvani potential differences [50]. The

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207

FIG. 15 Photocurrent responses associated with the heterogeneous quenching of ZnTPPC4 by diferrocenylethane at the water–DCE interface at various Galvani potential differences. The increase of the photocurrent upon illumination is remarkably faster than for the transients shown in Fig. 14(a). (Reprinted with permission from Ref. 50. Copyright 1998 American Chemical Society.)

porphyrin species does not transfer to the organic phase within the available potential region. A wealth of interesting features can be considered from these results: 1.

2.

Despite the large driving force involved in ET from Fc to the excited state of the porphyrin [compare potentials in Figs. 3(a) and 4], photocurrents are only observed at positive Galvani potential differences. Furthermore, photocurrent studies with various electron donors feature very similar potential dependencies [83]. As the Galvani potential increases, it is expected that the interfacial concentration of the ionic dye decreases; however, the photocurrent readily increases.

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3.

4.

The maximum photocurrent occurs simultaneously with the light perturbation within the millisecond time scale, except at rather positive Galvani potential difference where phase shift associated with photo-oxidation of the supporting electrolyte ðTPBCl ) and Ru Cdl attenuation is observed. Between 0.20 and 0.30 V, a decay of the initial photocurrent and a negative overshoot after interrupting the illumination are developed. This behavior resembles the responses observed at semiconductor–electrolyte interfaces in the presence of surface recombination of photoinduced charges [133–135] but at a longer time scale. These features are in fact related to the back-electron-transfer processes within the interfacial ion pair schematically depicted in Fig. 11.

Before each of these points is addressed, some other points should be discussed in connection with the nature of these photoresponses. The photocurrent dependence on the wavelength of illumination depicted in Fig. 16 clearly indicates that these responses are connected with the excited state of the dye species [73]. Furthermore, upon replacing an electron donor by an acceptor in the organic phase such as TCNQ, the sign of the photocurrent is reversed as contrasted for a photoactive porphyrin ion pair in Figs. 17(a) and (b). It is also observed that the back ET responses are rather strong, i.e., the steady-state photocurrent is effectively zero. Figure 11 shows that aqueous phase redox couples, which are able to react swiftly with the intermediate species, can eventually decrease the probability of back ET. This is exempliﬁed in Fig. 17(b), where the backelectron-transfer responses are effectively diminished upon addition of the hexacyanoferrate couple to the aqueous phase. This effect is analogous to supersensitization processes familiar from the dye-sensitized semiconductor–electrolyte interface [136].

C.

Basic Aspects Concerning Dynamic Photocurrent Measurements

The advantage of employing periodic perturbation of light intensity, e.g., using a chopper, and phase-sensitive detection are beyond a simple enhancement of the signal-to-noise ratio. For photoinduced electron-transfer mechanisms, as schematized in Fig. 11, the

FIG. 16 Photocurrent spectra corresponding to the photo-oxidation of DCMFc by ZnTPPC4 at the water–DCE interface under chopped illumination and lock-in detection. The main features of the spectra coincide with the onset of the Soret band and the Q-bands of the porphyrin ring. (From Ref. 73. Reproduced by permission of the Royal Society of Chemistry.)

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209

FIG. 17 Reversal of the photocurrent sign upon replacing the electron donor DCMFc (a) by the electron acceptor TCNQ (b) in the presence of the porphyrin heterodimer ZnTMPyP–ZnTPPS at the water–DCE interface. The strong back electron-transfer features in the photoreduction of TCNQ were diminished upon addition of an equimolar ratio of ferri/ferrocyanide acting as supersensitizer in the aqueous phase (b). The mechanism of supersensitization is described in Fig. 11. From the potential relationship between these redox couples (Fig. 4), these phenomena can be regarded as interfacial photosynthetic processes as deﬁned in Fig. 3(b). (Reprinted with permission from Ref. 87. Copyright 1999 American Chemical Society; and from Ref. 166 with permission from Elsevier Science.)

amplitude and phase shift of the frequency-dependent photocurrent contain information on the dynamics of each of the steps involved. Intuitively, photoresponses at low frequencies comprise contributions from the various processes in the overall mechanism, i.e., steady-state conditions, while as the frequency is increased only the faster processes are observed. Under potentiostatic conditions, the photocurrent dynamics is not only determined by faradaic elements, but also by double layer relaxation. A simpliﬁed equivalent circuit for the liquid–liquid junction under illumination at a constant DC potential is shown in Fig. 18. The difference between this case and the one shown in Fig. 7 arises from the type of perturbation introduced to the interface. For impedance measurements, a modulated potential is superimposed on the DC polarization, which induces periodic responses in connection with the ET reaction as well as transfer of the supporting electrolyte. In principle, periodic light intensity perturbations at constant potential do not affect the transfer behavior of the supporting electrolyte, therefore this element does not contribute to the frequency-dependent photocurrent. As further clariﬁed later, the photoinduced ET

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FIG. 18 Simpliﬁed equivalent circuit for externally biased ITIES under illumination. The perturbations introduced by the photoreactions in Fig. 11 are contained within the generator term g. Cdl and Ru are associated with the interfacial capacitance and the uncompensated resistance. (From Ref. 83. Reproduced by permission of the Royal Society of Chemistry.)

step is effectively in phase with light perturbations at low illumination levels, consequently the faradaic component can be treated as a generator factor. In essence, the representation in Fig. 18 describes the generation of an excess charge at the interface, which relaxes through the Cdl and Ru [83]. From the schematic representation in Fig. 18, it follows that for a perturbation featuring a DC bias light (I0 ) and a sinusoidal component of amplitude I1 , I ¼ I0 þ I1 expði!tÞ

ð42Þ

the frequency-dependent photocurrent (j1 ) is given by j1 ¼ g1 ½1=ð1 þ Ru Cdl i!Þ

ð43Þ

where g1 corresponds to the AC ﬂux of electron transfer across the interface. Equation (43) describes the behavior of an ideal diode, from which the maximum frequency accessible under potentiostatic conditions can be determined. As we discuss later in this section, Eq. (43) can be further developed in order to include the various kinetic parameters associated with the photoinduced electron-transfer mechanism. The most common types of light intensity perturbations include light pulses as well as periodic square and sinusoidal functions. Short light pulses from femto- to nanosecond time scales have been extensively employed for time-resolved photovoltage measurements at semiconductor–electrolyte interfaces [137–142]. To our knowledge, no reports on timeresolved photovoltage measurements at ITIES have been published so far. However, considering the large Ru Cdl characterizing these junctions, it could be anticipated that photovoltage measurements can provide direct access to photoinduced ET rate constants. Mauzerall and coworkers have also employed this technique for studying photoprocesses involving porphyrin species at lipid bilayers [143–147]. The basic experimental arrangements for photocurrent measurements under periodic square and sinusoidal light perturbation are schematically depicted in Fig. 19. In the previous section, we have already discussed experimental results based on chopped light and lock-in detection. This approach is particularly useful for measurement at a single frequency, generally above 5 Hz. At lower frequencies the performance of lock-in ampliﬁer and mechanical choppers diminishes considerably. For rather slow dynamics, DC photocurrent transients employing optical shutters are more advisable. On the other hand, for kinetic studies of the various reaction steps under illumination, intensity modulated photocurrent spectroscopy (IMPS) has proved to be a very powerful approach [132,133,148– 156]. For IMPS, the applied potential is kept constant and the light intensity is sinusoid-

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FIG. 19 Block diagrams for photocurrent measurements with chopped light and lock-in detection (a) as well as for intensity-modulated photocurrent spectroscopy (b). (Adapted from Ref. 85.)

ally modulated employing an acousto-optic modulator [Fig. 19(b)]. The frequency range available for these measurements spanned from mHz to just below 100 kHz. Of course, the high-frequency limit is often determined by the Ru Cdl constant of the cell or the bandwidth of the potentiostat. Photocurrent analysis under chopped illumination and lock-in detection is largely complementary to IMPS. While the former provides a simple approach for studying the dependence of the photocurrent on applied potential or illumination wavelength (see examples in Figs. 13, 14, and 16), the latter allows reliable kinetic analysis as a function

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of the frequency of perturbation. In both approaches, the periodic optical response should be synchronized with the phase-sensitive detector or the DTF analyzer. This can be simply done by collecting either the reﬂected or transmitted light from the liquid–liquid junction into a fast light detector (fast photodiode or a photomultiplier tube). D.

Dynamics of the Various Processes Involved in Photoinduced ET

The ﬁrst estimations of ket for photoinduced processes were reported by Dvorak et al. for the photoreaction in Eq. (40) [157,158]. In this work, the authors proposed that the ‘‘impedance under illumination’’ could be estimated from the ratio between the AC photopotential under chopped illumination and the AC photocurrent responses. Subsequently, the ‘‘faradaic impedance’’ was calculated following a treatment similar to that described in Eqs. (22) to (26), i.e., subtracting the impedance under illumination and in the dark. From this analysis, a pseudo-ﬁrst-order photoinduced ET rate constant of the order of 102 to 103 m s1 was estimated, corresponding to a rather unrealistic ket > 106 M1 cm s1 . Considering the nonactivated limit for adiabatic outer sphere heterogeneous ET at liquid–liquid interfaces given by Eq. (17) [5], the maximum bimolecular rate constant is approximately 1000 smaller than the values reported by these authors. In our opinion, the interesting photoresponses described by Dvorak et al. were incorrectly interpreted by the spurious deﬁnition of the photoinduced charge transfer impedance [157]. Formally, the impedance under illumination is determined by the AC admittance under constant illumination associated with a sinusoidal potential perturbation, i.e., under short-circuit conditions. From a simple phenomenological model, the dynamics of photoinduced charge transfer affect the charge distribution across the interface, thus according to the frequency of potential perturbation, the time constants associated with the various rate constants can be obtained [156,159–163]. It can be concluded from the magnitude of the photoeffects observed in the systems studied by Dvorak et al., that the impedance of the system is mostly determined by the Ru Cdl time constant. Analysis of the ZnTPPC4 –Fc system within the framework of the model schematically described in Fig. 11 has delivered self-consistent information on the dynamics of photoinduced ET [50]. The dependence of the photocurrent on the porphyrin concentration at various Galvani potential differences is displayed in Fig. 20. These results were obtained in the linear region of the photocurrent with the light intensity. Under these conditions, diffusion effects can be neglected, and the excited-state generation can be taken as constant at a given potential and light intensity. The behavior in Fig. 20 suggests that the photoresponses are associated with adsorbed porphyrin species, and that the coverage effectively decreases as the Galvani potential difference increases. Neglecting back electron transfer and Ru Cdl attenuation effects at the measuring frequency, the photocurrent responses can be expressed in terms of the ﬂux of photoinduced electron injection (g) from the quencher to the excited state, ket cb g ¼ eI0 N ð44Þ ket þ kd 1 þ cb s where e is the electronic charge, I0 is the photon ﬂux, is the optical capture cross-section of the adsorbed porphyrin, is the Langmuir isotherm parameter, cb is the porphyrin bulk concentration, and Ns is the maximum surface density. This expression is based upon a competition between photoinduced ET and relaxation of the excited state. Fitting of Eq. (44) to the data in Fig. 20 conﬁrmed the effective desorption of the porphyrin with increasing potential, indicating that ket must increase in order to account for the increase

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FIG. 20 Photocurrent dependence on the concentration of the porphyrin ZnTPPC4 at the water– DCE interface in the presence of Fc at various Galvani potential differences. (Reprinted with permission from Ref. 50. Copyright 1998 American Chemical Society.)

in the overall photocurrent response. Furthermore, the photoinduced ket should be also of the same order as kd , i.e. 105 ; s1 as obtained from ﬂash photolysis experiments in TIR. In order to compare this magnitude with previous studies on heterogeneous ET, the value of pseudo-ﬁrst-order ket estimated from the photocurrent analysis has to be integrated over the distance separating the reactants. Assuming a reaction distance of 1 nm, a value of 102 cm s1 can be estimated for the pseudo-ﬁrst-order and 10 M1 cm s1 for the bimolecular heterogeneous rate constants. Despite the fact that this value is rather close to the Marcus limit for ET [see Eq. (17) and Ref. 45], the observed potential dependence of ket indicates that the photoinduced ET still involves activation energy. It should also be recalled that the photocurrent measurements do not provide a direct estimation of ket . Only the ratio ket =ðket þ kd Þ is available after considering porphyrin coverage and back ET responses. E.

Intensity-Modulated Photocurrent Spectroscopy (IMPS) Studies on Heterogeneous Quenching of Porphyrin

A more quantitative description of the photocurrent responses, taking into account the contributions from back electron transfer and Ru Cdl attenuation, was achieved by IMPS measurements [83]. Considering the mechanism in Fig. 11, excluding the supersensitization step, and the equivalent circuit in Fig. 18, the frequency-dependent photocurrent for a perturbation as in Eq. (42) is given by kps þ i! 1 ð45Þ j 1 ¼ g1 krec þ kps þ i! 1 þ RCint i! where the parameter g1 corresponds to the AC ﬂux of electron injection, ket cb g1 ¼ eI1 N ket þ kd þ i! 1 þ cb s

ð46Þ

Equation (45) resembles the generalized expression of IMPS for semiconductor– electrolyte interfaces [149,164]. This similarity between the dynamic photoresponses for both types of interfaces is only valid in phenomenological terms, as the natures of the

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photoinduced charge generation processes are essentially different. For instance, charge separation in the semiconductor space charge region occurs in the 1012 s time scale, which is out of the frequency range available under potentiostatic conditions. Charge separation in the context of liquid–liquid interfaces corresponds to the photoinduced electron-transfer step, which may occur in the range of 106 s. This time scale is also out of the experimental frequency range due to the large Ru Cdl time constant that characterizes these junctions, i.e., ket þ kd i!. Therefore, despite the fact that the generation term is developed at completely different rate, it can be considered effectively in phase with the light intensity perturbation below the MHz range. A complex representation of IMPS data obtained for the heterogeneous quenching of ZnTPPC4 –diferrocenylethane is displayed in Fig. 21(a). The semicircular response in the ﬁrst quadrant corresponds to the competition between product separation and back electron transfer, while the lower quadrant is determined by the Ru Cdl time constant. The Ru Cdl attenuation limited the frequency range to less than 1 kHz. Equation (45) describes the experimental spectra at various Galvani potential differences [solid lines in Fig. 21(a)],

FIG. 21 Complex IMPS spectra obtained for the photo-oxidation of DFcET by ZnTPPC4 at the water–DCE interface (a). The opposite potential dependencies of the phenomenological ET rate constant and the porphyrin coverage (b) are responsible for the maximum on the ﬂux of electron injection obtained from IMPS responses for DFcET and Fc (c). The potential dependence of the back electron-transfer rate constant is also shown in (d). (From Ref. 83. Reproduced by permission of The Royal Society of Chemistry.)

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allowing the evaluation of the AC ﬂux of electron injection as well as the phenomenological rate constants of product separation (kps ) and back electron transfer (krec ). Very similar behavior was observed for ferrocene and diferrocenylethane concerning the competing processes at low frequencies. For instance, a potential independent kps of the order of 5 s1 was obtained from this analysis. This rather slow value is difﬁcult to rationalize within classical photoelectrochemical models in the homogeneous phase [128]. The dependence of the ﬂux of electron injection and the back electron-transfer rate constant on the applied potential did reveal very interesting trends as depicted in Figs. 21(b)–(d). The behavior of g1 for both quenchers conﬁrmed the porphyrin desorption and the increase of ket with increasing Galvani potential differences. Both trends are schematically shown in Fig. 21(b). The combined effect of these two phenomena is responsible for the maximum observed in the ﬂux of electron injection as obtained from IMPS spectra [Fig. 21(c)]. The adsorption of ZnTPPC4 showed a weak dependence on the applied potential taking into account the charge of the anion. More recent studies have shown that rather complex processes such as partial protonation and interfacial ion pairing are related to the speciﬁc adsorption of the porphyrins [165]. The behavior of ket in Fig. 21(b) can be described as a ﬁrst approximation by a Tafel type of expression, ket ¼ ket0 expðFw o =RT Þ

ð47Þ

where ket0 is the phenomenological rate constant for Galvani potential difference equal to 0 V. The difference in g1 between ferrocene and diferrocenylethane only lies in the value of ket0 . By contrast, the rate constant krec features an inverse exponential dependence on the applied potential [Fig. 21(d)] but with a similar transfer coefﬁcient, 0 krec ¼ krec expðFw o =RT Þ

ð48Þ

where the observed value was around 0.4. The similar potential dependence of the phenomenological rate constant for the two ET processes was rationalized in terms of effective changes in the Gibbs activation energy [83]. From a qualitative point of view, a decrease in the activation energy for the photoinduced ET step should bring about an increase of this parameter for the back electron transfer within the framework of the mechanism considered in Fig. 11. However, the exact physical meaning of in this approach remains unknown. In the case of ZnTPPC4 , not only interfacial ion pairing but also speciﬁc adsorption introduces strong perturbations of the interfacial potential as indicated from capacitance–potential curves [50]. Inversion of the local electric ﬁeld at positive potential can be envisaged as a result of the excess charge associated with the anionic porphyrin. It is believed that these effects are responsible for the apparently serendipitous onset potential of the photocurrent and porphyrin desorption. It is clear that one of the major limitations of this analysis is the assumption of constant excited-state coverage. Deviations from the behavior described by Eq. (45) in the low frequency range have been observed at photocurrent densities higher than 106 A cm2 [50]. These deviations are expected to be connected to excited-state diffusion proﬁles similar to those considered by Dryfe et al. [see Eq. (38)] [127]. A more general expression for IMPS responses is undoubtedly required for a better understanding of the dynamics involved in back electron transfer as well as separation of the photoproducts.

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V.

TECHNOLOGICAL RELEVANCE OF HETEROGENEOUS ET PROCESSES AT ITIES

The recent experimental developments on ‘‘dark’’ and photoinduced ET reactions give support to the previous speculations on the relevance of these interfaces in such ﬁelds as catalysis and solar energy conversion. These disciplines have been, and still are centered on processes at solid–solution interfaces. However, particular applications require molecularly deﬁned interfaces, where reactants exhibit different solubility properties. In this section, we shall consider some of these systems and the advances reported so far. A.

Solar Energy Conversion at ITIES

As mentioned earlier, a great deal of literature has dealt with the properties of heterogeneous liquid systems such as microemulsions, micelles, vesicles, and lipid bilayers in photosynthetic processes [114,115,119]. At externally polarizable ITIES, the control on the Galvani potential difference offers an extra variable, which allows tuning reaction paths and rates. For instance, the rather high interfacial reactivity of photoexcited porphyrin species has proved to be able to promote processes such as the one shown in Fig. 3(b). The inhibition of back ET upon addition of hexacyanoferrate in the photoreaction of Fig. 17 is an example of a photosynthetic reaction at polarizable ITIES [87,166]. At Galvani potential differences close to 0 V, a direct redox reaction involving an equimolar ratio of the hexacyanoferrate couple and TCNQ features an ‘‘uphill’’ ET of approximately 0.10 eV (see Fig. 4). However, the excited state of the porphyrin heterodimer can readily inject an electron into TCNQ and subsequently receive an electron from ferrocyanide. For illumination at 543 nm (2.3 eV), the overall photoprocess corresponds to a 4% conversion efﬁciency. An alternative photosynthetic (supersensitization) mechanism has been recently described by Lahtinen et al. in a very similar system [51]. Upon replacing TCNQ by benzoquinone, the redox potential of the organic couple is shifted by approximately 500 mV toward more negative values. The decrease in the driving force for the photoinduced ET brings about a decrease in the photocurrent response and an increase in the back electron-transfer rate. The effect of the hexacyanoferrate redox couple under these con4 M. The increase of the ditions is observed at higher concentrations, ½FeðCNÞ4 6 > 5 10 hexacyanoferrate (II) concentration introduced an increase of the overall photocurrent and a decrease of the back ET rate constant. Analysis of IMPS data suggested that the excited state is rapidly quenched by FeðCNÞ4 6 , generating an intermediate species which subsequently reduces benzoquinone across the liquid–liquid junction. Unfortunately, complications, probably due to coupled ion-transfer processes, hindered quantitative analysis of the dynamic photoresponses. Despite the potential impact of novel photosynthetic routes based on these developments, the most ambitious application remains in the conversion of solar energy into electricity. Dvorak et al. showed that photocurrent as well as photopotential response can be developed across liquid–liquid junctions during photoinduced ET reactions [157,158]. The ﬁrst analysis of the output power of a porphyrin-sensitized water–DCE interface has been recently reported [87]. Characteristic photocurrent–photovoltage curves for this junction connected in series to an external load are displayed in Fig. 22. It should be mentioned that negligible photoresponses are observed when only the platinum counterelectrodes are illuminated. Considering irradiation AM 1, solar energy conversions from 0.01 to 0.1% have been estimated, with ﬁll factors around 0.4. The low conversion

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FIG. 22 Characteristic output power for water–DCE junctions in the presence of ZnTPPS– ZnTMPyP and TAA (a), SnTPPS and TAA (b), and SNTPPS and TCNQ (c). The supporting electrolytes were Li2 SO4 and BTPPATPFB. The supersensitizer for all cases was the couple Fe3þ =Fe2þ at pH 1 with equimolar ratio for (a) and (b), and 1/10 for (c). Light input was 103 W cm2 at 543 (a and c) and at 442 nm (b).

efﬁciencies are mostly related to the very poor light harvest at the liquid-liquid junction. On the other hand, the low ﬁll factors could be associated with the strong potential dependence of the photoresponses for the porphyrin-sensitized interfaces. Despite these limitations, the preliminary conversion efﬁciencies estimated so far should be regarded as very promising. One of the most important goals in solar cell design is to separate the generation and transport of photogenerated carriers. In solid-state devices, this feature is rather difﬁcult to achieve efﬁciently and at low cost due to the occurrence of interfacial defects at the semiconducting heterojunctions. Solar cells based on dye-sensitized colloidal semiconducting ﬁlms feature rather efﬁcient generation–collection properties; this has created a huge interest in the photoelectrochemical community [167,168]. The photogeneration of charge carriers occurs at the semiconductor–dye interface, while the transport takes place through the highly defective ﬁlm until the back contact. Although very high efﬁciencies exceeding 7% have been reported, the complex generation–collection dynamics remains rather controversial [169]. In the case of liquid–

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liquid interfaces, the electron transport is replaced by the relatively simple ionic transport in a homogeneous medium. In order to further develop liquid–liquid interfaces towards photovoltaic applications, thin electrolyte layer systems must be considered. In this respect, the interesting studies on surfaces modiﬁed by thin organic electrolyte layers [78,97] as well as by hydrophilic polypeptide multilayer ﬁlms [170] are important steps forward.

B.

Electrochemical Phase Formation at ITIES

Despite the fact that the electrodeposition of copper and silver at the water–DCE and the water–dichloromethane interfaces has been generally regarded as the ﬁrst experimental evidence for heterogeneous ET at externally biased ITIES [171], a very limited amount of work has dealt with this type of process. This reaction has also theoretical interest because the molecular liquid–liquid interface can be seen as an ideal substrate for electrochemical nucleation studies due to the weak interactions between the interface and the newly formed phase and the lack of preferential nucleation sites always present at metallic electrodes. As discussed in Section III.A, heterogeneous electrodeposition of metals at liquid– liquid junctions requires that the metallic complex and the reducing agent remain in the respective phases in the potential range where the electron transfer occurs. This condition is exempliﬁed in Fig. 23 for the generation of Au particles via the reduction of TOAAuCl4 by ferrocyanide at the water–DCE interface [89]. The charge-transfer reaction observed at potentials around 0.10 V corresponds to the transfer of the gold complex from DCE to water. In the presence of ferrocyanide, two additional peaks are observed at more negative potentials, which the authors assumed to correspond to the heterogeneous reduction of gold complex. In-situ and ex-situ spectroscopy of the interfacial deposit clearly conﬁrmed the generation of Au particles. In particular, in-situ spectrophotometric analysis showed a red shift in the plasmon resonance of maximum absorbance, indicating the growth of the metal particles at the interface. However, the choice of the experimental system was rather adverse, resulting in complex voltammetric behavior and hindering any systematic analysis on the nucleation reaction at ITIES.

FIG. 23 Cyclic voltammograms for ET between 0.2 mM TOAAuCl4 and 0.1 mM K4 FeðCNÞ6 at the water–DCE interface at 0.05 V s1 (a). The control experiments in the absence of the aqueous couple (b) and the metal complex (c) are also displayed. (From Ref. 89. Reproduced by permission of The Royal Society of Chemistry.)

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Recent studies have shown that the reduction of tetrachloropalladate in aqueous solution by ferrocene derivatives in the organic solvent leads to the generation of Pd particles at the water–DCE interface [90,91,172]. A typical voltammogram for the Pd nucleation by Fc is shown in Fig. 24. By contrast to the case AuCl 4 , the transfer of does not take place within the polarizable window. Upon cycling from negative to PdCl2 4 positive potentials, a large increase of the current is observed at potentials close to 0.2 V. A loop is observed at more positive potentials, and a transfer response occurs in the reverse cycle. The quasireversible response corresponds to the transfer of Fcþ generated during the irreversible reduction of palladate. The onset of the PdCl2 4 reduction is shifted toward more negative values in the second cycle, indicating the presence of electroactive Pd particles at the interface. Johans et al. derived a model for diffusion-controlled electrodeposition at liquid– liquid interface taking into account the development of diffusion ﬁelds in both phases [91]. The current transients exhibited rising portions followed by planar diffusion-controlled decay. These features are very similar to those commonly observed in three-dimensional nucleation of metals onto solid electrodes [173–175]. The authors reduced aqueous ammonium tetrachloropalladate by butylferrocene in DCE. The experimental transients were in good agreement with the theoretical ones. The nucleation rate was considered to depend exponentially on the applied potential and a one-electron step was found to be rate determining. The results were taken to conﬁrm the absence of preferential nucleation sites at the liquid–liquid interface. Other nucleation work at the liquid–liquid interface has described the formation of two-dimensional metallic ﬁlms with rather interesting fractal shapes [176]. Recent advances on electrochemical phase formation at ITIES include electropolymerization reactions. Cunnane and Evans reported the accumulation of oligomers of methyl- and phenylpyrrole at externally biased water–DCE interface [177]. The oligomerization reaction was initiated by heterogeneous oxidation of the monomer by Fe3þ located in the aqueous phase. The radical cation undergoes various chemical reactions in the homogeneous phase leading to the formation of oligomers in solution. More recent studies by the same group include the oligomerization of 2,2 0 :5 0 ,2 00 -terthiophene in DCE [178]. In this case, the oligomerization reaction seems to occur in a more controlled fashion at externally biased as well as open-circuit junctions.

FIG. 24 Cyclic voltammograms for the heterogeneous reduction of 0.01 M PdCl2 4 by 1 mM Fc at the water–DCE interface at 0.03 V s1 . The loop observed in the ﬁrst cycle and the changes observed in the second cycle correspond to the formation of interfacial Pd nuclei.

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C.

Two-Phase Catalysis and Photocatalysis

Catalysis at interfaces between two immiscible liquid media is a rather wide topic extensively studied in various ﬁelds such as organic synthesis, bioenergetics, and environmental chemistry. One of the most common catalytic processes discussed in the literature involves the transfer of a reactant from one phase to another assisted by ionic species referred to as phase-transfer catalyst (PTC). It is generally assumed that the reaction process proceeds via formation of an ion-pair complex between the reactant and the catalyst, allowing the former to transfer to the adjacent phase in order to carry out a reaction homogeneously [179]. However, detailed comparisons between interfacial processes taking place at externally biased and open-circuit junctions have produced new insights into the role of PTC [86,180]. Cunnane et al. compared the oxidation of SnðPCÞ2 by ferri/ferrocyanide at externally biased and open-circuit water–DCE junctions [86]. Under open-circuit conditions, the potential was controlled by the partition of tetra-aryl ammonium cations, which are commonly employed as phase transfer catalysts. Good correlation was obtained for the formal redox potential measured under potentiostatic conditions and from the partition ratio of TEAþ or TPAþ . These important results suggest that the role of the PTC is to ﬁx a Galvani potential difference between the two liquid phases, allowing heterogeneous ET processes to take place. This approach was adopted by Tan et al. [180] in the study of the Williamson ether synthesis and later Forssten et al. [181] for the oxidation of cis-cyclooctene in DCE or dichloromethane by aqueous permanganate. Also in these cases the role of the PTC was seen in ﬁxing the Galvani potential difference which then acted as the driving force for transferring the aqueous ionic reactants to the organic phase. Catalytic cycles can also be achieved via interfacial redox mediators acting as charge shuttles between redox species separated by long distance. In Section III.C, we discussed the experiments by Cheng and Schiffrin where TCNQ acted as a redox mediator for the oxidation of a Ru complex by ferricyanide at water–DCE interfaces modiﬁed by phospholipid monolayers [76]. Recently, Willner and Joselevich introduced a new concept based on ‘‘shuttle photosensitizers’’ at water-in-oil microemulsions [182]. In their approach, ethyl eosin is employed as sensitizer initially located in the water phase also in the presence of the electron acceptor ferricyanide, while tributylamine is the electron donor. The basic mechanism is illustrated in Fig. 25(a), in which the homogeneous quenching of the sensitizer by ferricyanide leads to the formation of a hydrophobic eosin radical. This radical readily transfers to the organic media where it is reduced by tributylamine. The transfer of the eosin radical to the organic phase decreases the probability of back electron transfer from ferrocyanide similarly to the principle developed by Brugger and Gra¨tzel on charged micelles [120]. Recently, Shao et al. [183] demonstrated how ITIES could be used in studying complex catalytic microemulsion reactions. The problem in investigating electrochemical kinetics in microemulsions is the undeﬁned interfacial area. Using the well-deﬁned liquid– liquid interface as a model system, together with the established electrochemical methods described in the previous sections of this review, offers a clear advantage for kinetic and mechanistic considerations. In their approach, Shao et al. used SECM to study the reaction between CoðIÞ form of vitamin B12 electrochemically generated in the aqueous phase with trans-1,2-dibromocyclohexane in benzonitrile. They were able to extract some information on apparent heterogeneous rate constants, and the effects of reactant concentration, Galvani potential difference and surfactant adsorption on the kinetics.

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FIG. 25 (a) Schematic representation for a photocatalytic mechanism based on ‘‘shuttle photosensitizers’’ at liquid–liquid interfaces. (Reprinted with permission from Ref. 182. Copyright 1999 American Chemical Society.) (b) This mechanism is compared to the photo-oxidation of 1-octanol by the heterodimer ZnTPPS–ZnTMPyP in the presence of the redox mediator ZnTPP. (From Ref. 185.)

A more complex catalytic mechanism has been presented by Tabushi and Noboru involving a synergetic combination of redox mediators and ‘‘phase transfer catalyst’’ at liquid–liquid interfaces [184]. For instance, the oxidation of benzyl alcohol and other organic substrates by NaOCl has been reported to be catalyzed by trioctylmethylammonium and MnTPPCl acting as PTC and redox mediator respectively at the water–CH2 Cl2 interface. This process is rather difﬁcult to control electrochemically due to the rather high reactivity of NaOCl in the aqueous phase. Lahtinen et al. proposed a different approach in which the NaOCl is substituted by the photoactive heterodimer ZnTPPS–ZnTMPyP in the water phase and the hydrophobic ZnTPP is used instead of MnTPPCl in the DCE phase [185]. As illustrated in Fig. 25(b), the main goal is the photo-oxidation of 1-octanol in DCE by the porphyrin heterodimer, employing ZnTPP as a mediator and replacing the PTC by potentiostatic control. Preliminary results indicate that the heterodimer can effectively oxidize ZnTPP to ZnTPPþ upon illumination, although relatively fast back electron transfer is observed. The back electron transfer effectively competes with the homogeneous oxidation of 1-octanol in the DCE phase [see Fig. 25(b)]. In the presence of the aqueous couple Fe2þ =Fe3þ acting as supersensitizer, the back electron-transfer features were partially diminished. Under these conditions, a substantial increase of the photocurrent was readily observed upon increasing concentration of 1-octanol, suggesting the regeneration of ZnTPP by 1-octanol at the interface.

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The catalytic properties of electrodeposited metallic particles at liquid–liquid interfaces are yet to be systematically explored. The only data available were presented by Cheng and Schiffrin at the Kyoto meeting on ‘‘Charge Transfer at Liquid–Liquid and Liquid–Membrane Interfaces’’ in 1996. The authors reported the catalytic dehalogenation of 2-bromoacetophenone to acetophenone in the presence of electrogenerated Pd particles at the water–DCE interface. In this respect, electroactive metallic particles at liquid–liquid junctions can be regarded as ‘‘surface states,’’ employing a terminology familiar from surface science. This kind of surface state might be able to enhance electron transfer by enhancing adsorption or coadsorption of redox species. Another kind of interaction, which can be envisaged, is the photoinduced charging of particles via interfacial dye species. The stored charge can subsequently induce reduction processes in the organic phase. A recent report by Lahtinen et al. provided the ﬁrst demonstration of photocatalytic reduction of species in DCE catalyzed by in-situ generated Pd particles at the ZnTPPC4 sensitized water–DCE junction [172]. VI.

CONCLUDING REMARKS

A consistent picture for dynamics of heterogeneous ET has been emerging in the last 5 years with the development of new experimental approaches. Techniques such as AC impedance, modulated and time-resolved spectroscopy, SECM, and photoelectrochemical methods have extended our knowledge of charge-transfer kinetics to a wide range of time scales. This can be exempliﬁed by comparing impedance analysis, which is limited to ket of the order of 101 M1 cm s1 , against SECM studies that have provided values close to 102 M1 cm s1 . The dependence of ket on the ET driving force given by Eqs. (13) and (14) has provided an experimental validation to the continuum model. Although molecular dynamics and lattice-gas modeling provide pictures rather different from the mathematically ﬂat liquid–liquid junctions employed by Marcus, the main derivations of his model appear consistent with experimental results assuming an average distance of 107 cm between redox centers at the interface. This distance can be modiﬁed by adsorption of amphiphilic species at the molecular junction. Among the most important aspects that remain to be solved, is the dependence of the observed ket on the Galvani potential difference. This issue holds essential information on the potential distribution and structure of the interface. Photoinduced heterogeneous ET at ITIES is opening new perspectives in the area of photoelectrochemistry. Vectorial control of the electron injection can be achieved not only by selecting appropriate redox species and photoactive redox dyes, but also by the applied Galvani potential difference. Photocatalytic and photosynthetic mechanisms initiated by the heterogeneous quenching of dyes have already been described at these interfaces. Finally, we do believe that these developments have provided a realistic alternative to solar energy conversion and photovoltaics. In conclusion, the increasing understanding on charge-transfer processes at liquid–liquid interfaces is not only establishing ﬁrm ground to potential technological applications, but also providing new alternatives in areas traditionally associated with solid-state junctions. ACKNOWLEDGMENTS We would like to express our gratitude to Professor Hubert Girault and Dr Pierre Franc¸ois Brevet for their encouragement and fruitful discussions. Our special thanks go

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also to Zhifeng Ding, Hong Duong, Henrik Jensen, Rodrigo Iglesias, Hirohisa Nagatani, Christoffer Johans, Bernadette Quinn, Laure Tomaszewski, Nicolas Eugster, and Stephane Gorgerat for their contributions and discussions. R. L. acknowledges the ﬁnancial support by the Neste Foundation, Finland. D. J. F. is also grateful for the support by the Fonds National Suisse de la Recherche Scientiﬁque (project 20-055692.98/1). The Laboratory of Physical Chemistry and Electrochemistry and the Laboratoire d’Electrochimie are part of the European Training and Mobility Network ODRELLI (Organization, Dynamics and Reactivity at Electriﬁed Liquid–Liquid Interfaces).

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9 Dynamic Behaviors of Molecules at Liquid^Liquid Interfaces Using the TimeResolved Quasi^Elastic Laser Scattering Method ISAO TSUYUMOTO Department of Environmental Systems Engineering, Kanazawa Institute of Technology, Ishikawa, Japan TSUGUO SAWADA Department of Advanced Materials Science, University of Tokyo, Tokyo, Japan

I.

INTRODUCTION

Experimental probes of liquid–liquid interfaces have been done mainly by spectroscopic and electrochemical techniques, which are suited to monitoring the interface between two bulk phases because their measurements result in no mechanical perturbation [1,2]. The quasi-elastic laser scattering (QELS) method has advantages as a tool for in situ, noncontact time-resolved measurements of dynamic behavior of molecules at liquid–liquid interfaces and liquid–air interfaces [3–9]. The method monitors the frequencies of capillary waves, which are spontaneously generated by a thermal ﬂuctuation at liquid–liquid interfaces. Since the capillary wave frequency is a function of interfacial tension, and the change in the interfacial tension reﬂects the change in the number density of surfactant molecules at the interface, the QELS method allows observation of dynamic changes of liquid–liquid interfaces such as the change in number density of surfactant molecules and the formation of a lipid monolayer. Owing to its improved time resolution, each power spectrum can be obtained in 1 ms to 1 s, so the method can be used to monitor dynamic changes at liquid–liquid interfaces in a real environment. Furthermore, this method has good interface selectivity for overcoming the problem of interference by bulk phases, because the capillary wave is a characteristic phenomenon at the interfaces and its frequency can be detected by an optical heterodyne technique. In the past ﬁve years, it has been demonstrated that the QELS method is a versatile technique which can provide much information on interfacial molecular dynamics [3–9]. In this review, we intend to show interfacial behavior of molecules elucidated by the QELS method. In Section II, we present the principle and the experimental apparatus of the QELS along with the historical background. The dynamic collective behavior of molecules at liquid–liquid interfaces was ﬁrst obtained by improving the time resolution of the QELS method. In Section III, we show the molecular collective behavior of surfactant molecules derived from the analysis of the time courses of capillary wave frequencies. Since the 229

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method is useful for monitoring the interfacial behavior of surfactants, it is applicable to practical systems which utilize the speciﬁcity of liquid–liquid interfaces, such as phase transfer catalysis and chemical oscillation systems. In Section IV we present an application of the QELS method to a phase-transfer catalyst system and describe new results on the reaction place of the catalyst. This is the ﬁrst application of the QELS method to a practical liquid–liquid interface system.

II.

QUASI–ELASTIC LASER SCATTERING METHOD

A.

Capillary Waves

Capillary waves occur spontaneously at liquid surfaces or liquid–liquid interfaces due to thermal ﬂuctuations of the bulk phases. These waves have been known as surface tension waves, ripples, or ripplons for the last century, and Lamb described their properties in his book Hydrodynamics in 1932 [10]. Before that, William Thomson (Lord Kelvin) mentioned these waves in some of his many writings. Here we brieﬂy present the relevant theory of capillary waves. The thermally excited displacement ðr; tÞ of the free surface of a liquid from the equilibrium position normal to the surface can be Fourier-decomposed into a complete set of surface modes as X ðr; tÞ ¼ 0 exp½ik r þ t ð1Þ k

The complex wave frequency ð¼ i!0 Þ is related to k via a dispersion relation. For an inviscid liquid, Lamb’s equation is well-known as a classical approximation for the dispersion relation [10] 12 3 1 k2 f ¼ 2 U þ L

ð2Þ

where f is the capillary wave frequency; , the interfacial tension; U , the density of the upper phase; L , the density of the lower phase; and k, the wavenumber of the capillary wave. This equation is valid for both liquid surfaces and liquid–liquid interfaces. For capillary wave at a liquid surface, U is regarded as zero in Eq. (2). In this equation, only the normal component of the interfacial tension is considered to act as a restoring force on the thermally excited displacement ðr; tÞ. Although this equation neglects the effect of surface viscosity, it gives a good ﬁt in the relation between frequency and wavenumber of capillary waves at a liquid surface such as ethanol, anisole, or water [10,11]. For the surface of a low-viscosity liquid, Levich [12] has derived the following dispersion relation: DðSÞ ¼ ðS þ 1Þ2 þ y ð2S þ 1Þ1=2 ¼ 0

ð3Þ

where S ¼ =2k2 , y ¼ =42 k. Here is the kinematic viscosity ð=, where is the viscosity of the liquid). In this equation, both the normal components of the surface tension and the stress by the viscosity are considered to act as a restoring force on the displacement ðr; tÞ. Based on this equation, a heterodyne power spectrum in the frequency domain becomes a Lorentzian proﬁle centered at !0 ¼ 2f ¼ jImðÞj

ð4Þ

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having the full width at half-maximum (FWHM) f ¼ jReðÞj Equation (3) is simpliﬁed to 1 1 2 32 k f ¼ 2

ð5Þ

ð6Þ

and f ¼ 2k2 =

ð7Þ

Equation (6) is the same as Lamb’s classical approximation, Eq. (2).

B.

Historical Overview

Capillary waves at liquid surfaces were observed some years before the invention of lasers. Goodrich [13] reported on using a cathetometer to observe the damping of water waves by monomolecular ﬁlms. Strictly speaking, this wave was a forced one and not a spontaneously generated capillary wave. The observation of spontaneously generated capillary waves was ﬁrst reported by Katyl and Ingard [14,15]. They measured spectra from a methanol surface and an isopropanol surface using a He–Ne laser. Lucassen [16,17] theoretically derived the transverse mode of capillary waves and experimentally veriﬁed its existence. Bouchiat and Meunier [18] measured the liquid–gas interface of carbon dioxide near the critical point and reported agreement with theoretical predictions on the surface tension and viscosity. Mann et al. [19] investigated the dispersion relation at air–water interfaces using the QELS method and reported conformity with Lamb’s equation. They also mentioned the possibility of application to interfacial tension measurements. Ha¨rd et al. [20] measured surface tensions using the QELS method and reported that the experimental values agreed with the theoretical ones within deviations of 2–10%. Sano et al. [11] measured the surface tensions of water and anisole and reported they were within deviations 5% of the theoretical values. They also reported that the ﬁrst-order approximation, i.e., Lamb’s equation, was sufﬁcient to calculate the surface tensions from capillary wave frequencies. Earnshaw and coworkers [21–23] have investigated liquid surfaces of surfactant solutions and reported on such fundamental properties as surface viscosity. As reviewed above, there have been many QELS studies on liquid surfaces. However, until a few years ago, reports were scarce on molecular dynamics at liquid– liquid interfaces which used time courses of capillary wave frequency. Molecular collective behavior at liquid–liquid interfaces from a QELS study was ﬁrst reported by Zhang et al. in 1997 [5].

C.

Principle

The incident beam normal to the interface is quasi-elastically scattered by the capillary wave with a Doppler shift at an angle determined by the following equation (Fig. 1): K tan ¼ k

ð8Þ

where K and k are the wavenumbers of the incident beam and the capillary wave, respectively. Thus, the wavenumber k of the capillary wave is obtained by giving . A transmis-

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FIG. 1 Principle of the quasielastic laser scattering method.

sion diffraction grating is arranged in front of the cell to adjust the angle [20]. The angle is determined by the following equation using the spacing d and the order n of the diffraction grating, d sin ¼ n

ð9Þ

where is the wavelength of the laser beam. From Eqs. (8) and (9), we obtain the wavenumber k and the wavelength of the observed capillary wave: k ¼ 2n=d

ð10Þ

¼ d=n

ð11Þ

The capillary wave frequency is detected by an optical heterodyne technique. The laser beam, quasi-elastically scattered by the capillary wave at the liquid–liquid interface, is accompanied by a Doppler shift. The scattered beam is optically mixed with the diffracted beam from the diffraction grating to generate an optical beat in the mixed light. The beat frequency obtained here is the same as the Doppler shift, i.e., the capillary wave frequency. By selecting the order of the mixed diffracted beam, we can change the wavelength of the observed capillary wave according to Eq. (11).

D.

Experimental Apparatus

A schematic diagram of the experimental setup is shown in Fig. 2. The beam from a diode-pumped YAG laser is incident on the transmitting diffraction grating and passes through the bottom of the sample cell. The cell is made of quartz glass and has an optically ﬂat bottom, which is indispensable to maintaining good reproducibility of the experimental results. After passing through the sample, the diffracted beams are mixed with scattered light from the capillary wave, and one of them is selected by an aperture positioned in front of a photodiode. The optical beat of the mixed light is measured by the photodiode. The signals are Fourier transformed and saved by a digital spectrum analyzer.

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FIG. 2 Schematic diagram of the experimental setup. T, glass tube; W, water phase; NB, nitrobenzene; PD, photodiode; AMP, preampliﬁer; FFT, FFT analyzer.

III.

DYNAMIC MOLECULAR BEHAVIOR OF SURFACTANT MOLECULES AT LIQUID–LIQUID INTERFACE

The molecular collective behavior of surfactant molecules has been analyzed using the time courses of capillary wave frequency after injection of surfactant aqueous solution onto the liquid–liquid interface [5,8]. Typical power spectra for capillary waves excited at the water–nitrobenzene interface are shown in Fig. 3: (a) without CTAB (cetyltrimethylammonium bromide) molecules, and (b) 10 s after the injection of CTAB solution to the water phase [5]. The peak appearing around 10–13 kHz represents the beat frequency, i.e., the capillary wave frequency. The peak of the capillary wave frequency shifts from 12.5 to 10.0 kHz on the injection of CTAB solution. This is due to the decrease in interfacial tension caused by the increased number density of surfactant molecules at the interface. Time courses of capillary wave frequency after the injection of different CTAB concentrations into the aqueous phase are reproduced in Fig. 4. An anomalous temporary decrease in capillary wave frequency is observed when the CTAB solution beyond the CMC (critical micelle concentration) was injected. The capillary wave frequency decreases rapidly on injection, and after attaining its minimum value, it increases

FIG. 3 Power spectra for capillary waves excited at the water–nitrobenzene interface (a) without CTAB molecules and (b) 10 s after injection of a CTAB solution (0.5 mL, 10 mM) into the water phase.

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FIG. 4 Capillary wave frequency vs. time after injection of the CTAB aqueous solutions (0.5 mL, 2–30 mM). The concentrations of the injected solution (C) are shown, along with the average concentrations (Ceq ) in the aqueous phase.

gradually. The initial sudden change means an abrupt increase in the molecular number density at the interface. The relationship between the interfacial coverage and the concentration of CTAB was estimated using the minimum value of the capillary wave frequency, as shown in Fig. 5. The experimental data are in good agreement with the calculated Langmuir adsorption isotherm. The experimental adsorption energy of CTAB onto the interface is calculated as 29:4 kJ/mol from the isotherm. The theoretical adsorption energy of the CTAB micelles is estimated as 25:0 kJ/mol from the difference between the theoretical adsorption energy of CTAB molecules (51:4 kJ/mol) and the micelle formation energy (26:4 kJ/mol). The experimental adsorption energy ð29:4 kJ/mol) calculated from the Langmuir isotherm is in agreement with the theoretical adsorption energy of CTAB micelles (25:0 kJ/mol), and not with that of CTAB molecules (51:4 kJ/mol). This indicates that the CTAB micelles are in equilibrium with the adsorbed CTAB molecules, and consequently, the CTAB micelles collapse to molecules immediately before the adsorption onto the interface.

FIG. 5 Interface coverage with CTAB molecules vs. CTAB average concentration in the water phase. Experimental data are shown as squares, and the calculated Langmuir adsorption isotherm is the solid line.

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FIG. 6 Time courses of the capillary wave frequencies after injection of (a) SDS and (b) Triton X100 aqueous solutions into the interface.

Similar experiments and discussions have also been made for different surfactant molecules, such as SDS (sodium dodecyl sulfate) and Triton X-100 [8]. SDS, Triton X-100, and CTAB are anionic, nonionic, and cationic surfactants, respectively. The relationship between the relative number density of SDS molecules and the bulk aqueous concentration is shown in Fig. 6(a). When the concentration is below the CMC (9.8 mM at 25 C), the number density increases with an increase in concentration. The experimental data are in agreement with the Langmuir adsorption isotherm, suggesting that the SDS molecules are adsorbed onto the interface as a monolayer. The adsorption energy of the SDS molecules at the interface is estimated as ca. 21:9 kJ/mol from the experimental data. The theoretical free energy change when the molecules move from the water phase to the interface is estimated as higher than 37:6 kJ/mol. This discrepancy suggests that about 60% of the methylene groups in the SDS molecules are transported to the nitrobenzene phase and may be a reﬂection of molecular orientation, because SDS does not form a well-ordered monolayer at the water–nitrobenzene interface. When the concentration is above the CMC, the number density of SDS molecules at the interface decreases with an increase in the concentration. This may be due to a local change in the aggregation state at the interface from the monolayer to molecular aggregates. The molecular aggregates observed here are assumed to be micelles or reversed micelles, but further investigation is necessary to verify this. Using resonant TIR-SFG, Richmond’s group observed a reduction in ordering of the chain of the SDS at the D2 O/CCl4 interface at higher concentrations [24,25]. They also reported that the alkyl chains of the cationic surfactants DTAC and DAC possess the fewest gauche defects, whereas the anionic surfactants SDS and DDS display more disorder in the hydrocarbon chains at similar surface concentrations [25]. Similar results have been reported by others for SDS adsorption onto hydrophobic substrates from water [26,27].

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The relationship between the relative number density of Triton X-100 molecules and the bulk aqueous concentration is shown in Fig. 6(b). When the concentration is below the CMC (0.2 mM at 25 C), the experimental data in Fig. 6(b) are in good agreement with the calculated Langmuir adsorption isotherm. This indicates that the adsorbed Triton X-100 molecules are conﬁned to a monolayer. When the concentration is above the CMC, a slight decrease in the number density appears. It is reasonable to consider that the slight decrease is due to a change in aggregation state at the interface, such as by formation of micelles, whereas the latter slow increase is due to the increase of molecular aggregates at the interface. This result suggests that the phase transition from a monolayer to molecular aggregates occurs at a certain concentration, unlike the case with SDS. The molecular behavior at the interface may be affected by the ionic nature, ion pair formation, solvent polarity, or the chain conformation of surfactants.

IV.

MOLECULAR BEHAVIOR OF PHASE-TRANSFER CATALYST AT LIQUID–LIQUID INTERFACE IN ITS CYCLIC REACTION

The interfacial behavior of a phase-transfer catalyst, tetrabutylammonium bromide (TBAB), has been investigated using the QELS method [9]. The scheme of the phasetransfer catalytic reaction in a water–nitrobenzene system is shown in Fig. 7 [28]. At the beginning of the reaction, TBAB reacts with C6 H5 ONa to form TBAþ C6 H5 O . This ion pair is transported into the organic phase where it reacts with DPPC to produce triphenyl phosphate [ðC6 H5 OÞ3 PO]. During this reaction, TBAþ Cl is also formed and transported into the water phase to react again with C6 H5 ONa. TBAB activates the production of triphenyl phosphate by circulating between the two phases. Capillary wave frequency dependence on concentrations of TBAB and C6 H5 ONa is shown in Fig. 8. The adsorption behavior of the ion pair, TBAþ C6 H5 O , in one transfer process in which the formed ion pair is transferred from the water phase to the nitrobenzene phase is described by the data. When C6 H5 ONa alone is in the water phase, the frequency is independent of the C6 H5 ONa concentration. On the other hand, when both TBAB and C6 H5 ONa are present, the frequency decreases gradually and only slightly with increasing C6 H5 ONa concentration and then becomes constant at a certain C6 H5 ONa concentration. Thus, the decrease of frequency corresponds to the formation of ion pairs such as TBAþ C6 H5 O , and these ion pairs are adsorbed at the interface. The constant frequency above a certain concentration indicates that the

FIG. 7 Reaction scheme between C6 H5 ONa and DPPC in the water–nitrobenzene system. The part surrounded by the dashed line is the investigated process.

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FIG. 8 Capillary wave frequency dependence on the concentrations of TBAB and C6 H5 ONa.

number of interfacial adsorptions of ion pairs that occurs has become constant. This suggests that the reaction between C6 H5 ONa and TBAB is in equilibrium, and the number of ion pairs that occurs has become constant. This stable formation brings about the saturated interface. The equilibrium concentration of C6 H5 ONa above which the adsorption was saturated depends on the TBAB concentration. The relationship between the TBAB concentration and the C6 H5 ONa concentration is shown in Fig. 9. These equilibrium concentrations were used to analyze the reaction between the two reactants, assuming that at these concentrations the reaction proceeds without residue and deﬁciency. The ratio of the TBAB concentration to the C6 H5 ONa concentration deviates from the line for 1:1 below 50 mM. When the TBAB concentration is above 50 mM, the ratio of the TBAB concentration to the C6 H5 ONa concentration at the water–nitrobenzene interface is unity. On the other hand, when the TBAB concentration is below 50 mM, the ratio of the C6 H5 ONa concentration to the TBAB concentration is more than unity. In general, the formation of an ion pair TBAþ C6 H5 O occurs by the reaction between one TBAB molecule and one C6 H5 ONa molecule in the water phase. Thus, the ratio of the C6 H5 ONa concentration to the TBAB concentration should be unity if the reaction has occurred in the water phase. The behavior above 50 mM can be simply explained by the reaction in the water phase between one TBAB molecule and one C6 H5 ONa molecule. However, the behavior below 50 mM cannot be explained by this

FIG. 9 Relationship between the TBAB and C6 H5 ONa concentrations in equilibrium.

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simple water phase reaction. It is generally said that the concentration or activity at the interface differs from that in the water phase. From these results, the following model is suggested. Below 50 mM, the ratio of the two concentrations at the interface is unity, and the reaction between the TBAB molecules and the C6 H5 ONa molecules occurs at the interface. Below 50 mM the formation reaction for ion pairs occurs at the interface, while above 50 mM the reaction occurs in the water phase.

V.

FINAL REMARKS

In this chapter, the quasi-elastic laser scattering (QELS) method was introduced and recent reports on molecular dynamics at liquid–liquid interfaces using this method are reviewed. The QELS method has been applied to monitor the dynamics of surfactant molecules at the liquid–liquid interfaces. Time-resolved measurements of interfacial molecular number density can provide new information on molecular collective behavior of surfactants at the liquid–liquid interface. The transfer of CTAB micelles across the interface was found to occur according to the following scheme: the collapse of micelles at the interface region; the oriented adsorption onto the interface with formation of a monolayer; and the desorption from the interface. Findings suggested that below the critical micelle concentration (CMC), sodium dodecyl sulfate (SDS) molecules were adsorbed onto the interface, forming a monolayer; above the CMC the monolayer was disrupted and some molecular aggregates such as micelles or reversed micelles were formed. In the case of Triton X-100 molecules below the CMC the molecules were adsorbed onto the interface, forming a monolayer; above the CMC, the monolayer was disrupted and some molecular aggregates such as micelles were formed, and with further increases in concentration, the number of micelles increased. The QELS method was also applied to monitor the interfacial molecular behavior of phase-transfer catalyst. Findings suggested that the reaction place between tetrabutylammonium bromide (TBAB) and C6 H5 ONa changed with TBAB concentration; the reaction place was in the water phase above 50 mM, whereas it was at the interface below 50 mM. The results above reﬂect interfacial speciﬁcity for mass transfer and chemical reaction. In future studies the advantages of the QELS method can be used to provide details on interfacial speciﬁcity for chemical processes by nonperturbative measurements.

REFERENCES 1. 2.

R. M. Corn and D. A. Higgins. Chem. Rev 94:107 (1994). J. C. Wright, M. J. LaBuda, D. E. Thompson, R. Lascola, and M. W. Russell. Anal. Chem.68:600A (1996). 3. S. Takahashi, A. Harata, T. Kitamori, and T. Sawada. Anal. Sci. 7:645 (1991). 4. S. Takahashi, A. Harata, T. Kitamori, and T. Sawada. Anal. Sci. 10:305 (1994). 5. Z. Zhang, I. Tsuyumoto, S. Takahashi, T. Kitamori, and T. Sawada. J. Phys. Chem. A 101:4163 (1997). 6. I. Tsuyumoto, N. Noguchi, T. Kitamori, and T. Sawada. J. Phys. Chem. B 102:2684 (1998). 7. S. Takahashi, I. Tsuyumoto, T. Kitamori, and T. Sawada. Electrochim. Acta 44:165 (1998). 8. Z. Zhang, I. Tsuyumoto, S. Takahashi, T. Kitamori, and T. Sawada. J. Phys. Chem. B 102::10284 (1998). 9. Y. Uchiyama, I. Tsuyumoto, T. Kitamori, and T. Sawada. J. Phys. Chem. B 103:4663 (1999). 10. H. Lamb,, Hydrodynamics, 6th edn, Dover, New York, 1945.

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11. M. Sano, M. Kawaguchi, Y. L. Chen, R. J. Skarlupka, T. Chang, G. Zograﬁ, and H. Yu. Rev. Sci. Instrum. 57:1158 (1986). 12. V. G. Levich, Physiochemical Hydrodynamics, Prentice-Hall, New York, 1962, Ch. 11. 13. F. C. Goodrich. J. Phys. Chem. 66:1858 (1962). 14. R. H. Katyl and U. Ingard. Phys. Rev. Lett. 19:64 (1967). 15. R. H. Katyl and U. Ingard. Phys. Rev. Lett. 20:248 (1968). 16. J. Lucassen. J. Chem. Soc. Farad. Trans. 64:2221 (1968). 17. J. Lucassen. J. Chem. Soc. Farad. Trans. 64:2230 (1968). 18. M. A. Bouchiat and J. Meunier. Phys. Rev. Lett. 23:752 (1969). 19. J. A. Mann, J. F. Baret, F. J. Dechow, and R. S. Hansen. J. Colloid Inter. Sci. 37:14 (1971). 20. S. Ha¨rd, Y. Hamnerius, and O. Nilsson. J. Appl. Phys. 47:2433 (1976). 21. J. C. Earnshaw, R. C. McGivern, A. C. McLaughlin, and P. J. Winch. Langmuir 6:649 (1990). 22. J. C. Earnshaw, and P. J. Winch. J. Phys. Condens. Matter 2:8499 (1990). 23. J. C. Earnshaw and E. McCoo. Langmuir 11:1087 (1995). 24. M. C. Messmer, J. C. Conboy, and G. L. Richmond. J. Am. Chem. Soc. 117:8039 (1995). 25. J. C. Conboy, M. C. Messmer, and G. L. Richmond. J. Phys. Chem. B 101:6724 (1997). 26. R. N. Ward, D. C. Duffy, and P. B. Davies. J. Phys. Chem. 98:8536 (1994). 27. C. D. Bain, P. B. Davies, and R. N. Ward. Langmuir 10:2060 (1994). 28. S. Asai, H. Nakamura, M. Tanabe, and K. Sakamoto. Ind. Eng. Chem. Res. 33:1687 (1994).

10 Microstructure E¡ects on Transport in Reverse Microemulsions JOHN TEXTER

I.

Strider Research Corporation, Rochester, New York

INTRODUCTION

Isotropic single-phase microemulsions of oil and water can adopt a variety of microstructures, including water-in-oil droplets (reverse microemulsions), swollen oil-in-water micelles, and irregular bicontinuous microstructures of low to zero mean curvature with interpenetrating oil and water domains separated by a monolayer of surfactant. Various ﬁeld variables can drive transitions from one of these microstructures to another. The transport of charge, ions, and molecular species as monitored by electrical conductivity or faradaic electron transfer and by NMR self-diffusion measurements, respectively, can be used to experimentally deﬁne an order parameter for quantitatively tracking the onset of microstructure formation and the amount of a particular microstructure present at equilibrium under a given set of ﬁeld variables. Transitions from isolated reverse micelles in reverse microemulsions through the formation of percolating clusters to the formation of irregular bicontinuous microstructure are reviewed. Electrochemistry [1], synthesis [2], and catalysis [3,4] in reverse microemulsions [5] are signiﬁcantly affected by microstructure and the effects of microstructure on ionic and molecular transport. Such transport can occur by several distinct mechanisms. The ﬁrst involves diffusion of ions and molecules through the oil (pseudocontinuous) phase of the reverse microemulsion. This kind of transport is encountered in simple solutions, except that additional factors affecting viscosity and tortuosity come into play. A second mechanism involves the diffusion of reverse micelles with the concomitant transport of solutes contained therein. Such diffusive transport is generally more than an order of magnitude slower than the ﬁrst mechanism. A third mechanism of transport involves ion and molecular transport through reverse micelles (droplets) and exchange between such droplets [6,7]. This third mechanism has most often been probed by percolation in electrical conductivity [8], in faradaic electron transfer [9], in dielectric susceptibility [10], and in selfdiffusion measured by NMR pulsed gradient spin-echo (PGSE) techniques [11,12].

A.

Percolation

Percolation in microemulsions and concomitant microstructural changes are the focal points of this review. A complete understanding of percolation phenomena in reverse microemulsions will require an understanding of droplet interactions and the associated thermodynamics of droplet fusion, ﬁssion, aggregation to form clusters of varying fractal 241

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dimension, and the transformation of droplets and clusters of droplets to irregular bicontinuous [13] microstructures of low to zero mean curvature. This last transformation has generated some controversy in the literature. The observation of percolation has at times been equated with bicontinuous microstructure formation [14]. Alternatively, percolation is equated with droplet aggregation and clustering [15,16]. A prime objective of this review is to illustrate how to experimentally distinguish between these alternative microstructures, each of which appears attendant to percolation-related transitions. B.

Disperse Phase Volume Fraction

Electrical conductivity is an easily measured transport property, and percolation in electrical conductivity appears a sensitive probe for characterizing microstructural transformations. A variety of ﬁeld (intensive) variables have been found to drive percolation in reverse microemulsions. Disperse phase volume fraction has been often reported as a driver of percolation in electrical conductivity in such microemulsions [17–20]. Lagu¨es et al. [17] found that the percolation theory for hard spheres could be used to describe dramatic increases in electrical conductivity in reverse microemulsions as the volume fraction of water was increased. They also showed how certain scaling theoretical tools were applicable to the analysis of such percolation phenomena. Cazabat et al. [18] also examined percolation in reverse microemulsions with increasing disperse phase volume fraction. They reasoned the percolation came about as a result of formation of clusters of reverse microemulsion droplets. They envisioned increased transport as arising from a transformation of linear droplet clusters to tubular microstructures, to form wormlike reverse microemulsion tubules. C.

Temperature

Temperature is also an often-studied ﬁeld variable in driving percolation and associated microstructural transitions [21–25]. Jada et al. [21] found that the percolation induced by temperature increases in a water, decane, AOT reverse microemulsion could be nicely correlated with the bimolecular rate constant for solute exchange between colliding droplets. Kim and Huang [22] found that temperature-driven percolation in reverse microemulsions occurred when the effective droplet volume as deﬁned by a hopping range exceeded the hard-sphere close-packing limit of 0.65. Peyrelasse and Boned [23] showed that temperature-driven percolation yielded similar critical exponents to those obtained in scaling analyses of disperse phase volume-fraction-driven percolation. An extensive study by Alexandridis et al. [24] suggests that temperature-driven percolation involves enthalpically disfavored clustering of droplets. The net driving force emanates from positive entropic changes that increase with temperature and that are attributed to free volume dissimilarity between the surfactant tails and the respective organic solvents. D.

Chemical Potential

The last, and less extensively studied ﬁeld variable driving percolation effects is chemical potential. Salinity was examined in the seminal NMR self-diffusion paper of Clarkson et al. [12] as a component in brine, toluene, and SDS (sodium dodecylsulfate) microemulsions. Decreasing levels of salinity were found to be sufﬁcient to drive the microemulsion microstructure from water-in-oil to irregular bicontinuous to oil-in-water. This paper was

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one of the ﬁrst to demonstrate the power of PGSE NMR determinations of self-diffusion coefﬁcients in resolving microstructure in surfactant systems. The inﬂuence of alcohols as cosurfactants also falls in this chemical potential category. Lang et al. [26] found that a variety of alkanols and benzyl alcohol tended to suppress percolation in reverse microemulsions otherwise induced by disperse phase volume fraction increases. They studied water, chlorobenzene, TBDAC (tetradecylbenzyldimethylammonium chloride) reverse microemulsions and found that longer-chained alcohols retarded the onset of percolation to a greater extent. Somewhat similar retarding effects of alcohols have more recently been reported by Naza´rio et al. [27]. At ﬁxed disperse phase volume fraction, increasing straight-chain alcohol (cosurfactant) concentration suppressed percolation until higher temperatures were reached, relative to the temperature at which percolation was driven in the absence of cosurfactant. It was surmised that the physical effect of added alcohol was to decrease interfacial ﬂuidity and hypothesized that the alcohols intercalate between AOT tail groups, thereby increasing the alkyl chain packing density. This decrease in ﬂuidity then necessitates a higher temperature for overcoming the enthalpic barrier to cluster formation and ensuing percolation. Electrochemical redox studies of electroactive species solubilized in the water core of reverse microemulsions of water, toluene, cosurfactant, and AOT [28,29] have illustrated a percolation phenomenon in faradaic electron transfer. This phenomenon was observed when the cosurfactant used was acrylamide or other primary amide [28,30]. The oxidation or reduction chemistry appeared to switch on when cosurfactant chemical potential was raised above a certain threshold value. This switching phenomenon was later conﬁrmed to coincide with percolation in electrical conductivity [31], as suggested by earlier work from the group of Francoise Candau [32]. The explanations for this amide-cosurfactant-induced percolation center around increases in interfacial ﬂexibility [32] and increased disorder in surfactant chain packing [33]. These increases in ﬂexibility and disorder appear to lead to increased interdroplet attraction, coalescence, and cluster formation. Another example of chemical-potential-driven percolation is in the recent report on the use of simple poly(oxyethylene)alkyl ethers, Ci Ej , as cosurfactants in reverse water, alkane, and AOT microemulsions [27]. While studying temperature-driven percolation, Naza´rio et al. also examined the effects of added Ci Ej as cosurfactants, and found that these cosurfactants decreased the temperature threshold for percolation. Based on these collective observations one can conclude that linear alcohols as cosurfactants tend to stiffen the surfactant interface, and that amides and poly(oxyethylene) alkyl ethers as cosurfactants tend to make this interface more ﬂexible and enhance clustering, leading to more facile percolation. E.

Microstructural Transitions

Self-diffusion NMR measurements have been shown to be very useful in characterizing microstructural transitions in microemulsions [9,34]. Much uncertainty remains, however, in describing transitions from oil-in-water to irregular bicontinuous to water-in-oil microemulsions. Irregular bicontinuous microstructure of low to zero mean curvature has often been inferred on the basis of intermediate to large magnitudes of self-diffusion coefﬁcients [35]. However, it has recently been shown that diffusion coefﬁcients of such magnitude arise naturally in reverse microemulsions as a result of a dynamic partitioning of various solutes (e.g., water and cosurfactant) between continuous and disperse pseudophases [36]. It will be illustrated here that quantitative consideration of such partitioning provides means to quantify effects on transport attendant to percolation processes.

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The remainder of this chapter develops this quantitative treatment of percolation as it relates to self-diffusion data from NMR PGSE experiments and to an overarching qualitative treatment also derived from self-diffusion data and from conductivity data. This qualitative treatment focuses upon the coincidence of the upturn in water proton selfdiffusion with the onset of percolation in electrical conductivity. This treatment also focuses upon observations that the upturn in surfactant self-diffusion usually occurs at a higher ﬁeld variable than do the water proton self-diffusion increase and the onset of electrical conductivity percolation. The fact that these processes occur at different ﬁeld variables is used to qualitatively distinguish reverse microemulsion droplet aggregation and clustering of percolating droplets from the onset of irregular bicontinuous structure formation A more quantitative approach is based upon a two-state analysis of the NMR water proton self-diffusion data. This two-state analysis is used to derive an order parameter for percolating cluster formation, and this order parameter is applied to the analysis of percolation driven by disperse phase volume fraction, temperature, and cosurfactant chemical potential.

II.

VOLUME-FRACTION-INDUCED PERCOLATION

The inﬂuence of disperse phase volume fraction and of temperature on driving microstructure transitions in a brine (0.6% aqueous NaCl), decane, and AOT (12% w/w) microemulsion system was studied extensively by Chen et al. [20]. They used smallangle neutron scattering to measure the mean curvature over an extensive range of disperse phase volume fraction and over a range in temperature. The Shinoda diagram for this system is illustrated in Fig. 1, where denotes the weight ratio of decane to decane plus brine. The quantity 1 denotes the weight ratio of brine to brine plus decane, and

FIG. 1 Partial phase diagram of brine, decane, and AOT system as a function of temperature (T) and decane-to–brine weight fraction (). The brine is aqueous 0.6% (w/w) NaCl; the AOT composition is constant at 12% (w/w). The double-ended arrow depicts the isothermal composition range examined in this study at 45 C. The lamellar (L ), and two-phase regions (2; 2 ) are described in the text. (Adapted from Fig. 5 of Ref. 20.)

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the disperse phase (brine) volume fraction is proportional to 1 . This diagram illustrates a large single-phase isotropic microemulsion domain bounded by a lamellar region (L ), an upper two-phase region (2) comprising a decane-rich phase and a decane-in-brine microemulsion, and a lower two-phase region (2 ) comprising a brine-rich phase and a brine-in-decane microemulsion. Chen et al. [20] found that the mean curvature changed sign and went through zero as composition in the single-phase region changed with from brine-in-water droplets at high , to irregular bicontinuous microstructure at intermediate , to oil-in-brine droplets at low and higher temperatures (60–80 C). The measurements described shortly were all obtained [37] at 45 C along the double arrow-ended isotherm pictured in Fig. 1 in the isotropic single-phase microemulsion domain. Results for lowfrequency conductivity and self-diffusion over the composition range 1:0 ! 0:3 in are described along this isotherm. Low-frequency conductivity data [37] obtained along this 45 C isotherm are illustrated in Fig 2. The initial oscillatory variation in the conductivity for > 0:9 can be assigned to variations in AOT partitioning among dimers and other low aggregates and reverse micelles, as reverse micelles are nucleated by added water (brine). These variations will be discussed in greater detail in another publication. The key behavior for the purposes of this exposition is the onset of the electrical conductivity percolation at ¼ 0:85. The conductivity increases two orders as decreases from 0.85 to 0.70, and as shown in the inset, the conductivity increases another two orders as a decreases from 0.7 to 0.3. Self-diffusion data [37] derived from NMR PGSE measurements for decane, water, and AOT are illustrated in Fig. 3. The self-diffusion of decane decreases gradually as decreases from 1.0 to 0.3. The magnitude of decane self-diffusion suggests that the microstructure remains substantially continuous in decane over this composition range. Both water and AOT diffusion initially decrease as decreases. One can readily see that in this

FIG. 2 Low-frequency conductivity at 45 C as a function of composition, (weight fraction decane relative to decane and brine) for brine, decane, and AOT microemulsions exhibiting the phase behavior illustrated in Fig. 1. The breakpoint at ¼ 0:85 corresponds to the onset of percolation. This conductivity increases by two orders as decreases from 0.85 to 0.7. (Reproduced by permission of the American Institute of Physics from Ref. 37.)

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FIG. 3 Self-diffusion coefﬁcients of decane (~), water (&), and AOT (*) in brine, decane, and AOT microemulsions at 45 C as a function of decane weight fraction, (relative to decane and brine). Breakpoints in the self-diffusion data for both water and AOT are observed at ¼ 0:85 and at 0.7. (Reproduced by permission of the American Institute of Physics from Ref. 37.)

system, at least, water is necessary for the existence of reverse micelles. In the absence of added water (brine), the AOT diffusion approaches that of monomeric water, suggesting that very, very small aggregates (e.g., dimers) of AOT form at very low water contents. These reverse micelles grow as added brine (water) increases ( decreases), and the selfdiffusion of water and of AOT concomitantly slow. Water proton self-diffusion exhibits a break point and begins to increase at ¼ 0:85. In the case of AOT self-diffusion, a breakpoint also occurs, but AOT self-diffusion continues to slow as decreases further. These breakpoints in both water and AOT selfdiffusion behavior at ¼ 0:85 coincide with the breakpoint in electrical conductivity illustrated in Fig. 1, where the onset of electrical conductivity percolation occurs. At ¼ 0:7 two more breakpoints in the water proton and AOT self-diffusion are seen. Water proton self-diffusion increases more markedly and AOT self-diffusion beings to increase markedly. A.

Two-State Model

A simple two-state model for the observed water proton self-diffusion may be put forward in the form Dobs ¼ xDc þ ð1 xÞDmic

ð1Þ

where Dobs is the observed water proton self-diffusion coefﬁcient, Dc is the self-diffusion coefﬁcient of molecular water in decane, Dmic is the self-diffusion coefﬁcient of the reverse micelles, and x is the mole fraction of water dispersed molecularly in the decane. The coefﬁcient Dc was taken as 0:93 105 cm2 s1 from independent measurements [37] of molecular water diffusion in decane. The coefﬁcient Dmic was approximated by the observed self-diffusion coefﬁcient for AOT for 0:7 and by the dotted curve illustrated in Fig. 3 for < 0:7. With these assumptions and measurements, the mole fraction x of

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FIG. 4 Apparent mole fraction (x) water in continuous phase of brine, decane, and AOT microemulsion system derived from the water self-diffusion data of Fig. 3 using the two-state model of Eq. (1).

water in the continuous phase may be derived from these self-diffusion data. This derivation is illustrated in Fig. 4, where it appears that the amount of water in the continuous decane pseudophase increases steadily as decreases below 0.85. B.

Order Parameter

The apparent increase in water solubilized in the continuous decane pseudophase that is illustrated in Fig. 4 goes counter to chemical intuition. The amount of water in the decane pseudophase should partition between micelles and the decane relatively quickly as brine is added to the microemulsion. This in fact appears to occur by the time has decreased to 0.95, and this partitioning may be expected to remain constant over some interval of further brine increase. The mole fraction of water in decane should hold constant and then decrease as total water (brine) in the system increases. The horizontal asymptote illustrated in Fig. 4 and extrapolated to the right in the direction of decreasing represents this partitioning approximation. The mole fraction of water in decane should not go above this level, no matter how much total brine is added to the system. We deﬁne x^ as the anomalous mole fraction of water in the continuous phase and as the quantity represented by the vertical arrow in Fig. 4. We further assign this quantity as the amount of water in percolating clusters and irregular bicontinuous microstructure. With this deﬁnition, we can deﬁne the following order parameter S for the amount of water in such clusters and microstructures, S¼

x^ 1 x þ x^

ð2Þ

where 1 x is simply the amount of water in nonpercolating clusters and isolated reverse microemulsion droplet and where 0 S 1. This order parameter describes quantita-

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FIG. 5 Order parameter for disperse pseudophase water (percolating clusters versus isolated swollen micelles and nonpercolating clusters) derived from self-diffusion data for brine, decane, and AOT microemulsion system of single-phase region illustrated in Fig. 1. The a and arrow denote the onset of percolation in low-frequency conductivity and a breakpoint in water self-diffusion increase. The other arrow (b) indicates where AOT self-diffusion begins to increase.

tively how water is distributed among disperse phase microstructures: (1) isolated reverse micelles and nonpercolating micellar clusters; (2) percolating micellar clusters and irregular bicontinuous microstructures. The order parameter values calculated from the data of Fig. 4 are illustrated in Fig. 5. The data there suggest the existence of two continuous transitions, one at ¼ 0:85 and another at ¼ 0:7. The ﬁrst transition at ¼ 0:85, denoted by the arrow labeled ‘‘a’’ in Fig. 5, is assigned to the formation of percolating clusters and aggregates of reverse micelles. The onset of electrical percolation and the onset of water proton self-diffusion increase at this same value of (0.85) as illustrated in Figs. 2 and 3, respectively, are qualitative markers for this transition. This order parameter allows one to quantify how much water is in these percolating clusters. As decreases from 0.85 to 0.7, this quantity increases to about 2–3% of the water. Another more abrupt transition in this order parameter occurs at ¼ 0:7 under the arrow labeled ‘‘b.’’ This transition is assigned to the onset of irregular bicontinuous microstructure formation, and is indicated qualitatively by the marker illustrated in Fig. 3, where the onset in AOT self-diffusion increase occurs.

III.

TEMPERATURE-INDUCED PERCOLATION

A somewhat different water, decane, and AOT microemulsion system has been studied by Feldman and coworkers [25] where temperature was used as the ﬁeld variable in driving microstructural transitions. This system had a composition (volume percent) of 21.30% water, 61.15% decane, and 17.55% AOT. Counterions (sodium ions) were assigned as the dominant charge transport carriers below and above the percolation threshold in electrical

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conductivity. A charge-hopping mechanism above the percolation threshold was also invoked. This mechanism was outlined as emanating from the hopping of AOT molecules between droplets in percolating clusters. Low-frequency conductivity data and NMR PGSE self-diffusion results for water protons and for AOT were obtained [25] over 6–40 C. These data are illustrated in Fig. 6. The water self-diffusion data exhibit a breakpoint at about 18–19 C in close proximity to the onset of percolation in electrical conductivity. This ‘‘onset’’ is highlighted in Fig. 6 by the arrow labeled p at about 18 C. A separate breakpoint in the AOT self-diffusion data appears at about 28 C. This coincidence in the onset of percolation in electrical conductivity with a breakpoint in water self-diffusion increase appears similar to the qualitative markers seen for the onset of formation of percolating clusters in the discussion of the previous section, where disperse phase volume fraction was the ﬁeld variable driving percolation. Additionally, the separate breakpoint for increasing AOT self-diffusion at higher ﬁeld variable (temperature 28 C) is similar to the breakpoint seen in Fig. 3 at ¼ 0:7. Again, this surfactant self-diffusion increase marker can be assigned to the onset of irregular bicontinuous microstructure formation. These qualitative similarities to the system analyzed in the previous section suggest a similar order parameter analysis may be warranted. Independent self-diffusion measurements [38] of molecularly dispersed water in decane over the 8–50 C interval were used, in conjunction with the self-diffusion data of Fig. 6, to calculate the apparent mole fraction of water in the pseudocontinuous phase from the two-state model of Eq. (1). In these calculations, the micellar diffusion coefﬁcient, Dmic , was approximated by the measured self-diffusion coefﬁcient for AOT below 28 C, and by the linear extrapolation of these AOT data above 28 C. This apparent mole fraction x was then used to graphically derive the anomalous mole fraction x^ of water in the pseudocontinuous phase. These mole fractions were then used to calculate values for

FIG. 6 Self-diffusion and conductivity data reported by Feldman et al. [25] for reverse water, decane, and AOT microemulsion as a function of temperature. The p and arrow between 18 and 19 C shows the approximate onset of percolation in low-frequency conductivity and a breakpoint in water self-diffusion increase. Another breakpoint, at about 28 C, occurs in the AOT self-diffusion data where AOT self-diffusion begins to markedly increase.

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FIG. 7 Order parameter for disperse pseudophase water derived from self-diffusion data for water, decane, and AOT reverse microemulsion illustrated in Fig. 6. The p and arrow denote the approximate onset of percolation in low-frequency conductivity and a breakpoint in water self-diffusion increase. The arrow labeled AOT shows a second continuous transition corresponding to the onset of AOT self-diffusion increase.

the order parameter of Eq. (2). This order parameter is illustrated in Fig. 7, where breakpoints suggest the occurrence of two continuous transitions. The ﬁrst of these at about 18 C and marked with an arrow labeled p occurs at the temperature at which the onset in electrical conductivity percolation begins and at the temperature at which the water selfdiffusion data exhibit a breakpoint. This ﬁrst continuous transition corresponds to the onset of percolating cluster formation. The second breakpoint in the order parameter occurs at about 28–29 C where the AOT self-diffusion coefﬁcients begin to increase. This second transition is assigned to the onset of irregular bicontinuous microstructure formation. These qualitative microstructure transition assignments may be extended to other reverse microemulsion systems reported in the literature. Geiger and Eicke [39] applied both electrical conductivity and NMR self-diffusion measurements to the study of a water, isooctane, and AOT microemulsion driven into percolation by increasing temperature. Inspection of the data published in their ﬁgures indicates a coincidence in the temperature at which electrical conductivity percolation commences and at which water proton selfdiffusion markedly begins to increase. In addition, the self-diffusion of AOT begins to increase markedly at a higher temperature, indicating the existence of two distinguishable microstructural transitions, such as those discussed here. Similar qualitative markers may be seen by inspection of the data published by Jonstro¨mer et al. [40], where reverse microemulsions of water (HDO), N-methylformamide (NMF), isooctane, and AOT were examined. Their NMR self-diffusion data showed that the HDO and NMF selfdiffusion exhibited a breakpoint in the neighborhood of 19–20 C where they markedly began to increase. These breakpoints correspond to the onset of electrical conductivity percolation. At higher temperature, at about 26 C, the self-diffusion of AOT begins to increase signiﬁcantly. Again, these qualitative markers strongly suggest that the processes of percolating cluster formation and irregular bicontinuous microstructure formation are experimentally distinguishable, at least for the microemulsion system reviewed herein.

Microstructure Effects on Transport

IV.

251

CHEMICAL-POTENTIAL-DRIVEN PERCOLATION

As described in the introduction, certain cosurfactants appear able to drive percolation transitions. Variations in the cosurfactant chemical potential, RT ln (where is cosurfactant concentration or activity), holding other compositional features constant, provide the driving force for these percolation transitions. A water, toluene, and AOT microemulsion system using acrylamide as cosurfactant exhibited percolation type behavior for a variety of redox electron-transfer processes. The corresponding low-frequency electrical conductivity data for such a system is illustrated in Fig. 8, where the water, toluene, and AOT mole ratio (11.2 : 19.2 : 1.00) is held approximately constant, and the acrylamide concentration, , is varied from 0 to 6% (w/w). At about ¼ 1:2%, the arrow labeled p in Fig. 8 indicates the onset of percolation in electrical conductivity. NMR PGSE self-diffusion coefﬁcients obtained [36] for toluene, water, acrylamide, and AOT in this microemulsion system are illustrated in Fig. 9 as a function of , the acrylamide concentration. The self-diffusion coefﬁcients for water, acrylamide, and AOT exhibit breakpoints at about ¼ 1:2%, as marked by the arrow labeled p . Again, the onset of percolation in electrical conductivity coincides with the onset of water proton selfdiffusion increase, and these markers indicate that percolating cluster formation (alternatively, cluster percolation) commences at about ¼ 1:2%. While water and acrylamide self-diffusion coefﬁcients coincide for 1:2%, they diverge for 1:2%. The AOT and acrylamide self-diffusion coefﬁcients run parallel to one another, but the AOT values are much lower. The higher values observed for acrylamide may be assigned to the partitioning of acrylamide into the continuous toluene pseudophase, resulting from the nontrivial solubility of acrylamide in toluene. A major qualitative difference observed in this system, compared to the two systems described, respectively, in the previous two sections, is that the self-diffusion of AOT does not exhibit a signiﬁcant increase at any observed ﬁeld variable. There is no qualitative marker, therefore, for the formation of irregular bicontinuous microstructure in this system. A quantitative analysis of these self-diffusion data according to the two-state model of Eq. (1) to generate the order parameter of Eq. (2) is straightforward. Dc was found to be

FIG. 8 Low-frequency conductivity () of water, toluene, and AOT reverse microemulsions at 25 C as a function of acrylamide (cosurfactant) concentration, (wt%). The p and arrow at ¼ 1:2% shows the approximate onset of percolation in low-frequency conductivity.

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FIG. 9 Measured self-diffusion coefﬁcients at 25 C for toluene (~), water (*), acrylamide (&), and AOT (^) in water, toluene, and AOT reverse microemulsions as a function of cosurfactant (acrylamide) concentration, (wt%). The breakpoint at about 1.2% acrylamide approximately denotes, the onset of percolation in electrical conductivity.

5:41 105 cm2 s1 by measuring molecularly dispersed water in toluene and by correcting for local viscosity differences between toluene and these microemulsions [36]. Values for Dmic were taken as the observed self-diffusion coefﬁcient for AOT. The apparent mole fraction of water in the continuous toluene pseudophases was then calculated from Eq. (1) and the observed water proton self-diffusion data of Fig. 9. These apparent mole fractions are illustrated in Fig. 10 (top) as a function of . The apparent mole fraction in Fig. 10 is approximately constant at x ¼ 0:013 for 1:2%. This constancy corresponds to equilibrium partitioning of water between toluene and the reverse micelles. An extrapolation of this partitioning to higher is illustrated in Fig. 10 (top) by the dashed line. In analogy to the process illustrated in Fig. 4, the anomalous mole fraction of water in the pseudocontinuous phase, x^ , is deﬁned as the difference between this dashed line and x. The corresponding order parameter is then calculated according to Eq. (2) and is illustrated in Fig. 10 (bottom). A single breakpoint is depicted by the arrow labeled p at about ¼ 1:2%. This breakpoint corresponding to the single continuous transition is assigned to the onset of percolating cluster formation. Since no additional continuous transition is revealed in this order parameter with increasing , it can be concluded that there is no indication of irregular bicontinuous microstructure formation in this system, at least over the composition range investigated.

V.

EQUILIBRIUM MODEL

Several unifying conclusions may be based upon the order parameter results illustrated here for microstructural transitions driven by three different ﬁeld variables, (1) disperse phase volume fraction, (2) temperature, and (3) chemical potential. It appears that the onset of percolating cluster formation may be experimentally and quantitatively distinguished from the onset of irregular bicontinuous structure formation. It also appears that

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FIG. 10 (Top) Mole fraction (x) of water in the continuous (toluene) phase as a function of acrylamide content, (wt%), for water, toluene, and AOT reverse microemulsions. (Bottom) Order parameter for disperse pseudophase water derived from mole faction data above. The p and arrow at about 1.2% (w/w) acrylamide indicate the approximate onset of percolation in lowfrequency conductivity

the formation of percolating clusters does not necessarily lead to formation of irregular bicontinuous microstructure, as exempliﬁed in the system driven by acrylamide (cosurfactant) chemical potential. The order parameter approach reviewed here provides explicit support for the cluster-bicontinuous cartoon presented in 1990 by Chen et al. [20] in their neutron scattering study of curvature evolution. Furthermore, this order parameter approach provides a quantitative measure of the amount of water present in each disperse pseudophase. Such a quantitative measure should provide a basis for testing phenomenological and statistical mechanical theories that advance to the point of being able to discern such microstructural transitions. The quantitative estimates for the distribution of water among the different microstructures provide a basis for new thinking about these isotropic microemulsion domains. It appears that irregular bicontinuous microstructure evolves gradually from reverse microemulsion droplets and/or from percolating clusters of such droplets. The formation of such irregular bicontinuous microstructure has heretofore only been considered in the context of ﬁrst-order transitions between multiple phase domains [41]. While the order parameters derived from the self-diffusion data provide quantitative estimates of the distribution of water among the competing chemical equilibria for the various pseudophase microstructures, the onset of electrical percolation, the onset of water self-diffusion increase, and the onset of surfactant self-diffusion increase provide experimental markers of the continuous transitions discussed here. The formation of irregular bicontinuous microstructures of low mean curvature occurs after the onset of conductivity increase and coincides with the onset of increase in surfactant self-diffusion. This onset of surfactant diffusion increase is not observed in the acrylamide-driven percolation. This combination of conductivity and self-diffusion yields the possibility of mapping pseudophase transitions within isotropic microemulsions domains.

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ACKNOWLEDGMENTS The collaboration of Edwin Garcı´ a of Eastman Kodak Company in the early stages of this work is gratefully acknowledged. The skillful collaboration of Brian Antalek of Eastman Kodak and of Tony Williams while at Kodak has been essential and invaluable in generating the extensive NMR PGSE data upon which the order parameter approach reviewed here was based. Many fruitful ideas and results were also generated in collaboration with Nissim Garti and Yuri Feldman, and their students, at the Hebrew University of Jerusalem.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

24. 25. 26. 27. 28. 29.

R. A. Mackay and J. Texter (eds.), Electrochemistry in Colloids and Dispersions, VCH Publishers, New York, 1992. M.-P. Pileni (ed.), Structure and Reactivity in Reverse Micelles, Elsevier, Amsterdam, 1989. P. Douzou, E. Keh, and C. Balny. Proc. Natl. Acad. Sci. U.S.A. 76:681 (1979). N. Miyoshi and G. Z. Tomita. Z. Naturforsch. 35b:107 (1980). S.-H. Chen and R. Rajagopalan (eds.), Micellar Solutions and Microemulsions, Springer-Verlag, New York, 1990. R. Zana and J. Lang, in Microemulsions: Structure and Dynamics (S. E. Friberg and P. Bothorel, eds.), CRC Press, Boca Raton, pp. 153–172. H.-F. Eicke, J. C. W. Shepherd, and A. Steinemann. J. Colloid Interface Sci. 56:168 (1976). J. Peyrelasse and C. Boned. Phys. Rev. A 41:938 (1990). J. Texter, B. Antalek, E. Garcı´ a, and A. J. Williams, in Amphiphiles at Interfaces (J. Texter, ed.), Steinkopff Verlag, Darmstadt, 1997, pp. 160–169; Prog. Colloid Polym. Sci. 106:160 (1997). Y. Feldman, N. Kozlovich, I. Nir, and N. Garti. Phys. Rev. E 51:478 (1995). B. Lindman and U. Olsson. Ber. Bunsenges. Phys. Chem. 100:344 (1996). M. T. Clarkson, D. Beaglehole, and P. T. Callaghan. Phys. Rev. Lett. 54:1722 (1985). L. E. Scriven. Nature 263:123 (1976). B. Lagourette, J. Peyrelasse, C. Boned, and M. Clausse. Nature 281:60 (1979). M. Lagu¨es. J. Phys. (Paris) Lett. 40:L331 (1979). R. Jo´hannsson, and M. Almgren. Langmuir 9:2879 (1993). M. Lagu¨es, R. Ober, and C. Taupin. J. Phys. 39:L487 (1978). A.-M. Cazabat, D. Chatenay, D. Langevin, and J. Meunnier. Faraday Discuss. Chem. Soc. 76:291 (1982). D. Chatenay, W. Urbach, A.-M. Cazabat, and D. Langevin. Phys. Rev. Lett. 54:2253 (1985). S.-H. Chen, S.-L. Chang, and R. Strey. J. Chem. Phys. 93:1907 (1990). A. Jada, J. Lang, and R. Zana. J. Phys. Chem. 93:10 (1989). M. W. Kim and J. S. Huang. Phys. Rev. A 34:719 (1986). J. Peyrelasse and C. Boned, in Structure and Dynamics of Strongly Interacting Colloids and Supramolecular Aggregates in Solution (S.-H. Chen, J. S. Huang, and P. Tartaglia, eds.), Kluwer Academic Publishers, Dordrecht, 1992, pp. 801–806. P. Alexandridis, J. F. Holzwarth, and T. A. Hatton. J. Phys. Chem. 99:8222 (1995). Y. Feldman, N. Kozlovich, 1. Nir, N. Garti, V. Archipov, Z. Idiyatullin, Y. Zuev, and V. Fedotov. J. Phys. Chem. 100:3745 (1996). J. Lang, N. Lalem, and R. Zana. J. Phys. Chem. 95:9533 (1991). L. M. M. Naza´rio, T. A. Hatton, and J. P. S. G. Crespo. Langmuir 12:6326 (1996). E. Garcı´ a and J. Texter. Proc. Electrochem. Soc. 93(1):2166 (1993). E. Garcı´ a, S. Song, L. E. Oppenheimer, B. Antalek, A. J. Williams, and J. Texter. Langmuir 9:2782 (1993).

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30. E. Garcı´ a and J. Texter. J. Colloid Interface Sci. 162:262 (1994). 31. B. Antalek, A. Williams, E. Garcı´ a, D. H. Wall, S. Song, and J. Texter, in Dynamic Properties of Interfaces and Association Structures (V. Pillai and D. O. Shah, eds.), Champaign, IL: AOCS Press, 1996, pp. 183–196. 32. M. T. Carver, E. Hirsch, J. C. Whittmann, R. M. Fitch, and F. Candau. J. Phys. Chem. 93:4867 (1989). 33. B. Antalek, A. J. Williams, E. Garcı´ a, and J. Texter. Langmuir 10:4459 (1994). 34. P. Stilbs, B. Lindman. Progr. Colloid Polymer Sci. 69:39 (1984). 35. P. Gue´ring and B. Lindman. Langmuir 1:464 (1985). 36. B. Antalek, A. J. Williams, and J. Texter. Phys. Rev. E 52:R5913 (1996). 37. J. Texter, B. Antalek, and A. J. Williams. J. Chem. Phys. 106:7869 (1997). 38. B. Antalek, A. J. Williams, J. Texter, Y. Feldman, and N. Garti. Colloids Surf. A. Physiochem. Eng. Aspects 128:1 (1997). 39. S. Geiger and H.-F. Eicke. J. Colloid Interface Sci. 110:181 (1986). 40. M. Jonstro¨mer, U. Olsson, and W. O. Parker, Jr. J. Phys. Chem. 11:61 (1995). 41. Y. Talmon and S. Prager. J. Chem. Phys. 69:2984 (1978).

11 Investigation of Oil^Water Interfaces by Spectroscopic Methods. Relations with Rheological Properties of Multiphasic Systems ERIC DUFOUR De´partement Qualite´ et Economie Alimentaires, ENITA Clermont-Ferrand, Lempdes, France C. LOPEZ and S. HERBERT

I.

INRA-LEIMA, Nantes, France

INTRODUCTION

Emulsions and gels are important in the formulation of products in the food and pharmaceutical industries, and they must be stable throughout the lifetime of the product. Proteins are often used to stabilize food emulsions. Due to their amphipathic nature, proteins adsorb efﬁciently at the oil–water interface and both lower the surface tension and stabilize the systems. The emulsifying activity of a protein depends on its molecular properties and environmental factors. In general, proteins with a ﬂexible structure display a better emulsifying activity than those with a rigid structure [1]. The ﬂexible casein molecules can spread widely over the interface, whereas the spreading is not as great in the case of more rigid proteins, such as whey proteins [2]. In all cases, the adsorption of a protein onto an interface induces conformational changes of the protein. It may be assumed that hydrophobic amino acids will be close to the oil surface and that hydrophilic residues will point toward the aqueous phase, but this will be constrained by the amino acid sequence of the protein. Texture is an important criterion used to evaluate the quality of gels. It is a reﬂection of their structure at the microscopic and molecular levels. For example, milk gel is a complex matrix of milk proteins, fat globules, minerals, and water. It is well established that milk composition and treatment affect the microstructure of the coagulum. Milk treatments performed in dairy plants, i.e., ultraﬁltration, homogenization, and heating, modify the fat particle size and change the milk fat globule membrane [3–6]. As a consequence, cheeses made from skim milk standardized with homogenized cream have different properties in comparison with those made from fresh whole milk [7,8] It is important to characterize the material adsorbed at the interface, as well as the conformation of the adsorbed proteins, because it determines the properties of the emulsions and gels. However, little is known about the conformational changes of proteins upon adsorption at oil–water interfaces. The main reason for this is the lack of experi257

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mental techniques allowing structural informatiaon to be obtained directly from complex systems.

II.

SPECTROSCOPIC STUDY OF TURBID AND CONCENTRATED SAMPLES

Adsorption of proteins onto surfaces has long been a subject of interest in the emulsion and biomaterial worlds. It is possible to assess the dimensions of the adsorbed protein layers of emulsions droplets using the techniques of dynamic light scattering, small-angle x-ray scattering, and neutron reﬂectance. This makes it possible to distinguish between the caseins, which provide rather extended layers, up to about 12 nm thick [9], and whey proteins such as -lactoglobulin (BLG), giving layers which are only about 2 nm thick [10]. It indicates that the thickness of the layer is made up by one layer of BLG molecules, given that the diameter of the monomeric protein in solution is about 3 nm. Access to the ﬁne three-dimensional structure of adsorbed proteins should be a key to the evaluation of the energy variation associated with the conformational changes [11]. The most efﬁcient techniques used for protein structure determination are, however, not adapted to adsorbed proteins. X-ray diffraction implies the use of crystalline samples, which cannot be used in adsorption studies. In NMR the size of the protein, as well as the size of the adsorption surface, is a limited factor. Circular dichroism is a technique routinely used to quantify the secondary structure of proteins and peptides in solution. This technique also gives quantitative information on the secondary structures of adsorbed proteins, but it is severely limited by light scattering of particles with diameters above 20 nm. For this reason, studies of secondary structure changes in protein upon adsorption are scarce. Nevertheless, circular dichroic data on the effect of surface adsorption of synthetic peptides [12], melittin [13], bovine serum albumin [14], and BLG [15,16] have been published. The data were obtained using a cell containing several quartz surfaces [12,13,15,16] and also ultraﬁne silica particles [14]. For example, the interactions of BLG with phospholipid monolayers were studied by circular dichroism [15,16]. Phospholipid monolayers were formed at a ﬁxed ﬁlm pressure and then the protein was added in the subphase. The protein–lipid complexes were transferred to quartz plates and the spectra were recorded. It was shown that the interactions were mainly electrostatic at acidic pH and that the binding of BLG induced no conformational changes. Secondary structure alterations were only observed when BLG in chloroform–methanol solution was injected in the ﬁlm subphase. In this case, BLG conformation was primarily -helical [15]. Conformational changes of bovine serum albumin on its adsorption to gas–liquid or solid–liquid interfaces have been investigated by intrinsic ﬂuorescence and circular dichroism of resolubilized foamed protein [17], by total internal reﬂection ﬂuorescence measurements [18,19], and by direct circular dichroism measurements [14]. However, methods allowing one to study directly the conformational changes of adsorbed proteins on nonplane liquid–liquid interfaces are still in development. It is generally assumed the ﬂuorescence and Fourier transform mid-infrared (FT-IR) spectroscopies do not suffer from the above-mentioned inconveniences and may be applied to turbid samples. Front-face (ﬂuorescence) and attenuated total reﬂection (FTIR) techniques may provide information on the structure of adsorbed proteins. Fluorescence spectroscopy offers several inherent advantages for the characterization of molecular interactions and reactions. First, it is 100–1000 times more sensitive than spectrophotometric techniques. Second, ﬂuorescent compounds are extremely sensitive to their environment. Tryptophan residues that are buried in the hydrophobic interior of a

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protein, for example, have different ﬂuorescent properties than residues that are on a hydrophilic surface. This environmental sensitivity enables to characterize conformational changes such as those attributable to the thermal, solvent, or surface denaturation of proteins, as well as the interactions of proteins with other food components. Third, most ﬂuorescence methods are relatively rapid. Fluorescent probes are divided in two categories, i.e., intrinsic and extrinsic probes. Tryptophan is the most widely used intrinsic probe. The absorption spectrum, centered at 280 nm, displays two overlapping absorbance transitions. In contrast, the ﬂuorescence emission spectrum is broad and is characterized by a large Stokes shift, which varies with the polarity of the environment. The ﬂuorescence emission peak is at about 350 nm in water but the peak shifts to about 315 nm in nonpolar media, such as within the hydrophobic core of folded proteins. Vitamin A, located in milk fat globules, may be used as an intrinsic probe to follow, for example, the changes of triglyceride physical state as a function of temperature [20]. Extrinsic probes are used to characterize molecular events when intrinsic ﬂuorophores are absent or are so numerous that the interpretation of the data becomes ambiguous. Extrinsic probes may also be used to obtain additional or complementary information from a speciﬁc macromolecular domain or from an oil–water interface. Most ﬂuorescence experiments are done on dilute solutions with absorbance of the sample below 0.1: it is a classical right-angle ﬂuorescence spectroscopy. When the absorbance of the sample is higher than 0.1, the screening effect (or inner ﬁlter effect) induces a decrease of ﬂuorescence intensity and a distortion of excitation spectra [21]. To avoid these problems, an alternative method – frontal illumination ﬂuorescence spectroscopy, has been developed [22]. Front-face ﬂuorescence allows investigation of the ﬂuorescence of powdered, turbid, and concentrated samples (Fig. 1). The method has been used to quantitatively determine hemoglobin in undiluted blood [23], and to study hemoglobin R ! T transition kinetics [24] or proteins in wheat gluten [25]. But searching in the literature, very few papers are encountered dealing with the application of front-face ﬂuorescence in the characterization of food products. This could be explained by the fact that food products are complex products containing numerous ﬂuorescent compounds. In such a case the signals of the different chromophores may overlap and, for example, it becomes difﬁcult to predict the concentration of one particular compound. However, ﬂuorescence spectroscopy in combination with multivariate statistical methods has been used for predicting the concentrations of two component synthetic mixtures [26].

III.

FRONT-FACE FLUORESCENCE SPECTROSCOPY APPLIED TO THE STUDY OF PROTEIN CONFORMATION AT THE OIL–WATER INTERFACE OF EMULSIONS

To our knowledge, there are few publications dealing with direct study of conformational changes of proteins adsorbed on nonplane liquid–liquid interfaces, such as those found in emulsions [27,28]. Detailed information on the conformation of caseins at the oil–water interface have been obtained using proteases [27,29,30]. By comparing the peptides produced during the proteolysis of the protein in solution or adsorbed at the interface, it has been possible to identify the proteinase-sensitive bonds which are masked by being adsorbed to the oil phase. Antibodies to s1 -casein have also been used to probe its topography at an oil–water interface [31].

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FIG. 1 Schematic representations for (a) right-angle and (b) front-face ﬂuorescence spectroscopies.

Among spectroscopic methods, essentially front-face ﬂuorescence has been used to investigate modiﬁcations of the conformation of a protein upon its adsorption at the oil– water interface. Castelain and Genot [28] have shown for the ﬁrst time that front-face ﬂuorescence measurements performed directly on oil-in-water emulsion provide information on the structural changes of proteins upon their adsorption at interface. They conclude from the protein ﬂuorescence spectra recorded directly on the emulsion that the adsorption of bovine serum albumin (BSA) onto the interface to stabilize dodecane-inwater emulsions involve drastic conformational changes in the protein molecule. A 15 nm blue shift of the emission maximum of BSA tryptophans and a signiﬁcant increase of its quantum yield were observed following the adsorption of the protein onto the interface. As the tryptophan residues of the protein move to an apolar environment, it suggests that they are in contact with dodecane or that aromatic amino acids are buried in hydrophobic pockets located inside the protein structure. These authors also indicate that the method may be used to evaluate the partition of adsorbed and nonadsorbed protein in a complex system. However, conformational changes of proteins rarely induce such a large shift as the one observed following bovine serum albumin adsorption of the oil–water interface. For -lactoglobulin (BLG) adsorption at the oil–water interface, the emission maximum of tryptophan residues is blue shifted by only 3 nm [32]. Experiments were carried out on emulsion samples with ratios of soluble BLG/adsorbed BLG ranging between 0 and 2.88, which were prepared by adding known amounts of BLG in solution to the cream and were used in order to investigate the changes in tryptophan emission ﬂuorescence upon BLG adsorption at the oil–water interface. When the BLG in solution was in excess over the adsorbed BLG, the emission spectrum was typical of the native BLG spectrum with a maximum at 329 nm (Fig. 2). The decrease in the soluble BLG/adsorbed BLG ratio induced a shift of the maximum emission toward lower wavelengths. For the sample containing only adsorbed BLG, the maximum emission was located at 326 nm. These results suggested that the tertiary structure of BLG was modiﬁed upon adsorption at the oil–water interface and that at least one tryptophan in adsorbed BLG was in a more hydrophobic environment. In addition, circular dichroism and mid-infrared experiments indicate that the secondary structure of adsorbed BLG is slightly modiﬁed [32,33]. The observed ﬂuorescence blue shift following BLG adsorption was, however, small compared with the one observed for bovine serum albumin [28]. Univariate analysis

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FIG. 2 Emission ﬂuorescence spectra of -lactoglobulin tryptophans for three different samples: R ¼ 0 (---), R ¼ 0:96 ( ), and R ¼ 2:24 (—). R ¼ ðsoluble BLG/adsorbed BLG).

FIG. 3 PCA similarity map deﬁned by principal components 1 and 2. Each label corresponds to a spectrum. Soluble BLG/adsorbed BLG ratios of 0 (0), 0.32 (1), 0.64 (2), 0.96 (3), 1.33 (4), 1.92 (5), and 2.56 (6). The spectrum of each sample was recorded in triplicate using different aliquots.

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techniques are not always appropriate for the study of systems exhibiting slight differences. Principal component analysis (PCA), a multivariate analysis technique, has been used by Dufour et al. [32] to extract information related to protein conformation changes following emulsiﬁcation. This method is well suited to optimize the description of the data collection with a minimum loss of information. Moreover, the eigenvectors corresponding to the principal components are homologous to spectra. They provide information about the regions of the ﬂuorescence spectrum which explain the differences between the samples observed on the map. In this study, the collection contained tryptophan emission spectra of samples with different ratios of soluble BLG/adsorbed BLG. In practical terms, a discrimination of the samples in relation to the ratio of soluble BLG/adsorbed BLG was observed according to principal component 1 (Fig. 3). The corresponding eigenvector indicates a shift toward lower wavelengths for the emulsions containing mainly adsorbed BLG. PCA results tally with the ﬂuorescence spectra recorded at different soluble BLG/ adsorbed BLG ratio [32]. It appears that multivariate analysis techniques are well suited to analyze sets of ﬂuorescence spectra exhibiting slight differences. Indeed, PCA has been successfully applied to front-face ﬂuorescence spectra in order to discriminate between bulk, heated, and/or homogenized samples of milk [5] (Fig. 4). The treatments applied to milk are well known to modify protein structure, fat globule shape, and protein–lipid interactions. Indeed, heating may denature proteins. Denaturation is characterized by the changes of protein structure modifying tryptophan quantum yield, and by the exposure to the surface of hydrophobic regions. Homogenization breaks up fat globules into smaller ones, increasing drastically the area of the lipid–water interface. The stabilization of the interface created by homogenization

FIG. 4 PCA similarity map deﬁned by the principal components 1 and 2 for the tryptophan emission spectra. Samples were coded NHO, NHP, HOM, and HOP for raw, heated, homogenized, and homogenized þ heated milks, respectively. Each label corresponds to a spectrum.

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results from the adsorption of proteins at the interface [34]. The adsorption of proteins at the interface changes their structure, as well as their binding and ﬂuorescence properties [28,32]. The differences observed in the spectra recorded on raw, heated, or homogenized milks clearly indicate that the physical treatments applied to the milk modify the characteristics of the ﬂuorescent probe investigated. The changes of tryptophan quantum yields upon heating suggest that the thermal treatment of the samples partly denatured the milk proteins. Based on the ﬂuorescence data only, it appears more difﬁcult, however, to explain, at a molecular level, the effects of homogenization on milk components. In this case, the modiﬁcation of fat globule size may also perturb light scattering and induce changes in the ﬂuorescence spectra which would not be related to the quantum yield of the probes. In order to get more explanations of the observed ﬂuorescence modiﬁcations of milk samples following physical treatments, tryptophan ﬂuorescence of washed creams, fat globule size, and the kind of proteins adsorbed at the surface of the fat globule were studied. The tryptophan ﬂuorescence intensity of washed cream from raw milk is relatively weak, since the proteins associated with the native membrane of the fat globule are found in small amounts [34]. After heating of raw milk, the ﬂuorescence intensity of the washed cream doubled, suggesting that heat treatment induces binding of proteins to the fat globules. The highest ﬂuorescence was observed for the homogenized sample. This dramatic increase of the ﬂuorescence intensity at about 330 nm indicates that the interface created by the homogenization of milk is stabilized by proteins [5]. These assumptions were conﬁrmed by the electrophoresis study of the washed creams. Electrophoresis of puriﬁed fat globules is a convenient method to characterize and quantify proteins adsorbed at the oil–water interface [35]. Electrophoretic data indicate that no casein, nor whey proteins, were adsorbed at the surface of raw-milk fat globule. Upon homogenization, caseins adsorbed preferentially at the lipid–water interface. In this case, bound -lactalbumin accounted for 16% of the total interfacial proteins. Heat treatment also induced the interaction of proteins with the fat globules. The amount of bound proteins (per mg of lipids) for heated raw milk was half that for homogenized milk.

IV.

FLUORESCENCE SPECTROSCOPY INVESTIGATION OF THE EFFECTS OF THE COMPOSITION OF THE FAT GLOBULE SURFACE ON THE COAGULATION OF MILK

Texture is an important criterion used to evaluate the quality of dairy products. It is a reﬂection of their structure at the microscopic and molecular levels. Structurally, milk gel is a complex matrix of milk proteins, fat globules, minerals, and water. It is well established that milk composition and treatment affect the microstructure of the coagulum. Milk treatments performed in daily plants, i.e., ultraﬁltration, homogenization, and heating, modify the fat particle size and change the milk fat globule membrane [3–6]. Milk proteins are surface-active compounds that constitute a group of strongly interacting proteins and caseins adsorb efﬁciently at the fat–water interface stabilizing emulsions. The molecular state of caseins, whether in the micellar or soluble form, is important in determining their functionality as an emulsiﬁer. The emulsifying activity of a protein depends on its molecular properties and on environmental factors. In general, proteins with a ﬂexible structure display a better emulsifying activity than those with a rigid structure. The ﬂexible casein molecules can spread widely over the interface [27], whereas

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the spreading is not as important in the case of globular proteins, such as -lactoglobulin [32]. As a consequence, cheeses made from skim milk standardized with homogenized cream have different properties in comparison with those made from fresh whole milk [7,8]. There is evidence in the literature that fat globules participate in the protein network formation, and that the fat globule membrane plays a structural role in milk gels [36–38]. Acid–milk–fat composite gels formed by heating reconstituted milk made with skim milk and emulsiﬁed fat prepared using different proteins were investigated by Xiong and Kinsella [38]. The kinetic and structural aspects of protein–protein and protein–fat globule interactions determine the rheological properties of coagula and their syneresis behavior. It has been reported recently that the changes in tryptophan ﬂuorescence emission spectra corresponding to an evolution in the environment of the intrinsic probe allow one to follow the different stages of the acidiﬁcation and coagulation phases and to characterize the gelation times [39,40]. Tryptophan ﬂuorescence spectra also allow to discriminate the coagulation processes of reconstituted milks stabilized by different fat–water interfaces. The time course evolutions of tryptophan ﬂuorescence emission spectra during the coagulation kinetics studied differ as a function of fat–water interface, resulting in different paths and different gel textures [39]. Fluorescence methods may be useful to investigate at a molecular level the fat–water interface evolution during the coagulation kinetics of milks varying by the composition of fat globule surface. An amphiphilic and extrinsic ﬂuorescent probe, Laurdan, known to bind essentially at the oil–water interface, was used in this study. The structural evolutions of reconstituted milks characterized by different fat–water interfaces were studied during the 2 h of an acidiﬁcation phase by glucono--lactone and during the 3 h of a rennetinduced coagulation phase using front-face ﬂuorescence spectroscopy.

A.

Material and Methods

Anhydrous milk fat (melting point ¼ 28 C) was provided by Socie´te´ France Beurre (Quimper, France). Skim milk powder and -lactoglobulin were provided by INRA Rennes (France) and Lactalis (Retiers, France), respectively. -Casein (90% pure) was puriﬁed in the laboratory as described previously [41]. Cream, obtained after skimming of fresh whole milk purchased from a local dairy plant, is constituted by natural milk fat globules. Glucono()lactone (GDL, 99% pure), commercial calf rennet (520 mg/L) and Laurdan were purchased from Roquette (France), SKW (Baupte, France) and Sigma (St Quentin, France), respectively. 1. Milk Reconstitution Skim milk (35 g/L) and -lactoglobulin (5 g/L) solutions were prepared by dissolving skim milk powder and -lactoglobulin powder in distilled water and stirring at room temperature for 4 h. -Casein (5 g/L) had been hydrated in a phosphate buffer (100 mM, pH 8) and stirred at 4 C for one night [27]. Sodium azide (0.1%, wt/v) was added to prevent bacterial growth. After heating at 40 C, liquid anhydrous milk fat (1 v) and the different protein solutions (10 v) were premixed using a polytron (PT 3000, Kinematica) and emulsiﬁed with a homogenizer (ALMO, Legrand, France) at about 40 C in order to obtain oil-inwater emulsions. After separation from the aqueous phase by centrifugation for 5 min at 1000g, milk fat droplets stabilized by different proteins were washed twice with a phos-

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phate buffer (100 mM) in the case of the -casein-stabilized emulsions and with a mineral solution (30 mM CaCl2 ; 25 mM NaCl) for the others in order to remove proteins not bound at the fat–water interface. Four reconstituted milks were prepared by blending hydrated skim milk powder (35 g/L) with four different emulsions (35 g/L) differing by composition of the fat–water interface. Whole reconstituted milks were coded MP (milk proteins), BCAS ( -casein), and BLG5 ( -lactoglobulin 5 g/L): Skimming fresh whole milk allowed us to obtain milk fat globules with natural membranes that were blended at a concentration of 35 g/L with hydrated skim milk powder (35 g/L). This reconstituted milk was coded CREAM. 2.

Coagulation

The pH of the reconstituted milks was adjusted to 6.4 with 1 N HCL. First, the acidiﬁcation phase was carried out with glucono()lactone (2 g/L) at 30 C in order to exponentially decrease the pH and obtain a stabilized value corresponding to pH ¼ 6:0 after 2 h incubation. Then, rennet was added to the acidiﬁed reconstituted milks at a ﬁnal concentration of 19.5 mg/L and the coagulation phase was performed at 30 C for 3 h. 3. Characterization of the Milks and Gels A Malvern Mastersizer (Malvern Instruments Ltd, Malvern, UK) with optical parameters deﬁned by the manufacturer’s presentation code 0505 was used to determine the droplet size distribution. The measurement was made in triplicate at room temperature. Water was used to disperse the emulsion droplets. Gel formation was monitored using a controlled-stress rheometer (Carri-Med CS50, TA Instruments, France) with a cone-plate geometry (4 cm diameter, 3 58 0 angle). The bottom plate was equipped with a Peltier temperature controller that allowed regulation of the temperature at 30 C. The surface of the sample set to the plate was covered with silicone oil to prevent evaporation. The evolutions of the storage (G 0 ) and loss (G 00 ) moduli of the acidiﬁed reconstituted milks were recorded just after rennet addition in the following conditions: frequency 1 Hz, deformation 1%, and strain 6 mN=m2 , considered to be low enough to make a measurement without disturbing the gelation process. Data were collected and rheological parameters calculated using Carri-Med 50 software. The experiments were done in triplicate for all the reconstituted milks. 4.

Front-Face Fluorescence Spectroscopy and Mathematical Processing

Fluorescence spectra were recorded using an SLM 4800C spectroﬂuorimeter (Bioritech, Chamarande, France) mounted with a variable-angle front-surface accessory. The incidence angle of the excitation radiation was set at 56 to ensure that reﬂected light, scattered radiation, and depolarization phenomena were minimized. Emission spectra (resolution: 0.5 nm, averaging: 10) were recorded at 30 C with emission and excitation slits set at 4 nm. All spectra were corrected for instrumental distortions in excitation using a rhodamine cell in the reference channel. The ﬂuorescence excitation spectra of Laurdan (250–420 nm) were recorded with emission wavelength set at 439 nm. For each reconstituted milk studied, the measurement was made in triplicate during the 2 h of the acidiﬁcation phase and the 3 h of the coagulation phase. To reduce scattering effects and to allow a comparison between the different reconstituted milks, the data were normalized by reducing the area under each spectrum to a

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value of 1 [42]. Principal component analysis (PCA) was applied to the normalized data. This method is well suited to optimize the description of the ﬂuorescence data sets by extracting the most useful data and rejecting the redundant data [43]. From a data set, PCA assesses principal components and their corresponding spectral pattern. The principal components are used to draw maps that describe the physical and chemical variations observed between the samples. While the similarity maps allow the comparison of the spectral in such a way that two similar spectra are represented by two neighbouring points, the spectral patterns exhibit the absorption bands that explain the similarities observed on the maps. PCA software has been written by D. Bertrand (INRA Nantes) and is described elsewhere [44]. B.

Results and Discussion

1. Size Characterization of Fat Droplets The average sizes of the emulsion droplets dispersed in reconstituted milks and stabilized by different fat–water interfaces are presented in Table 1. Fat globules in CREAM have an average diameter of 4:5 m, which is similar to fat globule size in whole milk without any treatments [5]. Similar average diameters were obtained for fat droplets in BCAS and BLG5, whereas MP showed larger values. Considering MP emulsion, the large average diameter (7:2 0:5 m) was quite surprising. However, this result was obtained with a good reproducibility. 2. Spectral Changes During the Coagulation Kinetics of BLG5 Milk The excitation spectrum of Laurdan presented a maximum at 363 nm and two shoulders at 320 and 386 nm (Fig. 5). During the kinetics, the changes in the normalized spectra were mainly observed at 320 and 386 nm. As the ﬂuorescence intensity at 320 nm increased between 30 and 300 min, the intensity of the shoulder at 386 nm decreased with time. Figure 6 shows the changes of the ﬂuorescence intensity at 363 nm during the time course of the BLG5 coagulation. During the acidiﬁcation step (0–120 min), the ﬂuorescence intensity remained roughly constant. The addition of rennet induced an increase in ﬂuor-

TABLE 1 Average Diameter of the Natural Milk Fat Globules and Emulsiﬁed Milk Fat Droplets Stabilized by Different Fat– Water Interfaces in Reconstituted Milks Fat–water proteins interface Milk fat globule (CREAM)a -casein (BCAS)a -lactoglobulin 5 g/L (BLG5)a Milk (MP)a a

Code of the different reconstituted milks.

Average diameter ðmÞ 4:5 0:7 4:2 0:3 3:8 0:8 7:2 0:5

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FIG. 5 Laurdan ﬂuorescence excitation spectra recorded between 250 and 420 nm (emission wavelength, 439 nm) at different times during the acidiﬁcation and the rennet-induced coagulation kinetics of BLG5 reconstituted milk: 35, 70, 125, 175, and 300 min. A:U: ¼ arbitrary units.

escence intensity, remaining constant between 120 min and 140 min, followed by a sharp increase from 145 to 165 min. Then the ﬂuorescence intensity continued to increase, but with a smaller slope. The change in the slope of the ﬂuorescence intensity evolution observed between 140 and 300 min corresponded to the gelation point determined visually. PCA was applied to the set of spectra recorded during BLG5 milk coagulation in order to obtain additional structural information. This method is well suited to optimize the description of data collection by extracting the most useful data and rejecting redundant data. Figure 7 shows a PCA similarity map deﬁned by the principal components 1 and 2 for Laurdan excitation ﬂuorescence spectral data of the BLG5 system. The ﬁrst two principal components accounted for 99.4% of the total variability with a predominance of component 1 (98.7%). A separation of spectra was observed as a function of time according to component 1. Moreover, it appeared that the spectrum T160, corresponding to the gelation time determined by the rheology method, exhibited co-ordinates close to ð0; 0Þ. The spectra recorded before gelation (T5–T155) had negative scores according to component 1, whereas spectra recorded after milk gelation (T160–T300) had positive scores. These results showed that acidiﬁcation and gelation of milk induced different modiﬁcations in the ﬂuorescence properties of protein tryptophans. However, considering the data variablities explained by principal components 1 and 2, it appears that gelation modiﬁes milk protein ﬂuorescence properties more dramatically than acidiﬁcation. The spectral pattern associated with principal component 1 is presented in Fig. 8. It provided the characteristic wavelengths which were the most discriminant to separate the

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FIG. 6 Evolution of the maximal ﬂuorescence intensity of Laurdan at 363 nm (expressed in arbitrary units) recorded vs. time during BLG5 reconstituted milk acidiﬁcation and coagulation phases (excitation: 250–420 nm; emission: 439 nm).

FIG. 7 Principal component analysis similarity map deﬁned by the principal components 1 and 2 (A1, A2) for Laurdan ﬂuorescence excitation spectral data recorded during the BLG5 milk coagulation. The digits correspond to the elapsed time. Each label corresponds to a spectrum.

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FIG. 8 Spectral pattern corresponding to the principal component 1 (—).

spectra on the map. The most discriminant wavelengths were 315 and 385 nm. In addition, the contrast between a positive peak at 315 nm and a negative one at 385 nm was observed, indicating opposite changes of the ﬂuorescence intensities of the shoulders at 320 and 385 nm during the kinetics. 3.

Comparison of the Fluorescence Data Set of the Four Milks

The tryptophan emission spectra of the four milks were pooled in one matrix and this table was analyzed by PCA to obtain a maximum of information concerning the differences observed with the recording of ﬂuorescence spectra and relative to the structural changes in the environment of the extrinsic probe studied. Figure 9 presents a PCA similarity map deﬁned by the principal components 1 and 2 for Laurdan ﬂuorescence excitation spectral data of BCAS, MP, BLG5, and CREAM reconstituted milks. The ﬁrst two principal components accounted for 98.9% of the total variability, with a predominance of component 1 (96.6%). The similarity map clearly discriminated between the different systems investigated along the second principal component. The scores were negative for MP and mainly positive for BLG5, CREAM, and BCAS. The principal component 1 (PC1) separated the acidiﬁcation phases of BLG5, CREAM, BCAS, and MP clustered with negative values, from their rennet-induced coagulation phases that spread in a speciﬁc order associated with time from the left to the right of the map. These results showed that acidiﬁcation and gelation of reconstituted milks induced different modiﬁcations in the ﬂuorescence properties of Laurdan. Few techniques allow one to investigate, at a molecular level, structural evolutions during milk coagulation. Fluorescence spectroscopy allows one to characterize weak changes in protein environment or structure. For example, the titration of -lactoglobulin in the micromolar concentration range by fatty acids can be monitored by this technique [45]. But classical right-angle ﬂuorescence spectroscopy only allows one to investigate

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FIG. 9 Principal component analysis similarity map deﬁned by the principal components 1 and 2 (A1, A2) for Laurdan ﬂuorescence excitation spectral data. The letter corresponds to the type of milk and the digits correspond to the elapsed time. Each label corresponds to a spectrum. The letters B, C, L, and P correspond to BLG5, BCAS, CREAM, and MP, respectively.

dilute solutions. Considering emulsions or colloidal systems such as food products, frontface ﬂuorescence can be used, since it makes it possible to record the excitation and emission spectra of powdered, turbid, and concentrated samples. The results reported in this study demonstrate that changes in Laurdan ﬂuorescence excitation spectra corresponding to an evolution in the environment of the extrinsic probe allow one to follow the coagulation phase and to characterize the gelation times. Front-face ﬂuorescence spectroscopy also allows one to discriminate between the coagulation processes of reconstituted milks stabilized by different fat–water interfaces. The time course evolutions of Laurdan ﬂuorescence excitation spectra during the coagulation kinetics studied differ as a function of fat–water interface, resulting in different paths, as shown on the PCA similarity map (Fig. 9).

4. Dynamic Rheological Properties of the Reconstituted Milks During the Coagulation Kinetics Rheological measurements were carried out to investigate the rheological properties of emulsions stabilized by different fat–water interfaces and the inﬂuence of fat droplets on the formation of the protein networks during a process of gelation. The starting time for rheological measurements correspond to t ¼ 120 min. Indeed, the rheological parameters were only recorded during the rennet-induced coagulation phase to avoid structural modiﬁcations during the acidiﬁcation phase which may consequently inﬂuence the gelation process. Elastic and viscous properties of reconstituted milks

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were characterized during coagulation kinetics by the recording of the storage modulus (G 0 ) and the loss modules (G 00 ), respectively. The evolutions of the elastic modulus (G 0 ) recorded vs. time during the rennet-induced coagulation phase of the different reconstituted milks are shown in Fig. 10. All the samples showed a pregel stage characterized by a G 0 modulus close to the 0 N=m2 value. Considering the gelation time, the samples can be divided in two distinct groups with characteristic rheological behaviors. The gel point times for BCAS, BLG5, and MP were observed between 40 and 46 min after rennet addition, whereas CREAM presented a shorter gel point time corresponding to 32 and 33 min after rennet addition, respectively (Table 2). The elastic modulus (G 0 ) of MP, BCAS, and BLG5 rapidly rose to plateaus that corresponded to different G 0 saturations (G0sat ) (Table 2). MP and BCAS coagula showed 0 value (142 N=m2 ), meaning that the emulsions stabilized by skim the more important Gsat milk proteins (mainly casein micelles) and -casein formed the coagula with the strongest protein network. Considering CREAM, a sudden decrease in G 0 modulus was observed 15 min and 32 min after the gel point time, respectively. The rapid increase in the G 0 modulus followed by a sudden decrease was always observed for this sample. This experiment has been carried out three times giving reproducible results. As this phenomenon could result from a sliding of the cone caused by syneresis, experiments were performed using a ridge cone and reduced stress conditions. The shape of the G 0 curve obtained in these conditions was similar to the results reported in Fig. 10. It was concluded that this

FIG. 10 Evolution of the elastic modulus (G 0 ) recorded during the 3 h of the rennet-induced coagulation phase of the reconstituted milks.

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TABLE 2 Rheological Parameters Measured for the Reconstituted Milks and Skim Milk During Coagulation Kinetics

CREAMb;c BCASb BLG5b MPb

Gelation time (min)a

0 Gsat (N/m2 )

00 Gsat (N/m2 )

32:0 0:4 40:3 4:2 42:3 4:0 42:3 2:0

— 142 2 108 4 142 3

— 36 1 28 2 37 1

a

Elapsed time after rennet addition. Reconstituted milks with natural milk fat globules (CREAM) or emulsiﬁed milk fat droplets stabilized by -casein (BCAS), -lactoglobulin 5 g/L (BLG5), skim milk proteins (MP). c Atypical curve (see the text and Fig. 10). b

reproducible phenomenon did not result from the syneresis of the mixed system. But, at the moment, we are not able to explain this phenomenon. 0 The rheological properties, such as Gsat allow one to know the strength of the coagulum resulting from protein–protein and/or protein–fat globule interactions formed during milk coagulation. There is evidence in the literature that fat globules participate in the protein network formation, and that the fat globule membrane plays a structural role in milk gels (36–38). Acid–milk–fat composite gels formed by heating reconstituted milk made with skim milk and emulsiﬁed fat prepared using different proteins were investigated by Xiong and Kinsella [38]. They showed that, under equal gelling conditions, milk fat emulsions stabilized by whey protein isolate form the strongest gels, followed by the emulsions stabilized by sodium caseinate and whole skim milk proteins, as indicated by the G 0 modulus. The Tween 80 emulsiﬁed milk fat and the blank without fat presented similar gel properties. As it is generally assumed that the number of crosslinks in protein gels at equilibrium is proportional to the magnitude of G 0 , the authors concluded that the presence of fat droplets covered with caseins or whey proteins increases the rate of crosslinking. Considering our experiments, the pHs of the milks were 6.0 at the time of renneting. It has been reported [46,47] that the ﬁrmness of a renneted-milk curd attains a maximum at about pH 6. Increased activity of the chymosin at this pH increases the enzymatic phase of coagulation, whereas diminution of micelle stability, linked to both charge neutralization and the liberation of the calcium, increases the aggregation reaction [48–50]. Nevertheless, there are marked differences in the rheological properties of the reconstituted milk coagula containing fat droplets stabilized by different emulsiﬁers (Fig. 10). While the G 0 modulus values for MP, BLG5, and BCAS gels range between 108 and 142 N=m2 , CREAM gel exhibits a particular behavior with G 0 modulus values lower than 20 N=m2 after 300 min. Although the same results have been reported for raw milk [51], this phenomenon is still discussed. It is generally assumed that the interactions between the proteins adsorbed at the fat–water interface and the proteins in the continuous phase likely inﬂuence the viscoelastic behavior of the coagula. Concerning CREAM, the natural milk fat globule membrane plays a particular role during the gelation process. Fat globules in CREAM obtained after skimming of fresh whole milk are stabilized by a membrane constituted by phospholipids, proteins, and lipo- and glycoproteins [34]. As the

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natural milk fat globule membrane is devoid of caseins and whey proteins [5], the fat globules are weakly or noninteractive with the protein network and may behave like plasticizers during shearing. Due to the charge and the composition of the milk fat globule membrane, hydrophobic interactions cannot take place between the membrane and the proteins of the aqueous phase forming the matrix. In addition, casein micelles and milk fat globule membranes exhibit negative charges at pH 6.0, prohibiting ionic interactions. In the case of CREAM, it is possible that native fat globules are loosely entrapped in the gel matrix. This result supports the observations of van Vliet and Dentener-Kikkert [37] and Xiong and Kinsella [38] who showed that Tween 80- and polyvinyl alcohol-stabilized emulsions have little effect on the rheological properties of milk gel. While the rheological measurements differentiate MP, BLG5, and BCAS gels from CREAM gel, a different trend is observed with ﬂuorescence data (Fig. 9). According to principal component 2, the scores were negative for MP, while BCAS, BLG5, and CREAM formed a cluster with positive scores. It is concluded that the interactions and the organizations of protein networks are different. The results suggest that fat globules can either act as copolymers and be integrated into the matrix of the casein–fat globule network, or act as ﬁllers [38]. Considering our data, it appears that the small fat globules (3–4 m) do not perturb the formation of the protein network and can serve as ﬁllers. Indeed, the ﬂuorescence results (Fig. 9) suggest similar organizations of the protein networks for the coagula obtained with BLG5, BCAS, and CREAM. However, in the case of MP, the larger fat globules (6–7 m) perturb the formation of the protein network during coagulation and can serve as copolymers forming a casein–fat globule network [38]. Fats emulsiﬁed with MP present casein micelles at the surface of the droplets that can strongly interact with the casein network during the coagulation process.

V.

FLUORESCENCE SPECTROSCOPY INVESTIGATION OF ACID- OR RENNET-INDUCED COAGULATION OF MILK

Milk coagulation is the primary step in the production of most dairy products. Coagulation can be induced by acid, rennet, or both. Rennet coagulation is characterized by three phases. The ﬁrst of these is an enzymatic phase which involves the cleavage of the surface -casein in the casein micelles to para--casein and soluble caseinomacropeptides. The resulting para-casein micelles spontaneously aggregate in a second phase of the process before a rearrangement step takes place [3,52]. In the case of the acid-induced gelation, the process is different. Upon lowering the pH of milk, colloidal calcium phosphate is solubilized from casein micelles, micellar disintegration takes place and the caseins associate to form a gel [21,32]. The major driving force for protein–protein interactions during the enzymatic and acid coagulation of casein micelle are hydrophobic interactions [53,54]. However, electrostatic and hydrogen bonds contribute to the speciﬁcity and stability of the interactions and, as a consequence, to speciﬁc structures. Generally, the caseins associate during coagulation to form a protein network entrapping fat globules [55,56]. The kinetics of coagulation and the structural aspects of protein–protein and protein–fat globule interactions determine the rheological properties of gels and thus their syneresis behavior. The six major proteins of milk, s1-, s2-, - and -casein, -lactoglobulin, and lactalbumin, contain at least one tryptophan residue [57], the ﬂuorescence of which allows the monitoring of the structural modiﬁcations of proteins and their physicochemical environment during the coagulation processes. Emission ﬂuorescence spectra of the protein tryptophanyl residues were recorded for the milk coagulation kinetics induced by

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acidiﬁcation, rennet, or both [51]. Principal component analysis was applied to the collections of normalized ﬂuorescence spectral data of the three systems to optimize their description. The results showed that front-face ﬂuorescence allowed the detection of the structural changes in casein micelles during coagulation and the discrimination of the different dynamics of the three coagulation systems. Using front-face ﬂuorescence spectroscopy, it has been possible to demonstrate that gels exhibiting different rheological properties have different structures at the molecular level [51]. In addition, it was possible to follow the different steps of the gelation process using intrinsic ﬂuorescence properties of protein tryptophans. Milk retains also fat-soluble vitamins such as vitamins A, D, E, and K. Vitamin A occurs in more than one form, but it is generally found as retinol. Because of its alcohol group, retinol readily forms esters. In milk, almost all the vitamin occurs in the palmitate or acetate ester forms. Vitamin A (about 1 mol/L in bovine milk) is located in the core and in the membrane of the fat globule [58]. Due to its conjugated double bonds, retinol is a good ﬂuorescent probe with excitation and emission wavelengths at about 330 and 450 nm, respectively. A very weak ﬂuorescence is observed for aqueous solution of retinol, but its quantum yield is drastically enhanced in apolar environments [59]. As the ﬂuorescence properties of vitamin A change as a function of its environment, it may be an interesting intrinsic ﬂuorescent probe of milk. It could be very useful to monitor fat–water interface evolution during milk coagulation and to investigate the changes of protein–lipid interactions during the milk coagulation process. In order to reach this goal, the ﬂuorescence properties of vitamin A located in the fat globules was considered. Indeed, ﬂuorescence transfer may occur between protein and vitamin A in the membrane of the fat globule when the two ﬂuorescence probes are close enough (less than 40 A˚) [60]. This approach requires the ability to discriminate between different dynamic and structural changes. For this reason, the study was conducted using three different milk coagulation processes known to yield different structures and textures [53]. A.

Materials and Methods

1. Coagulation Systems Raw bovine milk was purchased from a local dairy plant. For all experiments, the pH of the milk was adjusted to 6.7 using 1 N HCl. Sodium azide (0.02%) was added to the milk to prevent bacterial growth. Three types of coagulation were considered. The gluconoðÞlactone (GDL)-induced coagulation system (GDL system) was prepared by acidiﬁcation with 1.75 g/L GDL (Roquette, Lestrem, France). The rennet-induced coagulation system (rennet system) was prepared by the addition of calf rennet (SKW, Baupte, France) at 25:6 g/L of milk. The GDL þ rennet-induced coagulation system (mixed system) was prepared by acidiﬁcation with 0.45 g/L GDL for 2 h followed by the addition of rennet at 15:4 g=L of milk. The experimental conditions for each system were selected in order to achieve gelation without syneresis. Coagulation kinetics were performed at 30 C. 2. Rheology Gel formation was monitored using a controlled-stress rheometer (Carri-Med CS 50, TA Instruments, Guyancourt, France) with cone-and-plate geometry (cone diameter 4 cm, angle 3 58 0 ). The bottom plate was ﬁtted with a Peltier temperature controller that

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allowed regulation of the temperature at 30 C. The surface of the sample was covered with silicone oil to prevent evaporation. The storage modulus (G 0 ) was recorded at a frequency of 1 Hz under 0.015 strain amplitude until stabilization of the protein network. In order to reduce stress in the sample, G 0 recording started just before the gelation time which corresponds to the time at which G 0 deviated from the baseline. Data were collected and rheological parameters were calculated using Carri-Med 50 software. For each system, the experiments were performed in triplicate. 3.

Front-Face Fluorescence Spectroscopy and Mathematical Processing of the Spectra Fluorescence spectra were recorded using an SLM 4800 spectroﬂuorimeter (Bioritech, Chamarande, France) ﬁtted with a thermostat-controlled (30 C) front-surface accessory. The incidence angle of the excitation radiation was 60 . Coagulation kinetics were performed in a quartz cuvette 1 cm 1 cm. All spectra were corrected for instrumental distortions in excitation using a rhodamine cell in the reference channel. Vitamin A was selected as intrinsic probe of fat globules. The excitation spectrum of vitamin A (250 to 350 nm) was recorded with emission wavelength set at 410 nm. The spectra of vitamin A were recorded throughout the whole coagulation time (i.e., 5 h). For the GDL and rennet systems, the excitation spectrum of vitamin A was recorded every 5 min during the ﬁrst 3 h and every 10 min for the last 2 h. Considering the mixed system, a spectrum was collected every 5 min during the ﬁrst, third, and fourth hours and every 10 min for the second and ﬁfth hours. Three coagulation kinetics were performed for each coagulation system. To reduce intensity effects, the data were normalized by reducing the area under each spectrum to a value of 1 [42]. Principal component analysis (PCA) was applied to the normalized data. This method is well suited to optimize the description of the ﬂuorescence data sets by extracting the most useful data and rejecting the redundant ones [43]. From a data set, PCA assesses principal components and their corresponding spectral pattern. The principal components are used to draw maps that describe the physical and chemical variations observed between the samples. Software for PCA has been written by D. Bertrand (INRA Nantes) and is described elsewhere [44]. B.

Results and Discussion

1.

Investigation of Protein–Lipid Interaction Development During Acid-Induced Milk Coagulation Kinetics

Fluorescent properties of ﬂuorophores are very sensitive to changes of environment [61]. Applications of front-face ﬂuorescence to food systems have been scarce due to the complexity of these systems and to the lack of familiarity with the technique principles among the food scientists. However, the potential for research and quality control applications of this technique to food systems is enormous. Recently, it has been reported that the shape of the vitamin A excitation spectrum is correlated with the physical state of the triglycerides in the fat globules of an emulsion [20]. If structural changes occur in fat globules during cheese ripening, front-face ﬂuorescence should allow one to characterize them. As a consequence, vitamin A ﬂuorescence properties may allow one to characterize the development of protein–fat globule interaction during milk coagulation. It has been reported that the shape of the excitation spectrum of vitamin A is modiﬁed following milk homo-

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FIG. 11 Vitamin A excitation spectra between 250 and 350 nm (emission wavelength: 410 nm) recorded during the coagulation kinetics for GDL system at 0 (—), 120 ( ), and 300 (---) min.

genization or pasteurization. These changes are induced by the binding at the fat–water interface of milk proteins, i.e., caseins and whey proteins [5]. The excitation ﬂuorescence spectra of vitamin A located in the fat globules of milk showed a maximum of 322 nm and two shoulders at 309 and 296 nm. As shown in Fig. 11, the shape of the spectra changes during the kinetics of acid-induced milk coagulation. Between 0 and 300 min, the shapes of the spectra are characterized by a decrease of the intensities at 322 nm and 310 nm and an increase of the intensity at 296 nm. These changes indicate that the environment of the ﬂuorescent probe is modiﬁed during acid-induced coagulation of milk. In order to visualize all the data collection (50 spectra), PCA was applied to the set of normalized ﬂuorescence spectra. The ﬁrst principal component took into account 96% of the total variation and discriminated between the samples as a function of time [62]. The spectra recorded at the beginning of the kinetics have negative scores, whereas positive scores were observed or spectra recorded at the end of the kinetics. The examination of the spectral pattern associated wit the principal component 1 showed an opposition between a positive peak at 296 nm and a negative peak at 322 nm. This pattern is in agreement with a ﬂuorescence transfer between vitamin A and proteins during the time course of the acidinduced gelation. Moreover, the plot of the changes of ﬂuorescence intensity at 322 nm versus the pH evolution during the kinetics shows that any change in the ﬂuorescence intensity is observed between pH 6.7 and 5.1. For pH below 5.1, the ﬂuorescence intensity at 322 nm decreases drastically. This second phase begins with gelation of the milk [62]. A similar trend was observed when the emission ﬂuorescence intensity of tryptophan at 320 nm was plotted versus pH [51].

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These modiﬁcations in the ﬂuorescence properties of milk proteins can be paralleled with the well-known effects of pH on micelle structure and milk gelation [48–50,55,63,64]. Indeed, the alteration of micelle structure during milk acidiﬁcation involves two main steps. The ﬁrst step from pH 6.7 to pH 5.3–5.1 is characterized by the solubilization of micellar calcium phosphate [48–50]. Between pH 5.8 and pH 5.3–5.1, solubilization of micellar calcium becomes faster and at pH 5.3–5.1, practically all the micellar inorganic phosphate is transferred to the serum phase. In this study, the end of the ﬁrst phase corresponds to pH 5.1. It has also been reported that the release of calcium phosphate on lowering the pH involves the dissociation either of -caseins only from micelles into the serum phase [50,64] or of all caseins (s1-, s2-, -, and -caseins) from the micelles [49,63]. However, casein dissociation is temperature dependent and, at 30 C, less than 10% of total caseins dissociate [63]. Moreover, this ﬁrst phase is characterized by a diminution in micelle voluminosity [49,50,64] from pH 6.7 to pH 6.0–5.8 and by an increase in the voluminosity of casein micelles with a maximum at pH 5.4–5.2, which is attributed to the swelling of the micelles and the dissociation of casein micelles [50,64]. During this ﬁrst step, a partial micellar disintegration takes place, which causes a looseness in the micelle. The second stage from pH 5.2 to pH 4.45 is marked mainly by the reabsorption of caseins and the aggregation of micelles involving the formation of new particles completely different in structure and composition from the original micelles [49,55]. These changes induce a large decrease in the voluminosity of casein micelles, with a minimum at pH 4.6 [50,64], and from 4.6 the voluminosity increases again [64], leading to the formation of the ﬁnal network of the acid milk gel [49,55]. The change in ﬂuorescence intensity at 320 nm parallels the changes of casein micelle structure induced by lowering of the pH. It appears that the change in the ﬂuorescence intensity at 320 nm reﬂects pH-induced physicochemical changes of casein micelles and in particular, structural changes in the micelles. The alteration of casein micelle structure results in casein–fat globule interaction inducing speciﬁc modiﬁcations in the shape of the ﬂuorescence spectra of vitamin A. The PCA map deﬁned by the principal components 1 and 2 describes the modiﬁcations of protein–fat globule interactions during milk coagulation. 2.

Structural Evolution During the Three Different Coagulation Processes The vitamin A excitation spectra of the three systems were pooled in one matrix and this table was analyzed by PCA. Figure 12 presents a PCA similarity map deﬁned by the principal components 1 and 2 for vitamin A ﬂuorescence spectral data of GDL, rennet, and mixed systems. The ﬁrst two principal components account for 99.5% of the total variability, with a predominance of component 1 (93%). Discrimination among the three systems is observed on the map. The results clearly show that the ﬁrst principal component discriminates among the spectra as a function of time, whereas the principal component 2 allows one to discriminate among the three coagulation systems. Figure 13 shows the spectral pattern associated with principal component 1. Its shape is similar to that described above (Section V.B.1) and is characterized by an opposition between a negative peak at 296 nm and a positive peak at 322 nm. Again, these data indicate that protein–fat interactions develop during the cogulation kinetics of the three systems. It appears that vitamin A is a valuable probe to monitor the changes in fat–protein interactions during milk coagulation. From the map deﬁned by principal components 1 and 2, we also conclude that the interactions developed during the gelation are different for the three coagulation systems.

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FIG. 12 Principal component analysis similarity map deﬁned by the principal components 1 and 2 for vitamin A excitation ﬂuorescence spectral data. Sample coding: L, R, and X stand for the GDL, rennet, and mixed systems, respectively; the digits are for the time elapsed since the beginning of the kinetics.

FIG. 13

Spectral pattern corresponding to the principal component 1.

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279

Kinetics of Gelation Studied by Dynamic Rheological Measurements

In order to check that different gel structures – as deduced from ﬂuorescence experiments, induce different rheological properties, rheological measurements were performed during the milk coagulation process by the recording of the G 0 modulus [51]. The changes in the G 0 modulus over the 600 min experiment are very different for the three coagulation procedures. For the rennet system, initiation of gel formation begins at 180 min and the G 0 modulus increases slowly and reaches a plateau after 470 min. The GDL system has a gelation time of 110 min and the G 0 modulus increases more rapidly to reach a plateau after 270 min. For the mixed system, the gelation time is at 190 min and the change in the G 0 modulus is more rapid, exhibiting a gel strength greater than that of the other systems. Moreover, a sudden decrease in G 0 is observed at 240 min. After the addition of rennet (at 120 min of acidiﬁcation), the mixed system shows a shorter gelation time and a greater strength of gel than the rennet system. The differences observed result from the differences in pH between the two systems. Whereas the pH is 6.7 for the rennet system, the mixed system is pH 6.1 at the time of renneting. It has been reported [46,47] that the ﬁrmness of a renneted-milk curd reaches a maximum at about pH 6. Increased activity of the chymosin increases the enzymatic phase, whereas diminution of micelle stability, linked to both charge neutralization and the liberation of the calcium, increases the aggregation reaction. On the other hand, the gel obtained with the GDL system was weaker, since lowering of the pH involves disintegration of the micelles: the resulting gel consists of dispersed clusters of demineralized caseins, devoid of suitable binding to develop a contraction strength [65]. The mixed system is characterized by a rapid increase in the G 0 modulus followed by a sudden decrease. This study has shown that the process used to coagulate milk has a broad effect on fat globule–protein interactions and on the molecular structure of the gel. In addition we have shown that the different molecular structures of the three coagula correspond to different rheological properties.

VI.

CONCLUSION

The aim of this review was to summarize those aspects of ﬂuorescence spectroscopy that may have value for solving problems in food science and technology. The techniques described, which are mainly based on front-face ﬂuorescence spectroscopy coupled with multidimensional statistical methods, have been illustrated by examples taken from the literature and the work done in our laboratory. Although ﬂuorescence spectroscopy is a technique whose theory and methodology have been extensively exploited for studies of both chemistry and biochemistry, the utility of ﬂuorescence spectroscopy for molecular studies has not yet been fully recognized in food science. Fluorescence spectroscopy has the same potential to address molecular problems in food science as in the biochemical science ﬁeld, because the scientiﬁc questions that need to be answered are closely related. We hope that this coverage will introduce a novel class of techniques in the emulsion and gel ﬁelds.

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12 Scanning Electrochemical Microscopy as a Local Probe of Chemical Processes at Liquid Interfaces ANNA L. BARKER, CHRISTOPHER J. SLEVIN, PATRICK R. UNWIN, and JIE ZHANG Department of Chemistry, University of Warwick, Coventry, England

I.

INTRODUCTION

In just a few years, scanning electrochemical microscopy (SECM) has emerged as a powerful technique for investigating chemical kinetics at liquid interfaces, as described in several recent reviews [1–3]. The considerable interest in SECM is that it overcomes many of the problems inherent in conventional methodologies for studying reactions at liquid–liquid interfaces, particularly charge transfer at the interface between two immiscible electrolyte solutions (ITIES). SECM employs an ultramicroelectrode (UME) [4–7], typically a diskshaped electrode with a diameter on the micrometer scale, positioned in close proximity to a target interface, to initiative and/or monitor an interfacial process of interest. The response of the UME probe provides local kinetic and chemical information. In this chapter we highlight the SECM techniques that can be used to study electron transfer (ET), ion transfer (IT), and various molecular transfer processes at liquid–liquid interfaces. We also discuss developments in the methodology that facilitate the investigation of liquid–gas interfaces and molecular monolayers at liquid surfaces. We begin by reviewing the principles of SECM methods, and present an overview of the instrumentation needed for experimental studies. A major factor in the success of SECM, in quantitative applications, has been the parallel development of theoretical models for mass transport. A detailed treatment of the theory for the most common SECM modes that have been used to study liquid interfaces is therefore given, along with key results from these models. A comprehensive assessment of the applications of SECM is provided and the prospects for the future developments of the methodology are highlighted.

II.

PRINCIPLES AND MODES OF OPERATION

One of the attractive features of SECM is that the UME tip response is based on wellestablished electrochemical principles, making the technique quantitative. This aspect of SECM can be illustrated by considering the case of simple diffusion-limited electrolysis at an amperometric disk-shaped tip. When the tip is positioned a long way from the target 283

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FIG. 1 (a) Schematic of the hemispherical diffusion-ﬁeld established for the steady-state diffusionlimited oxidation of a solution species, Red, at a disk-shaped UME, giving rise to a current ið1Þ. (b) When the UME is positioned close to an inert target interface, diffusion of Red is hindered and the current, i, is less than that measured in (a).

interface, d > 10a, where d is the tip–interface distance and a is the electrode radius, it behaves as a conventional UME. In this situation, a steady-state current, ið1Þ, is rapidly established due to hemispherical diffusion of the target species [Red in Fig. 1(a)]. As the tip is brought close to an interface which is inert with respect to the species involved in the electrode process, diffusion to the UME becomes hindered [Fig. 1(b)] and the steady-state current, i, decreases compared to ið1Þ. In general, measurements of i=ið1Þ as a function of d are termed ‘‘approach curves,’’ This type of experiment has been used most to study liquid interfaces. Since the dependence of the i=ið1Þ ratio on d and the tip geometry can be calculated theoretically [8], simple current measurements with mediators which do not interact at the interface can be used to determine d. When either the solution species of interest, or electrolysis product(s), interact with the target interface, the hindered mass transport picture of Fig. 1(b) is modiﬁed. The effect is manifested in a change in the tip current, which is the basis of using SECM to investigate interfacial reactivity. Hitherto, there are primarily three ways in which an amperometric electrode can be used to simultaneously induce and monitor interfacial processes. These are illustrated schematically in Fig. 2 for the most general case where diffusion may occur in both of the liquid phases, which comprise the interface of interest. The feedback mode [Fig. 2(a)] is one of the most widely used SECM techniques, applicable to the study of interfacial ET processes. The basic idea is to generate a species at the tip in its oxidized or reduced state [generation of Ox1 in Fig. 2(a)], typically at a diffusion-controlled rate, by electrolysis of the other half of a redox couple (Red1 ). The tip-generated species diffuses from the UME to the target interface. If it undergoes a redox

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FIG. 2 Principal methods for inducing and monitoring interfacial processes with SECM: (a) feedback mode, (b) induced transfer, and (c) double potential step chronoamperometry.

reaction, which converts it to the original form, it diffuses back to the tip, thereby establishing a feedback cycle and enhancing the current at the UME. The theory of this mode is developed in Section IV and applications are discussed in Section V. SECM-induced transfer [SECMIT; Fig. 2(b)] can be used to characterize reversible phase transfer processes at a wide variety of interfaces. The basic idea is to perturb the process, initially at equilibrium, through local amperometry at the UME. Hitherto, diffusion-limited electrolysis has mainly been used in conjunction with metal tips, but ion transfer voltammetric probes (discussed brieﬂy in Section III, and in detail in Chapter 15) can also be used. The application of a potential to the tip, sufﬁcient to deplete the

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species of interest in phase 1 [oxidation of Red1 to Ox1 in Fig. 2(b)], drives the transfer of species Red from phase 2 to phase 1. Collection of this species at the tip enhances the current ﬂow compared to the situation where there is no net transfer across the target interface and species Red reaches the tip by hindered diffusion through phase 1 only. For a given tip–interface separation, the overall current response is governed by diffusion in the two phases and the interfacial kinetics [9]. The technique was originally employed in a time-dependent potential step chronoamperometric mode to probe desorption processes at solid–liquid interfaces [10], and was subsequently shown to be a powerful probe of dissolution kinetics under both steady-state and time-dependent operation [11–17]. As will be discussed in Sections V and VI, the technique has very recently proven a powerful approach for probing the kinetics of solute transfer across interfaces formed between immiscible liquids [9,18] and between liquids and gases [19]. When there are no kinetic limitations to the interfacial transfer process, SECMIT is also an effective analytical technique for determining the permeability, concentration, and diffusive properties of a solute in a phase, without the UME having to enter or contact that phase, as discussed in Section IV. This is obviously advantageous for situations where direct voltammetric measurements would otherwise be impractical, for example, due to high resistivity or a limited solvent window. This aspect of SECMIT has also been used to great effect where the intimate presence of the UME would damage the structural integrity of the sample under investigation, as in the case of biological tissues [20,21]. To expand the range of interfacial processes that can be studied with SECM, our group has recently introduced double potential step chronoamperometry (DPSC) for initiating and monitoring reactions on a local scale. When employed at UMEs, DPSC has proven a powerful technique for characterizing the lifetime of transient species involved in solution processes down to the microsecond time scale [22] and the diffusion coefﬁcients of electrogenerated species, independent of knowledge of the concentration and number of electrons transferred [23]. In the SECM conﬁguration, the follow-up chemical reaction involving the tip-generated species is effectively conﬁned to the interface under study. The basic concept [Fig. 2(c)] is to employ the UME to generate a reactive species in an initial (forward) step for a ﬁxed period. The potential is stepped from a value where there are no redox reactions to one where Red1 is oxidized to Ox1 at a diffusioncontrolled rate. During this step, the tip-generated species (Ox) diffuses away from the UME and intercepts the interface. If Ox interacts with the interface (e.g., by adsorption, absorption, or a chemical reaction), its concentration proﬁle is modiﬁed compared to the situation where there is no interaction and Ox simply leaks out of the tip–interface gap by hindered diffusion. Consequently, when the potential is reversed, in a ﬁnal step to collect Ox by electrolysis, the ﬂux at the UME, and the corresponding current–time characteristics, depend strongly on the nature of the interaction of species Ox with the target interface. The application of this technique to probe transfer processes at liquid–liquid and liquid–air interfaces will be discussed further in Sections V and VI.

III.

INSTRUMENTATION

A.

Probes

SECM employs a mobile UME tip (Fig. 3) to probe the properties of a target interface. Although both amperometric and potentiometric electrodes have found application in SECM, amperometry – in which a target species is consumed or generated at the probe UME – has found the most widespread use in kinetic studies at liquid interfaces, as

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FIG. 3 (a) Block schematic of the typical instrumentation for SECM with an amperometric UME tip. The tip position may be controlled with various micropositioners, as outlined in the text. The tip potential is applied, with respect to a reference electrode, using a potential programmer, and the current is measured with a simple ampliﬁer device. The tip position may be viewed using a video microscope. (b) Schematic of the ‘‘submarine’’ UME conﬁguration, which facilitates interfacial electrochemical measurements when the phase containing the UME is more dense than the second phase. In this case, the glass capillary is attached to suitable micropositioners and electrical contact is made via the insulated copper wire shown.

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discussed in Section II. Typically, amperometry involves electrolysis at a solid UME, usually a disk-shaped electrode, with a diameter of 0.6–25 m. This type of electrode is readily fabricated by sealing a wire of the material of interest in a glass capillary, making an electrical connection, and polishing the end ﬂat [24–28]. Pt, Au, and C electrodes have been successfully fabricated in this way. For most SECM studies, the ratio of the diameter of the entire tip end (electrode plus surrounding insulator, 2rs ) to that of the electrode itself, 2a, RG ¼ rs =a is typically around 10. A polarized ITIES can also be used to drive ET processes [29], and microelectrode probes for use in SECM may be fabricated using capillary tips to support the liquid–liquid interface. This type of probe also enables the amperometric detection of ions which cannot be determined by conventional electrolysis at solid electrodes, e.g., Kþ [30,31]. Such probes have been used in SECM [29,32,33], but will not be considered further here, as they are discussed in detail in Chapter 15. When a liquid–liquid interface is to be investigated using an electrode in the more dense phase, or for studies at the water–air interface, a ‘‘submarine’’ electrode can be deployed [18,19,34], depicted schematically in Fig. 3(b). In this case, the electrode is inverted in the cell, such that the tip points upwards, and an insulated connection is made through the solution. Metal electrodes down to the nanometer scale can also be fabricated by sealing an etched Pt or Pt–Ir wire in a suitable insulating material, leaving just the etched end exposed [35–37].

B.

Positioning

The tip is attached to positioners, which allow it to be moved and positioned relative to the interface under investigation. A variety of positioners have been employed in SECM instruments, with the choice depending on the type of measurement and spatial resolution required. For the highest (nanometer) resolution, piezoelectric positioners similar to those used in STM are mandatory [38]. In contrast to SECM at solid–liquid interfaces, where high-resolution x, y, z positioning and scanning is usually required, most SECM measurements at liquid–liquid interfaces simply involve the translation of a tip towards and/or away from a speciﬁc spot on an interface, in the perpendicular (z) direction. In this situation, it is only necessary to have high-resolution z-control of the tip, typically using a piezoelectric positioner, while manual stages sufﬁce for the other two axes [2,9,18]. The use of a video microscope, aligned such that the electrode may be observed from the side, has proved useful in facilitating the positioning of the UME relative to the interface [9,18]. As mentioned above, when the electrode is positioned in the more dense liquid phase, a ‘‘submarine’’ electrode may be employed. An alternative conﬁguration is to form the interface at the tip of a capillary positioned in the base of the cell, through which the lower density phase may be delivered. This approach allows the use of conventional UMEs [39].

C.

Electrochemical Instrumentation

The electrochemical circuitry required for SECM is relatively straightforward. Since the interface is not generally externally polarized in SECM measurements of liquid–liquid interfaces, a simple two-electrode system sufﬁces (Fig. 3). A potential is applied to the tip, with respect to a suitable reference electrode, to drive the process of interest at the tip and the corresponding current that ﬂows is typically ampliﬁed by a current-to-voltage converter.

SECM as a Local Probe of Chemical Processes

IV.

289

THEORY

The success of SECM methodologies in providing quantitative information on the kinetics of interfacial processes relies on the availability of accurate theoretical models for mass transport and coupled kinetics, to allow the analysis of experimental data. The geometry of SECM is not conducive to exact analytical solution and hence a number of semianalytical [40,41], and numerical [8,10,42–46], methods have been introduced for a variety of problems. The treatment of the two-phase SECM problem applicable to immiscible liquid– liquid systems, requires a consideration of mass transfer in both liquid phases, unless conditions are selected so that the phase that does not contain the tip (denoted as phase 2 throughout this chapter) can be assumed to be maintained at a constant composition. Many SECM experiments on liquid–liquid interfaces have therefore employed much higher concentrations of the reactant of interest in phase 2 compared to the phase containing the tip (phase 1), so that depletion and diffusional effects in phase 2 can be eliminated [18,47,48]. This has the advantage that simpler theoretical treatments can be used, but places obvious limitations on the range of conditions under which reactions can be studied. In this section we review SECM theory appropriate to liquid–liquid interfaces at the full level where there are no restrictions on either the concentrations or diffusion coefﬁcients of the reactants in the two phases. Speciﬁc attention is given to SECM feedback [49] and SECMIT [9], which represent the most widely used modes of operation. The extension of the models described to other techniques, such as DPSC, is relatively straightforward. For the two modes of interest in this section we ﬁrst describe the relevant diffusion equations and boundary conditions and then present results from numerical simulations obtained using the alternating direction implicit ﬁnite-difference method (ADIFDM) [50]. This is an efﬁcient digital technique for solving two-dimensional time-dependent problems. It was ﬁrst used to model diffusion at UMEs by Heinze [51–53] and for SECM by Unwin and Bard [43], and has since proved to be a versatile method for treating a wide variety of steady-state and transient problems in the SECM geometry, particularly by our group. The advantages of the ADIFDM are typical of most successful digital methods; involving relatively simple algorithms with a high efﬁciency of computation and ﬂexibility that allows easy adaptation to different kinetic situations and SECM operating modes. Most SECM experiments at liquid–liquid interfaces have principally involved the determination of the steady-state tip current response as a function of the separation between the tip and the interface (approach curve measurements). However, in some situations complementary information can be gleaned from the transient behavior (as illustrated below for SECMIT). We therefore describe models for the time-dependent problem from which the steady-state characteristics can be developed from the longtime limit. All the simulations reported in this chapter relate to a disk-shaped UME, characterized by RG ¼ 10, which is typical of the probes used in SECM experiments and for most previous theoretical treatments. A.

Feedback Mode

In SECM feedback studies of ET reactions at ITIES, four main processes contribute to the magnitude of the tip current (Fig. 4); (1) mediator diffusion in phase 1 between the tip and the ITIES, (2) mediator diffusion in phase 2, (3) the rate of the ET reaction at the ITIES, and (4) charge compensation by ion transport across the ITIES.

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FIG. 4 Schematic of SECM feedback at an ITIES with the co-ordinate system used for the theoretical model. The co-ordinates r and z are measured from the center of the UME in the radial and normal directions, respectively. The UME is characterized by an electrode radius, a, while rs is the distance from the center of the electrode to the edge of the surrounding insulating sheath. The ITIES is located at a distance, d, from the UME in the z direction. Species Red1 and Ox1 are conﬁned to phase 1, while species Red2 and Ox2 are present in phase 2.

Under conditions where mediator diffusion in phase 2 and ion transport across the ITIES are nonlimiting [conditions (2) and (4)], the steady-state tip current response has been found to be accurately described by the following equations [44,47,48]: ! ITins k k IT ¼ IS 1 c þ ITins ð1Þ IT ISk ¼

0:78377 ½0:68 þ 0:3315 expð1:0672=LÞ þ Lð1 þ 1=Þ ½1 þ FðL; Þ

ð2Þ

where ITc , ITk , and ITins denote the normalized tip currents for diffusion-controlled regeneration of a redox mediator, ﬁnite substrate kinetics and insulating subtrate (i.e., no mediator regeneration), respectively, and ISk is the kinetically controlled normalized substrate current. These various currents are normalized with respect to the steady-state tip current, ið1Þ. The remaining terms in these two equations are deﬁned as follows: L ¼ d=a is the normalized tip–substrate separation; ¼ kf d=D1 , where kf is the apparent heterogeneous rate constant (cm s1 ) for the ET reaction at the ITIES and D1 is the diffusion coefﬁcient of the redox mediator in phase 1; FðL; Þ is given by FðL; Þ ¼ ð11 þ 7:3Þ=½ð110 40LÞ

ð3Þ

Approximations for the quantities ITc and ITins have been given previously [54]: 0:78377 þ 0:3315 expð1:0672=LÞ þ 0:68 ð4Þ L ¼ 1= 0:15 þ 1:5358=L þ 0:58 expð1:14=LÞ þ 0:0908 exp½ðL 6:3Þ=ð1:017LÞ ð5Þ

ITc ¼ ITins

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Although the use of this model considerably simpliﬁes the quantitative analysis of data, it implicitly assumes that phase 2 is maintained at a constant composition during a measurement. Henceforth, we refer to the model described by Eqs. (1)–(5) as the constantcomposition model. 1.

Beyond the Constant-Composition Model

To extend the applicability of the SECM feedback mode for studying ET processes at ITIES, we have formulated a numerical model that fully treats diffusional mass transfer in the two phases [49]. The model relates to the speciﬁc case of an irreversible ET process at the ITIES, i.e., the situation where the potentials of the redox couples in the two phases are widely separated. A further model for the case of quasireversible ET kinetics at the ITIES is currently under development. For the case where the oxidized form of a redox species, Ox1 , is electrolytically generated at the tip in phase 1 from the reduced species, Red1 , the reactions at the tip and the ITIES are: Tip: ITIES:

Red1 ne ! Ox1 k12 Ox1 þ Red2 ! Ox2 þ Red1

ð6Þ ð7Þ

where Red2 and Ox2 denote, respectively, the reduced and oxidized form of the redox couple conﬁned to phase 2 and k12 is the heterogeneous bimolecular rate constant (cm s1 M1 ). Under constant-composition conditions, k12 ¼ kf =cRed2 where cRed2 denotes the initial bulk concentration of Red2 in phase 2. In the development of the model, the diffusion coefﬁcients of Red1 and Ox1 are considered to be equal, i.e., DRed1 ¼ DOx1 with only the reactant, Red1 , initially present in phase 1, at concentration cRed1 . This assumption allows the principle of mass conservation to be invoked in phase 1: 0 r rs ; 0 < z < d:

cOx1 ðr; zÞ ¼ cRed1 cRed1 ðr; zÞ

ð8Þ

where cOx1 ðr; zÞ and cRed1 ðr; zÞ are the spatial-dependent concentrations of Ox1 and Red1 , respectively, within the region of interest (see Fig. 4), deﬁned in terms of r and z, which are the co-ordinates in the directions radial and normal to the electrode surface measured from the center of the electrode. The use of Eq. (8) simpliﬁes the problem to the consideration of species Red1 and Red2 alone. Although the diffusion coefﬁcients of Red1 and Ox1 may differ slightly in real systems [55–59], it has been shown that under steady-state conditions (the primary interest in this application) the ratio DOx1 =DRed1 has no effect on the diffusion-limited positive feedback current characteristics [55]. Time-dependent diffusion equations, appropriate to the axisymmetrical cylindrical geometry of the SECM can be written for the species of interest in each phase, " # @cRed1 @2 cRed1 1 @cRed1 @2 cRed1 ¼ DRed1 þ Phase 1: þ ð9Þ r @r @t @r2 @z2 " # @cRed2 @2 cRed2 1 @cRed2 @2 cRed2 ¼ DRed2 þ Phase 2: þ ð10Þ r @r @t @r2 @z2 where cRed2 and DRed2 are, respectively, the concentration and diffusion coefﬁcient of species Red2 in phase 2 and t is time. In order to calculate the tip current response, the diffusion equations must be solved subject to the boundary and initial conditions of the system. Prior to the potential step,

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phase 1 and 2 contain only species Red1 and Red2 , respectively. The initial condition is thus t ¼ 0;

0 r rs ; 0 z d:

cRed1 ¼ cRed1

ð11Þ

0 r rs ; z d:

cRed2 ¼ cRed2

ð12Þ

At time t > 0, the potential of the UME tip is stepped from a value where no electrode reaction occurs, to one sufﬁcient to drive the oxidation of Red1 at a diffusioncontrolled rate. Species Red1 is assumed to be inert with respect to the insulating glass sheath surrounding the electrode and to remain at bulk concentration values beyond the radial edge of the tip (throughout phase 1). In phase 2, species Red2 attains its bulk concentration for r > rs and at a semi-inﬁnite distance from the electrode. Consequently, the exterior boundary conditions may be summarized as follows: 0 r a; z ¼ 0:

cRed1 ¼ 0

a < r rs ; z ¼ 0:

DRed1

@cRed1 ¼0 @z

ð13Þ ð14Þ

0 r rs ; z ! 1:

cRed2 ¼ cRed2

ð15Þ

r > rs ; 0 < z < d:

cRed1 ¼ cRed1

ð16Þ

r > rs ; z > d:

cRed2

ð17Þ

cRed2 ¼

Equations (16) and (17) are reasonable assumptions provided that RG 10 [8]. The axisymmetrical geometry of the SECM implies that there is no radial ﬂux of the species at the cylindrical axis of symmetry: r ¼ 0; 0 < z < d: r ¼ 0; z > d:

@cRed1 ¼0 @r @cRed2 DRed2 ¼0 @r

DRed1

ð18Þ ð19Þ

The ﬁnal internal boundary condition applies to the interface between phase 1 and phase 2, and relates the ﬂux of species Red1 and Red2 , at the ITIES, to the rate of the second-order redox reaction occurring at the interface. z ¼ d; 0 r rs :

DRed1

@cRed1 @cRed2 ¼ DRed2 ¼ k12 cRed1 cRed1 cRed2 @z @z

ð20Þ

To obtain general solutions, the problem is reformulated in terms of the following dimensionless quantities: tDRed1 a2 r R¼ a z Z¼ a ¼

ð21Þ ð22Þ ð23Þ

SECM as a Local Probe of Chemical Processes

DRed2 DRed1 cRed ¼ i cRedi

¼ CRedi

293

ð24Þ ðinteger i ¼ 1 or 2Þ

ð25Þ

K¼

k12 acRed2 DRed1

ð26Þ

Kr ¼

cRed2 cRed1

ð27Þ

The UME current is related to the ﬂux of Red1 at the electrode surface and hence the dimensionless current ratio for the tip UME is given by [12,14–16]: ð i 1 @CRed1 ¼ R dR ð28Þ ið1Þ 2 0 @Z Z¼0 where the steady-state diffusion-limited current at an inlaid disk electrode positioned at an effectively inﬁnite distance from the interface is given by [60]: ið1Þ ¼ 4nFaDRed1 cRed1

ð29Þ

where n is the number of electrons transferred per redox event and F is Faraday’s constant. The numerical model developed to treat this problem [49], involves the parameters K, , Kr and the normalized tip–interface distance, L ¼ d=a. To develop an understanding of the factors governing the SECM feedback response, which is of importance in the interpretation of experimental data, we brieﬂy describe the effect of these parameters on the tip current. A key aim is to deﬁne precisely the conditions under which the simpler constant-composition model Eqs. (1)–(5) can be used. 2. When Does the Constant–Composition Model Apply? The effect on the normalized approach curves of allowing Kr to take ﬁnite values is illustrated in Fig. 5, which shows simulated data for three rate constants, for redox couples characterized by ¼ 1. The rate parameters considered: K ¼ 100 (A), 10 (B), and 1 (C), are typical of the upper, medium, and lower constants that might be encountered in feedback measurements at liquid–liquid interfaces. In each case, values of Kr ¼ 1000 or 100 yield approach curves which are identical to the constant-composition model [44,47,48]. This behavior is expected, since the relatively high concentration of Red2 compared to Red1 ensures that the concentration of Red2 adjacent to the liquid–liquid interface is maintained close to the bulk solution value, even when the interfacial redox process is driven at a fast rate. For Kr 10, the normalized currents are lower than predicted by the constantcomposition model, particularly at close tip–interface separations, where the diffusion rate of the Red1 =Ox1 couple in phase 1 is highest and competes effectively with the diffusion of Red2 in phase 2. The deviation of the current from that predicted assuming constant-composition conditions becomes increasingly signiﬁcant as Kr is reduced, resulting in increasing diffusional limitations from Red2 in phase 2. The constant-composition assumption breaks down for Kr 10, irrespective of the size of the rate constant characterizing the interfacial process (within the range considered).

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FIG. 5 Simulated normalized steady-state current as a function of tip-interface distance for (A) K ¼ 100, (B) K ¼ 10, and (C) K ¼ 1. In each case ¼ 1 and Kr takes the values (a) 1000, (b) 100, (c) 10, (d) 5, (e) 2, and (f) 1. (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)

The reasons for the deviation of the constant-composition model from the full model are apparent when the concentrations of Red1 and Red2 are examined. Due to the axisymmetrical SECM geometry, the concentration proﬁles of Red1 and Red2 are best shown as cross-sections over the domain R 0, Z 0, as illustrated schematically in Fig. 6. Note that in this ﬁgure the tip position has been inverted compared to that in Fig. 4. Figure 7

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FIG. 6 Schematic of the region (cross-hatched) represented by the concentration proﬁles. The ITIES is located at Z ¼ d=a.

FIG. 7 Steady-state concentration proﬁles for species Red1 and Red2 in phases 1 and 2, respectively, for K ¼ 100 and ¼ 1, with Kr taking the values (A) 1000, (B) 10, and (C) 5. The normalized concentrations of Red in phases 1 and 2 are, respectively, denoted by CRed1 and CRed2 . (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)

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shows proﬁles for K ¼ 100, at a normalized tip–interface separation, d=a ¼ 0:1 (which is typical of the smallest d=a attainable in SECM measurements). The normalized concentration distributions are shown in terms of CRedi (where the integer i ¼ 1 or 2) for Kr ¼ 1000, 10, and 5. With the former value of Kr , phase 2 is maintained at constant composition and the proﬁle for this case [Fig. 7(A)] is thus provided for phase 1 only. This proﬁle shows the characteristic concentration distribution for positive feedback, where concentration changes in phase 1 are maintained primarily within the zone directly under the tip. For lower Kr , the turnover of Red1 at the portion of the interface directly under the tip is sufﬁciently fast that Red2 is depleted in this interfacial region, even when Kr ¼ 10, and consequently a quasihemispherical diffusion ﬁeld of Red2 is established in phase 2 [Fig. 7(B)]. The effect is to diminish the extent of positive feedback, as reﬂected by the change in the phase 1 proﬁle between Fig. 7(A) and (B), resulting in the lower current observed at close tip–interface separations, compared to the constant–composition case. For Kr ¼ 5, the depletion of Red2 in phase 2 becomes very signiﬁcant, such that the Red1 proﬁle in phase 1 develops a considerable hindered diffusion component [Fig. 7 (C)]. Although the tendency for depletion in phase 2 becomes less signiﬁcant as the interfacial rate constant is decreased, there are still considerable diffusional limitations from Red2 in phase 2 even for K ¼ 1, with Kr ¼ 5. An assessment of the applicability of the constant-composition assumption, compared to the full model, is shown in Fig. 8. This is a plot of the percentage error in the interfacial rate constant that would result from analyzing experimental data at logðd=aÞ ¼ 1:0, obtained with arbitrary Kr , using the earlier constant-composition theory [44,47,48]. The use of the constant-composition model to analyze data obtained under conditions of ﬁnite Kr results in an underestimation of the rate constant. Figure 8 shows that for Kr > 40, the constant-composition model is a good one, resulting in errors of less than 10–15%, over the full range of rate constants. For Kr < 20, however, sizeable errors result, particularly in the fast kinetic regime. This diagram can be used as a guide as to the likely errors involved in analyzing data for particular conditions with the constant-composition model. 3. Accessing Rapid ET Kinetics In addition to extending the range of conditions under which SECM feedback measurements can be made at ITIES, lifting the restriction on the composition of phase 2 is particularly beneﬁcial for enhancing both the range and precision with which fast kinetics can be investigated. This is not only due to the fact that decreasing the bulk concentration of Red2 in phase 2 lowers the dimensionless rate constant for the system [Eq. (26)], but also because the approach curves in the fast kinetic limit are more readily distinguished from one another when Kr < 10. This point is well-illustrated by the data presented in Fig. 9, which shows simulated tip approach curves for a range of normalized rate constants: (A) under the constant-composition approximation, and (B) with Kr ¼ 3 and ¼ 1. Although there are differences in the approach curves with the constant-composition model, it would be extremely difﬁcult to distinguish between any of the K cases practically, unless K was below 10. Even for K ¼ 10, an uncertainty in the tip position from the interface of 0:1d=a would not allow the experimental behavior for this rate constant to be distinguished from the diffusion-controlled case. For a typical value of DRed1 ¼ 105 cm2 s1 and electrode radius, a ¼ 12:5 m, this corresponds to an effective ﬁrst-order heterogeneous rate constant of just 0:08 cm s1 . Assuming Kr 20 is necessary

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FIG. 8 Contour plot of percentage error in the rate constant k12 that results from analyzing data in terms of the constant-composition model, rather than the full diffusion model. The data are for a tip–ITIES separation, d=a ¼ 0:1, with a range of K and Kr values. (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)

to ensure constant composition conditions, and that phase 1 contains 0.5 mM of mediator for reasonable measurements (as in many previous experimental investigations of ITIES by SECM), this corresponds to an upper limit on k12 of 8 cm s1 M1 . In contrast, for Kr ¼ 3, the approach curves are such that ready kinetic discrimination should be possible for K 100 [Fig. 9(B)]. For the same values of DRed1 and a, with a bulk concentration of Red2 in phase 2, cRed2 ¼ 1:5 mM, this corresponds to a bimolecular rate constant, k12 of ca. 500 cm s1 M1 . It is also interesting to note that since the approach curves in Fig. 9(B) have peaks (at least for the fast kinetic cases that are most of interest), it is not necessary to know the tip to ITIES separation absolutely. Rather, the rate constant for the process of interest could be deduced by simply measuring the peak current value of a tip approach curve. These attributes have been exploited in the practical measurement of rapid ET kinetics at ITIES as discussed in Section V.

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FIG. 9 Simulated approach curves of i=ið1Þ versus normalized tip–interface separation, d=a, for (A) constant-composition conditions with K ¼ ðaÞ 100, (b) 50, (c) 20, (d) 10, (e) 5, (f) 2, and (g) 1; (B) full model conditions with Kr ¼ 3 and K ¼ ðaÞ 1000, (b) 100, (c) 50, (d) 20, (e) 10, (f) 5, (g) 2, and (h) 1. (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)

SECM as a Local Probe of Chemical Processes

B.

299

SECMIT Mode

In SECMIT, the UME tip is positioned in phase 1, close to the interface between two phases, such as two immiscible liquids, each containing a common electroactive species, Red. The partitioning of this species between the two phases can be represented as follows: k1 Red1

Ð Red2

ð30Þ

k2 where k1 and k2 are ﬁrst-order interfacial rate constants for the transfer of Red from phases 1 and 2, respectively. Assuming that the target interface can be modeled as a quiescent, sharp boundary, with Eq. (30) initially at equilibrium there is zero net ﬂux of species Red across the interface and each phase has a uniform composition of Red, cRedi (where the integer i ¼ 1 or 2). The initial condition is identical to Eqs. (11) and (12). A potential step is subsequently applied to the UME in phase 1, sufﬁcient to electrolyze Red1 at the tip, at a diffusion-controlled rate. This perturbs the interfacial equilibrium, inducing the transfer of the target species across the interface, from phase 2 to phase 1, as shown in Fig. 10. The time-dependent diffusion equations for Red appropriate to the axisymmetrical geometry, shown in Fig. 10, are identical to Eqs. (9) and (10), given earlier. Although phase 2 is assumed to be semi-inﬁnite in the z-direction, the model can readily be modiﬁed for the situation where phase 2 has a ﬁnite thickness [61]. The boundary conditions relevant to the problem under consideration are given by Eqs. (13)–(19), together with the following: 0 r rs ;

z ¼ d:

DRed1

@cRed1 @cRed2 ¼ DRed2 ¼ k2 cRed2 Ke cRed1 @z @z

ð31Þ

where Ke ¼

cRed2 k1 ¼ cRed1 k2

FIG. 10 The co-ordinate system used to deﬁne the two-phase model for SECMIT.

ð32Þ

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Thus, the problem is similar to the feedback mode case except for the internal boundary condition described by Eqs. (31) and (32), which relate to the ﬁrst-order process at the target interface. The internal boundary condition describes the net diffusive ﬂux of Red across the interface from phase 2 to phase 1, as the system attempts to reattain equilibrium following the electrolytic depletion of Red1 in phase 1. For the formulation of a general solution, the dimensionless quantities deﬁned by Eqs. (21)–(25) are used, but the dimensionless rate constant is deﬁned by Eq. (33) rather than Eq. (26). K¼

k2 a DRed2

ð33Þ

The normalized tip current response is again calculated from Eq. (28). Further details of the solution of the problem using the ADIFDM have been given elsewhere [9]. For the SECMIT mode the tip current response is governed primarily by K, Ke , , and the dimensionless tip–substrate distance, L. Here, we brieﬂy examine the effects of these parameters on the chronoamperometric and steady-state SECMIT characteristics. All chronoamperometric data are presented as normalized current ratio versus 1=2 in order to emphasize the short-time characteristics, for the reasons outlined previously [12,14–16]. Steady-state characteristics, derived from the chronoamperometric data in the long-time limit, are considered over the full range of tip–substrate separations generally encountered in SECM. For completeness it should be mentioned that some of the theoretical conclusions for SECMIT are analogous to earlier treatments for the transient and steady-state response for a membrane-covered inlaid disk UME, which was investigated for the development of microscale Clark oxygen sensors [62–65]. An analytical solution for the steady-state diffusion-limited problem has also been proposed [66,67]. 1. Effect of Partition Coefﬁcient, Ke The effect on the current–time behavior of varying Ke while keeping the kinetics of the interfacial process high and nonlimiting is shown in Fig. 11, for a typical tip–interface distance logðLÞ ¼ 0:5. The general trends in Fig. 11 can be explained as follows. At short times, the diffusion ﬁeld at the UME tip is not of sufﬁcient size to intercept the interface, and there is thus no perturbation of the interfacial equilibrium. In this time regime, 1=2 > 8, the tip current is similar for all of the cases considered. This is a common feature of SECM potential step chronoamperometry [10,12,14–16,42,43]. At longer times, the diffusion ﬁeld of the UME intercepts the interface and the ﬂux of Red1 to the UME (and hence current) is then governed by the value of Ke . Given that, under the deﬁned conditions, there is no interfacial kinetic barrier to transfer from phase 2 to phase 1, the concentrations immediately adjacent to each side of the interface may be considered to be in dynamic equilibrium throughout the course of a chronoamperometric measurement. For high values of Ke the target species in phase 2 is in considerable excess, so that the concentration in phase 1 at the target interface is maintained at a value close to the initial bulk value, with minimal depletion of Red in phase 2. Under these conditions, the response of the tip (Fig. 11, case (a)] is in agreement with that predicted for other SECM diffusion-controlled processes with no interfacial kinetic barrier, such as induced dissolution [12,14–16] and positive feedback [42,43]. A feature of this response is that the current rapidly attains a steady state, the value of which increases

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301

FIG. 11 SECMIT chronoamperometric characteristics for logðd=aÞ ¼ 0:5, K ¼ 105 and ¼ 1. The curves correspond to the equilibrium partition coefﬁcient, Ke , taking the values (a) 1000, (b) 50, (c) 10, (d) 5, (e) 2, (f) 1, (g) 0.5, and (h) 0.1. The lower dashed curve represents the behavior for an inert interface (i.e. no transfer from phase 2 to phase 1). (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)

dramatically as the separation between the tip and interface decreases, as illustrated by case (a) in Fig. 12. At the other extreme, for low Ke , the relatively small concentration of Red2 compared to Red1 , is insufﬁcient to maintain the concentrations of Red on both sides of the interface at their initial bulk values, during SECMIT measurements. Consequently, there is extensive depletion of Red in both phases. The smaller the value of Ke the more extensive is the depletion of Red, as illustrated by Fig. 13, which depicts the steadystate concentration proﬁles of Red for Ke ¼ 0:1 (a), 1 (b), and 10 (c). Notice, however, that although Red is depleted in both phases, equilibrium conditions prevail at the interface, i.e., there is no abrupt discontinuity in the normalized concentrations of Red on crossing the interface (for any value of R). The main result of the preceding observations for SECMIT measurements is that as Ke decreases, the current tends to increasingly smaller values (Figs. 11 and 12). In the limit Ke ! 0, the chronoamperometric (Fig. 11) and steady-state (Fig. 12) current responses approach the characteristics predicted previously for an inert interface [8,42,43]. The plot of normalized steady-state current vs. tip–interface distance, shown in Fig. 12, demonstrates that as the tip–interface distance decreases the steady-state current becomes more sensitive to the value of Ke . Under the deﬁned conditions the shape of the approach curve is highly dependent on the concentration in the second phase, for Ke values over a very wide range, with a lower limit less than 0.1 and upper limit greater than 50. This suggests that SECMIT can be used to determine the concentration of a target solute in a phase, without the UME entering that phase, provided that the diffusion coefﬁcients of the solute in the two phases are known.

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FIG. 12 Simulated normalized steady-state current as a function of normalized tip–interface distance for K ¼ 105 , ¼ 1, and Ke taking the values (a) 1000, (b) 50, (c) 10, (d) 5, (e) 2, (f) 1, (g) 0.5, and (h) 0.1. The lower dashed line represents the approach curve for an inert interface (i.e., no transfer from phase 2 to phase 1). (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)

2. Effect of Diffusion Coefﬁcient Ratio, As might be expected, similar trends to those identiﬁed above are observed as is varied, while maintaining Ke constant and K high and nonlimiting. The transient and steady-state current responses, shown respectively in Figs. 14 and 15 for Ke ¼ 1 and K ¼ 105 , vary between a lower limit which is close to the response for an inert interface when < 0:01, and an upper limit (when 1000) which is characteristic of SECM diffusion-control in phase 1 with no resistance from interfacial kinetics or transport in phase 2. The effect of increasing is to increase the diffusion coefﬁcient of the solute in phase 2 compared to that in phase 1. For a given value of Ke this means that when a SECMIT measurement is made, the higher the value of the less signiﬁcant are depletion effects in phase 2 and the concentrations at the target interface are maintained closer to the initial bulk values. Consequently, as increases, the chronoamperometric and steady-state currents increase from a lower limit, characteristic of an inert interface, to an upper limit corresponding to rapid interfacial solute transfer, with no depletion of phase 2. Under conditions of nonlimiting interfacial kinetics the normalized steady-state current is governed primarily by the value of Ke , which is the relative permeability of the solute in phase 2 compared to phase 1, rather than the actual value of Ke or . In contrast, the current–time characteristics are found to be highly dependent on the individual Ke and values. Figure 16 illustrates the chronoamperometric behavior for K ¼ 105 , logðLÞ ¼ 0:8 and for a ﬁxed value of Ke ¼ 2. It can be seen clearly from this plot that whereas the current-time behavior is sensitive to the value of Ke and , in all cases the curves tend to be the same steady-state current in the long-time limit. This difference between the steadystate and chronoamperometric characteristics could, in principle, be exploited in determining the concentration and diffusion coefﬁcient of a solute in a phase that is not in direct contact with the UME probe.

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FIG. 13 Steady-state proﬁles of the distribution of Red in the two phases during SECMIT, for K ¼ 105 , ¼ 1 and Ke taking the values (a) 0.1, (b) 1.0, and (c) 10. The normalized concentrations for phases 1 and 2 are, respectively, denoted by CRed1 and CRed2 . (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)

3.

Effect of Interfacial Kinetics

The inﬂuence of an interfacial kinetic barrier on the transfer process is readily illustrated by ﬁxing the concentrations and the diffusion coefﬁcients of Red for the two phases and examining the current response of the UME as K is varied. For illustrative purposes, we arbitrarily set Ke and ¼ 1, i.e., initially the equilibrium conditions are such that there are equal concentrations of the target solute in the two phases, and the solute diffusion coefﬁcient is phase-independent. Figure 17 shows the chronoamperometric characteristics for several K values from zero up to 1000. Under the deﬁned conditions, these values of K reﬂect the ease with which the transfer process can respond to a perturbation of the local concentration of Red in phase 1, due to electrolytic depletion.

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FIG. 14 SECMIT chronoamperometric characteristics for log(d=aÞ ¼ 0:5, K ¼ 105 , and Ke ¼ 1. The curves correspond to the ratio of the diffusion coefﬁcients, , taking the values (a) 1000, (b) 100, (c) 10, (d) 2, (e) 1, (f) 0.5, (g) 0.1, and (h) 0.01. The lower dashed curve represents transient behavior for an inert interface. (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)

For small K, i.e., K ¼ 0:5 in Fig. 17, the response of the equilibrium to the depletion of species Red1 in phase 1 is slow compared to diffusional mass transport, and consequently the current-time response and mass transport characteristics are close to those predicted for hindered diffusion with an inert interface. As K is increased, the interfacial process responds more rapidly to the electrochemical perturbation in phase 1. The transfer of the target species across the interface generates an enhanced ﬂux to the UME, causing

FIG. 15 Simulated normalized steady-state current as a function of normalized tip–interface distance for K ¼ 105 , Ke ¼ 1 and taking the values (a) 1000, (b) 100, (c) 10, (d) 2, (e) 1, (f) 0.5, (g) 0.1, and (h) 0.01. (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)

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FIG. 16 SECMIT chronoamperometric characteristics for logðd=aÞ ¼ 0:8, K ¼ 105 for constant Ke ¼ 2:0. The curves correspond to (a) Ke ¼ 40:0, ¼ 0:05, (b) Ke ¼ 20:0, ¼ 0:1, (c) Ke ¼ 4:0, ¼ 0:5, (d) Ke ¼ 2:0, ¼ 1:0, (e) Ke ¼ 1:0, ¼ 2:0, (f) Ke ¼ 0:5, ¼ 4:0, (g) Ke ¼ 0:1, ¼ 20:0, and (h) Ke ¼ 0:05, ¼ 40:0.

the long-time current to be larger than predicted for an inert interface. The higher the value of K, the greater the extent of interfacial transfer and the larger the current ﬂow. For large K (K ¼ 1000 in Fig. 17) an upper limit is reached, where the interfacial kinetics are sufﬁciently fast – on the time scale of the SECM measurement – such that the concentrations of Red in the two phases, adjacent to the interface, are always in equilibrium even though Red is generally depleted. The tip current response is then dependent

FIG. 17 SECMIT chronoamperometric characteristics for log ðd=aÞ ¼ 0:5, ¼ 1, and Ke ¼ 1. The curves correspond to K taking the values (a) 1000, (b) 20, (c) 5, (d) 2, (e) 1, (f) 0.5, and (g) 0.0. (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)

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on the rate of mass transfer within both phases, and for Ke ¼ 1 and ¼ 1 resembles that predicted for a conventional UME in bulk solution [68]. The normalized steady-state current vs. tip–interface distance characteristics (Fig. 18) can be explained by a similar rationale. For large K, the steady-state current is controlled by diffusion of the solute in the two phases, and for the speciﬁc Ke and values considered is thus independent of the separation between the tip and the interface. For K ¼ 0, the current–time relationship is identical to that predicted for the approach to an inert substrate. Within these two limits, the steady-state current increases as K increases, and is therefore diagnostic of the interfacial kinetics.

4. Experimental Implications The theoretical results described have implications for the design of experimental approaches for the study of transfer processes across the interface between two immiscible phases. The current response in SECMIT is clearly sensitive to the relative diffusion coefﬁcients and concentrations of a solute in the two phases and the kinetics of interfacial transfer over a wide range of values of these parameters. For comparable diffusion coefﬁcients of the target solute in the two phases and nonlimiting transfer kinetics, systems characterized by different Ke should be resolvable on the basis of transient and steady-state current responses to a value of Ke up to 50 at practical tip–interface separations. If the diffusion coefﬁcient in phase 2 becomes lower than that in phase 1, diffusion in phase 2 will be partly limiting at even higher values of Ke . On the other hand, as the value of increases or interfacial kinetics become increasingly limiting, lower values of Ke sufﬁce for the constant-composition assumption for phase 2 to be valid. A further practical consequence relates to the different dependencies of the steadystate and transient currents on Ke and . It should be possible to determine independently

FIG. 18 Simulated normalized steady-state current as a function of normalized tip–interface distance for ¼ 1 and Ke ¼ 1 with K taking the values (a) 1000, (b) 20, (c) 5, (d) 2, (e) 1, (f) 0.5, and (g) 0.0. (Reprinted from Ref. 9. Copyright 1998 American Chemical Society.)

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both Ke and by correlating measurements of the steady-state current, as a function of distance of the tip from the interface, with chronoamperometric measurements (if there is no interfacial kinetic barrier). Alternatively, steady-state measurements alone provide a powerful approach to determining the product Ke . These observations are of considerable practical importance, opening up a new route for measuring concentrations and diffusion coefﬁcients in phases that have, hitherto, been difﬁcult to study with dynamic electrochemistry [9,20,21]. As with previous kinetic applications of SECM, it should be noted that experimental measurements can be tuned to the kinetic region of interest by varying the radius of the electrode [Eq. (33)] and the separation between the tip and interface. In essence, the smaller the UME, and/or tip–interface separation, the higher the diffusion rates that may be generated and, consequently, the greater the tendency for interfacial kinetic limitations.

V.

EXPERIMENTAL APPLICATIONS TO LIQUID–LIQUID INTERFACES

A.

Electron-Transfer (ET) Kinetics

Since the ﬁrst use of SECM to study ET kinetics at a liquid–liquid interface in 1995 [47], the methodology has been proven a powerful approach for investigating the dependence of ET rate constants on the Galvani potential drop across an ITIES. The basic concept of using the SECM feedback mode to probe ET reactions at an ITIES was highlighted in Section II and theoretical characteristics for this mode were considered in Section IV. A key feature of the SECM approach is that a well-deﬁned interfacial area is targeted for investigation and conditions are generally such that the overall contributions to the tip current, from mass transport and interfacial processes, can readily be resolved. The high local mass transport rates generated as a result of the small sizes of the UME probes employed in SECM, and the close tip–interface separations that can be attained, enable accurate quantiﬁcation of rapid interfacial processes under welldeﬁned and calculable conditions. In particular: (1) the SECM current allows discrimination between electron- and ion-transfer processes at the interface, (2) distortions associated with iR drop and charging current are eliminated, and (3) it is not necessary to externally polarize the interface, thereby avoiding complications due to the polarization window of the ITIES and the possible variation of the interfacial properties with applied potential. In pioneering studies [47], the SECM feedback mode was used to study the ET reaction between ferrocene (Fc), in nitrobenzene (NB), and the aqueous mediator, FcCOO , electrochemically generated at the UME by oxidation of the ferrocenemonocarboxylate ion, FcCOO . Tetraethylammonium perchlorate (TEAP) was applied in both phases as the partitioning electrolyte. The results of this study indicated that the reaction at the ITIES was limited by the ET process, provided that there was a sufﬁciently high concentration of TEAP in both phases. In initial ET rate measurements, both the NB and aqueous phases contained 0.1 M TEAP, enabling measurements to be made with a constant Galvani potential difference across the liquid junction. In these early studies, the concentration of Fc used in the organic phase (phase 2) was at least 50 times the concentration of the electroactive mediator in the aqueous phase which contained the probe UME (phase 1). This ensured that the interfacial process was not limited by mass transport in the organic phase, and that the simple constant-composition model, described brieﬂy in Section IV, could be used.

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Tip approach curve measurements indicated a ﬁrst-order dependence of the interfacial rate on the concentration of Fc in the organic phase, from which a value of 0.6 cm M1 s1 was extracted for the bimolecular ET rate constant. Good agreement between the measured rate constant and that predicted from Marcus theory [69–71], was considered, by assuming the ITIES to have a thickness of 2 nm. These studies, however, may have been compromised by the partitioning of Fc and Fcþ into the aqueous phase. 1. Potential Dependence of ET Rates According to Marcus theory [69–71], in the absence of work terms, the Gibbs free energy of activation for an ET reaction is given by: G 2 6¼ 1þ G ¼ ð34Þ 4 where is the reorganization energy. For a system where the ET reaction occurs between an electrogenerated oxidant in the organic phase and an electron donor in the aqueous phase, G is given by: G ¼ F ðE þ ow Þ

ð35Þ

where E is the difference of the standard potentials between the redox couples in the organic and aqueous phases and ow ¼ o w is the potential drop across the oil–water interface. When the driving force (E þ ow ) is close to zero, a Butler–Volmer type approximation can be considered to apply as a simpliﬁcation of Eq. (34): G6¼ ¼ F ðE þ ow Þ

ð36Þ

where is the ET coefﬁcient. With a ﬁxed concentration of redox species in phase 2, the dependence of the ET rate constant, kf , on the driving force can be written as [48,70]: kf ¼ const exp ðG6¼ =RTÞ

ð37Þ

According to Eqs. (34)–(37), an increase in the rate constant with the driving force, with an value of 0.5 should be observed in the limit where the driving force is close to zero. At much higher driving forces, the rate constant should pass through a maximum and then decrease with increasing driving force. Although Marcus theory has been examined and veriﬁed in a number of chemical and biological systems [72], there is no general consensus on whether this model should apply to ET kinetics at ITIES [73]. Building on initial work [47], the main focus of SECM in the study of ET at ITIES has been to identify and understand the potential-dependence of ET rates. In these studies, the potential drop across an ITIES has been controlled by varying the concentration of potential-determining ions in the two phases. The potential drop across an ITIES follows the Nernst–Donnan equation [74,75], RT a w w

¼

8 þ ð38Þ ln o o o zF aw w o is the standard ion-transfer potential (these values for some ions can be found in Ref. 74), z is the number of the charge of the potential-determining ion, ao and aw are the activities of the potential-determining ion in the oil and water phases, respectively.

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For studies with ClO 4 as the potential-determining ion, under conditions where the activity coefﬁcients of the ion in each phase remain constant, Eq. (38) can be written as: 0

w 0:059 log w o ¼ o ClO 4

½ClO 4 w ½ClO 4 o

ð39Þ

0

where w is the formal transfer potential of ClO o ClO 4 . For a reaction between a parti4 cular redox couple in each phase the E value is ﬁxed. Moreover, if the ½ClO 4 o is a , then the combination of Eqs. constant and the potential is varied by changing ½ClO 4 w (36), (37), and (39) yields

log kf ¼ const 2:303 log½ClO 4 w

ð40Þ

log½ClO 4 w

dependence should be linear with a slope proportional to Thus, the log kf vs. in the limit of low driving force. A method advocated by Bard and coworkers [48] for measuring the relative interfacial potential drop is to record steady-state linear sweep voltammograms for a reversible redox couple in the organic phase, with respect to a reference electrode in the aqueous phase. According to Eq. (39), the formal potential of the organic couple, measured with respect to the aqueous reference electrode, should shift by 59 mV with a decade change in ½ClO 4 w (with ½ClO4 o ﬁxed) assuming that the activity coefﬁcients of the potential-determining ion remain constant. Typical experimental results obtained from such measurements are shown in Fig. 19. In early work on the effect of potential on ET reactions [76], Solomon and Bard showed that an ET reaction between FeðCNÞ4 6 in an aqueous phase and 7,7,8,8-tetracyanoquinodimethane (TCNQ) in 1,2-dichloroethane (DCE) could be promoted by judiciously adjusting the potential drop across the ITIES, using tetraphenylarsonium cation as a potential determining ion. In a similar period, Selzer and Mandler [77] reported a study of the ET reaction between aqueous IrCl2 6 and Fc in a NB phase, without any potential determining ion in either phase. A ﬁrst-order rate constant of 0:013 cm s1 was obtained

FIG. 19 Dependence of the half-wave potentials for Fc (curve 1) and ZnPor (curve 2) oxidation in benzene on C1O 4 concentration in the aqueous phase. In these measurements, half-wave potentials were extracted from reversible steady-state voltammograms obtained at a 25 mm diameter Pt UME. The benzene phase contained 0.25 M tetra-n-hexylammonium perchlorate (THAP) and either 5 mM Fc or 1 mM ZnPor. All potentials were measured with respect to an Ag/AgCl reference electrode in the aqueous phase. (Reprinted from Ref. 48. Copyright 1996 American Chemical Society.)

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for this process, for which the rate-determining step could have involved Fcþ transfer from NB to the aqueous phase. Tsionsky et al. [48] investigated the potential-dependence of the ET rate for the reaction between 5,10,15,20-tetraphenyl-21H,23H-porphine zinc cation (ZnPorþ ) which served as an oxidant in benzene and aqueous electron donors, using ClO 4 in each phase as a potential-determining ion. In this study, ZnPorþ was generated in the organic phase by oxidation of the neutral species, ZnPor, at the SECM tip electrode. ZnPorþ diffused to the 4 ITIES where it was reduced to ZnPor by reaction with RuðCNÞ4 6 or FeðCNÞ6 . The measured ET coefﬁcient was about 0.5, suggesting that conventional Butler–Volmer theory was applicable to heterogeneous ET at an ITIES. The results were consistent with a sharp boundary model for the interface [69–71], rather than a relatively thick mixed solvent layer with signiﬁcant penetration by the redox species [78,79]. Liu and Mirkin [80] subsequently studied the oxidation of neutral ZnPor in benzene by aqueous oxidants (e.g., RuðCNÞ3 6 ), with the potential drop across the ITIES estabas the potential determining ion. A ﬁxed concentration of 0.05 M tetralished using ClO 4 n-hexyl ammonium perchlorate (THAP) was used as the supporting electrolyte in the organic phase, with various concentrations of ClO 4 in the aqueous phase. The measured ET rate constants were found to be independent of interfacial potential drop, but dependent on the driving force contributed by the aqueous redox species. They concluded that this result agreed with Schmickler’s model for ET at an ITIES [79]. Based on these results, it was suggested that the -value obtained in previous investigations [48], could have been complicated by diffuse layers effects, similar to the Frumkin effect [81] at metal electrodes. These effects were considered to be negated by employing neutral ZnPor as the reactant in the organic phase. The rate constant for the forward ET reaction between ZnPorþ and RuðCNÞ4 6 was compared to that of the reverse reaction at zero driving force. The reverse ET rate constant was about 20 times the forward ET rate constant, which was attributed to diffuse layer effects. As discussed in Section IV, many studies of ET kinetics with SECM have been under conditions where constant composition in phase 2 can be assumed, but this severely restricts the range of kinetics that can be studied. With the availability of a full model for diffusion, outlined in Section IV, that lifts this restriction, Barker et al. [49] studied the reaction between ZnPorþ in benzene or benzonitrile and aqueous reductants, using ClO 4 or tetraﬂuoroborate as potential-determining ions. Figure 20 shows approach curves for the reaction between electrogenerated ZnPorþ 4 and FeðCNÞ4 6 at the benzene–water interface, for a range of concentrations of Fe(CN)6 in the aqueous phase. This case highlights the advantages of using low relative concentrations of a reactant in phase 2 in the study of rapid kinetics. For the highest concentration ratio in these experiments (Kr ¼ 14 and 7), the interfacial redox reaction appears to be diffusion-controlled and the rate constant cannot be determined, as found in previous studies on the same system [55]. However, as Kr decreases it becomes possible to distinguish the measured approach curves from those predicted for a diffusion-controlled process. In particular, at low Kr , the approach curves for fast ET have characteristic peaks with magnitudes that are diagnostic of the rate constant. This allows the peak to be ﬁtted to a theoretical approach curve with a precise knowledge of the distance between the tips and ITIES. From an analysis of the approach curves, for the lowest three concentration ratios in Fig. 20, a rate constant of 91 cm s1 M1 was determined [49]. Similar experiments were performed to measure the ET rate constants for the reac4 tion between ZnPorþ in benzonitrile and aqueous reductants, RuðCNÞ4 6 , MoðCNÞ8 and 2 FeEDTA (where EDTA denotes ethylenediaminetetra-acetic acid). Although the

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FIG. 20 Experimental approach curves (&) for the oxidation of ZnPor at a tip UME in benzene approaching a benzene–aqueous interface, with the aqueous phase containing Fe(CN)4 6 . The bulk concentration conditions in the organic and aqueous phases, respectively, were as follows: (a) 4 [ZnPor] ¼ 0:500 mM, [Fe(CN)4 6 ¼ 7:00 mM; (b) [ZnPor] ¼ 0:500 mM, [Fe(CN)6 ¼ 3:50 mM; 4 (c) [ZnPor] ¼ 0:380 mM, ½FeðCNÞ6 ¼ 0:700 mM; (d) [ZnPor] ¼ 0:380 mM, [Fe(CN)4 6 ¼ 0:350 mM; (e) [ZnPor] ¼ 0:380 mM, [Fe(CN)4 6 ¼ 0:255 mM. The solid lines show the behavior predicted for ¼ 1:7 and a bimolecular rate constant, k12 ¼ 91 cm s1 M1 , while the dashed lines show the behavior for a diffusion-controlled process for each of the ﬁve cases considered. The diffusioncontrolled characteristics for the two cases with the highest Kr are indistinguishable. (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)

organic solvent used in the FeðCNÞ4 6 study was different from that used for the other three reductants, the rate constants obtained for the four systems investigated in Ref. 49 showed an interesting dependence on the driving force for the reaction (Fig. 21). The overall trend was consistent with the predictions of Marcus theory, showing ﬁrst an increase in ET rate with increasing driving force, followed by a decrease in the inverted region. The proposed existence of interfacial inverted region behavior suggested by these studies is in agreement with an earlier study of ET at an ITIES modiﬁed with a monolayer of surfactant [82] and with later observations of electrogenerated chemiluminescence at an unmodiﬁed ITIES [83] The ET reaction between aqueous FeðCNÞ4 6 and the neutral species, TCNQ, has been investigated extensively with SECM, in parallel with microelectrochemical measurements at expanding droplets (MEMED) [84], which are discussed in Chapter 13. In the SECM studies, a Pt UME in the aqueous phase generated FeðCNÞ4 6 by reduction of FeðCNÞ3 6 . TCNQ was selected as the organic electron acceptor, because the half-wave potential for TCNQ ion transfer from DCE to water is 0.2 V more positive than that for ET from FeðCNÞ4 6 to TCNQ [85]. This meant that the measured kinetics were not compromised by TCNQ transfer from DCE to the aqueous phase within the potential window of these experiments. In these studies, ClO 4 was used as the potential-determining ion, with 0.1 M THAP employed as the supporting electrolyte in the DCE phase, together with various concentrations of NaClO4 in the aqueous phase. In contrast to studies of ZnPor oxidation [80],

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FIG. 21 Plot of log k12 vs. E1=2 showing the dependence of ET rate on the driving force for the reaction between ZnPorþ and four aqueous reductants. The difference between the half-wave potentials for an aqueous redox species and ZnPor, E1=2 ¼ E80 þ ow , where E80 is the difference in the formal potentials of the aqueous redox species and ZnPor and ow is the potential drop across the ITIES. The solid line is the expected behavior based on Marcus theory for ¼ 0:55 eV and a maximum rate constant of 50 cm s1 M1 . (Reprinted from Ref. 49. Copyright 1999 American Chemical Society.)

the ET rates were found to depend strongly on the interfacial potential drop with an ET coefﬁcient () in the range of 0.3–0.4. Typical tip approach curves from this investigation are shown in Fig. 22. As the concentration of ClO 4 in the aqueous phase increases, the driving force for TCNQ reduction at the ITIES decreases, resulting in a diminution in the feedback effect and thus a lower tip current. An value of 0:41 0:04 was obtained for this ET process. The ET reaction between aqueous oxidants and decamethylferrocene (DMFc), in both DCE and NB, has been studied over a wide range of conditions and shown to be a complex process [86]. The apparent potential-dependence of the ET rate constant was contrary to Butler–Volmer theory, when the interfacial potential drop at the ITIES was adjusted via the ClO 4 concentration in the aqueous phase. The highest reaction rate was observed with the smallest concentration of ClO 4 in the aqueous phase, which corresponded to the lowest driving force for the oxidation process. In contrast, the ET rate increased with driving force when this was adjusted via the redox potential of the aqueous oxidant. Moreover, a Butler–Volmer trend was found when TBAþ was used as the potential-determining ion, with an value of 0.38 [86]. A feature of these studies was the further demonstration that higher ET rate constants can be measured more readily by using a lower relative concentration of the redox reactant in the second phase. For example, Fig. 23 shows approach curves for the oxidawhich is characterized by a rate constant of tion of DMFc by tip-generated IrCl2 6 180 cm s1 M1 , with 0.1 M ClO 4 in each phase, and readily distinguished from a diffusion-limited ET process.

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FIG. 22 Dependence of ET rates on ClO 4 concentration in the aqueous phase for the reduction of . The aqueous phase contained 0.1 M Li2 SO4 with various TCNQ in DCE by aqueous Fe(CN)4 6 concentrations of NaClO4 , while the DCE phase contained 0.1 M THAP. The SECM approach 3 curves for the generation of Fe(CN)4 6 by the reduction of Fe(CN)6 present in the bulk aqueous phase, were obtained with a 25 mm diameter Pt UME. From top to bottom, the ﬁrst four solid experimental curves are shown for: [ClO 4 ]w ¼ 0:01, 0.025, 0.1, and 0.25 M. For the bottom solid line, there was no TCNQ in the DCE phase. The dashed lines are the corresponding theoretical curves for: k12 ¼ 0:3, 0.2, 0.04, 0.015, and 0 cm s1 M1 . (Reprinted from Ref. 84. Copyright 2000 American Chemical Society.)

FIG. 23 SECM approach curves for the reaction between tip-generated aqueous IrCl2 6 (via the oxidation of IrCl3 6 ) and DMFc in DCE obtained with a 25 mm diameter Pt UME. The potential across the ITIES was established with 0.1 M NaClO4 in the aqueous phase and 0.1 M THAP in the DCE phase. The aqueous phase also contained 0.1 M NaCl and 1 mM IrCl3 6 . The solid curves are the experimental data for Kr ¼ 2 (upper curve) and 1 (lower curve), and the dashed theoretical curves are for k12 ¼ 180 cm s1 M1 for these two cases. The dotted theoretical curves are shown for k12 ¼ 1000 cm s1 M1 with Kr ¼ 2 (top curve) and 1 (bottom curve) which is close to the diffusion-limited behavior. (Reprinted from Ref. 86. Copyright Elsevier Science.)

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2. Distance Dependence of ET Rates The effect on the ET rate of changing the distance between the aqueous and organic redox centers has been investigated by adsorbing phospholipid monolayers with a range of chain lengths on the ITIES [82]. The ET rate constants measured in the presence of the phospholipid monolayer were lower than for the lipid-free interface and generally decreased as the number of methylene groups in the hydrocarbon chain of the phospholipid increased. Some deviations from this trend were observed that were attributed to possible partial penetration of the ZnPorþ species into the lipid monolayer. A further important outcome from these studies was that at high overpotentials the ET rate appeared to decrease with increasing driving force, consistent with the predictions from Marcus theory of an inverted reaction free energy proﬁle. In a separate study [87], the rate of the interfacial ET reaction when conjugated phospholipids were adsorbed at the ITIES was found to be at least twice as rapid as that measured when saturated phospholipids were used. This effect was ascribed to the delocalized conjugated chain acting as a ‘‘conductive wire embedded in an insulating matrix’’ and thereby increasing the rate of the reaction. The difference between the ET rates was sufﬁciently high to enable the SECM feedback mode to be used to image the reactivity of the adsorbed monolayer [87]. When a 25 m diameter UME was scanned laterally across a mixed monolayer comprising a saturated and a conjugated phospholipid, regions of relatively high and low ET rate were detected. These had dimensions of tens of microns and were identiﬁed as being associated with domains that were rich in one of the types of lipid. The effect of temperature on the interfacial ET rates for saturated phospholipids was also investigated. A sharp decrease in the rate constant at a critical temperature was attributed to a phase transition changing the tunneling distance between the redox species contained in the two contacting solutions, and hence changing the ET rate. The ITIES with an adsorbed monolayer of surfactant has been studied as a model system of the interface between microphases in a bicontinuous microemulsion [39]. This latter system has important applications in electrochemical synthesis and catalysis [88–92]. Quantitative measurements of the kinetics of electrochemical processes in microemulsions are difﬁcult to perform directly, due to uncertainties in the area over which the organic and aqueous reactants contact. The SECM feedback mode allowed the rate of catalytic reduction of trans-1,2-dibromocyclohexane in benzonitrile by the Co(I) form of vitamin B12 , generated electrochemically in an aqueous phase to be measured as a function of interfacial potential drop and adsorbed surfactants [39]. It was found that the reaction at the ITIES could not be interpreted as a simple second-order process. In the absence of surfactant at the ITIES the overall rate of the interfacial reaction was virtually independent of the potential drop across the interface and a similar rate constant was obtained when a cationic surfactant (didodecyldimethylammonium bromide) was adsorbed at the ITIES. In contrast a threefold decrease in the rate constant was observed when an anionic surfactant (dihexadecyl phosphate) was used.

B.

Ion and Molecular Transfer Process

The transfer of neutral molecules and ions across immiscible liquid–liquid interfaces can be studied by both SECMIT and SECM DPSC.

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1.

315

SECM-Induced Transfer

SECMIT is particularly suitable for investigating the reversible transfer of neutral molecules and ions across liquid–liquid interfaces. As discussed in Sections II and IV, this mode of SECM can be used to measure interfacial kinetics and also as a noninvasive analytical probe for determining the permeability of a solute in a two-phase system. In the ﬁrst category, SECMIT has been used to investigate the kinetics of Cu2þ extraction and stripping between an aqueous phase and an organic medium (DCE or heptane) containing the oxime ligand Acorga P50 (LH) [9,18]. The extraction–stripping process, deﬁned by Eq. (41), was ﬁrst allowed to come to equilibrium. ð41Þ

The interfacial transfer kinetics were then investigated by perturbing the equilibrium, through the depletion of Cu2þ in the aqueous phase, by reduction to Cu at an UME located in close proximity to the aqueous–organic interface. This process promoted the transfer of Cu2þ into the aqueous phase, via the transport and decomplexation of the cupric ion–oxime complex, resulting in an enhanced steady-state current at the UME. Approach curve measurements of i=ið1Þ vs. d allowed the kinetics of the transfer process to be determined unambiguously [9,18]. In the second category, SECMIT has been used to probe the relative permeability of oxygen between water and DCE or NB, with no supporting electrolyte present in any phase. Under the conditions employed, direct voltammetric measurements in the organic phase would be impractical due to the high solution resistivity (DCE or NB) or limitations of the solvent window available (NB). Figure 24 shows the steady-state current for the

FIG. 24 Steady-state diffusion-limited current for the reduction of oxygen in water at an UME approaching a water–DCE (*) and a water–NB () interface. The solid lines are the characteristics predicted theoretically for no interfacial kinetic barrier to transfer and for ¼ 1:2, Ke ¼ 5:5 (top solid curve) or ¼ 0:58, Ke ¼ 3:8 (bottom solid curve). The lower and upper dashed lines denote the current–distance characteristics for the situation where there is no interfacial transfer and where transfer occurs without limitations from diffusion in the organic phase. (Adapted from Ref. 9. Copyright 1998 American Chemical Society.)

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diffusion-limited reduction of oxygen at an UME tip approaching an aqueous–DCE and aqueous–NB interface [9]. The measured currents in both cases were lower than predicted for Ke ! 1, indicating that there were diffusional limitations in the organic phase. By ﬁtting the approach curves to the model outlined in Section IV, the relative permeabilities of oxygen between the aqueous and organic phases were assigned. The advantages of using the SECMIT mode in applications where the physical presence of the UME could damage the structural integrity of the target phase being studied have been well illustrated by investigations of solute transfer in cartilage [20,21]. 2. SECM DPSC To expand the range of processes that can be studied with SECM, we have recently suggested the use of DPSC for the investigation of irreversible phase transfer processes [34]. This approach was used to measure the rate of transfer of Br2 from aqueous 0.5 M sulfuric acid solution to DCE. In the forward potential step, Br2 was generated at the tip UME through the diffusion-limited oxidation of Br (present at mM levels). The current– time characteristics for this forward-step process provided a very accurate measure of the tip–interface separation, since the form of the transient is governed by the hindered diffusion of Br through the aqueous phase to the UME which, in turn, depends only on the normalized tip–interface separation, L, and the diffusion coefﬁcient of Br , both parameters are known with high precision. The driving force for the transfer process was the enhanced solubility of Br2 in DCE, ca 40 times greater than that in aqueous solution. To probe the transfer processes, Br2 was recollected in the reverse step at the tip UME, by diffusion-limited reduction to Br . The transfer process was found to be controlled exclusively by diffusion in the aqueous phase, but by employing short switching times, tswitch , down to 10 ms, it was possible to put a lower limit on the effective interfacial transfer rate constant of 0:5 cm s1 . Figure 25 shows typical forward and reverse transients from this set of experiments, presented as current (normalized with respect to the steady-state diffusion-limited current, ið1Þ, for the oxidation of Br ) versus the inverse square-root of time. DPSC was recently used to examine whether DMFcþ transfers across the water– DCE interface at typical interfacial potential drops encountered in SECM studied [86]. For this measurement, the DCE phase contained 10 mM DMFc and 0.1 M THAP, while the aqueous phase contained 0.01 M NaClO4 and 0.1 M NaCl. In general, DPSC data obtained for tip–interface separations of 4:4 m to 14:6 m were found to be in close agreement with the theoretical predictions for no transfer of electrogenerated DMFþ c across the interface on the SECM time scale. Typical forward and reverse step data for a tip–interface distance of 4:4 m and tswitch ¼ 0:371 s, are shown in Fig. 26.

VI.

PROBING MOLECULAR TRANSFER AT LIQUID–GAS INTERFACES AND LIQUID INTERFACES MODIFIED WITH LANGMUIR MONOLAYERS

SECM has been extended successfully to investigate chemical processes at aqueous–air interfaces and Langmuir monolayers supported on them [19,34,93]. Initial work concentrated on molecular transfer processes across the aqueous–air interface, with and without a monolayer of surfactant. A ‘‘submarine’’ UME (described in section III) was utilized which could approach the air–water interface from below. The ﬁrst study employed the DPSC mode to investigate the transfer kinetics of electrogenerated Br2 , from aqueous

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FIG. 25 Typical DPSC data for the oxidation of 10 mM bromide to bromine (forward step; upper solid curve) and the collection of electrogenerated Br2 (reverse step; lower solid curve) at a 25 mm diameter disk UME in aqueous 0.5 M sulfuric acid, at a distance of 2.8 mm from the interface with DCE. The period of the initial (generation) potential step was 10 ms. The upper dashed line is the theoretical response for the forward step at the deﬁned tip–interface separation, with a diffusion coefﬁcient for Br of 1:8 105 cm2 s1 . The remaining dashed lines are the reverse transients for irreversible transfer of Br2 (diffusion coefﬁcient 9:4 106 cm2 s1 ) with various interfacial ﬁrstorder rate constants, k, marked on the plot. (Reprinted from Ref. 34. Copyright 1997 American Chemical Society.)

FIG. 26 Typical DPSC data for the oxidation of DMFc to DMFcþ (forward step of 0.371 s duration, upper solid line) and the collection of DMFcþ by reduction to DMFc (reverse step, lower solid line) at a tip in a DCE phase, positioned at a distance of 4.4 mm from the DCE–aqueous interface. The upper dashed line shows the theoretical characteristics for hindered diffusion of DMFc to the tip. The lower dashed line is the theoretical response when there is no DMFcþ transfer across the ITIES. (Reprinted from Ref. 86. Copyright Elsevier Science.)

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0.5 M sulfuric acid to air [34]. As discussed above, for the aqueous–DCE interface, the rate of this irreversible transfer process (with the air phase acting as a sink) was limited only by diffusion of Br2 in the aqueous phase. A lower limit for the interfacial transfer rate constant of 0:5 cm s1 was found [34]. The transfer of oxygen across an air–aqueous interface in the absence and presence of a monolayer of 1-octadecanol was subsequently investigated [19]. The interface was formed in a Langmuir trough, enabling the effect of monolayer compression on the oxygen transfer rate to be assessed. The study provided information on reaeration rates, which are of value in natural environments [94,95]. The conﬁguration could also be considered as a simple model for studies of oxygen transfer across biomembranes. For these investigations, the UME was positioned in the aqueous subphase containing 0.1 M KNO3 and held at a potential to reduce oxygen at a diffusion-controlled rate, in order to promote the transfer of O2 from air (phase 2) to the aqueous solution (phase 1), with subsequent collection at the tip (Fig. 27). Under SECMIT conditions, the ﬂux of oxygen from air to water is given by: jo2 ¼ kaw ca kwa cw;i

ð42Þ

where kwa and kaw are the ﬁrst-order interfacial rate constants for transfer from water to air and from air to water, respectively, and cw;i is the interfacial concentration of oxygen in the water phase. Due to the high diffusion coefﬁcient and effective concentration, ca , of oxygen in the air phase, depletion effects were unimportant, so that jo2 ¼ k 0 kwa cw;i

ð43Þ

where k 0 represents the zero-order rate constant for oxygen transfer from air to water. At equilibrium the following holds: k 0 ¼ kaw ca ¼ kwa cw

ð44Þ

FIG. 27 Schematic (not to scale) of the SECM-induced transfer of oxygen across a 1-octadecanol monolayer, at the air–water interface, in a Langmuir trough.

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FIG. 28 Normalized steady-state diffusion-limited current vs. UME–interface separation for the reduction of oxygen at an UME approaching an air–water interface with 1-octadecanol monolayer coverage (*). From top to bottom, the curves correspond to an uncompressed monolayer and surface pressures of 5, 10, 20, 30, 40, and 50 mN m1 . The solid lines represent the theoretical behavior for reversible transfer in an aerated atmosphere, with zero-order rate constants for oxygen transfer from air to water, k0 =108 mol cm2 s1 of 6.7, 3.7, 3.3, 2.5, 1.8, 1.7, and 1.3. (Reprinted from Ref. 19. Copyright 1998 American Chemical Society.)

The results of this study demonstrated that the rate of oxygen transfer across a clean air–water interface was diffusion-controlled on the time scale of SECM measurements. The rate of this transfer process was, however, signiﬁcantly reduced with increasing compression of a 1-octadecanol monolayer. Figure 28 illustrates this point, showing approach curves for O2 reduction recorded with the monolayer at different surface pressures. The transfer rate was found to depend on the accessible free area of the interface, as described by the following equation: A 0 0

¼ k ¼1 1 ¼0 k 0 ¼ k ¼1 ð45Þ A where represents the fraction of the interface that is free from surfactant, A is the surface area, usually written as the area per molecule of surfactant, and A ¼0 is the area per molecule for which the transfer rate is zero. Figure 29 is the analysis of the data in Fig. 28 in terms of Eq. (45), which can be seen to provide a good description of the effect of monolayer density on the transfer process. A similar approach has been used to investigate lateral diffusion processes in monolayers [93], speciﬁcally, the transport of protons along a stearic acid assembly. Lateral diffusion processes of this type are crucial in deﬁning the activity of membrane-bound reactive centers in cellular bilayers. For initial studies, a submarine UME was positioned in a Langmuir trough, ﬁlled with an aqueous solution containing protons (2.0– 5:0 105 M), close to the air–water interface on which a monolayer of stearic acid was spread. Operating in a conﬁguration analogous to the SECMIT mode described in Section II, the UME was biased to reduce protons to hydrogen at a diffusion-controlled rate. The resulting local depletion drove the acid dissociation reaction, which in turn created a proton diffusion gradient, both in solution and at the surface (Fig. 30). The transport-

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FIG. 29 Oxygen-transfer rate constants derived from Fig. 28 as a function of the reciprocal of the interfacial area per molecule. (Reprinted from Ref. 19. Copyright 1998 American Chemical Society.)

limited current ﬂowing at the electrode provided a measure of the rates of the two processes, which were investigated as a function of the surface coverage of stearic acid by controlling the monolayer compression. These measurements showed that in-plane lateral proton diffusion was facilitated at air–water interfaces on which stearic acid monolayers were formed, with a surface diffusion coefﬁcient that depended critically on the physical state of the monolayer, and which was at most ca. 15% of the magnitude in bulk solution. These promising initial studies

FIG. 30 Schematic (not to scale) of the arrangement for SECM measurements of proton transport at a stearic acid monolayer deposited at the air–water interface. The UME typically had a diameter, 2a, in the range 10–25 mm and the tip–interface distance, d 2a.

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suggest that SECM is a potentially powerful probe of a variety of chemical processes in ultrathin two-dimensional assemblies. We are currently extending these studies to investigate the lateral diffusion of amphiphiles at liquid–air interfaces.

VII.

CONCLUSIONS

This chapter has highlighted the signiﬁcant impact SECM has had on the electrochemical investigation of chemical processes at liquid–liquid interfaces, particularly fundamental studies of ET, IT, and molecular transfer. The key general attributes of SECM include the possibility of carrying out measurements on a targeted portion of an interface, under conditions of variable and high mass transport. The ability to model mass transport in the SECM geometry allows interfacial kinetic effects to be resolved over a wide dynamic range from tip current measurements. In the ﬁeld of charge transfer at ITIES – where SECM has found most application – the methodology overcomes problems in conventional techniques used to investigate ET and IT. In particular, distortions associated with iR drop are eliminated, the tip current discriminates between ET and IT, and it is not necessary to externally polarize the interface to change the potential across the ITIES. SECM has already provided interesting insights into the nature of ET processes at ITIES, although many further studies are needed to examine existing theories for the dependence of ET rates on potential. Although the study of IT using both SECMIT and SECM DPSC has received some attention, there is clearly scope for much further work in this area and in the study of interfacial molecular transfer processes. The demonstration that SECM can be used to study chemical processes at liquid–gas interfaces and monolayers on water surfaces, in particular, opens up a number of exciting possibilities for further studies. In addition to investigations of solute transfer across organized molecular assemblies, the diverse range of SECM modes available should facilitate local, noninvasive studies of various physiochemical processes in ultrathin ﬁlms. Our group has begun studies of lateral proton diffusion at molecular monolayers, and we are currently extending this approach to amphiphile diffusion, lateral charge transfer, and adsorption–desorption kinetics.

ACKNOWLEDGMENTS The support of our SECM studies of liquid–liquid interfaces and related areas, by the EPSRC, BBSRC, Avecia, and the Wellcome Trust, is gratefully acknowledged. We have beneﬁted from helpful discussions with several colleagues, including Prof. A. J. Bard and his group (University of Texas at Austin), Prof. D. E. Williams, Dr J. Strutwolf and Dr D. Caruana (University College London, UK), and Dr J. H. Atherton (Avecia, Huddersﬁeld). At Warwick, Dr M. Gonsalves, and Dr J. V. Macpherson have provided valuable contributions to some of the work described in this chapter.

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13 Hydrodynamic Techniques for Investigating Reaction Kinetics at Liquid^Liquid Interfaces: Historical Overview and Recent Developments CHRISTOPHER J. SLEVIN, PATRICK R. UNWIN, and JIE ZHANG Departme nt of Chemistry, University of Warwick, Coventry, England

I.

INTRODUCTION

As discussed throughout this book, reactions that occur at the interface between two immiscible liquids are common in a wide range of areas. For example, industrially important processes, such as solvent extraction [1,2] and phase transfer catalysis [3], rely on optimizing reactions at liquid–liquid interfaces. In addition, immiscible liquid–liquid interfaces can be considered as useful analogs of biomembranes [4–6] for the experimental investigation of cell membrane transfer processes, including drug delivery systems [7]. On a more general level, interest in the fundamental aspects of charge transfer processes at the interface between two immiscible electrolyte solutions (ITIES) has been increasing recently [8,9]. This research has led to developments in areas such as analysis with amperometric ion-selective electrodes [10], as well as in understanding the fundamentals of charge transfer mechanisms at liquid–liquid interfaces [8,11]. Many of the areas highlighted require an understanding of the kinetics and mechanisms of interfacial processes. An important aspect of progress in this ﬁeld has been the introduction of new techniques which are able to provide increasingly improved kinetic and mechanistic insight. The investigation of the kinetics of reactions that occur at liquid– liquid interfaces requires a number of factors to be considered. As depicted in the schematic in Fig. 1, the overall rate may be limited by the transport of reactants, intermediates, or products to and from the interface, interfacial processes, reactions in solution (not shown), or by a combination of factors. In order to accurately measure interfacial reaction rates, it is necessary to either operate under conditions where the overall rate is limited only by the interfacial (or solution) chemical reaction, i.e., ensure that the transport step is relatively fast and nonlimiting, or to make the transport step well-deﬁned and calculable, so that its effect can be accounted for when interpreting rate data [3,12,13]. For the study of reactions at immiscible liquid–liquid interfaces, achieving welldeﬁned contact between the two phases, with known interfacial area, under conditions where variable and high rates of mass transport are attainable, is nontrivial. 325

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FIG. 1 Simpliﬁed schematic illustrating the types of steps involved in an interfacial reaction at a liquid–liquid interface.

Complications introduced when a liquid–liquid interface, rather than a solid–liquid interface, is studied include the possibility that transport on both sides of the interface, in each of the phases, may need to be considered, and achieving a stable interface of known area is much more difﬁcult. The general criteria for an experimental investigation of the kinetics of reactions at liquid–liquid interfaces may be summarized as follows: known interfacial area and welldeﬁned interfacial contact are essential; controlled, variable, and calculable mass transport rates are required to allow the transport and interfacial kinetic contributions to the overall rate to be quantiﬁed; direct interfacial contact is preferred, since the use of a membrane to support the interface adds further resistances to the overall rate of the reaction [14,15]; a renewable interface is useful, as the accumulation of products at the interface is possible. Finally, direct measurements of reactive ﬂuxes at the interface of interest are desirable. Many of the electrochemical techniques described in this book fulﬁll all of these criteria. By using an external potential to drive a charge transfer process (electron or ion transfer), mass transport (typically by diffusion) is well-deﬁned and calculable, and the current provides a direct measurement of the interfacial reaction rate [8]. However, there is a whole class of spontaneous reactions, which do not involve net interfacial charge transfer, where these criteria are more difﬁcult to implement. For this type of process, hydrodynamic techniques become important, where mass transport is controlled by convection as well as diffusion. In this chapter, we describe some of the more widely used and successful kinetic techniques involving controlled hydrodynamics. We brieﬂy discuss the nature of mass transport associated with each method, and assess the attributes and drawbacks. While the application of hydrodynamic methods to liquid–liquid interfaces has largely involved the study of spontaneous processes, several of these methods can be used to investigate electrochemical processes at polarized ITIES; we consider these applications when appropriate. We aim to provide an historical overview of the ﬁeld, but since some of the older techniques have been reviewed extensively [2,3,13], we emphasize the most recent developments and applications.

Hydrodynamic Techniques

II.

THE LEWIS CELL

A.

Methodology

327

Some of the earliest attempts to address the difﬁculties associated with making kinetic measurements at immiscible liquid–liquid interfaces were made by Lewis [16,17] using the stirred cell design illustrated in Fig. 2. The Lewis cell employs direct contact between the two immiscible liquids, and reaction rates are evaluated by measuring concentration changes in the bulk of one of the two phases, usually by a batch extraction technique. The rate of change of concentration, dc=dt, is related to the interfacial reaction ﬂux, j, by dc jAint ¼ dt V

ð1Þ

where Aint is the interfacial area and V is the volume of the phase in which the concentration change is monitored. Stirrers are employed in each phase to generate convective transport on both sides of the interface. This reduces the contribution of diffusion to the overall kinetics, and it is generally assumed that the reaction rate can be evaluated by neglecting diffusion. This, of course, places limitations on the range of kinetics that can be investigated, as discussed shortly. The basic cell employs stirrers rotating at the same speed to minimize surface breakup, resulting in a relatively ﬂat interface of determinable area. Although the rate of mass transport to the interface can be enhanced by increasing the rate of stirring, the hydrodynamics are relatively ill-deﬁned and transport rates cannot be calculated absolutely. This technique therefore relies on the determination of interfacial reaction kinetics from the plateau region of a plot of reaction rate vs. stirring rate, with the assumption that the interfacial kinetics can be outrun by generating sufﬁciently high mass transport rates. At the maximum attainable stirring rate, the size of the concentration boundary layer (or diffusion layer) is in fact still relatively large, since high stirring rates cannot be used, as convective effects close to the interface would cause excessive break-up of the interface. In practice, the minimum diffusion layer thickness, D , is ca. 100 m, introducing a mass transport resistance, kT ðcm s1 ), which may be evaluated using kT ¼

D D

FIG. 2 Schematic of the basic Lewis cell design.

ð2Þ

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where D is the diffusion coefﬁcient of the reactant of interest. For typical values of D ¼ 105 cm2 s1 and D ¼ 100 m, the mass transport resistance is of the order of 103 cm s1 . This limits the technique to rather slow kinetics, with ﬁrst-order interfacial rate constants, ki kT . Another complication, caused by stirring the two phases at the same speed, occurs when the two solutions have different viscosities, which is common for immiscible liquids. The key ﬂuid ﬂow parameter is the Reynolds number, Re, which is the ratio of inertial to viscous forces in the solution, as indicated by Re ¼

vl

ð3Þ

where v is the ﬂuid velocity, l is a characteristic length, and is the kinematic viscosity of the ﬂuid. When the two phases have different viscosities, the Reynolds numbers are different for each side of the interface. Developments in the Lewis cell were made to overcome some of the problems associated with the initial design. With the introduction of screens close to the interface, on either side [18], stirring could be carried out at different speeds in each phase, allowing the same Reynolds number to be attained on both sides of the interface. This modiﬁcation to the cell also allowed more vigorous stirring and efﬁcient mixing in the bulk region without disturbances to the interface, thereby reducing the size of the stagnant diffusion layer and increasing the kinetic range of the technique. A further useful development in the design was the introduction of a ﬂow loop [19], eliminating the need for large volumes of solution, and enhancing the batch sampling procedures. Additional advances included the use of a porous gauze [20] to support the interface with stirring close to the gauze employed to enhance mass transport. However, even with these improvements, the main problems associated with using this type of cell remain, primarily that mass transport is poorly characterized and rather slow. The technique is essentially limited to the measurement of ﬁrst-order interfacial rate constants, ki < 105 cm s1 [3]. B.

Applications

Although the Lewis cell was introduced over 50 years ago, and has several drawbacks, it is still used widely to study liquid–liquid interfacial kinetics, due to its simplicity and the adaptable nature of the experimental setup. For example, it was used recently to study the hydrolysis kinetics of n-butyl acetate in the presence of a phase transfer catalyst [21]. Modeling of the system involved solving mass balance equations for coupled mass transfer and reactions for all of the species involved. Further recent applications of modiﬁed Lewis cells have focused on stripping–extraction kinetics [22–24], uncatalyzed hydrolysis [25,26], and partitioning kinetics [27].

III.

CONSTANT INTERFACIAL CELL WITH LAMINAR FLOW

Controlled contact between two immiscible liquids has also been achieved by ﬂowing one liquid along a solid support submerged in the second phase [28,29]. Several different arrangements have been used, although all are based on similar principles. For example, a wetted wall column which offered liquid–liquid contact times of 0.5–10 s was used to measure solute transfer rates [29].

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A signiﬁcant advance in this area was recently made by Li and coworkers [30,31], who developed a laminar ﬂow technique, that allowed the direct contact of two liquids with better-deﬁned mass transport compared to the Lewis cell. Laminar ﬂow of the two phases parallel to the interface was produced through the use of ﬂow deﬂectors. By forcing ﬂow parallel to, rather than towards, the interface, it was proposed that the interface was less likely to be disrupted. Reactions were followed by sampling changes in bulk solution concentrations. A schematic of the apparatus developed is shown in Fig. 3. Stirrers mix and push the lighter and heavier phases in each compartment, with the maximum rotation speed governed by the need to maintain the interface steady. Flow deﬂectors ensure that the phases are circulated in each chamber and that ﬂow near the interface is laminar. The interfacial plate (thickness 2 mm) is rectangular with a hole at its center. The distance from the interface to the ﬂow deﬂectors is less than 6 mm. The two phases are analyzed by withdrawing small volumes via sampling holes. The hydrodynamic and diffusion theory of this technique were obtained based on the following assumptions: isothermal operation; constant densities; constant viscosities; constant diffusivities; negligible diffusion along the interfacial plate direction; steady-state operation; negligible ﬂow in the y and z directions (see Fig. 4); and negligible stagnation regions near the edges of the interfacial plates. The thickness of the concentration boundary layer, D , was found to be governed by: 0 sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ1 1 96LDH 2 A ð4Þ 2D ¼ @9H 2 81H 4 U 2 where H is the distance between the interface and ﬂow deﬂectors, L is the length of contacting interface in the ﬂow direction, and U is the mean solution velocity. The mass transfer equation applicable to the transport-limited extraction of a solute from an aqueous solution to an organic phase (sink conditions), was derived: V w cw 3 Aint Dt b;0 1 exp Tr ¼ ð5Þ 2 V w D Aint ð1 þ Þ where Tr is the mass transferred per unit area, is the partition coefﬁcient of the solute between the organic and aqueous phase, V w is the volume of aqueous phase, cw b;0 is the initial concentration of the solute in the aqueous phase and t is time. Equation (5) can be also written as " # w 1 cb 1 A k w þ1 w ð6Þ f ðcb Þ ¼ ln ¼ intw T ð þ 1Þt cb;0 V

FIG. 3 Schematic of the constant interfacial cell with laminar ﬂow.

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FIG. 4 The co-ordinate system for the constant interfacial cell.

where cw b denotes the bulk aqueous solute concentration at time, t. The mass transfer coefﬁcient is kT ¼

3 D o 2 w D þ D

ð7Þ

The superscripts o and w denote the organic and aqueous phases, respectively. Equation (6) suggests a linear dependence of f ðcw b Þ on t for a diffusion-controlled process. This technique has been used to study the extraction kinetics of rare-earth elements from an aqueous phase into heptane by 2-ethylhexyl phosphonic acid mono-2-ethylhexyl ester (HEH/EHP) [31]. The linear dependence of f ðcw b Þ on t in Fig. 5 was considered to indicate that the extraction of ErCl3 by HEH/EHP is a diffusion-controlled process. The technique offers a known interfacial area under convective ﬂow conditions that are quite well-deﬁned, with mass transport rates that are enhanced compared to the Lewis cell and its analogs. However, in common with many other approaches, interfacial ﬂuxes must be determined indirectly from bulk solution measurements.

FIG. 5 Extraction of ErCl3 by HEH/EHP–heptane at pH 2.49 and 30 C. The experimental system was characterized by the following parameters: L ¼ 6:0 cm, Aint ¼ 21:0 cm2 , H ¼ 0:6 cm, 3 u ¼ 3:4 cm s1 , V w ¼ 96 cm3 , and cw M. The organic phase initially contained 3:0 b;0 ¼ 3 10 2 10 M HEH/EHP. (Reprinted from Ref. 31. Copyright 1998, Elsevier Science Ltd.)

Hydrodynamic Techniques

IV.

THE ROTATING DIFFUSION CELL

A.

Principles

331

The rotating diffusion cell (RDC) [14] enables the study of liquid–liquid reaction kinetics under conditions where interfacial hydrodynamics are well-deﬁned and calculable. The design of the RDC is based on the rotating disk electrode (RDE) [32], which has been widely used for kinetic measurements at solid electrodes. The RDE consists of a diskshaped electrode sealed in an insulating cylinder rotated in solution, giving rise to welldeﬁned hydrodynamics, which have been calculated to give a complete description of the ﬂow ﬁeld in the contacting solution [33]. The mass transfer coefﬁcient for this device, under transport-limited conditions, is given by [33]: kT ¼ 1:554D2=3 1=6 W 1=2

ð8Þ

where W is the rotation frequency of the disk (Hz). The assumptions behind the derivation of Eq. (8) are that ﬂow is laminar and the Schmidt number, Sc ¼ =D, is in excess of 103 . These assumptions generally hold for most practical conditions [34]. In practice, the rate of mass transport to the disk can be controlled readily through the rotation speed. For rotation speeds up to 100 Hz, which is experimentally accessible for a solid electrode, the corresponding mass transport parameter, for typical D and values of 1 105 cm2 s1 and 1 102 cm2 s1 , respectively, is variable up to 1:5 102 cm s1 . This corresponds to a diffusion layer (concentration boundary layer) thickness of ca.7 m. The RDC, depicted schematically in Fig. 6, operates with the interface supported at a thin porous membrane between the inner and outer compartments of the cell. A number of different arrangements are possible, with a common conﬁguration involving aqueous solutions in both the inner and outer compartments, with the organic phase impregnated within the membrane. Abbreviated to w/o/w, this results in two aqueous–organic phase interfaces. Alternatively, w/o/o, w/w/o, and o/o/o arrangements, etc., have also been used [15]. The membrane is rotated in the solution and the hydrodynamic proﬁles of the rotating disk are established on both sides of the membrane. Liquid–liquid contact is achieved with a known area by treating the membrane with a solution which blocks the pores, except in a small circular section in the center, which is untreated. Interfacial reactions are usually studied by measuring changes in the bulk concentrations of reacting

FIG. 6 Schematic of the rotating diffusion cell. The reaction is usually followed by sampling the bulk solution of the outer phase using a suitable analytical technique.

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species, as described above for the Lewis cell, although interfacial ﬂuxes can be measured directly by modifying the technique with the addition of a ring electrode, as described later. The kinetics of the reaction must be calculated from the measured ﬂux, taking into account transport to and from the disk-shaped contacting area and through the membrane. The ﬂux of a target species may be quantiﬁed according to the following equations; here we consider a simple solute transfer reaction from an organic donor phase to an aqueous receptor phase in the o/o/w conﬁguration. Firstly, the ﬂux across the diffusion layer towards the membrane on the donor side is given by j ¼ Do ðcob coi Þ=oD

ð9Þ coi

cob

and are the where Do is the diffusion coefﬁcient of the solute in the oil phase, concentrations of the solute in the organic donor phase at the membrane surface, and in the bulk of the organic solution, respectively. The diffusion layer thickness for the hydrodynamic rotating disk arrangement, D , is given by gD ¼ 0:643D1=3 1=6 W 1=2

ð10Þ

where g denotes phase o or w. This applies to both donor and receptor compartments. The ﬂux through the membrane is given by j ¼ Do ðcom cw m Þ=lm

ð11Þ

and are the where is the membrane porosity, lm is the membrane thickness, and concentrations of the solute within the membrane, speciﬁcally, where the membrane meets the organic donor and water receptor, respectively. For this particular arrangement, coi and com are equal, since there is no transfer resistance on the donor compartment side. The interfacial transfer reaction is controlled by com

w j ¼ ðkow cw m kwo ci Þ

cw m

ð12Þ

cw i

is the corresponding concentration at the other side of this interface. The rate where constants kwo and kow are for transfer across the organic–water interface from the water to the organic and the organic to the water phases respectively. Finally, the diffusion away from the interface into the receptor phase may be evaluated from w w j ¼ Dw ðcw i cb Þ=D

ð13Þ

cw b

is the bulk concentration of the solute in the water receptor phase. where Given that Pow ¼ kwo =kow is the solute partition coefﬁcient, then the expression for the total ﬂux for this particular case can be written as P cob Pow cw o l 1 b ¼ ow D;w þ D þ m þ j Dw Do Do kow

ð14Þ

Combining Eq. (10) and (14) yields

! 1=6 cob Pow cw Pow 1=6 l 1 w b 1=2 o ¼ 0:643W þ þ m þ 2=3 2=3 j

Do kow Do Dw

ð15Þ

Analysis of data obtained from the RDC usually involves plotting the reciprocal of the measured ﬂux, j 1 , against W 1=2 , and extrapolating to inﬁnite rotation speed (W 1=2 ! 0), such that the diffusion layer thicknesses tend to zero and diffusion in the solution on either side of the membrane is discounted. The intercept on the j 1 axis then gives a measure of the ﬂux, governed by the interfacial kinetics and the transport resistance

Hydrodynamic Techniques

333

[for example, the last two terms on the right-hand side of Eq. (15)]. The membrane transfer resistance must be subtracted in order to obtain the true interfacial resistance. B.

Drawbacks and Improvements

In contrast to the RDE, the range of rotation speeds used in the RDC is rather limited. The upper limit is around 6–8 Hz, while Eq. (8) breaks down below approximately 1–2 Hz, where the hydrodynamic boundary layer, H ¼ 1:4ð=WÞ1=2

ð16Þ

becomes comparable with the rotating disk radius [35]. Consequently, rate data are obtained over a very narrow range of mass transport coefﬁcients, the maximum kT available being ca. 4 103 cm s1 . Signiﬁcant extrapolation of reciprocal ﬂux data to W 1=2 ! 0 has been suggested to be an unreliable way to determine interfacial kinetics [15]. A modiﬁcation of the RDC design, based on the ring–disk arrangement of the RDE [36], incorporated an arc electrode [37,38] deposited on the surface of the membrane around the untreated area. This facilitated the electrochemical detection of species reacting at the interface at short times following the reaction. This method was used to study the solvent extraction of cupric ions, which were detected by reduction to copper metal at the arc electrode. The resulting current ﬂow was related to the interfacial ﬂux at the membrane. There are several drawbacks to the RDC that need to be emphasized. First, the fact that the interface must be supported adds a considerable resistance to the transport of species, which is in addition to that from the concentration boundary layers on both sides of the membrane. This limits the range of kinetics that can be studied. Second, in practical applications, blocking of the membrane can be problematic for some reactions. Third, measurements are generally made in the bulk of the solution and not at the interface although, as mentioned above, for certain processes it is possible to measure ﬂuxes via a ring or an arc electrode. C.

Applications

The majority of RDC studies have concentrated on the measurement of solute transfer resistances, in particular, focusing on their relevance as model systems for drug transfer across skin [14,39–41]. In these studies, isopropyl myristate is commonly used as a solvent, since it is considered to serve as a model compound for skin lipids. However, it has since been reported that the true interfacial kinetics cannot be resolved with the RDC due to the severe mass transport limitations inherent in the technique [15]. The RDC has also been used to study more complicated interfacial processes such as kinetics in a microemulsion system [42], where one of the compartments contains an emulsion. A comprehensive study of the complex interfacial processes involved in the solvent extraction of cupric ion by oxime ligands represents one of the most detailed and successful studies carried out with the RDC [37,38]. Recently, the technique was also used to study the transfer of tetrabutylammonium cations [43] and the kinetics of partitioning of compounds between octanol and water [44]. In the latter study, Fisk and coworkers investigated the rates of partitioning of 23 compounds from octanol to an aqueous phase. The RDC arrangement used most frequently in this work is of the o/o/w type. So according to Eq. (15), Pow and kow can be calculated from the gradient and intercept of

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FIG. 7 Analysis of RDC data for the partition kinetics of cyanazine between octanol and water.

a plot of c 0 =j vs. W 1=2 , where c 0 ¼ cob Pow cw b . Figure 7 illustrates some typical results for cyanazine transfer from octanol to the aqueous phase.

V.

THE LIQUID JET RECYCLE REACTOR (LJRR)

Developed by Freeman and Tavlarides [45,46], and based on the liquid jet technique [47,48], the LJRR provides a method of measuring liquid–liquid reaction kinetics with direct contact, known interfacial area, renewable interface, and reasonably deﬁned hydrodynamics. This method operates by employing an aqueous liquid jet in a concurrent, coaxially ﬂowing organic solution, shown schematically in Fig. 8. The aqueous solution ﬂows from the jet nozzle to a receiving capillary with no overﬂow into the outer stream, resulting in short contact times of around 0.05 s. Analysis is implemented by ﬂowing the outer organic phase continually through a closed loop and monitoring concentration changes spectrophotometrically. The apparatus used by Freeman and Tavlarides employed capillaries with internal diameters of 2 mm, and the

FIG. 8 Schematic diagram of the liquid jet recycle reactor (LJRR).

Hydrodynamic Techniques

335

jet length was 3.54 cm. The aqueous jet was arranged vertically, and a gravity fed ﬂow system was used. This approach enabled measurements to be made on a clean interface with a known area (measurable by photography). The following equations of mass transfer from the jet are based on certain assumptions, namely, isothermal operation; constant densities, viscosities, and diffusivities; no ionization or homogeneous reactions; small penetration depth; negligible curvature; negligible axial diffusion; and steady-state operation: @co @c @2 c þ v o ¼ Do 2o @x @y @y

y>0

ð17Þ

@cw @c @2 c þ v w ¼ Dw 2w @x @y @y

y<0

ð18Þ

u u

where u is the velocity in the x direction and v is the velocity in the y direction. The coordinate system for the liquid–liquid jet is shown in Fig. 9. The main complication with this technique is that the mass transfer analysis is nontrivial. For example, the change of velocity as a function of the distance down the jet was not taken into account in modeling the system. The LJRR has been used to study the diffusivities of benzene and toluene in water [41] and cupric ion extraction [42,49].

VI.

MOVING-DROP TECHNIQUES

The moving-drop method [2] employs a column of one liquid phase through which drops of a second liquid either rise or fall. The drops are produced at a nozzle situated at one end of the column and collected at the other end. The contact time and size of the drop are measurable. Three regimes of mass transport need to be considered: drop formation, free rise (or fall) and drop coalescence. The solution in the liquid column phase or drop phase (after contact) may be analyzed to determine the total mass transferred, which may be related to the interfacial reaction only after mass transfer rates have been determined.

FIG. 9 Co-ordinate system for the LJRR.

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The hydrodynamics of the moving drop are difﬁcult to calculate, particularly the ﬂow characteristics within the droplet itself. However, this technique is still used widely, because it is a simple and straightforward method. It was recently applied to study the stripping–extraction kinetics of Mn(II) in an aqueous–kerosene system [50,51]. The effect of anionic surfactants on the kinetics of extraction of lactic acid from an aqueous phase by Alamine 336 in a toluene phase was also studied by this technique [52]. A growing-drop method has been reported [53] for measuring interfacial liquid– liquid reactions, in which mass transport to the growing drop was considered to be well-deﬁned and calculable. This approach was applied to study the kinetics of the solvent extraction of cupric ions by complexing ligands.

VII.

TECHNIQUES BASED ON DISPERSED LIQUID–LIQUID SYSTEMS

Stirred suspensions of droplets have proven to be a popular approach for studying the kinetics of liquid–liquid reactions [54–57]. The basic principle is that one liquid phase takes the form of droplets in the other phase when two immiscible liquids are dispersed. The droplet size can be controlled by changing the agitator speed. For droplets with a diameter < 0:15 cm the inside of the drop is essentially stagnant [54], so that mass transfer to the inside surface of the droplet occurs only by diffusion. In many cases, this technique can lack the necessary control over both the interfacial area and the transport step for determination of fundamental interfacial processes [3], but is still of some value as it reproduces conditions in industrial reactors. A signiﬁcant advance was made in this ﬁeld by Watarai and Freiser [58], who developed a high-speed automatic system for solvent extraction kinetic studies. The extraction vessel was a 200 mL Morton ﬂask ﬁtted with a high speed stirrer (0–20,000 rpm) and a teﬂon phase separator. The mass transport rates generated with this approach were considered to be sufﬁciently high to effectively outrun the kinetics of the chemical processes of interest. With the aid of the separator, the bulk organic phase was cleanly separated from a ﬁne dispersion of the two phases in the ﬂask, circulated through a spectrophotometric ﬂow cell, and returned to the reaction vessel. The absorbance data enabled the determination of extraction rate constants. For a pseudo-ﬁrst-order reaction, the following equation describes the extraction process: AF A0 ð19Þ ln ¼ kobs t AF At where A0 , At , and AF correspond to absorbance values for the extracted solute at t ¼ 0, t, and equilibrium, respectively, and kobs is the rate constant observed experimentally. The extraction of nickel (II) by dithizone in a chloroform phase was studied using this technique by recording the absorbance for nickel dithizonate. A typical result is shown in Fig. 10. A ﬁrst-order rate constant of 1:42 102 s1 was obtained. To relate this to an interfacial ﬂux, one needs to know the area/volume ratio in the system. This can be obtained, but requires that the experimental system is ‘‘calibrated’’ by studying a process with known interfacial kinetics. Extraction rates of zinc (II) and nickel (II) with ethyldithizone, butyldithizone, or hexyldithizone in an organic phase (chloroform, CCl4 , n-heptane, or benzene) showed a ﬁrst-order dependence on the ligand and metal ion concentration and an inverse-ﬁrstorder dependence on the proton concentration. The results were explained by chelate formation in the interfacial region [59]. The effects of stirring on the distribution equili-

Hydrodynamic Techniques

337

FIG. 10 Extraction of nickel (II) by dithizone in chloroform. (a) Absorbance of the nickel (II) dithizone complex in chloroform vs. time. (b) Kinetic analysis in terms of Eq. (19).

brium of n-alkyl-substituted dithizones in several aqueous–organic (chloroform, CCl4 , nheptane, or benzene) systems were also reported [60].

VIII.

CENTRIFUGAL LIQUID MEMBRANE (CLM) METHOD

The CLM method is a new technique, developed by Nagatani and Watarai [61]. This method produces a stable, ultrathin two-phase liquid membrane by the centrifugal force due to the rotation of a cylindrical cell, using the arrangement shown in Fig. 11. The inner diameter and inner height of the cylindrical cell were 19 and 29 mm, respectively. The rotation speed was controlled in the range 6000–7500 rpm. The summation of the absorption spectra of both interfacial and bulk organic phase species was measured in the direction perpendicular to the rotation axis with a diode array spectrophotometer. Mass transfer for this technique was examined by studying the protonation and aggregation kinetics of 5,10,15,20-tetraphenylporphyrin (H2 TTP) at the dodecane–aqueous interface [61]. The rate law for the diffusion-controlled protonation of H2 TTP at the interface was derived.

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FIG. 11 Schematic of the centrifugal liquid membrane apparatus. Typically, the organic phase, 0:150 cm3 , and the aqueous phase, 0:250 cm3 , are spread as an inner liquid membrane of 79 m ﬁlm thickness and an outer liquid membrane of 145 m thickness, respectively. (Reprinted from Ref. 61. Copyright 1998, American Chemical Society.)

The demetalation kinetics of ZnTTP by an acidic aqueous phase have also been reported [61]. In this study, ZnTTP was considered to adsorb at the interface producing Zn2þ and free base porphyrin by proton attack. The demetalation kinetics of ZnTTP were analyzed as a pseudo-ﬁrst-order reaction, because the proton concentration in the aqueous phase was in large excess. The rate law was found to be described by

d½ZnTTPT A ¼ kobs int dt Vo

ð20Þ

where kobs ðs1 Þ is the observed rate constant, is the surface excess concentration (mol cm2 ) of ZnTTP and [ZnTTPT is the total or initial concentration of ZnTTP dissolved in the bulk organic phase. Typical ﬁrst-order kinetic proﬁles derived from these studies are shown in Fig. 12. The dependence of the observed demetalation rate constant of ZnTTP on the proton concentration in the aqueous phase is shown in Fig. 13. The results indicate that the observed demetalation rate constant has a ﬁrst-order dependence on the proton concentration. Based on this observation, the authors suggested that the rate-determining step was the ﬁrst attack of protons on ZnTTP at the interface. A further interesting application of CLM involves the ﬂuorescence quenching reaction between (5,10,15,20-tetraphenylporphyrinato) zinc (II) and methylviologen at a dodecane–water interface. [62] This study demonstrated that the quenching reaction could occur only in the presence of an anionic surfactant, sodium dodecyl sulfate (SDS). The quenching efﬁciency depended on the concentration of SDS in the aqueous phase with a maximum value of 13.5%

Hydrodynamic Techniques

339

FIG. 12 First-order kinetic proﬁles observed from CLM measurements of the diprotonation of H2 TTP (a) and the demetalation of ZnTPP (b). The initial concentrations of H2 TPP and ZnTPP were 1:71 105 and 8:9 106 mol dm3 , respectively. The concentration of hydrochloric acid was 2:0 mol dm3 . (Reprinted from Ref. 61. Copyright 1998, American Chemical Society.)

IX.

ELECTROLYTE DROPPING METHOD

The electrolyte dropping electrode [63] method, introduced in 1976, and subsequently used in conjunction with the four-electrode potentiostat [64], is a hydrodynamic technique, offering controlled convective transport. In essence, this approach is identical to the dropping mercury electrode [65]; however, the drop consists of a ﬂowing electrolyte liquid phase which forms a polarized ITIES with an immiscible continuous (receptor) phase. In

FIG. 13 Logarithmic plot of the observed demetalation rate constants of ZnTPP vs. acidity function of hydrochloric acid, at 298 K. The slope of the straight line is close to unity. The concentration of ZnTPP was 8:9 106 mol dm3 , and the ionic strength was maintained at 2.0 mol dm3 . (Reprinted from Ref. 61. Copyright 1998, American Chemical Society.)

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this approach, the interface is continually refreshed, minimizing the possible problems of interfacial blocking (by reactants, intermediates, and products). A fast miniaturized version of this technique has recently been reported [66]. The electrolyte dropping electrode has found particular application in the study of ion transfer at the polarized ITIES, with an emphasis on analysis. A range of species have been detected amperometrically by measuring the transport-limited current: i ¼ nFD1=2 q2=3 td1=6 cb

ð21Þ

where is the Ilkovich constant, n is the charge number of the ion transferred, F is Faraday’s constant, cb is the bulk concentration of the species of interest, q is the volume ﬂow rate, and td is the drop time. Many aqueous ions which are not accessible to amperometric detection by conventional electrolysis may be measured through the application of this technique, with suitable complexing ligands in the organic phase. A review focusing on the analytical applications of the method has appeared [67]. A comprehensive and systematic investigation of the fundamental factors in ion transfer measurements in the electrolyte dropping electrode arrangement has been carried out in order to develop a quantitative method for analysis [68]. It was reported that the limiting currents were proportional to the concentration of monovalent ions such as Csþ , tetramethylammonium ion, ClO 4 , IO4 , I , Br , ReO4 , and BF4 in the concentration 5 3 range between 10 and 10 M in aqueous solution, when 1,2-dichloroethane (DCE) was used as the organic phase. A hanging electrolyte drop has also been applied to determine ionic species in solution using differential-pulse-stripping voltammetry procedures [69]. Particular emphasis was given to assessing the selectivity and sensitivity of the method. The technique of current-scan polarography has also been applied in the study of electron-transfer [70] and coupled electron-transfer–ion-transfer [71,72] reactions at the ITIES in this conﬁguration.

X.

MICROELECTROCHEMICAL MEASUREMENTS AT EXPANDING DROPLETS (MEMED)

A.

Methodology and Theory

In the majority of methods described thus far, the interfacial kinetics are deduced by measuring concentration changes in the bulk of the solution rather than at the interface, where the reaction occurs. This introduces a time lag, limiting the resolution of the measurement in the determination of interfacial kinetics. A more direct approach is to identify the interfacial ﬂux. This can be achieved in the electrolyte dropping electrode, via the current ﬂow, but this method is only applicable to net charge-transfer processes at externally polarized interfaces. We have developed a new approach, for measuring reaction rates at liquid–liquid interfaces using ultramicroelectrodes (UMEs). Termed microelectrochemical measurements at expanding droplets (MEMED), the technique overcomes many problems inherent in previous approaches used to investigate spontaneous reactions at liquid–liquid interfaces. In MEMED, liquid–liquid contact is established by forming drops of one liquid from a capillary submerged in a second immiscible liquid. The internal diameter of the capillary is typically in the range 100–200 m. The feeder solution, either an organic or an aqueous phase, ﬂows into the receptor solution at a constant rate, such that drops form at

Hydrodynamic Techniques

341

the capillary tip, grow and eventually detach, periodically in a well-deﬁned manner. This approach is similar to the dropping mercury electrode (DME) [65] and electrolyte dropping electrode [63,64,67–70], discussed above, and conveys the same advantage by providing a constantly renewable, clean interface. In MEMED, the interfacial reaction is monitored with a stationary UME, positioned directly beneath or above (depending on the relative densities of the two liquids) the expanding drop. The electrode operates in either an amperometric or potentiometric mode, to measure local changes in concentration in the receptor phase, at the probe tip, as the drop approaches the electrode. The probe penetrates, and measures directly the developing concentration proﬁle adjacent to the drop surface in the receptor phase, due to the two-phase reaction. By solving the convective-diffusion equation for this particular conﬁguration, with appropriate boundary conditions, theoretical concentration proﬁles can be generated for comparison with experiment. In this way, the nature of mass transport and the interfacial reaction can be investigated quantitatively. To ensure that the detector electrode used in MEMED is a noninvasive probe of the concentration boundary layer that develops adjacent to the droplet, it is usually necessary to employ a small-sized UME (less than 2 m diameter). This is essential for amperometric detection protocols, although larger electrodes, up to 50 m across, can be employed in potentiometric detection mode [73]. A key strength of the technique is that the electrode measures directly the concentration proﬁle of a target species involved in the reaction at the interface, i.e., the spatial distribution of a product or reactant, on the receptor phase side. The shape of this concentration proﬁle is sensitive to the mass transport characteristics for the growing drop, and to the interfacial reaction kinetics. A schematic of the apparatus for MEMED is shown in Fig. 14. Mass transfer to an expanding droplet has been considered previously for the DME arrangement [33,74,75] and other growing liquid drop techniques [53,76]. At a simple level,

FIG. 14 Schematic diagram of the experimental arrangement for MEMED.

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Slevin et al.

convective diffusion to a growing drop may be treated by assuming a symmetrically expanding sphere geometry: ! @c @2 c 2 @c @c ¼D þ vr @t @r @r2 r @r

ð22Þ

In Eq. (22), r is the spherical co-ordinate starting at the center of the drop. The variable vr represents the convective velocity due to the moving surface of the expanding drop. Within a reference framework centered on the moving drop surface, this is given by vr ¼

q 1 1 4 r2 r20

ð23Þ

where r0 is the (time-dependent) drop radius. This equation assumes that the drop behaves as a symmetrically expanding sphere, i.e., that the drop expands from a ﬁxed center. While this is not the case for a droplet growing from a capillary, since the center of the drop moves, it has been found to be a reasonable approximation to the real system at the relatively slow ﬂow rates employed. A second approach is to assume that the drop surface approaching the electrode is a moving plane. This is appropriate, since the diffusion layer is almost always considerably smaller than the size of the drop, for most of its lifetime under practical conditions. To a good approximation, the convective effect close to the moving front is then calculated based on velocities which are twice those determined from Eq. (23), in order to account for the moving center of the drop. The convective-diffusion equation which describes this case is given by @c @2 c @c ¼ D 2 2vr @t @r @r

ð24Þ

A linear approximation for the velocity term, used to treat the DME problem [74], does not work for MEMED, because the concentration boundary layers tend to be much larger for MEMED due to the longer drop times employed. The presence of the capillary can be ignored in the simulation of mass transport in MEMED since, for most of its lifetime, the dimensions of the drop are much larger than the capillary diameter. Moreover, the capillary is not expected to inﬂuence measurements that are made (in a micrometer region) at the opposite side of the drop, given the time scale of the measurements. For applications of MEMED hitherto, depletion or accumulation inside the drop have been neglected for two reasons. First, the probe is positioned close to the portion of the drop where the surface is constantly renewed (see Fig. 15). Internal streamlines in a drop expanding from a capillary have been investigated experimentally [77,78], and these observations suggest that fresh material is carried from the capillary to the front face of the drop, directly opposite the capillary. Second, for the systems studied, the concentrations of reactants have been carefully chosen such that neither depletion nor accumulation inside the droplet would be important. This means that in solving the mass transport problem for MEMED, it is only necessary to consider the domain r r0 by solution of either Eq. (22) or (24) Equations (22) and (24) are readily cast into dimensionless form using the following terms [74]:

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FIG. 15 Schematic of the internal streamlines in a drop expanding from a capillary tip into a second immiscible ﬂuid phase.

r R ¼ pﬃﬃﬃﬃﬃﬃﬃﬃ Dtd t ¼ td c C¼ cb rﬃﬃﬃﬃ t Vr ¼ vr d D

ð25Þ ð26Þ ð27Þ ð28Þ

where cb is typically the initial or bulk concentration of the reactant in the receptor solution, but may be the concentration at the surface of the drop (for processes involving transport-limited transfer from the drop to the receptor phase). The variable td is the total drop time from the beginning of growth to the point of contact with the probe electrode. The resulting normalized equations can readily be solved subject to boundary conditions describing the chemical processes of interest. For the expanding sphere and the moving plane models, mass transport is described by Eqs. (29) and (30), respectively: @c @2 c 2 @c @c ¼ Vr þ @ @R2 R @R @R

ð29Þ

@c @2 c @c ¼ 2Vr @ @R2 @R

ð30Þ

Models have been formulated to enable the simulation of the concentration vs. radial distance proﬁle as it develops with time, from which the time-dependent concentration vs. distance, d, proﬁle, observed at the probe, can be extracted for comparison with experimental data. Models based on Eqs. (29) and (30) give similar results for conditions encountered practically.

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Typical theoretical concentration proﬁles, observed at a probe electrode, for the consumption of a receptor phase species in a ﬁrst-order interfacial reaction are shown in Fig. 16. The simulation involved solving Eq. (30) with appropriate boundary conditions. These results show that the reactant concentration becomes increasingly depleted close to the drop surface as the rate constant increases, until a limiting case is reached, where the reaction becomes transport controlled. MEMED can be used to measure quite a wide range of rate constants, but is particularly sensitive to rate constants in the low– medium range. In its present form, ﬁrst-order rate constants higher than 0:01 cm s1 cannot readily be distinguished from a transport-controlled process, although this upper limit can be increased slightly by the use of shorter drop times. The nature of mass transport in MEMED has been conﬁrmed with both amperometric and potentiometric studies of bromine transfer from an aqueous phase to DCE [79]. Figure 17 shows typical amperometric data for this case, in which the DCE phase acts as a sink for Br2 , and a depleted region of Br2 is measured adjacent to the droplet in the aqueous phase. Video images are also provided, which correspond to particular times during the amperometric transient: at position (3) the edge of the developing concentration boundary layer, around the drop, reaches the electrode; the concentration proﬁle is then mapped out between points (3) and (4). The measured current, i, can be related to the local concentration, c, via i ¼ 4nFDac

ð31Þ

where n is the number of electrons transferred, F is Faraday’s constant, and a is the radius of the UME.

FIG. 16 Theoretical ﬁrst-order reaction approach curves for MEMED. Final drop radius ¼ 0:05 cm, drop time ¼ 6:3 s, and D ¼ 7:0 106 cm2 s1 were used in the simulation. From top to bottom the curves are for ﬁrst-order interfacial rate constants of 1 105 , 1 104 , 1 103 , and 1 102 cm s1 , and a transport-controlled process.

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FIG. 17 (a) Typical current (i)–time (t) characteristics for bromine transfer from an aqueous phase to an expanding DCE drop measured at a 1 m diameter Pt UME positioned beneath the growing drop. The images (1)–(4) correspond to the points indicated on the transient. The ﬁnal drop size in (4) is 1.00 mm. Data are analyzed to produce (normalized) concentration vs. distance proﬁles, such as that in (b), showing experiment (*) and theory for a transport-limited process (—).

B.

Applications

MEMED has been used to study the hydrolysis of triphenylmethyl chloride (TPMCl) in a two-phase DCE–aqueous arrangement [73]: TPMClðDCEÞ þ H2 O ! TPMOHðDCEÞ þ Hþ ðwÞ þ ClðwÞ

ð32Þ

The reaction was followed by the local measurement of chloride ions, at a potentiometric Ag/AgCl microelectrode probe, positioned in the aqueous receptor phase, as DCE droplets containing TPMCl were grown (feeder phase). The reaction was shown unambiguously to occur interfacially, and was ﬁrst-order in TPMCl with a hydrolysis rate constant of 6:5 105 cm s1 . A typical concentration–distance proﬁle determined in these experiments is shown in Fig. 18. MEMED has also been used to investigate the nature of coupled ion-transfer processes involved in spontaneous electron transfer at ITIES [80]. In this application, a key strength of MEMED is that all of the reactants and products involved in the reaction can be measured, as shown in Figs. 19 and 20. The redox reaction studied involved the oxidation of either ferrocene (Fc) or decamethylferrocene (DMFc) in a DCE phase 0 3 (denoted by FcDCE ) by either IrCl2 6 or FeðCNÞ6 in the aqueous phase (denoted by Oxw ): 0

0 þ Oxw ! Fc þ þ Redw FcDCE

ð33Þ

The results in Figs. 19 and 20 clearly show that these reactions occur at a transport0 controlled rate. For example, the concentration of FcDCE is zero at the interface [Figs. 19(a) and 20(a)] with DCE as the receptor phase, and the IrCl2 6 interfacial concentration

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FIG. 18 Chloride concentration proﬁle recorded by a microelectrode probe during the hydrolysis of TPMCl at a DCE drop–aqueous interface (*). The concentration of TPMCl in the organic phase was 50 mmol dm3 , the drop time from formation to contact with the probe was 4.80 s, and the ﬁnal drop radius was 0.55 mm. The solid lines represent theoretical time-dependent concentration proﬁles, from top to bottom, generated for k ¼ 3:50 109 , 3:25 109 , and 3:00 109 mol cm2 s1 . A value of 1:8 105 cm2 s1 was employed for the diffusion coefﬁcient of chloride. (Reprinted from Ref. 73. Copyright 1997, American Chemical Society.)

is zero with an aqueous receptor phase. The ability to probe all of the reactant and product proﬁles is also of value in demonstrating that DMFcþ effectively remains in the DCE phase under the experimental conditions, while Fcþ is lost extensively from DCE. The recent applications of MEMED to electron-transfer reactions demonstrate that it complements scanning electrochemical microscopy (SECM) [81,82] which is discussed in detail in Chapter 12. MEMED can be used to measure rate constants at the lower scale of those measurable by SECM, but in the region where the two techniques overlap, they provide consistent information. In applications hitherto, the reduction of 7,7,8,8-tetracyanoquinodimethane (TCNQ) in DCE by aqueous ferrocynide and the oxidation of DMFc by aqueous oxidants have been studied. The purpose of these investigations was to determine the dependence of heterogeneous electron transfer rate constants on the interfacial potential drop, which was controlled through the use of potential-determining ions. For a single potential-determining ion system, the potential drop across an ITIES follows the Nernst–Donnan equation [5,8], RT a w w o ln o ð34Þ o ¼ o þ zF aw w o w o where w o ¼ is the potential drop across the water–oil interface, o is the standard ion-transfer potential across the water–oil boundary, z is the charge number of the potential-determining ion, R and T have their usual meanings, and ao and aw are the activities of the potential-determining ion in the oil and aqueous phases, respectively. Under experimental conditions where ao is ﬁxed and the activity coefﬁcient of the potential-determining ion (typically ClO 4 ) in the aqueous phase is constant within the concentration range of interest, Eq. (34) can be simpliﬁed to

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FIG. 19 Normalized concentration proﬁles (solid lines) of the reactants and products in the DCE (a) or aqueous (b) receptor phase for the reaction between Fc (DCE) and IrCl2 6 (aqueous) with 0.1 M ClO 4 in both DCE and the aqueous phase. In each case, the reactant concentration in the receptor phase was 1 mM, with 10 mM reactant inside the droplet. Drop times and ﬁnal sizes were (a) 5.54 s and 0.96 mm, and (b) 6.32 s and 1.00 mm. The theoretical proﬁles (dashed lines) are for a transport-controlled reaction, with no transfer of the product ions. (Reprinted from Ref. 80. Copyright 1999, Royal Society of Chemistry.)

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FIG. 20 Normalized concentration proﬁles (solid lines) of the reactants and products in the DCE (a) and aqueous (b) receptor phases for the reaction between DMFc (DCE) and IrCl2 6 (aqueous), with 0.1 M ClO 4 in both DCE and the aqueous phase. In each case, the reactant concentration in the receptor phase was 1 mM, with 10 mM reactant inside the droplets. Drop times and ﬁnal sizes were (a) 5.54 s and 0.96 mm, and (b) 6.32 s and 1.00 mm. The theoretical proﬁles (dashed lines) are for a transport-controlled reaction, with no transfer of the product ions. (Reprinted from Ref. 80. Copyright 1999, Royal Society of Chemistry.)

Hydrodynamic Techniques

ow ¼ const 0:059 log½ClO 4 w

349

ð35Þ

Previous SECM studies have suggested that a Butler–Volmer type approximation could be used for the ITIES at low driving forces [83]. For a system where an ET reaction occurs between an aqueous electron donor and an oxidant in the organic phase, the free energy barrier is given by ð36Þ G6¼ ¼ 0F E 0 þ ow

where E 0 is the standard potential difference between the organic oxidant and aqueous electron donor and is the transfer coefﬁcient. ðE 0 þ ow Þ denotes the driving force for the reaction. With a ﬁxed concentration of oxidant in the organic phase, the dependence of the ET rate on the driving force can be written as [83,84] k ¼ const 0 expðG6¼ =RTÞ

ð37Þ

where k is the bimolecular interfacial reaction rate constant. For a reaction between a redox couple in each phase, the E 0 value is ﬁxed and the combination of equations (35), (36), and (37) yields log k ¼ const 00 2:303 log½ClO 4 w

ð38Þ

log½ClO 4 w

Thus, the log k vs. dependence should be linear with a slope proportional to . Typical results, shown in Fig. 21(a), demonstrate that the rate constant for the reaction between TCNQ and aqueous FeðCNÞ4 6 increases with increasing driving force, 4 concentration promoted by decreasing ½ClO 4 w as evidenced by the steeper FeðCNÞ6 4 proﬁles. Moreover, the Tafel plot obtained for ET between FeðCNÞ6 and TCNQ is linear with an apparent measured value of 0:31 0:02. In these studies, the concentration of reactant in the droplet phase was always at least 10 times the concentration of the reactant in the receptor phase, to ensure that depletion (and diffusional) effects within the droplet were negligible. Recently, MEMED was also used to investigate cupric ion extraction-stripping kinetics in an aqueous–DCE system containing the oxime extractant ligand, Acorga P50 [85,86]. The stripping process showed a ﬁrst-order dependence on both proton concentration in the aqueous phase and the complex concentration in the DCE phase. This information was consistent with a reaction mechanism involving the ﬁrst attack of protons on the cupric ion complex as the rate limiting step, as found in recent studies of Zn2þ stripping from acidic complexing ligands in an immiscible liquid–liquid system [61]. The stripping rate constants measured by MEMED were comparable with those derived from earlier SECM studies [87].

XI.

CONCLUSIONS AND SUGGESTIONS

This review has highlighted the wide range of techniques, which have been used to investigate reaction kinetics at liquid–liquid interfaces. While signiﬁcant progress has been made in the last few years, in particular, many of the techniques currently in use have a number of drawbacks, and there is considerable scope for the introduction of further techniques which can match the criteria proposed in Section I. Of the methodologies considered, the Lewis cell, employs direct contact of the two liquids, but does not have well-deﬁned hydrodynamics. The constant interface cell with laminar ﬂow has better-deﬁned hydrodynamics, but the interfacial ﬂux is not measured

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FIG. 21 (a) Normalized concentration proﬁles (solid lines) of FeðCNÞ4 6 (1 mM) in the aqueous receptor phase, obtained using MEMED technology. The reaction involved the reduction of 10 mM TCNQ in DCE (feeder phase) by FeðCNÞ4 6 . In all measurements, the DCE phase contained 0.1 M tetra-n-hexylammonium perchlorate. The drop time and ﬁnal size were 9.2 s and 0.99 mm. From bottom to top, the solid experimental curves are shown for ½ClO 4 w ¼ 0:01, 0.025, 0.1, and 0.25 M, while the corresponding dashed curves (also bottom to top) are for the theoretical behavior for k ¼ 0:22, 0.09, 0.04, and 0.02 cm s1 M1 . (b) Dependence of k on ClO 4 concentration in the aqueous phase; the data are those from (a).

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directly. The RDC introduces the added transport resistance of a supported interface in an effort to obtain well-deﬁned hydrodynamics. The LJRR possesses both direct contact and reasonably deﬁned hydrodynamics, but mathematical modeling of the ﬂowing solutions is complex, and the method is difﬁcult to use experimentally. The centrifugal liquid membrane method is a promising new approach, and it will be interesting to see how this develops with further applications. However, as with all of these methods, the measurement of concentration changes occurs in the bulk of solution and not at the interface where the reaction occurs. MEMED meets all of the criteria listed in Section I, for the investigation of liquid– liquid interfacial kinetics, but is limited in the range of rate constants that can be determined. While SECM, discussed in Chapter 12, enhances the kinetic domain that can be measured with ultramicroelectrodes, there are many spontaneous reactions to which SECM cannot be applied. The development of hydrodynamic techniques which allow the direct measurement of interfacial ﬂuxes and interfacial concentrations is likely to be a key trend of future work in this area. Suitable detectors for local interfacial or near-interfacial measurements include spectroscopic probes, such as total internal reﬂection ﬂuorometry [88–90], surface second-harmonic generation [91], probe beam deﬂection [92], and spatially resolved UVvisible absorption spectroscopy [93]. Additionally, building on the ideas in MEMED, submicrometer or nanometer scale electrodes may prove to be relatively noninvasive probes of interfacial concentrations in other hydrodynamic systems. The construction and application of electrodes of this size is now becoming more widespread and general [94–96].

ACKNOWLEDGMENTS We wish to thank Dr. John Atherton (Avecia, Huddersﬁeld) for helpful discussions on liquid–liquid reactions over the past few years. The support of our research in this area by the EPSRC, Avecia (formerly Zeneca Specialities), and the University of Warwick is gratefully acknowledged.

REFERENCES 1. 2. 3. 4.

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14 Catalytic E¡ect of the Liquid^Liquid Interface in Solvent Extraction Kinetics HITOSHI WATARAI Department of Chemistry, Osaka University, Osaka, Japan

I.

INTRODUCTION

The liquid–liquid interface is not only a boundary plane dividing two immiscible liquid phases, but also a nanoscaled, very thin liquid layer where properties such as cohesive energy, density, electrical potential, dielectric constant, and viscosity are drastically changed along with the axis from one phase to another. The interfacial region was anticipated to cause various speciﬁc chemical phenomena not found in bulk liquid phases. The chemical reactions at liquid–liquid interfaces have traditionally been less understood than those at liquid–solid or gas–liquid interfaces, much less than the bulk phases. These circumstances were mainly due to the lack of experimental methods which could measure the amount of adsorbed chemical species and the rate of chemical reaction at the interface [1,2]. Several experimental methods have recently been invented in the ﬁeld of solvent extraction [3], which have made a signiﬁcant breakthrough in the study of interfacial reactions. Solvent extraction is intrinsically dependent on the mass transfer across the interface and the chemical inversion at the interfacial region. Researchers in the ﬁeld of solvent extraction, especially in the ﬁeld of analytical chemistry and hydrometallurgy, observed effects of interfacial phenomena in the solvent extraction systems. This gave them a strong motivation to measure what happened at the interface. From the beginning of the 1980s, some effective experimental approaches based on new principles have been invented for the study of interfacial reactions in solvent extraction chemistry. Recently, some methods were developed from our laboratory, the highspeed stirring (HSS) method [4,5], the two-phase stopped ﬂow method [6], the capillary plate method [7], the reﬂection spectrometry [8], and the centrifugal liquid membrane (CLM) method [9]. One of the most attractive roles of liquid–liquid interfaces that we found in solvent extraction kinetics of metal ions is a catalytic effect. Shaking or stirring of the solvent extraction system generates a wide interfacial area or a large speciﬁc interfacial area deﬁned as the interfacial area divided by a bulk phase volume. Metal extractants have a molecular structure which has both hydrophilic and hydrophobic groups. Therefore, they have a property of interfacial adsorptivity much like surfactant molecules. Adsorption of extractant at the liquid–liquid interface can dramatically facilitate the interfacial complexation which has been exploited from our research. 355

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II.

HOW TO STUDY THE INTERFACIAL REACTION IN SOLVENT EXTRACTION KINETICS

A.

Experimental Techniques

In this section we will focus on the methods applicable to the study of interfacial extraction kinetics which were developed in our group.

1. High-Speed Stirring (HSS) Method [4,5] There are several classical methods used to investigate extraction kinetics which include a Lewis cell, single drop method, and rotating disk method [2]. These methods could not measure the extraction rate and interfacial amount of extractant simultaneously. However, for the ﬁrst time the HSS method made this technique possible by a relatively simple principle: when a two-phase system is highly stirred or agitated, the interfacial area is extremely enlarged. With this method, the interfacial area can easily be increased to 500 times larger than that in a standing condition. The ratio of the interfacial area to the volume of the bulk phase, termed as a speciﬁc interfacial area, is a good measure of the contribution of the interfacial phenomena in a whole system. The HSS conditions can produce a high speciﬁc interfacial area. This means that the bulk phase concentration of an adsorbable solute is decreased due to the interfacial adsorption generated by the highspeed stirring. In the HSS method, the concentration depression was successfully measured spectrophotometrically using a teﬂon phase separator and photodiode array spectrometer. The extraction rate can also be measured by this method simultaneously [3]. A schematic drawing of the apparatus is shown in Fig. 1.

2. Centrifugal Liquid Membrane (CLM) Method [9] A high speciﬁc interfacial area and a direct spectroscopic observation of the interface were attained by the centrifugal liquid membrane (CLM) method shown in Fig. 2. A two-phase system of about 100 L in each volume is introduced into a cylindrical glass cell with a diameter of 19 mm. The cell is rotated at a speed of 5000–10,000 rpm. By this procedure, a two-phase liquid membrane with a thickness of 50–100 m is produced inside the cell wall which attains the speciﬁc interfacial area over 100 cm1 . UV/VIS spectrometry, spectroﬂuorometry, and other spectroscopic methods can be used for the measurement of the interfacial species and its concentration as well as those in the thin bulk phases. This is an excellent method for determining interfacial reaction rates on the order of seconds.

3. Two-Phase Stopped Flow Method [6] Stopped ﬂow mixing of organic and aqueous phases is an excellent way to produce dispersion within a few milliseconds. The speciﬁc interfacial area of the dispersion can become as high as 700 cm1 and the interfacial reaction in the dispersed system can be measured by a photodiode array spectrophotometer. A drawback of this method is the limitation of a measurable time, although it depends on the viscosity. After 200 ms, the dispersion system starts to separate, even in a rather viscous solvent like a dodecane. Therefore, rather fast interfacial reactions such as diffusion-rate-limiting reactions are preferable systems to be measured.

Catalytic Effect of the Liquid–Liquid Interface

357

FIG. 1 Schematic drawing of the high-speed stirring (HSS) apparatus. An organic phase separated from the dispersed system by the teﬂon phase separator is continuously circulated through the photodiode array detector.

4. Total Internal Reﬂection Spectrometry By the total internal reﬂection condition at the liquid–liquid interface, one can observe interfacial reaction in the evanescent layer, a very thin layer of a ca. 100 nm thickness. Fluorometry is an effective method for a sensitive detection of interfacial species and their dynamics [10]. Time-resolved laser spectroﬂuorometry is a powerful tool for the elucidation of rapid dynamic phenomena at the interface [11]. Time-resolved total reﬂection ﬂuorometry can be used for the evaluation of rotational relaxation time and the viscosity of the interface [12]. Laser excitation can produce excited states of adsorbed compound. Thus, the triplet–triplet absorption of interfacial species was observed at the interface [13].

FIG. 2 Schematic drawing of the centrifugal liquid membrane (CLM) cell.

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Computational Approach

The molecular dynamics simulation is highly useful in understanding the structure of the liquid–liquid interface, the location and orientation of an adsorbed molecule, and the stability of the molecule at the interface. The heptane–water and toluene–water interfaces were simulated by the use of the DREIDING force ﬁeld on the software of Cerius2 Dynamics and Minimizer modules (MSI, San Diego) [6]. The two-phase systems were constructed from 62 heptane molecules and 500 water molecules or 100 toluene molecules and 500 water molecules in a quadratic prism cell. Each bulk phase was optimized for 500 ps at 300 K under NPT ensemble in advance. The periodic boundary conditions were applied along all three directions. The calculations of the two-phase system were run under NVT ensemble. The dimensions of the cells in the ﬁnal calculations were 23.5 A˚ 22.6 A˚ 52.4 A˚ for the heptane–water system and 24.5 A˚ 24.3 A˚ 55.2 A˚ for the toluene–water system. The timestep was 1 fs in all cases and the simulation almost reached equilibrium after 50 ps. The density vs. distance proﬁle showed a clear interface with a thickness of ca. 10 A˚ in both systems. The result in the heptane–water system is shown in Fig. 3. Interfacial adsorption of an extractant can be simulated by a similar procedure after the introduction of the extractant molecule at the position from where the dynamics will be started. After an MD simulation was performed to obtain the trajectory of the extractant, a molecular mechanics calculation was carried out to evaluate the solute–solvent interaction

FIG. 3 MD simulation of the heptane–water interface. (a) Conﬁguration of solvent molecules in a two-phase cell; (b) density vs. distance proﬁle along the axis from aqueous phase to heptane phase.

Catalytic Effect of the Liquid–Liquid Interface

359

energy of the extractant at various positions. The adsorption energy was calculated as the difference between those in the bulk organic phase and at the interface. The adsorption energies calculated for the transfer process from a bulk phase to the interface well explained the adsorptivities of extractants and complexes observed in experiments.

III.

SOLVENT EXTRACTION KINETICS AND CATALYTIC INTERFACIAL COMPLEXATION

A.

Chelate Extraction Systems

1. n-Alkyl Substituted Dithizone The extraction system which was measured by the HSS method for the ﬁrst time was the extraction kinetics of Ni(II) and Zn(II) with n-alkyl substituted dithizone (HL) [14]. The observed extraction rate constants linearly depended on both concentrations of the metal ion ½M2þ and the dissociated form of the ligand ½L . This seemed to suggest that the rate determining reaction was the aqueous phase complexation which formed a 1 : 1 complex. However, the observed extraction rate constant k 0 was not decreased with the distribution constant KD of the ligands as expected from the aqueous phase mechanism. When the extraction kinetics is governed by the aqueous phase reaction, M2þ þ L ! MLþ

k1 : formation rate constant

ð1Þ

the rate law for the extraction is obtained as

d½M2þ ½M2þ ½HLo ¼ k0 dt ½Hþ

ð2Þ

Thus, the extraction rate constant k 0 is related to k1 and a dissociation constant Ka by k 0 ¼ k1 Ka =KD

ð3Þ

The extraction rate constants for Ni(II) and Zn(II) with n-alkyl substituted dithizone did not obey the above relationship (see Fig. 4). In addition, the calculated value for k1 in the extraction of Zn(II) with dihexyldithizone gave an impossibly large value of 1013 M1 s1 . These experimental results strongly suggested a signiﬁcant contribution of other processes than just the aqueous reaction. On this issue, the HSS method revealed that the dissociated form of the n-alkyl-dithizone did adsorb at the interface generated by vigorous agitation [5]. Therefore, the extraction rate was analyzed by introducing the interfacial reaction þ M2þ þ L i ! MLi

ki : interfacial formation rate constant

ð4Þ

The extraction rate constant in this circumstance is represented by k 0 ¼ k1 þ ki KL0 Ai =V Ka =KD

ð5Þ

where Ai =V refers to the speciﬁc interfacial area. Under the conditions of k1 ki KL0 Ai =V, the above equation is reduced to log k 0 KD =Ka ¼ log ki þ log KL0 Ai =V

ð6Þ

The value of KL0 Ai was determined by the HSS method. The linear relationship of the above equation was determined experimentally and gave log ki ¼ 8:08 for the Zn2þ system and log ki ¼ 5:13 for the Ni2þ system, respectively [4].

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FIG. 4 Dependence of the extraction rate constants, k 0 , of Zn(II) and Ni(II) on the number of carbon atoms in the substitution of n-alkyl dithizones. The solid lines trace the observed values and the broken lines the values predicted from the aqueous mechanism.

From these results, one can understand that the liquid–liquid interface can assist effectively in the interfacial reaction through the adsorption of extractants like a solid catalyst. The whole extraction scheme of the chelate extraction system is represented in Scheme 1. 2. 2-Hydroxy Oxime The second example is the extraction of Ni(II) with 2-hydroxy oxime. 2-Hydroxy oxime including 5-nonylsalicylaldoxime (P50) [15], 2-hydroxy-5-nonylacetophenone oxime (SME529) [16], and 2-hydroxy-5-nonylbenzophenone oxime (LIX65N) [17], are widely used as commercial extractants of Ni(II), Cu(II), and Co(II) in hydrometallurgy. These extractants are adsorbed at the interface even in their neutral forms following the Langmuir isotherm, ½HLi ¼aK 0 ½HLo = a þ K 0 ½HLo

SCHEME 1 Interfacial mechanism in chelate extraction.

ð7Þ

Catalytic Effect of the Liquid–Liquid Interface

361

where ½HLi and ½HLo refer to the concentrations at the interface and organic phase, respectively, a the saturated interfacial concentration, and K 0 the interfacial adsorption constant deﬁned by K 0 ¼ ½HLi =½HLo under the condition of ½HLo ! 0. The reaction between the dissociated form , L , and metal ions at the interface governed the extraction rate. We determined the adsorption constants of the three 2-hydroxyoximes and the complexation rate constants with Ni(II) ion at the interface of heptane–water system by means of the HSS method [15–17]. The measurements were carried out by employing 50 mL for each phase at the stirring speed of 5000 rpm. A linear proportionality between the initial extraction rate and the interfacial concentration of the extractant was conﬁrmed experimentally. The adsorption constant ðK 0 ) of the neutral forms were all in the order of 103 cm and the complexation rate constants of the dissociated form with Ni(II) ion at the interface were in the order of 105 M1 s1 for the three extractants, regardless of the large difference in the distribution constants (log KD ) as listed in Table 1. The complexation rate constants at the heptane–water interface did not seriously differ from those in bulk aqueous solutions. The adsorptivity and the reactivity of the 2-hydroxy oxime were well simulated by — N — OH the MD simulations as shown in Fig. 5 where the polar groups of — OH and — of the adsorbed LIX65N molecule are accommodated in the aqueous phase so as to react with Ni(II) ion in the aqueous phase [18]. This is the reason why the reaction rate constants of Ni(II) at the interface have almost same magnitude as those in aqueous phase. 3. Pyridylazo-Ligand Pyridylazo-ligands (Scheme 2) have widely been used in colorimetric analyses of various metal ions. For example, 1-(2-pyridylazo)-2-naphthol (Hpan) is one of the most wellknown reagents for the colorimetric determination and complexometric titration of metal ions. However, it showed a slow extraction rate for some metal ions including Ni(II) and Pd(II). 2-(5-Bromo-2-pyridylazo)-5-diethylaminophenol (5-Br-PADAP) is a relatively new reagent which is more sensitive than Hpan for Cu(II), Ni(II), Co(II), and Zn(II), giving metal complexes of molar absorptivities in the order of 105 M1 cm1 . In addition, 5-BrPADAP and its complex can readily be extracted into organic solvents. 5-Br-PADAP showed a signiﬁcant adsorption at the interface of heptane–water under high-speed stirring conditions (5000 rpm). At the toluene–water interface, the

TABLE 1 Parameters in the Adsorption and Extraction of Ni(II) with 2-Hydroxy Oxime in Heptane–0.1 M(H,Na)ClO4 at 25 C 2-Hydroxy oxime

pKa

log KD

log a (mol cm2 )

log Ai (cm2 )

log K 0 (cm)

log ki (M1 s1 )

5-Nonylsalicylaldoxime (P50) 2-Hydroxy-5-nonylacetophenone oxime (SME529) 2-Hydroxy-5-nonylbenzophenone oxime (LIX65N)

9.00 9.79

3.36 3.99

9:60 9:70

4.11 4.29

3:34 3:29

4.57 5.11

8.70

5.69

9:76

4.28

2:97

5.14

a: saturated interfacial concentration; Ai : total interfacial area under high-speed stirring of 50 mL org./50 mL aq.: K 0 : adsorption constant in the Langmuir isotherm [15].

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FIG. 5 MD simulation of 2-hydroxy-5-nonylbenzophenone oxime (LIX65N) at the heptane–water interface after 120 ps. Heptane molecules are not shown.

SCHEME 2 Structure of pyridylazo-ligand.

Catalytic Effect of the Liquid–Liquid Interface

363

adsorptivity was signiﬁcantly reduced in contrast to Hpan which did not adsorb at the toluene–water interface at all. By the use of Langmuir isotherm, the adsorption constants of 5-Br-PADAP (HL) at the heptane–water and toluene–water interfaces were obtained as listed in Table 2 [6]. When a heptane solution of 5-Br-PADAP and an aqueous solution of Ni2þ were stirred, the ligand in the organic phase was continuously consumed according to the complexation, but there was no extraction of the complex. The complex formed was completely adsorbed at the interface. On the other hand, in a toluene system the complex was extracted very slowly (Fig. 6). The complexation mechanism in the two solvent systems could be analyzed by taking into account the interfacial adsorption of the ligand. The next equation was derived for the initial rate of the consumption of HLo in the heptane system: V k k 0 K 0 Ai r ¼ d½HLo =dt ¼ þ ½Ni2þ ½HLo V þ K 0 A1 KD V o

ð8Þ

where V refers to the organic phase volume and k and k 0 to the 1 : 1 formation rate constants in a bulk aqueous phase and at the interface, respectively. The value of k ¼ 5:3 102 M1 s1 was determined by a stopped-ﬂow spectrometry in the region where the formation rate was independent of pH. The experimentally obtained kinetic results were well explained by the above equation. The values of k 0 ¼ 3:8 102 M1 s1 for heptane– water and k 0 ¼ 1:8 10 M1 s1 for toluene–water were determined. These results mean that the percentage of the interfacial reaction rate over the total reaction rate was 99.9% in heptane–water and 94.5% in toluene–water in the high-speed stirring condition. The molecular dynamics simulations of the adsorptivities of 5-Br-PADAP at heptane–water and toluene–water interfaces explain the solvent effect on the interfacial complexation. The MD simulation was started by putting one molecule of 5-Br-PADAP at the center of the interface. Figures 7 and 8 show the averaged location of the ligand after 100 ps in the two liquid-liquid systems. In the heptane–water system (Fig. 7), the interfacial region is not ﬁlled with solvent molecules because of poor interaction between water and heptane molecules. The 5-Br-PADAP stayed at the interfacial region almost parallel to the interface during the simulation and the diethylamino group interacted with water molecules. This moiety was preferentially attracted to the interface (or repelled from the heptane phase). Consequently, the 5-Br-PADAP could react with the Ni2þ ion with the same rate constant in the aqueous phase. The interfacial region of the toluene–water system is composed of a mixture of water and toluene molecules as a result of attractive interaction. During the simulation 5-Br-PADAP and solvent molecules moved around the interface. In Fig. 8, 5-Br-PADAP is located near the interface, probably by the attractive interaction

TABLE 2 Distribution Constants and Interfacial Adsorption Constants of 5-Br–PADAP (HL) at 25 C Solvent

K 0 Ai (dm3 )a

aAi (mol)b

log KD

Heptane Toluene

4:4 102 4:3 104

1:7 106 —

3.22 4.78

a b

K 0 ¼ ½HLi =½HLo Ai : total interfacial area (ca. 2 104 cm2 ).

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(a)

(b)

FIG. 6 Measurements of the interfacial adsorptivity and the extraction rate from the absorbance changes of the organic phase by means of the high-speed stirring method. (a) Heptane–water system containing 7:9 106 M 5-Br–PADAP and 1:0 104 M Ni2þ at pH ¼ 5:95 observed at 452 nm for the ligand and 511 nm for the complex; (b) toluene–water system containing 4:8 105 M 5-Br– PADAP and 2:0 103 M Ni2þ at pH ¼ 5:61 observed at 462 nm for the ligand and 524 nm for the complex. L and H correspond to low-speed stirring (200 rpm) and high-speed stirring (5000 rpm), respectively.

with the water phase, although it is surrounded by toluene molecules. It can be expected that the 5-Br-PADAP molecule at the interface can react with Ni2þ ion in the aqueous phase, but the probability is less than that in the heptane–water interface because of the solvation by toluene molecules. Thus, the MD simulation can explain the experimentally observed solvent effects in the interfacial formation rate of Ni(II)-5-Br-PADAP complex as well as the interfacial adsorptivity. B.

Ion-Association Extraction Systems

In the ion-association extraction systems, hydrophobic and interfacially adsorbable ions are encountered very often. Complexes of Fe(II), Cu(II), and Zn(II) with 1,10-phenanthroline (phen) and its hydrophobic derivatives exhibited remarkable interfacial adsorptivity, although the ligands themselves can hardly adsorb at the interface, except for protonated species [19–21]. Solvent extraction photometry of Fe(II) with phen is widely used for the determination of trace amounts of Fe(II). The extraction rate proﬁles of Fe(II) with phen and its dimethyl (DMP) and diphenyl (DPP) derivatives into chloroform are shown in Fig.9. In the presence of 0.1 M NaClO4 , the interfacial adsorption of phen complex is most remarkable. The adsorption of the extractable complex must be considered in the analysis of the extraction kinetic mechanism of these systems. The observed initial rate ro shows the relation ro ¼ kobs ½Fe2þ ½Lo

ð9Þ

Catalytic Effect of the Liquid–Liquid Interface

365

FIG. 7 MD simulation of the adsorption of 5-Br–PADAP at the heptane–water interface after 100 ps.

where kobs refers to the observed extraction rate constant. According to Scheme 3, the initial extraction rate can be described by ðd½FeL3 X2 =dtÞt¼0 ¼ k1 ½Fe2þ ½L þ k10 ½Fe2þ ½Li Ai =Vo k10

where k1 and stand for 1 : 1 formation rate constant of FeL at the interface, respectively. Thus kobs is written as 1 k1 0 Ai kobs ¼ þ k K i L Vo 1 þ KC0 Ai =Vo KD

ð10Þ 2þ

in the aqueous phase and ð11Þ

where KL0 and KC0 refer to the adsorption constants of L and FeL3 X2 from organic phase to the interface, respectively. The values of parameters are listed in the Table 3. The results showed that (1) the rate-determining step was the 1 : 1 complex formation in the aqueous phase and the interface, (2) the extraction rate was lowered by the adsorption of FeL3 X2 , (3) the adsorption of ligand accelerated the extraction (a positive catalytic effect), although the adsorption of the complex apparently suppresses the extraction rate (a negative catalytic effect), and (4) the effects of anion and solvent on the extraction rate can be explained through the change of the adsorption constant KC0 of FeL3 X2 . C.

Synergistic Extraction Systems

When an auxiliary ligand is added to a chelate extraction system and it enhances the extractability and extraction rates, such a phenomenon is termed synergism. A typical

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FIG. 8 100 ps.

MD simulation of the adsorption of 5-Br–PADAP at the toluene–water interface after

synergism has been reported for the Ni(II)–dithizone(Hdz)–phen-chloroform system [22]. The extraction equilibrium constant ðlog Kex Þ was enhanced from 0:7 to 5.3 in the extraction reaction Ni2þ þ 2HDzo þ phen Ð NiDz2 pheno þ 2Hþ

ð12Þ

At the same time, the extraction rate was accelerated by the reactions in the aqueous phase [23], Ni2þ þ phen ! Niphen2þ

k ¼ 6:8 103 M1 s1

Niphen2þ þ Dz ! NiDzphenþ

k ¼ 9:2 104 M1 s1

ð13Þ

and at the interface NiDzphenþ 2 was produced during the extraction as shown in Fig. 10, Niphen2þ þ phen ! Niphen2þ 2

k ¼ 7:4 103 M1 s1

þ Niphen2þ 2 þ Dz ! NiDzphen2

ð14Þ

An interfacially trapped complex ion, most probably NiDzphenþ 2 , showed an interfacial disproportionation reaction, 2þ 2NiDzphenþ 2;i ! NiDz2 pheno þ Niphen3

k ¼ 3:1 103 s1

ð15Þ

The synergistic effect of DPP on the extraction of Ni(II) with dithizone was also studied and conﬁrmed the formation of an interfacial complex [24].

Catalytic Effect of the Liquid–Liquid Interface

367

FIG. 9 Extraction rate proﬁles of the ion-association extraction of Fe(II) with phen and its dimethyl (DMP) and diphenyl (DPP) derivatives into chloroform in the presence of 0.1 M NaClO4 . Effect of stirring (4700 rpm) indicates the interfacial adsorption of the complexes.

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SCHEME 3 Interfacial mechanism in the ion-association extraction of Fe(II) with phen or its derivatives (L) including an anion X.

Synergistic extraction systems include various new types of interesting interfacial reactions. These systems should be studied more extensively.

D.

Design of Interfacial Catalysis in Metal Extraction

1. Catalytic Effect of PADA on the Extraction of Ni(pan)2 From the fundamental knowledge concerning the interfacial complexation mechanism obtained from the kinetic studies on chelate extraction, ion-association extraction, and synergistic extraction, one can design the interfacial catalysis. The main strategy is to raise the concentration of the reactant or intermediate at the interface. The extraction rate of NiðpanÞ2 from toluene is known to be very slow even under a high-speed stirring condition, whereas the addition of PADA even at the diluted concentration as 105 M could accelerate the extraction rate about ten times. At this time, only NiðpanÞ2 was extracted without any consumption of PADA, except a signiﬁcant decrease in the organic phase concentration of PADA during the stirring as shown in Fig. 11. Analyses of the experimental results suggested the interfacial adsorption of the NiðpadaÞ2þ complex was rapidly formed in the aqueous phase. Thus, the catalytic role of PADA could be ascribed to the interfacial ligand-exchange mechanism, k0

þ þ NiðpadaÞ2þ i þ Hpano !NiðpanÞðpadaÞi þ H

ð16Þ

þ NiðpanÞðpadaÞþ i þ Hpano ! NiðpanÞ2;o þ padao þ H

The value of k 0 was obtained as 90 M1 s1 [25]. The whole extraction mechanism is shown in Scheme 4. The key process of the catalytic extraction of the Ni(II)–Hpan–PADA system is the raising of the interfacial concentration of Ni2þ by the facilitated adsorption of NiðpadaÞ2þ .

TABLE 3 Extraction Parameters in the Ion-Association Extraction of Fe(II) with Phen and Its Derivatives Ligand/ CHCl3 Phen Dimethylphen Diphenylphen

Anion (0.1 M)

log KD

ClO 4 ClO 4 ClO 4 Cl SO2 4

2.85 3.62 7.45 7.13 7.14

KC0 Ai (dm3 ) 0.368 0.278 0.00452 0.473 >1

log k1 (M1 s1 )

log k10 (M1 s1 Þ

5.65 5.70 5.52 — 5.32

n.d. 6.36 5.00 4.30 5.19

Catalytic Effect of the Liquid–Liquid Interface

369

FIG. 10 Extraction rate proﬁles of Ni(II) with dithizone and phen in which an interfacially adsorbed intermediate complex is formed.

FIG. 11 Concentration change of Hpan and PADA in the catalytic extraction of NiðpanÞ2 into the toluene phase. Initial concentrations are ½Ni2þ ¼ 1:0 105 M, ½Hpan ¼ 4:0 105 M and ½PADA ¼ 1:7 105 M at pH ¼ 5:6.

SCHEME 4

Catalytic role of PADA in the extraction of Ni(pan)2 .

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MD calculations could simulate the high adsorptivity of the complex ion, affording the adsorption energy from aqueous phase to the interface as 7:4 kcal mol1 . 2. Acid Catalysis in Metal Extraction In general, an acidic condition is not favored for the extraction rate of metal ions, because the dissociation of an extractant is suppressed or a co-ordinating atom in the extractant is protonated. However, we found an interesting phenomenon in the extraction of Pd(II) with 5-Br–PADAP; a lowering of pH accelerated the extraction rate [26]. This phenomenon was ascribed to the interfacial adsorption of the protonated 5-Br–PADAP which accelerated the interfacial complexation. The protonation of 5-Br–PADAP was made at the nitrogen atom of diethylamine, which is a nonco-ordinating atom. Therefore, the interfacial protonation in this system worked so as to increase the interfacial concentration of a reactable ligand. Interfacial reactions in this system are represented by þ PdCl2 þ H2 Lþ i ! PdLClo þ Cl þ 2H

ki1 1:0 103 M1 s1

þ þ PdCl 3 þ H2 Li ! PdLClo þ 2Cl þ 2H

ki2 3:3 102 M1 s1

PdCl 4

ki3 3:2 10 M

þ

H2 L þ i

! PdLClo þ 3Cl þ 2H

þ

2

ð17Þ

1 1

s

This ﬁnding a new type of catalysis will provide a useful hint for the design of molecular structures of interfacially adsorbable and strongly reactive ligands for a speciﬁc metal ion. E.

Analysis of Interfacial Complex by a Time-Resolved Fluorescence Spectroscopy

In the mechanism of an interfacial catalysis, the structure and reactivity of the interfacial complex is very important, as well as those of the ligand itself. Recently, a powerful technique to measure the dynamic property of the interfacial complex was developed; time resolved total reﬂection ﬂuorometry. This technique was applied for the detection of the interfacial complex of Eu(III), which was formed at the evanescent region of the interface when bathophenanthroline sulfate (bps) was added to the Eu(III) with 2-thenoyltrifuluoroacetone (Htta) extraction system [11]. The experimental observation of the double component luminescence decay proﬁle showed the presence of dinuclear complex at the interface as illustrated in Scheme 5. The lifetime (31 s) of the dinuclear complex was much shorter than the lifetime (98 s) for an aqua-Eu(III) ion which has nine co-ordinating water molecules, because of a charge transfer deactivation. Rotational dynamics of a ﬂuorescent dye adsorbed at the interface provides useful information concerning the rigidity of the microenvironment of liquid–liquid interface in terms of the interfacial viscosity. The rotational relaxation time of the rhodamine B dye was studied by time-resolved total internal reﬂection ﬂuorescent anisotropy. In-plane

SCHEME 5 Interfacial formation of dinuclear europium(III) complex.

Catalytic Effect of the Liquid–Liquid Interface TABLE 4 Interface

371

Rotational Relaxation of Octadecylrhodamine B at Toluene–Water

Surfactant

Conc. (M)

No Triton X-100 SDS

— 1:0 106 1:0 107 1:0 106 1:0 107 1:0 106

HDHP

In-plane rotational Interfacial viscosity relaxation time (ns) (Pa s) <1 <1 0.9 5.2 2.7 20.8

— — — 0.023 0.012 0.091

rotational relaxation time of octadecylrhodamine B cation was evaluated under the presence or absence of surfactant [12]. Table 4 shows that by the addition of surfactant both of the relaxation time and the interfacial viscosity were increased. Anionic surfactant, SDS, and HDHP (hydrogen dihexadecylphosphate) were more effective in reducing the rotational motion because of the electrostatic interaction. However, HDHP with double long chains hindered the interfacial rotation [27]. F.

Diffusion-Controlled Interfacial Reaction

An interfacial reaction is accompanied by a diffusion process which provides reactants from the bulk phase to the interface. When the reaction rate is faster than the diffusion rate, the overall reaction has to be governed by the diffusion rate of the reactant. Diffusion, in general, takes place in the stagnant layers (the region on both sides of the interface) and is not disturbed even under the stirring of a bulk region. A typical example is the protonation of tetraphenylporphirin (TPP) at the dodecane– acid solution interface. The interfacial protonation rate was measured by a two-phase stop ﬂow method [6] and a CLM method [9]. In the former method, the stagnant layer of 1:4 m still existed under the highly dispersed system. In the CLM method, the liquid membrane phase of 50–100 m thickness behaved as a stagnant layer where the TPP molecule has to migrate according to its self-diffusion rate. IV.

SUMMARY

The catalytic role of the liquid–liquid interface in the solvent extraction of metal ions described in this chapter and some important remarks on the interfacial phenomena reported in other studies are summarized: 1. 2. 3.

4.

Interfacial adsorption of extractant increases the interfacial concentration, thus accelerating the interfacial complexation and extraction rate. Interfacial formation of labile and charged complexes can facilitate a subsequent substitution reaction to produce an extractable complex. Interfacial accumulation of a ligand or complex greatly increases the two-dimensional interfacial concentration and facilitates the formation of aggregates of those adsorbed compounds [7]. The interfacial region is a layer of nanometer thickness, and adsorption is basically of monomolecular character. Therefore, the interfacial reaction is highly

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5. 6.

7. 8. 9.

affected by the co-adsorption of surfactant. Adsorption, rotation, and translation of a solute at the interface are restricted by the surfactant when the solute is adsorbed from the organic phase side. On the other hand, when the adsorption of an ionic solute is caused by the aqueous phase, it can be effectively controlled by the charge of the surfactant [28]. Interfacial adsorption of ionic solute can be controlled by an external electrical potential [29]. The kinetic solvent effect of the liquid–liquid interface is very sensitive to the location where the adsorbed molecules react [6]. The interfacial solvent effect has to be studied more extensively. The design of the catalytic complexation system will be developed utilizing the fundamental knowledge of the interfacial complexation. The computational approach introduced in our research promises to be very useful in future study. The effort to invent new experimental methods for the measurement of interfacial reaction should be continued.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

P. R. Danesi, in Principles and Practices of Solvent Extraction (J. Rydberg, C. Musikas, and G. R. Choppin, eds.), Marcel Dekker, New York, 1992, pp. 157–207. G. J. Hanna and R. D. Noble. Chem. Rev. 85:583 (1985). H. Watarai. Trends Anal. Chem. 12:313 (1993). H. Watarai and H. Freiser. J. Am. Chem. Soc. 105:189 (1983). H. Watarai and H. Freiser. J. Am. Chem. Soc. 105:191 (1983). H. Watarai, M. Gotoh, and N. Gotoh. Bull. Chem. Soc. Jpn. 70:957 (1997). H. Watarai and Y. Chida. Anal. Sci. 10:105 (1994). H. Watarai and Y. Saitoh. Chem. Lett. 283 (1995). H. Nagatani and H. Watarai. Anal. Chem. 70:2860 (1998). H. Watarai and F. Funaki. Langmuir 12:6717 (1996). M. Fujiwara, S. Tsukahara, and H. Watarai. Phys. Chem. Chem. Phys. 1:2949 (1999). S. Tsukahara, Y. Yamada, T. Hinoue, and H. Watarai. Bunseki/Kagaku 47:945 (1998). S. Tsukahara and H. Watarai. Chem. Lett. 89 (1999). H. Watarai, L. Cunningham, and H. Freiser. Anal. Chem. 54:2390 (1982). H. Watarai and K. Satoh. Langmuir 10:3913 (1994). H. Watarai, M. Takahashi, and K. Shibata. Bull. Chem. Soc. Jpn. 59:3469 (1986). H. Watarai and M. Endo. Anal. Sci. 7:137 (1991). Y. Onoe and H. Watarai. Anal. Sci. 14:237 (1998). H. Watarai. J. Phys. Chem. 89:384 (1985). H. Watarai. Talanta 32:817 (1985). H. Watarai and Y. Shibuya. Bull. Chem. Soc. Jpn. 62:3446 (1989). B. Freiser and H. Freiser. Talanta 17:540 (1970). H. Watarai, K. Sasaki, K. Takahashi, and J. Murakami. Talanta 42:1691 (1995). H. Watarai, K. Takahashi, and J. Murakami. Solv. Extr. Res. Develop. Jpn. 3:109 (1996). Y. Onoe, S. Tsukahara, and H. Watarai. Bull. Chem. Soc. Jpn. 71:603 (1998). A. Ohashi, S. Tsukahara, and H. Watarai. Anal. Chim. Acta 364:53 (1998). S. Tsukahara, Y. Yamada, and H. Watarai. Langmuir (in press). Y. Saitoh and H. Watarai. Bull. Chem. Soc. Jpn. 70:351 (1997). R. Okumura, T. Hinoue, and H. Watarai. Anal. Sci. 12:393 (1996).

15 Voltammetry at Micro-ITIES BIAO LIU and MICHAEL V. MIRKIN Department of Chemistry and Biochemistry, City University of New York, Queens College, Flushing, New York

I.

INTRODUCTION

Heterogeneous charge transfer (CT) reactions at the interface between two immiscible electrolyte solutions (ITIES), i.e., electron transfer (ET), and simple and facilitated ion transfers (IT), are of fundamental importance for many biological and technological systems. During the last two decades, electrochemical methods have been extensively used to probe the thermodynamics and kinetics of these processes [1]. The charge transfer rates at the ITIES are often very fast and hard to measure. Measurements of fast kinetics at larger ITIES are prone to errors due to the uncompensated resistive drop (iR-drop) and charging current. In 1986, Taylor and Girault introduced a micrometer-sized liquid–liquid interface supported at the tip of a pulled glass micropipette [2]. Later, Girault’s group developed another approach to micro-ITIES fabrication by making a microhole in a thin inert membrane using a UV laser photoablation technique [3a]. While the shape of a micropipette and the small size of its tip are most suitable for sensor applications (see Sections IV.D and IV.E below), the higher symmetry of a microhole simpliﬁes theoretical analysis of steady-state voltammetric measurements. During the next decade, several research groups reported voltammetric studies of CT processes at the micro-ITIES [3–8]. Compared to large ITIES, a micro-ITIES has a number of advantages typical of ultramicroelectrodes (UMEs), i.e., the absence of the limitations caused by the charging current and iR-drop, relative simplicity of data analysis, and high mass-transfer rate essential for fast kinetic measurements. Because of a much lower ohmic drop, one can carry out electrochemical measurements at a micro-ITIES with low (or zero) concentrations of supporting electrolytes [3e]. This helps to alleviate the ionpairing effect on charge transfer reactions. The possibilities of sensor applications of micro-ITIES have also been explored [4]. A micro-ITIES is usually formed either at the tip of a pulled glass micropipette (the tip radius, r, is typically a few microns or smaller) or within a small hole made in a thin membrane [2,3]. Unlike metal UMEs, small pipettes or microholes are easy to make. Pipettes as small as a few nanometers radius have recently been prepared using a laser micropipette puller [8a,9]. Dual-pipette electrodes (or -pipettes) can also be produced by pulling borosilicate -tubing [10,11]. The resulting device consists of two micrometer- or submicrometer-sized pipettes separated by a submicrometer-thick band of glass. Cunnane et al. developed a simple method for forming micro-ITIES in a microcavity created by the chemical dissolution of a glass–encapsulated microwire [6]. 373

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In this chapter our focus is on principles, theory, and applications of micro-ITIES to quantitative voltammetric measurements of CT processes and ionic reactions in solution. The questions of characterization of the interfacial geometry and surrounding insulator, which are essential for both kinetic measurements and analytical applications of microITIES, will also be discussed.

II.

THEORY

Most electrochemical studies at the micro-ITIES were focused on ion transfer processes. Simple ion transfer reactions at the micropipette are characterized by an asymmetrical diffusion ﬁeld. The transfer of ions out of the pipette (ejection) is controlled by essentially linear diffusion inside its narrow shaft, whereas the transfer into the pipette (injection) produces a spherical diffusion ﬁeld in the external solution. In contrast, the diffusion ﬁeld at a microhole-supported ITIES is approximately symmetrical. Thus, the theoretical descriptions for these two types of micro-ITIES are somewhat different. A.

Microholes

In a typical voltammetric experiment, a constant voltage or a slow potential sweep is applied across the ITIES formed in a micrometer-size oriﬁce. If this voltage is sufﬁciently large to drive some IT (or ET) reaction, a steady-state current response can be observed (Fig. 1) [12]. The diffusion-limited current to a micro-ITIES surrounded by a thick insulating sheath is equivalent to that at an inlaid microdisk electrode, i.e.,

FIG. 1 Cyclic voltammogram of acetylcholine cation transfer from water to DCE. The liquid– liquid interface was supported at a 20 m-diameter hole formed in the 12 m-thick polyester ﬁlm. The sweep rate was 10 mV/s. (Reprinted with permission from Ref. 3a. Copyright 1989 Elsevier Science S.A.)

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id ¼ 4zFDcr

375

ð1Þ

where c and D are the concentration and diffusion coefﬁcient of species responsible for the interfacial charge transfer reaction, F is the Faraday constant, z is the transferred charge, and r is the microhole radius. Thus the theory developed for microdisk electrodes can be extended to CT processes at a microhole-supported ITIES. The shape of steady-state voltammograms depends strongly on the geometry of the microhole [13,14]. Wilke and Zerihun presented a model to describe diffusion-controlled IT through a microhole [15]. In that model, a cylindrical microhole is assumed to be ﬁlled with the organic phase, so that a planar liquid–liquid interface is located at the aqueous phase side of the membrane. Assuming that the diffusion is linear inside the cylindrical pore and spherical outside [Fig. 2(a)], the expression for the steady-state IT voltammogram is RT w o ’1=2 w 1 þ exp ’ ð2Þ i ¼ id o zF w Where w o ’ is the applied interfacial voltage and o ’1=2 is the half-wave potential of the IT reaction.

FIG. 2 Schematic representation of different microhole geometries. (a) Recessed microdisk interface, spherical–linear, linear–spherical diffusion. (b) quasi-inlaid microdisk interface, spherical–spherical diffusion. (c) Long microhole with quasi-inlaid interface, spherical–linear diffusion. (Reprinted with permission from Ref. 13. Copyright 1999 Elsevier Science S.A.)

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The dependence of the half-wave potential on the geometrical parameters RT D w o RT 4d w w ln ln þ1 þ o ’1=2 ¼ o ’ þ D o w zF zF r

ð3Þ

where Dw and Do are the diffusion coefﬁcients in the aqueous and organic phase, o and w are the activity coefﬁcients in organic and aqueous solutions, respectively, w o ’ is the standard IT potential, and d is the thickness of the membrane, can be used to characterize the mass transfer within the microhole. When the membrane is very thin [d ! 0, Fig. 2(b)], the planar diffusion inside the hole becomes fast, and the last term in Eq. (3) can be neglected: RT D w o w w ln o ’1=2 ¼ o ’ þ ð4Þ zF D o w Josserand et al. [13] considered a more general situation where the interface is located inside the hole at distance dw and do from respective bulk phases, so that the thickness of the ﬁlm is d ¼ dw þ do [Fig. 2(a)]. In this case, the half-wave potential is RT Dw do þ r=4 w 0 ln w ’ ¼ ’ þ ð5Þ o 1=2 o zF Do dw þ r=4 The theory has been veriﬁed by voltammetric measurements using different hole diameters and by electrochemical simulations [13,15]. The plot of the half-wave potential versus log½ð4d=rÞ þ 1 yielded a straight line with a slope of 60 mV (Fig. 3), but the experimental points deviated from the theory for small radii. Equations (3) to (5) show that the half-wave potential depends on the hole radius, the ﬁlm thickness, the interface position within the hole, and the diffusion coefﬁcient values. When do is rather large or the diffusion coefﬁcient in the organic phase is very low, steady-state diffusion in the organic phase cannot be achieved because of the linear diffusion ﬁeld within the microcylinder [Fig. 2(c)]. Although no analytical solution has been reported for non-steady-state IT across the microhole, the simulations reported in Ref. 13 showed that the diffusion ﬁeld is asymmetrical, and concentration proﬁles are similar to those in micropipettes (see

FIG. 3 Effect of the hole radius on the half-wave potential for a quasi-inlaid geometry [Fig. 2(c)]. The depth of the microhole is 12 m. (Reprinted with permission from Ref. 13. Copyright 1999 Elsevier Science S.A.)

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Section II.B). The peak-shaped voltammograms are observed at higher scan rates because the ions do not have enough time to diffuse from the pore into the bulk organic solution. The lower Do and larger the do =r ratio, the lower the minimum scan rate value at which voltammograms become peak-shaped and the half-wave potential begins to vary with the scan rate. The concentration of the transferred ion in organic solution inside the pore can become much higher than its concentration in the bulk aqueous phase [15]. (This is likely to happen if r d.) In this case, the transferred ion may react with an oppositely charged ion from the supporting electrolyte to form a precipitate that can plug the microhole. This may be one of the reasons why steady-state measurements at the microhole-supported ITIES are typically not very accurate and reproducible [16]. Another problem with microhole voltammetry is that the exact location of the interface within the hole is unknown. The uncertainty of dw and do values affects the reliability of the evaluation of the formal transfer potential from Eq. (5). The latter value is essential for the quantitative analysis of IT kinetics [17]. Because of the above problems no quantitative kinetic measurements employing microhole ITIES have been reported to date and the theory for kinetically controlled CT reactions has yet to be developed.

B.

Micropipettes

The mathematical formulations of the diffusion problems for a micropippette and metal microdisk electrodes are quite similar when the CT process is governed by essentially spherical diffusion in the outer solution. The voltammograms in this case follow the well-known equation of the reversible steady-state wave [Eq. (2)]. However, the peakshaped, non-steady-state voltammograms are obtained when the overall CT rate is controlled by linear diffusion inside the pipette (Fig. 4) [3].

FIG. 4 Cyclic voltammogram of the ion transfer between the aqueous solution inside a 15 mmradius pipette and the external DCE solution of TEAþ (60 M). (Reprinted with permission from Ref. 18a. Copyright 1990 Elsevier Science S.A.)

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Assuming that the oriﬁce is disk-shaped, one can calculate the steady-state diffusionlimiting current to a pipette from Eq. (1). However, current values about three times higher than expected from Eq. (1) were measured for interfacial IT [18] and ET [5]. The following empirical equation for the limiting current at a pipette electrode was proposed [18b]: Ipip ¼ AzFDcr

ð6Þ

and the empirical factor A was found to be 3:35. The large difference between this value and the factor 4 in Eq. (1) can be partially attributed to a small amount of the ﬁlling aqueous solution which escapes from the pipette and forms a thin layer on its outer wall. The effective area of the ITIES gets much larger than geometrical area of the pipette oriﬁce, hence a signiﬁcant increase in the diffusion current [19]. This effect can be eliminated by making the outer pipette wall hydrophobic (see Section III.B). Another factor contributing to the diffusion current to a pipette oriﬁce is the additional ﬂux from the back of the pipette due to small thickness of its wall (this may account for 40% increase in the diffusion-limiting current [20]). Equation (1) is suitable only for a disk surrounded by a fairly thick insulating sheath, e.g., RG > 10 (RG ¼ rg =r, where rg is the radius of the glass insulator). The diffusion current to a microdisk signiﬁcantly increases when the insulating sheath thickness is reduced [20]. The correction for the ﬁnite insulator thickness can be introduced by substituting a suitable value of the factor A from Table 1 into Eq. (6). No steady-state theory for kinetically controlled heterogeneous IT has been developed for micropipettes. However, for a thin-wall pipette (e.g., RG 2) the micro-ITIES is essentially uniformly accessible. When CT occurs via a one-step ﬁrst-order heterogeneous reaction governed by Butler–Volmer equation, the steady-state voltammetric response can be calculated as [8a] i¼

id

þ 1=

ð7Þ 0

0

w w w where ¼ 1 þ exp½ðw o ’ o ’ ÞzF=RT Do =Dw , and ¼ exp½ðo ’ o ’ ÞF=RT xk =m, k and are the standard rate constant and the transfer coefﬁcient, respectively, and m ¼ AD=r is the effective mass transfer coefﬁcient. The value of the factor A depends on RG (Table 1). A similar kinetic equation derived from a microdisk electrode [21] should be more suitable for thick-wall pipettes (i.e., RG 1). For more complicated CT mechanisms appropriate kinetic equations can be adapted from the theory developed for microelectrodes [22].

TABLE 1 Factor A from Eq. (6) for Different RG values [20c,30] RG

A

1.1 1.5 2.0 3.0 5.1 10.0

5.14 4.64 4.43 4.27 4.15 4.06

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The egress of ions from the pipette results in peak-shaped voltammograms, as shown in Fig. 4. As in classical linear sweep voltammetry, the peak current is proportional to the square root of scan rate, according to Randles–Sevc˘ik equation. The shape of voltammograms is similar to those obtained at a large ITIES, and it was concluded that the IT out of the pipette is controlled by semi-inﬁnite linear diffusion [18]. Stewart et al. [18a] obtained a pseudoanalytical expression (including a tabulated function) for the entire cyclic voltammogram of simple IT at a micropipette. However, quantitative analysis of non-steadystate voltammetric data may be problematic because the geometry of the pipette’s inside is not strictly linear.

C.

Dual-Pipette Electrodes

An electrochemical generation–collection (G/C) technique based on the use of -pipettes was recently developed for studying heterogeneous IT reactions and homogeneous chemical reactions of ionic species in solution [10,11]. This technique allows quantitative separation of different charge transfer processes simultaneously occurring at the liquid– liquid interface (e.g., simple transfer of potassium, facilitated transfer of the same ion with a crown ether and IT of supporting electrolyte). Such parallel processes often impair the studies of charge transfers at the liquid–liquid interface [17]. Another advantage of this technique is the possibility to overcome potential window limitations and study numerous important reactions occurring at high positive or negative potentials (e.g., transfers of alkali metals from water to organic media). In a typical generation–collection experiment, two barrels of the -pipette are ﬁlled with water [10,11]. If one of the barrels (‘‘generator’’) contains a cation, it can be transferred to the outer organic solvent by biasing this pipette at a sufﬁciently positive potential (Eg ). A signiﬁcant fraction of ejected cations reaches the negatively biased second pipette (‘‘collector’’) and gets transferred back into the aqueous phase [Fig. 5(a)]. When only one

FIG. 5 Probing ionic reactions with a dual-pipette device. (a) Simple transfer of a cation; (b) and (c) IT is followed by a chemical reaction in solution. (b) The reaction product is not transferred into the collector pipette. (c) Both the cation and the reaction product are collected. (Reprinted with permission from Ref. 10. Copyright 1998 American Chemical Society.)

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IT process occurs at a generator pipette and the transferred species do not participate in any homogeneous reaction, the collection efﬁciency, , is essentially independent of Eg [10]. In this case is determined by collector potential and device geometry and independent of ig . Thus one can measure the maximum value of ðmax ) when all ions reaching the opening of the collector pipette are transferred into it. max is a constant characteristic for a given -pipette. Consequently, it is possible to reconstruct the generator voltammogram from an ic vs. Eg dependence. For an uncomplicated IT reaction with diffusion-controlled collection, the generator current at any Eg can be calculated as ig ¼ ic =max

ð8Þ

This procedure is useful for more-complicated processes in which more than one IT reaction contribute to the ig , and the analysis of generator voltammograms is difﬁcult. If only one kind of ions is collected, Eq. (8) gives the component of the ig produced by transfer of this ion. If some species contained in the outer solution (‘‘ligand’’) can react with an ion ejected from the generator pipette, such a reaction affects the collection efﬁciency. Two possibilities are outlined in Figs. 5(b) and 5(c). In Fig. 5(b), the reaction product does not contribute to the collector current (i.e., either this product cannot be transferred into water or its diffusion coefﬁcient is too small; ion binding to high molecular weight DNA is a typical example of the latter). Hence the collection efﬁciency decreases with increasing rate of ion complexation. If the product of chemical reaction is transferred to water [Fig. 5(c)], the collector voltammogram consists of the product and cation transfer waves occurring at different potentials. This technique is promising for kinetic studies of fast homogeneous reactions involving ionic reactants or intermediates. Unlike single-barrel pipettes whose oriﬁce is typically disk-shaped, the apertures of a dual pipette look like two halves of an ellipse separated by a very thin line of glass. An advantage of such a geometry compared to a more symmetrical group of two coplanar disks is a somewhat higher collection efﬁciency [11,23]. For a diffusion-limited process, the theoretical value of max for two coplanar disks is about 40% [23], whereas 50% was obtained experimentally for -pipettes [11]. However, simulating mass transfer in such a system is challenging, and no exact theory is currently available for -pipettes. In the absence of chemical reactions in solution, max depends only on the normalized distance between the centers of the disks (d=r, where d is the center-to-center separation). The theory developed for two identical coplanar disks gives the following approximation (valid at d=r 2) [23]: max 21 ðd=rÞ1

ð9Þ

In the case of -pipettes, the collection efﬁciency also decreases markedly with increasing separation. The situation becomes more complicated when the transferred ion participates in a homogeneous chemical reaction. For the pseudo-ﬁrst-order reaction a semiquantitative description is given by the family of dimensionless working curves calculated for two disks (Fig. 6) [23]. Clearly, at any separation distance the collection efﬁciency approaches zero when the dimensionless rate constant ( ¼ 2kr2 =D, where k is the ﬁrst-order rate constant of the homogeneous ionic reaction) becomes 1:

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FIG. 6 The collection efﬁciency for the two coplanar disk conﬁguration as a function of the normalized center-to-center distance, d=r ¼ ðaÞ 2, (b) 2.1, (c) 2.3, (d) 2.5, (e) 2.8, (f) 3, (g) 3.5, (h) 4, (i) 5, and (j) 6. Solid curves show the results of numerical calculations. The symbols (*) indicate the ¼ 0 limit. Dashed curves show the large-d approximation. (Reprinted with permission from Ref. 23. Copyright 1997 Elsevier Science S.A.)

III.

CHARACTERIZATION AND SURFACE TREATMENT OF PIPETTES

A.

Characterization of Micro-ITIES

The use of micropipette electrodes for quantitative voltammetric measurements of ion transfer (IT) and electron transfer (ET) reactions at the ITIES requires knowledge of geometry of the liquid interface. For the micrometer-sized micropipettes, both the oriﬁce radius and the thickness of the pipette wall can be measured microscopically. A typical error of the microscopic determination of a radius was estimated to be 0:5 m for a micropipette and 1 m for a microhole [24]. Unlike solid electrodes, the shape of the ITIES can be varied by application of an external pressure to the pipette. The shape of the meniscus formed at the pipette tip was studied in situ by video microscopy under controlled pressure [19]. When a negative pressure was applied, the ITIES shape was concave. As expected from the theory [25a], the diffusion current to a recessed ITIES was lower than in absence of negative external pressure. When a positive pressure was applied to the pipette, the solution meniscus became convex, and the diffusion current increased. The diffusion-limiting current increased with increasing height of the spherical segment (up to the complete sphere), as the theory predicts [25b]. Importantly, with no external pressure applied to the pipette, the micro-ITIES was found to be essentially ﬂat. This observation was corroborated by numerous experiments performed with different concentrations of dissolved species and different pipette radii [19]. The measured diffusion current to such an interface agrees quantitatively with Eq. (6) if the outer pipette wall is silanized (see next section). The effective radius of a pipette can be calculated from Eq. (6) and compared to the value found microscopically [19].

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The radius and shape of the solution meniscus and the thickness of the glass wall can also be evaluated from SECM measurements, in which a pipette can be used as a scanning microprobe (see Section IV.D). Another parameter essential for quantitative applications of micropipettes is the internal ohmic resistance, R. It is largely determined by the solution resistance inside the narrow shaft of the pipette, and can be minimized by producing short (patch-type) pipettes. The micropipette resistance has been evaluated from AC impedance measurements. Beattie et al. measured the resistance of micropipettes ﬁlled with aqueous KCl solutions (0.01, 0.1, and 1 M) [18b]. The value obtained for a 3:5 m-radius pipette was within the range from 104 to 106 . As expected, the tip resistance was inversely proportional to the concentration of KCl in the ﬁlling solution. In ref. 18b, the effect of pipette radius on the tip resistance was evaluated using a constant concentration of KCl. The pipette resistance varied inversely with the tip radius. The iR drop was found to be 4.5– 8 mV for the pipette radii of 0.6 to 19 m when 10 mM KCl was used. The evaluation of R is even more important when the pipette is ﬁlled with a resistive organic solvent. From impedance measurements, the resistance of a typical 10 m-radius pipette ﬁlled with DCE and containing 0.01 M supporting electrolyte was found to be about 10 M. Such a resistance produces 15 mV iR drop when 0.5 mM TEAþ is transferred into the pipette from the external aqueous solution. The resistance is approximately inversely proportional to the pipette radius [19]. The iR drop can be minimized by using higher concentrations of supporting electrolyte inside a pipette, but the resistance may not be strictly proportional to 1=celectrolyte (as was observed in water [8a,18b]) because of ion pairing, and the potential window gets narrower with increasing celectrolyte . B.

Silanization of Micropipettes

The silanization of the surface of a glass pipette may be necessary for different reasons [19]. If the pipette is to be ﬁlled with an aqueous solution, its outer wall should be made hydrophobic to prevent the formation of a thin aqueous ﬁlm that may cause large deviations of the experimental diffusion-limiting current from the theory (see Section II.B). Experimental voltammograms were found to quantitatively agree with the theory after the aqueous layer was eliminated by silanizing the outer pipette wall. The outer wall of a pipette can be silanized by immersing the pipette into a solution of trimethylchlorosilane. For experiments with water-ﬁlled pipettes, it is crucial to avoid silanization of the inner wall because the outer organic solvent is drawn inside a pipette if its inner surface is hydrophobic. Thus the ﬂow of argon should pass through the pipette from the back while its tip is immersed in a solution of trimethylchlorosilane. In experiments with dual-pipette electrodes, the purpose of silanizing the outer glass wall is to prevent the formation of an aqueous ﬁlm between the two pipettes and mixing of the ﬁlling solutions. The procedure is similar to the above except that argon should be passed through both barrels of the pipette. When one needs to put an organic solvent inside a pipette, its inner wall has to be silanized to render it hydrophobic. This can be done by putting the back of the pipette in a solution of trimethylchlorosilane, which penetrates inside the pipette, and then pushing it toward the tip by a syringe from the back. The solution is removed from the pipette in about 30 min with a syringe, and the silanized pipette is allowed to dry in the air overnight. The silanization of the inner surface can also be effected by dipping the pipette tip into trimethylchlorosilane. In this case, both the inner and the outer walls become silanized. However, voltammetric responses of organic-ﬁlled pipettes silanized by these two

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approaches were practically identical [19]. To ensure proper silanization, voltammetric responses of both water-ﬁlled and organic-ﬁlled pipettes should be checked and should quantitatively agree with the theory. C.

Ultrasmall Pipettes

Since the mass-transfer coefﬁcient at a micropipette is inversely proportional to its radius, the smaller the pipette the faster heterogeneous rate constants can be measured. Micrometer-sized pipettes are too large to probe rapid CT reactions at the ITIES. Such measurements require smaller (nm-sized) pipettes. Nanopipettes are also potentially useful as SECM tips (see Section IV.D) because they can greatly improve spatial resolution of that technique. The fabrication of nanopipettes was made possible by the use of a microprocessor-controlled laser pipette puller capable of puling quartz capillaries [26]. Using this technique, Wei et al. produced nanopipettes as small as 20 nm tip radius and employed them in amperometric experiments [9]. Even smaller pipettes, down to 3 nm radius, were used to measure facilitated IT kinetics [8a]. Unlike micrometer–sized pipettes, the size and shape of a nanometer-radius ITIES cannot be evaluated by optical microscopy. Thus, a thorough electrochemical characterization of nanopipettes is required. Another problem is a higher internal resistance, which increases with decreasing radius and can become as high as 100 M [8a]. A pulling program was developed to produce short (patch-type) pipettes in order to minimize the resistive potential drop inside the narrow shaft. The effective radius values were obtained from Eq. (6) with A ¼ 3:3. The ohmic solution resistance was measured for a broad range of pipette radii (4 nm to 20 m radius). The measured resistances provided an independent estimate for pipette radius. For micrometer-sized pipettes, the dependence of R on the pipette radius was in a good agreement with the previous results [18b,24]. For nanopipettes the measured resistance was somewhat less than expected, probably because of the shorter length of the narrow shaft. The resistance was always inversely proportional to cKCl inside the pipette. At higher concentrations of KCl (i.e., 25 and 100 mM), the maximum iR drop corresponding to the limiting current was signiﬁcantly less than 1 mV. For all nanopipettes, the IR drop was found to be smaller than 2 mV within the range of concentration of supporting electrolyte (0.01–0.1 M KCl) [8a]. D.

Dual Pipettes

A -pipette consists of two micrometer- or submicrometer-sized pipettes separated by a submicrometer-thick band of glass. It can be made from borosilicate -tubing (OD ¼ 1:5 mm, Sutter Instrument Co.) using a Sutter Model P-2000 laser-based puller[10]. The shape of a pulled -pipette is determined by choice of laser puller parameter values. These values are speciﬁc for a given puller, i.e., two different pullers of the same type (e.g., P-2000) may require signiﬁcantly different programs to produce similar pipettes. Moreover, the performance of each puller changes slightly with time, so the pulling program has to be modiﬁed. A proper choice of pulling parameters yields two very similar closely spaced oriﬁces. Unless there is a special need for two halves of the -pipette to be different, the similarity of the two radii is advantageous because the symmetry of the device can somewhat simplify the data analysis. As with single pipettes, the internal resistance is largely determined by the length of the narrow shaft leading to the oriﬁce [8a,18a], and thus the short (patch-type) pipettes are preferable for voltammetric experiments. The pipettes can be ﬁlled with either aqueous or organic solutions from the back

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using a microsyringe (10 to 25 L). Either the outer or the inner glass wall can be silanized, as described above. The radii of both oriﬁces can be either on a micrometer or a submicrometer scale. If the device is micrometer-sized, it can be characterized by optical microscopy. The purposes of electrochemical characterization of a dual pipette are to determine the effective radii and to check that each of two barrels can be independently polarized. The radius of each oriﬁce can be evaluated from an IT voltammogram obtained at one pipette while the second one is disconnected. After the outer surface of glass is silanized, the diffusionlimiting current to each water-ﬁlled barrel follows Eq. (1). The effective radius values calculated from that equation for both halves of the -pipette must be close to the values found from optical microscopy. Without adequate silanization, an aqueous ﬁlm can short-circuit the -pipette by linking its two halves. In the absence of a surface aqueous layer the currents ﬂow between each of two pipettes and the external reference electrode. In contrast, when the liquid ﬁlm connects two oriﬁces, the current ﬂows directly from one barrel to the other. Two experiments allowing the distinction between these two cases were carried out using a wellcharacterized reaction of potassium transfer from water into DCE facilitated by dibenzo-18-crown-6 (DB18C6) [11] Kþ ðwÞ þ DB18C6 ðDCEÞ ! ½Kþ DB18C6 ðDCEÞ

(generator pipette)

ð10aÞ

½Kþ DB18C6 ðDCEÞ ! Kþ ðwÞ þ DB18C6 ðDCEÞ

(collector pipette)

ð10bÞ

The generator and collector pipettes were as follows (Cell 1): Ag=AgTPBCl=x mM DB18C6 þ 10 mM TBATPBCl outer DCE solution

==

20 mM KCl=Ag Cl=Ag generator pipette ðCell 1Þ

Ag=AgTPBCl=x mM DB18C6 þ mM TBATPBCl

== 10 mM MgCl2 =AgCl=Ag

outer DCE solution

collector pipette

Both pipettes were initially biased at the same potential (with respect to the external reference) at which no appreciable current ﬂows at either pipette. Then the potential of the generator pipette (Eg ) was scanned in a positive direction to induce ejection of potassium ions, while the collector potential (Ec ) was kept constant. In the absence of aqueous surface layer the steady-state generator [curve 1 in Fig. 7(a)] and collector (curve 2) voltammograms were obtained. In contrast, with the water ﬁlm linking two oriﬁces, the positive (generator) and negative (collector) currents of exactly same magnitude were observed in an analogous experiment [Fig. 7(b)]. Both current-voltage curves in Fig. 7(b) are linear because the current is controlled by resistance between two Ag=AgCl electrodes rather than by the interfacial IT rate, and a large current magnitude is due to the ﬂow of supporting electrolyte between two pipettes. The resistance of the aqueous ﬁlm was estimated to be about 50 M, which indicates that the layer is only a few nanometers thick. Another way to detect the short-circuit is by sweeping the potential of one of the pipettes while the second pipette is disconnected from the potentiostat. When the surface ﬁlm is present, the voltammograms obtained in this way are practically identical for both pipettes. This can be expected because both curves are produced by IT across the same interface (i.e., the interface between the aqueous ﬁlm and DCE) and the ﬁlling solutions in

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FIG. 7 (a) Generator (1) and collector (2) voltammograms of the transfer of Kþ between water and DCE containing DB18C6. (b) ig vs. Eg and ic vs. Eg curves obtained with an aqueous ﬁlm linking two barrels of the -pipette. Ec was: (a) 0.25 and (b) 0.1 V vs. AgTPBCl. DCE contained 1 mM DB18C6. In (b), the collector pipette contained 10 mM LiCl instead of MgCl2 . Generator potential was swept at (a) 20 and (b) 100 mV/s. For other parameters see Cell 1. (Reprinted with permission from Ref. 11. Copyright 2000 American Chemical Society.)

two barrels are mixed. In contrast, when no aqueous ﬁlm is present on the outer pipette wall, the collector voltammogram is ﬂat and featureless because this pipette contains no transferable ion.)

IV.

APPLICATIONS

A.

Ion Transfer Reactions

Steady-state voltammetry at metal ultramicroelectrodes has been used extensively to measure rapid heterogeneous ET kinetics [21,27]. The developed methodologies are applicable to charge transfer reactions at micro-ITIES. Assuming that the potential dependence of the rate constant follows Butler–Volmer equation [7,17,18b,24], quasireversible steadystate voltammograms can be calculated from Eq. (7). If one assumes that the rate-determining step is slow diffusion through the boundary layer, Eq. (7) can be easily modiﬁed by substituting an appropriate expression for the effective rate constant [28]. Girault et al. employed steady-state voltammetry and impedance spectroscopy to study the kinetics of simple IT (e.g., transfer of TMAþ from water to DCE) and facilitated transfer of potassium by DB18C6 at micro-ITIES [18b, 24]. In both cases, the standard

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apparent rate constant was too high to be measured with micrometer-sized pipettes (r 0:6 m). The lower limit for the standard rate constant for the latter reaction was estimated to be 3 cm/s assuming that the micropipette tip-supported ITIES is hemispherically shaped [18b]. To increase the mass transfer rate, Tokuda et al. [7] carried out normal and differential pulse voltammetry at micropipettes and extracted the rate constant values within the range from 0.009 to 0.2 cm=s for facilitated transfers of Liþ , Naþ , Ca2þ , Sr2þ , and Ba2þ to nitrobenzene (NB) with two different crown ethers (DB18C6 and DB24C8). The assumption of ¼ 0:5 for all IT reactions and the use of iR-drop compensation may have affected the accuracy of those results. The upper limit for the measurable rate constant was about 0.5 cm/s, too slow to probe facilitated transfer of potassium ions. It was shown later that a mass transfer rate sufﬁciently high to measure the rate constant of potassium transfer [reaction (10a)] under steady-state conditions can be obtained using nanometer-sized pipettes (r 250 nm) [8a]. Assuming uniform accessibility of the ITIES, the standard rate constant (k ) and transfer coefﬁcient () were found by ﬁtting the experimental data to Eq. (7) (Fig. 8). (Alternatively, the kinetic parameters of the interfacial reaction can be evaluated by the three-point method, i.e., the half-wave potential, E1=2 , and two quartile potentials, E1=4 and E3=4 [8a,27].) A number of voltammograms obtained at 5–250 nm pipettes yielded similar values of kinetic parameters, ko ¼ 1:3 0:6 cm/s, and ¼ 0:4 0:1. Importantly, no apparent correlation was found between the measured rate constant and the pipette size. The mass transfer coefﬁcient for a 10 nm-radius pipette is 10 cm=s (assuming D ¼ 105 cm2 =s). Thus the upper limit for the determinable heterogeneous rate constant is at least 50 cm/s. Alternatively, a higher rate of mass transport in steady-state measurements with a larger UME can be obtained by using it as a tip in the scanning electrochemical microscope (SECM). The SECM has typically been employed for probing interfacial ET reactions [29]. Recently, micropipettes have been used as SECM probes (see Section IV.B below) [8b,30]. Although the possibility of probing simple and assisted IT at ITIES by this technique was demonstrated, no actual kinetic measurements have yet been reported.

FIG. 8 Background-subtracted steady-state voltammograms of transfer of Kþ from water to DCE at 54 nm nanopipette electrodes facilitated by DB18C6. DCE contained 0.25 mM DB18C6 and 10 mM TBATBCl; cKCl was 100 mM. Solid lines show the best theoretical ﬁt. Sweep rate was 20 mV/s. The inset shows the original voltammogram before subtraction (curve 1) and the background current (curve 2). (Reprinted with permission from Ref. 8a. Copyright 1997 American Chemical Society.)

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The studies of IT reactions are often complicated by potential window limitations [17]. For example, the transfer of alkali metals to organic solvents occur at very positive w o ’. Studying kinetics of these important reactions is hard because of the interfering transfer of organic anions into the aqueous phase. Such concurrent IT reactions can be probed independently using the dual-pipette setup [11]. In Fig. 9, the simple transfer of potassium from water to DCE occurs at a positively biased generator pipette simultaneously with the transfer of TPBCl into the aqueous ﬁlling solution. Unlike the generator voltammogram (curve 1 in Fig. 9), which is produced by two different IT reactions and consequently is hard to analyze, a collection voltammogram (curve 2) is only due to the transfer of Kþ from DCE to water. The ﬂux of Kþ ejected from the generator (ig;Kþ ) can be calculated using Eq. (8) with max ¼ 0:31 determined independently for the employed pipette, i.e., ig;Kþ ¼ ic =max (curve 3 in Fig. 9). The subtraction of ig;Kþ from the original voltammogram (i.e., the subtraction of curve 3 from curve 1) yields the TPBCl transfer current at the generator oriﬁce as a function of Eg (curve 4). One should notice that the half-wave potential of TPBCl transfer is 100 mV more positive than the E1=2 of potassium transfer. The observation of this wave would not be possible without the use of a generation–collection scheme.

B.

Ionic Reactions in Solutions

Many homogeneous ionic reactions may be coupled with heterogeneous ion transfer reactions (e.g., SN 2-type reactions, organic transformations involving charged metal complexes, ion binding to polyelectrolytes and DNA). Relatively few electrochemical studies of such processes at the micro-ITIES have been reported. Recently, Horrocks et al. proposed two micropipette-based approaches to study the binding of cations to DNA in aqueous solutions [31]. In the ﬁrst method, the cation of interest is initially present in the aqueous phase and transferred to the organic phase contained in a micropipette when its potential is made sufﬁciently negative. Upon addition of high-molecular-weight DNA to the aqueous phase the concentration of free cation decreases, which results in a decrease in the ion transfer current (Fig. 10). The corresponding binding constant can be extracted

FIG. 9 Separation of two concurrent IT processes. Generator voltammogram (curve 1) is produced by simultaneously occurring transfer of Kþ and TPBCl . The ﬂux of Kþ ejected from generator pipette (curve 3) was obtained from collection current of Kþ (curve 2) using Eq. (4). The transfer current of TPBCl (curve 4) was obtained by subtraction of curve 3 from curve 1. Ec ¼ 0:15 V vs. AgTPBCl. cDB18C6 ¼ 0. For other parameters see Fig. 7. (Reprinted with permission from Ref. 11. Copyright 2000 American Chemical Society.)

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FIG. 10 Sequence of voltammograms of the transfer of methyl viologen (MV2þ ) between water and DCE. The aqueous phase contained 0.01 M LiCl, 0.2 mM MVCl2 , 10 mM Tris buffer pH 7 and highmolecular-weight DNA in the following concentrations: (1) 0, (2) 0.6, (3) 1.5, and (4) 3.0 mM. The DCE phase contained 0.1 M TBATPB as electrolyte (in the pipette). The sweep rate was 20 mV/s, and the pipette radius was 10 m. (Reprinted with permission from Ref. 31. Copyright 1998 American Chemical Society.)

from the dependence of normalized steady-state current vs. DNA concentration without the knowledge of micropipette size, binding kinetics, or diffusion coefﬁcient values. In the second method, the cation of interest is present in the organic phase inside the pipette and oligonucleotides (fragments of DNA) are added to the external aqueous phase. The transfer of a cation to the aqueous phase may be facilitated by the oligonucleotides present in the aqueous phase. The facilitated transfer appeared as a steady-state wave dependent on the concentration of oligonucleotides in the aqueous phase. The binding constant can be estimated from the shift in the transfer potential between the facilitated and nonfacilitated transfer. The cation chosen, N-methylphenanthroline, is a known DNA intercalator, and analysis of the steady-state wave or facilitated transfer allowing an estimate of the number of ions transferred per molecule of oligonucleotide arriving at the interface. The binding constants of methyl viologen and N-methylphenanthroline determined by this technique were 1:44 103 M1 and 1:33 104 M1 , respectively. Several workers have shown that the binding constants can be obtained from straightforward voltammetric experiments in which the DNA is titrated against the metal complex [32]. However, these electrochemical experiments are limited to redox active molecules. The technique employed in Ref. 31 has the advantage that it is suitable for the measurements of nonredox active ions. Homogeneous ionic reactions can also be probed by electrochemical generation– collection technique using -pipette [Fig. 5(b), (c)] [11]. If an ion ejected from the generator pipette participates in a homogeneous chemical reaction, and such a reaction affects the collection efﬁciency, its kinetics and/or thermodynamics can be probed. If the reaction product does not contribute to the collector current (i.e., either it cannot be transferred into water or its diffusion coefﬁcient is too small), the collection efﬁciency decreases with increasing rate of coupled homogeneous reaction [Fig. 5(b)]. If the reaction product is charged and can be transferred to water [Fig. 5(c)], the collector voltammogram consists of two waves occurring at differential potentials and corresponding to the product and cation transfers. For example, when potassium transfer is conducted in the presence of DB18C6 in organic phase (cDB18C6 cKCl ) and a large positive potential is applied to the generator

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pipette, the generator current is produced by two IT processes, i.e., facilitated transfer of potassium by DB18C6 [reaction (10a)] and simple transfer of Kþ : ig ¼ ig;KDB18C6 þ ig;Kþ

ð11Þ

The collector current in this case consists of two components ic ¼ ic;KDB18C6 þ ic;Kþ

ð12Þ

where the ic;KDB18C6 term represents interfacial dissociation [reaction (10b)] and ic;Kþ corresponds to simple transfer of potassium to the aqueous ﬁling solution of the collector pipette. Figure 11 contains a generator voltammogram (curve 1) and two corresponding ic vs. Eg curves obtained at Ec ¼ 0:25 V (curve 2) and 0.6 V (curve 3) with cKCl ¼ 20 mM, cDB18C6 ¼ 0:25 mM and cTPBCl ¼ 10 mM. Since cKCl cDB18C6 , the ig at positive Eg is much higher than the diffusion current of crown ether to the generator pipette (ig;KDB18C6 ) which appears as a small wave at Eg 0:4 V. The collector voltammograms in Fig. 11 are different because at Ec ¼ 0:25 V both complexed and uncomplexed form of potassium are collected, while only uncomplexed Kþ is collected at Ec ¼ 0:6 V (ic ¼ ic;Kþ because the interfacial dissociation of ½Kþ DB18C6] at this potential is slow). Accordingly, a small steady-state wave corresponding to reaction (10b) can be seen in curve 2, but not in curve 3. One might expect the difference between two collector voltammograms to be equal to the height of that wave, but the actual difference between those curves at positive Eg is much larger. Apparently, Kþ ejected from the generator pipette at more positive Eg participates in a homogeneous complexation reaction with DB18C6 in DCE: kf

Kþ ðDCEÞ þ DB18C6 ðDCEÞ !½Kþ DB18C6 ðDCEÞ

ð13Þ

At Ec ¼ 0:25 V (but not at 0.6 V) potassium from ½Kþ DB18C6 species produced by both interfacial and homogeneous complexation reactions can be transferred into the collector pipette. Therefore the difference between curves 2 and 3 (¼ ic;KDB18C6 Þ represents the total

FIG. 11 Analysis of IT coupled with a homogeneous ion complexation reaction. Generator voltammogram (1) of the transfer of potassium from the aqueous solution into DCE containing 0.25 mM DB18C6 and corresponding background-subtracted collector curves obtained at Ec ¼ 0:25 (2) and 0.6 V (3) vs. AgTPBCl. Collector pipette contained 0.01 M LiCl. For other parameters see Cell 1. (Reprinted with permission from Ref. 11. Copyright 2000 American Chemical Society.)

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amount of ½Kþ DB18C6 species produced via reactions (10a) and (13) that reach the collector oriﬁce. The rate of reaction (13) can be evaluated from the difference between ic values at Ec ¼ 0:25 V and Ec ¼ 0:6 V, which represents the total amount of complexed potassium arriving at the collector. Dividing this quantity by collection efﬁciency one gets an estimate for the total complexation rate in the system. To evaluate homogeneous complexation rate the contribution of interfacial complexation (i.e., ig;KDB18C6 Þ has to be subtracted: Homogeneous complexation rate ¼ ½ic ð0:25 VÞ ic ð0:6 VÞ=max ig;KDB18C6

ð14Þ

To explore the possibility of measuring the kinetics of reaction (13) G/C experiments were carried out with cKCl cDB18C6 [11]. The results indicated that homogeneous complexation of potassium ions by DB18C6 in DCE is too fast to be measured using micrometer sized dual pipettes. Thus, according to Ref. 23, the lower limit for the rate constant 6 1 1 s . Smaller (nanometer-sized) pipettes are required for of reaction (13) is kf > 10 M probing rapid complexation reactions. C.

Electron Transfer

Studies of electron transfer (ET) at micro-ITIES are scarce. Solomon and Bard ﬁrst observed the ET between TCNQ (in DCE) and ferrocyanide (in water) at a microITIES supported by micropipettes [5]. The pipette was used as a SECM probe for electrochemical imaging. The current was controlled by the rate of the bimolecular ET reaction at the micro-ITIES 3 TCNQ ðDCEÞ þ FcðCNÞ4 6 ðaqÞ Ð TCNQ ðDCEÞ þ FcðCNÞ6 ðaqÞ

ð15Þ

The concentrations of aqueous oxidized and reduced species inside the pipette were much larger than that of the redox species in the organic phase. As was shown previously at large ITIES [33], the voltammograms obtained under these conditions (Fig. 12) were similar to voltammograms of the same redox species at a Pt electrode. The aqueous phase, therefore, behaved as a metal electrode. Quinn et al. studied ET at micro-ITIES supported by micropipettes or microholes [16]. The studied systems involved ferri/ferrocyanide redox couple in aqueous phase and ferrocene, dimethylferrocene, or TCNQ in either DCE or o-nitrophenyl octyl ether. Sigmoidal, steady-state voltammograms were obtained for ET at the water–DCE interface supported at a micropipette. The semilogarithmic plot of E versus log½ðId IÞ=I was

FIG. 12 Voltammogram for the two-phase electron transfer at a micro-ITIES. The pipette contained 1.0 M Li2 SO4 , 0.4 M K4 FeðCNÞ6 , and 0.01 M K3 FeðCNÞ6 . The organic phase (DCE) contained 1 mM TCNQ and 1 mM TPAsTPB supporting electrolyte. (The potential sweep rate was 50 mV/s. Reprinted with permission from Ref. 5. Copyright 1995 American Chemical Society.)

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linear with the slope of 61 mV/decade, i.e., similar to the Nernstein value, 59 mV/decade, and the pipette resistance was too high for accurate kinetic measurements. The voltammograms at the microhole-supported ITIES were analyzed using the Tomes˘ criterion [34], which predicts jE3=4 E1=4 j ¼ 56:4=n mV (where n is the number of electrons transferred and E3=4 and E1=4 refer to the three-quarter and one-quarter potentials, respectively) for a reversible ET reaction. An attempt was made to use the deviations from the reversible behavior to estimate kinetic parameters using the method previously developed for UMEs [21,27]. However, the shape of measured voltammograms was imperfect, and the slope of the semilogarithmic plot observed was much lower than expected from the theory. It was concluded that voltammetry at micro-ITIES is not suitable for ET kinetic measurements because of insufﬁcient accuracy and repeatability [16]. Those experiments may have been affected by reactions involving the supporting electrolytes, ion transfers, and interfacial precipitation. It is also possible that the data was at variance with the Butler–Volmer model because the overall reaction rate was only weakly potential-dependent [35] and/or limited by the precursor complex formation at the interface [33b]. D.

Micropipettes as SECM Tips

In scanning electrochemical microscopy (SECM) a microelectrode probe (tip) is used to examine solid–liquid and liquid–liquid interfaces. SECM can provide information about the chemical nature, reactivity, and topography of phase boundaries. The earlier SECM experiments employed microdisk metal electrodes as amperometric probes [29]. This limited the applicability of the SECM to studies of processes involving electroactive (i.e., either oxidizable or reducible) species. One can apply SECM to studies of processes involving electroinactive species by using potentiometric tips [36]. However, potentiometric tips are suitable only for collection mode measurements, whereas the amperometric feedback mode has been used for most quantitative SECM applications. In a conventional feedback experiment the UME tip is placed in a solution containing some redox species. A redox mediator is reduced (or oxidized) at the tip electrode: O1 þ e ¼ R1

ð16Þ

The product of this reaction diffuses to the substrate where it may be reoxidized (or rereduced). This process produces an enhancement in the faradaic current at the tip electrode depending on the tip–substrate separation (positive feedback) [29]. This experiment can be modiﬁed by replacing metal tip with a micropipette ﬁlled with a solvent immiscible with the outer solution. Such a pipette can work as an amperometric UME. Solomon and Bard [5] used micropipettes for feedback mode SECM imaging. The tip process in Ref. 5 was electron transfer between aqueous ferrocyanide inside a micropipette and TCNQ in the outer DCE solution. Accordingly, the pipette behaved in the same manner as a metal tip. The micropipette tips have several advantages over metal tips. First, they are much easier to fabricate, especially for tips with submicrometer diameters. Moreover, although very small (nanometer) metal tips can be used in SECM to image insulator surfaces, high-resolution imaging of conductive surfaces by SECM is not possible because of the onset of tunneling when the tip approaches to within 5–10 nm of surface. Such tunneling may not occur with glass micropipettes. Recently [8b,30], a new IT feedback mode of SECM was introduced, in which the tip process is a simple or assisted ion transfer. In this mode, a micropipette ﬁlled with solvent (e.g., aqueous) immiscible with the outer solution (e.g., organic) serves as an SECM tip.

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The tip current in Ref. 8b was produced by transfer of Kþ from the aqueous solution inside the pipette into DCE assisted by DB18C6 [reaction (10a)]. With the tip biased at a sufﬁciently positive potential and the cKCl cDB18C6 , the tip current was limited by diffusion of DB18C6 to the pipette oriﬁce. When the tip approached the bottom (aqueous) layer potassium ions were released from the complex and transferred to the aqueous solution. DB18C6, which served as a mediator, was regenerated via interfacial dissociation mechanism [reaction (10b) occurring at the ITIES]. Similarly to conventional SECM feedback experiments, the interfacial dissociation produced an enhancement in the tip current (positive feedback). Unlike the assisted IT processes, no mediator species are involved in a simple IT reaction, e.g., transfer of a cation (Mþ ) from organic phase into the aqueous ﬁlling solution inside the pipette: Mþ ðoÞ ! Mþ ðwÞ

(at the pipette tip)

ð17aÞ

In this case, both the top and the bottom liquid phases contain the same ion at equilibrium. A micropipette tip is used to deplete concentration of this ion in the top solvent near the ITIES. This depletion results in the ion transfer across the ITIES (Fig. 13), which can produce positive feedback if the bottom phase contains a sufﬁciently high concentration of Mþ : Mþ ðwÞ ! Mþ ðoÞ

(at the ITIESÞ

ð17bÞ

The tip current depends on the rate of the interfacial IT reaction, which can be extracted from the tip current vs. distance curves. One should notice that the interface between the top and the bottom layers is nonpolarizable, and the potential drop is determined by the ratio of concentrations of the common ion (i.e., Mþ ) in two phases. Probing kinetics of IT at a nonpolarized ITIES under steady-state conditions should minimize resistive potential drop and double-layer charging effects, which greatly complicate voltammetric studies of IT kinetics. In Ref. 30, the transfer of tetraethylammonium (TEAþ ) across nonpolarizable DCE–water interface was used as a model experimental system. No attempt to measure kinetics of the rapid TEAþ transfer was made because of the lack of suitable quantitative theory for IT feedback mode. Such theory must take into account both ﬁnite quasireversible IT kinetics at the ITIES and a small RG value for the pipette tip. The mass transfer rate for IT experiments by SECM is similar to that for heterogeneous ET measurements, and the standard rate constants of the order of 1 cm/s should be accessible. This technique should be most useful for probing IT rates in biological systems and polymer ﬁlms. By scanning the pipette tip over the phase boundary the topographic images and maps of IT reactivity of the interface can be obtained. Figure 14 shows a gray-scale image of a 5 m pore in the 10 m-thick polycarbonate membrane obtained with an 3 mdiameter pipette. The feedback is negative when the pipette tip is over a solid surface, while a signiﬁcantly higher current corresponds to the tip facing the pore. The feedback mode images were obtained without any current ﬂowing across the interface. A high lateral resolution can be achieved because of the absence of diffusion broadening. Such an image represents distribution of IT reactivity on the interfacial boundary. Filling a pipette with an organic solvent was essential for experiments with polycarbonate membranes which are soluble in organic media. The same setup can be employed to map ion transfers occurring at a polymer–solution interface and in living cells which also have to be studied in water. A water-ﬁlled micropipette should be used as an SECM tip for imaging in organic media. A potential advantage of the pipette tips is that they can easily be made

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FIG. 13 Schematic illustration of the SECM feedback mode based on a simple ion-transfer reaction. Cations are transferred from the top (organic) phase into the aqueous solution inside the pipette tip. Positive feedback is due to IT from the bottom (aqueous) layer into the organic phase. Electroneutrality in the bottom layer is maintained by reverse transfer of the common ion across the ITIES beyond the close proximity of the pipette where its concentration is depleted. (Reprinted with permission from Ref. 30. Copyright 1998 American Chemical Society.)

very small (see Section III.C). Some technical problems, such as better tip–substrate alignment, have yet to be solved to make nanometer-scale IT imaging feasible.

E.

Micro-ITIES as Sensors

According to Eq. (1) the steady-state current across a micro-ITIES is proportional to the bulk concentration of the transferred species. Thus, the micro-ITIES can function as an amperometric ion-selective sensor. Similarly, the peak current in a linear sweep voltammogram of ion egress from the micropipette obeys the Randles–Sevc˘ik equation. Both types of measurements can be useful for analysis of small samples [18a].

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FIG. 14 Constant height mode gray–scale image of a 5 m-diameter pore in a polycarbonate membrane obtained with a 3 m pipette tip. The ﬁlling DCE solution contained 10 mM TBATPBCl. The aqueous phase contained 0.4 mM TEACl þ 10 mM LiCl. The scale bar corresponds to 10 m. The tip scan speed was 10 m/s. (Reprinted with permission from Ref. 30. Copyright 1998 American Chemical Society.)

Senda et al. [4b] studied the voltammetry of acetylcholine (Achþ ) at a polarizable NB–water interface formed at the tip of a micropipette. Both the height of a sigmoidal wave of the Achþ transfer into the pipette and the peak current of the reverse IT reaction were found to be proportional to bulk concentrations of Achþ in two liquid phases. An experimental scheme similar to conventional stripping voltammetry was used to improve sensitivity of amperometric ion detection. During the ﬁrst step (accumulation or preelectrolysis, 1 min long), a sufﬁciently negative potential was applied to the NB-ﬁlled pipette to induce the transfer Achþ from the outer aqueous solution. This was followed by a potential sweep in the positive direction, which resulted in a peak-shaped voltammogram of Achþ efﬂux from the pipette. The peak height was a linear function of the ion concentration in the aqueous phase and increased proportionally to the square root of the accumulation time. This preconcentration effect appears promising for determination of ions at very low concentration levels. (One should notice that pipette surface in Ref. 4b was not silanized, and water most likely has penetrated inside the pipette.) Using a similar technique, Huang et al. determined vitamin B1 down to 4:6 106 M in aqueous solution with a linear range of 5 105 to 1 103 M [37]. A microhole-based ITIES has been used by Osborne et al. for amperometric determination of ionic species in aqueous solutions [12]. They studied the assisted ammonium transfer with DB1816 at the water–DCE interface. Because the concentration of ionophore in the organic phase was high, the measured steady-state current was proportional to the concentration of ammonium in the aqueous phase. The time required to reach a steady state was relatively short (e.g., 5 s for an 11 m hole). A linear relationship was found between the steady-state plateau current and the ammonium concentration over the range 1 to 500 M.

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Although amperometric detection of ionic species based on ITIES is feasible, the mechanical instability of a liquid–liquid interface is a major problem which has to be circumvented to develop a commercial ion sensing system. A lot of work has been done to gelify the organic phase in order to achieve a better handling of liquid–liquid systems [38]. Most publications related to IT reactions at a liquid–gel interface have shown that although the diffusion coefﬁcients of ions in the gel are signiﬁcantly reduced, the IT processes could still be used for amperometric detection. The gelation of the organic phase increases its resistivity, and the higher uncompensated resistance impedes the amperometric determination. Osborne et al. found that this difﬁculty could be alleviated by using the arrays of microliquid–liquid interfaces [39]. They used this approach to develop the urea and creatinine sensors based on amperometric detection of ammonium. More recently, Girault’s group prepared microfabricated composite polymer membranes, which combine the advantages of the geliﬁed organic phase and micro-ITIES [40]. The composite membrane comprised two polymer layers, i.e., a supporting ﬁlm of polyethylene terephthalate on which an electrolyte ﬁlm containing polyvinylchloride was cast. The polyester layer had a laser-etched pattern of microholes (22 m diameter). The polyvinylchloride layer contained 2-nitrophenyl octyl ether plasticizing solution of TBATPBCl electrolyte. The ion transfer behavior of the microhole array interface between an analyte solution and a PVC gel electrolyte was similar to that of conventional micro-ITIES. The steady-state IT current through each hole could be estimated from Eq. (1) when the hole oriﬁces were well-separated. When a composite polymer membrane was used for amperometric sensing of choline [40], the plot of the plateau current against concentration was linear over the range from 0.1 to 0.9 mM of choline. By adding appropriate ionophores (e.g., DB18C6, valinomycin) to the PVC layer, Lee et al. made microinterface polymer membranes work as transducers for the amperometric sensing of alkali metal ions [41]. A composite polymer membrane has also been used as an effective amperometric detector for ion exchange chromatography [42] and showed detection limits similar to those obtained with a conductivity detector. An advantage of the amperometric detector based on micro-ITIES over the conductometric detector is that selectively can be tailored by proper choice of the ionophore. For instance, the selectivity of the membrane toward ammonium in the presence of an excess of sodium could be substantially increased by introducing an ammonium-selective ionophore (such as valinomycin) in the gel membrane [42]. A dual-pipette device can also be used as a sensor for water-soluble (or organic) gaseous species that can change the composition and ionic conductivity of the thin liquid layer linking its barrels [11]. When the outer glass surface is not silanized the pipette oriﬁces are linked by a thin aqueous ﬁlm formed on the outer pipette wall. Such a ﬁlm can be sufﬁciently thick and conductive to yield a reasonable quality voltammetric response suitable for qualitative and quantitative analytical determinations. The response of a -pipette ‘‘in air’’ is largely determined by the properties of the aqueous surface layer, and it is very sensitive to changes in ﬁlm composition. Such changes occur when the pipette is exposed to a soluble gas. A small ratio of the ﬁlm thickness to its surface area should result in a high sensitivity and fast response time of such a sensor. Voltammetric experiments without external solution were carried out using a -pipette with one barrel ﬁlled with an aqueous solution and the second barrel ﬁlled with organic phase. In a two-electrode setup, voltage was applied between Ag=AgCl and Ag=AgTPBCl reference electrodes inserted in two barrels.

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In Ref. 11, IT voltammograms of NHþ 4 and NO3 were obtained when a -pipette was exposed to vapors of ammonia and nitric acid, and linear dependence of the voltammetric response on concentration of vapor-generating solution has been demonstrated. The surface liquid layer in all pipettes used in that work was aqueous, and only the detection of water-soluble gases was discussed. However, the detection of organic compounds in the gas phase may also be possible using a -pipette with a nonaqueous sensing ﬁlm.

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2. 3.

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22. C. Amatore, in Physical Electrochemistry: Principles, Methods, and Applications (I. Rubinstein, ed.), Marcel Dekker, New York, 1995, pp. 131–163. 23. C. G. Phillips and H. A. Stone. J. Electroanal. Chem. 437:157 (1997). 24. P. D. Beattie, A. Delay, and H. H. Girault. Electrochim. Acta 40:2961 (1995). 25. (a) R. Ferrigno, P.-F. Brevet, and H. H. Girault. Electrochim. Acta 42:1895 (1997), (b) L. C. R. Alfred and K. B. Oldham. J. Phys. Chem. 100:2170 (1996). 26. User’s Manual for Micropipette Puller Model P-2000. Sutter Instruments, Novato, CA, 1998. 27. M. V. Mirkin and A. J. Bard. Anal. Chem. 64:2293 (1992). 28. T. Kakiuchi. J. Electroanal. Chem. 322:55 (1992). 29. A. J. Bard, F.-R. F. Fan, and M. V. Mirkin. in Electroanalytical Chemistry, vol. 18, (A. J. Bard, ed.), Marcel Dekker, New York, 1994, pp. 243–373. 30. Y. Shao and M. V. Mirkin. J. Phys. Chem. B 102:9915 (1998). 31. B. R. Horrocks and M. V. Mirkin. Anal. Chem. 70:4653 (1998). 32. (a) T. W. Welch and H. H. Thorp. J. Phys. Chem. 100:13829 (1996). (b). M. T. Carter, M. Rodriguez, and A. J. Bard. J. Am. Chem. Soc. 111:8901 (1989). (c) M. T. Carter and A. J. Bard. J. Am. Chem. Soc. 109:7528 (1987). (d) J. Swiatek. J. Coord. Chem. 33:191 (1994). 33. (a) G. Geblewicz and D. J. Schiffrin. J. Electroanal. Chem. 244:27 (1988). (b) H. H. Girault and D. J. Schiffrin. J. Electroanal. Chem. 244:15 (1988). 34. A. J. Bard and L. R. Faulkner. Electrochemical Methods, John Wiley, New York, 1980. 35. B. Liu and M. V. Mirkin. J. Am. Chem. Soc. 121:8352 (1999). 36. (a) G. Denuault, M. H. T. Frank, and L. M. Peter. Faraday Discuss. Chem. Soc. 94:23 (1992). (b) C. Wei, A. J. Bard, G. Nagy, and K. Toth. Anal. Chem. 67:1346 (1995). 37. B. Huang, B. Yu, P. Li, M. Jiang, Y. Bi, and S. Wu. Anal. Chim. Acta 312:329 (1995). 38. (a) F. Silva, M. J. Sousa, and C. M. Pereira. Electrochim. Acta 42:3095 (1997). (b) P. Vanysek. Adv. Chem. Ser. 235:55 (1994). (c) V. Marecek, H. Janchenova, M. Brezina, and M. Betti. Anal. Chim. Acta 244:15 (1991). (d) E. Wang and H. M. Ji. Electroanalysis 1:75 (1989). (e) T. Osakai, T. Kakutani, and M. Senda. Anal. Sci. 4:529 (1988). (f) O. Dvorak, V. Marecek, and Z. Samec. J. Electroanal. Chem. 284:205 (1990). 39. (a) M. D. Osborne and H. H. Girault. Electroanalysis 7:714 (1995). (b) M. D. Osborne and H. H. Girault. Mikrochim. Acta 117:175 (1995). 40. H. J. Lee, P. D. Beattie, B. J. Seddon, M. D. Osborne, and H. H. Girault. J. Electroanal. Chem. 440:73 (1997). 41. H. J. Lee, C. Beriet, and H. H. Girault. J. Electroanal. Chem. 453:211 (1998). 42. H. J. Lee and H. H. Girault. Anal. Chem. 70:4280 (1998).

16 Dynamics of Polar Solvent Motion at Liquid Interfaces NANCY E. LEVINGER Fort Collins, Colorado RUTH E. RITER Georgia

I.

Department of Chemistry, Colorado State University,

Department of Chemistry, Agnes Scott College, Decatur,

INTRODUCTION

As this volume attests, a wide range of chemistry occurs at interfacial boundaries. Examples range from biological and medicinal interfacial problems, such as the chemistry of anesthesia, to solar energy conversion and electrode processes in batteries, to industrialscale separations of metal ores across interfaces, to investigations into self-assembled monolayers and Langmuir–Blodgett ﬁlms for nanoelectronics and nonlinear optical materials. These problems are based not only on structure and composition of the interface but also on kinetic processes that occur at interfaces. As such, there is considerable motivation to explore chemical dynamics at interfaces. Kinetics of chemical reactions at liquid interfaces has often proven difﬁcult to study because they include processes that occur on a variety of time scales [1]. The reactions depend on diffusion of reactants to the interface prior to reaction and diffusion of products away from the interface after the reaction. As a result, relatively little information about the interface dependent kinetic step can be gleaned because this step is usually faster than diffusion. This often leads to diffusion controlled interfacial rates. While often not the rate-determining step in interfacial chemical reactions, the dynamics at the interface still play an important and interesting role in interfacial chemical processes. Chemists interested in interfacial kinetics have devised a variety of complex reaction vessels to eliminate diffusion effects systematically and access the interfacial kinetics. However, deconvolution of two slow bulk diffusion processes to access the desired the fast interfacial kinetics, especially ultrafast processes, is generally not an effective way to measure the fast interfacial dynamics. Thus, methodology to probe the interface speciﬁcally has been developed. In bulk solution dynamics of fast chemical reactions, such as electron transfer, have been shown to depend on the dynamical properties of the solvent [2,3]. Speciﬁcally, the rate at which the solvent can relax is directly correlated with the fast electron transfer dynamics. As such, there has been considerable attention paid to the dynamics of polar solvation in a wide range of systems [2,4–6]. The focus of this chapter is the dynamics of polar solvation at liquid interfaces. 399

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Solvation dynamics refers to the rate of solvent reorganization in response to an abrupt change in solute properties [2,4–7]. In most experiments measuring this phenomenon, the solute is a chromophore that undergoes an electronic transition resulting almost exclusively in a change in its charge distribution. The dynamic response of the system to this change in solute properties is usually monitored by measuring the time-resolved ﬂuorescence Stokes shift (TRFSS) in the chromophore’s emission spectrum [5] or through various photon echo spectroscopies [4,8–14]. In many chemical reactions, especially those involving electron transfer, the dynamic solvent response to a solute-induced electrostatic perturbation plays an important role, making solvation dynamics not only interesting in its own right, but an essential component of understanding the effects of solvents on chemical reactions [3,15–17]. This connection to chemical reactions, as well as experimental advances that have made it possible to observe solvation dynamics on the subpicosecond time scale, have generated a great deal of recent interest in this phenomenon and a considerable amount of new information about it. Several recent reviews summarize the advances in this ﬁeld, primarily focussing on solvation dynamics in bulk liquids [4,8–14]. In contrast to the well-studied bulk liquids, much less is known about the topic of this chapter, the dynamics of polar solvation occurring in heterogeneous media or at liquid interfaces. To investigate the solvation dynamics at liquid interfaces, researchers have primarily employed TRFSS methods or analogs thereof. TRFSS experiments measure solvation dynamics by monitoring the time evolution of the Stokes shift of the ﬂuorescence spectrum of chromophores, such as coumarin dyes, which undergo very little structural change on electronic excitation. Figure 1(a) displays a representative picture of the time-evolving shifting ﬂuorescence spectrum of coumarin 343 (C343 structure is shown in Fig. 2). The TRFSS arises primarily from the change in the solute–solvent interaction potential brought about by the solute S0 ! S1 electronic transition [4]. The frequency shift monitored in the experiment can therefore be expressed as ðtÞ ¼ g þ EðtÞ=h

ð1Þ

where g is the transition frequency for the isolated molecule, h is Planck’s constant, the overbar represents an average over different chromophores, and E ¼ U1 U0

ð2Þ

where U1 and U0 are the solute–solvent potentials for the solute in the S1 and S0 electronic states. For these chromophores that undergo a substantial change in dipole on electronic excitation, E is primarily electrostatic in nature, that is, due primarily to the change in the solute charge distribution, usually represented as a change in partial charges. In terms of E, the TRFSS response function CðtÞ is given by EðtÞ Eð1Þ CðtÞ SðtÞ ¼ ð3Þ Eð0Þ Eð1Þ where t, 0, and 1 refer to the time of the measurement, instantaneously after transition, and at equilibrium, respectively. Thus, experimentally E is estimated by the peak or average frequency of the ﬂuorescence spectrum. Figure 1(b) shows the CðtÞ function generated from the data in Fig. 1(a). To extrapolate back to t ¼ 0, the technique given by Fee and Maroncelli has been used [18]. Solvation dynamics have been measured for a wide range of polar (and some not so polar) solvents. In all solvents, two distinct types of motion comprise the response [7]. The

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FIG. 1 (a) Time evolution of the ﬂuorescence spectrum of coumarin 343 in water demonstrating the time-resolved ﬂuorescence Stokes shift; (b) experimentally derived CðtÞ function from data in part (a).

inertial response is always ultrafast occurring on the sub-75 fs timescale and is due to underdamped molecular motion. The diffusive response can range from subpicosecond to nanoseconds or longer and arises from collective motion of the solvent. Water, a component of most liquid–liquid interfaces, is a very fast relaxing solvent; both inertial and diffusive relaxation are complete for bulk water in less than a picosecond [19]. While completely nonpolar solvents do not contribute to polar solvation dynamics, solvents such as benzene can contribute to the polar solvation dynamics through induced dipole effects [5]. Thus, one could imagine liquid–liquid interfaces in which either only one or both phases contribute to the dynamics. For the remainder of this chapter, we discuss results for various studies of interfacial solvation dynamics. We ﬁrst discuss studies at liquid–liquid interfaces at planar interfaces and in microheterogeneous media in Section II. In Section III, we discuss solvation dynamics at liquid–solid interfaces. In Section IV, we review theoretical models and simulations of solvation dynamics at liquid interfaces. Finally, we conclude with a discussion of future studies.

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FIG. 2 Structures of the probe molecules used in the studies reviewed.

II.

DYNAMICS AT LIQUID–LIQUID INTERFACES

Dynamics of polar solvation have been studied at a range of differing liquid–liquid interfaces. These include planar liquid–liquid, and liquid–air interfaces as well as those found in microheterogeneous media. We discuss each case separately. A.

Planar Interfaces

The ﬁrst investigation of dynamical processes at well-deﬁned liquid–liquid boundaries was reported in the 1980s. Srinivasan and de Levie [20] examined the rates of nucleation and growth of organic ﬁlms at the interface between mercury and various aqueous solutions using mercury as an electrode. Since then, various studies allude to dynamical properties of the solvent at a liquid–liquid interface. To date, there has been only one report of solvation dynamics at a planar liquid–liquid interface. Bessho et al. [21] investigated the microenvironments of 8-anilino-1-naphthalensulfonate (ANS, structure shown in Fig. 2). at the heptane–water interface using time-resolved total internal reﬂection ﬂuorescence spectroscopy. They found a biexponential response to the ﬂuorescence dynamics. They interpreted this result as indicative of two distinct probe environments. Speciﬁcally, they report the longer response time, ¼ 1:8 ns, to indicate molecules residing within a few

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nanometers of the interface, and a shorter response time, ¼ 330–420 ps, corresponding to molecules in a range of positions further from the interface. While it is hard to imagine the surface perturbation extending nanometers away from the surface, the results reported demonstrate perturbation of the solvent dynamics by the interface. Unfortunately, the apparatus used for these experiments had limited time resolution (> 50 ps instrument response) precluding direct comparison with solvation dynamics in bulk water. Recently, Eisenthal and coworkers have developed time-resolved surface second harmonic techniques to probe dynamics of polar solvation and isomerization reactions occurring at liquid–liquid, liquid–air, and liquid–solid interfaces [22]. As these experiments afford subpicosecond time resolution, they are analogous to ultrafast pump–probe measurements. Speciﬁcally, they excite a dye molecule residing at the interface and follow its dynamics via the resonance enhance second harmonic signal. To date, the interfacial solvation dynamics studies by the Eisenthal group have probed water–air interfaces [23,24]. These experiments are analogous to TRFSS measurements. Zimdars et al. [23] have recently reported on the solvation dynamics of water at the air–water interface using the probe molecule coumarin 314 (C314, structure shown in Fig. 2). They found that interfacial solvation dynamics has a time constant of 790 30 fs, which is slightly slower but very similar to what is observed for diffusive water motion in bulk [19]. More recently, they have been able to investigate how the solute orientation at the interface affects the measured solvation dynamics response by taking advantage of the polarization sensitivity of the second harmonic generation [24]. As shown in Fig. 3, they ﬁnd that solvation dynamics measured for solute molecules lying in the plane of the interface are faster, ¼ 820 fs, than the solvation dynamics measured for solute molecules oriented perpendicular to the interface, ¼ 1215 fs. They interpret these results as indicative of shifting spectral envelopes for the differently oriented solute molecules. Eisenthal and coworkers have explored interfacial photoisomerization reactions and rotational dynamics for probe molecules at several interfaces including the water–air, water–alkane, and water–silica interface using femtosecond time-resolved second harmonic generation. While these studies do not probe solvation dynamics, they are related to solvation dynamics because they provide information about frictional forces that constitute a part of the polar solvent response. Eisenthal and coworkers have explored the photoisomerization of two different systems, DODCI at the water–air interface and malachite green at water–air and water–alkane interfaces [25,26]. These dye structures are shown in Fig. 2. In the case for DODCI at a water–air interface, the isomerization was faster at the interface than it was in bulk aqueous solution, 220 ps vs. 520 ps, respectively [25]. For malachite green, a molecule whose isomerization dynamics are quite insensitive to polarity but highly sensitive to viscosity in bulk solution, the interfacial isomerization occurred more slowly than in bulk, 2 ps vs. 700 fs at the water–air interface and in bulk water, respectively [26]. Surprisingly, the malachite green isomerization dynamics at water–alkane interfaces were insensitive to the viscosity of the alkane phase. At ﬁrst glance, these results appear to be contradictory as they indicate both decreased and increased friction at the same (water–air) interface. However, they can be reconciled by considering the exact portion of the interface that the probe molecule samples. Since DODCI and malachite green are signiﬁcantly different molecules, there is no reason to believe that they would occupy the same location or depth in the interface. Eisenthal and coworkers have also measured interfacial friction via the rotational dynamics of probe molecules at the interface. In their ﬁrst study, Eisenthal and coworkers probed the rotational dynamics of rhodamine 6G (R6G, structure shown in Fig. 2) at the

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FIG. 3 Solvation dynamics dependence of coumarin 314 probe molecule orientation at the air– water interface. Signals are generated with a 420 nm pump photon and probed by surface second harmonic signal with 840 nm (SH at 420), ð2Þ xzx element. The normalized change in SH ﬁeld is plotted vs. pump delay. is derived from a single exponential ﬁt to the data. (a) Pump polarization S (inplane), (b) Pump polarization P (out-of-plane). (Reprinted from Ref. 24 with permission from the American Chemical Society.)

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water–air interface [27]. They found that the rotational dynamics slowed down at the interface compared to bulk solution [27]. More recently, they measured rotational dynamics for the solvation dynamics probe molecule, C314, at the water–air interface [28]. Here they measured faster molecular rotation for motion out of the plane of the interface, r ¼ 350 ps, than for in-plane rotation, r ¼ 600 ps. They note that the reorientation times for both in-plane and out-of-plane motion are slower than rotation in bulk solution, where r ¼ 100 ps. The out-of-plane rotational time agrees well with their previous results on R6G. They attribute the increased rotation time to increased friction at the interface. These results are somewhat nonintuitive because theoretical predictions suggest that there should be decreased friction at the interface. However, as the authors note, it is possible that the probe molecule resides in a preferred orientation with respect to hydrogen bonding and that molecular rotation reﬂects the time necessary to break those hydrogen bonds. Overall, while the experiments probing photoisomerization and rotational motion are intriguing, there remains a lot to be done before we can develop intuition about the impact of the interface on such molecular motion. B.

Interfaces in Microheterogeneous Media

While solvation dynamics have only been studied at a few planar interfaces, the interface present in self-assembled systems has recently show signiﬁcant activity. While Sarkar et al. have measured solvation dynamics at the liquid interfaces of normal micelles, these systems have not been extensively examined [29]. Using picosecond time-resolved ﬂuorescence spectroscopy of coumarin 480 (C480, structure shown in Fig. 2) they have investigated solvation dynamics of three normal micelle solutions prepared with the neutral surfactant Triton X-100 (TX), cationic cetyltrimethylammonium bromide (CTAB), and anionic sodium dodecyl sulfate (SDS). Above the critical micellar concentration, these surfactants are well known to form spherical micellar aggregates of 100–150 surfactant molecules with radii of 50 A˚ for TX and CTAB and 30 A˚ for SDS. Small-angle x-ray, neutron scattering, NMR, and ﬂuorescence studies show that the micellar core consists of hydrocarbon chains and the Stern layer is a shell, 6–9 A˚ thick, comprising polar headgroups, counterions, and water. As with the results from Bessho et al. [21], these experiments were limited by time resolution of approximately 50 ps, thus any bulklike water motion would not be observed. The solvation dynamics of the three different micelle solutions, TX, CTAB, and SDS, exhibit time constants of 550, 285, 180 ps, respectively. The time constants show that solvent motion in these solutions is signiﬁcantly slower than bulk water. The authors attribute the observed time constants to water motion in the Stern layer of the micelles. This conclusion is supported by the steady-state ﬂuorescence spectra of the C480 probe in these solutions. The spectra exhibit a signiﬁcant blue shift with respect the spectrum of the dye in bulk water. This spectral blue shift is attributed to the probe being solvated in the Stern layer and experiencing an environment with a polarity much lower than that of bulk water. This work also shows that the time constants for the ionic surfactant micelle solutions are twice as fast as the TX solution time constant. Differences between the Stern layers of the micelles appear to be the charge of the surfactant polar headgroups and the presence of counterions. However, these differences do not account for the observed dynamics. Since the polar headgroups and counterions should interfact more strongly with the water molecules, the water motion at the interface should be slower. This view is supported by recent investigations where systematic variation of surfactant counter-

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cations revealed signiﬁcant effects on the solvation dynamics measured in reverse micelles [30,31]. In addition, the observed time-dependent Stokes shift of the probe in the TX solution is 1035 cm1 , while the magnitude of the Stokes shift is half that for the ionic surfactant solutions. Hence, these results suggest that the environment sensed by probe molecules differs signiﬁcantly for the three micellar solutions. In the past few years, a range of solvation dynamics experiments have been demonstrated for reverse micellar systems. Reverse micelles form when a polar solvent is sequestered by surfactant molecules in a continuous nonpolar solvent. The interaction of the surfactant polar headgroups with the polar solvent can result in the formation of a welldeﬁned solvent pool. Many different kinds of surfactants have been used to form reverse micelles. However, the structure and dynamics of reverse micelles created with Aerosol-OT (AOT) have been most frequently studied. AOT reverse micelles are monodisperse, spherical water droplets [32]. The micellar size is directly related to the water volume-tosurfactant surface area ratio deﬁned as the molar ratio of water to AOT, w¼

½H2 O ½surfactant

ð4Þ

AOT is an anionic surfactant complexed to the counterion, usually sodium. The water molecules in the intramicellar water pool are either free or bound to the interface. The bound water can interact with various parts of the surfactant. These interactions include hydrogen-bonding interactions with oxygen molecules on the sulfonate and succinate groups, ion–dipole interactions with the anionic surfactant headgroup and counterion, dipole–dipole interactions with the succinate group, and dispersive forces with the hydrocarbon tails. Several research groups have investigated the dynamical response of AOT reverse micellar systems. The ﬁrst work showing clear evidence for water motion in reverse micelles was done by Zhang and Bright [33]. They investigated the reorganization of water in the interior of AOT reverse micelles on the nanosecond time scale as a function of w and temperature using time-resolved ﬂuorescence spectroscopy of ANS. At low water levels, w < 2:5, they observed two relaxation processes with time constants of 0.5–1.7 and 3.5–11.8 ns, that they attributed to ‘‘free’’ and ‘‘bound’’ water motion, respectively. For w > 2:5, a single reorganization process with a time constant of 0.8–1.2 ns was reported. In general, they found that the observed rate constants decrease with increasing w. They also determined that at low water content, the activation barriers for ‘‘free’’ and ‘‘bound’’ water motion are essentially equivalent and that frequency factors inﬂuence the rates. While at higher water content, the height of the activation barrier for water motion is relatively small. Cho et al. [34] also probed the interior of AOT reverse micelles using timeresolved ﬂuorescence of ANS with time resolution of 50 ps. Their results were similar to Zhang and Bright observing the two characteristic relaxation times. They attributed the slowest water motion to water molecules near the surfactant interface behaving icelike owing to the strong interactions with the polar-headgroup surface of high curvature. Faster dynamics were attributed to bulklike water 6–18 A˚ from the interface. Using incoherent quasielastic neutron scattering (IQENS), Crupi et al. examined the low-frequency diffusive motions of water molecules in AOT reverse micellar solutions of deuterated cyclohexane [35]. IQENS follows the motion of water by measuring the incoherent cross-sections of H protons. They observed a narrowing of the quasielastic spectrum of water within the reverse micelles as compared to bulk. This narrowing suggests water motion inside the micelles is conﬁned to an approximately 3 A˚ region.

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The observation of slow, conﬁned water motion in AOT reverse micelles is also supported by measured dielectric relaxation of the water pool. Using terahertz timedomain spectroscopy, the dielectric properties of water in the reverse micelles have been investigated by Mittleman et al. [36]. They found that both the time scale and amplitude of the relaxation was smaller than those of bulk water. They attributed these results to the reduction of long-range collective motion due to the conﬁnement of the water in the nanometer-sized micelles. These results suggested that ‘‘free’’ water motion in the reverse micelles are not equivalent to bulk solvation dynamics. Investigation of water motion in AOT reverse micelles determining the solvent correlation function, CðtÞ, was ﬁrst reported by Sarkar et al. [29]. They obtained time-resolved ﬂuorescence measurements of C480 in an AOT reverse micellar solution with time resolution of > 50 ps and observed solvent relaxation rates with time constants ranging from 1.7 to 12 ns. They also attributed these dynamical changes to relaxation processes of water molecules in various environments of the water pool. In a similar study investigating the deuterium isotope effect on solvent motion in AOT reverse micelles, Das et al. [37] reported that the solvation dynamics of D2 O is 1.5 times slower than H2 O motion. Using time-resolved ﬂuorescence-upconversion spectroscopy with femtosecond resolution, the solvation dynamics of water in the AOT reverse micelles has been reported by Levinger and coworkers [30,31,38]. In general, as w increases, the mobility of water increases, as shown in Fig. 4. This suggests that micellar size plays a role in restricting solvent motion in the reverse micelles. However, the speciﬁc details of the micellar interior and morphology appear also to play signiﬁcant roles in the observed dynamics. In addition, the interior of the AOT reverse micelles is highly ionic, partially due to the presence of the surfactant’s countercation, and this highly concentrated, ionic environment may also play a role. In order to examine the effect of the countercation on water motion in the reverse micelles, Levinger and coworkers [30,31] exchanged the sodium ion commonly complexed to the AOT surfactant for various cations and measured the solvation dynamics in these þ micelles. The countercations examined were ammonium NHþ 4 , potassium K , and calcium 2þ Ca . This work showed that water motion inside the reverse micelles is slower than bulk water motion regardless of the counterion and that the countercation does play a role in reducing water motion in the reverse micelles. As the effective charge of the countercation increases, relatively stronger interactions between water and the cation occurs, resulting in slower solvation dynamics. However, this work also revealed that the immobilization or conﬁned water motion in the reverse micelles is largely due to the restrictive size of the micelles rather than speciﬁc water–ion interactions. Water motion in reverse micelles formed with other surfactants has also been examined. Willard et al. [39,40] have investigated the dynamics of water in lecithin reverse micelles as a function of morphology. For lecithin reverse micelles in cyclohexane with w ¼ 4:8, the reverse micelle solutions are nonviscous with isolated, spherical micelles, and a single, very slow relaxation time is observed for water motion inside the micelles. As small amounts of water are added to the sample, the micelles form into an entangled tube network and the micelle solutions become more and more viscous, while the water motion inside the micelle becomes more and more mobile. Three relaxation times are observed with time constants of 0.5, 15, and 200 ps, the fastest of which correlates to free water motion. These results were further conﬁrmed by investigating the water motion in lecithin reverse micelles in benzene [40]. In contrast to lecithin reverse micelles in alkanes, the micelles remain isolated and largely spherical with increasing w. This work suggests that the lecithin perturbs the water pool to a much greater extent than similar AOT reverse

408

Levinger and Riter

FIG. 4 Time-resolved ﬂuorescence Stokes shift of coumarin 343 in Aerosol OT reverse micelles; (a) normalized time-correlation functions, CðtÞ ¼ ðtÞ ð1Þ=ð0Þ ð1Þ, and (b) unnormalized time-correlation functions, SðtÞ ¼ ðtÞ ð1Þ, showing the magnitude of the overall Stokes shift in addition to the dynamic response. w0 ¼ 1:1 (*), 5 (!), 7.5 (&), 15 (^), and 40 (*) and for bulk aqueous Naþ solution (~). Points are data and lines that are multiexponential ﬁts to the data. (Reprinted from Ref. 38 with permission from the American Chemical Society.)

micelles and that the surfactant interface between the water pool and continuous nonpolar solvent phase sequesters water to a much greater degree than has been previously predicted. In addition, water motion has been investigated in reverse micelles formed with the nonionic surfactants Triton X-100 and Brij-30 by Pant and Levinger [41]. As in the AOT reverse micelles, the water motion is substantially reduced in the nonionic reverse micelles as compared to bulk water dynamics with three solvation components observed. These three relaxation times are attributed to bulklike water, bound water, and strongly bound water motion. Interestingly, the overall solvation dynamics of water inside Triton X-100 reverse micelles is slower than the dynamics inside the Brij-30 or AOT reverse micelles, while the water motion inside the Brij-30 reverse micelles is relatively faster than AOT reverse micelles. This work also investigated the solvation dynamics of liquid tri(ethylene glycol) monoethyl ether (TGE) with different concentrations of water. Three relaxation time scales were also observed with subpicosecond, picosecond, and subnanosecond time constants. These time components were attributed to the damped solvent motion, seg-

Dynamics of Polar Solvent Motion

409

mental motion, and the co-operative motion of the polymer solution, respectively. The results of this work show that while the restrictive micellar environment does play a role in the solvation dynamics of water inside nonionic reverse micelles, it is only a minor role. In fact, the interaction of water with the polymer-like headgroups of the surfactants plays the key role in immobilizing water in the micelles. Finally, polar solvation dynamics using solvents other than water has been reported in AOT reverse micelles. Riter et al. have measured the motion of formamide in AOT reverse micelles with w ¼ 1:1. The vibrational spectra of formamide in the reverse micelles indicate that the intramicellar formamide retains a large degree of hydrogen bonding character, and its structure appears signiﬁcantly less perturbed by the restricted environment than water. However, this work showed that the diffusive solvent motion in the reverse micelles is essentially frozen and the solvation dynamics is very similar to what is observed for water. In addition, Shirota and Horie [42] have reported on the solvation dynamics of methanol and acetonitrile in the AOT reverse micelles. They also found that the solvation dynamics in the reverse micelles are signiﬁcantly slower than observed in bulk solutions. As for water, methanol motion increases with increasing w. However, the solvation dynamics of acetonitrile in the micelle interior is independent of w. The authors attribute these results to the role of intermolecular hydrogen bonding of the polar solvent in the reverse micelles. The results of TRFSS experiments have shown us that the reverse micellar interior has the effect of limiting solvent mobility [30,31,38–40,42,43] The origin of this immobilization is still unclear. While speciﬁc interactions with the surfactant headgroups seem to play a role, the reverse micellar milieu seems more important than a high concentration of ions.

III.

DYNAMICS AT LIQUID–SOLID INTERFACES

Due to the interactions of solvent molecules with the solid surface, one would expect the dynamics at interfaces to differ from bulk solution. Yanagimachi et al. [44] studied solvation dynamics of 1-butanol at silica surfaces. While the shorter solvent relaxation time components could not be resolved due to the > 60 ps time resolution of their instrument, the longer time components increased for the interfacial butanol, and the solvent appeared to be inﬂuenced a substantial distance from the interface. Richert and coworkers have probed solvation dynamics in geometrically conﬁned silica sol–gel glass pores using TRFSS [45]. They ﬁnd that solvent at the silica–solvent interface can exhibit motion orders of magnitude slower than bulk solvent. Using time-resolved optical Kerr effect measurements, Fourkas and coworkers [46,47] have probed liquid dynamics in porous silicate sol– gel glasses. They demonstrate that for weakly wetting solvents, such as CS2 and CH3 I, the dynamics of the molecules at the surface are slowed down due to geometrical conﬁnement. In contrast, for more interacting solvents, such as acetonitrile, the dynamics are inﬂuenced by molecular interactions with the surface. Pant and Levinger have measured the solvation dynamics of water at the surface of semiconductor nanoparticles [48,49]. In this work, nanoparticulate ZrO2 was used as a model for the TiO2 used in dye-sensitized solar photochemical cells. Here, the solvation dynamics for H2 O and D2 O at the nanoparticle surface are as fast or faster than bulk water motion. This is interpreted as evidence for reduced hydrogen bonding at the particle interface.

410

Levinger and Riter

As discussed in Section II.A, Eisenthal and coworkers have studied the related problem of isomerization at liquid–solid interfaces. They used time-resolved second harmonic generation to investigate the barrierless photoisomerization of malachite green at the silica–aqueous interface using femtosecond time-resolved second harmonic generation [26]. They found that the photoisomerization reaction proceeded but was an order of magnitude slower at the water–silica interface than in bulk solution.

IV.

THEORETICAL DESCRIPTIONS OF SOLVATION DYNAMICS AT LIQUID INTERFACES

While there exist many models of liquids at interfaces, there are very few that consider solvation dynamics. Compared to experimental studies, there are even fewer models for solvent dynamics at any kind of liquid interface [50–52]. Molecular dynamics calculations have been used to simulate polar–nonpolar interfaces, e.g., water–benzene [53], water– hexanol [54], and water-1,2 dichloroethane [55]. The most striking results from these studies is that the interface is molecularly sharp in all three cases, and there is increased hydrogen bonding on the aqueous side of the interfaces. Molecular dynamics simulations investigating the dynamics of polar solvation occurring in interfacial environments, speciﬁcally dynamics of water at liquid–liquid interfaces, have recently been reported by Benjamin and coworkers [51,56–60]. Benjamin’s calculations following solvent relaxation in response to interfacial charge transfer show that the interfacial solvent molecules relax more slowly than bulk solvent [51]. However, as close as one monolayer away from the interface, the water dynamics appear completely bulklike [51]. Michael and Benjamin investigated the solvation dynamics at the water–octanol interface modeled by the 50/50 mixture that was phase separated. In this case, the solvent response occurred on a subpicosecond as well as picosecond time scale. In comparison, the relaxation rate observed one monolayer into the octanol layer, 5 A˚ thick, would be more than two orders of magnitude slower. These results suggest a probe molecule would not only be sensitive to solvation dynamics at interfaces, it would also probe the nature of the interface. In his work, Benjamin has also simulated solvent dynamics at the interface between water and 1,2 dichloroethane [55]. The solvation dynamics are predicted to be modestly affected by the nonisotropic interfacial environment with the largest difference in the calculated time correlation functions arising from increased hydrogen bonding. Chandra and his coworkers have developed analytical theories to predict and explain the interfacial solvation dynamics. For example, Chandra et al. [61] have developed a time-dependent density functional theory to predict polarization relaxation at the solid– liquid interface. They ﬁnd that the interfacial molecules relax more slowly than does the bulk and that the rate of relaxation changes nonmonotonically with distance from the interface They attribute the changing relaxation rate to the presence of distinct solvent layers at the interface. Senapati and Chandra have applied theories of solvents at interfaces to a range of model systems [62–64]. While they are not direct theories or simulations of solvation dynamics, per se, several groups have modeled liquid dynamics at interfaces. Ursenbach et al. [50] have developed a model for water at the surface of a silicon single crystal. Their results show that the vibrational modes of water molecules at the surface are virtually unchanged from their bulk values. However, they suggest that ultrafast motions of the interfacial solvent, occurring on the time scale of molecular vibrations, may impact interfacial electron transfer. Using molecular dynamics calculations, Hartnig et al. [65] have simulated water

Dynamics of Polar Solvent Motion

411

motion within model polar and nonpolar cylindrical pores. In nonpolar pores, reduced hydrogen bonding at the surface results in a translational motion and dipolar motion that is faster than bulk water. However, in polar pores, generated by adding surface charges to the model system, the translation motion and dipolar relaxation times are longer than bulk. Using molecular dynamics calculations, Shinto et al. [66] have modeled the response of water at NaCl surfaces. While their simulations show that the water diffusivity is reduced at the surface, they also observe a strong perturbation to the hydrogen-bonding network for solvent molecules at the solid surfaces. A few groups have modeled dynamics at interfaces and in the aqueous core of selfassembled structures. Brown and Clarke [67] modeled an aqueous reverse micelle in a nonpolar solvent using a cationic surfactant. They reported that the anions associated with the surfactant are tightly bound to the cation headgroup surface although water molecules can signiﬁcantly penetrate into the hydrophobic region. Additionally, water molecules at the interface interact strongly with the anions and therefore do not have bulklike characteristics. Linse [53] investigated the structure and dynamics of water in reverse micelles formed with an anionic surfactant similar to AOT. He reported that interactions of water molecules with the ionic headgroups of the surfactant interface essentially break the hydrogen-bonding network of the water and that although the hydrophobic portion of the interface plays a role in breaking this network, it is only a minor one. He also attributed the interaction of the water with sodium ions and anionic headgroup to reduced translational and rotational motion of water in the micellar environment. Very recently, Faeder and Ladanyi have modeled the interior of AOT reverse micelles including solvation dynamics [68]. They observe water motion that is strongly impacted by the interfacial chemistry and that water does not relax like bulk solvent at all. The slower relaxation in this case is attributed to strong interactions of the water molecules at the reverse micellar inner interface.

V.

CONCLUSIONS AND FUTURE WORK

The overall picture arising from a comprehensive view of the solvation dynamics studies at interfaces that have been done can be summarized; interfacial dynamics differ from bulk solution and cannot simply be considered the same as the bulk. In most cases, the structure of the interface appears to impact the dynamics by slowing them down. However, in a few cases, the dynamics appear to speed up. While apparent from the amount of work that can be reported, it is obvious that we really do not have a comprehensive view of the dynamics of polar solvation at liquid interfaces. Especially lacking are studies probing the inertial response to the dynamics of polar solvation occurring at interfaces. There is enormous room for growth in the entire ﬁeld as there exist such an extensive range of interfaces that are important in chemistry, biology, and physics. We can look forward to more detailed studies on the vast array of available systems.

REFERENCES 1. 2.

G. J. Hanna and R. D. Noble. Chem. Rev. 85:583 (1985). P. F. Barbara and W. Jarzeba, in Advances in Photochemistry, vol. 15 (eds. D. H. Volman, G. S. Hammond, and K. Gollnick) John Wiley, 1990, pp. 1–68.

412 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

Levinger and Riter P. F. Barbara, T. J. Meyer, and M. A. Ratner. J. Phys. Chem. 100:13148 (1996). M. Maroncelli. J. Mol. Liq. 57:1 (1993). M. L. Horng, J. A. Gardecki, A. Papazyan, and M. Maroncelli. J. Phys. Chem. 99:17311 (1995). G. R. Fleming and M. H. Cho. Annu. Rev. Phys. Chem. 47:109 (1996). R. M. Stratt and M. Maroncelli. J. Phys. Chem. 100:12981 (1996). J. D. Simon. Acc. Chem. Res. 21:128 (1988). J. D. Simon. Pure Appl. Chem. 62:2243 (1990). B. Bagchi. Annu. Rev. Phys. Chem. 40:115 (1989). B. Bagchi and A. Chandra. Adv. Chem. Phys. 80:1 (1991). P. F. Barbara and W. Jarzeba. Adv. Photochem. 15:1 (1990). W. Jarzeba, G. C. Walker, A. E. Johnson, and P. F. Barbara. Chem. Phys. 152:57 (1991). R. M. Stratt and M. Maroncelli. J. Phys. Chem. 100:12981 (1996). H. Heitele. Angew. Chem. 105:378 (1993). (See also Angew. Chem. Int. Ed. Engl. 1993, 1932(1993), 1359–1997.) J. T. Hynes. Understand. Chem. React. 7:345 (1994). P. J. Rossky and J. D. Simon. Nature (London) 370:263 (1994). R. S. Fee and M. Maroncelli. Chem. Phys. 183:235 (1994). R. Jimenez, G. R. Fleming, P. V. Kumar, and M. Maroncelli. Nature 369:471 (1994). R. Srinivasan and R. de Levie. J. Phys. Chem. 91:2904 (1987). K. Bessho, T. Uchida, A. Yamauchi, T. Shioya, and N. Teramae. Chem. Phys. Lett. 264:381 (1997). E. Eisenthal. Chem. Rev. 96:1348 (1996) D. Zimdars, J. I. Dalap, K. B. Eisenthal, and T. F. Heinz. Chem. Phys. Lett 301:112 (1999). D. Zimdars and K. B. Eisenthal. J. Phys. Chem. B 103:10567 (1999). E. V. Sitzmann and K. B. Eisenthal. J. Phys. Chem. 92:4579 (1988). X. Shi, E. Borguet, A. N. Tarnovsky, and K. B. Eisenthal. Chem. Phys. 205:167 (1996). A. Castro, E. V. Sitzmann, D. Zhang, and K. B. Eisenthal. J. Phys. Chem. 95:6752 (1991). D. Zimdars, J. I. Dalap, K. B. Eisenthal, and T. F. Heinz. J. Phys. Chem. B 103:3425 (1999). N. Sarkar, K. Das, A. Datta, S. Das, and K. Bhattacharyya. J. Phys. Chem. 100:10523 (1996). D. Pant, R. E. Riter, and N. E. Levinger. J. Chem. Phys. 109:9995 (1998). R. E. Riter, E. P. Undiks, and N. E. Levinger. J. Am. Chem. Soc. 120:6062 (1998). T. De and A. Maitra. Adv. Colloid Interface Sci. 59:95 (1995). J. Zhang and F. V. Bright. J. Phys. Chem. 95:7900 (1991). C. H. Cho, M. Chung, J. Lee, T. Nguyen, S. Singh, M. Vedamuthu, S. H. Yao, J. B. Zhu, and G. W. Robinson. J. Phys. Chem. 99:7806 (1995). V. Crupi, S. Magazu´, G. Maisano, D. Majolino, and P. Migliardo. Physica Scripta 50:200 (1994). D. M. Mittleman, M. C. Nuss, and V. L. Colvin. Chem. Phys. Lett. 275:332 (1997). S. Das, A. Datta, and K. Bhattacharyya. J. Phys. Chem. A 101:3299 (1997). R. E. Riter, D. M. Willard, and N. E. Levinger. J. Phys. Chem. B 102:2705 (1998). D. M. Willard, R. E. Riter, and N. E. Levinger. J. Am. Che. Soc. 120:4151 (1998). D. M. Willard and N. E. Levinger, J. Phys. Chem., submitted (2000). D. Pant and N. E. Levinger. Langmuir, submitted (2000). H. Shirota and K. Horie. J. Phys. Chem. B 103:1437 (1999). R. E. Riter, E. P. Undiks, J. R. Kimmel, and N. E. Levinger. J. Phys. Chem. B 102:7931 (1998). M. Yanagimachi, N. Tamai, and H. Masuhara. Chem. Phys. Lett. 200:469 (1992). C. Streck, Y. B. Melnichenko, and R. Richert. Phys. Rev. B Condensed Matter 53:5341 (1996). B. J. Loughnane, R. A. Farrer, and J. T. Fourkas. J. Phys. Chem. B 102:5409 (1998). B. J. Loughnane and J. T. Fourkas. J. Phys. Chem. B 102:10288 (1998). D. Pant and N. E. Levinger. Chem. Phys. Lett 292:200 (1998). D. Pant and N. E. Levinger. J. Phys. Chem. B 103:7846 (1999). C. P. Ursenbach, A. Calhoun, and G. A. Voth. J. Chem. Phys. 106:2811 (1997).

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51. I. Benjamin, in Reaction Dynamics in Clusters and Condensed Phases (J. Jortner, ed.), Kluwer Academic Publishers, Netherlands, 1994, pp. 179–194. 52. D. Michael and I. Benjamin. J. Phys. Chem. B 102:5145 (1998). 53. P. Linse. J. Chem. Phys. 86:4177 (1987). 54. J. Gao and W. L. Jorgensen. J. Phys. Chem. 92:5813 (1988). 55. I. Benjamin. J. Chem. Phys. 97:1432 (1992). 56. I. Benjamin. Chem. Phys. 180:287 (1994). 57. I. Benjamin, in Liquid–Liquid Interfaces (A. G. Volkov and D. W. Deamer, eds.), CRC Press, Boca Raton, FL, 1996, pp. 179–211. 58. I. Benjamin. Annu. Rev. Phys. Chem. 48:407 (1997). 59. D. Michael and I. Benjamin. J. Phys. Chem. 99:1530 (1995). 60. D. A. Rose and I. Benjamin. J. Phys. Chem. 96:9561 (1992). 61. A. Chandra, S. Senapati, and D. Sudha. J. Chem. Phys. 109:10439 (1998). 62. A. Chandra and S. Senapati. J. Mol. Liq. 77:77 (1998). 63. S. Senapati and A. Chandra. Theochem. J. Mol. Struct. 455:1 (1998). 64. S. Senapati and A. Chandra. Chem. Phys. 231:65 (1998). 65. C. Hartnig, W. Witschel, and E. Spohr. J. Phys. Chem. B 102:1241 (1998). 66. H. Shinto, T. Sakakibara, and K. Higashitani. J. Phys. Chem. B 102:1974 (1998). 67. D. Brown and J. H. R. Clarke. J. Phys. Chem. 92:2881 (1988). 68. J. Faeder and B. M. Ladanyi. J. Phys. Chem. B 104:1033 (2000).

17 Capacitance and Surface Tension Measurements of Liquid^Liquid Interfaces ZDENE˘K SAMEC J. Heyrovsky´ Institute of Physical Chemistry, Academy of Sciences of The Czech Republic, Prague, Czech Republic

I.

INTRODUCTION

The structure of the interface between two immiscible electrolyte solutions (ITIES) has been the matter of considerable interest since the beginning of the last century [1]. Typically, such a system consists of water (w) and an organic solvent (o) immiscible with it, each containing an electrolyte. Much information about the ITIES has been gained by application of techniques that involve measurements of the macroscopic properties, such as surface tension or differential capacity. The analysis of these properties in terms of various microscopic models has allowed us to draw some conclusions about the distribution and orientation of ions and neutral molecules at the ITIES. The purpose of the present chapter is to summarize the key results in this ﬁeld.

II.

THERMODYNAMIC ANALYSIS

A.

Gibbs Adsorption Equation

Thermodynamics of the ITIES was developed by several authors [2–6] on the basis of the interfacial phase model of Gibbs or Guggenheim. General treatments were outlined by Kakiuchi and Senda [5] and by Girault and Schiffrin [6]. At a constant temperature T and pressure p the change in the surface tension can be related to the relative surface excess concentrations iw;o of the species i with respect to both solvents [6], d ðT; p ¼ constÞ ¼

k X

~i w;o i d

ð1Þ

i¼1

where ~ i ¼ i þ zi F’ is the electrochemical potential, i is the chemical potential, zi is the number of the elementary charges (charge number) carried by the species i, F is the Faraday constant, and ’ is the inner (Galvani) potential of the phase and the summation is carried out over all species (i.e., ions and ion pairs) present in both phases. The relative surface excess concentrations iw;o are deﬁned by 415

416

Samec

w;o ¼ i nwi i

w noi o

ð2Þ

where i ¼ ni =A is the surface concentration (ni is the total number of moles of the species i in the interfacial region and A is the interfacial area), no and nw are the number of moles of a component (ion, ion pair, or solvent) in the organic and water phase respectively, and , w , or o are the following determinants: w o w no nww nw w no o ð3Þ ¼ ¼ ¼ o w o no nw no now o w o w Equation (2) is considerably simpliﬁed if the mutual solubility of the two solvents is low, i.e., now nww and nwo noo , w;o ¼ i i

nwi noi w w o o nw no

ð4Þ

Further simpliﬁcations are possible if the species i is not present in one or the other liquid phase ðni ¼ 0Þ, i.e., the second or the third term in Eq. (4) vanishes. The equilibrium partition of ions present in the system gives rise to the equilibrium Galvani potential difference wo ’ ¼ ’ðwÞ ’ðoÞ between the phases w and o (Nernst potential) [7,8] wo ’ ¼ wo ’0i þ ðRT=zi F Þ lnðaoi =awi Þ

ð5Þ

where ao and aw are the activities of ions in the organic and water phase respectively, and wo ’0i is the standard potential difference, which is related to the standard Gibbs energy of ion transfer from w to o, ow G0i , wo ’0i ¼ ow G0i =zi F

B.

ð6Þ

Nonpolarized ITIES

The simplest system is represented by the nonpolarized interface, which is formed in the presence of a single binary electrolyte RX completely dissociating into ions Rþ and X in each phase, Rþ X ðoÞ

j

Rþ X ðwÞ

ð7Þ

where the stroke represents the interface. At equilibrium the potential difference (distribution potential) will establish [7] wo ’ ¼ wo ’0R þ wo ’0X =2 þ f ði Þ ð8Þ where f ði Þ ¼ ðRT=2FÞ lnðþw o =þo w Þ is the activity coefﬁcients term. Note that Eq. (8) implies that the distribution potential of a single binary electrolyte is explicitly independent of electrolyte concentration. For this system the Gibbs adsorption equation, Eq. (1), takes the form [2] w;o w;o dRX ¼ 2RTRX d ln a d ðT; p ¼ constÞ ¼ RX

ð9Þ

where RX is the chemical potential of the electrolyte RX, a is its mean activity, and w;o RX is its relative surface excess concentration. In view of the electroneutrality condition, w;o RX equals the excess surface concentration of the cation and the anion,

Capacitance and Surface Tension

417

w;o w;o w;o RX ¼ Rþ ¼ X

ð10Þ

Girault and Schiffrin [4] used a similar approach to derive the expression for the relative surface excess of water with respect to the electrolyte RX and the organic solvent, dðT; p ¼ constÞ ¼ RX;o dw w

ð11Þ

where w;o w ¼ w

nww now w RX o o nRX no

ð12Þ

Examples of more complicated systems constituting the nonpolarized ITIES can be described by the schemes Cþ Y

j Rþ X ; Cþ X

ðoÞ

ð13Þ

ðwÞ

or Sþ Y ; Cþ Y ðoÞ

j Rþ X ; Cþ X ðwÞ

ð14Þ

where Cþ represents the common cation, which determines the equilibrium potential difference across the ITIES if the inequalities wo ’0Sþ , wo ’0X wo ’0Cþ wo ’0Y , wo ’0Rþ are fulﬁlled. When in the system (13) the reference electrodes reversible to anion X and cation Cþ are connected to the phase w and o respectively, the Gibbs adsorption equation reads w w;o w;o dðT; p ¼ constÞ ¼ QdEoþ þ Rþ dRX þ Y dCY

ð15Þ

with w;o w;o w;o Q=F ¼ Rþ X ¼ w;o Y Cþ

ð16Þ 0

w Eoþ

and is the potential difference between the metal contacts M and M to the aqueous w ¼ ’ðMÞ ’ðM 0 Þ. Analogously, and organic solvent reference electrodes respectively, Eoþ when in the system (14) the reference electrodes that are reversible to anion X and cation Sþ are connected to the phase w and o respectively, the Gibbs adsorption equation reads w w;o w;o dðT; p ¼ constÞ ¼ QdEoþ þ Rþ dRX þ Y dSY þ w;o Cþ dCX

ð17Þ

w;o w;o w;o w;o Q=F ¼ Rþ þ Cþ w;o X ¼ Y Sþ

ð18Þ

with

C.

Ideally Polarized ITIES

Koryta et al. [9] have shown that the system with two different electrolytes RX and SY in the phase w and o respectively, S þ Y ðoÞ

j Rþ X ðwÞ

ð19Þ

can have the properties of an ideally polarizable electrode, provided that the inequality wo ’0Sþ , wo ’0X wo ’0Y , wo ’0Rþ is fulﬁlled. Upon taking into account the ion pairing in the bulk phase or at the interface, e.g.

418

Samec

Rþ ðwÞ þ Y ðoÞ ¼ Rþ Y ðÞ

ð20Þ

Eq. (1) can be written in the form [6] w;o w w;o w;o þ Rþ þ RX þ RY dðT; p ¼ constÞ ¼ QdEoþ dRX w;o w;o w;o þ Y þ SY þ RY dSY

ð21Þ

w;o w;o w;o w;o w;o w;o w;o Q=F ¼ Rþ X þ RY w;o SX ¼ Y Sþ þ RY SX

ð22Þ

with

D.

Surface Excess Charge and Concentrations

w The extensive variable Q associated with the electrical potential Eoþ in Eqs. (15), (17), and (21) is the thermodynamic surface excess charge density, which is deﬁned by

@ Q¼ w @Eoþ

ð23Þ T;p;

Note that for systems (13) and (14) there is one salt component, i.e., CX and CY respectively, the chemical potential of which can be varied independently allowing for a change w w in Eoþ . On the other hand, for an ideally polarized ITIES a change in Eoþ at constant chemical potentials of all components can be accomplished by supplying the charge Q from the external electric source. As it has been pointed out [6], Q is not a surface charge density in the sense discussed for the metal–solution interface, but the amount of the electricity ﬂowing to the interphase when its area is increased by a unit amount, i.e., socalled total charge in Planck’s terminology [10]. The closely related quantity is the differential capacity C, which is deﬁned by:

@Q C¼ w @Eoþ

ð24Þ T;p;

Eqs. (15), (17), and (21) can be used to deﬁne other observable quantities, such as relative surface excess concentrations of ions, which also comprise the contributions from the free ionic and ion-pair surface excesses, e.g., for the ideally polarized ITIES,

@ w;o w;o ¼ Rþ þ RX þ w;o RY @RX T;p;E w ;SY oþ @ w;o w;o ¼ ¼ Y þ w;o SY þ RY @SY T;p;E w ;RX

w;o þ ¼ w;o

ð25Þ ð26Þ

oþ

w;o w;o Apparently, the relative surface excess concentrations þ and represent the total þ amount of the components R and Y (either as free ions or as ion pairs) that should be w added to the system to maintain SY and RX respectively as well as Eoþ constant when the area of the interface is increased by a unit amount.

Capacitance and Surface Tension

III.

MICROSCOPIC MODELS

A.

Modiﬁed Verwey–Niessen Model (MVN)

419

According to the earliest model by Verwey and Niessen [11] the ITIES can be represented by the diffuse double layer with one phase containing an excess of the positive space charge and the other phase an equal excess of the negative space charge [Fig. 1(a)]. The model was analyzed [11] with the help of the theory of Gouy [12] and Chapman [13] (GC). Following the analogy with Stern’s modiﬁcation [14] of the GC theory, Gavach et al. [2] introduced the concept of the ion-free layer of the oriented solvent molecules, which separates the two space charge regions at the ITIES. In this model, the potential difference wo ’ splits into three potential differences wo ’ ¼ wo ’i þ ’o2 ’w2

ð27Þ

o w where w o ’i is the potential difference across the inner layer and ’2 and ’2 are the potential differences across the space charge regions in the phases o and w, respectively. In the absence of the speciﬁc ion adsorption, the differential capacity C can be represented as a series combination of the capacity of the inner layer Ci and of the capacities of the space charge regions (diffuse double layer) C2w and C2o on the aqueous and the organic solvent side of the interface respectively [15],

1 dwo ’ 1 1 1 1 1 ¼ ¼ þ ¼ þ þ C dQ Ci Cd Ci C2w C2o

ð28Þ

where Ci ¼ dQ=dwo ’i and C2s ¼ dQ=d’s2 : Relatively high values of the experimental capacity Ci have led Samec et al. [16] to propose that ions can penetrate into the inner layer over some distance. The effect of the ion penetration was taken into account by solving the linearized Poisson–Boltzmann (PB) equation in all three regions of the MVN model with the result [17], 1 1 1 ¼ þ þ C Ci Cd

ð29Þ

where the correction term < 0 depends on the Debye screening length in the inner layer and is responsible for the increased value of the inner-layer capacity.

FIG. 1 Structure of the ITIES: (a) Verwey–Niessen model [11], (b) mixed solvent layer model [4], and (c) molecular dynamics simulation [24].

420

B.

Samec

Primitive Model

Torrie and Valleau [18] used the Monte Carlo technique to examine several features of the ITIES that are not properly accounted for by the GC theory. They considered in particular (a) ion–ion correlations in the space charge region, (b) ion–ion correlations between the two space charge regions, (c) interpenetration of the two space charge regions, and (d) image forces for the primitive model, which was represented by the hard-sphere ions placed in a uniform dielectric medium. An important consequence of allowing for the ﬁnite size of ions is the thinner diffuse layer and the smaller potential diffuse-layer potential difference, as compared with the estimates based on the GC theory. This feature was also examined [17] with other statistical–mechanical theories of the diffuse double layer [19]. The modiﬁed Poisson–Boltzmann (MPB) theory of Outhwaite et al. [20] was used to predict the theoretical dependence of the capacity C on the interfacial potential difference by Cui et al. [21]. These authors have taken into account the ion penetration into the inner layer by adding a linear term to the electrostatic potential. A lack of consistency in this approach was criticized by Wandlowski et al. [22]. The latter authors used the MPB theory for an estimate of the diffuse-layer potential difference from the experimental charge density, which was obtained by an integration of the capacity curves. On this basis, the inner-layer potential difference and the inner-layer capacity were evaluated [22]. C.

Mixed Solvent Layer

Girault and Schiffrin [4] proposed an alternative model, which questioned the concept of the ion-free inner layer at the ITIES. They suggested that the interfacial region is not molecularly sharp, but consist of a mixed solvent region with a continuous change in the solvent properties [Fig. 1(b)]. Interfacial solvent mixing should lead to the mixed solvation of ions at the ITIES, which inﬂuences the surface excess of water [4]. Existence of the mixed solvent layer has been supported by theoretical calculations for the lattice-gas model of the liquid–liquid interface [23], which suggest that the thickness of this layer depends on the miscibility of the two solvents [23]. However, for solvents of experimental interest, the interfacial thickness approaches the sum of solvent radii, which is comparable with the inner-layer thickness in the MVN model. Benjamin [24], Schweighofer and Benjamin [25], and Michael and Benjamin [26] investigated the structure and dynamics of the water–1,2-dichloroethane [24,25] or nitrobenzene [26] interfaces by using molecular dynamics computer simulations. The relevant molecular dynamics studies have been reviewed [27,28]. These simulation indicated that the liquid–liquid interfaces are molecularly sharp but very rough. The interfacial roughness can be described as the protrusion of water molecules, hydrogen-bonded to each other, into the organic solvent [24,26], or as thermally populated capillary waves on the sharp interface [28]. Hence, the interfacial structure is best represented by Fig. 1(c). It has been shown that the electric ﬁeld tends to broaden the interface by increasing the amplitude of ﬁngerlike distortions [25].

IV.

SURFACE TENSION MEASUREMENTS

A.

Nonpolarized ITIES

Surface tension of the nonpolarized ITIES was investigated by using the drop-weight [2,3,29], maximum bubble pressure [30] and pendant drop [4] methods. The latter method

Capacitance and Surface Tension

421

has been improved considerably by introducing computer analysis of the video image of the pendant drop [32,33]. Gavach et al. [2] measured the surface tension of the nonpolarized water–nitrobenzene interface in the presence of various tetra-alkylammonium halides. The relative surface excess w;o RX of the salt RX, Eq. (9), was found to be proportional to the square root of the equilibrium electrolyte concentration in the aqueous phase, in an agreement with the GC theory [2]. By solving the PB equation of the GC theory the following relationship was derived [2], w o w o w w w;o RX RX ¼ Rþ þ Rþ ¼ X þ X ¼ ðA =F Þ ½expðF’2 =2RT Þ 1 ð30Þ þp1=2 ½expðF’o2 =2RT Þ 1 where wi and oi are the surface concentrations of the ion i on the aqueous and the organic solvent side of the interface respectively, Aw ¼ ð2RTw 0 c0;w Þ1=2 , p ¼ ðo c0;o =w c0;w Þ, and 0 are the relative dielectric permittivity of the solvent and the permittivity of vacuum respectively, c0;w and c0;o are the equilibrium electrolyte concentrations in the aqueous and the organic solvent phase respectively. In addition [2], RT 1 þ p exp½F ðwo ’ wo ’i Þ=2RT w ln ’2 ¼ ð31Þ F 1 þ p exp½F ðwo ’ wo ’i Þ=2RT Provided that jwo ’ wo ’i j ¼ const, then also ’o2 and ’w2 are constant, and RX is proportional to ðc0;w Þ1=2 . The observed nonlinearity at higher electrolyte concentrations [2] is probably due to a change in the inner-layer potential difference w ’i with the surface excess charge density. The inner-layer potential difference (< 50 mV) was evaluated from the linear part of the RX vs. ðc0;w Þ1=2 plot, and was found to depend on the nature of the salt, i.e., on the distribution potential, Eq. (8). The same system has been studied previously by Boguslavsky et al. [29], who also used the drop weight method. While qualitatively the same behavior was observed over the broad concentration range up to the solubility limit, the data were ﬁtted to a Frumkin isotherm, i.e., the ions were supposed to be speciﬁcally adsorbed as the interfacial ion pair [29]. The equation of the Frumkin-type isotherm was derived by Krylov et al. [31], on assuming that the electrolyte concentration in each phase is high, so that the potential difference across the diffuse double layer can be neglected. Girault and Schiffrin [4] measured the surface tension of the nonpolarizable ITIES in the presence of various inorganic electrolytes (LiCl, NaCl, KCl, MgSO4 ). By using Eq. (11) they evaluated the relative surface excess of water at the water–nitrobenzene, water– 1,2-dichloroethane and water–n-heptane interfaces and estimated the thickness of the ionfree layer. Implicit assumption was that the second and the third term on the right-hand side of Eq. (12) can be neglected. Indeed, because the standard Gibbs energies of transfer of inorganic cations and anions involved are nearly equal, the distribution potential is close to zero and hence RX 0. Since the thickness of the ion-free layer was dependent on the polarity of the organic solvent, and for polar solvents was less than unity, the authors concluded that the interfacial region consists of a mixed solvent region with a continuous change in the solvent properties, cf. the Section II.C. Gross et al. [3] and Reid et al. [30] measured surface tension of the water–nitrobenzene interface in the presence of bromides of sodium and tetra-alkylammonium ions in water and tetra-alkylammonium tetraphenylborates in nitrobenzene, i.e., tetra-alkylammonium served as the potential-determining ion, cf. the scheme (13). The surface tension vs. the potential difference wo ’ plot (electrocapillary curve), cf. Eq. (15), was constructed by varying the concentration of tetra-alkylammonium bromide in water, while holding

422

Samec

constant the concentration of the electrolyte in nitrobenzene. A comparison of the measured surface tension with that calculated by an integration of the surface charge density suggested that the potential difference is concentrated in the diffuse double layer, and that the zero-charge potential difference wo; ’pzc ¼ wo ’i ¼ 1 mV [3] or 0 mV [30]. Note, however, that this conclusion is at variance with the analysis of the surface tension of the nonpolarized ITIES by the same authors [2], as well as with the results of the study of the ideally polarized ITIES reviewed in the next section. Recently, the newly developed time-resolved quasielastic laser scattering (QELS) has been applied to follow the changes in the surface tension of the nonpolarized water– nitrobenzene interface upon the injection of cetyltrimethylammonium bromide [34] and sodium dodecyl sulfate [35] around or beyond their critical micelle concentrations. As a matter of fact, the method is based on the determination of the frequency of the thermally excited capillary waves at liquid–liquid interfaces. Since the capillary wave frequency is a function of the surface tension, and the change in the surface tension reﬂects the ion surface concentration, the QELS method allows us to observe the dynamic changes of the ITIES, such as the formation of monolayers of various surfactants [34]. B.

Ideally Polarized ITIES

1. Structure of the ITIES in the Absence of the Speciﬁc Adsorption Kakiuchi and Senda [36] measured the electrocapillary curves of the ideally polarized water–nitrobenzene interface by the drop time method using the electrolyte dropping electrode [37] at various concentrations of the aqueous (LiCl) and the organic solvent (tetrabutylammonium tetraphenylborate) electrolytes. An example of the electrocapillary curve for this system is shown in Fig. 2. The surface excess charge density Q, and the w;o þ relative surface excess concentrations Liþ and w;o TPB of the Li cation and the tetraphenylborate anion respectively, were evaluated from the surface tension data by using Eq. w;o (21). The relative surface excess concentrations w;o Cl and TBAþ of the Cl anion and the tetrabutylammonium cation respectively were then evaluated by using Eq. (22), in which the contributions from the interfacial ion pairs are neglected. The dependencies of the relative surface excess concentrations of all four ions on the charge density Q were found to be consistent with the MVN model and with the prediction of the GC theory. In particular, these relative surface excesses can be calculated by using Eq. (2), with the surface ion concentration given by the expression that follows from the GC theory for the case of absence of the speciﬁc ion adsorption, e.g., for cations and anions of the aqueous phase [36] h 1=2 i ¼ w ¼ ðAw =F Þ y þ y2 þ 1 1 ð32Þ where y ¼ Q=2Aw . The absence of the speciﬁc ion adsorption is also corroborated by the w w =@RX Þq;SY and ð@Eoþ =@SY ÞQ;RX [36]. values of the Jesin–Markov coefﬁcients ð@Eoþ Recently, Samec et al. [38] have investigated the same system by the video-image pendant drop method. Surface tension data from the two studies are compared in Fig. 2, where the potential scale from the study [36] was shifted so that the positions of the electrocapillary maxima coincide. The systematic difference in the surface tension data of ca. 3%, cf. the dotted line in Fig. 2, was ascribed to the inaccurate determination of the drop volume, which was calculated from the shape of the drop image and used further in the evaluation of the surface tension [38]. A point of interest is the inner-layer potential difference wo ’i , which can be evaluated relative to the zero-charge potential difference wo ’pzc by using Eq.

Capacitance and Surface Tension

423

FIG. 2 Potential dependence of the surface tension of the interface between 0.1 M LiCl in water and 0.05 M tetrabutylammonium tetraphenylborate in nitrobenzene, taken from Ref. 38 (*) and Ref. 36 (&). The dotted line represents the data from Ref. 38 multiplied by a factor of 0.97. The potential scale from Ref. 36 was shifted so that the positions of the electrocapillary maxima coincide.

(27) and the GC relationship between the excess surface charge density Q and the potential differences ’w2 and ’o2 [36], Q ¼ 2Aw sinhðF’w2 =2RT Þ ¼ 2Ao sinhðF’o2 =2RT Þ

ð33Þ

where Ao ¼ ð2RTo 0 c0;o Þ1=2 . This potential difference was found to contribute signiﬁcantly to the interfacial potential difference wo ’ depending on the value of Q (cf. Fig. 3), which probably reﬂects the effect of the electric ﬁeld on the orientation of the surface dipole [38]. By using the standard potential difference for the tetrabutylammonium ion (wo ’0TBAþ ¼ 0:248 V) as a reference, the zero-charge potential difference wo ’pzc was evaluated as being equal to approximately 20 mV [36]. On the other hand, the value wo ’pzc ¼ 33 mV was found to be more consistent with the potential scale based on the equilibrium potential measurements for a series of tetra-alkylammonium ions [38]. The latter value suggests that in the absence of the electric ﬁeld the surface dipole points to the organic phase, in an agreement with the results of molecular dynamics simulations [26]. Girault and Schiffrin [6] and Samec et al. [39] used the pendant drop video-image method to measure the surface tension of the ideally polarized water–1,2-dichloroethane interface in the presence of KCl [6] or LiCl [39] in water and tetrabutylammonium tetraphenylborate in 1,2-dichloroethane. Electrocapillary curves of a shape resembling that for the water–nitrobenzene interface were obtained, but a detailed analysis of the surface tension data was not undertaken. An independent measurement of the zero-charge potential difference by the streaming-jet electrode technique [40] in the same system provided the value identical with the potential of the electrocapillary maximum. On the basis of the standard potential difference of 0:225 V for the tetrabutylammonium ion transfer, the zero-charge potential difference was estimated as equal to 8 10 mV [41].

424

Samec

FIG. 3 Inner-layer potential difference wo ’i relative to the zero-charge potential difference wo ’pzc vs. the excess surface charge Q for the interface between LiCl in water and tetrabutylammonium tetraphenylborate in nitrobenzene: Ref. 38 (full line) and Ref. 36 (dotted line).

2. Structure of the ITIES in the Presence of Ionic and Nonionic Surfactants Kakiuchi et al. [42–45] studied the adsorption of ionic and nonionic surfactants on the ideally polarized water–nitrobenzene interface by the drop-time method. The adsorption of hexadecyltrimethylammonium (HTMAþ ) cation was found to be markedly dependent on the interfacial potential difference [42] (cf. Fig. 4). No speciﬁc adsorption was observed when the aqueous phase was positive, while a strong adsorption occurred when the potential of the aqueous phase was negative with respect to the potential of the nitrobenzene phase. The speciﬁc adsorption of HTMAþ led to a change in the structure of the electrical double layer. The polar headgroup of this ion probably protrudes into the aqueous phase, which is accompanied by the inversion of the outer Helmholtz potential ’o2 in nitrobenzene from a negative to positive value. The magnitude of the surface tension depression due to the speciﬁc adsorption of HTMAþ ion was inﬂuenced by the counteranion [43]. The effect became larger in the order F < Cl < Br indicating a speciﬁc counterion binding at the ITIES in this order, i.e., the formation of the interfacial ion pair [43]. On the other hand, a strong adsorption of nonionic surfactants such as tetraethylene glycol monododecyl ether [44], hexa- and octaethylene glycol monododecyl ethers [45] was observed over the whole potential range of the ideally polarized ITIES. The adsorption was stabilized by the complex formation with the Liþ cation in the aqueous phase. The standard Gibbs energy of adsorption was found to depend on the number n of oxyethylene units, indicating an increasing preference for the complex formation with the increasing n. An effect of the interfacial potential difference on the adsorption has led the authors [45] to a conclusion that, owing to the complex formation at the interface, the adsorbed neutral ethers behave as cationic surfactants. In a closely related study, Marec˘ek et al. [46] used the pendant drop video-image method to investigate the adsorption and surface reactions of calix[4]arene ligands at the ideally polarized water–1,2-dichloroethane interface. The difference between the surface tensions in acidic and alkaline media was ascribed to a difference in the charge on the adsorbed ligand. A formation of the surface complex with Ba2þ and Ca2þ cations was found to reduce the change in the surface tension, as compared with the case of adsorbed

Capacitance and Surface Tension

425

FIG. 4 Electrocapillary curve for the interface between 0.05 M LiCl in water and (0:1 x) M tetrapentylammonium tetraphenylborate+x M hexadecyltrimethyammonium tetraphenylborate in nitrobenzene at 25 C: x ¼ 0 (*), 0.005 (~), 0.02 (&), 0.05 (*), and 0.1 (~). (From Ref. 42.)

dissociated ligands possessing a higher charge. The effect of the charge of adsorbed ions on their surface concentration was then studied for a series of negatively charged ions [47]. The limiting surface concentration s was found to be related to the charge number z of the adsorbed ions, in an agreement with the derived formula s ¼ 1:42 106 =z4=3 mol m2 . A conclusion was made that small charged molecules can hardly form a compact monolayer and that the formation of such a monolayer requires that the size of adsorbed molecules must be comparable with the distance between the adsorbed molecules which, however, depends on their charge number. Owing to repulsive interactions in the adsorbed layer, the drop in the surface tension can be large even if the limiting surface concentration is low. 3.

Adsorption of Compounds of Biological Signiﬁcance

Koryta et al. [48] ﬁrst stressed the relevance of adsorbed phospholipid monolayers at the ITIES for clariﬁcation of biological membrane phenomena. Girault and Schiffrin [49] ﬁrst attempted to characterize quantitatively the monolayers of phosphatidylcholine and phosphatidylethanolamine at the ideally polarized water–1,2-dichloroethane interface with electrocapillary measurements. The results obtained indicate the importance of the surface pH in the ionization of the amino group of phosphatidylethanolamine. Kakiuchi et al. [50] used the video-image method to study the conditions for obtaining electrocapillary curves of the dilauroylphosphatidylcholine monolayer formed on the ideally polarized water– nitrobenzene interface. This phospholipid was found to lower markedly the surface tension by forming a stable monolayer when the interface was polarized so that the aqueous phase had a negative potential with respect to the nitrobenzene phase [50,51] (cf. Fig. 5).

426

Samec

FIG. 5 Electrocapillary curve for the interface between 0.05 M LiCl in water and 0.1 tetrapentylammonium tetraphenylborate in nitrobenzene at 25 C in the presence of x M dilauroylphosphatidylcholine in nitrobenzene: x ¼ 0 (*), 0.5 (~), 1 (&), 2(^), 5 (*), 10 (~), 20 (&), and 50 (!). (From Ref. 51.)

On the other hand, when the aqueous phase became positively charged, the adsorbed molecules started to desorb from the interface, giving rise to the disruption of monolayer. Only in the former potential range, the electrocapillary curve was found to be thermodynamically meaningful. The area of the interface occupied by dialauroylphosphatidylcholine molecule in the saturated monolayer was estimated at 0.93 nm2 , indicating that the monolayer was in the liquid-expanded state [51]. The potential of zero charge shifted to a negative potential, probably due to the speciﬁc adsorption of Liþ ions to the headgroup of phospholipid exposed to the aqueous phase [51]. Monolayers of distearoylphosphatidylcholine spread on the water–1,2-dichloroethane interface were studied by Grandell et al. [52] in a novel type of Langmuir trough [53]. Isotherms of the lipid were measured at controlled potential difference across the interface. Electrocapillary curves derived from the isotherms agreed with those measured under the true thermodynamic equilibrium. Weak adsorption or a stable monolayer was found to be formed, when the potential of the aqueous phase was positive or negative respectively, with respect to the potential of the 1,2-dichloroethane phase [52]. This result

Capacitance and Surface Tension

427

is consistent with those obtained from measurements of phospholipid adsorption at the polarized water–nitrobenzene interface [50,51].

V.

CAPACITANCE MEASUREMENTS

A.

Analysis of Impedance Data

While the surface tension is accessible by direct measurement, the differential capacity C of the ITIES, Eq. (27), has to be evaluated by a careful analysis of experimental impedance data. Impedance measurements at the ITIES are usually carried out in a four-electrode electrochemical cell, where the interfacial potential difference is controlled or measured with the help of a couple of two reference electrodes and the current is supplied by means of two counterelectrodes [54]. Typically, a small sinusoidal voltage of a deﬁned frequency (0.1–1000 Hz) and amplitude (< 10 mV peak to peak) is applied across the ITIES and the corresponding sinusoidal current is measured by means of the alternating-current bridge or phase-selective detection yielding the complex impedance of the cell. The sinusoidal voltage is either superposed on the triangular voltage sweep (AC polarographic or AC voltammetric method), or it is applied at a constant cell potential (impedance method). The impedance data have been usually interpreted in terms of the Randles-type equivalent circuit, which consists of the parallel combination of the capacitance ZC of the ITIES and the faradaic impedances ZfN of the charge transfer reactions, with the solution resistance Rs in series [15], cf. Fig. 6. While this is a convenient model in many cases, its limitations have to be always considered. First, it is necessary to justify the validity of the basic model assumption that the charging and faradaic currents are additive. Second, the conditions have to be analyzed, under which the measured impedance of the electrochemical cell can represent the impedance of the ITIES. In particular, the coupling between the ion transfer and ion adsorption process has serious consequences for the evaluation of the differential capacity or the kinetic parameters from the impedance data [55]. This is the case, e.g., of the interface between two immiscible electrolyte solutions each containing a transferable ion, which adsorbs speciﬁcally on both sides of the interface. In general, the separation of the real and the imaginary terms in the complex impedance of such an ITIES is not straightforward, and the interpretation of the impedance in terms of the Randles-type equivalent circuit is not appropriate [54]. More transparent expressions are obtained when the effect of either the potential difference or the ion concentration on the speciﬁc ion adsorption is negli-

FIG. 6 Randles equivalent circuit for the ITIES: ZC is the interfacial capacitance, ZfN are the faradaic impedances of the charge transfer reactions, and Rs is the solution resistance.

428

Samec

gible. In the latter case, the system can exhibit the behavior of the Randles equivalent circuit, provided that certain kinetic conditions are fulﬁlled. Evaluation and interpretation of impedance data is often complicated by the nonideal behavior of the measuring device (e.g., potentiostat) and/or of the electrochemical cell itself. The role of experimental artifacts has been addressed ﬁrst by Reid et al. [56] and by Silva and Moura [57], who ascribed the high-frequency impedance semicircle to the geometrical bulk-phase capacitance [56] or to the capacitive coupling between the reference electrodes [57]. Cells of various designs were then tested and a conclusion was made that the main origin of the observed high-frequency dispersion is the high value of the resistance of the reference electrode connected to the organic solvent phase [58]. Samec et al. [59] analyzed the role of the parasitic couplings in the four-electrode cells employed in measurements at the ITIES or membranes. The cell was represented by an eight-element electrical equivalent circuit, which accounted for the ﬁnite impedances of the reference and counterelectrodes, as well as for various parasitic couplings. The model allowed prediction of the conditions under which the impedance plots exhibit the high-frequency capacitive and/or inductive features. An analytical expression was derived, which enables the valuation of the parasitic elements from experimental impedance data and the simulation of the impedance behavior. As a limiting case, the model also describes the behavior of a threeelectrode cell. Recent impedance measurements of the ideally polarized water–nitrobenzene interface [38] indicated that the potentiostatic circuit was not symmetrical in a sense that different impedance spectra were obtained when the input of the current follower was connected to the counterelectrode of the organic or the aqueous phase. The conclusion was made that the former conﬁguration should be avoided owing to the strong effect of the capacitive coupling between the counterelectrodes and reference electrodes connected to the organic solvent phase on the measured impedance [38]. Since the ion transfer is a rather fast process, the faradaic impedance Zf can be replaced by the Warburg impedance ZW corresponding to the diffusion-controlled process. Provided that the Randles equivalent circuit represents the plausible model, the real Z 0 and the imaginary Z 00 components of the complex impedance Z ¼ Z 0 jZ 00 [j ¼ ð1Þ1=2 ] are given by [60] 1 ð34Þ Z 0 ¼ Rs þ ZC X ðX þ 1Þ2 þ 1 1 ð35Þ Z 00 ¼ ZC XðX þ 1Þ ðX þ 1Þ2 þ 1 where ZC ¼ ð!CÞ1 , ! is the angular frequency and X ¼ ðZW =ZC Þð21=2 Þ. In the analysis of impedance data, the solution resistance Rs is evaluated ﬁrst as the high-frequency limit of the impedance Z and then X and C are obtained from Eq. (34) and Eq. (35). A more sophisticated approach makes use of the nonlinear least-square ﬁtting of impedance data obtained for a series of frequencies ! [61], which is nowadays provided by commercially available software packages (e.g., EQUIVCRT, ZVIEW). Alternatively, the capacity C can be evaluated by using the galvanostatic pulse technique [62,63]. When a current step I ¼ I0 ¼ const is imposed on the interface, the charging current IC decreases with time t, while the faradaic current If increases. At very short times, I ¼ I0 ¼ IC þ If ¼ CðdE=dtÞ þ If CðdE=dtÞ

ð36Þ

where dE=dt is the rate of the change of the interfacial potential difference measured. Under these conditions, the ohmic potential drop E0 ¼ I0 Rs appears as a step on the galvanostatic transient at the beginning of the pulse and the initial slope of the transient is controlled mainly by the capacity C.

Capacitance and Surface Tension

B.

429

Effect of the Interfacial Potential Difference

Samec et al. [15] used the AC polarographic method to study the potential dependence of the differential capacity of the ideally polarized water–nitrobenzene interface at various concentrations of the aqueous (LiCl) and the organic solvent (tetrabutylammonium tetraphenylborate) electrolytes. The capacity showed a single minimum at an interfacial potential difference, which is close to that for the electrocapillary maximum. The experimental capacity was found to agree well with the capacity calculated from Eq. (28) for 1=Ci ¼ 0 and for the capacities of the space charge regions calculated using the GC theory, qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ C2s ¼ ðFAs =RT Þ 1 þ ðQ=2As Þ2

ð37Þ

which indicated that the inner-layer potential difference remains constant and close to zero. A similar conclusion was made by Reid et al. [64]. However, it should be noted that the authors [15] assumed that the faradaic impedance Zf is much greater than the capacitance ZC and evaluated the capacity C from the imaginary component Z 00 ¼ ZC ¼ 1=!C. Therefore, the value of the capacity was overestimated, in particular at higher electrolyte concentrations. Analogously, an increasing overestimation of the capacity with the increasing electrolyte concentration was likely to be involved in the analysis of the galvanostatic transients [16,17] that was based on Eq. (36). Wandlowski et al. [22] remeasured the impedance data for the water–nitrobenzene [15] and water–1,2dichloroethane [65] interfaces at various concentrations of the aqueous (LiCl) and the organic solvent (tetrabutylammonium tetraphenylborate) electrolytes, and evaluated the capacity C with the help of Eq. (34) and Eq. (35) (cf. the capacity curves in Fig. 7). These results conﬁrmed an interesting feature noted earlier [17,65], namely that the plot of the inverse capacity 1=C against the inverse GC capacity of the diffuse double layer 1=Cd is not linear, contrary to expectation based on Eq. (28) (cf. Fig. 8). An appreciable drop from the expected straight line at low electrolyte concentrations, which is pronounced more for the water–1,2-dichloroethane interface, was ascribed to a relatively higher interpenetration

FIG. 7 Differential capacity C vs. interfacial potential difference wo ’ of the water–nitrobenzene interface. Concentrations (in mol dm3 ) of LiCl in water and tetrabutylammonium tetraphenylborate in nitrobenzene: 0.01 (*), 0.02 (*), 0.05 (!), and 0.1 (!). (From Ref. 22.)

430

Samec

FIG. 8 Inverse differential capacity C01 at the zero surface charge vs. inverse capacity Cd1 of the diffuse double layer for the water–nitrobenzene (*) and water–1,2-dichloroethane (*,), interface. The diffuse layer capacity was evaluated by the GC (*) or the MPB (*,), theory. (From Ref. 22.)

of ions at low electrolyte concentrations [17], or to the relatively higher effect of the ﬁnite ion size [22]. The latter effect was estimated [22] by using the MPB theory [20]. Recently, it has been shown that an increase of the capacity can also be caused by the corrugation of the interface by capillary waves [66]. The results of the capacitance measurements have been found consistent with those of the surface tension measurements for both the water–nitrobenzene and the water–1,2chloroethane interfaces [17,22,37–39,67]. Thus, the excess surface charge density Q obtained by an integration of the capacity curves agrees well with that obtained by a differentiation of the electrocapillary curve [37,67], at least in a limited potential range [38,39]. Analogously, the values of Q from the two measurements yield comparable values of the inner-layer potential differences [17,22,38,39] (cf. Fig. 3). On the other hand, at the potential differences that are about 100 mV more positive or negative than the zero-charge potential difference, the agreement is less satisfactory [38,39]. Unlike the surface excess charge density inferred from the surface tension measurements, that obtained by the integration of the capacity curve increases with the potential difference much more steeply, which corresponds to a higher capacity compared with the second derivative of the electrocapillary curve [38,39]. This capacity enhancement is not probably associated with the speciﬁc ion adsorption and can be explained by the model, which links the measured impedance to the electromechanical oscillations in the interfacial region during the impedance measurements [68,69]. The model is based on the theoretical considerations [28] that the thermally excited capillary waves give rise to an apparent width of a liquid–liquid

Capacitance and Surface Tension

431

interface, which was supposed [69] to represent the mean charge separation between the two electrolyte solutions, i.e., the thickness of the inner layer. Changes in the inner-layer thickness induced by the applied sinusoidal voltage result in a change in the ratio of the charging and the faradaic currents, which requires a modiﬁcation of the Randles equivalent circuit. The complex impedance Z~ a of the modiﬁed circuit is given by [68,69]. Z~ a ¼

Z~ I þ Rs 1 ðxZ~ I =Z~ C Þ

ð38Þ

where Z~ I ¼ ðZ~ f1 þ Z~ C1 Þ1 , Z~ C ¼ ðj!CÞ1 , Z~ f ¼ Rct þ Z~ W , Rct and Z~ W are the charge transfer resistance and the complex Warburg impedance respectively, and the parameter x ¼ jQðwo ’i wo ’pzc Þ=2j. The value of the latter parameter is negligible at the potential differences close to the zero-charge potential difference, where also Eq. (38) describes the behavior of the Randles equivalent circuit. However, with the increasing potential difference, x increases due to the increasing surface excess charge density Q and the increasing inner-layer potential difference wo ’i , and due to the decreasing surface tension . An analysis of the impedance data simulated with the help of Eq. (38) indicated that the effect of capillary waves can become signiﬁcant at approximately the same potentials, where the sharp increase in the capacity is observed experimentally [38].

C.

Effect of Electrolyte

The effect of electrolyte type on the capacity of an ideally polarized ITIES was studied ﬁrst by Homolka et al. [70]. These authors concluded that the formation of the inner layer at the water–nitrobenzene interface accompanied by a drop in the capacitance is associated with the presence of certain ions in the double layer, e.g., very hydrophilic Mg2þ cations in water or very hydrophobic tetraphenylarsonium cation in nitrobenzene. More recently, this effect was investigated systematically by Yufei et al. [71] and Pereira et al. [72] for the water–nitrobenzene [71] and water–1,2-dichloroethane [71,72] interfaces. A capacity increase was observed in the range of the potential differences wo ’ > 0, which followed the order of ions in water (Liþ < Naþ < Rbþ < Csþ Þ [71], and in the range of the potential differences wo ’ < 0, which followed the order of ions in 1,2-dichloroethane (tetraoctylammoniumþ < tetrabutylammoniumþ < tetrapropylammoniumþ ) [72]. This order corresponds to the order of the Gibbs energies of transfer [72]. Figure 9 shows the capacity curves for the water–o-nitrophenyl octyl ether interface in the presence of two different electrolytes in the organic solvent obtained by impedance measurements [68,73]. A comparison with the potential dependence of the faradaic admittance coefﬁcient Y0 [Fig. 10] points to a correlation between the capacity and admittance enhancements or the Gibbs energies of transfer. At a constant faradaic admittance, the ITIES appears to exhibit the same capacity irrespective of the nature of the ion that controls the faradaic process [39,68]. These results have been initially considered as evidence for speciﬁc ion adsorption at ITIES [71,72]. Its origin was ascribed to extensive ion pair formation between ions in the aqueous phase and ions in the organic phase [71] [cf. Eq. (20)], or to a penetration into the interfacial region [72]. The former model, which has been considered in this context earlier [60], allows one to interpret the enhanced capacity in terms of Eq. (22). Pereira et al. (74) presented more experimental data demonstrating the effect of electrolytes and proposed a simple model, which is based on the lattice-gas model of the liquid–liquid interface [23]. Theoretical calculations showed that ion pairing can lead to an increase in the stored

432

Samec

FIG. 9 Differential capacity C of the interface between 0.1 M LiCl in water and 0.02 M tetrabutylammonium tetraphenylborate (&) or tetrapentylammonium tetrakis[3,5-bis(triﬂuoromethyl)phenyl]borate (&) in o-nitrophenyl octyl ether as a function of the interfacial potential difference wo ’. (From Ref. 73.)

charge at the interface, while the space charge, and hence the potential difference across the interface, does not change much because the charges on the paired ions compensate each other [74]. The amount of ion pairing should depend on both the association constant and on the width of the interface and, therefore, it is generally not possible to obtain the interfacial association constant from the capacity data [74]. However, the surface tension data that would conﬁrm the speciﬁc adsorption of hydrophilic and semihydrophobic ions are lacking. Absence of the speciﬁc ion adsorption in these cases is corroborated by the analysis of the surface tension data for the nonpolar-

FIG. 10 Faradaic admittance coefﬁcient Y0 for the interface between 0.1 M LiCl in water and 0.02 M tetrabutylammonium tetraphenylborate (&) or tetrapentylammonium tetrakis[3,5-bis(triﬂuoromethyl)phenyl]borate (&) in o-nitrophenyl octyl ether as a function of the interfacial potential difference wo ’. (From Ref. 73.)

Capacitance and Surface Tension

433

ized [3] and ideally polarized [36] water–nitrobenzene interfaces. Besides, the electrocapillary curves in the latter case appear to have a parabolic shape, which would correspond to the linear dependence of the surface charge on the potential difference and to a constant differential capacity [37–39]. Simulations based on Eq. (38) show that both the capacity enhancement at far positive and far negative potential differences and its dependence on the electrolyte present can be explained by the model [68,69] that links the measured impedance to the thermally excited capillary waves.

D.

Effects of Adsorbed Layers

There is a group of substances, in the presence of which signiﬁcant changes in the surface tension of the ITIES were observed, which are also likely to inﬂuence the differential capacity of the ITIES correspondingly. These substances include various ionic and nonionic surfactants (Section IV.B.2) and amphiphilic phospholipids (Section IV.B.3) or afﬁnity dyes. Attention has focused on phospholipids. Kakiuchi et al. [75] used the capacitance measurements to study the adsorption of dilauroylphosphatidylcholine at the ideally polarized water–nitrobenzene interface, as an alternative approach to the surface tension measurements for the same system [51]. In the potential range, where the aqueous phase had a negative potential with respect to the nitrobenzene phase, the interfacial capacity was found to decrease with the increasing phospholipid concentration in the organic solvent phase (Fig. 11). The saturated monolayer in the liquid-expanded state was formed at the phospholipid concentration exceeding 20 mol dm3 , with an area of 0:73 nm2 occupied by a single molecule. The adsorption was described by the Frumkin isotherm,

FIG. 11 Equilibrium double layer capacity of the interface between 0.05 M LiCl in water and 0.1 tetrapentylammonium tetraphenylborate in nitrobenzene at 25 C in the presence of x M dilauroylphosphatidylcholine in nitrobenzene: x ¼ 0 (*), 1 (*), 2 (~), 10 (~), and 50 (&). (From Ref. 75.)

434

Samec

c ¼

expð2a Þ 1

ð39Þ

where ¼ expðG0ads =RTÞ is the adsorption coefﬁcient, G0ads is the standard Gibbs energy of adsorption, a is the interaction parameter, is the surface coverage, and c is the phospholipid concentration, with G0ads ¼ 31 kJ mol1 and a ¼ 0:25. The latter value points to weak attractive interactions between the adsorbed molecules corresponding to the penetration of nitrobenzene molecules and, possibly, ions between the hydrocarbon chains of phospholipid [75]. This penetration explains the rather high capacity of 11 C cm2 for the adsorbed monolayer. In the potential range, where the aqueous phase had a positive potential, the capacity increased with the increasing phospholipid concentration. Since in this potential range the surface tension shows a tendency to recover [51], the observed increase of the capacity was ascribed to a change in the orientation of adsorbed molecules, possibly accompanied by a partial desorption [75]. Wandlowski et al. [76,77] used the impedance technique to study the adsorption of dilauroyl-, dimyristoyl, and dipalmitoylphosphatidylcholine at the same interface. The surface coverage evaluated from the impedance measurements also ﬁts the Frumkin isotherm. The value of G0ads was found to decrease with the increasing number of methylene groups in the hydrocarbon chain from 35:7 kJ mol1 to 37:9 kJ mol1 and the value of the parameter a ¼ 0:4, which corresponds to weak attractive interactions between the absorbed molecules. Thus, the picture emerging from these studies is qualitatively the same as above, but the estimated parameters of the Frumkin isotherm are slightly different. Kakiuchi et al. [78] investigated the effects of temperature and the chainlength on the monolayer characteristics of six phosphatidylcholines on the polarized water–nitrobenzene interface at phospholipid concentrations higher than 10 mol dm3 . The dilauroyl- and dimyristoylphosphatidylcholine monolayers were found to be in the liquid-expanded state between 5 and 30 C (Cmin 10 C cm2 Þ, whereas distearoyl-, diarachidoyl-, and dibehenoylphosphatidylcholine monolayers were found to be in the liquid-condensed state over the same temperature range ðCmin 4 C cm2 ). The dipalmitoylphosphatidylcholine monolayer exhibited a temperature-induced phase transition at 13 C. Two interesting features were revealed by capacitance measurements of phospholipids containing the ethanolamine or serine moiety instead of choline. In contrast to dilauroylphosphatidylcholine forming liquid-expanded monolayers, dilauroylphosphatidylethanolamine has an adsorption isotherm with a characteristic kink, which is associated with the phase transition from the liquid-expanded to the liquid-condensed state as the concentration of the latter lipid in nitrobenzene is increased. The transition is accompanied by the change in the occupied area of this phospolipid from 0.83 nm2 to 0.5 nm2 [79]. The phospholipid monolayer is stable over the potential range of about 300 mV when the aqueous phase is neutral, while the potential dependence of the adsorption resembles an anionic or cationic surfactant when the pH is made alkaline or acidic respectively. The monolayer characteristics of dipalmitoylphospatidylserine at the water–nitrobenzene interface are similar to those of dipalmitoylphosphatidylcholine. However, in the presence of Ca2þ or Mg2þ at a concentration greater than 2 mol dm3 in the aqueous phase a striking drop in the capacity was observed, which was ascribed to the phase transition of the monolayer from the liquid-expanded state to the liquid-condensed or solid state [80]. Capacitance measurements of phospholipid monolayers at the ITIES have been proposed as a suitable tool for studying the enzyme activity under the precise control of the electrical state of the monolayer [81]. Kinetics of hydrolysis of phosphatidylcholine

Capacitance and Surface Tension

435

monolayers in the presence of phospholipase was followed by making use of the large difference in the capacity before and after hydrolysis [81–83]. Kakiuchi et al. [84] studied the adsorption properties of two types of nonionic surfactants, sorbitan fatty acid esters and sucrose alkanoate, at the water–nitrobenzene interface. These surfactants lower the interfacial capacity in the range of the applied potential with no sign of desorption. On the other hand, the remarkable adsorption– desorption capacity peak analogous to the adsorption peak seen for organic molecules at the mercury–electrolyte interface can be observed in the presence of ionic surfactants, such as triazine dye ligands for proteins [85].

VI.

CONCLUSIONS

Capacitance and surface tension measurements have provided a wealth of data about the adsorption of ions and molecules at electriﬁed liquid–liquid interfaces. In order to reach an understanding on the molecular level, suitable microscopic models have had to be considered. Interpretation of the capacitance measurements has been often complicated by various instrumental artifacts. Nevertheless, the results of both experimental approaches represent the reference basis for the application of other techniques of surface analysis.

ACKNOWLEDGMENTS Financial support from the Ministry of Education of the Czech Republic (Grant. No. ME 161) is gratefully acknowledged.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

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18 Liquid Membrane Ion-Selective Electrodes: Response Mechanisms Studied by Optical Second Harmonic Generation and Photoswitchable Ionophores as a Molecular Probe YOSHIO UMEZAWA Japan

I.

Department of Chemistry, University of Tokyo, Tokyo,

INTRODUCTION

Liquid membrane type ion-selective electrodes (ISEs) provide one of the most versatile sensing methods because it is possible to customize the sensory elements to suit the structure of the analyte. A wealth of different synthetic and natural ionophores has been developed, in the past 30 years, for use in liquid membrane type ISEs for various inorganic and organic ions [1]. In extensive studies [2–4], the response mechanism of these ISEs has been interpreted in terms of thermodynamics and kinetics. However, there have been few achievements in the characterization of the processes occurring at the surface of ISEs at molecular level. According to generally accepted theoretical models of poly(vinyl-chloride) (PVC)based liquid membrane type ion-selective electrodes (ISEs), the membrane potential is described as the sum of the diffusion potential across the membrane bulk and the phase boundary potentials at the interfaces of the membrane and the inner ﬁlling and sample solutions [5–8]. Of these factors, a change in the phase boundary potential at the membrane–aqueous sample solution interface contributes mainly to the quick response of ISEs, because a change in the diffusion potential in the membrane bulk takes place only very slowly [9–12]. The generation of the phase boundary potential is explained on the basis of the permselective uptake of primary ions, leaving the counterions on the aqueous side of the interface. It is therefore necessary to correlate the phase boundary potential with the amount as well as the distribution of electric charge at the interface to understand the molecular mechanism of the membrane potential. Recently, we [13,14] evidenced by ATR-IR spectroscopy that the membrane potential of ionophore-incorporated, PVC-based liquid membranes is governed by permselective transport of primary cations into the ATR-active layer of the membrane surface. More recently, we [14–16] observed optical second harmonic generation (SHG) for ionophore-incorporated PVC-based liquid membranes, and conﬁrmed that the membrane potential is primarily governed by the SHG active, oriented complexed cations at the 439

440

Umezawa

membrane surface, facing across the interface the hydrophilic counteranions in the adjacent aqueous phase. Also, an experimental method for evaluating the relationship between the surface charge density and the phase boundary potential was proposed by using photoswitchable ionophores as a molecular probe [17]. The purpose of this chapter is to describe these experimental approaches for understanding the molecular mechanism of the membrane potentials for ionophore-incorporated liquid membrane ion-selective electrodes.

II.

FTIR-ATR STUDY ON CATION PERMSELECTIVITY [13]

Pungor and coworkers ﬁrst observed the complex formation between a crown ether derivative and Kþ in ISE membranes by FTIR-ATR spectrometry. They found that there is only a low concentration of the Kþ -crown complex at the phase boundary between the membranes and aqueous KCl; these were easily removed by rinsing with water. In contrast, membranes treated with aqueous KSCN contain a large amount of the complexes accompanied by SCN ions; those complexes are not easily removed by rinsing and the transport rate of the complex into the bulk of the membrane was found to be much slower than the potentiometric response time. Pungor et al. concluded that the observed potential response of this type of ISE is determined essentially at the surface of the membrane and not in the bulk [9–15]. We further extended the above work and ﬁrst evidenced by FTIRATR spectrometry permselective cation transport into ISE liquid membranes in terms of the quantitative stoichiometric ratio of counteranions and complex cations. When primary ion solutions with an IR-active hydrophilic counteranion, SO2 4 , were used, the IR spectra of the membranes only indicated the presence of complexed cations, and no IR peak due to the counteranion was found. The intensity of the former peaks was found to be dependent on the membrane concentration of added anionic sites, introduced either by the use of carboxylated poly(vinyl chloride) or a derivative of tetraphenylborate, and also on the penetration depth of the IR beam used. In contrast, the use of a hydrophobic counteranion, SCN , led to IR signals from both the complexed cation and the corresponding counteranion. Their stoichiometric ratios depended on the concentrations of the primary ion and of the tetraphenylborate derivative in the membrane. It was also found that the depth of completely permselective transport of cations, that is, exclusion of the hydrophilic counteranions was as great as 1:0 m and that the type of ionophore and the presence of added anionic sites in the membrane were signiﬁcant factors governing the magnitude of this penetration depth [14]. FTIR-ATR has thus been demonstrated to be a very useful technique for the characterization of processes at the surface of liquid membrane ISEs. The depth accessible to FTIR-ATR is of the order of 0:1 1:0 m and is thus too large for the observation of phenomena at the very surface.

III.

SHG OBSERVATION OF LIQUID–LIQUID INTERFACE OF ISES [16]

Optical second harmonic generation (SHG), which is the conversion of two photons of frequency ! to a single photon of frequency 2!, is known to be an inherently surfacesensitive technique, because it requires a noncentrosymmetrical medium. At the interface between two centrosymmetrical media, such as the interface between two liquids, only the molecules which participate in the asymmetry of the interface will contribute to the SHG [18]. SHG has been used as an in-situ probe of chemisorption, molecular orientation, and

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adsorbate organization at a wide variety of surfaces, namely the air–solid [20–23,29], liquid–solid [19–21,29], liquid–air [20,24–29], and liquid–liquid [18,28,29] interfaces, because of its ability to discriminate between surface species and species in the adjacent bulk media. Corn et al. reported the application of surface SHG to monitor the adsorption of an anionic surfactant molecule at a liquid–liquid (water/1,2-dichloroethane) interface, to which an electrical potential was applied, and determined the surface concentration of the surfactant molecule as a function of the potential [18]. Shen et al. reported on the molecular orientation of surfactants at liquid–liquid (water–decane and water–carbon tetrachloride) interfaces [28]. The SHG technique is therefore a valuable probe for insight into the surface chemistry of liquid membrane ISEs. A.

SHG Induced by Surface Ionophore–Metal Ion Complexation

The SHG signal intensity, Ið2!Þ , arising at the liquid–liquid interface is known to be proportional to the square of the second-order nonlinear electric susceptibility, cð2Þ , at the surface [18,28,29], 2 2 ð1Þ Ið2!Þ / eð2!Þ ð2Þ eð!Þ eð!Þ Ið!Þ ð2Þ ¼ NhTið2Þ

ð2Þ

where Ið!Þ is the input light power, eð!Þ and eð2!Þ are the electric polarization vectors describing the input and output light ﬁelds, respectively, N is the surface concentration of SHG active species, ð2Þ the molecular and second-order nonlinear electric polarizability, T the co-ordinate transformation connecting the laboratory and molecular axes, and the angular brackets denote an average over all molecular orientations. From Eqs. (1) and pﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ (2) follows that the square root of the SHG intensity, Ið2!Þ , is directly proportional to N, hTi and ð2Þ ; namely pﬃﬃﬃﬃﬃﬃﬃﬃﬃ Ið2!Þ / NhTið2Þ ð3Þ The measurement of SHG intensities thus provides information on the concentration N, the molecular orientation hTi, and the polarization ð2Þ of SHG active species at the interface. The SHG measuring system is shown in Fig. 1. The dependence of the SHG intensity, Ið2!Þ , of a membrane incorporated with ionophore 2 (membrane 2, see Fig. 2) in contact with 0.18 M aqueous KCl on the power of the irradiation light beam, Ið!Þ , is shown in Fig. 3. A linear relationship is seen between the input power, Ið!Þ , and the square pﬃﬃﬃﬃﬃﬃﬃﬃﬃ root of the SHG intensity, Ið2!Þ . This relation satisﬁes the principle of SHG [see Eq. (1)] and thus conﬁrms that the light detected in this system is indeed arising from SHG. pﬃﬃﬃﬃﬃﬃﬃﬃﬃ Figure 4 shows the dependence of the square root of the SHG intensity, Ið2!Þ , on the concentration of Liþ ion (LiCl) in the aqueous solution, using membrane 1 with an ionophore concentration of 10 mM. The SHG intensity increased steeply at low Liþ ion concentrations but leveled off at higher concentrations. In the absence of Liþ ions, the SHG signal was found to be negligible. The SHG response for a membrane without ionophore, i.e., a PVC–DOS membrane, was also negligible at otherwise identical conditions. The generation of the SHG signal can be ascribed to the formation of oriented Liþ ionophore 1 complexes at the membrane surface, facing across the interface the hydrophilic counteranions, Cl , in the adjacent aqueous phase. In fact, when a relatively hydro-

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Umezawa

FIG. 1 Schematic diagram of the present SHG measuring system and detailed structure of the optical cell: (a) 45 right angle prism; (b) glass plate reﬂector; (c) infrared transparent ﬁlter (> 690 nm); (d) aqueous CuSO4 ﬁlter; (e) spherical quartz lens; (f) interference ﬁlter (530 nm, 10 nm of FWHM); (g) beam damper; (h) stainless cover; (i) silicone rubber packing; (j) solvent polymeric membrane; (k) slide glass; (l) sample cuvette. The s-polarized 1064 nm output of a Qswitched ND:YAG laser was used with an 8–9 ns pulse width and 10 Hz repetition rate. (From Ref. 15.)

phobic anion, SCN , was used instead of a Cl ion as the counteranion, the observed SHG signal decreased at high salt concentrations, probably due to a decrease in the number of oriented cation complexes at the surface upon extraction of SCN ions into the membrane bulk (vide infra). The fact that the SHG signal virtually leveled off at high Liþ ion concentrations means that the number of SHG active species located at the membrane interface became constant beyond a certain Liþ ion concentration, assuming negligible changes in the molecular orientation (see Eq. (3)]. The SHG response of membranes 2, 3, and 4, respectively, was similar to that of membrane 1; the SHG signal increased with increasing primary cation concentrations in the aqueous solution, and again leveled off at high cation concentrations (vide infra). The saturation of the SHG response at high cation concentrations suggests that the process of complex formation at the membrane surface may be treated by a Langmuirisotherm type analysis [24,27]. At constant temperature, the Langmuir equation is given by 1 1 1 1 ¼ ð4Þ þ N Nmax K Cb Nmax where N is the number of the cationic complexes located at the surface, Nmax the maximum of the cationic complexes at the interface, Cb the aqueous bulk cation concentration

Liquid Membrane Ion-Selective Electrodes

443

FIG. 2 Structures of the ionophores 1–4. 1=dibenzyl-14-crown-4; 2=bis(benzo-15-crown-5); 3=dibenzo-18-crown-6; 4=dibenzo-24-crown-8; these ionophores are selective for Liþ , Kþ , Kþ and Naþ , respectively. (From Ref. 15.)

and K the binding constant (M1 ) (the complexation stability constant between the cation and the ionophore at the membrane surface), respectively. It should be noted that 1=N is inversely proportional to the bulk cation concentration, Cb . A nearly linear relation was in fact found between the reciprocal of the square root of the SHG intensity and the reciprocal of the bulk cation concentration for membrane 1,

pﬃﬃﬃﬃﬃﬃﬃﬃﬃ FIG. 3 Dependence of the square root of the SHG intensity Ið2!Þ on the power of the irradiated fundamental light, as obtained with membrane 2 with an ionophore concentration of 3:0 102 M. The adjacent aqueous solution was 1:8 101 M KCl. Inset: dependence of the SHG intensity on the input optical power. (From Ref. 15.)

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Umezawa

pﬃﬃﬃﬃﬃﬃﬃﬃﬃ FIG. 4 Dependence of the square root of the SHG intensity Ið2!Þ on Liþ ion concentrations with 2 membrane 1 (&), (ionophore concentration 1:0 10 M) or with a membrane without ionophore 1 (*). (From Ref. 15.)

as shown in Fig. 5. Also for membranes 2, 3, and 4, Langmuir type binding isotherms were found (ﬁgures not shown). It seems that a Langmuir type ‘‘saturation’’ is indeed reached at the membrane surface. Figure 5 also shows the effect of the ionophore concentration of the Langmuir type binding isotherm. The slope of the isotherm fora membrane with 10 mM of ionophore 1 was roughly three times larger than that with 30 mM of the same ionophore. The binding constant, K, which is inversely proportional to the slope [Eq. (3)], was estimated to be 4:2 M1 and 11:5 M1 for the membranes with 10 mM and 30 mM ionophore 1, respectively. This result supports the validity of the present Langmuir analysis because the binding constant, K, should reﬂect the availability of the surface sites, the number of which should be proportional to the ionophore concentration, if the ionophore is not surface active itself. In addition, the intercept of the isotherm for a membrane with 10 mM of ionophore 1 was nearly equal to that of a membrane with 30 mM ionophore 1 (see Fig. 5). This suggests the formation of a closest-packed surface molecular layer of the SHG active Liþ -ionophore 1 cation complex, whose surface concentration is nearly equal at both ionophore concentrations. On the other hand, a totally different intercept and very small slope of the isotherm was obtained for a membrane containing only 3 mM of ionophore 1. This indicates an incomplete formation of the closest-packed surface layer of the cation complexes due to a lack of free ionophores at the membrane surface, leading to a kinetic limitation. In this case, the potentiometric response of the membrane toward Liþ was also found to be very weak (vide infra). The results of the above-mentioned Langmuir analysis of the SHG responses may be interpreted in terms of a tightly packed monolayer of the SHG active cation complexes at the membrane surface. The tight layer may, however, also be a layer thicker than a monolayer in which the potential aligns the complexes to the electric ﬁeld. As a consequence of the increase of the potential near the surface, the oriented complexes would on the average be nearer to the surface than the average of all complexes.

Liquid Membrane Ion-Selective Electrodes

445

pﬃﬃﬃﬃﬃﬃﬃﬃﬃ FIG. 5 Plots of the reciprocal of the square root of the SHG intensities 1= Ið2!Þ versus the reciþ procal of Li ion concentrations in the adjacent aqueous solutions (the Langmuir isotherm) as obtained with membrane 1. The ionophore concentrations were 3:0 103 M (~), 1:0 102 M (*), and 3:0 102 M (&), respectively. The data points present averages for three sets of measurements. Error bars show standard deviations. (From Ref. 15.)

B.

Correlation Between the SHG Signals and ISE Potentials

As shown in Fig. 6(a), the SHG response of membrane 2 to aqueous KSCN was found to be different from that to KCl. Upon increasing the KSCN concentration, the SHG signal initially increased but reached a maximum at 0.2 M, and then decreased. The potentiometric response of the same membrane also exhibited a maximum at a Kþ ion activity of ca. 0.1 M [see inset in Fig. 6(a)]. Thus, the decrease in the SHG and potentiometric responses were found to start roughly at the same KSCN concentration. This may be attributed to a decrease in the number of oriented Kþ -ionophore 2 complexes at the interface with the appearance of SCN ions in the membrane. To prevent such anionic effects, so-called added anionic sites are conventionally used as additives for ISE membranes [35]. In fact, upon addition of KTpClPB, a marked improvement of the SHG response for KSCN was observed at higher analyte concentrations [Fig. 6(b)]. Because a membrane containing only KTpClPB, i.e., a PVC–DOS– KTpClPB membrane, did not show any SHG response toward Kþ ions, this result suggests that TpCIPB may assist the surface orientation of the Kþ -ionophore 2 complexes by inhibiting the uptake of SCN ions from the adjacent aqueous solution. The parallel changes in membrane potentials and SHG signals allow us to conclude that the observed membrane potential changes in the above case are primarily governed by the SHG active oriented species at the membrane surface. Anionic effects were observed by FT-IR-ATR spectrometry with a membrane containing not ionophore 2 but a different kind of ionophore, ETH 129 [13]. When the lipophilic counteranion, SCN , was used for the primary ion solutions, the spectra from both the complexed cation and corresponding counteranion were seen, of which the stoichiometric ratio was nearly equal to that of ETH 129 complex-SCN salt at relatively high concentrations of the primary ion solutions. With KTpCIPB in the membrane,

pﬃﬃﬃﬃﬃﬃﬃﬃﬃ FIG. 6 Dependence of the square root of the SHG intensity ( Ið2!Þ Þ for membrane 2 without KTpCIPB (a) with þ KTpCIPB (b) on K ion concentrations in the adjacent aqueous solution containing KCl (*) and KSCN (*), respectively. Inset: The corresponding observed EMF to KCl and KSCN. The concentrations of ionophore 2 and KTpCIPB were 3:0 102 M and 1:0 102 M, respectively for both SHG and EMF measurements. The data points present averages for three sets of measurements. Error bars show standard deviations. (From Ref. 15.)

446 Umezawa

Liquid Membrane Ion-Selective Electrodes

447

the decrease in the uptake of SCN ions into the ETH 129-based membrane relative to the complexed cation was observed. The ATR results for the ETH 129-based membranes with and without KTpCIPB indicate that KTpCIPB resisted and inhibited by as much as 70% the uptake of SCN ions into the membrane phase, a trend which is inconsistent with the ﬁndings relevant to the anionic effects of the potentiometric and SHG responses of membrane 2. More explicit and in-depth discussion on the effect of charged (anionic) sites will be given in Section IV. Another important property of the SHG response of membranes 1–4 is that saturation occurs at higher cation concentrations, where Nernstian potentiometric responses are still observed [Figs. 7(a)–(d) and their insets]. This shows that the generation of the membrane potential at very high primary cation concentrations is governed not only by the SHG active cation complexes at the membrane surface but also by complexes located behind the SHG active layer, which are SHG inactive due to a lack of molecular orientation. One should remember, however, that electroneutrality requires that almost all cation complexes have to be within a few Debye lengths from the membrane surface as long as their charge is not balanced by an anionic site. To evaluate the contribution of the SHG active oriented cation complexes to the ISE potential, the SHG responses were analyzed on the basis of a space-charge model [30,31]. This model, which was proposed to explain the permselectivity behavior of electrically neutral ionophore-based liquid membranes, assumes that a space charge region exists at the membrane boundary: the primary function of lipophilic ionophores is to solubilize cations in the boundary region of the membrane, whereas hydrophilic counteranions are excluded from the membrane phase. Theoretical treatments of this model reported so far were essentially based on the assumption of a double-diffuse layer at the organic–aqueous solution interface and used a description of the diffuse double layer based on the classical Gouy–Chapman theory [31,34]. Following this model, the charge density of the complex cations, o , on the membrane side and that of the hydrophilic counteranions, a , on the aqueous side can be expressed as qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Fð 0 b Þ o ¼ 8RT C b v sinh ð5Þ 2RT pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Fð 0 b Þ a ¼ 8RTCb v sinh ð6Þ 2RT where Cb and Cb are the concentrations of the ions in the bulk of the membrane and of the aqueous solution, respectively, v the permittivity of free space, and the dielectric constants of the membrane and of water, 0 and 0 the electric potentials at the outer Helmholtz planes at the interface of the membrane and of the aqueous side, respectively,

b and b the electrical potential in the bulk of the membrane and of the aqueous solution, respectively, and R and T have their usual meanings. It is possible to describe the electrical potential difference between the aqueous and membrane bulk, b b , as a function of the charge densities, o and a , in the simpliﬁed case where 0 ¼ 0 , as 2RT o arcsinh pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

b b ¼ ð 0 b Þ 0 b ¼ F 8RTv Cb ð7Þ a arcsinh pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 8RTv Cb

FIG. 7 Dependence of the SHG signals and of the calculated charge densities for membranes 1, 2, 3, and 4, respectively, on the primary cation concentrations in the adjacent aqueous solutions, and the corresponding observed EMFs (inset). The ionophore concentrations for the membrane 1 (a), 2 (b), 3 (c), and 4 (d) are 1:0 102 M, 3:0 102 M, 2:5 102 M, and 3:0 102 M, and their primary ions are Liþ , Kþ , Kþ , and Naþ , respectively. The data points present averages for three sets of measurements. Error bars show standard deviations. (From Ref. 15.)

448 Umezawa

Liquid Membrane Ion-Selective Electrodes

449

When the extraction of the hydrophilic counteranion from the aqueous solution into the membrane bulk is negligible (cation permselectivity preserved), the concentration of the complex cation in the membrane bulk Cb , is equal to that of the ﬁxed anionic sites, X , in the membrane matrix, due to the electroneutrality condition within the membrane bulk: Cb ¼ X ¼ const:

ð8Þ

Because the net charge at the interface should be zero, ¼ 0, the electrical potential difference, b b , in Eq. (7) can be rewritten as 2RT o o arcsinh pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ arcsinh pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð9Þ

b b ¼ F 8RT v X 8RTv Cb o

a

The determination of the number of the SHG active complex cations from the corresponding SHG intensity and thus the surface charge density, o , is not possible because the values of the molecular second-order nonlinear electrical polarizability, að2Þ , and molecular orientation, hTi, of the SHG active complex cation and its distribution at the membrane surface are not known [see Eq. (3)]. Although the formation of an SHG active monolayer seems not to be the only possible explanation, we used the following method to estimate thep surface ﬃﬃﬃﬃﬃﬃﬃﬃﬃ charge density from the SHG results: since the square root of the SHG intensity, Ið2!Þ , is proportional to the number of SHG active cation complexes [see Eq. (3)], the observed SHG intensity is a measure of the charge density (C=cm2 ), o , at the membrane surface. Using the molecular area of the charged complex, as estimated from a CPK molecular model, and assuming a full coverage of the cation complexes, Nmax of the Langmuir equation was estimated [see Eq. (4) and Fig. 5]. Surface charge densities can then be obtained from Eq. (4). The surface charge density and the SHG intensity dependence on the cation concentration is shown in Figs. 7(a)–(d) for four different membrane types. The electrical potential differences, o b , calculated from the surface charge densities, o , according to Eq. (9) are shown in Fig. 8 together with the observed potentials. The concentration of anionic sites in the membrane, X , which is necessary for determining b b according to Eq. (9), was varied from 0.05 to 0.6 mM. This covers the reported concentration range of anionic sites in PVC–plasticizer membranes without added sites [36]. The change of the X value within this range however hardly affected the slope of the calculated potentials, whereas the absolute potentials shifted. For membrane 1 with 10 mM ionophore, the slope of the calculated membrane potential was 58 mV/decade in the Liþ ion concentration range from 2:0 103 M to 3:0 101 M, which is close to a Nerstian response (59.2 mV/decade, 25 C). This is consistent with the observed EMF response. This result indicates that the potential increase in this case is essentially determined by the SHG active cation complexes. However, for a membrane with a concentration of ionophore 1 of 30 mM, as a result of the SHG intensity saturation, the slope of the calculated potential became small at higher primary ion (Liþ ) concentrations. This is in clear contrast to the observed result showing a nearly Nernstian response in the same concentration range. For the membrane with 3 mM ionophore 1, the slope of the calculated potentials was calculated to be only 25 mV/decade, which is close to that of the observed value. This ionophore concentration dependence reﬂects the extent of surface coverage by the SHG active cation complexes; at high ionophore concentrations, the surface saturation of the SHG active complex cation occurs even at lower primary ion concentrations. The calculated membrane potentials consequently leveled off, deviating from the observed EMF function. Similar results were observed with other membranes: the slopes of the calculated potentials for membranes 2, 3, and 4 were consistent with those

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Umezawa

FIG. 8 Calculated potential differences, b b , across the membrane boundary as a function of the primary cation activity, as calculated from Eq. (9). The upper data set shows the corresponding observed EMF. (a) Membrane 1; primary ion: Liþ , ionophore concentration: 3:0 103 M(&), 1:0 102 M (*) and 3:0 102 M (*), respectively, (b) membrane 2; primary ion: Kþ , ionophore concentration: 3:0 102 M, (c) membrane 3; primary ion: Kþ , ionophore concentrations: 2:5 102 M, (d) membrane 4; primary ion: Naþ , ionophore concentration: 3:0 102 M. The following parameters were used: ¼ 4:0, ¼ 78:3, T ¼ 298 K, and X ¼ 1:0 107 mol=cm3 . (From Ref. 15.)

Liquid Membrane Ion-Selective Electrodes

451

of the observed EMFs at relatively low cation concentrations (Figs. 8(b)–(d)] and deviations between the calculated and observed potentials were found at relatively high cation concentrations. The increase in the extent of charge separation due to the increasing ionophore concentration without substantial change in the observed EMF, as can be seen in Fig. 8, may be surprising. One must, however, bear in mind that the increased ionophore concentration leads to an increase in the phase boundary potentials at both the outer and inner interface of the ISE membrane and that these two effects should cancel out. The deviation of the calculated EMF responses from Nernstian slopes at high cation and ionophore concentrations, in contrast to the observed EMFs, may be explained as follows: in the space charge model, the surface charge is treated as the sum of point charges that are Boltzmann distributed within the diffuse double layer. Due to neglect of ﬁeld-dipole forces and speciﬁc molecular interactions occurring at the phase boundary, saturation of the SHG active layer cannot be taken into account. Although the space charge model seems to be valid for the explanation of the electrical potential drop across the interface, the SHG observation is expected to provide reﬁnements of this model in terms of the charge distribution as well as the orientation of the cation complexes.

IV.

MOLECULAR PROBE FOR ISE MEMBRANE POTENTIALS BASED ON PHOTOSWITCHABLE AZOBIS(BENZO-15-CROWN-5) IONOPHORES [17]

Shinkai and coworkers [36–38] synthesized a series of azobis(benzo-15-crown-5), which can adopt the trans and cis forms by reversible photoisomerization. The cis-ionophore forms a stable sandwich-type 1 : 1 cation–ionophore complex with Kþ ions, whereas the corresponding complexation afﬁnity of the trans-ionophore is very weak [36]. Photocontrol of the cation-extracting [36,37] and cation-transport [38] properties of these compounds was intensively studied. More recently, Osa and coworkers [39–41] reported photoinduced potential changes with PVC-based liquid membranes containing photoswitchable ionophores such as azobenzene-linked crown ethers. When the membrane in contact with the primary cation solution was exposed to UV light, a change in the membrane potential due to photoisomerization of the ionophore in the membrane was observed. Although the direction of the photoinduced potential change was discussed in terms of the structural change of the ionophore, quantitative treatment of the potential change was not carried out. If the photoequilibrium concentrations of the cis and trans isomers of the photoswitchable ionophore in the membrane bulk and their complexation stability constants for primary cations are known, the photoinduced change in the concentration of the complex cation in the membrane bulk can be estimated. If the same amount of change is assumed to occur for the concentration of the complex cation at the very surface of the membrane, the photoinduced change in the phase boundary potential may be correlated quantitatively to the amount of the primary cation permeated to or released from the membrane side of the interface under otherwise identical conditions. In such a manner, this type of photoswitchable ionophore may serve as a molecular probe to quantitatively correlate between the photoinduced changes in the phase boundary potential and the number of the primary cations permselectively extracted into the membrane side of the interface. Highly lipophilic derivatives of azobis(benzo-15-crown-5), 1 and 2, as well as reference compound 3 were used for this purpose (see Fig. 9 for the structures) [43]. Compared to azobenzene-modiﬁed crown ethers reported earlier [39–42], more distinct structural difference between the cis

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Umezawa

FIG. 9 Chemical structures of photoswitchable ionophores 1–3. (From Ref. 17.)

and trans isomers can be expected for ionophores 1 and 2 because in the latter compounds the 15-crown-5 rings are directly attached to the benzene rings of the azobenzene group. A.

Photoinduced Changes in Phase Boundary Potentials

Similarly to Section II [6,30–33], Gouy–Chapman type double-diffuse layers were again assumed as a space charge region that enables charge separation across the membrane– aqueous solution interface (Fig. 10). But more explicit formulation will be given below because more ionic species are involved in this case. On the basis of this assumption, the phase boundary potential was quantitatively correlated with the amount of space charge in that region. However, since the factors controlling the amount of the space charge were not speciﬁed, the relationship between the phase boundary potential and the concentration of the primary cation in the aqueous sample solution could not be discussed. In the present photoswitchable molecular probe approach, the amount of space charge is quantitatively correlated with the number of cationic complexes at the membrane surface by considering the complexation equilibrium between the membrane and aqueous sides of the interface (vide supra). Consequently, the relationship between the photoinduced change in the phase

Liquid Membrane Ion-Selective Electrodes

453

FIG. 10 Schematic representation of the proposed surface model: (a) the concentration and (b) the electrical potential proﬁles at the interface of the membrane and aqueous sample solution. x ¼ 0 and 0 are the positions of ions in the planes of closest approach (outer Helmholtz planes) from the aqueous and membrane sides, respectively. (From Ref. 17.)

boundary potential and in the number of the cationic complex at the membrane surface can be evaluated in a quantitative manner. The sample solution contains a ﬁxed concentration of supporting electrolyte Eþ L and a varying concentration of primary salt Mþ X . The ionophore I is conﬁned in the membrane. Only the primary cation Mþ can be complexed with the ionophore I (given stoichiometry 1 : 1; stability constant bIM ). The complex MIþ and the anionic site A are the lipophilic species that are present only in the membrane phase. In this system, the electroneutrality condition at the membrane bulk leads to mem mem mem mem þ CM þ CEmem ¼ CA þ CX þ CLmem CIM mem ¼ CA þ

aq 2 kM kX ðCM Þ kE kL ðCEaq Þ2 þ mem CM CEmem

ð1Þ

with kspecies ¼ exp

o;aq o;mem species species RT

aq mem where Cspecies and Cspecies are the concentrations of each species in the membrane and sample aqueous solution bulk, respectively, kspecies is the distribution constant of each o;aq o;mem and species are the chemical standard potentials of each species at the species, species aqueous and membrane phases, respectively, and R and T have their usual signiﬁcance. In the proposed model, the phase boundary potential Eb can be expressed as aq aq aq mem Eb ¼ mem mem ð2Þ bulk bulk ¼ 0 bulk ð 0 bulk Þ

454

Umezawa

mem where aq bulk and bulk are the electrical potentials in the bulk of the aqueous solution and mem are the potentials at the outer Helmholtz planes membrane, respectively, and aq 0 and 0 (OHPs) on the aqueous and membrane sides of the interface, respectively. From the equilibrium requirement that the chemical potential involving all ionic species be uniform throughout the phase boundary, the distribution of ions within the electrical double layer can be expressed by the Boltzmann equation:

X

aq Cþð0Þ

X X X

aq Cð0Þ mem Cþð0Þ

mem Cð0Þ

aq F 0 aq bulk ¼ exp RT aq X aq F 0 aq bulk ¼ C exp RT X F ð mem mem 0 bulk Þ mem ¼ C exp RT X F ð mem mem 0 bulk Þ mem ¼ C exp RT X

aq C

ð3Þ

with X X X X

aq aq aq Cþð0Þ ¼ CMð0Þ þ CEð0Þ ;

X

aq aq aq Cð0Þ ¼ CXð0Þ þ CLð0Þ ;

aq aq aq C ¼ CM þ CEaq ¼ CX þ CLaq ; mem mem mem mem Cþð0Þ ¼ CIMð0Þ þ CMð0Þ þ CEð0Þ ;

X

mem mem mem mem Cð0Þ ¼ CAð0Þ þ CXð0Þ þ CLð0Þ ;

mem mem mem mem mem ¼ CIM þ CM þ CEmem ¼ CA þ CX þ CLmem C

aq mem where Cspeciesð0Þ and Cspeciesð0Þ are, respectively, the concentrations of the corresponding species at the OHPs on the aqueous and membrane sides of the interface. According to the Gouy–Chapman theory, the surface charge densities on the aqueous and membrane sides, aq and mem , respectively, can be expressed as

aq

mem

aq qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ X aq F 0 aq bulk C sinh ¼ 8RT0 aq 2RT qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ X F ð mem mem 0 bulk Þ mem ¼ 8RT0 mem C sinh 2RT

ð4Þ

where 0 is the permittivity of a vacuum, aq and mem are the relative permittivities of water and the membrane, respectively. Using Eqs. (3) and (4), the relationship between the surface charge density and the ionic concentrations at the OHPs on the membrane side of the interface can be expressed as X

mem Cþð0Þ þ

X

mem Cð0Þ ¼2

X

2

mem C þ

ð mem Þ 2RT0 mem

ð5Þ

Liquid Membrane Ion-Selective Electrodes

455

Equation (5) can be rewritten as pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ mem mem mem mem mem mem 2RT0 mem CIMð0Þ þ CMð0Þ þ CEð0Þ þ CXð0Þ þ CLð0Þ CAð0Þ 0 1 mem mem mem pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃBqﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ CIM þ CM þ CE C mem mem mem qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 2RT0 mem @ CIMð0Þ þ CMð0Þ þ CEð0Þ A mem mem mem CIMð0Þ þ CMð0Þ þ CEð0Þ

mem ¼

ð6Þ

This relationship implies that the membrane side of the interface becomes positively or negatively charged depending on whether the sum of the surface concentrations of each cationic species is larger or smaller than the total concentration of the corresponding mem mem mem mem þ CM þ CEmem ¼ CA þ CX þ CLmem Þ in the membrane bulk. cations ðCIM Next, the complexation equilibrium at the interface must be taken into account. Under the distribution equilibrium of the primary ion Mþ between the aqueous and membrane sides of the interface, the complexation reaction between the primary ion and the ionophore occurs at the membrane side of the interface, i.e., Mmemð0Þ Ð Maqð0Þ Mmemð0Þ þ Imemð0Þ Ð IMmemð0Þ

ð7Þ

where Maqð0Þ and Mmemð0Þ represent the ion Mþ at the OHPs on the aqueous and membrane sides of the interface, respectively, Imemð0Þ and IMmemð0Þ are, respectively, the uncomplexed and complexed ionophore at the OHP on the membrane side of the interface. Under the assumption that the concentration of the uncomplexed ionophore is constant mem throughout the membrane phase, the quantity CIMð0Þ can be expressed as mem mem mem CIMð0Þ ¼ IM CMð0Þ Cl ¼

mem mem mem IM CMð0Þ Cl;tot mem mem mem IM CMð0Þ Cl;tot CA 1 þ IM CM

ð8Þ

mem where Cl;tot is the total concentration of the complexed and uncomplexed ionophore in the mem membrane bulk. The quantity CMð0Þ can be expressed as a function of the concentration of aq , as the primary cation in the aqueous bulk, CM

2qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 3 aq P mem C þ CEaq mem CM aq ﬃﬃﬃﬃﬃﬃ p aq 5 pﬃﬃﬃ þ aq CM þ CE x qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ aq ﬃ pﬃﬃﬃﬃﬃﬃ aq þ CEaq þ aq CM þ CEaq xmem CM

aq 4 CM aq mem ¼ KI CMð0Þ ¼ CMð0Þ

ð9Þ

with x ¼ kM 1 þ

mem IM Cl;tot aq aq mem CM þ kE CE 1 þ IM CM

By inserting Eq. (8) into Eq. (6) the charge density at the membrane surface, mem , can be described in relation to the concentration of the primary cation at the aqueous aq solution side of the interface, CMð0Þ :

456

Umezawa

mem

8vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ

3 2 u > mem mem u aq 1 þ IM CM þ Cl;tot pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 þ IM CM CM : P mem C ﬃ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ mem mem aq 1 þ IM CM þ Cl;tot aq aq CE kM CMð0Þ þ kE CMð0Þ aq mem 1 þ IM CM CM

g

ð10Þ

Because the net charge at the interface should be zero, i.e., mem þ aq ¼ 0, the phase boundary potential (Eb Þ can be expressed by Eq. (11), which can be derived on the basis of ¼ aq Eq. (3) in the simpliﬁed case where mem 0 0 . 39 > = 7 6 archsinh pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Eb ¼ 5 P memﬃ þ arcsinh4qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ aq > F > 8RT0 mem C : þ CEaq ; 8RT0 aq CM 8 > 2RT <

"

#

mem

2

mem

ð11Þ When a membrane based on a derivative of azobis(benzo-15-crown-5) in contact with a solution of a primary cation is exposed to visible light, we assume that the ionophore within the membrane phase is exclusively in the trans isomer and forms a 1 : 1 ionophore (I)–cation (Mþ ) complex with a stability constant, IM , trans. According to mem , can Eq. (10), the corresponding charge density at the membrane side of the interface, vis be expressed as

mem vis

0 1 ﬃ mem pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃBqﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ CA C mem;vis ﬃA ¼ 2RT0 mem @ CIMð0Þ;trans qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ mem;vis CIMð0Þtrans

ð12Þ

mem mem mem ¼ 0, CEaq ¼ 0 (hence CLmem ¼ 0) and CIMð0Þ;trans CMð0Þ . By inserting in the case of CX Eq. (12) into Eq. (11) and using

x 1 arcsinh ¼ ln x 2 2x the phase boundary potential, Evis , is expressed as

Evis

mem vis CIMð0Þ;trans RT ln mem vis mem F CIM;trans þ CM

!

3 aq mem mem;vis k C C C M IM;trans l;tot IM;trans M RT 4 5 ln mem F CA 2

ð13Þ

Under UV light irradiation, cis–trans photoisomerization of the ionophore in the membrane occurs. We assume that the cis and trans isomers are both present in the membrane and the cis isomer forms a 1 : 1 (ionophore–cation) complex with a stability mem constant, IM;cis . In this case, the surface charge density, uv , and the phase boundary potential, Euv , can be expressed as

Liquid Membrane Ion-Selective Electrodes

mem uv

Euv

0 1 mem ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ q pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃB CA C mem;uv mem;uv ﬃA ¼ 2RT0 mem @ CIMð0Þ;trans þ CIMð0Þ;cis qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ mem;uv mem;uv CIMð0Þ;trans þ CIMð0Þ;cis

457

ð14Þ

! mem;uv mem;uv CIMð0Þ;trans þ CIMð0Þ;cis RT ln mem;uv mem;uv mem F CIM;trans þ CIM;cis þ CM h

i9 8 aq mem;uv mem;uv mem;uv mem;uv = RT
mem mem mem mem 0, CEaq 0 (hence CLmem 0) and CIMð0Þ;trans þ CIMð0Þ;cis CMð0Þ . in the case CX Accordingly the photoinduced change in the phase boundary potential Euv Evis , can mem;uv mem;uv and Cl;cis;tot . be expressed by Eq. (16) as a function of bIM;cis , bIM;trans , Cl;trans;tot ! mem;uv mem;uv CIMð0Þ;trans þ CIMð0Þ;cis RT ln Euv Evis ¼ mem;vis F CIMð0Þ;trans ð16Þ ! mem;uv mem;uv IM;trans Cl;trans;tot þ IM;cis Cl;cis;tot RT ln ¼ mem F IM;trans Cl;tot mem mem CA . where Cl;tot The fabrication of a PVC-membrane-coated electrode with only a single organic– aqueous interface between the membrane and the aqueous sample solution enabled us to evaluate the photoinduced changes in phase boundary potentials. Fig. 11(a) shows the time course of the observed membrane potentials (EMFs) by alternating UV and visible light irradiation of membrane 2 containing 1 mM ionophore and no added anionic site (KTpCIPB) in contact with aqueous 0.1 M RbCl. After a stable EMF was reached in the dark, a steep increase in the EMF was observed by UV light irradiation. The EMF under UV light stabilized in ca. 1 min, and the initial EMF was recovered within 1 min by visible light irradiation, showing complete reversibility of the photoinduced EMF change.

FIG. 11 Photoresponse of the EMF induced by UV and visible light irradiation for membrane 2 in contact with 0.1 M of aqueous solutions of (a) RbCl and (b) KCl. The concentration of ionophore 2 was 1.0 mM. (From Ref. 17.)

458

Umezawa

Under UV light irradiation, the cis isomer of ionophore 2 is predominant in the membrane. Therefore, the increase in the EMF by UV light irradiation can be ascribed to a light-induced increase in the uptake of Rbþ ions into the membrane side of the interface due to stronger afﬁnity for Rbþ ions of the cis isomer compared to the trans isomer. Compared to the case of Rbþ ions, the photoinduced change in EMF for membrane 2 in contact with aqueous KCl solution was opposite in direction. As shown in Fig. 11(b), upon UV light irradiation, the EMF in contact with 0.1 M aqueous KCl solution quickly decreased and leveled off within 1min. The decrease in the EMF for Kþ ion under UV light irradiation reﬂects smaller uptake of Kþ ions by the cis isomer compared to the trans isomer due to weaker binding afﬁnity of the former. The values of the photoinduced EMF changes, i.e., DEMF ¼ EMFUV EMFvis , for membranes 1–3 in contact with 0.1 and 0.01 M of KCl and RbCl are summarized in Table 1. Comparison of the calculated and observed changes in the EMF is shown in Table 1. It can be seen that the calculated changes in the phase boundary potential of membranes with 1.0 mM 1–3 in contact with 0.1 and 0.01 M aqueous KCl or RbCl were in good agreement with the corresponding observed values. Such an agreement indicates that it is reasonable to apply the present surface model to explain that the phase boundary potential is, in fact, determined by the amount of the primary cation permeated into or released out of the membrane side of the interface.

V.

CHARGED SITES ARE REQUISITE FOR THE POTENTIAL RESPONSE OF ISEs [16]

The response of ISEs based on liquid or solvent polymeric membranes containing an ionophore or ion carrier (i.e., a lipophilic complexing agent that reversibly binds ions) strongly depends on the amount of ionic sites trapped in the membrane phase. Deliberately added ionic sites are nowadays routinely used to reduce the interference of lipophilic counterions (for cation-selective electrodes: ‘‘anionic effect’’) [44] and the electrical membrane resistance, control the potentiometric selectivity and shorten response times [7,31,45–49]. A smaller concentration of ionic sites regularly originates from impurities of membrane components such as the membrane plasticizer or the polymer matrix [e.g., poly(vinyl chloride) (PVC)], or from membrane supports [50–54]. The presence of such ionic sites, whether introduced deliberately or not, has been commonly used to explain the permselectivity of neutral carrier ISE membranes, which is a prerequisite for primary ion-selective EMF responses. Only very little was, however, known on the properties of membranes free of ionic sites because with very few exceptions all investigators in the ﬁeld have so far used membranes containing at least ionic impurities. A better understanding of the potentiometric properties of membranes free of ionic sites seemed, however, necessary to fully assess the signiﬁcance of ionic sites for ISEs and ion-selective ﬁeld effect transistors (ISFETs). Only recently, we have shown experimentally for a selection of neutral ionophores and carefully puriﬁed, typical PVC plasticizers that in absence of ionic sites Nernstian EMF responses could not be obtained [55]. For plasticizers of low polarity no EMF responses were observed at all. Transient responses due to salt extraction even with the highly hydrophilic counterion chloride were observed in the case of the more polar nitrobenzene. Lasting primary ion-dependent charge separation at the liquid–liquid interfaces of ISEs, resulting in a stable EMF response, seemed therefore only possible in the presence of ionic sites conﬁned to the membrane phase. Because membranes free of impurity sites

17:2 0:5 12:5 0:3 8:2 0:3

17:1 0:3c 12:6 0:2 7:9 0:4

b

The ionophore concentration in the membrane was 1.0 mM in all cases. The potential changes were calculated from Eq. (16). c Standard deviations, n ¼ 20. Source: Ref. 17.

a

1 2 3

Ionophore

Observed (mV) 20:0 12:4 7:74

Calculatedb (mV)

KCl (0.01 M)

Observed (mV)

KCl (0.1 M)

DEMF

7:5 0:2 11:0 0:4 7:4 0:5

Observed (mV)

RbCl (0.1 M)

7:2 0:2 10:8 0:3 6:5 0:3

Observed (mV)

8:48 11:2 5:74

Calculatedb (mV)

RbCl (0.01 M)

TABLE 1 Photoinduced Potential Changes, DEMF (EMFUV EMFvis ), for Membranes Based on Ionophores 1, 2 and 3a

Liquid Membrane Ion-Selective Electrodes 459

460

Umezawa

have a very large bulk resistance, we worked with ﬁeld-effect transistors directly covered with polymer-free liquid membranes [55,56]. The quick response of such membranes to tetraphenylphosphonium chloride and subsequent establishment of a steady potential, as well as solvent extraction experiments, conﬁrmed the suitability of our experimental approach. To further corroborate these potentiometric results, we again used optical second harmonic generation (SHG). The SHG measurement system was essentially the same as used in the study described in Section II, except the laser beam was ﬁrst reﬂected by a mirror and then totally reﬂected by the liquid–liquid interface. To determine the inﬂuence of ionic sites on the charge separation at the membrane interface, we have measured in this study SHG with ionophore-free and ionophore-incorporated liquid membranes in absence and presence of ionic sites. The dependence of the SHG intensity on the activity of the primary ion in the aqueous solution is presented and compared to the corresponding EMF.

A.

1,2-Dichloroethane Membranes with Ionic Sites

As stated in Section II, changes in the charge separation across the phase boundary of ionophore-based ion-selective electrode membranes are accompanied by changes in the SHG intensity. The same is expected for ion-exchanger electrodes too. Fig. 12 (*) shows the EMF responses of a 1,2-dichloroethane membrane containing tridodecylmethylammonium (TDDMA) ions as ionic sites. A Nernstian response is obtained in the activity range between 104 and 101 M KSCN. The corresponding SHG intensities decreased steadily with the KSCN activity in the aqueous solution, attained a minimum at about 102 M KSCN and then strongly increased again [Fig. 13(a), *]. To interpret the p SHG ﬃﬃﬃﬃﬃﬃﬃﬃﬃ response, it is necessary to know that the square root of the SHG signal intensity, Ið2!Þ , is proportional to the surface concentration of SHG active species, N, the molecular second-order nonlinear electrical polarizability, ð2Þ , and the coordinate transformation, hTi, connecting the laboratory and molecular axes, where the angular brackets denote an average over all molecular orientations. Because Kþ ions, the

FIG. 12 1KSCN activity dependence of the EMF response of 1,2-dichloroethane containing (~) no or (*) 1 wt% TDDMA-SCN and (*) nitrobenzene membranes containing no TDDMA-SCN. (From Ref. 16.)

Liquid Membrane Ion-Selective Electrodes

461

FIG. 13 KSCN activity dependence of the SHG response of (a) 1,2-dichloroethane and (b) nitrobenzene membranes containing (*) no or (*) 1 wt% TDDMA-SCN. (From Ref. 16.)

water molecules and the solvent molecules (1,2-dichloroethane) are not signiﬁcantly SHGactive at 1064 nm and the same is also expected for the tridodecylmethylammonium cations, the only species with SHG activity at 1064 nm is, therefore, oriented SCN . The minimum in the plot of the SHG intensity vs. KSCN activity (Fig. 13) can, therefore, be explained by the disappearance of oriented SHG active SCN anions at the interface at this KSCN activity. For membranes with an ion exchanger [57], a surface excess of positive charges on the organic side of the membrane interface is expected at low SCN activities, where SCN ions are transferred from the organic into the aqueous phase. Due to the requirement of electroneutrality, an equal surface excess of negative charges must occur on the aqueous side of the interface. The SHG active species providing excess negative surface charge on the aqueous side must be SCN because the aqueous solution contains no other electrolyte than KSCN. When the activity of KSCN in the aqueous phase is increased, fewer SCN ions leave the membrane, leading ﬁnally to the disappearance of the charge separation of tridodecylmethylammonium ion, TDDMAþ , and oriented SHG active SCN across the liquid–liquid interface. Upon further increasing the KSCN activity, more SCN ions enter the organic phase. This results in a surface excess of negative charges on the organic side of the phase boundary. An analogous effect has been used to explain maxima in the interfacial tension at very similar liquid–liquid interfaces [58].

462

B.

Umezawa

1,2-Dichloroethane Membranes Free of Ionic Sites

In contrast to membranes with tridodecylmethylammonium thiocyanate, TDDMA-SCN, no signiﬁcant equilibrium EMF and SHG responses to KSCN were observed with 1,2dichloroethane membranes containing no ion exchanger [Fig. 12, ~, and Fig. 13 (a), *]. This suggests that, at equilibrium, the extent of charge separation of Kþ and oriented SHG active SCN across the membrane interface is very low and does not depend on the concentration of KSCN in the aqueous phase. This agrees with the theoretical expectation that partitioning of a single salt between two immiscible solvents gives a potential drop across the interface of the two solvents that does not depend on the salt activity [58]. The EMF response to KSCN of a water-saturated 1,2-dichloroethane membrane containing no ion exchanger was, however, time-dependent (Fig. 14; *), suggesting a transient charge separation due to extraction of KSCN into the organic solvent. Upon addition of KSCN to the aqueous phase, a very small transient decrease of the EMF (8 mV) upon addition of KSCN to electrolyte-free water to give a 0.01 M solution was observed. The measured potential passed, however, through a minimum after about 15 min and then increased again for several hours, with a derivative considerably larger than the background drift of the FET. Also the intensity of the second harmonic as generated at the 1,2-dichlorethane–water interface in a different measurement cell but under otherwise identical conditions was transient (Fig. 14, *). It increased immediately upon addition of KSCN to the aqueous phase but then decreased down to background level within 40 min. In contrast, very different EMF responses were obtained for the membranes with ionic sites: a strong and fast anionic response. It was followed by a drift that is not distinguishable from the background drift of the FET. The SHG response was also very quick and no substantial changes in the intensity were observed. The transient SHG and EMF responses for membranes without ionic sites thus conﬁrm the occurrence of time-dependent charge separation across the phase boundary due to transfer of Kþ as well as SCN into the organic phase.

FIG. 14 Time course of the (*) EMF and (*) SHG responses of 1,2-dichloroethane containing no TDDMA-SCN upon a concentration step from 0 to 102 M KSCN. (From Ref. 16.)

Liquid Membrane Ion-Selective Electrodes

C.

463

Nitrobenzene Membranes with and Without Ionic Sites

When we previously investigated the potentiometric properties of carefully puriﬁed plasticizers of low polarity, no EMF responses were observed, whereas for a more polar solvent (nitrobenzene), transient EMF responses were obtained [55,59]. Because of this large difference, we were also interested in the combined SHG and EMF response of more polar ion-exchanger membranes. As previously, we used nitrobenzene for this purpose. When allowing for complete equilibration with aqueous KSCN, no KSCN dependence of the EMF was obtained for nitrobenzene membranes without ionic sites (Fig. 12, *). Again, this suggests that the extent of charge separation across the interface of membranes without ionic sites does not change with the KSCN activity. This interpretation is conﬁrmed by the intensity of the second harmonic, which showed no dependence on the KSCN activity upon equilibration of the two liquid phases [Fig. 13(b), *). On the other hand, incorporation of TDDMA-SCN into nitrobenzene led to an SHG response [Fig. 13(b), *] closely resembling that for TDDMA-SCN containing 1,2-dichloroethane membranes [Fig. 13(a)], showing once more the correspondence between the EMF and the SHG response. As in the 1,2-dichloroethane case too, transient EMF and SHG responses to KSCN were observed for the nitrobenzene membranes without ionic sites. This suggests that here too not only SCN but also Kþ ions are transferred into the nitrobenzene phase. Salt extraction into the bulk of the organic phase, in analogy to similar observations previously reported for neutral ionophore-incorporated liquid membranes without ionic sites [55], was indeed independently conﬁrmed by atomic absorption spectrometry. Figure 15 shows the concentration of Kþ in nitrobenzene equilibrated at room temperature with a 102 M aqueous solution of KSCN as a function of equilibration time. The presence of the ion exchanger TDDMA-SCN efﬁciently suppresses KSCN extraction into the organic phase but in its absence a substantial amount of KSCN enters the nitrobenzene phase. The trends of the EMF and the SHG responses are therefore very similar in spite of the different polarities of the plasticizers.

FIG. 15 Time course of the potassium concentration in nitrobenzene containing (*) no or (*) 1 wt% TDDMA-SCN upon equilibration with 102 M KSCN, as determined by ASS. (From Ref. 16.)

464

D.

Umezawa

Ionophore-Incorporated Membranes

As stated in Section II, the SHG responses to primary cations of ISEs based on several crown ether ionophores could be correlated to the number of primary ion complexes at the phase boundary, which contributed to the membrane potential. We have now incorporated the Kþ ionophore bis[(benzo-15-crown-5)-4-methyl]pimelate into 1,2-dichloroethane and nitrobenzene membranes and determined EMF and SHG responses to KCl in presence and absence of ionic sites. Figure 16(a) (*) shows the EMF responses of a 1,2-dichloroethane membrane containing anionic sites (KTpClPB). A Nernstian response was obtained. An SHG response to KCl was observed at activities of the latter above 102 M [Fig. 16(b), *]. These results can be interpreted in the same way as for ionophore-incorporated PVC liquid membranes, for which we have shown that the concentration of oriented cation complexes at the liquid–liquid interface can explain both the observed SHG signal and EMF response. The present SHG responses thus suggest primary ion concentration dependent charge separation at the interface of the 1,2-dichloroethane membranes incorporated with ionic sites. For 1,2-dichloroethane membranes without anionic sites, on the other hand, negligible EMF responses were obtained [Fig. 16(a), *]. The intensity of the SHG signal did not depend on the KCl activity [Fig. 16(b), *]. This suggests that there is no change in the

FIG. 16 KCl activity dependence of the (a) EMP and (b) SHG responses of 1,2-dichloroethane membranes containing 1 wt% bis(benzo-15-crown-5) and (*) no ionic sites or (*) KTpCIPB in a mole ratio of 50% to the ionophore. (From Ref. 16.)

Liquid Membrane Ion-Selective Electrodes

465

FIG. 17 KCl activity dependence of the (a) EMF and (b) SHG responses of nitrobenzene membranes containing 1 wt% bis(benzo-15-crown-5) and (*) no ionic sites or (*) KTpCIPB in a mole ratio of 50% to the ionophore. (From Ref. 16.)

extent of charge separation across the membrane phase boundary upon increasing the primary ion activity in the case of the membranes without ionic sites. The EMF and SHG responses for nitrobenzene as solvent were qualitatively identical to those for 1,k2-dichloroethane [Fig, 17(b)]. The only difference between the results for the two solvents was that the SHG response to KCl of nitrobenzene membranes with ionic sites was more sensitive than for 1,2-dichloroethane membranes with ionic sites, where an increase in the SHG intensity was observed at KCl activities above 104 M KCl. Use of ionophore-incorporated membranes leads thus to the same conclusions as described above for the ionophore-free membranes. Here too, the SHG measurements suggest that a permanent, primary ion-dependent charge separation at the liquid–liquid interface, and therefore a potentiometric response, is only possible when the membrane contains ionic sites.

VI.

CONCLUSIONS

The above SHG studies exhibited several most important facts in the response mechanisms occurring at the surfaces of ionophore incorporated liquid membrane ISEs.

466

Umezawa

SHG active ions primarily determine the potentials of ISEs, which is oriented at the membrane surface facing its counterions across the membrane–aqueous interface. The ions located behind the surface-oriented species were found to contribute only when the concentration of primary ions was very high. But the location of these ions may still be around respective Debye lengths. This conclusion naturally leads to an idea to intentionally use surface-active ionophores for ISEs development. We recently synthesized several reasonably surface-active crown-ether-based ionophores. This type of ionophore in fact gave Nernstian slopes for corresponding primary ions with its ionophore of one order or less concentrations than the lowest allowable concentrations for Nernstian slopes with conventional counterpart ionophores. Furthermore, the detection limit was relatively improved; with increased offset potentials due to the efﬁcient and increased primary ion uptake into the vicinity of the membrane interface by surfactant ionophores selectively located there. These results were again well explained by the derived model essentially based on the Gouy–Chapman theory. Just like other interfacial phenomena, the surface and bulk phase of the ionophore incorporated liquid membrane may naturally be speculated to be more or less different. The SHG results presented here is one of strong evidence indicating that this is in fact true rather than speculation. Deliberately added ionic sites or existing impurities in ISE liquid membranes were found just requisite for generation of primary-ion-dependent potential outputs. This is conclusively conﬁrmed by comparative studies between SHG and EMF responses with and without ionic sites. This is not a technical issue, such as improving response time by reducing membrane impedance or for introducing ‘‘forced selectivity’’ for ISEs where dissimilar stoichiometries between primary and interfering metal cations and the corresponding co-ordinating ligands are involved. The requisite role of sites in ISE chemistry is essentially different from solvent extraction chemistry; the latter has no added ionic sites in the organic phase – probably needless to emphasize this point here. A molecular probe described in Section III indicates that membrane potentials can now be described as a number of primary or interfering ions uptaken into the organic membrane side of the interface. This concept is widely applicable for various problems pertinent to ISEs. One of the most important measurables for ISEs is the selectivity pot coefﬁcient KA;B for a target ion A over interfering ions, B. After a long-standing discussion in the IUPAC committee on electroanalytical chemistry, this committee recommended the pot so-called matched potential method for reporting KA;B for many electrodes wherever conditions are met for its usage [60]. This method was initially proposed as empirical pot values. Now this has been theoretically but gave analytically relevant practical KA;B backed up by such an approach described in Section III.

REFERENCES 1. 2. 3. 4.

Y. Umezawa. CRC Handbook of Ion-Selective Electrodes: Selectivity Coefﬁcients; CRC Press: Boca, FL, 1990. P. Bu¨hlmann, E. Pretch, and E. Bakker. Chem. Rev. 98:1593 (1998). W. E. Morf, The Principle of Ion-Selective Electrodes and of Membrane Transport, Elsevier, Amsterdam, 1981. E. Lindner, K. To´th, and F. Pungor, Dynamic Characteristics of Ion-Selective Electrodes, CRC Press, Boca Raton, FL, 1988.

Liquid Membrane Ion-Selective Electrodes 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42.

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43. K. Odashima, K. Tohda, S. Yoshiyagawa, S. Yamashita, M. Kataoka, and Y. Umezawa. Heterocycles 47:847 (1998). 44. J. H. Boles and R. P. Buck. Anal. Chem. 45:2057 (1973). 45. W. E. Morf, G. Kahr, and W. Simon. Anal. Lett. 7:9 (1974). 46. R. Eugster, P. M. Gehrig, W. E. Morf, U. E. Spichiger, and W. Simon. Anal. Chem. 63:2285 (1991). 47. U. Schaller, E. Bakker, U. E. Spichiger, and E. Pretsch. Anal. Chem. 66:391 (1994). 48. E. Bakker, M. Na¨gele, U. Schaller, and E. Pretsch. Electroanalysis 7:817 (1995). 49. E. Bakker. Electroanalysis 9:1 (1997). 50. M. Perry, E. Lobel, and R. J. Bloch. Membr. Sci. 1:223 (1976). 51. G. Horvai, E. Graf, K. Toth, E. Pungor, and R. P. Buck. Anal. Chem. 58:2735 (1986). 52. A. v d Berg, P. D. v d Wal, M. Skowronska-Ptasinka, E. J. R. Sudho¨lter, D. N. Reinhoudt, and P. Bergveld. Anal. Chem. 59:2827 (1987). 53. M. L. Iglehart, R. P. Buck, G. Horvai, and E. Pungor. Anal. Chem. 60:1018 (1988). 54. M. Na¨gele and E. Pretsch. Mikrochim. Acta 121:269 (1995). 55. P. Bu¨hlmann, S. Yajima, K. Tohda, and Y. Umezawa. Electrochim. Acta 40:3021 (1995). 56. T. Masadome, S. Wakida, Y. Kawabata, T. Imato, and N. Ishibashi. Anal. Sci. 8:89 (1992). 57. O. R. Melroy and R. P. Buck. J. Electroanal. Chem. 143:23 (1983). 58. H. H. J. Girault and D. J. Schiffrin, in Electroanalytical Chemistry, vol. 15 (A. J. Bard, ed.), Marcel Dekker, New York,, 1989, pp. 1–141. 59. P. Bu¨hlmann, S. Yajima, K. Tohda, K. Umezawa, S. Nishizawa, and Y. Umezawa. Electroanalysis 7:811 (1995). 60. Y. Umezawa, K. Umezawa, and H. Sato. Pure Appl. Chem. 67:507 (1995).

19 Water-in-Oil Microemulsions: Protein Encapsulation and Release DOUGLAS G. HAYES Department of Chemical and Materials Engineering, University of Alabama in Huntsville, Huntsville, Alabama

I.

INTRODUCTION

Water-in-oil microemulsions (w/o-MEs), also known as ‘‘reverse micelles,’’ provide what appears to be a very unique and well-suited medium for solubilizing proteins, amino acids, and other biological molecules in a nonpolar medium. The medium consists of small aqueous–polar nanodroplets dispersed in an apolar bulk phase by surfactants (Fig. 1). Moreover, the droplet size is on the same order of magnitude as the encapsulated enzyme molecules. Typically, the medium is quite dynamic, with droplets spontaneously coalescing, exchanging materials, and reforming on the order of microseconds. Such small droplets yield a large amount of interfacial area. For many surfactants, the size of the dispersed aqueous nanodroplets is directly proportional to the water–surfactant mole ratio, also known as wo . Several reviews have been written which provide more detailed discussion of the physical properties of microemulsions [1–3]. Surfactants employed for w/o-ME formation, listed in Table 1, are more lipophilic than those employed in aqueous systems, e.g., for micelles or oil-in-water emulsions, having a hydrophilic–lipophilic balance (HLB) value of around 8–11 [4–40]. The most commonly employed surfactant for w/o-ME formation is Aerosol-OT, or AOT [sodium bis(2-ethylhexyl) sulfosuccinate], containing an anionic sulfonate headgroup and two hydrocarbon tails. Common cationic surfactants, such as cetyl trimethyl ammonium bromide (CTAB) and trioctylmethyl ammonium bromide (TOMAC), have also fulﬁlled this purpose; however, cosurfactants (e.g., fatty alcohols, such as 1-butanol or 1-octanol) must be added for a monophasic w/o-ME (Winsor IV) system to occur. Nonionic and mixed ionic–nonionic surfactant systems have received a great deal of attention recently because they are more biocompatible and they promote less inactivation of biomolecules compared to ionic surfactants. Surfactants with two or more hydrophobic tail groups of different lengths frequently form w/o-MEs more readily than one-tailed surfactants without the requirement of cosurfactant, perhaps because of their wedge-shaped molecular structure [17,41]. w/o-Microemulsions are readily formed using nonpolar alkanes which are liquid at room temperature and possess an alcohol–water partition coefﬁcient, or log P value, in the range 3.5–8. The most frequently employed solvents include 2,2,4-trimethylpentane (isooctane) and the C6C8 n-alkanes. However, microemulsions also can form in near-critical 469

470

Hayes

FIG. 1 Illustration of an enzyme-containing water-in-oil microemulsion (w/o-ME).

C2C4 n-alkanes [42,43], and in supercritical carbon dioxide when employing novel surfactants with ﬂuorocarbon tails [38,44]. There is also interest in the further employment of lipids (triglycerides and wax esters, such as isopropyl myristate) as solvent to improve biocompatibility [45]. For a typical biomolecule-containing w/o-ME system, only a fraction of the w/o-ME population (e.g., 0.1–1%) will contain proteins. Because of their small concentration and the short (microsecond-scale) lifetime of any given w/o-ME droplet, due to the rapid collision and exchange rate for w/o-ME systems, isolation of the protein-containing, or ‘‘ﬁlled’’ w/o-ME populations is difﬁcult to achieve. Various techniques have demonstrated that encapsulated enzymes can alter the structural properties and behavior of the w/oMEs, and that ‘‘ﬁlled,’’ w/o-MEs may differ in properties from the ‘‘empty’’ w/o-MEs in a given microemulsion system [46–51]. However, a clear understanding of the structural and dimensional differences between ‘‘ﬁlled’’ and ‘‘empty’’ w/o-MEs has yet to be achieved. Microemulsions have been frequently employed for tertiary oil recovery and for hosting inorganic and organic syntheses, including the degradation of nerve gas and the formation of ultraﬁne metallic and ceramic superconductive materials, among other appliations [3,52,53]. In addition, a large body of literature exists on enzymatic reactions hosted in w/o-ME solution, and the use of the medium to purify biomolecules, refold denatured proteins, and serve as drug delivery vehicles [2,3,54–56]. The biological activity and stability, and the concentration of proteins and other biomolecules encapsulated in w/ o-MEs, and after their recovery from w/o-MEs, depends strongly on the methodology employed for their encapsulation and release. An overview of the encapsulation and release procedures will serve as the focus for this chapter.

II.

METHODS FOR ENCAPSULATING BIOMOLECULES

There are three general methods for solubilizing biomolecules in w/o-ME solutions [2] (Fig. 2): Injection of a small aliquot of aqueous phase into surfactant-containing organic solvent (injection method, INJ).

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TABLE 1 Surfactant Systems Employed for w/o-ME-Based Liquid–Liquid Extraction (LLE) of Biomolecules Surfactant Anionic Sodium bis(2-ethylhexyl sulfosuccinate) [AOT] Bicyclic sulfonates Di(2-ethylhexyl) phosphoric acid [DEHPA] Di(2-ethylhexyl) phosphorothioic acid [DEPTA] Di(oleyl) phosphoric acid [DOLPA] Di(tridecyl) phosphoric acid Sodium dodecylbenzenesulfonate [SDBS]/1-butanol

References

[4, and references therein] [5] [6,7] [8] [9,10] [11] [12]

Cationic Cetyl trimethyl ammonium bromide [CTAB]/n-alkanol n-Benzyl-n-dodecyl-n-bis(2-hydroxyethyl) ammonium chloride [BDBAC]/1-hexanol Dialkyl dimethyl ammonium bromides/n-alkanol Trialkyl methyl ammonium chloridea [TOMAC]/n-alkanol

[17–19] [17,20–22]

Zwitterionic Lecithin [phosphatidylcholine]

[23]

Nonionic Ci H2iþ1 (OC2 H4 )j OH ½Ci Ej b Ci H2iþ1 C6 H4 ðOC2 H4 Þj OHc Sucrose–fatty acid exters/2-propanol Sorbitol–fatty acid monoesterd Sorbitol–fatty acid monoester ethoxylatee Sorbitol–fatty acid triester ethoxylatef Sorbitol–fatty acid triester ethoxylatef =2-propanol

[24] [24] [25] [24] [24] [24,26] [27]

Mixed surfactant systems AOT/sorbitol–fatty acid monoester AOT/DEHPA AOT/DEHPA/DEPTA AOT/Ci Ej AOT/DOLPA AOT/sorbitol–fatty acid triester ethoxylate AOT/sorbitol–fatty acid monoester TOMAC/Ci Ej Lecithin/sorbitol–fatty acid triester ethoxylate

[28] [29] [8] [30,31] [32] [33] [33] [31] [23]

Afﬁnity surfactants and cosurfactants Alkyl monoglucoside (Concanavalin A) Boronic acid derivatives (-chymotrypsin) Surfactants with biotin-containing headgroup (Avidin) Metal chelating surfactant (cytochrome c) Cholesteryl-D-alanyl-D-alanine (Vancomycin)

[30,31,34–36] [35] [37,38] [39] [40]

a

Aliquat 336 (Henkel, Cincinnati, OH). Neodol (Shell Chemical Co). c Igepal CO-520 (Rhone-Poulenc). d Span surfactant series. e Tween surfactant series. f Tween 65 or 85. b

[13–15] [16]

472

Hayes

FIG. 2 Methods for encapsulating biomolecules into w/o-MEs.

Extraction of lyophilized protein powder by w/o-ME solution (solid-phase extraction method, SPE). Extraction of protein from aqueous solution by surfactant-containing lipophilic organic solvent (phase transfer method, or equivalently, w/o-ME-based liquid–liquid extracting, LLE). SPE has received the least amount of attention among the three, primarily because of the frequent desorption of w/o-MEs from solution by the protein powder [57,58]. However, SPE can yield a signiﬁcantly high level of solubilization, and may be useful as a method for refolding proteins [57–59]. INJ has been commonly used to solubilize enzymes into w/oME solutions for kinetic and spectroscopic studies [2]. It also has recently been applied for recovering proteins [60]. LLE has been investigated in the past 15 years as a potentially useful method for isolating, concentrating, and separating amino acids and proteins.

III.

ENCAPSULATION BY THE INJECTION TECHNIQUE (INJ)

The injection technique (INJ) consists of the mixing of a biomolecule-containing aqueous solution with a surfactant-containing organic phase, forming a one-phase, or Winsor IV, w/o-ME solution (Fig. 2). To ensure the success of INJ, the overall composition and temperature of the w/o-ME solution must coincide with the one-phase w/o-ME region of the triangular phase diagram, which usually occurs in the vicinity of the oil–surfactant axis near the oil vertex. For aqueous solutions highly concentrated in protein or other constituent (e.g., anions and cations), their effect on the position of the Winsor IV phase boundary must be taken into account. Enzymes frequently lose their activity and secondary and tertiary structural integrity immediately upon incorporation into w/o-MEs, particularly for systems containing ionic surfactants such as AOT [61–67]. It is the author’s belief that this occurs if INJ is not conducted quickly because of the exposure of biomolecules to macroscopic interfaces

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473

during the process. Moreover, many enzymes are known to inactivate at lipophilic–aqueous interfaces [68]. In addition, perhaps the partial solubilization of surfactant in the aqueous phase may be an initial step occurring during INJ. It is well known that many ionic surfactants, including AOT, inactivate enzymes in aqueous solutions [69]. Often the presence of substrate protects biomolecules from inactivation, presumably, by inducing a favorable change in the tertiary structure of the biomolecule or by preventing access of the surfactant to the active or binding site [61]. The author has discovered that the procedure employed for mixing the aqueous and organic phases has a strong effect on the observed activity of encapsulated lipases [70]. Thus, rapid mixing using vortex mixing, e.g., is recommended. Luisi and coworkers investigated the kinetics of the INJ process [71]. They found that it involves two overall stages. The ﬁrst, occurring rapidly, consists of the rapid uptake of aqueous solution by the organic phase, yielding random, nonequilibrium microemulsion formation. The second, slower stage is the relaxation of the system into an equilibrium w/o-ME structure. The ﬁrst stage is sensitive to the relative amounts of water, surfactant, salt, and protein, while the second stage is relatively insensitive to these parameters. The overall rate of solubilization was slowest when the pH was near the pI of the protein.

IV.

ENCAPSULATION BY SOLID-PHASE EXTRACTION (SPE)

This technique, consisting of the contact with a solid-phase, or lyophilized biomolecule, and a w/o-ME solution, has been employed primarily with the AOT surfactant system. Early work by Luisi and coworkers demonstrated that a variety of proteins, polypeptides, and amino acids can be incorporated into w/o-MEs via SPE [57,72,73]. The driving force appears to be either direct electrostatic or hydrophobic interactions between surfactant and biomolecule, or via the biomolecule’s afﬁnity for the encapsulated water. The nature of the driving force was determined through examination of the effect of the extractant’s water–surfactant mole ratio, or wo value, versus the percent extraction of protein. An optimal wo value near 10, reﬂecting a nanodroplet size similar in magnitude to most proteins (ca. 33 nm [1]), reﬂects a biomolecule–surfactant afﬁnity driving force, while an increasing trend in extraction with wo demonstrates biomolecule-encapsulated water afﬁnity [57]. (In subsequent work, it was revealed that the surfactant-protein mole ratio of the solid phase was a more suitable dependent variable than percent extraction for determining the nature of the driving force [58].) The occurrence of electrostatic attractions was detected by examining the effect of the solid phase’s ‘‘pH memory’’ on the percent extraction [57]. The SPE technique proved to be very effective for encapsulating hydrophobic and poorly-water-soluble proteins such as myelin basic protein and transmembrane proteins [74,75]. Subsequently, a mechanistic study demonstrated that protein solubilization in the organic phase occurred simultaneously with the adsorption of w/o-MEs by the solid phase [58]. Moreover, the results of this study supported the following proposed mechanism for SPE: 1. 2.

The solid phase desorbs w/o-MEs. A protein–surfactant–water complex forms in the solid phase. Upon adsorption of a certain number of surfactant molecules, the complex’s hydrophobicity increases, driving its transport into the liquid phase.

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3.

The solubilized aggregate interacts and exchanges with the remaining w/o-MEs in the solvent phase.

For instance, the time course of SPE demonstrates that the solvent phase surfactant concentration steadily decreases (Fig. 3) [58]. The w/o-ME solution’s water content decreases at the same rate as the surfactant [58]. The protein concentration at ﬁrst increases, presumably due to the occurrence of Steps 2 and 3 above, but then decreases due to the adsorption of ‘‘ﬁlled’’ w/o-MEs by the solid phase (Fig. 3) [58]. Additional evidence supporting the mechanism given above is the occurrence of a single Langmuirtype isotherm describing surfactant adsorption in the solid phase for several SPE experiments employing a given protein type (Fig. 4) [58]. Here, solid-phase protein molecules can be considered as surfactant adsorption sites. Similar adsorption isotherms occurred also for water adsorption [58]. Regarding the optimization of operating conditions, the ﬁnal protein concentration in w/o-MEs increases linearly with the ratio of solid-phase protein to w/o-ME extractant until an optimal ratio is reached, above which protein extraction decreases due to an excessive desorption of ‘‘ﬁlled’’ w/o-MEs from the organic phase by the solid phase [58]. A high protein concentration in w/o-ME solution was obtained when the proteinand surfactant-containing solid phase occurring after a ﬁrst cycle of SPE was exposed to a second SPE cycle [58]. In addition, protein solubilization can be maximized by stopping the extraction process early (e.g., at ca. 0.4 h for the experimental depicted in Fig. 3), before adsorption of ﬁlled w/o-MEs becomes dominant [58]. The condition of the solid phase–its crystal structure and salt and water content–also strongly affect SPE [58]. Recently, SPE was determined to be useful in a protein refolding process. Goto, Hatton, and coworkers demonstrated that SPE was the most efﬁcient method for solubilizing denatured ribonuclease into AOT-based w/o-MEs [59]. The w/o-ME encapsulated

FIG. 3 Time course of the solid-phase extraction of bovine serum albumin by an AOT-based w/oMe solution. Conditions: 500 mg of solid-phase protein; 20 mL of iso-octane containing 25 mM AOT and 1000 mM water (wo ¼ 40Þ. (Reprinted with permission from Ref. 58.)

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475

FIG. 4 Relationship between the ﬁnal AOT and protein amounts in the solid phase for several different experiments, using a w/o-ME extractant of 50 or 100 mM AOT (uniﬁlled and ﬁlled symbols, respectively), wo ¼ 20. Proteins: (upward-pointing triangles) bovine serum albumin; (downward-pointing triangles) -chymotrypsin; (diamonds) lysozyme. (Reprinted with permission from Ref. 58.)

enzyme was treated with a redox reagent. The w/o-ME-based refolding technique was more effective than aqueous-based methods [59]. An improved protein refolding technique is important for the treatment of proteins recovered in the form of inclusion bodies, resulting from recombinant DNA processes [76].

V.

MICROEMULSION-BASED LIQUID–LIQUID EXTRACTION (LLE)

Depicted in Fig. 2, microemulsion-based liquid–liquid extraction (LLE) of biomolecules consists of the contacting of a biomolecule-containing aqueous solution with a surfactantcontaining lipophilic phase. Upon contact, some of the water and biomolecules will transfer to the organic phase, depending on the phase equilibrium position, resulting in a biphasic Winsor II system (w/o-ME phase in equilibrium with an ‘‘excess’’ aqueous phase). Besides serving as a means to solubilize biomolecules in w/o-MEs, LLE has been frequently used to isolate and separate amino acids, peptides and proteins [4, and references therein]. In addition, LLE has recently been employed to isolate vitamins, antibiotics, and nucleotides [6,19,40,77–79]. Industrially relevant applications of LLE are listed in Table 2 [14,15,20,80–90]. Downstream puriﬁcation and isolation of proteins and biomolecules is often the most expensive and challenging aspect of their production [91]. Many of the downstream separation processes used by industry today, e.g., ultraﬁltration, chromatography, and centrifugation, are slow, inherently batch, nonspeciﬁc, expensive, overconsume energy, and generate wastes, particularly for downstream product puriﬁcation, an important cate-

476 TABLE 2

Hayes Applications of LLE to Separations of Commercial Relevance

Application

Reference

Isolation of lipase A from lipase B from crude Chromobacterium viscosum extract Recovery of alkaline protease from fermentation broth Recovery of cellulases from wheat-straw hydrolysis fermentation broth Recovery of inulinase from Kluyveromyces marxianus fermentation broth Recovery of mycelium-bound tannase from Aspergillus niger fermentation broth Isolation of -amylase and protease from Bacillus subtilis fermentation broth Recovery of intracellular proteins from Candida utilis Recovery of peroxidase from soybean hulls Recovery of peroxidase from horseradish roots Recovery of lysozyme from chicken egg white Isolation of trypsin from bovine pancreatin

[80,81] [82] [83] [16] [84] [20] [14,85] [86] [87] [88,89] [90]

gory within bioseparations. Moreover, the efﬁciency of bioproduct isolation usually controls the overall cost [76]. Although w/o-ME-based LLE has many advantages for bioseparations, such as a rapid rate and its ability to be scaled-up, further work is needed to improve selectivity, capacity, versatility, and biocompatibility. In addition, current methods to recover w/oME-encapsulated species are insufﬁcient and/or are not adaptable to a wide variety of situations. Furthermore, although large-scale and continuous operation has been demonstrated (Table 3) [15,28,85,89,92–101], the ability to predict operation a priori, i.e., the generation of the necessary theory and equations required to design such equipment, has not yet been achieved. However, work is ongoing in several research laboratories worldwide to solve these problems. Reviews of w/o-ME-based LLE of biomolecules are readily available [4,57,102–104]. However, new results have been generated in this ﬁeld since the publication of the cited reviews. For instance, there has been a large amount of research involving new surfactant and surfactant systems, particularly those involving nonionic and natural surfactants such as phosphatidylcholine and bioafﬁnity surfactants (Table 1), in order to increase biocompatibility and selectivity and prevent denaturation that occurs using ionic surfactants. The more recent results along these lines will be presented here, along with an overview of the LLM process.

TABLE 3

Applications of LLE for Use in Continuous Operation

Continuous process scheme

Reference

Integrated MPE and back-extraction Use of w/o-MEs for transport in liquid emulsion membrane separations Perforated rotating disk contactor Spray column Packed column w/o-ME solution enclosed in hollow ﬁber membranes as a chromatographic stationary phase

[15,92–05] [28] [96–98] [85,99] [100] [89,101]

Water-in-Oil Microemulsions

A.

477

LLE Employing Ionic Surfactants

The major underlying driving force for LLE employing ionic surfactants, particularly for small biomolecules and proteins, involves the electrostatic interactions between the headgroup of the surfactant molecule and the charged groups on the surface of proteins. These interactions are on the length scale of the protein’s diameter [105]. Moreover, the maximum extent of extraction occurs when the surfactant headgroup and protein surface are oppositely charged. For example, when w/o-ME extractants containing the anionic surfactant AOT are employed, extraction is maximized when the aqueous solution’s pH is below the protein’s pI value [103], while the opposite pH–pI relationship must hold true when using systems based on cationic surfactants [102]. (Microemulsion solutions based on nonionic surfactants also may extract proteins via weak electrostatic interactions [24]. See Section V.C.) The role of electrostatic interactions has been supported by theoretical models [105,106]. It is believed that solubilization is initiated when a biomolecule with charged surface groups approaches the bulk aqueous–lipophilic solvent interface, where the interactions cause the bulk interface’s surfactant layer to bend, such that the protruding biomolecule becomes surrounded by the surfactant layer [105]. Ultimately, a ‘‘ﬁlled’’ w/o-ME forms, and partitions to the bulk organic phase [105]. Alternatively, a mechanism has been proposed which is similar to that described above for SPE. It involves the solubilization of surfactant in the aqueous phase, which promotes the formation of biomolecule–surfactant complexes based on ion pairing or hydrophobic interactions [107,108]. As the aggregates adsorb further amounts of surfactant molecules, their hydrophobicity increases, driving them to solubilize in the bulk liquid–liquid interface, and ultimately in the organic phase. Once solubilized in the organic phase, the aggregates combine with, or are entrapped by, existent ‘‘empty’’ w/o-MEs (since water is extracted much more rapidly than proteins). If the surfactant–protein ratio for the system is too low, then the aggregates will remain at the bulk interface or the aqueous phase, often causing denaturation–inactivation of the biomolecule to occur [107,109]. But, when this ratio is very large, solubilization of the aggregate can revert back to the aqueous phase, because an additional layer of surfactant adsorbs via hydrophobic interaction, with surfactant headgroups in this layer extending from the aggregates’ surfaces [109]. A similar event can occur for w/o-ME-encapsulated biomolecules exposed to long residence times, i.e., a more hydrophilic aggregate forms which partitions to the bulk aqueous phase [110]. If the rate of phase contacting is slow, then LLE can lead to precipitate formation [108]. The mass transfer rate for hydrophilic biomolecules during LLE is convection-controlled by the resistance in the aqueous boundary layer bordering the bulk interface, and/ or by an interfacial process involving a ‘‘bud mechanism’’ [100,111–115]. The rate-limiting step of this mechanism is the collision of w/o-MEs with surfactant and solute molecules present at the bulk water–lipophilic solvent interface [112,116,117]. The source and degree of the mass transfer limitation is a function of the protein type and the pH and ionic strength of the aqueous feed. Water transport is relatively fast and convection mass transfer limited, with the main resistance being transport across the organic phase boundary layer [112]. However, metal ions and hydrophobic molecules have mass transfer rates that are several orders of magnitude smaller than hydrophilic proteins and are mass transfer limited by an interfacial ‘‘bud mechanism’’ process [112,116,117]. The mass transfer behavior for the slightly polar amino acid tyrosine was similar to that for metal ions, while that of the hydrophobic amino acid tryptophan mirrored protein transport at high solute concentration and metal ion transport at low solute concentation [117,118].

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The composition of the w/o-ME solution also strongly controls LLE. For instance, with AOT, the surfactant concentration must be above ca. 10 mM for phase transfer to occur [107,119,120]. If the surfactant concentration is very low (ca. 1 mM), near the critical micellar concentration, then the phase transfer of proteins (but not water) occurs due to the formation of surfactant–protein aggregates [108]. High surfactant concentrations are required to solubilize large proteins such as bovine serum albumin (66 kDa) [60,121] and to extract proteins from highly concentrated aqueous solutions [119,122], in agreement with the mechanism proposed above. In addition, the overall mass transfer coefﬁcient for LLE increases with AOT concentration [120]. However, high concentrations (greater than 100 mM) can produce emulsions at the bulk liquid–liquid interface which are difﬁcult to break [123] and also reduce the rate of protein recovery [120]. The composition of the surfactant–cosurfactant system (more speciﬁcally, the geometrical packing of the surfactant and cosurfactant at the interface) dictates the amount of water transported to the organic phase, or equivalently, dictates the size of the resultant w/ o-MEs [8]. In addition, the ionization state of the surfactant headgroups, controlled by the aqueous pH, also affects water transport [29,124]. This limitation of water solubility and w/o-ME size, referred to as the ‘‘natural radius of curvature,’’ also controls the LLE of biomolecules through lowering the capacity for solubilization. Water solubilization is lessened by the presence of short-chain solvent molecules, long-chain cosurfactants, and high aqueous ionic strength, as discussed in more detail elsewhere [125]. The presence of biomolecules in the aqueous phase usually does not affect the water solubilization [126], unless they strongly interact with the interface [22]. The nature of the ions in the aqueous feed solution has a major impact on the success of LLE. High ionic strength reduces the extent of extraction due to Debye screening of the electrical charges on the surfactant headgroups and the surface of biomolecules [4, and references therein], and by reducing the size of w/o-MEs, or equivalently, by increasing the natural radius of curvature (discussed above). In addition, the atomic size of ions strongly affects LLE [73,121,122,127,128]. The structure of the biomolecule also has a signiﬁcant impact on the operation of LLE. For instance, the larger the molecular weight, the greater the electrostatic potential driving force required for LLE [26,60,129]. Moreover, larger proteins require a larger pH– pI difference for solubilization to occur using cationic surfactant systems and a smaller pH–pI difference for anionic surfactant systems). The distribution of charges on the biomolecule’s surface also has a signiﬁcant effect. Wolbert et al. demonstrated that protein extraction is greatest when the protein’s charge distribution was asymmetrical [129]. Along these same lines, selective alteration of the biomolecule’s structure by adding charged groups via recombinant DNA technology led to improved protein extraction [130–132]. In addition, the hydrophobicity of the biomolecule, moreover, hydrophobic interactions between proteins and the w/o-ME interface, can control LLE [126,133–135]. In such cases, biomolecules act as cosurfactants and affect w/o-ME structure and behavior [136,137]. Surfactant and cosurfactant structure play a strong role [13,17,24]. For instance, from screening experiments involving cationic ammonium surfactants, those with three tail groups yielded higher extraction and more rapid phase separations than di- and monoalkyl surfactants, hence inactivation of enzymes was reduced [17]. A careful analysis of the effect of surfactant tail structure on LLE has recently been investigated by Goto et al. [138]. To provide an example of the cosurfactant structural effect, cosurfactants with short-chain lengths yield higher extraction of phenylalanine, whereas long-chain cosurfactants lessen the extent of extraction [139]. The trends are believed to be related to the changes in the interfacial properties promoted by alcohol type [125]. The solvent type can

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affect LLE for interfacially-solubilizing biomolecules by its effect on the natural radius of curvature [136]. B.

Bioafﬁnity-Based LLE

LLE has also been successful using afﬁnity surfactants or cosurfactants, which contain a binding group speciﬁc to a target biomolecule as headgroup (Table 1). Alternatively, afﬁnity extraction of trypsin was achieved using a nonionic surfactant system containing the afﬁnity protein soybean trypsin inhibitor (SBTI) [90,140]. By ﬁrst covalently modifying SBTI with hydrophobic groups, it was effectively immobilized on the w/o-ME phase [90,140]. Similarly, Sun and coworkers have selectively isolated lysozyme by encapsulating the afﬁnity ligand cibacron blue to the interface of lecithin w/o-MEs [23,141]. The afﬁnity system did not extract cytochrome c, a contaminant nonafﬁnity protein, nor BSA, a protein that has afﬁnity for cibacron blue, because of the size limitation of the w/oMEs controlled by the natural radius of curvature [23,141]. Dordick and coworkers isolated peroxidase for soybean by ﬁrst forming a bioafﬁnity complex between peroxidase and the lectin concanavalin A in the aqeous processing broth, followed by a selective LLE step to recover the bioafﬁnity complex [86]. The complex was recovered by employing an elevated temperature (discussed in Section VI), followed by solubilization in mannose to break the bioafﬁnity attractions [86]. C.

Nonionic Surfactant-Based LLE

Nonionic surfactants have received great attention recently, due to their increased biocompatibility and their inability to strongly bind with biomolecules compared to traditional ionic surfactants, which lessens enzyme inactivation and protein unfolding. In addition, microemulsion phase behavior for nonionic surfactants is more sensitive to temperature, meaning that this parameter can be varied to promote recovery of w/oME-encapsulated proteins (Section VI). Recent investigations have indicated that fatty acid–sorbitan ester and ester alkanoate surfactants, the Span and Tween surfactant series, respectively, achieved the highest degree of protein extraction among the nonionic surfactants screened [24,27]. (Likewise, sucrose ester surfactants have also been demonstrated to extract cytochrome c [25].) These surfactants appear to operate based on a weak electrostatic driving force [26]. However, the sorbitan ester systems do not yield the same degree of extraction as ionic surfactants, such as AOT [24,27]. In addition, the degree of protein extraction is very sensitive to ionic strength; and, operation is limited to salt concentrations less than 1 mM [24,27]. Also, the aqueous phase must possess a pH value between 5 and 9 to prevent acid- or base-catalyzed hydrolysis of the surfactant. Furthermore, separation of the bulk aqueous and w/o-ME phases is considered to be too slow for practical application [24,27]. Fatty alcohol- (or alkyl-)ethoxylates, Co Ej , are considered to be better candidates for LLE based on their ability to induce rapid phase separation for Winsor II and III systems. (Winsor III systems consist of ‘‘excess’’ aqueous and organic phases, and a middle phase containing bicontinuous microemulsions.) However, Ci Ej -type surfactants alone cannot extract biomolecules, presumably because they have no net negative charge, in contrast to sorbitan esters [24,26,30,31]. But, when combined with an additional anionic surfactant such as AOT or sodium benzene dodecyl sulfonate (SDBS), or afﬁnity surfactant, extraction readily occurs [30,31]. The second surfactant must be present beyond a minimum threshold value so that its interfacial concentration is sufﬁciently large to be ‘‘seen’’ by

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biomolecules, to overcome the steric hindrance of the palisade layer at the droplet side of the interface [31]. The palisade layer consists of the polar polyethylene glycol (PEG) headgroups, known to have very low binding speciﬁcity for proteins. Likewise, the headgroup size of the second surfactant must be sufﬁciently large and induce a sufﬁciently large protein–surfactant attraction to overcome the repulsion of the PEG groups [31]. The mixed Ci Ej –SBDS surfactant system performed LLE through use of a Winsor III system [31]. D.

Use of Mixed Surfactant Systems for LLE

To reduce the strong interactions occurring between protein and surfactant with AOT systems during LLE, anionic [8,32] and nonionic surfactants [30,33,142] and other interfacial additives [88,124,143] have been included. An improvement on the percent extraction of protein has also been reported for several of these cases [29,32,33,124,142,143].

VI.

RELEASE OF BIOMOLECULES FROM WATER-IN-OIL MICROEMULSIONS

The most common biomolecule releases, or ‘‘back-extraction’’ method, consists of contacting the w/o-ME solution with aqueous stripping solution high in ironic strength and with a pH value that will promote electrostatic repulsion between charged surface groups on the encapsulated biomolecules and the surfactant headgroups. This reduces the driving force for solubilization in w/o-MEs. In addition, ionic strength promotes release to differing degrees for various proteins, suggesting that this method can be used to selectively release a biomolecule from a w/o-ME-encapsulated biomolecule mixture [144]. However, the traditional back-extraction processes are quite slow, requiring hours of processing time, due to the slow mass transfer rates involved [114,115]. Furthermore, some proteins lose activity or form protein–surfactant precipitates at the bulk interface when exposed to high ionic strength [60,126]. Thus, a great need exists to develop new ways to recover biomolecules encapsulated in w/o-MEs. In addition, traditional back-extraction is not successful for recovering biomolecules which strongly interact with the w/o-ME interface such as hydrophobic proteins [34,81,145]. A common approach to improve back-extraction for such cases is to include a polar cosolvent, such as ethanol, isopropanol, butanol, or ethyl acetate, in the aqueous stripping solution [12,29,34,81,145]. It is believed that polar solvents promote release of proteins by increasing interfacial curvature, i.e., decreasing w/o-ME size [29,81]. Great care must be used to prevent the inactivation or unfolding of proteins which often occurs when polar solvents are present in aqueous media (68,145–147]. (It also appears that the addition of alcohols greatly improves the recovery of proteins extracted by surfactant systems based on di-oleyl phosphoric acid, DOLPA [10,32].) Other approaches to improve protein release, such as the use of multivalent ions in the stripping phase [6,77] and extraction by supercritical CO2 [78], are useful only for speciﬁc proteins and surfactant systems. Another approach for recovering interfacially-solubilized protein is the inclusion of saccharides in the dispersed aqueous phase, which perhaps disrupts protein–surfactant interactions [142]. Proteins can also be recovered via liquid chromatography for smallscale applications [148]. A more promising approach to release encapsulated biomolecules is to disrupt or change the phase behavior of the w/o-ME solution. One such method is to employ temperature; however, the change in temperature required to alter the phase behavior changes

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greatly with surfactant system and type and concentration of encapsulated species [86,149]. A second method is to dilute protein-containing w/o-ME solutions so that the surfactant concentration approaches the critical micellar concentration, or CMC, yielding protein as a separable solid phase, without contaminating surfactant [150]. This technique released proteins that interact with the AOT w/o-ME interface (e.g., lysozyme) and that are large in size (e.g., BSA), but not proteins that solubilize in the nanodroplet interior (chymotrypsin). In addition, the technique worked only when the encapsulated protein concentration was very large. Protein recovery via disruption has also been achieved by adsorbing water from the w/o-ME solution, which causes protein to precipitate out of solution. Methods of water removal include adsorption using silica gel [73,151], molecular sieves [152], or salt crystals [58,163], or formation of clanthrate hydrates [154]. In most of the cases reported, the released protein appeared as a solid phase that, importantly, was virtually surfactantfree. In contrast to the dilution technique, it appears that dehydration more successfully released biomolecules that are hydrophilic rather than hydrophobic. Disruption is also induced when certain surface-active species are introduced into the w/o-ME system. Stuckey and coworkers released three different interfacially solubilized proteins quantitatively from an anionic surfactant-based w/o-ME solution by adding a cationic surfactant [155]. A surfactant complex consisting of anionic–cationic pairs formed in the organic phase, resulting in the rapid release of encapsulated water and protein into an aqueous stripping solution (within 3 min). The released proteins retained their catalytic activity. In addition, the surfactant complex was easily isolated by adsorption, leading to the recovery of both surfactants. However, the authors have examined only a narrow set of operating conditions. Similarly, Shiomori and coworkers included a fatty amide in an AOT extractant phase [124]. LLE was operated using an aqueous phase containing a pH above 7 to so that the amine group was not protonated. Otherwise, at lower pH values, the protonated amine surfactant forms a complex with AOT based on ion pairing, leading to ineffective extraction. By the same principle, encapsulated protein was recovered from w/ o-ME based on this surfactant system simply by employing an aqueous phase of moderately low pH to induce AOT–fatty amide complex formation. Likewise, the direct addition of n-alkanols has been demonstratd to release several w/ o-ME-encapsulated biomolecules as solid-phase material, including proteins known to be difﬁcult to recover by traditional back-extraction methods [156]. The surfactant (AOT) remains in the organic (liquid) phase. Mechanistically, the alkanols promote release by changing the thermodynamic phase behavior of the w/o-ME system. The release of proteins increased with the further addition of cosurfactant (ca. 0.01–0.2 mL per mL of w/o-ME solution), reaching approximately 100% protein release for all proteins examined, even when the proteins were present at small concentrations. The optimal alkanol chain length appears to vary with protein type [153,156]. For instance, short-chain alkanols (e.g., 1-butanol) release proteins effectively without release of encapsulated water, while long-chain alkanols (e.g., 1-decanol) release both encapsulated protein and water. Perhaps protein release by long-chain alkanols occurs based on a dehydration mechanism, as discussed above. An alternate approach for biomolecule recover is to employ degradable surfactants [157]. A series of nonionic surfactants has been synthesized that contain the acidic pHdegradable cyclic ketal linkage [153]. These surfactants readily form w/o-MEs when at neutral pH or higher; but, the surfactants readily degrade at moderately low pH (ca. 5), releasing the encapsulated aqueous phase and its constituents. Work is ongoing to develop these surfactants in w/o-ME protein extraction processes [153].

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CONCLUSIONS

Water-in-oil microemulsions have potential utility in biotechnology, particularly for downstream puriﬁcation of biomolecules and for protein refolding. These applications require careful methodology for biomolecule encapsulation and release to permit fast rates without loss of biological activity, and for process scale up. The operating conditions and general mechanisms of these procedures have been shared in this chapter. These procedures require further understanding and optimization for microemulsions to achieve greater acceptance in the ﬁeld of biotechnology.

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Water-in-Oil Microemulsions 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157.

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P. Plucinski and W. Nitsch. Langmuir 10:371 (1994). P. Plucinski and W. Nitsch. Langmuir 1:4691 (1995). S. Ichikawa, M. Imai, and M. Shimizu. Biotechnol. Bioeng. 39:20 (1992). M. Hentsch, P. Menoud, L. Steiner, E. Flaschel, and A. Renken. Biotechnol. Techn. 6:359 (1992). K. Shiomori, N. Ebuchi, Y. Kawano, R. Kuboi, and I. Komasawa. J. Ferment. Bioeng. 86:581 (1998). T. Nishiki, I. Sato, T. Kataoka, and D. Kato. Biotechnol. Bioeng. 42:596 (1993). K. E. Goklen and T. A. Hatton. Biotechnol. Prog. 1:69 (1985). K. Shiomori, Y. Kawano, R. Kuboi, and I. Komasawa. J. Chem. Eng. Jpn. 32:177 (1999). D. G. Hayes and E. Gulari. Langmuir 11:4695 (1995). G. L. Lye, J. A. Asenjo, and D. L. Pyle. Chem. Eng. Sci. 49:3195 (1994). B. A. Andrews, D. L. Pyle, and J. A. Asenjo. Biotechnol. Bioeng 43:1052 (1994). E. B. Leodidis and T. A. Hatton. J. Phys. Chem. 94: 6400 (1990). R. B. G. Wolbert, R. Hilhorst, G. Voskuilen, H. Nachtegaal, M. Dekker, K. van’t Riet, and B. H. Bijsterbosch. Eur. J. Biochem. 184:627 (1989). C. E. Forney and C. E. Glatz. Biotechnol. Prog. 10:499 (1994). C. E. Forney and C. E. Glatz. Biotechnol. Prog. 11:260 (1995). M. J. Pires, P. Martel, A. Baptista, S. B. Petersen, R. C. Willson, and J. M. S. Cabral. Biotechnol. Bioeng. 44:773 (1994). R. Kuboi, D. R. Li, Y. Yamada, and I. Komasawa. Kagaku Kogaku Ronbunshu 18:66 (1992). E. B. Leodidis and T. A. Hatton. J. Phys. Chem. 94:6411 (1990). M. Adachi, M. Harada, A. Shioi, and Y. Sato. J. Phys. Chem. 95:7925 (1991). E. B. Leodidis, A. S. Bommarius, and T. A. Hatton. J. Phys. Chem. 95:5943 (1991). E. B. Leodidis and T. A. Hatton. J. Phys. Chem. 95:5957 (1991). M. Goto, T. Ono, F. Nakashio, and T. A. Hatton. Biotechnol. Bioeng. 54:26 (1997). P. Plucinski and J. Reitmeir. Coll. Surf. A Physicochem. Eng. Aspects 97:157 (1995). M. Adachi, M. Yamazaki, M. Harada, A. Shioi, and S. Katch. Biotechnol. Bioeng. 53:406 (1997). Y. Sun, S. Ichikawa, S. Sugiura, and S. Furusaki. Biotechnol. Bioeng. 58:58 (1998). G. Spirovska and J. B. Chaudhuri. Biotechnol. Bioeng. 58:374 (1998). K. Nagayama, R. Nishimura, T. Doi, and M. Imai. J. Chem. Eng. Jpn. 74:227 (1999). K. Shiomori, Y. Kawano, R. Kuboi, and I. Komasawa. J. Chem. Eng. Jpn. 27:410 (1994). A. Carlson and R. Nagarajan. Biotechnol. Prog. 8:85 (1992). V. V. Mozhaev, Y. L. Khmelnitsky, M. V. Sergeeva, A. B. Belova, N. L. Klyachko, A. V. Levashov, and K. Martinek,. Eur. J. Biochem. 184:597 (1989). G. Toscano, D. Pirozzi, and G. Greco, Jr. Biotechnol. Lett. 12:821 (1990). J. B. Chaudhuri and G. Spirovska. Biotechnol. Tech. 8:909 (1994). M. Dekker, K. van’t Riet, J. J. Van Der Pol, J. W. A. Baltussen, R. Hilhorst, and B. H. Bijsterbosch. Chem. Eng. J. 46: B69 (1991). C. Marchio and D. G. Hayes. Biotechnol. Tech. 10:699 (1996). M. E. Leser, K. Mrkoci, and P.L. Luisi. Biotechnol. Bioeng. 41:489 (1993). R. B. Gupta, C. J. Han, and K. P. Johnston. Biotechnol. Bioeng. 44:830 (1994). D. G. Hayes, unpublished data, 2000. J. B. Philips, H. Nguyen, and V. T. John. Biotechnol. Prog. 7:43 (1991). S. Jarudilokkul, L. H. Poppenborg, and D. C. Stuckey. Biotechnol. Bioeng. 62:593 (1999). D. G. Hayes and C. Marchio. Biotechnol. Bioeng. 59:557 (1998). K. Holmberg. in Novel Surfactants: Surfactant Science Series, vol. 74 (K. Holmberg, ed.), Marcel Dekker, New York, 1998, pp. 333–358.

20 Biomimetic Charge Transfers Through Arti¢cial Membranes SORIN KIHARA, HIROYUKI OHDE, KOHJI MAEDA, and YUMI YOSHIDA Department of Chemistry, Kyoto Institute of Technology, Kyoto, Japan OSAMU SHIRAI Department of Nuclear Energy System, Japan Atomic Energy Research Institute, Ibaraki, Japan

I.

INTRODUCTION

It is well known that the selective transport of ions through a mitochondrial inner membrane is attained when the oxygen supplied by the respiration oxidizes glycolysis products in mitochondria with the aid of such substances as ﬂavin mononucleotide (FMN), nicotinamide adenine dinucleotide (NADH), and quinone (Q) derivatives [1–3]. The energy that enables ion transport has been attributed to that supplied by electron transport through the membrane due to a redox reaction occurring at the aqueous–membrane interface accompanied by respiration [1–5]. A quantitative understanding of the energetics involved in the coupling of ion transport with electron transport is considered to be very important for elucidating physiological reactions in a living system as well as to develop novel biomimetic separation methods of ions. Since real biosystems contain substances such as enzymes and proteins the functions of which have not been fully analyzed, however, the present stage is far from a quantitative understanding. The voltammetry for the charge transfer at the aqueous–organic solutions interface [6–9] is expected to offer much information available to analyze the charge transfer at the aqueous solution–membrane interface [10–12]. Here, organic solutions are often regarded as membranes or even biomembranes [13]. By the voltammetry, not only can transfer energies of charges and amounts of charges transferred at the interface be evaluated precisely, but also kinetics of the charge transfer and the interfacial adsorption can be investigated [14–16]. In this chapter, a novel interpretation of the membrane transport process elucidated based on a voltammetric concept and method is presented, and the important role of charge transfer reactions at aqueous–membrane interfaces in the membrane transport is emphasized [10,17,18]. Then, three respiration mimetic charge (ion or electron) transfer reactions observed by the present authors at the interface between an aqueous solution and an organic solution in the absence of any enzymes or proteins are introduced, and selective ion transfer reactions coupled with the electron transfer reactions are discussed [19–23]. The reaction processes of the charge transfer reactions and the energetic relations 487

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in the coupling of ion transfer with electron transfer are elucidated with the aid of voltammetry, polarography, and controlled potential electrolysis for charge transfer at the aqueous–organic solutions interface.

II.

VOLTAMMETRIC ELUCIDATION OF THE CHARGE TRANSPORT PROCESS THROUGH A LIQUID MEMBRANE OR A BILAYER LIPID MEMBRANE IN THE PRESENCE OF SUFFICIENT ELECTROLYTES [10,17,18]

The membrane potential which determines the membrane transport of a charge (ion or electron) from one aqueous solution, W1, to another, W2, through a membrane, M, is composed of potentials due to transfers of the charge at the W1/M and M/W2 interfaces and those due to mass transfers within W1, M and W2 phases. Here, the membrane potential is deﬁned as the potential difference between W1 and W2. It has been widely supposed that the potential for the mass transfer in M contributes signiﬁcantly to the membrane potential, since most investigations on the membrane transport so far carried out employed membranes of high electrical resistances containing negligible concentrations of electrolytes. However, the membrane transport in the presence of rather concentrated electrolytes in the membrane is also important, especially in connection with the charge transfer at biomembranes or bilayer lipid membranes (BLMs). These membranes concentrate hydrophobic ions spontaneously into their lipid phases [24–26] and even hydrophilic ions when the membranes contain hydrophobic complexing agents [25,26]. In this case, the share of the potential for the interfacial charge transfer in the membrane potential is considered to be more signiﬁcant than that for the mass transfer in the membrane. In this section, the charge transport process through a liquid membrane (LM) in the presence of sufﬁcient electrolytes is elucidated by comparing the voltammogram for charge transfer through a membrane (VCTTM) with voltammograms for charge transfers at the W1/LM and LM/W2 interfaces, and, on the basis of the results, various membrane phenomena are interpreted. The relation between the charge transport process through an LM and that through a BLM is also discussed. In connection with the content of this section, dynamic features of ion transports through polyvinyl chloride membranes [27,28], ion-exchange resin membranes [29,30], or BLMs [31–36] have been discussed in the light of VCTTMs. For wide and pertinent applications of the VCTTM, however, further investigations have been required on the experimental and theoretical methods to analyze VCTTM quantitatively.

A.

Voltammograms for Ion Transfers Through a Liquid Membrane and at Aqueous–Membrane Interfaces

An example of the electrolytic cell with an LM used for the voltammetric investigation is

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ð1Þ

In the cell, W1 and W2 (5 mL each) containing MgSO4 as the supporting electrolyte, SE, were separated by a nitrobenzene solution, NB, containing crystalviolet tetraphenylborate, CVþ TPhB , as SE. The NB worked as the LM of thickness of 1 cm. Dibenzo-18-crown-6 was added into the LM to facilitate the transfer of Kþ from W1 or W2 to LM. The concentrations of MgSO4 in W1 and W2 were made to be 1 M and 2 M (M = mol dm3 ), respectively, in order to stabilize the LM between W1 and W2 by means of the difference in speciﬁc gravities [16]. The VCTTM was recorded by scanning the potential difference between W1 and W2, EW1W2 , and measuring the current between W1 and W2, IW1W2 . Here, EW1W2 was applied by using two silver– silver chloride reference electrodes, SSE, in W1 and W2, RE1 and RE2, as the potential of RE1 vs. RE2, and IW1W2 were measured by two platinum wire counter electrodes, CE1 and CE2. During the recording of the VCTTM, variations of potential differences at the W1/LM and LM/W2 interfaces, EW1=LM and ELM=W2 , were monitored as a function of IW1W2 , and voltammograms for the ion transfer at the W1/LM and LM/W2 interfaces were obtained. Here, EW1=LM and ELM=W2 were measured as the potential difference of RE1 vs. RE3 and that of RE4 vs. RE2, respectively, where RE3 and RE4 were TPhB ion-selective electrodes, TPhBE [9], placed in LM near to the interfaces. The VCTTM recorded with the LM cell of Eq. (1) and voltammograms at the W1/ LM and LM/W2 interfaces are realized as curves 1, 2, and 3, respectively, in Fig. 1. A positive peak and a negative peak exist in voltammograms 1 and 2. The positive peak, the ﬁnal rise, and the ﬁnal descent in curve 2 are attributable to the transfer of Kþ from W1 to LM facilitated by dibenzo-18-crown-6, TPhB from LM to W1, and CVþ from LM to W1, respectively. The negative peak is due to the transfer of Kþ that has moved into LM during the positive scan from LM to W1. The ﬁnal rise and the ﬁnal descent in curve 3 correspond to the transfer of CVþ from LM to W2 and that of TPhB from LM to W2, respectively. Comparing curve 1 (VCTTM) with curves 2 and 3 (voltammograms at the W1/LM and LM/W2 interfaces), it is obvious that (1) the potential window in curve 1 is about twice that in curve 2 or 3, (2) the potential regions where the positive and the negative peaks appear in curve 1 are different from those in curve 2, and (3) the slopes of the positive peak, negative peak, ﬁnal rise, and ﬁnal descent in curve 1 are much smaller than those in curves 2 and 3. In order to elucidate the reactions involved in curve 1, the relation lying among EW1W2 in curve 1, EW1=LM in curve 2, and ELM=W2 in curve 3 was investigated at a deﬁnite membrane current, IW1W2 0 , taking into account that currents ﬂowing across both the W1/LM and LM/W2 interfaces must be the same and equal to IW1W2 0 . The relation as Eq. (2) was found to hold at any IW1W2 0 .

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FIG. 1 Voltammograms for the ion transfer from one aqueous solution (W1) to the other (W2) through a liquid membrane (LM) (curves 1 and 10 ), at the W1/LM interface (curves 2 and 20 ) and at the LM/W2 interface (curves 3 and 30 ). Compositions of W1, LM, and W2 for curves 1, 2, and 3; 2:5 104 M K2 SO4 + 1 M MgSO4 in W1, 0.02 M dibenzo-18-crown-6 + 0.1 M CVþ TPhB in LM, 2 M MgSO4 in W2: for curves 10 , 20 , and 30 , the same as those for curves 1, 2, and 3, but in the presence of 0.01 M MgBr2 in W2. Scan rate of EW1W2 : 0.01 V s1 .

EW1W2 ¼ EW1=LM þ ELM=W2 þ IW1W2 0 R

ð2Þ

where R is the resistance between RE1 and RE2. When W1, W2, and LM contain sufﬁcient concentrations of electrolytes, the contribution of IWIW2 0 R to EW1W2 is not signiﬁcant, and Eq. (2) can be approximated by Eq. (3). EW1W2 ¼ EW1=LM þ ELM=W2

ð3Þ

As for the LM system of Eq. (1), resistances of W1 and W2 containing MgSO4 were negligibly small and that of nitrobenzene solution containing 0.1 M CVþ TPhB was 1.05 k cm1 which induces 13.4 mV of IW1W2 0 R when IW1W2 0 is 10 A. Equation (3) suggests that the membrane potential in the presence of sufﬁcient electrolytes in W1, W2, and LM is primarily determined by the potential differences at two interfaces which depend on charge transfer reactions at the interfaces, though the potential differences at interfaces are not apparently taken into account in theoretical equations such as Nernst–Planck, Henderson, and Goldman–Hodgkin–Katz equations which have often been adopted in the discussion of the membrane potential.

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The characteristics of VCTTM in Fig. 1 can easily be understood taking into account the relation of Eq. (3) as follows: since the membrane potential where the positive wave appears ðEW1W2 indicated by A in curve 1) is the sum of EW1=LM indicated by B in curve 2 and ELM=W2 indicated by C in curve 3, the positive wave in curve 1 is considered to be caused by the composite reactions of both the transfer of Kþ from W1 to LM facilitated by dibenzo-18-crown-6 (the positive wave in curve 2) and that of CVþ from LM to W2 (the ﬁnal rise in curve 3). Hence, the potential region for the positive wave in curve 1 differs from that in curve 2. On the basis of similar analysis, the negative wave in curve 1 is considered to be consisted of the transfer of Kþ from LM to W1 (the negative wave in curve 2) and that of TPhB from LM to W2 (the ﬁnal descent in curve 3). The ﬁnal rise in curve 1 involves the transfer of TPhB from LM to W1 (the ﬁnal rise in curve 2) and that of CVþ from LM to W2 (the ﬁnal rise in curve 3), and the ﬁnal descent in curve 1 involves the transfer of CVþ from LM to W1 (the ﬁnal descent in curve 2) and that of TPhB from LM to W2 (the ﬁnal descent in curve 3). These coupled reactions are responsible for the wide potential window. One of the reasons for the small slope of positive wave in curve 1 is the membrane resistance [R in Eq. (2)]. However, the slope is still smaller than the slope of the positive wave in curve 2 even after it has been corrected for the membrane resistance employing R ¼ 1:05 k cm1 . The small slope after the correction can be explained by considering that the slope of the positive wave in curve 1 is composed of the slope of the positive wave in curve 2 and that of the ﬁnal rise in curve 3. The small slopes of the ﬁnal rise and the ﬁnal descent in curve 1 are also attributable to the membrane resistance and the composite reactions at two W/LM interfaces. B.

Inﬂuence of Ion Transfer Reaction at One Aqueous–Membrane Interface on That at Another Aqueous–Membrane Interface Under an Applied Membrane Potential

Voltammograms shown as curves 10 , 20 , and 30 in Fig. 1 were recorded under the same conditions as those for cuves 1, 2, and 3 in Fig. 1, respectively, but adding 0.01 M MgBr2 into W2. The positive wave in curve 1 (VCTTM) appears at a potential about 0.19 V less positive than that in the absence of MgBr2 (curve 1). The effect of MgBr2 on the positive wave in the VCTTM can be understood by considering ion transfer reactions at the W1/ LM and LM/W2 interfaces. Though the voltammogram at the W1/LM interface is indifferent to the presence of MgBr2 in W2 (cf. curves 2 and 20 ), the ﬁnal rise in the voltammogram at the LM/W2 interface in the presence of MgBr2 in W2, which is attributable to the transfer of Br from W2 to LM, lies at a potential about 0.19 V less positive than that in the absence of MgBr2 , which is attributable to the transfer of CVþ from LM to W2 (cf. curves 3 and 3 0 ), indicating that the Gibbs energy of transfer of Br is 18.3 kJ mol1 less than that of CVþ at the LM/W2 interface. Consequently, the positive wave in the VCTTM (curve 10 ) composed of the transfer of Kþ from W1 to LM and that of Br from W2 to LM appears at a membrane potential about 0.19 V less positive than that (curve 1) composed of the transfer of Kþ from W1 to LM and that of CVþ from LM to W2. The voltammetric information given here suggests that the transfer of an objective cation from W1 to LM can be achieved under a smaller membrane potential when an anion for which the Gibbs transfer energy at the LM/W2 interface is smaller is added into W2. In the case of the above-mentioned membrane system, the transfer of Kþ from W1 to LM in the presence of 0.01 M MgBr2 in W2 is expected to be attained even at the membrane potential 0.19 V (which corresponds to the Gibbs energy of transfer of 18.3

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kJ mol1 ) less positive than that required for the transfer in the absence of MgBr2 . Actually, when the electrolysis was carried out for 60 h, applying a membrane potential of +0.20 V to the cell of Eq. (1), 72% of Kþ was transferred from W1 to LM or W2 in the presence of 0.01 M MgBr2 in W2, though practically no transfer of Kþ was observed in the absence of MgBr2 . The results given here suggest that, though Eq. (3) is simple, the relation involved in the equation might be very important to elucidate the membrane transport phenomena under a membrane potential applied not only by an external electric source but also by chemicals such as redox agents.

C.

Voltammograms for Ion Transfer Through a Liquid Membrane in the Presence of the Objective Ion in W1, LM, and/or W2

Voltammogram 1 realized in Fig. 2(a) or (b) is a VCTTM recorded while adding Kþ into W1 and W2 or LM of the cell containing the same concentrations of supporting electrolyte and dibenzo-18-crown-6 as those in the cell of Eq. (1). Two positive and two negative waves were observed in the VCTTM as shown as curve 1 in Fig. 2(a), when 5 104 M Kþ was added in both W1 and W2. A positive and a negative wave symmetrical about the origin (the point of 0 V and 0 A) to each other were observed in the VCTTM [curve 1 in Fig. 2(b)], when 0.1 M Kþ was added in both W1 and W2 and 103 M Kþ in LM. Though the assignment of the above-mentioned waves in VCTTMs seems to be complicated, it is easily attained if we take the relation of Eq. (3) into account and consult with the voltammograms at the W1/LM and LM/W2 interfaces which are realized as curves 2 and 3, respectively, in Figs. 2(a) and (b). For example, the positive wave in curve 1 in Fig. 2(b) is composed of the ﬁnal rise in curve 2 due to the transfer of Kþ from W1 to LM and the positive wave in curve 3 due to the transfer of Kþ from LM to W2, and the negative wave in curve 1 is composed of the ﬁnal descent in curve 3 due to the transfer of Kþ from W2 to LM and the negative wave in curve 2 due to the transfer of Kþ from LM to W1. Since both the positive and the negative waves in curve 1 in Fig. 2(b) involve the same ion transfer reactions as mentioned above, i.e., the transfer of Kþ from an aqueous (W1 or W2) to LM and that from LM to an aqueous (W1 or W2), these waves appear symmetrically to each other about the origin.

D.

Voltammograms for Ion Transfer Through a Bilayer Lipid Membrane

The curves in Fig. 3 are voltammograms recorded with the BLM system, as in Eq. (4), scanning EW1W2 in the potential region between 0:1 and þ0:1 V with the aid of two SSEs (RE1 and RE2) and two platinum wire electrodes (CE1 and CE2):

ð4Þ

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FIG. 2 (a)Voltammograms for the ion transfer from W1 to W2 through an LM (curve 1), at the W1/LM interface (curve 2) and at the LM/W2 interface (curve 3). Compositions of W1, LM, and W2; 2:5 104 M K2 SO4 + 1 M MgSO4 in W1, 0.02 M dibenzo-18-crown-6 + 0.1 M CVþ TPhB in LM, 2:5 104 M K2 SO4 + 2 M MgSO4 in W2. Scan rate of EW1W2 : 0.01 V s1 . (b) Voltammograms the same as those in (a), but in the presence of 0.1 M Kþ in W1 and W2 and 103 M Kþ in LM. Compositions of W1, LM, and W2; 0.1 M KCl + 1 M MgSO4 in W1, 103 M Kþ TPhB + 0.02 M dibenzo-18-crown-6 + 0.1 M CVþ TPhB in LM, 0.1 M KCl + 2 M MgSO4 in W2.

Here, the BLM was obtained as a black lipid membrane by brushing an n-decane solution of a 1:1 mixture of phosphatidylcholine and cholesterol on an aperture of 1 mm in diameter in a tetraﬂuoroethylene resin sheet of 0.2 mm thick [37–39]. The BLM was not sufﬁciently stable when EW1W2 out of the region was applied. There was no peak in curve 1 recorded with W1 and W2 containing only 0.1 M KCl. When 106 M Kþ TPhB was added into W1 and/or W2, however, a positive peak and a negative peak symmetrical to each other about the origin were clearly observed as shown by curve 2 in Fig. 3. Here, it should be stressed that the peak currents are considerably larger than the background current (cf. curve 1) in spite of the fact that the concentration of Kþ TPhB added into aqueous phases is as small as 106 M. In this regard, the ordinary

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FIG. 3 Voltammograms for the ion transfer through a BLM. Curve 1; 0.1 M KCl in both W1 and W2 and none in BLM. Curve 2; as curve 1, but in the presence of 106 M Kþ TPhB in W1 and W2. Scan rate of EW1W2 ; 0.1 V s1 .

diffusion-controlled current for the ion transfer from W to O can hardly be observed because of the interference of the background current when the concentration of the objective ion is less than 105 M. The peak currents in curve 2 were nearly proportional to the concentration of TPhB in the range between 5 107 and 2 105 M, but less proportional when TPhB was more than 2 105 M. When the electrolyte in aqueous phases was 0.1 M NaCl or 0.05 M MgCl2 instead of 0.1 M KCl, the peak currents (200 30 or 135 10 nA cm2 , respectively) were smaller than that with 0.1 M KCl (235 30 nA cm2 ). The peak currents were almost proportional to the square root of the scan rate of EW1W2 in the range between 0.01 and 0.1 V s1 . In order to explain the well-established peak currents at the BLM, the spontaneous concentration of Kþ TPhB (up to 103 M) into BLM during or after the preparation of the BLM was assumed, and the VCTTM measured with the BLM system containing 0.1 M KCl + 106 M Kþ TPhB in W1 and W2 (curve 2 in Fig. 3) was compared with the VCTTM measured with the LM system containing 0.1 M KCl in W1 and W2 and 103 M Kþ TPhB in LM [curve 1 in Fig. 2(b)]. The shape of curve 2 in Fig. 3 resembles well that of curve 1 in Fig. 2(b) in the potential range between þ0:1 and 0:1 V, which supports the assumption of the spontaneous concentration of Kþ TPhB into BLM. Consequently, by reference to the ion transfer reactions involved in the VCTTM with the LM [curve 1 in Fig. 2(b)], it may be reasonable to conclude that the positive peak observed with the BLM system is composed of the transfer of Kþ from W1 to BLM and that of Kþ (which has been concentrated in BLM) from BLM to W2, and the negative peak is composed of the transfer of Kþ from W2 to BLM and that of Kþ (which has been concentrated in BLM) from BLM to W1. Adopting this explanation, the characteristics of the VCTTM with the BLM (curve 2, Fig. 3) can be understood as follows: (1) since the positive and the negative peaks in the VCTTM involve the same ion transfer reactions, these peaks appear symmetrically to each other about the origin. (2) Since the peak heights are determined by the concentration of Kþ TPhB in the BLM which depends on the distribution ratios of Kþ and TPhB between W and BLM, the peak heights are proportional to the concentration of TPhB in W. (3) Since Naþ and Mg2þ are more hydrophilic and hence distribute to BLM less easily than Kþ , the peak height is small when Naþ or Mg2þ is added into W instead of Kþ . The results given here suggest that even the ion transfer through a BLM is controlled mainly by the ion transfer reactions at two aqueous–membrane interfaces in analogy with

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that through a thick membrane such as LM, as far as the BLM contains sufﬁcient electrolytes.

III.

SELECTIVE ION TRANSFER AT THE W/O INTERFACE COUPLED WITH REDOX REACTIONS BETWEEN FLAVIN MONONUCLEOTIDE IN W AND A FERROCENE DERIVATIVE IN O AND CO2 EVOLUTION [19,21]

When W containing ﬂavin mononucleotide (FMN), pyruvic acid, and O2 was put into contact with a nitrobenzene solution (NB), containing Naþ , Kþ , valinomycin (Val) and bis(1,2,3,4,5-pentamethylcyclopentadienyl) iron (DMFC), Naþ was transferred from NB to W, though Kþ remained in NB. The evolution of CO2 was also observed in W. This respiration mimetic interfacial phenomenon accompanied by the selective ion transfer was elucidated by referring to the ion and electron transfer voltammograms at the W/NB interface and by taking into account the energetics of the coupling between the ion and electron transfers. A.

Spontaneous Ion Transfer and Evolution of CO2 Observed with the W/NB System

As an example, the spontaneous transfer of 1:92 105 moles of Naþ from NB to W, the evolution of 9:8 106 moles of CO2 in W and the decrease of pyruvic acid in W to be 5:3 104 M were found, when the W/NB system as Eq. (5) had been stood for 5 h with bubbling O2 into W. The transfer of Kþ was negligible as less than 107 moles.

ð5Þ

where TFPB denotes tetrakis[3,5-bis(triﬂuoromethyl)phenyl]borate. Though 1:84 105 moles of Naþ was transferred from NB to W, even in the absence of pyruvic acid, the transfer was not found in the absence of FMN or DMFC. In the absence of one of reagents among Naþ TFPB , DMFC, FMN, and pyruvic acid, CO2 was scarcely generated (less than 5 107 moles). When N2 was bubbled into W instead of O2 , Naþ transferred and CO2 formed were much less than those observed with O2 bubbling. These results indicate that (1) the selective transfer of Naþ from NB to W occurs even when W contains only FMN (in the absence of O2 and pyruvic acid), (2) the existence of FMN, O2 , and pyruvic acid and in W and DMFC and Naþ in NB is necessary for the spontaneous evolution of CO2 , and (3) although the coexistence of O2 enhances the transfer of Naþ , the transfer is independent of pyruvic acid. B.

Evolution of CO2 by Controlled Potential Electrolysis at the W/NB Interface

The evolution of CO2 was also observed when controlled potential electrolysis was carried out by applying a deﬁnite potential difference at the W/NB interface in the cell of Eq. (6)

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in which W contained FMN, pyruvic acid, phosphate buffer, and an SE, and NB contained DMFC and an SE, but in the absence of Naþ and Kþ :

ð6Þ

where TPenAþ denotes tetrapentylammonium ion. The electrolysis was attained by applying the potential difference as the potential of SSE in W vs. TPhBE in NB. After the electrolysis for 5 h at 0:15 V with the bubbling of O2 into W, the amount of CO2 produced was found to be 1:6 105 moles. A photoabsorption spectrum of the NB after electrolysis gave a peak at 780 nm. The peak was identical with that of the one electron oxidation product of DMFC, DMFCþ , which had been prepared coulometrically by using a column electrode with glassy carbon ﬁber working electrode [40]. This fact indicates that the electrolysis product was DMFCþ . The DMFCþ produced by the electrolysis was estimated to be 3:08 105 moles. When the applied potential difference was 0:55 or 0:35 V instead of 0:15 V, or when one of reagents among FMN, O2 , pyruvic acid, and DMFC was not added, the evolution of CO2 was negligible. However, 2:89 105 moles of DMFCþ was found in NB after the electrolysis at 0:15 V for 5 h in the absence of pyruvic acid, and 9:20 106 moles of DMFCþ was found in NB after the electrolysis in the absence of both O2 and pyruvic acid. C.

Estimation of Reaction Processes Involved in Electrolytic CO2 Evolution

Curve 1 in Fig. 4 realizes the current-scan polarogram at the interface between W containing 2:5 104 M FMN, 0.02 M phosphate buffer (pH = 7.0) and 0.1 M Li2 SO4 (SE) and NB containing 0.01 M DMFC and 0.05 M TPenAþ TFPB (SE). The polarogram was recorded by scanning the current applied at the W/NB interface and measuring the variation of potential difference at the interface [9]. Prior to polarographic measurement, both W and NB were carefully deaerated by bubbling high-purity N2 gas. Consulting the polarogram [19] measured under the same conditions as those presented in this section, and taking into account that the product in NB of the controlled potential electrolysis was DMFCþ , it may be reasonable to conclude that the polarographic current was caused by one electron transfer due to the interfacial redox reaction between FMN in W and DMFC in NB as Eq. (7). FMNðWÞ þ DMFCðNBÞ þ Hþ ðWÞ>FMNH: ðWÞ þ DMFCþ ðNBÞ

ð7Þ

where ( ) denotes the phase where the species exists. The limiting current of the polarogram was proportional to the square root of the height of aqueous-solution reservoir and to the concentration of FMN in the range

Biomimetic Charge Transfers

497

FIG. 4 Polarograms for electron and ion transfers at the aqueous (W)–nitrobenzene (NB) solution interface. 1, electron transfer observed with deaerated W containing 2:5 104 M FMN and 0.02 M phosphate buffer, and deaerated NB containing 0.01 M DMFC; 2, the same as curve 1, but O2 was bubbled into W; 3, ion transfer observed with W containing 5:0 104 M Naþ TFPB and NB containing 4:0 103 M valinomycin; 4, the same as curve 3, but Kþ was employed instead of Naþ ; 5, supporting electrolytes only; Supporting electrolytes, 0.1 M Li2 SO4 in W and 0.05 M TPenAþ TFPB in NB.

between 5 105 to 103 M, which suggests that the electron transfer reaction for the wave is reversible [41,42], i.e., controlled by the diffusion of FMN in W. A logarithmic analysis based on the theoretical equation for a reversible electron transfer at the aqueous– organic interface [41,42] supported that the current was caused by one electron transfer at the W/NB interface. Polarogram 2 in Fig. 4 was recorded at the same interface as curve 1, but bubbling O2 into W instead of N2 . Although a positive current wave appeared in the potential range identical with that in curve 1, the limiting current was about six times larger than that in curve 1 with the daerated solution. The large current can be explained by considering the reduction of O2 catalyzed by a FMN/FMNH: couple, as in Eq. (8) [19], i.e., the reduction product, FMNH: , at the interface was oxidized by O2 in the vicinity of the interface regenerating FMN that can be reduced again through the reaction of Eq. (7): 2FMNH: ðWÞ þ O2 ðWÞ>2FMNðWÞ þ H2 O2 ðWÞ

ð8Þ

Summarizing the results obtained by controlled potential electrolysis and polarography, the reaction process for the electrolytic evolution of CO2 was estimated to be as follows: the ﬁrst step was one electron transfer from DMFC in NB to FMN in W as in Eq. (7). The second step was the catalytic reduction of O2 by FMNH: as in Eq. (8). The ﬁnal step was the oxidation of pyruvic acid by the reduction product of O2 , H2 O2 , in W as in Eq. (9), well-known as an oxidative decarboxylation of -keto acids [43]: CH3 ðCOÞCOOHðWÞ þ H2 O2 ðWÞ>CH3 COOHðWÞ þ CO2 þ H2 O

ð9Þ

498

D.

Kihara et al.

Polarogram for Transfer of Na+ or K+ from NB to W

Curves 3 and 4 in Fig. 4 are polarograms for transfers of Naþ and Kþ from NB containing 5:0 104 M Naþ TFPB and Kþ TFPB , respectively, in addition to 4:0 103 M valinomycin to W. The SEs in W and NB were 0.1 M Li2 SO4 and 0.05 M TPenAþ TFPB . Valinomycin was added to facilitate the ion transfers. The characteristics of the negative current waves suggested that the transfer processes were controlled by the diffusion of Naþ or Kþ in NB. E.

Voltammetric Evaluation of Coupling of Ion Transfer with Electron Transfer at the W/NB Interface

The selective transfer of Naþ from NB to W in the cell of Eq. (5) can be understood by referring to the ion transfer and electron transfer polarograms shown in Fig. 4. When simultaneous transfers of ions and electrons occur spontaneously at one W/ NB interface, the rate of the transfer of electrons (which carry minus charges) from NB to W should be equal to that of the transfer of cations (which carry plus charges) from NB to W in order to maintain the electroneutrality in both phases [44]. In other words, the positive current due to the electron transfer should be equal to the negative current due to the cation transfer in their absolute values, since the currents correspond to the rates of electron and ion transfers. Applying this condition to the present case, the potential difference established by the coupling of transfers of Naþ and electron at the W/NB interface is expected to be A in Fig. 4, where the magnitude of the current (indicated as A) in polarogram 2 for the electron transfer is equivalent to that in polarogram 3 for the transfer of Naþ . When Kþ is added to NB instead of Naþ , the potential difference established by the coupling of transfers of electron and Kþ was expected to be B in Fig. 4. The potential b is more negative than A, and the magnitude of the current at this potential is much smaller than A, since the polarogram for the transfer of Kþ lies at much more negative potentials than that for the transfer of Naþ . Here, the hydrophobicity of the ion and the stability constant of the ion with a ligand in NB essentially determine the potential region where the polarogram for the ion transfer appears [45–47]. The difference in magnitudes of the currents for ion transfers coupled with the electron transfer from DMFC in NB to FMN in W is responsible for that Naþ transfers from NB to W spontaneously in the system of Eq. (5), though Kþ does not.

IV.

REDOX REACTIONS BETWEEN NADH IN W AND QUINONE DERIVATIVES IN O AT THE W/O INTERFACE [22]

The oxidation of reduced -nicotinamide adenine dinucleotide (NADH) by quinone derivatives (Q) by has been investigated extensively, since the reaction was considered to be essential in the proton transport and the energy accumulation occurring at the mitochondrial inner membrane [2]. However, most of fundamental work in this ﬁeld has been done in homogeneous solutions [48–52] though the reaction in living bodies has been believed to proceed at the solution–membrane interface. The famous model for the oxidation of NADH coupled with the proton transport in a mitochondria is the ‘‘Q cycle’’ [53], as follows: NADH in the aqueous solution (matrix) is oxidized to NADþ by Q in the membrane producing hydroquinone (QH2 ).

Biomimetic Charge Transfers

499

With the aid of dehydrogenase complex which contains FMN and iron-sulfur center, and the QH2 diffused to cytochrome bc1 complex is oxidized to Q via the semiquinone radical (Q ) which complexes with a proton. During these processes, a proton is transported from the matrix to the intermembrane space. Though the ‘‘Q cycle’’ is widely accepted, the quantitative energetic explanation has not been given so far for the relation among redox reactions of NADH/Q and QH2 /Q: and the proton transport. In this regard, oxidation processes of NADH by Q in aqueous [48–50] or nonaqueous solutions such as acetonitrile [51,52] were proposed based on static and kinetic studies to be the simultaneous transfers of two electrons and one proton [48–50] or the successive transfers of one electron – one proton – one electron [51,52]. However, it is difﬁcult to connect these processes in homogeneous solutions to the heterogeneous reaction occurring at the aqueous–membrane interface. In this section, redox reactions between NADH in an aqueous solution (W) and Q in an organic solution (O) at the W/O interface are investigated as a function of potential differences between W and O, EW=O . The ion transfer at the W/O interface coupled with the redox reaction is also discussed.

A.

Polarograms for the Reduction of Quinones to Quinone Anion Radicals by NADH at the W/DCE Interface

In order to investigate the redox reaction between NADH in W and Q in 1,2-dichloroethane (DCE), a current-scan polarogram was recorded at the interface of W and DCE, for which the compositions were as in Eq. (10), by scanning the current applied between W and O and measuring EW=O . The Q employed in this study was chloranil (CQ):

ð10Þ

where TDAþ denotes tetradecylammonium ion. A negative current wave appeared in the polarogram as shown in curve 1 of Fig. 5, though the wave was not observed in the absence of NADH in W or CQ in DCE. The logarithmic analysis of the current wave based on the theoretical equation for the electron transfer [42,54,55] indicated that the wave was caused by two-electron transfer at the interface and controlled by the diffusion of NADH in W. When toluquinone (TQ) was employed instead of CQ, any special currents other than the residual current were not observed as shown by curve 2 in Fig. 5. The difference in polarographic behaviors between TQ and CQ is attributable to the difference between 0 : , and that of the CQ/CQ the standard redox potential of the TQ/TQ: couple, ETQ=TQ 0 couple, ECQ=CQ: , in DCE since the potential range available for the appearance of polarographic wave due to the redox reaction at the W/O interface as in Eq. (11) depends strongly on the difference between the standard redox potential of the O1(W)/R1(W)

500

Kihara et al.

FIG. 5 Polarograms for oxidation of NADH in aqueous, W, by quinone derivatives in 1,2-dichloroethane, DCE (curves 1 and 2), and for transfers of R4 Nþ from W to DCE (curves 3 to 5) at the W/ DCE interface. Curve 1:5 103 M NADH in W and 102 M chloranil, CQ, in DCE. Curve 2: 5 103 M NADH in W and 102 M toluquinone, TQ, in DCE. Curves 3 to 5: 104 M (TPenAþ )2 SO4 (curve 3), (TBAþ )2 SO4 (curve 4), or (TEAþ )2 SO4 (curve 5) in W and supporting electrolyte only in DCE. Curve 6: background current in the absence of NADH, CQ, and R4 Nþ . As supporting electrolytes, 0.5 M Li2 SO4 and 0.05 M TDAþ TPhB were added in W and DCE, respectively.

0 0 couple in W, EO1ðWÞ=R1ðWÞ , and that of the O2(O)/R2(O) couple in O, EO2ðOÞ=R2ðOÞ [42,54,55]:

O1ðWÞ þ R2ðOÞ>R1ðWÞ þ O2ðOÞ

ð11Þ

where O1(W) and R1(W) denote the oxidized species and its reduced form in W, and 0 : R2(O) and O2(O) the reduced species and its oxidized form in O. In this regard, ETQ=TQ 0 : and ECQ=CQ in DCE were estimated to be 0:78 and 0:13 V vs. SSE, respectively, by voltammetry at a platinum disk electrode. B.

Reduction of Quinones by NADH at the W/DCE Interface Observed by Controlled Potential Electrolysis

Controlled potential electrolysis was carried out for 4 h by applying a deﬁnite potential difference, Eappl , at the stationary interface between W containing 103 M NADH and 0.01 M borate buffer and DCE containing 103 M CQ, and the concentration of NADH in W after the electrolysis was determined spectrophotometrically. Ratios of concentrations of NADH reacted (and hence decreased) by the electrolysis are plotted as curve 1 in Fig. 6 as the function of Eappl . The Eappl available for the reaction of NADH were not only those in the range (Range A) where the negative current wave had been observed in the polarogram in Fig. 5, but also in the range (Range B) where the wave had not been observed. The products in W after the electrolysis at Eappl in Ranges A and B were conﬁrmed to be NADþ based on the reduction currents observed by ﬂow coulometry at the column electrode [40]. The products in DCE obtained at Eappl in Ranges A and B were conﬁrmed to be CQ and CQH2 , respectively, based on the absorption spectra. Ratios of CQ produced and plotted as curve 2 in Fig. 6. Though polarographic current was not observed at the interface between W containing NADH and DCE containing TQ, the decrease of NADH in W was observed after the

Biomimetic Charge Transfers

501

FIG. 6 Ratios of NADH reacted (curve 1) and CQ produced (curve 2) after the electrolysis for 4 h by applying a constant potential difference, Eappl at the interface between W containing 103 M NADH and DCE containing 103 M chloranil, CQ. As supporting electrolytes, 0.5 M Li2 SO4 and 0.05 M TPenAþ TFPB were added in W and DCE, respectively. The buffer solution used was the same as that in Fig. 5.

electrolysis at Eappl in a deﬁnite range (Range C) as shown in Fig. 7. The products in W and DCE were conﬁrmed to be NADþ and TQH2 by ﬂow coulometry and spectrophotometry, respectively. The negative limit of Range C depended strongly on pH in W, but the positive limit was practically independent of pH as seen in Fig. 7. In this connection, it was difﬁcult to observe the pH dependence in the case of CQ instead of TQ since CQ was decomposed through the hydrolysis at the W/DCE interface when pH of W was higher than 8.

FIG. 7 Ratios of NADH reacted (curves 1, 2, and 3) after the electrolysis for 4 h by applying a constant potential difference at the interface between W containing 103 M NADH and DCE containing 103 M toluquinone, TQ. Supporting electrolytes used were the same as those in Fig. 6. pH in W were adjusted by 0.01 M borate buffer to be 7.0 (curve 1), 8.0 (curve 2), and 9.0 (curve 3).

502

C.

Kihara et al.

Reactions Between NADH in W and CQ or TQ in DCE at the W/DCE Interface

Taking into account the results obtained by polarography as well as controlled potential electrolysis, the reaction which proceeded in Range A and gave the polarographic wave was estimated to be composed of two-electron oxidation of NADH and one-electron reduction of CQ at the W/DCE interface. The oxidation of NADH is accompanied by the dissociation of one Hþ in W. NADHðWÞ þ 2CQðDCEÞ>NADþ ðWÞ þ Hþ ðWÞ þ 2CQ ðDCEÞ

ð12Þ

The reaction in Range B did not give any polarographic currents but produced NADþ and CQH2 . Hence, the reaction was estimated to be two-electron oxidation of NADH by CQ accompanied by two-Hþ transfer at the W/DCE interface, NADHðWÞ þ CQðDCEÞ þ Hþ ðWÞ>NADþ ðWÞ þ CQH2 ðDCEÞ

ð13Þ

In this reaction, currents are canceled out due to the simultaneous transfers of two positive (Hþ ) and two negative (e ) charges at the W/DCE interface. The reaction of NADH with TQ in Range C was considered to be similar to that with CQ in Range B: NADHðWÞ þ TQðDCEÞ þ Hþ ðWÞ>NADþ ðWÞ þ TQH2 ðDCEÞ

ð14Þ

Since the negative limit of Range C depended on pH in W, but the positive limit did not, it may be reasonable to consider that potentials more positive than the negative limit and those more negative than the positive limit are effective for the participation of Hþ and electrons, respectively, in the reaction of Eq. (14). Here, if the electron participates in the reaction as the electron transfer subsequent to the one-electron transfer to TQ (which may proceed at potentials more negative than the ﬁnal descent of the polarogram in Fig. 5), the successive electron transfer should occur at potentials more negative than those for the one-electron transfer. However, Range C appeared at much more positive potentials than those for the one-electron transfer, which suggest that the reaction at Range C must be different from the successive electron transfer. Although further investigation is necessary, we assumed the formation of an activated complex, such as (NADH-Hþ -TQ)interface containing NADH, Hþ , and TQ at the W/DCE interface at potentials more positive than the negative limit of Range C and the successive decomposition of the complex to NADþ in W and CQH2 in DCE at potentials more negative than the positive limit of Range C: NADHðWÞ þ Hþ ðWÞ þ TQðDCEÞ>ðNADH Hþ TQÞinterface

>NADþ ðWÞ þ TQH2 ðDCEÞ

ð15Þ

This assumption was supported by the fact that the residual current observed by potential scan polarography at the W/DCE interface was larger in Range C than that in other ranges, indicating the increase of the capacitance due to the change of the interfacial structure. Similarly, the reaction between NADH and CQ in Range B was assumed as NADHðWÞ þ Hþ ðWÞ þ CQðDCEÞ>ðNADH Hþ TQÞinterface

>NADþ ðWÞ þ CQH2 ðDCEÞ

ð16Þ

Biomimetic Charge Transfers

D.

503

Ion Transfer Coupled with Interfacial Redox Reaction Between NADH and CQ or TQ

A 10 mL portion of W containing 103 M NADH, 2 103 M tetra-alkylammonium ion (R4 Nþ ; tetrapentylammonium (TPenAþ ), tetrabutylammonium (TBAþ ), or tetraethylammonium (TEAþ ), ion) and 0.01 M borate buffer was shaken for 1 h with 10 mL of DCE containing 103 M CQ. Prior to the shaking, W and DCE were deaerated by bubbling N2 gas. After the phase separation, concentrations of R4 Nþ transferred into DCE, NADþ produced in W, and CQ and CQH2 produced in DCE were determined as summarized in Table 1. The results clearly demonstrate that, when TBAþ or TPenAþ had been added in W, about 1/2 of R4 Nþ was transferred into DCE, almost all of CQ in DCE was reduced to CQ and about 1/2 of NADH was oxidized to NADþ after the shaking. When TEAþ was added, however, the ion was not transferred into DCE, and all of the NADH and CQ was converted to NADþ and CQH2 , respectively. The experiment in the absence of R4 Nþ yielded NADþ and CQH2 . When TQ was employed instead of CQ, the transfer of R4 Nþ was not observed, and the products were NADþ and TQH2 irrespective of the kind of R4 Nþ added in W. In order to elucidate the transfer behavior of R4 Nþ at the W/DCE interface, polarograms were recorded at the interface between W containing 2 104 M TEAþ , TBAþ , or TPenAþ , and DCE as curves 3, 4, or 5 in Fig. 5. The polarographic wave of TBAþ or TPenAþ is observed at potentials where the polarographic current (curve 1) due to the electron transfer appears, which suggests that the coupling of the transfer of TBAþ or TPenAþ with the electron transfer occurs when W containing NADH and TBAþ or TPenAþ is shaken with DCE containing CQ [44]. Since

TABLE 1 Tetra-alkylammonium Ion, R4 Nþ , Transferred from W to DCE by the Coupling with the Redox Reaction Between NADH in W and a Quinone Derivative in DCE. Results After Shaking W Containing 103 M NADH and 103 M (R4 Nþ )2 SO4 with DCE Containing 103 M Quinone [Q; Chloranil (CQ) or Toluquinone (TQ)] for 1 h. TPenAþ , TBAþ , and TEAþ Denote Tetrapentylammonium, Tetrabutylammonium, and Tetraethylammonium ions, Respectively Concentrations after shaking (M)

Quinone in DCE CQ

TQ

a

R4 N þ added in W

NADH

NADþ

R4 Nþ

Q

QH2

TPenAþ TBAþ TEAþ None TPenAþ TBAþ TEAþ None

4:5 104 4:3 104 N.D. N.D. 7:3 104 6:8 104 7:0 104 6:6 104

5:5 104 5:7 104 ca. 103 ca. 103 2:7 104 3:2 104 3:0 104 3:4 104

9:7 104 9:5 104 N.D. N.D. N.D. N.D. N.D. N.D.

ca. 103 9:4 104 N.D. N.D. N.D.a N.D.a N.D.a N.D.a

N.D. N.D. ca. 103 ca. 103 —b —b —b —b

in W

in DCE

The adsorption maximum of 496 nm characteristic of one electron reduction product of TQ was not observed. TQH2 in DCE could not be determined because of the distribution of TQH2 to W. N.D.: not detected. b

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Kihara et al.

the potentials available for the transfer of TEAþ are different from those for the electron transfer, the coupling of the ion transfer with the electron transfer hardly occurs. In the absence of the coupling, the reaction of Eq. (13) proceeds and Hþ is transferred from W to DCE. The coupling between the transfer of R4 Nþ and the electron transfer cannot be expected when TQ is used instead of CQ, since the electron transfer was not observed in the polarogram at the W/DCE interface. Therefore, the reaction as in Eq. (14) proceeds when W containing NADH is shaken with DCE containing TQ even in the presence of R4 Nþ in W.

V.

REDOX REACTIONS BETWEEN OXYGEN IN W AND A HYDROQUINONE DERIVATIVE IN O AT THE W/O INTERFACE [23]

The reduction of O2 in W by hydroquinone derivatives (QH2 ) in O is a subject of interest, since the reaction might offer the fundamental information on the electron transport coupled with the proton transport at a biomembrane realized by the respiration [2,3,56]. The reduction of ground state O2 with organic substances is fairly slow in aqueous or nonaqueous solutions [57] in spite of the high redox potential of O2 . The O2 is utilized effectively, however, as the terminal oxidant in the respiratory chain in a biomembrane with redox enzymes composed of membrane proteins such as heme proteins containing cytochrome c oxidase [58–60] or quinol oxidase [61,62]. The ﬁnal reduction products of O2 in W are H2 O2 and H2 O in the respiratory chain, and the control of H2 O2 production is very important in physiological phenomena, since H2 O2 works as a toxic substance causing the destruction of cell or the decomposition of organic compounds essential to the living body on the one hand, and works as a useful substance to decompose substances harmful to the living body on the other [57]. The effect of concentrations of quinone derivatives or uncouplers in a biomembrane on the formation of H2 O2 has been investigated extensively from this viewpoint [57,63–65]. The reduction of O2 is usually believed to proceed accompanying the transfer of protons or other ions through a biomembrane [5], and the reaction rate or even the process is considered to vary depending on the kind of transferring ions. An ion channel or ion pump composed of membrane proteins has often been assumed in the explanation of the dependency of the reaction rate [5]. In the present section, in order to elucidate the essential part of chemistry in the respiration, the redox reaction between O2 in W and QH2 in O was investigated by adopting QH2 the structure and chemical property of which is well known, and the proton transfer at the W/O interface accompanied by the redox reaction was elucidated. The transfer of various ions other than protons coupled with the redox reactions was also discussed.

A.

The Polarogram for the Reduction of O2 by QH2 at the W/DCE Interface

The redox reaction between O2 in W and QH2 in DCE was investigated by current-scan polarography at the W/DCE interface by using a cell system as Eq. (17). The QH2 adopted was tetrachlorohydroquinone (CQH2 ):

Biomimetic Charge Transfers

505

ð17Þ

Curve 1 in Fig. 8 is the current-scan polarogram recorded at the W/DCE interface. A negative current wave was observed at EW=DCE more negative than 0:5 V vs. TPhBE. The range of EW=DCE will be deﬁned as Range A, hereafter. The theoretical analysis of the wave indicated that the charge transfer reaction for the wave was controlled by the diffusion of CQH2 in DCE [66]. In this regard, the oxidation of CQH2 by O2 dissolved in DCE was hardly observed, which suggests that the oxidation occurs at the W/DCE interface but not in the bulk of DCE.

B.

Products of the Redox Reaction Between O2 in W and CQH2 in DCE at the W/DCE Interface

The controlled potential electrolysis was carried out for 4 h by applying a deﬁnite Eappl at the stationary interface between W and DCE for which the compositions were as Eq. (17), and concentrations of CQ: and CQ produced in DCE were determined as curves 1 and 2, respectively, in Fig. 9. The dominant species produced in DCE by the reaction between

FIG. 8 Polarograms observed at the W/DCE interface. Curve 1: for the redox reaction between O2 (saturated with air) in W and 103 M CQH2 in DCE. Curve 2: for the transfer of CQ from DCE containing 103 M CQ to W. Curve 3 (imaginary polarogram): for the redox reaction between O2 (saturated with air) in W and 103 M CQH2 in DCE under the assumption that the transfer of CQ does not participate in the reaction. As supporting electrolytes, 0.5 M Li2 SO4 and 0.05 M TPenAþ TFPB were added in W and DCE, respectively. pH of W was adjusted with the aid of 0.1 M phosphate buffer to be 7.0.

506

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FIG. 9 Concentrations of CQ (curve 1), CQ (curve 2), and H2 O2 (curve 3) produced after electrolysis for 4 h by applying a potential difference, Eappl , at the interface between W containing O2 (saturated with air) and DCE containing 103 M CQH2 . Supporting electrolytes and pH buffer used were the same as those in Fig. 8.

CQH2 in DCE and O2 in W was CQ: when Eappl was more negative than 0:7 V (the potential range will be deﬁned as Range A1) where the negative current wave was observed in polarogram 1 in Fig. 8. The oxidation of CQH2 in DCE by O2 in W also proceeded at Eappl more positive than those in Range A1, though the oxidation product was different from CQ . When Eappl was between 0:7 and 0:5 V vs. TPhBE (this potential range will be called as Range A2), the dominant oxidation product was CQ. When Eappl was more positive than 0:3 V (this potential range will be called as Range B) where the polarographic wave was not observed, the main oxidation product was also CQ, and CQH2 was oxidized to CQ almost quantitatively at 0:1 V. The concentration of H2 O2 produced in W by the controlled potential electrolysis was determined as curve 3 in Fig. 9. Taking into account the stoichiometry of the reaction between O2 and CQH2 (i.e., [H2 O2 ]W /[CQ: DCE ¼ 1=2 when the oxidation product is CQ: and [H2 O2 ]W/[CQ]DCE ¼ 1 when the oxidation product is CQ; [ ]a denotes concentration in a phase), concentrations of H2 O2 produced in W, [H2 O2 ]W , were compared with those of CQ: and CQ produced in DCE. The [H2 O2 ]W at Eappl in Ranges A1 and A2 were less than those calculated from [CQ: DCE and ½CQDCE , though ½H2 O2 W at Eappl in Range B were identical with the calculated [CQ]DCE . When the controlled potential electrolysis had been carried out at Eappl in Range A1 by employing a system the same as Eq. (17) but in the absence of phosphate buffer in W, the decrease of pH in W to around 3 was found after the electrolysis, though oxidation products of CQH2 were the same as those in the presence of the buffer (CQ: or CQ). The pH change was negligible, however, when Eappl had been that in Range A2 or Range B. Here, pH of W before electrolysis had been around 7.

Biomimetic Charge Transfers

C.

507

Redox Reaction Between H2 O2 in W and CQH2 in DCE at the W/DCE Interface

Since H2 O2 was found in W as the reduction product of O2 , the possibility of the redox reaction between H2 O2 in W and CQH2 in DCE at the W/DCE interface was examined based on the controlled potential electrolysis. The electrolysis was carried out for 4 h under the deaerated condition by applying Eappl in Range A1, A2, or B (0:85, 0:6, or 0:1 V, respectively) at the interface of the cell system identical with Eq. (17), but in the presence of 103 M H2 O2 in W instead of O2 . Table 2 summarizes [CQ]DCE , [CQ: DCE and [H2 O2 ]W after the electrolysis. In the table, the concentrations after the electrolysis in the absence of H2 O2 are added as the background that might be caused by the reaction of O2 remaining even after the deaeration. As is clear from Table 2, almost all of CQH2 in DCE was oxidized in CQ and about 1/2 of H2 O2 in W was consumed when Eappl was that in Range A1, and about 1/3 of CQH2 in DCE was oxidized to CQ and about 1/3 of H2 O2 in W was consumed when Eappl was that in Range A2, though the redox reactions between H2 O2 in W and CQH2 in DCE were negligible when Eappl was that in Range B. In connection with the reaction, the change of pH in W was hardly observed after the electrolysis at any Eappl with the cell system in the absence of phosphate buffer. The reaction between H2 O2 in W and CQH2 in DCE at the W/DCE interface was also investigated polarographically by dropping W containing H2 O2 into DCE containing 103 M CQH2 . The polarographic current was negligible, when the concentration of H2 O2 was 103 M. However, a small current was observed at potentials in Range A when the concentration was 10 times higher, 102 M. This result indicates that the reaction between H2 O2 in W and CQH2 in DCE at the W/DCE interface is much slower than that controlled by the diffusion of H2 O2 or CQH2 .

TABLE 2 Concentrations of Redox Products After the Electrolysis for 4 h by Applying a Deﬁnite Eappl at the Stationary Interface Between W Containing 103 M H2 O2 and DCE containing 103 M Tetrachlorohydroquinone, CQH2 , Under the Deaerated Condition. As Supporting Electrolytes, 0.5 M Li2 SO and 0.05 M TPenAþ TFPB Were Added in W and DCE, Respectively. The pH of W Was Adjusted with the Aid of 0.1 M Phosphate Buffer to be 7.0 Concentrations after electrolysis (M) CQ and CQ found in DCE Potential difference applied ðEappl =V vs. TPhBE)

CQ

0:7 V (in Range A1) as above, but without H2 O2 0:55 V (in Range A2) as above, but without H2 O2 0 V (in Range B) as above, but without H2 O2

9:1 104 9 105 N.D. N.D. N.D. N.D.

N.D.: not detected.

H2 O2 found in W

CQ 6 105 N.D. 3:8 104 1:2 104 1:2 104 9 105

5:9 104 N.D. 7:2 104 7 105 1:1 103 1:2 104

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The Transfer of CQ from DCE to W

The oxidation product in DCE, CQ , has a charge, and hence it may be liable to transfer to W. The transfer of CQ at the W/DCE interface was investigated by current-scan polarography. Here, CQ in DCE had been prepared by reducing CQ in DCE at a column electrode with carbon ﬁber working electrode [40]. The polarogram (curve 2 in Fig. 8) indicates that CQ transfers from DCE to W in the potential range more positive than 0:7 V. E.

Redox Process Between O2 in W and CQH2 in DCE at the W/DCE Interface

The redox process has been estimated on the basis of the experimental results described above. 1. The Process Occurring when E appl is in Range A1 In Range A1, a negative current wave was found in the polarogram at the W/DCE interface (cf. Fig. 8). After the electrolysis by applying Eappl in the range at the W/DCE interface, CQ: was produced as the dominant species in DCE, H2 O2 of concentration less than that of CQ: was produced in W, and an obvious change of pH in W was observed in the absence of pH buffer. The reaction of Eq. (18) is consistent with the experimental results: O2 ðWÞ þ 2CQH2 ðDCEÞ>H2 O2 ðWÞ þ 2CQ: ðDCEÞ þ 2Hþ ðWÞ

ð18Þ

In this reaction, two electrons (which carry negative charges) move from DCE to W due to the interfacial redox reaction between one O2 (W) and two CQH2 (DCE), and four protons (which carry positive charges) liberated from two CQH2 (DCE) move from DCE to W. Consequently, two positive charges transfer from DCE to W across the interface as the balance, which causes the negative current wave in the polarogram (curve 1 in Fig. 8). The reduction product of O2 in W, H2 O2 , also reacts with CQH2 in DCE at the W/DCE interface producing CQ: in DCE when Eappl is in Range A1 or A2. This reaction can be expressed as H2 O2 ðWÞ þ 2CQH2 ðDCEÞ>2H2 OðWÞ þ 2CQ: ðDCEÞ þ 2Hþ ðWÞ

ð19Þ

The fact that the concentration of H2 O2 after the electrolysis at Eappl in Range A2 or A2 was less than that of CQ or CQ, respectively, can be understood by considering the consumption of H2 O2 produced by the reaction of Eq. (18) through the reaction of Eq. (19). Since transfers of two electrons and four protons from DCE to W participate in reaction (19), two positive charges are expected to transfer from DCE to W across the interface as the net. However, distinct waves were not observed in the polarogram at the interface between W containing H2 O2 and DCE containing CQH2 , because the reaction between H2 O2 and CQH2 is fairly slow. On the other hand, the rate of the reaction between H2 O2 immediately after its production at the W/DCE interface (which will be denoted as H2 O2 , hereafter) and CQH2 is expected to be similar to or faster than that between O2 and CQH2 [reaction (18)], judging from the result given in Fig. 9 that concentrations of H2 O2 remained in W after the electrolysis at Eappl in Range A1 or A2 were much less than those calculated from concentrations of CQ and CQ produced in DCE indicating the consumption of H2 O2 during the electrolysis. Here, if the rate of the reaction of H2 O2 with CQH2 is much slower than that between O2 and CQH2 , O2 may react with CQH2 preferentially at the W/DCE interface and the reaction between H2 O2 and

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CQH2 may be negligible. Consequently, the authors assume that H2 O2 produced at the interface might be different from H2 O2 , which has been diffused into the bulk of W, in their chemical states and/or reactivities, though further investigation is required. 2.

The Process Occurring when E appl is in Range A2

When electrolysis at the W/DCE interface had been carried out by applying Eappl in Range A2, CQ was produced as the dominant species in DCE, and H2 O2 for which the concentration was less than that of CQ in DCE was produced in W. The reactions of Eqs. (18) and (19) are assumed to proceed also in this range. Because the transfer of CQ: from DCE to W is possible at potentials in this range (cf. curve 2 in Fig. 9), however, the CQ: produced in DCE by reactions (19) and (20) moves into W: CQ: ðDCEÞ>CQ: ðWÞ

ð20Þ

The CQ: transferred into W protonates, producing Hþ CQ: (W), which disproportionates resulting in CQ and CQH2 : :

CQ: ðWÞ þ Hþ ðWÞ>Hþ CQ ðWÞ

ð21Þ

2Hþ CQ: ðWÞ>CQH2 ðWÞ þ CQðWÞ

ð22Þ

CQH2 and CQ thus produced in W are considered to transfer easily into DCE, since they are neutral and hydrophobic: CQH2 ðWÞ; CQðWÞ>CQH2 ðDCEÞ; CQðDCEÞ

ð23Þ

The CQH2 transferred to DCE participates in reactions of Eqs. (18) and (19), again. As mentioned above, the difference of the reaction in Range A2 from that in Range A1 is attributable to the transfer of CQ: from DCE to W followed by reactions (21) to (23). In this connection, it is speculated that the two electron reduction of O2 by CQH2 [Eq. (18)] might proceed even at potentials more positive than those for the polarogram of curve 1 in Fig. 9 as illustrated by the broken line (curve 3), though the current due to the reaction might be canceled out by the current due to the interfacial transfer of CQ: [Eq. (20)]. 3.

The Process Occurring when E appl is in Range B

In Range B where any polarographic currents were not observed (cf. Fig. 9), CQ was produced as the dominant species in DCE, and H2 O2 of which concentration was almost identical with that of CQ was produced in W after the electrolysis at the W/DCE interface. The change of pH in W by the electrolysis was scarcely observed. The reduction of H2 O2 by reaction (19) did not proceed by the electrolysis at potentials in this range. These characteristics of the reaction in Range B can be understood by considering reaction (24) without contradiction: O2 ðWÞ þ CQH2 ðDCEÞ>H2 O2 ðWÞ þ CQðDCEÞ

ð24Þ

By this reaction, two positive charges (Hþ ) and two negative charges (e ) transfer simultaneously across the W/DCE interface, and hence currents due to transfers of charges at the interface are canceled out.

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Redox Reaction Between O2 in W and CQH2 in DCE at the Interface Coupled with Ion Transfer Reactions

The above-mentioned results indicate that the reaction between O2 in W and CQH2 in DCE at the interface depends on the potential difference at the W/DCE interface, and therefore, the reaction process can be controlled by changing Eappl . The potential difference can be controlled not only by the potential applied at the interface, but also by the ion transfer occurring at the interface. The redox reaction between O2 in W and CQH2 in DCE controlled by (or coupled with) an ion transfer reaction at the interface was investigated by shaking W with DCE for 4 h. Compositions and volumes of W and DCE adopted were as follows:

ð25Þ

After shaking, concentrations of R4 Nþ distributed into DCE, CQ: , and CQ in DCE and H2 O2 in W were determined as summarized in Table 3. The result clearly demonstrates that about 1/2 of R4 Nþ was transferred into DCE, and CQH2 in DCE was oxidized mainly to CQ when TPenAþ or TBAþ had been added as R4 Nþ in W. The concentrations of H2 O2 produced in W were much less than those corresponding to the production of CQ and CQ . When TEAþ had been added as R4 Nþ in W, however, TEAþ was not transferred into DCE though almost all of CQH2 was converted to CQ, and the concentration of H2 O2 produced in W was about 1/2 of that corresponding to the production of CQ. In order to clarify the reason for the coupling of the redox reaction between O2 and CQH2 with the ion transfer at the W/DCE interface in system of Eq. (25), currentscan polarograms for ion transfers at the W/DCE interface (cf. curves 3 to 5 in Fig. 5) were compared with that for the interfacial redox reaction (cf. curve 1 in Fig. 8). From the comparison, it is clear that transfers of TPenAþ and TBAþ from W to DCE proceed at potentials in Range A where the polarographic wave due to the redox reaction

TABLE 3 Concentrations of Products After Shaking for 4 h W Containing O2 (Saturated with Air), 103 M (R4 Nþ Þ2 SO4 and 0.1 M Phosphate Buffer (pH = 7.0) with DCE Containing 103 M CQH2 . TPenAþ , TBAþ and TEAþ Denote Tetrapentylammonium, Tetrabutylammonium and Tetraethylammonium Ions, Respectively Concentrations after shaking (M) in DCE R4 Nþ in W TPenAþ TBAþ TEAþ N.D.: not detected.

CQ 8:5 104 7:2 104 N.D.

in W CQ 1:2 104 1:8 104 8:9 104

H2 O 2 1:4 104 1:8 104 5:0 104

R4 Nþ 1:1 103 1:07 103 N.D.

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between O2 and CQH2 [Eq. (18)] was observed, which suggests that the coupling of the transfer of TPenAþ or TBAþ from W to DCE with the charge transfer (2Hþ , 1e ) from DCE to W caused by the redox reaction of Eq. (18) occurs when W containing O2 and TBAþ or TPenAþ is shaken with DCE containing CQH2 , and electroneutoralities in both W and DCE phases are maintained [44]. The transfer of TEAþ from W to DCE (cf. curve 5 in Fig. 5) occurs at a more positive region than that for the negative current wave for the interfacial redox reaction (cf. curve 1 in Fig. 8). Since there are no excess transfers of minus charges (e or anions) from W to DCE or plus charges (cations) from DCE to W to preserve the electroneutrality in the potential region available for the transfer of TEAþ , the transfer of TEAþ cannot occur when W containing O2 and TEAþ is shaken with DCE containing CQH2 . In the potential region, CQ is expected to be produced by reactions of Eqs. (18) to (24), which explains the result in Table 3 obtained with TEAþ .

VI.

CONCLUSION

It has been demonstrated that mainly charge transfers at two aqueous–membrane interfaces control the charge transport through a LM or BLM when the membrane system contains sufﬁcient electrolytes. This fact means that the quantitative understanding of charge transfers at two interfaces is inevitable for the elucidation of the membrane transfer process. In Sections III to V, three examples of respiration mimetic interfacial redox reactions at the W/O interface were introduced. The processes of these reactions depended strongly on the potential differences at the W/O interface, and the redox reactions could be controlled not only by the potential difference applied at the interface, but also by selecting an ion transfer reaction occuring at the interface. The redox processes introduced here may endow some views on the interpretation of such phenomena occurring at biomembranes as the reduction of FMN followed by the reduction of O2 and CO2 evolution due to the oxidation of a glycolysis product by the reduction product of O2 , oxidation of NADH by Q, reduction of O2 by QH2 , the control of H2 O2 production, and transports of Hþ or other ions coupled with the interfacial redox reactions. Finally, it should be stressed that the voltammetric concept and methods are very useful for the elucidation of electrochemical reactions (redox or ion transport reactions) at artiﬁcial membranes as well as biomembranes.

ABBREVIATIONS BLM: CE: CQ: CQH2 : CVþ : DCE: DMFC: EW1=LM ;ELM=W2 : EW=O : EW1W2 :

bilayer lipid membrane counter electrode chloranil tetrachlorohydroquinone crystalviolet ion 1,2-dichloroethane (1,2,3,4,5-pentamethyl-cyclopentadienyl)iron potential difference at aqueous–membrane interfaces potential differences at the aqueous–organic interface membrane potential

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FMN: IW1W2 : LM: M: NADH: NB: O: Q: RE: R4 Nþ : SE: SSE: TBAþ : TDAþ : TEAþ : TFPB : TPenAþ : TPhB : TPhBE: TQ: VCTTM: W: W1, W2:

ﬂavin mononucleotide membrane current liquid membrane membrane -nicotinamide adenine dinucleotide nitrobenzene organic solution quinone derivative reference electrode tetra-alkylammonium ion supporting electrolyte silver–silver chloride reference electrode tetrabutylammonium ion tetradecylammonium ion tetraethylammonium ion tetrakis[3,5-bis(triﬂuoromethyl)phenyl]borate tetrapentylammonium ion tetraphenylborate ion tetraphenylborate ion-selective electrode (reference electrode) toluquinone voltammogram for charge transfer through a membrane aqueous solution aqueous solutions in a membrane system

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21 DNA-Modi¢ed Electrodes. Molecular Recognition of DNA and Biosensor Applications KOJI NAKANO Department of Chemical Systems and Engineering, Kyushu University, Fukuoka, Japan

I.

INTRODUCTION

Molecular recognition is fundamental to most biochemical phenomena – it is crucial in enzymatic catalysis, immune reactions, and DNA replication, as well as cell–cell signaling via nerves, hormones, and growth factors. Such an extraordinary property of life has been stimulating a considerable research interest in every discipline of chemistry. For example, selective binding through molecular recognition is the basis of many important techniques in chemical analyses and separations, including those that employ enzymes and antibodies. On the other hand, it has become a challenging target for chemists trying to develop synthetic materials that capture some of the exquisite sensitivity that biological systems have to recognize speciﬁc molecules. Incidentally, nucleic acids occupy a position of central importance in biological systems [1]. Even though based on relatively simple nucleotide monomers, these biopolymers participate in a complex array of cellular functions. From the deoxyribonucleic acid (DNA) duplex structure, genetic information is stored, accessed, and replicated as a linear nucleotide code. In partnership with DNA, ribonucleic acid (RNA) transports genetic information to the ribosome which synthesizes protein products. Due to such an essential role as the genetic information storehouse, the study of nucleic acids has become a broad area spanning many diverse ﬁelds of science. Recent ﬁndings that some RNA polymers participate in the catalysis of their own replication and chemical manipulation (ribosymes) have also promoted such research activities [2]. Increasing knowledge of the human DNA has led to the discovery that some inherited human diseases are associated with speciﬁc changes in normal DNA base sequences. From the viewpoint of chemical sensor development, it should be pointed out that sequence-speciﬁc methods for detecting nucleic acids are critical to the diagnosis of genetic and pathogenic diseases. The most promising way for this purpose is to use a DNA probe, a synthetic, single-stranded oligonucleotide that has been labeled with a reporter group. The sequence of the probe is complementary to the sequence of interest, so that the hybridization results in retention of the label to give an analyte-dependent signal. Radioactive isotopes (RI) such as 32 P are widely used as labels because of their high detection sensitivity. However, due to their hazardous nature and short shelf life, the 515

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development of an alternative detection system that is convenient and practical without relying on RI is eagerly awaited. As a substitute, a ﬂuorophore [3] and chemiluminophore [4] have been studied in the combined use of optical [5] or mass-sensitive [6] devices. More recently, electrochemically active biosensors which rely on monitoring of the redox currents of DNA nucleobases [7] or a redox-active indicator molecule [8] have been introduced. Given their biological importance, it should not be surprising that nucleic acids constitute a primary target for binding or chemical modiﬁcation by several classes of molecules [9]. For example, gene regulatory proteins bind to the DNA duplex to repress or stimulate the natural ﬂow of genetic information. Alternatively, some polycyclic aromatic molecules from extracellular sources bind to DNA double strands by inserting themselves between the base pairs of the DNA (intercalation) [10]. Binding of these exogeneous agents may lead to a useful result such as antibacterial or anticancer activity, but may also invoke undesirable responses such as carcinogenesis or mutagenesis. With these understandings, one may notice the possibility of developing a bioafﬁnity sensor that selectively responds to DNA-binding substrates. The sensor would provide a certain method for the evaluation of inherited, carcinogenic compounds. The initial hurdle to overcome in the biosensor application of a nucleic acid is that involving its stable attachment on a transducing element which commonly includes a metallic electrode. In the ﬁrst part of this chapter, we wish to introduce our approach for DNA immobilization (Scheme 1). A detailed characterization of the immobilization chemistry is also presented. In the second part, we follow the development of work from our laboratory on chemical sensor applications of the DNA-modiﬁed electrode involving a biosensor for DNA-binding molecules and an electrochemical gene sensor.

II.

IMMOBILIZATION CHEMISTRY OF DNA

A rational manipulation of the electrode surface functionality by immobilizing selected types of molecules is an essential key for the development of electrochemical sensors and devices. One of the recent studies in this area has focused on monolayer formation on gold surfaces from organosulfur precursors [11]. Stable attachment of organic molecules to gold

SCHEME 1 Modiﬁcation of double-stranded DNA with organosulfur precursor and immobilization on Au surface via chemisorption.

DNA-Modified Electrodes

517

and other metal surfaces is attained through the use of reagents having thiol, sulﬁde, disulﬁde, or other sulfur-containing headgroups by immersing the gold substrate into their dilute solutions. This attachment has been described as due to the formation of some type of thiolate complex on the gold surface, and therefore, the use of a sulfurcontaining species as an anchor for immobilization seems to be especially attractive because of the stability of the formed surface complex. From this viewpoint, we took advantage of a chemical modiﬁcation of DNA with sulfur-containing groups.

A.

Chemical Modiﬁcation of Terminal Phosphate Group of DNA

Carbodi-imides are used to mediate the formation of amide linkage betwen a carboxylate and an amine or phosphoramidate linkages between a phosphate and an amine [12]. The following is essentially the method of Rockwood [13] and is modiﬁed to give a phosphodiester link between the terminal monophosphate of the oligonucleotide and the hydroxyl group of 2-hydroxyethyl disulﬁde (HEDS) [14]. Calf thymus (CT) DNA was ﬁrst fragmented by sonication, then puriﬁed by a standard procedure. Agarose gel electrophoresis for the sonicated CT DNA revealed a distribution in molecular weight ranging from 30 kDa to 260 kDa which is equivalent in base pairs (bp) from 40 to 400 (1 bp = 660 Da). The DNA fragments were reacted with HEDS in the presence of 1-cyclohexyl-3-(2-morpholinoethyl) carbodi-imide metho-ptoluenesulfonate (CMCpTs). Finally, the reaction mixture was gel-ﬁltered and the macromolecular fractions, when displayed the characteristic absorption of 260 nm of the nucleic bases, were collected. Several precautions were taken to ensure the immobilization chemistry. First, the sulfhydryl groups containing the macromolecular fraction was spectrophotometrically determined according to the literature [15]. We found that every set of 150 base pairs contained approximately one disulﬁde group. Since the DNA fragment used has hundreds of base pairs, each DNA strand seems to have one disulﬁde as its terminal group. Next, we made IR spectral measurements in a reﬂection–absorption (RA) mode [14b]. A freshly evaporated gold substrate was immersed into the DNA solution for 24 h at 58C. The substrate was carefully rinsed with deionized water, dried under vacuum and was immediately used for the measurements. An Au substrate treated with unmodiﬁed, native sonicated CT DNA solution was also prepared as the control measurement. The p-polarized radiation was introduced on the sample at 858 off the surface normal and data were collected at a spectral resolution of 4 cm1 with 2025 scans. Figure 1 shows the IR spectra of the disulﬁde-modiﬁed DNA in the midfrequency region found in the immobilized state on an Au substrate and in the cast state on a CaF2 plate. The RA spectrum of the Au substrate, which was treated with the disulﬁde-modiﬁed DNA, shows a spectrum fundamentally similar to the transmission spectrum of DNA measured in the cast state. In the RA spectrum, two intense peaks at 1216 and 1121 cm can be identiﬁed as P — O stretches for the antisymmetrical and symmetrical modes, respectively, of the phosphate group in the DNA backbone. In addition, adsorption due to the C — O — C stretch of the deoxyribose in the backbone is observed at around 1032 — O stretches of the cm1 . The broad, partially resolved peaks can be assigned to the C — 1 nucleic bases. The slightly obscure peak around 1550 cm , on the other hand, may be due to purine bases in the DNA double strands. In contrast, an Au substrate, which was treated with the native, sonicated DNA, did not show an RA spectrum characteristic of DNA at all. Taking these observations into account, we can conclude that organosulfur

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FIG. 1 FT-IR spectra in midfrequency region. DNA-treated gold substrate measured in reﬂection– absorption mode (a) and transmittance spectrum of DNA cast on CaF2 (b).

precursors, which were chemically introduced to the double-stranded DNA, play an essential role to immobilize the entire DNA entities.

B.

Chemical Synthesis of DNA – Terminal Modiﬁcation

Recent developments in DNA/RNA chemical synthesis have allowed us to attach some functional groups covalently to nucleic acids, thus permitting the introduction of a functionality or properties not normally present in the native biomolecule The use of nonnucleosidic linkers is probably the most popular approach for the 50 -terminal modiﬁcation of chemically synthesized nucleic acid oligonucleotides and a number of such linkers are commercially available. The linker shown in Fig. 2 is designed as a phosphoramidate derivative so that it can be incorporated into the 50 -terminus of the sequence as the last

FIG. 2 Nonnucleoside linker containing a masked amino or sulfhydryl reactive center.

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coupling step [16]. Deprotection of the masked sulfhydryl functional group gives oligonucleotides having a mercaptohexyl group. Applications of the thiol-modiﬁed oligonucleotides in combined use with a mass-sensing device [6c] and electrochemical measurements [17] have been reported.

C.

Chemical Synthesis of DNA – Backbone Modiﬁcation

A variety of methods for modiﬁed oligonucleotide preparations have been reported including (1) the C5 and C4 positions for the pyramidines, (2) the exocyclic amino groups and the C8 positions of the purines, and (3) the 20 -hydroxyl group of the carbohydrate residue. Every method should be important as the basis for new immobilization chemistry, however, we especially focused our attention on the use of oligodeoxyribonucleotide phosphorothioates (Fig. 3). A phosphorotioate-containing oligodeoxynucleotide results when one of the nonbridging oxygens of an internucleotide phosphodiester linkage is replaced with a sulfur atom. By the use of Beaucage’s reagent, 3H-1,2-benzoedithiole-3-one 1,1-dioxide [18], in an automated oligodeoxynucleotide synthesis, the chemical conversion is attained with high reaction efﬁciency. This is a conservative modiﬁcation because the nucleic acid retains both its negative charge and its overall geometry. More importantly, oligodeoxyribonucleotide phosphorothioates are also expected to adsorb on gold surfaces forming gold– thiolate complexes. As described in the subsequent section, we have reported the use of an oligodeoxyribonucleotide having ﬁve successive phosphorothioates for modiﬁed electrode preparations [19]. The IR-RAS spectrum for an Au substrate treated with the oligodeoxyribonucleotide (Fig. 4) conﬁrmed that the formed surface phase reﬂects the intended adsorbate. Recently, Willner et al. also reported the use of an oligodeoxynucleo-

FIG. 3 The primary structure of oligodeoxyribonucleotide phosphorothioates.

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FIG. 4 FT-IRRAS spectrum in midfrequency region for gold substrate treated with 50 -TsTsTsTsTsTCTCATACATG-30 . The p-polarized radiation was introduced on the sample at 858 off the surface normal and data were collected at a spectral resolution of 4 cm1 with 256 scans.

tide phosphorotioate for microgravimetric [20a] and electrochimical [20b] analyses of the Tay–Sachs gene.

III.

ELECTROCHEMICAL PROPERTIES OF DNA-MODIFIED ELECTRODES

Detailed studies of the electrode reacations of nucleobases and nucleotides have clariﬁed that the redox reactions irreversibly occur under a high overpotential [21]. This makes the electroanalytical applications of nucleic acids difﬁcult. In addition, afﬁnity reactions of nucleic acids are stoichiometric and are not directly linked to redox processes; these are in a marked contrast to enzyme reactions which often give potentiometrically or amperometrically measurable reaction products in an ampliﬁed manner. In this context, the concept of ‘‘ion-channel sensors’’ proposed by Umezawa [22] is very promising, since the sophisticated mechanism occurring in cell membranes is successfully mimicked by using a lipidmade Langmuir–Blodgett (LB) membrane. The LB membrane coated on a solid electrode functions as an ‘‘ion channel’’ which can be speciﬁcally ‘‘opened’’ by the analyte ion, leading to the permeability change in the electrochemically detectable indicator ions. The present section is intended to outline the electrochemical properties of the CT DNA-immobilized electrode as the basis of such chemical sensor applications. A.

Characterization by Cyclic Voltammetry

Cyclic voltammograms of the [Fe(CN)6 ]4 /Fe[(CN)6 ]3 redox couple with the bare and the DNA-modiﬁed electrodes are shown in Fig. 5 [14a]. The peak currents due to the reversible electrode reaction of the redox system on the bare Au electrode were signiﬁcantly suppressed by the treatment with DNA. In contrast, the treatment with unmodiﬁed, native DNA made no suppression, and that with HEDS caused only a slight one, as seen in Fig.

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FIG. 5 Cyclic voltammograms of [Fe(CN)6 ]4=3 redox couple on bare (solid line), DNA-modiﬁed (heavy line), and HEDS-modiﬁed Au electrodes (dotted line). Electrolyte solution, aqueous each 5 mM of K4 ½FeðCNÞ6 and K3 [Fe(CN)6 ] containing 10 mM KCl; scan rate 25 mV s1 ; temperature, 258C; electrode area, 0.02 cm2 (geometrical).

5. These results indicate that the surface-anchored DNA blocks the electrochemical reaction of [Fe(CN)6 ]4=3 with the underlying Au electrode, due to the electrostatic repulsion between the polyanionic DNA and the anionic redox couple ions.

B.

Characterization by Electrochemical Impedance Measurements

Figure 6 shows the impedance diagrams taken for the [Fe(CN)6 ]4=3 redox couple with the bare and the DNA-modiﬁed electrode [14b]. For reactions on the bare Au electrode, the impedance diagram is characterized by a well-deﬁned semicircle followed by a diffusion line at the lower frequencies. The DNA-modiﬁed electrode, on the other hand, gave an impedance response of slightly depressed semicircle loci with a larger diameter, and as a result, the diffusion line was partially masked in the investigated frequency range. Displacement of the semicircle locus from the real axis reveals unideality in the electrical properties of the surface adlayer and this should be partially ascribed to the molecular weight distribution of the DNA. We further characterized the impedance properties of the electrode systems with mathematical simulation and complex nonlinear least-squares ﬁtting. Under this electrochemical conﬁguration, it is commonly accepted that the system can be expressed by the Randles-type equivalent circuit (Fig. 6, inset) [23]. For reactions on the bare Au electrode, mathematical simsulations based on the equivalent circuit satisfactorily reproduced the experimental data. The parameters used for the simulation are as follows: solution resistance, Rs ¼ 40 k cm2 ; double-layer capacitance, C ¼ 28 F cm2 ; equivalent resistance of Warburg element, W R ¼ 1:1 109 cm2 ; equivalent capacitance of Warburg element, W T ¼ 1:1 109 F cm2 (’ ¼ 0:5); and charge-transfer resistance, Rct ¼ 80 k cm2 . Note that these equivalent parameters are normalized to the electrode geometrical area. On the other hand, results of the mathematical simulation were unsatisfactory due to the nonideal impedance behavior of the DNA adlayer. This should

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FIG. 6 Complex impedance plots for the electrode reaction of [Fe(CN)6 ]4=3 on bare (open circle) and DNA-modiﬁed (ﬁlled circle) Au electrodes. An equivalent circuit for the electrode system is shown in the inset and solid lines represent theoretical responses from the circuit. Parameters used in simulation are cited in the text. Electrode potential, +205 mV (vs. Ag/AgCl); AC amplitude, 25 mV (p–p). Other conditions are the same as those in Fig. 5.

be addressed in the future. For the present circumstances, the equivalent parameters are as follows: Rs ¼ 25 k cm2 , C ¼ 10 F cm2 , W-R ¼ 3:4 108 cm2 , W-T ¼ 3:4 108 F cm2 (’ ¼ 0:5Þ, and Rct ¼ 410 k cm2 : Finally, if one assumes that the faradaic reaction of the solution species occurs only on the uncovered, bare Au site (the uncovered site within the DNA adlayer), one can obtain the surface coverage, , of the DNA using the following equation:

¼ 1 ½Rct;bare =Rct;DNA Here, Rct;bare and Rct;DNA indicate the charge transfer resistance for the redox couple on the bare and the DNA-modiﬁed Au electrodes, respectively and was calculated to be 80%.

IV.

BIOAFFINITY SENSOR FOR DNA-BINDING MOLECULES AND IONS

By taking advantage of the ‘‘ion-channel concept,’’ we have previously reported a bioafﬁnity sensor in which DNA double strands serve as a chemoreceptive entity (Scheme 2) [14,17]. As noted in the preceding section, the DNA layer spread on the electrode surface effectively blocks the electrode reaction of the solution species. However, the redox wave reappears which a certain kind of DNA-binding molecule is added to the measurement solution. Neither the bare Au electrode nor that treated with HEDS showed any response to the molecules. Such ﬁnding should witness the versatile application for the sensing of compounds having a DNA-binding ability. In the present section, we will follow the development of such work from our laboratory.

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SCHEME 2

A.

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DNA-dependent ion-channel mechanism.

Electrode Response to DNA-Binding Small Molecules

Figure 7 shows the electrode response to quinacrine, which is a well-known antimalarial drug [14a]. The peak currents increased with increasing concentration of the drug, showing almost a linear relationship with the concentration of the drug in the range of 107 5 107 M (1 M ¼ 1 mol dm3 ) which then became saturated over the concentration of 8 107 M. The binding of the quinacrine having a cationic charge on the immobilized polyanionic host (i.e., DNA) should reduce the negative charge on the electrode surface, resulting in the enhancement of the current intensity. Complex impedance diagrams taken in the presence of various concentrations of quinacrine are shown in Fig. 8 [14b]. On the basis of the Randles equivalent circuit, we analyzed the diagram by a standard graphical procedure. Results of the analysis are as follows: the addition of

FIG. 7 The quinacrine-dependent changes in cyclic voltammograms of the DNA-immobilized Au electrode. Experimental conditions are the same as those in Fig. 5.

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FIG. 8 The quinacrine-dependent changes in complex impedance plots for the electrode reaction of [Fe(CN)6 ]4=3 on DNA-modiﬁed Au electrodes. Quinacrine concentration, (a) 0 M, (b) 2 107 M, (c) 106 M. Other experimental conditions are the same as those in Figs. 5 and 6.

quinacrine reduced Rct and its quinacrine concentration dependence was almost similar to that observed in the CV measurements. In contrast, the Cdl did not show such clear concentration-dependent changes and was almost constant (10 to 11 F cm2 ). The Z vs. !1=2 plots, on the other hand, revealed that enhancement in the diffusion of the redox couple was associated with the quinacrine addition. The electrode response can be attributed to the speciﬁc and strong interaction between the DNA double helix and quinacrine. Here, we assume a 1:1 binding reaction between quinacrine and a binding site composed of two adjacent base pairs on the DNA duplex. It has been reported that intercalation binding of quinacrine has maximum saturation at one bound molecule per two base pairs; after one site is occupied, binding at the neighboring site is excluded [24a]. This means that the concentration of the occupied site should be the same as that of the free site at saturation, and therefore, the binding constant can be simply expressed by the reciprocal of the concentration of the free quinacrine. We obtained an apparent binding constant of 1:6 106 M1 assuming the saturation of the CV peak current would correspond to the saturation of quinacrine binding to the DNA (the concentration of free quinacrine at the saturation point was 6:2 107 M). According to the literature [24a], quinacrine has a binding constant of 1:5 106 M1 under conditions similar to the present ones in terms of the temperature and concentration of coexisting salts. Figure 9 summarizes the electrode responses toward a variety of DNA-binding substrates [14c]. For intercalators (quinacrine, acridine orange, and safranin) and groove binders (spermine and spermidine), a steep rise followed by a saturation of the concentration–response curve is commonly observed. If one compares the speciﬁc concentration which gives a 50% response in the increment of the cathodic peak current (Ipc Þ for each substrate, a selectivity order of quinacrine acridine orange > spermine > spermidine > safranin can be estimated. The binding constants measured in aqueous media for the afﬁnity reaction with ds DNA are as follows: quinacrine, 1:5 106 M1 (38 mM NaCl)

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FIG. 9 The substrate-dependent changes in cathodic peak current (Ipc Þ of CVs taken similarly to those in Figs. 5 and 7.

[24a]; acridine orange, ð1:2 0:3Þ 106 M1 (ionic strength, 0.02) [24b]; spermine, 2:1 105 M1 (94 mM NaCl) [24c]; and spermidine, 5:8 104 M1 (94 mM NaCl) [24c]. The selectivity order using the present sensor system seems consistent with the binding afﬁnity of the substrates with ds DNA. In contrast, methylviologen, which has a binding constant of 1:8 105 M1 (1.5 mM cacodylate, pH 6) [24d], gives a much more insensitive CV response than that of the other investigated substrates. One possible explanation for the anomalous behavior is that methyl viologen binds to the exterior of the DNA helix via an electrostatic interaction; intercalative and groove bindings cause some structural changes in the polymeric host molecule [10], e.g., unwinding of the duplex and enlongation/collapse of the pitch between the stacked nucleobases, while such structural changes do not associate with methylviologen binding. It seems to be natural that the conformational state of the DNA double strands also relates to the kinetic aspects of the electrode reaction of the solution species.

B.

Electrode Response to DNA-Binding Metal Ions

Certain kinds of metal ions bind to the DNA double strands by an electrostatic interaction with the phosphate group(s) or by complex formation with the sugar moiety or the nucleic

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base [25]. In particular, Mg2þ complexes with nucleic acids have attracted much attention in relation to their unique roles in biological processes. We examined the electrode response for the series of alkaline and alkaline earth metal ions [26]. Figure 10 shows the relationship between Ipc and the concentrations of Mg2þ , 2þ Ca , and Ba2þ . The DNA-modiﬁed electrode thus showed a highly sensitive response toward Mg2þ in the concentration around 106 M. The electrode was also found to be responsive toward Ca2þ and Ba2þ as seen in Fig. 10, although the onset concentrations of the electrode responses were ca. 105 , 50 times larger than that for Mg2þ . As for Naþ , such a concentration-dependent change was not observed in the range of 107 103 M. Meanwhile, all the CV measurements were made in the presence of 102 M KCl as the supporting electrolyte. The selectivity order of Mg2þ >Ca2þ , Ba2þ Naþ , Kþ seems consistent with the binding afﬁnity of the metal ions with double-stranded DNA. These results suggest that the electrode responses were due to the speciﬁc interaction of the immobilized DNA with the alkaline earth metal ions, among which Mg2þ was the most strongly bound to DNA to give the discriminating response.

C.

Electrode Response to DNA-Binding Protein

The host–guest reaction of DNA is not limited to that with small molecules and ions. The hydrogen bond formation between the nucleobases and the guest makes a host molecule for biopolymers with a DNA double strand. For example, gene regulatory proteins recognize a particular sequence of DNA and bind to that site to repress or stimulate the natural ﬂow of genetic information. As described in the preceding section, the DNA-modiﬁed electrode system is expected to provide a certain means for the assay of proteins possessing the DNA-binding ability. The following is an example of work from our laboratory [27].

FIG. 10 The metal-ion-dependent changes in the cathodic peak current (Ipc Þ on DNA-modiﬁed Au electrode. Experimental conditions are the same as those in Fig. 5. * and *, Mg2þ (two different electrodes); ~, Ca2þ ; &, Ba2þ . For ﬁlled symbols, the same electrode was used.

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We used an anti-DNA antibody as an exploratory model system. The antibody was monoclonal from mouse sources and its subclass was IgM. Mouse IgG (MW 1:5 105 Da) and IgM (MW 9 105 Da) antibodies from normal plasma, and bovine serum albumin were used for the control measurements. To prevent the nonspeciﬁc adsorption of proteins to the uncovered, bare Au site in the modiﬁed electrode surface, the DNAmodiﬁed electrode prepared by the standard procedure was further treated with aqueous 2-mercaptoethanol solution and was used for the measurements. CV measurements showed that the reversible electrode reaction of the [Fe(CN)6 ]4=3 redox couple was suppressed to some extent by the treatment with the DNA. The addition of the anti-DNA antibody further suppressed the redox reaction thus decreasing the magnitudes of the CV peak currents. This is most likely caused by a steric hindrance of the bulky protein, which binds to the DNA double strands on the electrode surface, to mainly reduce the effective area of the electrode. The electrostatic repulsive effect may also contribute to the electrode response, since the isoelectric point of mouse IgM is commonly in the range of 4.5 to 7.0. Figure 11 shows the relationship between the decrease in the anodic peak current (Ipa Þ and the antibody concentration. As seen in this ﬁgure, the electrode system responded to the anti-DNA antibody in the concentration range of 1 100 nM. For the case of the mouse IgM, which does not interact with double-stranded DNA, the present system gave almost no response. The sensor did not respond to other serum proteins as well (data not shown). The anti-DNA antibody has been used as a marker molecule of Systemic Lupus Erthematosus (SLE) which is a severe autoimmune disease. Enzyme immunoassay is the most reliable, widely used method of assay; however, the electrochemical detection method reported here should be interesting for the purpose of a rapid and convenient diagnostic tool of SLE.

FIG. 11 Effect of antibodies (IgM) on anodic peak current (Ipa Þ of [Fe(CN)6 ]4=3 on DNA-modiﬁed Au electrodes. *, anti-DNA antibody; *, mouse IgM antibody. Electrolyte solution, aqueous each 10 mM of K4 (Fe(CN)6 ] and K3 [Fe(CN)6 ] containing 0.1 M KCl. Other conditions are the same as those in Fig. 5.

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ELECTROCHEMICAL GENE SENSOR

A biosensor capable of detecting a speciﬁc sequence of DNA has been gathering substantial research interest directed to the gene analysis and detection of speciﬁc changes in normal DNA base sequences. More recently, signiﬁcant progress has been accomplished with the assembly of biochips which relies on an optical transduction of the formation of DNA double strands with particular sequences of interest [28]. Electrochemistry, which necessarily uses an electrode, is fundamentally compatible to methods using a solid support since simple tailoring of an electrode surface readily gives an interface with sensing/ transducing ability. To date, electrochemical gene sensors are based on (1) the direct measurement of the redox reaction of purine bases constituting DNA duplexes [7], and (2) the use of a redoxactive reporter molecule which binds to DNA double strands [8]. However, both methods are expected to have their own drawbacks. The former reaction requires a high overpotential to occur [21], while the background current due to the redox reaction of the coexisting, free molecule limits the detection sensitivity for the latter case. From this viewpoint, we have been investigating an electrochemical technique for gene detection in which the sandwich-type complex from an oligodeoxynucleotide (ODN) immobilized on an Au electrode, target DNA, and the ferrocenyl ODN is formed to give a response (Scheme 3) [19]. The ODNs used here were prepared on an automated DNA synthesizer and with the standard -cyanoethyl phosphoramidite coupling reaction. The ferrocenyl ODN (T12Fc) was synthesized by the coupling of amino-terminated ODN with the activated ester of ferrocenecarboxylic acid. A 16 mer ODN (e16S), which has ﬁve successive phosphorothioate units on its 50 -terminus, was synthesized using Beaucage’s reagent

SCHEME 3 The electrochemical gene sensing system based on the formation of complementary sandwich-type complex. (a) Target DNA combines the ferrocenyl ODN with the probe ODN on the electrode. Redox currents due to the surface-conﬁned ferrocenyl units should reﬂect the concentration of the target. (b) Ferrocenyl units are not deposited onto the electrode using nontarget DNA.

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and was anchored on an Au electrode via chemisorption as conﬁrmed by the IR-RAS measurements (Fig. 2). CV measurements for the [Fe(CN)6 ]4=3 redox couple on the bare and the ODN-treated Au electrodes revealed that the peak currents due to the reversible electrode reaction of the redox couple were signiﬁcantly suppressed by the treatment with e16S. In contrast, the Au electrode treated with e16, which does not have any sulfur atoms, showed almost no suppression. We can conclude that derivatization of the phosphate moieties to phosphorothioates enables us to immobilize the entire DNA entity on Au surfaces. Treatment of the e16S-modiﬁed electrode with a 50 M aqueous solution of an equimolar mixture of T12Fc and t19 to form the sandwich-type complex makes the surface adlayer electroactive. As shown in Fig. 12, the modiﬁed electrode exhibited a reversible wave which was consistent with a surface-conﬁned redox-active species. Integration of the charge under the anodic peak gave the amount of the bound T12Fc of 22–55 p mol cm2 while the peak separation (50 mV) corresponded to the heterogeneous rate constant of 0.6 s1 [29]. The formal potential was +645 mV (vs. Ag/AgCl) and was exceedingly positive compared with that in bulk solution (+430 mV vs. Ag/AgCl). Such a large positive shift may suggest that the free anions, which would be a counteranion of the newly generated ferrocenium cation, are extremely limited in a microenvironment in the highly concentrated ODN layer on the electrode surface. Based on a differential pulse voltammetric measurement (Fig. 13), the target sample, t19, gave a redox wave that agreed with the CV one. On the other hand, the mismatch control sample, m19, was in striking contrast to t19; the e16S-modiﬁed electrode treated with T12Fc–m19 also showed a redox wave but only slightly. The amount of charge passed during the oxidation was 5% of that observed for T12Fc–t19. For the case of the control sample, c19, DPV measurements gave results similar to that of m19 (data not shown). There was a clear difference between the target and the nontarget samples in their DPV responses when the resulting electrodes were operated or treated under

FIG. 12 Cyclic voltammogram for Au electrode modiﬁed with e16S–t19–T12Fc ternary complex. Electrolyte solution, aqueous 0.1 M KCl; scan rate 25 mV s1 ; temperature, 58C; electrode area, 0.02 cm2 (geometrical).

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FIG. 13 Differential pulse voltammograms for Au electrode modiﬁed with e16S–t19–T12Fc ternary complex (ﬁlled circle) and e16S–m19–T12Fc mismatch complex (open circle). Pulse amplitude, 50 mV; pulse width, 50 ms; pulse period, 200 ms. Other conditions are the same as those in Fig. 12.

raised temperatures. For example, the current peak for the target sample, T12Fc–t19 was only slightly changed by rinsing the electrode with 100 mM KCl solution at 58C and 108C while a similar treatment at 208C signiﬁcantly decreased the peak current ca. to 25%. Contrary to the sample target, the small peaks observed for the T12Fc–m19 and the T12Fc–c19 duplexes scarcely changed using a similar treatment. The difference in temperature dependence of the DPV signal between the target and the controls indicates that the driving force behind the redox-active adlayer formation is different. The target was recognized by means of complementary basepairing with the ODN immobilized on the electrode, providing the speciﬁc sandwich-type ternary complex including the probe, T12Fc, on the electrode surface. Meanwhile, the slight current observed in the controls should be ascribed to the nonspeciﬁc binding of T12Fc–c19 and –m19 to the ODN. Optimizing the measurement conditions such as temperature, salt concentration or coexisting nonspeciﬁc binding blocker (mRNA or sonicated calf thymus DNA) should promise a signiﬁcant development in the selectivity of this sensing system.

VI.

SUMMARY

The study of nucleic acids has become a broad area spanning many diverse ﬁelds of science. Signiﬁcant progress which has been made in recent years clearly shows important directions for study of DNA-modiﬁed electrode. For example, the nucleic acid ligand (aptamer), an oligonucleotide that has ranged from 8 to 120 nucleotides in length and exhibits high-afﬁnity speciﬁc binding with selected target molecules [30] should ﬁnd use in biosensor applications as a chemoreceptive element. The accumulated knowledge and practice of microelectrodes should contribute to the successful development of oligonucleotide arrays (DNA chips) [28] that enable rapid DNA sequence analysis and multilocus DNA screening.

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ACKNOWLEDGMENTS I thank colleagues and collaborators including Professor Makoto Takagi (Kyushu University), Professor Mizuo Maeda (Kyushu University), Professor Yoshiki Katayama (Kyushu University), Professor Toshihiro Ihara (Kumamoto University), Dr. Hiroaki Taira, Yoshiharu Mitsuhashi, Shinji Uchida, Masamichi Nakayama, Mitsuru Murata, and Hiroshi Irie for their work, help, discussions, and encouragement in the investigation of DNA-modiﬁed electrode. Financial support by a Grant-in-Aid for Scientiﬁc Research from the Ministry of Education, Science, Sports, and Culture of Japan is gratefully acknowledged.

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22 Phospholipids at Liquid^Liquid Interfaces and Their E¡ect on Charge Transfer ¨ KI Department of Chemical Technology, Helsinki LASSE MURTOMA University of Technology, Espoo, Finland ´ Department of JOSE´ A. MANZANARES and SALVADOR MAFE Thermodynamics, University of Valencia, Burjasot, Valencia, Spain ¨ STI KONTTURI Department of Chemical Technology, Helsinki University KYO of Technology, Espoo, Finland

I.

INTRODUCTION

Phospholipid monolayers provide a convenient model system for studying molecular interactions in the lipid backbone of biomembranes [1,2]. Traditionally, monolayers are studied by Langmuir techniques, i.e., spreading them on an aqueous surface and following the surface pressure of the ﬁlm as a function of the monolayer compression. The advantage of spreading a monolayer on an water–oil interface is that due to weaker cohesion among the hydrocarbon chains of lipid molecules, interactions can be followed over a larger range of molecular separations [3]. Langmuir ﬁlm studies of phospholipids have given valuable information of the phase transitions of the lipids as a function of monolayer composition, temperature, and the aqueous phase composition and pH [4]. In the study of ion transfer across a lipid monolayer, electrochemical methodology becomes more convenient than Langmuir techniques. This is accomplished by the use of an organic solvent phase which allows sufﬁcient dissociation of organic salts into free ions and is nonpolar enough to prevent signiﬁcant partitioning of aqueous electrolytes. Monolayers are then either adsorbed on the interface from the bulk organic phase or directly added to the interface after which the establishing of an adsorption equilibrium has to be waited for, which may take several hours. Electrochemical studies of phospholipids deposited at the interface between two immiscible electrolyte solutions (ITIES) have recently been reviewed by Kakiuchi [5] who has also mostly been responsible for the work carried out in this area during the last two decades. This chapter is basically divided in two parts, namely, the study of surface pressure– molecular area ( AÞ isotherms of phospholipids at ITIES and their effect on ion transfer. In the ﬁrst part, the emphasis is put on topics which have been left out from Ref. [5], i.e., Langmuir ﬁlm techniques and theoretical modeling of A isotherms, as well as on the latest progress in the ﬁeld, especially on experiments that combine Langmuir techni533

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ques with electrochemical methods. In the second part, the emphasis is put on the theoretical background of the description of interfacial ion transfer and how the perturbation of the electrical double layer at the ITIES due to the adsorbed phospholipids can modify the rate of ion transfer. The effect of the phospholipids on the rate of ion transfer has been controversial over the last years. While the early studies found a retardation effect [6–8], more recent ones reported that the rate of ion transfer is either not retarded [9,10] or even enhanced due to the presence of the monolayer [11–14]. Furthermore, the theoretical efforts to explain this effect were unsatisfactory. The retardation observed in the early studies was explained in terms of the blocking of the interfacial area by the phospholipids, and therefore was related to the size of the transferring ion and the state of the monolayer [8,15]. The enhancement observed in the following years was attributed to electrical double layer effects, but a Frumkin-type correction to the Butler–Volmer (BV) equation was found unsuitable to explain the observations [11,16]. Recently, Manzanares et al. showed that the enhancement can be described by an electrical double layer correction provided that an accurate picture of the electrical double layer structure is used [17]. This theoretical approach will be the subject of Section III.C.

II.

pA ISOTHERMS AT LIQUID–LIQUID INTERFACES

A.

Literature Review

The ﬁrst modern studies of phospholipids at the water–oil interface date to the 1960s when Brooks and Pethica constructed a Langmuir trough which was operated at the water–oil interface [18]. Later, a systematic study of isotherms of the lecithin (phosphatidylcholine) monolayers at the aqueous NaCl–n-heptane interface was carried out in two collaborative research groups at Unilever research laboratories and in Washington University, St. Louis (see, e.g., Refs 3,19, and 20, and references therein). Based on over 2000 isotherm runs, the phase transition from the liquid expanded to the liquid condensed state (Fig. 1) was concluded to be of second order in character [3] (see Section II.C). At surface pressures below the transition point, A isotherms were reported to be independent of the length of the acyl chain and salt concentration or pH of the aqueous phase, but dependent on the temperature and the polar headgroup [19]; in the last case a comparison was made with cephalin with the same acyl chain length [3]. This high area behavior could not be completely explained, but was partly accounted for by dipole–dipole interactions of the zwitterionic headgroup [19,20]. The transition point was shifted towards lower surface pressures and higher molecular areas as the chain length was increased (see Fig. 2). The heat (enthalpy) of phase transition, as calculated from the 2D Clapeyron equation H ¼ TðAt AS Þd=dT

ð1Þ 1

also increased with the increasing chain length from ca. 20 to 100 kJ mol [20]. In Eq. (1), At is the molecular area of the lipid at the transition, AS is the molecular area in the solid lipid phase, taken as 47 A˚2 , and T is the absolute temperature. The next development on water–oil isotherms was presented by Mo¨hwald’s group at the Max-Planck Institute in Berlin [21,22]. They investigated monolayers of dipalmitoyl phosphatidylethanolamine (DPPE) at interfaces of water and hydrocarbons n-dodecane (C12 , n-hexadecane (C16 ), and bicyclohexyl (BCH). The transition pressure was increased and the molecular area at transition decreased in the order C16C12 – BCH. Also the heat of transition was decreased in the same order, and was more strongly decreasing with

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FIG. 1 A isotherms for 1,2-distearoyl lecithin at the water–n-heptane interface at different temperatures (8C, shown on the curves). (Reproduced from Ref. 20 with permission from The Royal Society of Chemistry.)

FIG. 2 Composite plot of A isotherms for various-chain-length lecithins typically at 208C (Reproduced from Ref. 20 with permission from The Royal Society of Chemistry.)

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temperature as in the case of n-heptane [20]. These phenomena were interpreted by a stabilization of the ordered phase [21] so that longer-chain alkanes created a more stable ordered phase. During the isotherm runs, ﬂuorescence micrographs were taken [21,22]. The micrographs clearly showed that in the plateau region of the lipid, aggregates were formed whose size increased as the compression proceeded. In the case of C16 , the aggregates were not of a regular shape and fused together rather easily, while in the other cases the aggregates were round and repelled each other. It was concluded that C16 was dissolved in the condensed phospholipid phase and squeezed out on further compression. For C12 and BCH a pure lipid phase was readily achieved on compression. This was explained by the size of the solvent molecules: hydrocarbons with the same length as the aliphatic tail of the lipid accommodate themselves between the tails also in an ordered phase. Since optical measurements of monolayers at the water–oil interface are rather difﬁcult to carry out, a conﬁguration was suggested where a monolayer at the water–air interface was in contact with an oil lens which was partly wetting the monolayer [23]. The thermodynamic relation between this monolayer and that residing at the water–oil interface was discussed. This conﬁguration was utilized in the X-ray diffraction experiments [24] where the structural changes of dipalmitoyl phosphatidylcholine (DPPC) and DPPE were followed. The interfacial tension of the water–oil interface can easily and accurately be measured by the axisymmetrical drop shape analysis of the image of a pendant drop [25] whose size can be controlled. Li et al. [26] introduced this technique in the study of DPPC monolayer at the water– n-dodecane interface. The advantage of the pendant drop techniques is that dynamics of the lipid organization can more easily be followed than in a Langmuir trough. The isotherm obtained agreed with that measured in a Langmuir trough. Recently, Wege et al. [27] described a complete apparatus similar to that of Ref. [26], and showed isotherms of distearoyl phosphatidylcholine (DPSC) and DPPC. No proper dynamic experiments were, however, performed. Quite recently, Allen et al. [28] followed the relaxation of the DSPC monolayer at the water–1,2-dichloroethane (DCE) interface as a function of the interfacial Galvani potential difference and lipid concentration. These experiments are described in greater detail in the next section. B.

Novel Experimental Techniques

The area of the lipid covered interface can be adjusted in a very precise fashion as mentioned above [28]. In the method [9], a microsized aqueous droplet is formed at the tip of a microsyringe by extrusion into an organic phase, 1,2-DCE. The size of the droplet can be stepped via a syringe plunger connected to a piezoelectric driver. Electrodes are placed in the two solvent phases containing some appropriate electrolyte. On expansion of the droplet, a current transient is observed where the ﬁrst 50 ms can be assigned to the charging of the freshly formed interface after which current decays under diffusion control. The direction of the current depends on the cell potential, and the potential where the sign of the current changes can be regarded as the potential of zero charge. On contraction a current transient with the opposite sign is observed. After addition of lipid DSPC into the organic phase a monolayer is formed at the interface, and the steady-state current increased at all potentials. On expansion, the time constant of the charging current is reduced to ca. 5 ms and a shift of ca. 100 mV is observed in the potential of zero charge. From the video image of the droplet a highly distorted and heterogeneous interface is seen which relaxes after the fast stage (a few

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seconds) very slowly. A smooth interface is observed again after ca. 20 min. For the quantitative determination of the relaxation dynamics a method was developed where an air bubble is dispersed inside the microsyringe. Hence the changes of the interfacial tension are reﬂected in the vapor pressure (or size) of the air bubble [29]. Dynamic surface tension has also been measured by quasielastic light scattering (QELS) from interfacial capillary waves [30]. It was shown that QELS gives the same result for the surface tension as the traditional Wilhelmy plate method down to the molecular area of 70 A˚2 . QELS has recently utilized in the study of adsorption dynamics of phospholipids on water–1,2-DCE, water–nitrobenzene and water–tetrachloromethane interfaces [31]. This technique is still in its infancy in liquid–liquid systems and its true power is to be shown in the near future. C.

Theoretical Modeling

There is an abundance of literature on theoretical – usually statistical mechanical – models to describe phase transitions of amphiphilic monolayers; these phenomena have been reviewed by Bell et al. [32]. Bell and coworkers [33] were ﬁrst to interpret the secondorder phase transitions of lecithins observed at the water–oil interface [3,19] with a lattice gas model. By the second-order transition is meant a discontinuity in the slope d=dA without an associated discontinuity in the monolayer density. In their model, lipid molecules could have two different orientations. Molecules with similar orientation had attractive, and in the opposite orientation, repulsive interaction energy. In the model, there was also an orientation-independent energy term which might take positive or negative values [33]. Interactions only with the nearest neighbors were considered. The co-ordination number z, i.e., the number of nearest neighbors, was taken to be six, corresponding to a 2D triangular lattice. The model was able to explain the observed phase transitions only qualitatively due to simpliﬁcations and the statistical approximations made. The difference between the ‘‘expanded’’ and ‘‘condensed’’ state was shown to be the degree of order, deﬁned as ðN2 =N1 Þ1=z , where N1 and N2 are the numbers of molecules in different orientations. The interaction energy parameters mentioned above were temperature dependent, indicating that they should be regarded as free energies with an entropy term included, rather than as simple energy parameters. The lattice gas model of Bell et al. [33] neither gave any detailed mechanism of the orientational ordering nor separated the contributions of the headgroup and the acyl chain. Lavis et al. [34] discussed Ref. 33 critically and concluded that the sharp kink point in the isotherm at transition was an artifact of the mean ﬁeld approximation used. An improved correspondence to experimental data was claimed by the use of the real-space renormalization group method [35]. The same authors returned to the problem [35] and concluded that in addition to the orientation of the molecules, chain melting had to be included in a model which could interpret the phase transitions. In monolayers of charged or zwitterionic amphiphiles, electrostatic interactions become important because they extend over longer range than the nearest neighbors. Stigter and Dill [36,37] considered the low surface pressure region of the isotherms of Ref. 19. Based on the temperature dependence of the coefﬁcients which were determined ﬁtting the experimental data to a virial equation of state, the orientation of the electrical dipole moment of phosphatidylcholine (PC) or phosphatidylethanolamine (PE) headgroups at the water–n-heptane interface was studied. It was concluded that the ammonium group at the end of the headgroup becomes increasingly submerged in the oil phase with increasing temperature which gives raise to a strong repulsive force between the PC head-

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groups. For the PE headgroup orientation is weaker which results in smaller lateral repulsion, explaining also the higher melting temperature of high-density PE monolayers. Cantor and Dill [38] worked out a theoretical model for the interaction among the phospholipids in bilayers and monolayers that considers four area-dependent contributions to the interfacial free energy: the two-dimensional (2D) translation of the surfactants in the plane of the interface due to the 2D entropy of mixing of the surfactants with solvent, the headgroup interactions, the intramolecular interactions due to the chain conﬁgurations, and the volume dependence of chain packing. The theoretical approach can describe quantitatively the pressure–area isotherms and phase transitions of monolayers of lecithins having different chain lengths as well as predict temperatures, area, volume changes, and enthalpies of melting of the corresponding bilayers. Ruckenstein and Li proposed a relatively simple surface pressure–area equation of state for phospholipid monolayers at a water–oil interface [39]. The equation accounted for the clustering of the surfactant molecules, and led to second-order phase transitions. The monolayer was described as a 2D regular solution with three components: singly dispersed phospholipid molecules, clusters of these molecules, and sites occupied by water and oil molecules. The effect of clusterng on the theoretical surface pressure–area isotherm was found to be crucial for the prediction of phase transitions. The model calculations ﬁtted surprisingly well to the data of Taylor et al. [19] in the whole range of surface areas and the temperatures (Fig. 3). The number of molecules in a cluster was taken to be 150 due to an excellent agreement with an isotherm of DSPC when this

FIG. 3 A isotherms measured for ﬁve lecithins at 158C. (Experimental data from Ref. 20. Reproduced from Ref. 39 with permission from The American Chemical Society.)

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number was used. The free energy of transfer of a lipid molecule from singly dispersed state to the bulk of a cluster varied between 4 kJ mol1 ðC14 Þ and 25 kJ mol1 ðC22 Þ, decreasing slightly with increasing temperature. Mafe´ et al. considered the phospholipid adsorption and surface pressure–area isotherms at interfaces using two models that incorporated a minimum number of adjustable parameters and predicted ﬁrst-order phase transitions [40]. The ﬁrst model was based on the 2D lattice statistics of binary solutions and the molecular parameters introduced were the energy change involved in the mixing process of the phospholipid and organic solvent molecules and the phospholipid head effective area. The state of aggregation of the lipids at the interface was showed by evaluating the difference in the number of solvent–lipid interactions between a random distribution of lipids and that predicted by a quasichemical approximation. The second model made use of a nonlocalized adsorption model for the calculation of the surface concentration of the phospholipids at the interface as a function of the volume concentration in the organic solvent phase, and a 2D hard disks gas model with a mean-ﬁeld term accounting for the attractive interactions between the tails of the adsorbed phospholipids. The equation of state predicted by this second model was the 2D van der Waals (vdW) equation uA ð2Þ þ 0 2ex ðA Aex Þ ¼ kT 2A where Aex is the excluded area of a phospholipid head and u0 is the interaction energy between the phospholipid tails. When the theoretical results were compared with experimental data for the water–1,2-DCE and water–air interfaces [41], the two models appeared to predict correctly the qualitative features of the experimental isotherms (Fig. 4).

FIG. 4 A isotherms measured for DSPC at water–1,2-DCE (*) and water–air (*) interfaces from Ref. 41 and simulated with a real gas model [40]: ideal gas with Aex ¼ 0 and u0 ¼ 0 (thin solid line), hard disks gas with Aex ¼ 40 A˚2 and u0 ¼ 0 (thick solid line), vdW gas with Aex ¼ 40 A˚2 and u0 =kT ¼ 3 (thin dashed line), and vdW gas with Aex ¼ 40 A˚2 and u0 =kT ¼ 7 (thick dashed line). The inset shows part of the thick dashed line. (Reproduced from Ref. 40 with permission from Elsevier Science.)

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III.

ION TRANSFER ACROSS ITIES IN THE PRESENCE OF ADSORBED PHOSPHOLIPIDS

A.

Literature Review

Monolayers of organic surfactants at water–air interfaces are known to decrease the rate of solute transfer across them [42,43]. Similarly, the studies on ion transfer across lecithin and protein monolayers at ITIES found a retardation effect [6–8]. The ﬁrst studies of ion transfer across monolayers of pure lipids at ITIES showed that the state of monolayer has a great effect on the rate of ion transfer. Monolayers in an expanded state appeared to be completely transparent to the transfer of small ions [5], while those in a condensed state decreased the rate of ion transfer. Long hydrophobic tails (large attractive interaction between lipids), low temperatures, and large size of the transferring ion were identiﬁed as factors decreasing the rate of ion transfer [11,15]. Hence, the blocking effect observed with egg yolk lecithin monolayers could be attributed to the fact that this mixture of natural phospholipids forms a more closely packed structure than pure lipids. In some cases, an acceleration of the rate of ion transfer was observed [12]. Kakiuchi et al. [11,16] studied by AC impedance perchlorate, tetramethylammoniun (TMAþ ), and tetraethylammonium (TEAþ ) ion transfer across water–nitrobenzene interfaces covered by different PCs in the temperature range 58C < t < 308C. Short-tail lipids, such as DLPC and DPPC, showed a clear enhancement of the rate of ion transfer (Fig. 5). Kontturi et al. studied TEAþ ion transfer across water–1,2-DCE microinterfaces covered by different PCs using short potential step techniques [12]. The enhancement in the forward rate constant was observed for all lipids and increased with the surface coverage (Fig. 6). Chesniuk et al. studied the transfer of alkali and alkaline-earth cations across phospholipid monolayers at water–1,2-DCE macrointerfaces by cyclic voltammetry. These authors considered the effect of the cation nature, the concentration of the transferring ion, and the applied potential (at the positive end of the polarization window), and noticed either an enhancement of the current or a blocking of the transfer process [13,14]. The enhancement factors observed were very much larger than in other studies, especially at

FIG. 5 Enhancement factor observed in the forward rate constant for TMAþ (*) and TEAþ (&) ion transfer at the water-nitrobenzene interface due to the presence of different PCs. (Experimental data are taken from Ref. 11 and correspond to 308C.)

Phospholipids at Liquid–Liquid Interfaces

541

FIG. 6 Enhancement factor observed in the forward rate constant for TEAþ ion transfer at the water–1,2-DCE interface due to the presence of PCs: DLPC (*), DMPC (&), DPPC (~), and DSPC (!). (Experimental data are taken from Ref. 12.)

low applied potentials and at low concentrations of the transferring ion. A noteworthy difference between this and previous studies is that the transfer of the supporting electrolyte ions themselves, and not a tracer ion added to the supporting electrolyte solution, was studied.

B.

Novel Experimental Techniques

Since the state of the lipid layer was known to have a great effect on the rate of charge transfer through the layer, Grandell and Murtoma¨ki designed a novel type of Langmuir trough to achieve simultaneous electrochemical and surface pressure control [41]. Organic solvent phases previously used in the liquid–liquid Langmuir troughs are electrochemically unsuitable because they either do not dissolve electrolytes or exhibit a narrow polarization window. 1,2-DCE was used as the organic phase and isotherms of the DSPC monolayer were measured. Due to the high solubility of the lipid in the organic phase, or the high mobility of the small solvent molecules within the ﬁlm, the surface pressure remained rather low, ca. 20 mN m1 , at maximum compression. In the subsequent paper [10] isotherms were recorded under potential control and the observed potential dependent adsorption of the lipid agreed with that measured earlier [44]. The effect of the monolayer on the transfer rate of the two probe ions, cationic propranolol and anionic picrate, was practically insigniﬁcant, even at maximum values of surface pressure reached [45]. An inherent problem with the electrochemical Langmuir trough is its uneven potential distribution [45]. Therefore, a Langmuir–Blodgett approach was designed to achieve a known surface pressure for the ﬁlm under study. A lipid ﬁlm is spread at the water–air interface and compressed to a desired surface pressure, after which an electrochemical cell containing an o-nitrophenyltoctylether gel is dipped through the ﬁlm into the aqueous phase. A lipid ﬁlm is transferred on the top of the gel thus forming a lipid coated liquid– liquid interface [46]. Preliminary results show the retardation of the propranolol transfer, whereas the rate of TEAþ cation remained unaltered.

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More recently, Manzanares et al. [17] presented additional experimental evidence of the enhanced cation transfer across a hemispherical water–1,2-DCE interface covered with DSPC by using a syringe experimental set up described elsewhere [9,28]. Figure 7 shows the cyclic voltammograms measured in the cell [17],

before (a) and after (b) the addition of DSPC. The organic supporting electrolyte is tetrapentylammonium tetrakis-(4-chlorophenyl)borate. The carbonate–bicarbonate buffer sets the pH at 8.7, where the headgroup of this phospholipid is in zwitteronic form. It is observed that the current density increases at both sides of the window. At the positive side of the window, Liþ ion transfer from the aqueous to the organic phase. The enhancement factor (i.e., the ratio of current densities) observed for Liþ ion tranfer varies slightly with cell potential, and takes values between 5 and 10, thus being of the same order as those observed in Refs. 11 and 12. An analogous apparatus to that of Ref. 9 was used to follow the effect of the lipid monolayer on the rate of electron transfer (ET). In this setup [47], an organic phase droplet (1,2-DCE) is continuously expanded into the aqueous phase, and the resulting current transient was monitored in the absence and presence of the adsorbed lipid monolayer. The rate of ET was decreased as a function of the lipid concentration. Perhaps the most important experimental progress made recently in electrochemistry was the introduction of a scanning electrochemical microscope (SECM). Tsionsky et al. have used SECM to study also the rate of ET across a lipid monolayer at the water– benzene interface [48,49]. The presence of the monolayer decreased the rate of ET, being the decrease more signiﬁcant for longer hydrocarbon chains and larger lipid concentration in solution. It was thus concluded that the ET reaction does not occur at defect sites in the lipid monolayer.

FIG. 7 Comparison of cyclic voltammograms recorded at 1 mV/s before (a) and after addition (b) of 59 M DSPC to the organic phase. (Reproduced from Ref. 17 with permission from Elsevier Science.)

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C.

Theoretical Modeling

1.

Kinetics of Interfacial Ion Transfer

543

The description of the ion transfer process is closely related to the structure of the electrical double layer at the ITIES [50]. The most widely used approach is the combination of the BV equation and the modiﬁed Verwey–Niessen (MVN) model. In the MVN model, the electrical double layer at the ITIES is composed of two diffuse layers and one ion-free or inner layer (Fig. 8). The positions delimiting the inner layer are denoted by xo2 and xw2 , and represent the positions of closest approach of the transferring ion to the ITIES from the organic and aqueous side, respectively. The total Galvani potential drop across the interfacial region, wo w o , is then decomposed as w0 ¼ od þ wo 2 þ wd

ð3Þ

The elementary step of ion transfer is considered to take place between positions xo2 and xw2 , and therefore the electrical potential drop affecting this transfer is wo 2 . The ion transfer involves the renewal of the solvation shell. The change in standard chemical potential w0 0i associated with this process takes place over very short distances in the interfacial region [51] and can be assumed to occur between positions xo2 and xw2 . Thus, the BV equation for the ﬂux density Ji of an ionic species i is [52] h i w w 0 2 w 0 ð4Þ Ji ¼ k0i ci ðxw2 Þezi f ðo 2 o i Þ ci ðxo2 Þeð1Þzi f ð0 2 o i Þ where k0i is the true standard rate constant, ci ðxw2 Þ and ci ðxo2 Þ are the molar concentrations of the transferring ion at positions xw2 and x02 , zi is its charge number, is the forward transfer coefﬁcient, and f F=RT, where F is Faraday’s constant, R is the gas constant, and T is the absolute temperature. Alternatively, the ﬂux density Ji can be expressed in terms of the ion concentrations, cwi and coi at the positions xw0 and xo0 just outside the diffuse layers, and the total Galvani potential difference wo . In this case, the BV equation takes the form [53,54] h i w w 0 w w 0 Ji ¼ k0i;app cwi ezi f ðo o i Þ coi eð1Þzi f ðo o i Þ ð5Þ where

FIG. 8 Schematic representation of the electrical potential proﬁle ðxÞ at the ITIES. The potential drops are: od in the organic diffuse layer xo0 < x < xo2 , wo 2 in the inner layer xo2 < x < xw2 , and wd in the aqueous diffuse layer xw2 < x < xw0 .

Murtoma¨ki et al.

544 w

o

k0i;app ¼ k0i eð1Þzi f d ezi f d

ð6Þ

is the apparent standard rate constant. Since the potential drops wd ¼ w w2 and od ¼ o2 o are different to each other, the apparent rate constant k0i;app differs from the true constant k0i even when ¼ 1=2. Note that Eqs. (4) and (5) implicitly consider the transfer across the interface as the rate-determining step in the ion transfer processes [51], and neglect other steps involved in the process such as the ion transport across the diffusion boundary layers [55] and across the diffuse electrical double layer [50]. 2. Electrostatic Enhancement of the Ion Transfer Due to the Presence of Phospholipids According to Eq. (5) the rate of interfacial ion transfer is determined by the rate constant k0i , the interfacial concentrations ci ðxw2 Þ and ci ðxo2 Þ, and the potential difference w0 2 2o 0i . The phospholipids adsorbed at the ITIES are likely to modify one or several of the above factors, and hence the rate of ion transfer. The rate constant k0i depends on the nature of the transferring ion and the solvents, and would be expected to change when the phospholipid monolayer is so condensed that the state of the solvents at the interface is modiﬁed. The local concentrations ci ðxw2 Þ and ci ðxo2 Þ depend on the concentrations in the respective bulk phases and the electrical potentials w2 and o2 ; other effects might also become important in highly condensed monolayers. Thus, phospholipid headgroups bearing electrical charges (either net or zwitteronic charge) are expected to modify the local concentrations. Similarly, these electrical charges could also affect the value wo 2 . From a practical point of view, the potential drop across the inner layer wo 2 must be determined by ﬁtting the experimental data to the equations derived from this theoretical approach, which led to some controversy about its value [53,54,56,57]. For the sake of simplicity, and also because recent studies of the ITIES structure do not conﬁrm the presence of an inner layer [51,58], we neglect the ﬁnite size of the transferring ion and take xw2 ¼ xo2 ¼ 0 and wo 2 ¼ 0. This is equivalent to accepting that the potential difference wo 2 wo 0i is not modiﬁed by the presence of the phospholipids. Phospholipid monolayers in liquid expanded state are likely to modify mostly the interfacial concentrations, and this electrostatic effect can be described by Eq. (6). Taking 1=2, in agreement with most experimental results, and introducing the approximation wo 2 ¼ 0, Eq. (6) simpliﬁes to [59] ~

k0i;app ¼ k0i ezi f ð0Þ

ð7Þ

where ~ð0Þ ð0Þ ð w þ o Þ=2 and ð0Þ is the potential at the ITIES. The exponential factor in Eq. (7) can result in either a decrease or an enhancement of the rate of ion transfer. For every value of wo , we deﬁne the enhancement factor as k0i;app ðpresenceÞ ¼ ezi f ½ ð0Þpresence ð0Þabsence k0iapp ðabsenceÞ

ð8Þ

and compare it to the ratio of currents across the ITIES in the presence and in the absence of phospholipids. Note, ﬁnally, that condensed monolayers could also modify the true standard rate constant k0j , which would account for the observed partial blocking of the ion transfer [8,15]. The present study, however, is restricted to the electrostatic effect.

Phospholipids at Liquid–Liquid Interfaces

3.

545

The Electrical Potential Distribution at the ITIES in the Presence of Zwitterionic Phospholipids

When a monolayer of phospholipids is adsorbed at the ITIES, there must be a modiﬁcation of the electrical structure of the interface [60]. Since we aim at describing the effect of this monolayer on the rate of ion transfer in a simple way, we assume a sharp interface also in the presence of phospholipids. The hydrophobic tails are located in the organic phase (negative x region), and the hydrophilic headgroups are located in the aqueous phase (positive x region). A key issue in the description of the monolayer is the orientation of the zwitterionic headgroups. At water–air interfaces, Standish and Pethica [61] showed that the headgroup is oriented parallel to the interface. In lipid bilayers in electrolyte solutions, however, Ashcroft et al. concluded [62] and that the phosphatidylcholine headgroup changed its orientation with respect to the membrane–solution interface from normal in 1 mM KCl to parallel in 1000 mM KCl (see also Ref. 63). Taking into account that the dipole moment of the phosphatidylcholine headgroup has been estimated to be 19 D [64], even a small inclination will produce a large effect on the electrical potential distribution at the interface. Therefore, the orientation of the headgroups might be approximately but not exactly parallel to the interface, with the negative phosphonic groups closer to the ITIES and the positive amine groups further away into the aqueous phase. Following previous work on the electrostatic properties of lipid membranes [61] and zwitteronic micelles [65,66] and surfaces [63], and considering the aqueous supporting electrolyte concentration to be in the range 10–1000 mM, we propose a value of 3 to 4 A˚ for the distance d between the positive and negative charges in the headgroup in the direction normal to the interface. For the sake of simplicity, the negative phosphonic groups are considered to be located at the ITIES, x ¼ 0, and therefore a negative charge density is associated to this plane. Similarly, a charge density > 0 is associated with the plane x ¼ d corresponding to the amine groups. Moreover, since the headgroups are likely to affect the water structure in the interfacial region, a dielectric permittivity "i 30"0 , where "0 is the vacuum permittivity, is considered in this region [61,67]. When the ITIES is polarized with a potential difference wo , there is a separation of electrical charge across it. According to the Gouy–Chapman theory, the charges in the aqueous and organic diffuse layers are related to the potential drops wd and od in the respective layers by the equations qw ¼

2"w w f wd sinh f 2

qo ¼

2"o o f od sinh f 2

ð9Þ

ð10Þ

where w ¼ ð2F 2 cw ="w RTÞ1=2 and o ¼ ð2Fc2 o="o RTÞ1=2 are the reciprocal Debye lengths in the aqueous and organic electrolyte solutions; cw and co denote the concentrations of the supporting electrolytes in the respective phases. In the absence of phospholipids, the condition qo þ qw ¼ 0 allows us to evaluate the surface potential as [68,69] w r1 f o

~ tanh

ð0Þ ¼ 2arctanh ð11Þ rþ1 4 where r "w w =ð"o o Þ.

Murtoma¨ki et al.

546

The presence of the phospholipids modiﬁes the electrical double layer and the evaluation of the surface potential ~ð0Þ requires then the solution of the PB equation in the aqueous region in between the two planes of charge, 0 < x < d [59]. The inﬂuence of the phospholipids is expected to be the largest when the ionic strength of the solutions is low, since then there are fewer ions to screen the zwitterionic charges. Furthermore, the effect of the phospholipids is determined by the charge separation due to the polar headgroups in relation to the charge separation due to the applied potential difference wo . Since the latter is larger for higher applied potentials, it is expected that the effect of the phospholipids decreases with increasing wo . Considering that the ions of the aqueous supporting electrolyte can be present in the region 0 < x < d, the PB equation takes the form 2 d2

¼ i sinh½f ð w Þ ð12Þ 2 dx where i ¼ ð2F 2 cw ="i RT Þ1=2 is the reciprocal Debye length of this region, and the boundary conditions for this equation are d

¼ qo ð13Þ "i dx x¼0þ i d

" ¼ þ qw ð14Þ dx x¼d

f

where qo and qw are given by Eqs. (9) and (10) with wd ¼ w ðdÞ and od ¼ ð0Þ o . The integration of Eq. (12) from x to x ¼ d yields the following relation between the electrical potential ðxÞ and its gradient d =dx: 2 i i 2 2" f ð w Þ i d

w 2 i 2 w2 sinh " ¼ ð þ q Þ r q þ ð15Þ dx 2 f where Eq. (14) has been used and ri "i i =ð"w w Þ ¼ ð"i ="w Þ1=2 . This equation can be used to determine the potentials ð0Þ and ðdÞ for given values of and wo . The solution procedure starts with an intial guess of ð0Þ. Then, qw and ðdÞ can be obtained from i i 2 2 2 2 2" f ½ ð0Þ w sinh qw ð1 ri Þ qo þ 2ðqo þ qw Þ ¼ ð16Þ 2 f which results from Eq. (15) applied to position x ¼ 0þ and boundary condition Eq. (13). The initial guess of ð0Þ is then iteratively improved until the condition Zd

d

¼d d =dx

ð17Þ

0

is satisﬁed; note that d =dx can only vanish when qw is negative and large in magnitude. 4. Simulated Enhancement Factors The theory presented above accounts for the electrostatic effects on the apparent rate constant for ion transfer by relating the observed changes in k0i;app to changes in cwi ð0Þ, or equivalently to ð0Þ. In the following, we present the simulated electrical potential distributions and the corresponding enhancement factors for a cation transferring from the aqueous phase across the water–1,2-DCE interface ("wr ¼ 78:39; "or ¼ 10:36Þ. The rela-

Phospholipids at Liquid–Liquid Interfaces

547

tive permittivity of the interfacial region is estimated as "ir ¼ 30, and the separation between the charged plans is d ¼ 3A˚. The surface charge concentration is expressed as a molecular area for the zwitterionic headgroups, with values ranging from condensed (a ¼ 50 A˚2 , ¼ 32:0 C=cm2 Þ to very dilute (a ¼ 150 A˚2 , ¼ 10:7 C/cm2 ) monolayers. Figure 9 shows the electrical potential and the space charge density proﬁles for concentrations cw ¼ 1000 mM and co ¼ 20 mM and Galvani potential difference f wo ¼ 5 in the absence (a) and in the presence (b) of a phospholipid monolayer with a molecular area of 150 A˚2 ( ¼ 10:7 C=cm2 Þ. The ITIES has been marked with a continuous vertical line, and the plane where amine groups are assumed to be located has been marked with a dashed line. The potential distributions in the region 0 < x < d are nonlinear due to the presence of aqueous ions. The phosphonic groups located at the ITIES makes the potential ð0Þ smaller in case (b) than in case (a), which according to Eq. (8) implies an enhancement of the rate of ion transfer. The space charge density proﬁles shown in Fig. 9 evidence clearly how strongly the presence of the phospholipids modiﬁes the ionic concentrations close to the ITIES. In particular it is observed that the charge density in the aqueous phase is positive in the absence of phospholipids (note that wo > 0Þ and becomes then large and positive in the interfacial region 0 < x < d and negative in the aqueous phase x > d when the phospholipids are present. From the integration of these proﬁles the charge distribution in the different regions can be evaluated as qo ¼ qw ¼ 2:85 C/cm2 in case (a) and qo ¼ 1:06 C/cm2 , qw ¼ 4:40 C/cm2 , qi ¼ 5:46 C/cm2 in case (b), which indicates that the excess positive charge in the interfacial region is of the same order as the charge density associated with the headgroups. Hence, the enhancement of the rate of ion transfer is attributed to a signiﬁcant increase of the interfacial concentration of the transferring ion. Figure 10 shows the enhancement factor, ezi f ½ ð0Þpresence ð0Þabsence , theoretically predicted for the concentrations cw ¼ 1000 mM, co ¼ 20 mM and different values of the phospholipid molecular area. The potential different varies from wo ¼ 0 to 10/f

FIG. 9 Simulated electrical potential and space charge density proﬁles at the water–1,2-DCE interface polarized at f wo ¼ 5 in the absence (a) and in the presence (b) of zwitterionic phospholipids. The supporting electrolyte concentrations are co ¼ 20 mM and cw ¼ 1000 mM. The molecular area of the phospholipids is 150 A˚2 , and the corresponding surface charge density is ¼ 10:7 C/cm2 . The distance between the planes of charge associated with the headgroups is d ¼ 3 A˚.

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FIG. 10 Simulated enhancement factor for monolayers of zwitterionic phospholipids with different molecular areas (shown on the curves) at the polarized water–1,2-DCE interface. The supporting electrolyte concentrations are co ¼ 20 mM and cw ¼ 1000 mM.

257 mV at 258C. As could be expected, the enhancement factor is larger when the surface charge density associated to the phospholipids is large compared to the charge density qo ¼ qw separated across the ITIES due to wo (in the absence of phospholipids). These results are in agreement with the experimental observations in Refs. 11 and 13. Figure 11 analyzes the effect of the electrolyte concentration in the aqueous phase, for ﬁxed electrolyte concentrations in the organic phase co ¼ 10 mM and 50 mM, and a Galvani potential difference f wo ¼ 5. These theoretical results are in agreement with the observations in Ref. 13. Moreover, it is shown that a decrease in the electrolyte concentration in the organic phase has a similar effect to a decrease in the electrolyte concentration in the aqueous phase.

FIG. 11 Simulated enhancement factor against electrolyte concentration in aqueous phase. The potential different across the water–1,2-DCE interface is f wo ¼ 5 and the electrolyte concentration in the organic phase is co ¼ 10 mM and 50 mM. The phospholipid molecular area is 50 A˚2 .

Phospholipids at Liquid–Liquid Interfaces

IV.

549

CONCLUSIONS

Phospholipid monolayers at liquid–liquid interfaces inﬂuence the charge transfer processes in two ways. On the one hand, the phospholipids constitute a barrier that blocks the process by impeding the transferring species to reach the interface [1,15,48]. On the other hand, the phospholipids modify the electrical potential difference governing the process [60]. While the ﬁrst inﬂuence invariably leads to a decreased rate, the second one might result in either a decreased or an increased rate of charge transfer. The net effect of the phospholipids on the charge transfer process depends on the state of the monolayer, and therefore studies with simultaneous electrochemical and surface pressure control are preferable [10,41,45]. The effect of phospholipid monolayers on the rate of charge transfer has been the subject of several experimental studies, but still there is a need for additional experimental evidence. For large molecular areas, the effect on the rate of ion transfer seems to be negligible [5]. An increasing surface concentration of lipids leads to liquid expanded states where the electrostatic effects are noticeable. An enhanced rate of ion transfer across monolayers of pure phospholipids has then been observed both for the cases of tracer [11,12] and supporting electrolyte ion transfer [13,17]. Finally, the blocking effect is dominant in liquid condensed monolayers [15]. A theoretical approach based on the electrical double layer correction has been proposed to explain the observed enhancement of the rate of ion transfer across zwitterionic phospholipid monolayers at ITIES [17]. If the orientation of the headgroups is such that the phosphonic group remains closer to the ITIES than the ammonium groups, the local concentration of cations is increased at the ITIES and hence the current observed due to cation transfer is larger than in the absence of phospholipids at the interface. This enhancement is evaluated from the solution of the PB equation, and calculations have been carried out for the conditions of the experiments presented in the literature. The theoretical results turn out to be in good agreement with those experimental studies, thus showing the importance of the electrostatic correction on the rate of ion transfer across an ITIES with adsorbed phospholipids. This type of theoretical analysis has been used also to study the effect of ionic surfactants and coadsorbed layers on the rate of ion transfer and the theoretical results have been again in agreement with experimental observations [59]. Thus, other experimental situations might be analyzed similarly. However, some comments must be stressed. The electrical double layer correction is based on the Gouy–Chapman theory, which leads to unrealistically high interfacial concentrations in most cases and therefore might overrestimate the enhancement factor. More importantly, other effects such as steric hindrance, giving rise to partial blocking of ion transfer are expected to overcome the electrostatic effects in condensed monolayers.

ACKNOWLEDGMENTS Financial support from the European Union under project No. FMRX-CT96-0078 and from the Ministry of Education and Culture of Spain under DGICYT project No. PB980419 is acknowledged. L. M. acknowledges the Academy of Finland for the research position.

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23 Biocatalysis in Liquid^Liquid Biphasic Media: Coupled Mass Transfer and Chemical Reactions MOHAMED GARGOURI Department of Biological and Chemical Engineering, National Institute for Applied Science and Technology, Tunis, Tunisia

I. A.

INTRODUCTION Biotransformation

The technological applications of biocatalysts have been steadily growing in recent decades [1,2]. Biocatalysis offers both organic synthesis and process engineering important advantages over traditional chemical catalysis. In fact, biocatalysts function under mild operating conditions with high regio-, stereo-, and reaction speciﬁcities [3,4]. The biotransformation process has been improved by signiﬁcant advances in biochemical engineering: advances in genetic and protein engineering, microbiological manipulations for the production of enzymes, and the use of biocatalysts in immobilized form and large-scale puriﬁcation methods. B.

Biotransformation in the Presence of an Organic Solvent

However, the transfer of this technology from laboratory to industrial scale requires advances in the engineering of biocatalysis environment, particularly when one or more components are poorly water soluble [5–8]. The use of organic solvent in the medium is one stategy that has been proposed for biocatalysis [9–15]. In the organic phase, the reactant has a much greater solubility than in the aqueous phase. This could signiﬁcantly reduce the volume of the reaction mixture. Enzymes and micro-organisms have been shown to be active in the presence of organic solvents [16–20]. Heterogeneous liquid–liquid media are attractive, particularly when the reaction involves water-soluble as well as sparingly water-soluble reactants [21–25]. The organic phase consists of the reactant alone or the reactant dissolved in a water-immiscible organic solvent. In other bioreactors, components are distributed differently between the phases. C.

The Advantages and Disadvantages of Two-Liquid Phase Systems

There are many advantages of two-phase systems over aqueous systems when they are used as biocatalysis media [21,22,26,27]; components (substrates and/or products) can be 553

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dissolved with high concentrations in the reactor, thermodynamically unfavorable reactions become possible [28], microbiological contamination is avoided in the presence of the organic solvent, component separation and product recovery after reaction become easier [29], and substrate and/or product inhibition can be reduced in the presence of a liquid– liquid interface. On the other hand, two-phase systems have potential disadvantages. Biocatalyst inhibition or denaturation may occur in contact with organic solvent dissolved in the aqueous phase or at the organic–aqueous interface. The system may be complex and inﬂammable. D.

History

Since the beginning of the 20th century, organic solvents have been used in enzymatic reaction media [30]. Biocatalytic reactions in water–organic biphasic media were ﬁrst carried out by Cremonesi et al. [31] and by Buckland et al. [32] less than 30 years ago. Their work aimed at the conversion of high concentrations of poorly water soluble components, particularly steroids. Later, biphasic systems were used for enzyme-catalyzed synthesis reactions that were unfavored in water, changing the reaction equilibrium towards the higher yield of the product, such as esters or peptides. The majority of biocatalytic reactions are thermodynamically controlled. Product yield is thus dependent on the equilibrium position of a reaction. Optimization of the product yield requires knowledge of the equilibrium position in different organic solvents. Several works described and compared models for the prediction of the equilibrium position in two-phase media [6, 28, 29, 33]. Most biphasic systems use sparingly water-soluble substrates and yield hydrophobic products. Therefore, the aqueous phase serves as a biocatalyst container [34,35]. However, in some systems, one of the reactants (substrate or product) can be soluble in the aqueous phase [23,36–38]. E.

Reviews on Biocatalysis in Biphasic Systems

In 1982, Lilly [21] reviewed the ﬁrst two-liquid phase biocatalysis. In 1987 and 1992, Lilly’s group [39,40] published reviews dealing with process engineering of biphasic bioreactors. In 1993, Van Sonsbeek et al. [41] gave an overview on biocatalysis in different biphasic systems. The present review deals with the same topic as the articles cited above, but modiﬁed with different parameters inﬂuencing biocatalysis and reactant partition in water–organic two-liquid phase bioreactors. Interactions between these phenomena are also discussed. Different type of reaction system containing organic solvent can be classiﬁed in a simple way. To accomplish this we ﬁrst distinguished between microaqueous organic systems with a continuous organic phase, then reversed micelles stabilized with surfactant and a liquid–liquid biphasic system in which distinct organic and aqueous phase are mixed. The latter medium is discussed in this paper. F. Study of the Process The development of the two-liquid phase biocatalytic processes requires the knowledge of different phenomena and problems that are not necessarily encountered in monophase aqueous media [40].

Biocatalysis in Liquid–Liquid Biphasic Media

1.

555

Which Principles are Changed?

When an organic phase is added to the medium, transfer of a poorly water-soluble organic component from organic to aqueous phase is observed across the liquid–liquid interface. A sparingly water-soluble substrate may make up the organic phase, or be dissolved in an apolar organic solvent. This can affect the transfer over the organic–aqueous interface. In a biphasic medium, two situations are distinguished for the reaction. Biocatalysis occurs at the liquid–liquid interface [42,43] or in the bulk of the aqueous phase [25,27]. Models have been developed for both types, and interaction between mass transfer and enzyme-catalyzed reactions has been also studied. Investigations on phase ratio are also useful. This does not only affect partition and concentration of components (both water-soluble and poorly water-soluble), but also reduces the reaction inhibition by the product, the substrate excess or any other chemical inhibitor [37,40]. 2. What Are the General Rules? The development of biphasic media requires a knowledge of general rules based on observation. The choice of the biocatalyst and the organic solvent is very important. Estimation of the biocatalyst tolerance to an organic solvent is based on various indicators, described later in this chapter. Biocatalysts are also sensitive to the process of the liquid–liquid interface. They can be used in two different forms: free, soluble or immobilized. 3.

What Are the Experiments Needed for Optimization?

General rules need to be adapted for different biotransformation processes because they are not based on the speciﬁc study of all systems. Biocatalysis conditions are optimized when carrying out experiments designed to increase knowledge of the process. Several experiments using different organic solvents in different biphasic media are necessary to ﬁnd the adequate distribution of the reaction components. A series of experiments are essential for the choice of a process and for scaling-up. Experiments using Lewis cells [44] may yield useful results for understanding equilibrium, kinetics, and interactions between organic solvent–substrate and/or organic solvent–biocatalyst. A study of twoliquid phase biotransformation systems is detailed below in Sections II–IX.

II.

ORGANIC SOLVENTS IN THE BIOCATALYTIC SYSTEMS: POSSIBLE CONFIGURATIONS

Most nonconventional media used for bioreaction consist of more than one distinct phase. The organic phase can be used as nonpolar ﬂuid, which acts as a reservoir for one or many reactants. It is generally a continuous phase. The other phase contains the biocatalyst and is generally the site for the reaction. This relatively polar phase is continuous or dispersed in the organic phase. A.

Microaqueous Organic Media

The reaction system contains a unique continuous phase: the organic solvent, in which biocatalyst is free or immobilized [5,10,14,17,45–49,134]. Organic solvents that are used as media for biochemical reactions are not completely anhydrous. Yamane et al. [50]

556

Gargouri

proposed the term: ‘‘microaqueous organic medium,’’ in order to show that the system is neither aqueous nor completely anhydrous. It is a state in which the system has a small amount of water [Fig. 1(a)]. Several enzymes like lipases, esterases, and dehydrogenases have been active in hydrophobic environments. Thermodynamic water activity is a good predictor of the optimal hydration conditions for catalytic activity [51]. Enzyme preparation can be equilibrated at a speciﬁc water activity before the reaction [52]. When water concentration is very low, enzyme is suspended in the solid state in the water-immiscible organic solvent [46]. Enzymes are easily recovered after the reaction by the method of ﬁltration. Thermostability of enzymes increases in apolar organic solvents increasing the stability and rigidity of the molecules. This effect is probably due to low-water activity [130]. Many studies have demonstrated that enzymes in organic media keep their conventional Michaelis–Menten or ping-pong behavior [10,132,133,137]. Nevertheless, enzyme activity usually decreases and kinetic parameters are dramatically changed when compared to biocatalysis in aqueous media [136]. B.

Reversed Micelles

Enzymes are suspended in hydrated microemulsion surrounded by a monolayer of surfactant molecules dispersed in an apolar solvent [53–60,135] [Fig. 1(b)]. Micelles ( 2 nm sphere) are formed when lyophilized or aqueous preparation of enzymes are introduced with stirring or shaking into a solution of synthetic or natural surfactant in an organic solvent. The protein-containing colloidal solutions of water-in-organic solvents are optically transparent. Hence, absorption spectroscopy, circular dichroism spectroscopy and ﬂuorescence spectroscopy are found to be convenient for studying biocatalysis [53]. The reversed micelles are interesting models for studying bioconversion, since the majority of the enzymes in vivo act inside or on the surface of biological membranes. C.

Biphasic Systems

Biphasic systems are composed of two continuous liquid phases: the organic and the aqueous phases [13,25,27,31,36]. An interface generally separates the aqueous phase containing the biocatalyst from the organic phase containing the substrate. Moreover, the reaction product, if poorly soluble in water, can be easily separated from the biocatalyst. The use of carefully measured concentrations in hydrophobic reactants becomes facile in such systems, and substrate excess inhibition of the biocatalyst is reduced. Biocatalysis localization in the biphasic medium depends on physicochemical properties of the reactants. When all the chemical species involved in the reaction are hydrophobic, catalysis occurs at the liquid–liquid interface. However, when the substrate is hydrophobic (initially dissolved in the apolar phase) and the product is hydrophilic (remains in the aqueous phase), the reaction occurs in the aqueous phase [25]. The majority of biphasic systems use sparingly water-soluble substrates and yield hydrophobic products; therefore, the aqueous phase serves as a biocatalyst container [34,35] [Fig. 2(a)]. Nevertheless, in some systems, one of the reactants (substrate or product) can be soluble in the aqueous phase [23,36–38] (Fig. 2(b), (c)). Biphasic media are macroheterogenous, with a well-deﬁned liquid–liquid interface [25,63] [Fig. 1(g), (h)], or microheterogeneous consisting of an emulsion with a very important interface area [37,38] [Fig. 1–f]. The ﬁrst medium is used for kinetic studies

Biocatalysis in Liquid–Liquid Biphasic Media

557

FIG. 1 Reaction systems containing organic solvent, and corresponding theoretical concentration proﬁles for water insoluble substrate. &: solid biocatalyst; &: organic phase; &: aqueous phase or biocatalyst dissolved in aqueous phase.

558

Gargouri

FIG. 2 Localization of the biocatalyst with different phase distributions of substrate and product in two-phase medium. S: substrate; P: product; B: biocatalyst.

and the second is generally used for optimization of reaction yield and/or selectivity. The study of bioconversion in systems containing an organic solvent needs optimization of parameters less or unfamiliar in classical enzymology. Only biphasic organic–aqueous media will be studied in further sections [Fig. 1(c)–(h)]. The term ‘‘biphasic system’’ is used to describe a medium composed of a biocatalyst–containing aqueous phase and an organic phase consisting of a water-immiscible organic solvent [61,64].

III.

BIOCATALYST STABILITY

One of the most interesting research ﬁelds in biocatalysis is the study of biocatalyst denaturation and stabilization in the reaction environment. In nonconventional media,

Biocatalysis in Liquid–Liquid Biphasic Media

559

the presence of certain compounds allows a signiﬁcant decrease or increase in biocatalyst stability. The presence of organic solvent and proportion of water are determining factors in thermal denaturation of proteins. Enzyme solutions can be stabilized using sugars, polyhydric alcohols, polymers, or salts [65]. These compounds affecting the enzyme stability are ligands (substate, product, inhibitor, coenzymes) or nonspeciﬁc additives. We generally use the enzyme half-life (t1=2 ) or the enzyme remaining activity (%) as decriptive criteria of enzyme stability (Table 1). The choice of organic solvent in the biphasic system is very important and depends on the type and origin of the enzyme. There is a great variability regarding the stability of enzymes in the presence of low concentrations of organic solvents added to the aqueous phase. Several enzymes like cholesterol oxidase, lactase, peroxydase, and lipase show good stability in the presence of immiscible solvents such as n-hexane, octane, cyclohexane, carbon tetrachloride, toluene, benzene, trichloroethylene, ethylene dichloride, chlorobenzene, chloroform, methyl chloride, diethyl ether, butyl acetate, methyl ethyl ketone, and ethyl acetate [61]. Nevertheless, many other enzymes such as 20 -hydroxysteroid dehydrogenase, lipoxygenase, and isomerase are more unstable and their use in biphasic aqueous–organic systems is sometimes more complicated [21]. On the other hand, biocatalyst stability can be affected by the presence of organic– aqueous interface. In our previous work [25], we studied the effect of interface with octane on the lipoxygenase stability in an octane–buffer pH 9.6 biphasic system. This loss in activity is more pronounced than that observed in the aqueous system. During lipoxygenation, the active enzyme concentration ½E in the aqueous phase of our biphasic bioreactor was: ½E ¼ ½Einitial 100:006t

ð1Þ

Time ðtÞ in minutes and enzyme concentration ½E in mM. The liquid–liquid interface has been identiﬁed as the major factor responsible for papain deactivation in a biphasic system [66]. If the interfacial tension can be decreased to a small value using surfactant, the biocatalyst stability will be expected to increase. Stability of several enzymes like proteases from thermophilic micro-organisms can be increased in aqueous–organic biphasic systems. Owusu and Cowan [67] observed a strong positive correlation between bacterial growth temperature, the thermostability of free protein extracts, and enzyme stability in aqueous–organic biphasic systems (Table 1). Enzymes, like other cell components (membranes, DNA, t RNA ribosomes), are adapted to withstand the environmental conditions under which the organism demonstrates optimal growth.

IV.

BIOCATALYST FORM

Several kinds of states in which enzymes may be used for various reactions in aqueous– organic biphasic systems have been developed in previous work (Table 2). In biphasic media, the biocatalyst is easily recovered after the reaction; then it is not always necessary to be immobilized. Nevertheless, the immobilization can confer important properties, such as improved stability of biocatalyst. Furthermore, protection of the biocatalyst against a damaging turbulent environment can also play a role. With biphasic media, as free biocatalyst, the catalyst support material is generally immersed in the aqueous phase (Fig. 1). Most of the support materials which are already

OS–water (87/13)

OSa –water (87/13)

OS–water (87/13)

OS–trisHCl pH 7 (7/3)

OS–TrisHCl pH 7 (7/3)

OS–TrisHCl pH 7 (7/3)

OS–TrisHCl pH 7 (7/3)

OS–TrisHCl pH 7 (7/3)

OS–TrisHCl pH 7 (7/3)

7

7

7

2

2

2

2

3.5

3.5

4.5

Hydrosol IP 230 (isoparafﬁn) Hydrosol IP 230 (isoparafﬁn) Hydrosol IP 230 (isoparafﬁn) n-Hexanol

n-Hexanol

Chloroform

Chloroform

n-Hexane

n-Hexane

n-Octane

OS–TrisHCl pH 7 (7/3)

OSa –water (87/13)

7

Hydrosol IP 230 (isoparafﬁn)

Biphasic medium

Log P

Organic solvent Immobilized spores of Penicillium roquefortii Free spores of P. roquefortii Immobilized spores of P. roquefortii Free spores of P. roquefortii Protein extract from T. aquaticus Proten extract from Desulfurococcus mobilis Protein extract from T. aquaticus Protein extract from D. mobilis Protein extract from T. aquaticus Protein extract from D. mobilis Protein extract from T. aquaticus

Biocatalyst

— —

— — — — —

66c 114c

9c 9c 115c 114c 114c

Proteolysis on azocasein

Proteolysis on azocasein

Proteolysis on azocasein

Proteolysis on azocasein

Proteolysis on azocasein

Proteolysis on azocasein

20

0.74b —

67

67

67

67

67

67

67

20

1.2b

20

6.15b —

—

20

5.29b

Reference

Methyl ketone from C8 fatty acid Methyl ketone from C10 fatty acid Methyl ketone from C10 fatty acid Proteolysis on azocasein

—

Biocatalyst stability Activity

Methyl ketone from C8 fatty acid

Reaction

TABLE 1 Effect of the Organic Solvent on Stability and/or Activity of Biocatalysts in Biphasic Media

560 Gargouri

2

3.2

Chloroform

Cyclohexane

1.9

Trichloroethylene

2

1.9

Trichloroethylene

Chloroform

2.5

—

Ethyl acetate

Toluene

—

Butyl acetate

0.4

—

Diethyl ether

3

OS–trisHCl pH 7 (7/3) OS–trisHCl pH 7 (7/3) OS–trisHCl pH 7 (7/3) OS–trisHCl pH 7 (7/3) OS–phosphate buffer pH 7 (2/1) OS–phosphate buffer pH 7 (2/1) OOS–phosphate buffer pH 7 (2/1) OS–phosphate buffer pH 7 (2/1) OS–acetate buffer pH 5.15 (4/1) OS–acetate buffer pH 5.15 (4/1) OS–acetate buffer pH 5.15 (4/1) OS–acetate buffer pH 5.15 (4/1) OS–acetate buffer pH5.15 (4/1+Tween 80) OS–Phosphate buffer pH 7.2 (1/1) OS–phosphate buffer pH 7.2 (1/1) OS–phosphate buffer pH 7.2 (1/1)

0.8 0.8 0.8 0.8 1.9

n-Butanol n-Butanol n-Butanol n-Butanol Trichloroethylene

Carbon tetrachloride Cyclopentanone

OS–tris HCl pH 7 (7/3)

4.5

n-Octane

C. rugosa lipase

Candida rugosa lipase Wheatgerm lipase

Papain

Papain

Papain

Papain

Protein extract from D. mobilis Thermolysin protease Type II protease Type IV protease Papain protease 20 -Hydroxysteroid dehydrogenase 20 -Hydroxysteroid dehydrogenase 20 -Hydroxysteroid dehydrogenase 20 -Hydroxysteroid dehydrogenase Papain

Prenyl acetate hydrolyxis

Prenyl acetate hydrolysis

Prenyl acetate hydrolysis

Synthesis of Gly-Phe

Synthesis of Gly-Phe

Synthesis of Gly-Phe

Synthesis of Gly-Phe

Synthesis of Gly-Phe

Reduction of cortisone

Reduction of cortisone

Reduction of cortisone

Proteolysis on azocazein Proteolysis on azocazein Proteolysis on azocazein Proteolysis on azocazein Reduction of cortisone

Proteolysis on azocasein

61

66 7 7 7

20e 12e — — — — — 0.2h 0.14h 0.42h

— 35f 5g 15g 20g 8g 50g

—

—

—

(continued)

66

66

66

66

61

61

16e

—

67 67 67 67 61

— — — — 38e

162d 2d 11d 31d —

67

—

104c

Biocatalysis in Liquid–Liquid Biphasic Media 561

OS–phosphate buffer pH 7.1 (1/3)

OS–phosphate buffer pH 7.1 (1/3)

OS–trisHCl pH 8 (1/25)

OS–trisHCl pH 8 (1/25)

OS–phosphate buffer pH 7.2 (1/1) OS–trisHCl pH 8 (1/25)

Biphasic medium

P. cepecia lipase

Pseudomonas cepecia lipase

P. cepecia lipase

P. cepecia lipase

P. cepecia lipase

Wheatgerm lipase

Biocatalyst

b

OS: organic solvent. Reaction rate in mM/h. c Percent stability at 608C. d Percent activity remaining at 508C. e activity in mA340 /min. f Percent of remaining activity after 8 days of use. g Complete deactivation (hours). h mol product/h mg enzyme. i Maximal reaction rate relative to the rate at thermodynamic activity of the substrate ¼ 1. j Initial rate (M/min).

a

0.49

2.5

Toluene

Tetrahydrofuran

4.5

Iso-octane

1:3

2.9

Dibutyl ether

Dimethylsulfoxide

3.2

Cyclohexane

Log P

(continued)

Organic solvent

TABLE 1

Decyl chloroacetate hydrolysis Decyl chloroacetate hydrolysis Decyl chloroacetate hydrolysis Asymmetrical hydrolysis of(+)1-chloro-2-acetoxy3-(1–naphthyloxy)-propane Asymmetrical hydrolysis of (+)1-chloro-2-acetoxy-3(1-naphthyloxy)-propane

Prenyl acetate hydrolysis

Reaction

15 15 15 8

8

1.19i 0.88i 1.12i 82.3j

19j

—

—

—

—

—

—

7

Reference

0.68h

Biocatalyst stability Activity

562 Gargouri

Biocatalysis in Liquid–Liquid Biphasic Media

563

used for aqueous systems can be used in biphasic media, especially when the support is not sensitive to the organic solvent dissolved in the aqueous phase. Denaturation and physical phenomena such as cell aggregation at the water–organic interface can be eliminated by entrapment of the biocatalyst [68,69]. In addition, the immobilization increases the diffusion limitations and can then reduce the biocatalyst inhibition by substrate concentration. The classiﬁcation of organic–aqueous biphasic systems takes into account the biocatalyst form (Fig. 1). The concentration proﬁles for a water-insoluble reactant, such as a substrate initially dissolved in the organic phase, depend on this classiﬁcation [22]. When the biocatalyst is dissolved in the aqueous phase [Fig. 1(e)–(h)], reactant concentration changes on both sides of the liquid–liquid interface. The concentration proﬁle is different when the biocatalyst is immobilized cells, enzymes, or cells in suspension. The aqueous phase containing the solid biocatalyst is continuous [Fig. 1(d), [g], discrete [Fig. 1(c)], or reduced to a ﬁlm surrounding the biocatalyst (Fig. 1(a),(b)]. Several biphasic reactor conﬁgurations have been used with immobilized lipolytic enzymes, particularly in the processing of oils and fats [70–72]. This technology facilitates the development of continuous large-scale commercial processes. Immobilization permits multiple use of the enzyme, increasing the system efﬁciency. It often enhances the thermal and chemical stability of the biocatalyst [24,73,74].

V.

THE IMPORTANCE OF THE ORGANIC SOLVENT

Various criteria can inﬂuence the choice of organic solvent that can be used in a biphasic bioreactor: degree of solubility of substrates and/or products, inactivation effect, toxicity, ﬂammability, and essentially reactant partition between the phases. Much research has been carried out on this topic [7,8,14,15,33,67]. Another important argument for the use of the organic solvent is the reverse hydrolytic reactions that become feasible [61,75]. The inhibition of the biocatalyst can be reduced, since the substrate is initially concentrated in the organic phase and inhibitory products can be removed from the aqueous phase. This transfer can shift the apparent reaction equilibrium [28,62] and facilitates the product recovery from the organic phase [20,29,33]. A wide range of organic solvents can be used in bioreactors, such as alkanes, alkenes, esters, alcohols, ethers, perﬂuorocarbons, etc. (Table 1). Organic solvent can affect the enzyme speciﬁcity [76]. Authors have indicated that transesteriﬁcation of 1,4-butyloxy-2-octylbenzene and butanol in presence of lipases from Pseudomonas can produce two different products when using hydrophilic (acetonitrile) or hydrophobic (toluene) solvents. Zaks and Klibanov [16], demonstrated that subtilisine and -chymotrypsine speciﬁcites can be changed as a function of solvent types. This is true for a limited number of biocatalysts. In general, there is a positive correlation between hydrophobicity of solvents and nontoxicity for biocatalysts. The log P value was demonstrated to be a suitable parameter for characterization of solvent hydrophobicity (Table 1). Log P is the logarithm of the partition coefﬁcient of a solvent in a water–1-octanol two-phase system [11,12,41,77]. Solvents with log P > 4 are very hydrophobic and generally nontoxic for biocatalysts. Nevertheless, in some cases, this criterion is not sufﬁcient for the choice of the solvent. For instance, Kuo and Parkin [78], demonstrated that hydrophobicity of solvent in the presence of lipase also affect selectivity and partition of reactants in esteriﬁcation reactions. On the other hand, in the presence of certain solvents, even in low concentration, enzyme can be activated [13].

Immobilized soybean lipoxygenase Crude powder lipase from Pseudomonas cepecia

Immobilized spores of P. roquefortii -D-Xylosidase in extract from Trichoderma reesei Free soybean lipoxygenase

Octane–borate buffer pH9 (5/2)

13-Hydroperoxy-acid from linoleic acid

With carbonyldiimidazoleactivated matrix termed Reacti-Gel1 —

Asymmetrical hydrolysis Tetrahydrofuran– phosphate of (+)1-chloro-2buffer pH 7.1 (1/3) acetoxy-3-(1naphthyloxy)-propane

Hexane–borate buffer pH 6.5(1/1)

—

Isoparafﬁn–water (87/13) Butanol–acetate buffer pH 4.5

Isoparafﬁn–water (87/13)

Methyl ketone from octanoic acid Transxylosylation with methyl- -xyloside and 1-butanol 9-Hydroperoxy-acid from -linolenic acid

Methyl ketone from octanoic acid

—

Isoparafﬁn–water (87/13)

Biphasic system

Entrapment in Caalginate/ Eudragit RL beads —

Methyl ketone from octanoic acid

Catalyzed reaction

—

Immobilization method

Enzyme Preparations Used in Organic–Aqueous Biphasic Media

Suspended spores of Penicillium roquefortii Frozen spores of P. roquefortii

Biocatalyst preparation

TABLE 2

No lag period observed for the product formation

High production only in presence of anionic surfactants No surfactant is required

After thawing, only external spores are active Improvement in catalyst stability Kinetically controlled process

Rapid swelling

Characteristics

8

24

23

128

20

20

20

Reference

564 Gargouri

Candida rugosa lipase immobilized in polypropylene membrane C. rugosa lipase immobilized in regenerated cellulose C. rugosa lipase immobilized in meta-aramid Immobilized lipase from C. rugosa Immobilized lipase from Mucor miehei Immobilized lipase from Humicola lanuginosa Lipase from Candida cylindracea

Precipitation

Stirred-tank reactor

Stirred-tank reactor

Cyclohexane–water

Oil–water

Hydrolysis of triacylglycerol esters Hydrolysis of olive oil

Alcoholysis of 1-phenyl ethyl butyrate and 1-heptanol

Olive oil–water

Olive oil hydrolysis

Molecular weight cutoff = 500Da, Product name: BM5, Berghof Stirred-tank reactor

Stirred-tank reactor

Ethyl laurate–water

Ethyl laurate hydrolysis

Pore size = 0.2 m, Product name: Celgard 2400, Hoechst Pore size = 2 nm, Product name: Cuprophan, Enka

Olive oil–water

Ethyl laurate–water

Ethyl laurate hydrolysis

Lipase solution ﬁltered through the membrane in the batch reactor Lipase solution ﬁltered through the membrane in the batch reactor Covalent binding on polyethylene glycol Adsorption on duolite

Entrapment on polyurethane

Ethyl laurate–water

Ethyl laurate hydrolysis

Physical adsorption on membrane in a batch ﬂat sheet membrane reactor

120

119

118

117

116

116

116

Biocatalysis in Liquid–Liquid Biphasic Media 565

566

Gargouri

In 1958 Sarda and Desnuelle [79] discovered the lipase activation at the interfaces. They observed that porcine pancreatic lipase in aqueous solution was activated some 10fold at hydrophobic interfaces which were created by poorly water-soluble substrates. An artiﬁcial interface created in the presence of organic solvent can also increase the activity of the lipase. This interfacial activation was hypothesized to be due to a dehydration of the ester substrate at the interface [80], or enzyme conformational change resulting from the adsorption of the lipase onto a hydrophobic interface [42,81,82]. The volumetric ratio of the two liquid phases ( ¼ Vorg =Vaq Þ can affect the efﬁciency of substrate conversion in biphasic media. The biocatalyst stability and the reaction equilibrium shift are dependent on the volume ratio of the two phases [29]. In our previous work [37], we studied the importance of the nonpolar phase in a biphasic system (octane– buffer pH 9) by varying the volume of solvent. The ratio ¼ 2=10 has been the most appropriate for an improvement of the yield of the two-enzyme (lipase–lipoxygenase) system. We found that a larger volume of organic phase decreases the total yield of conversion. Nevertheless, Antonini et al. [61] afﬁrmed that changes in the ratios of phases in water–organic two-phase system have little effect upon biotransformation rate.

VI.

TRANSFER AND PARTITION OF THE REACTANTS

A novel phenomenon to be considered in an organic–aqueous biphasic system regards the transfer of reactants between the two phases [61,131], especially substrate transfer from the organic to the aqueous phase containing enzymes or cells. The transfer depends on shaking or stirring the two phases. In fact, the maximum biotransformation is generally obtained with moderate shaking [31,61]. Biocatalysts can become destabilized or denatured at very high rates of shaking. At equilibrium, in biphasic system, distribution of a chemical species (i) between the two phases is given by its partition coefﬁcient: Pi ¼ ½iorg =½iaq

ð2Þ

The presence of an organic phase in the bioreaction medium is only useful when the partition coefﬁcient of at least one reactant is signiﬁcantly greater than the unity. The characteristics of the selected solvent clearly inﬂuence the partition coefﬁcients of substrates and products between the two phases. When enzyme is inhibited by high substrate or product concentrations, it is convenient to use solvents with high partition coefﬁcients while the opposite has to be done when enzyme has low afﬁnity with its substrate. Eggers et al. [29] deﬁne the overall biphasic concentration referred to the total volume of the system: ½ibiph ¼ ½iaq

1 þ Pi 1 þ Pi ¼ ½iorg 1þ Pi ð1 þ Þ

ð3Þ

Martinek et al. [28] deﬁned the apparent reaction equilibrium in a biphasic system by the constant Kbi . In their model, the ratio Kbi =Kaq represents the equilibrium change when using a biphasic or pure aqueous medium. When the biocatalysis occurring in the aqueous phase involves four chemical species: AþB$CþD the reaction equilibrium may be expressed as a function of partition coefﬁcients of the components:

Biocatalysis in Liquid–Liquid Biphasic Media

Kbi ð1 þ PC Þð1 þ PD Þ ¼ Kaq ð1 þ PB Þð1 þ PA Þ

567

ð4Þ

Considering only the aqueous phase of the biocatalytic system, the equilibrium constant for the reaction is given as a function of thermodynamic activities of the components shown: Kaq ¼

a C aD aA aB

ð5Þ

When water as a reaction medium is replaced with an organic–aqueous biphasic system the equilibrium shift predicted theoretically is observed experimentally by determining the partition of the reagents between the phases [28]. There can be dependence of Kbi on phase volume ratio and hydrophobicity of reagents. Reactions with hydrophobic products (PC 1Þ are most appropriate for biphasic systems [29]. The equilibrium concentrations of a hydrolytic reaction may be shifted by decreasing water activity; however, this change also inﬂuences the activities of the other components and the enzyme stability. Semenov et al. [62] and Eggers et al. [29] concluded that the partition capability is the key advantage of biphasic systems for the synthesis of organic compounds. The extractive catalysis reaction yield can be improved by removing product continuously from the reaction phase. Janssen et al. [33] compared several models describing the thermodynamically controlled reaction equilibrium in aqueous–organic biphasic systems. They explained that each model can be used to predict product concentration using different organic solvents in different biphasic systems.

VII.

KINETIC BEHAVIOR IN TWO-PHASE SYSTEMS

There have been many papers reporting studies on the inﬂuence of structure and conditions of the medium. Speciﬁcally, the kinetic behavior of enzymatic reactions in two-phase media was probed [7,25,27,63]. The reaction localization and the interaction between mass transfer and metabolism in compartmentalized media are interesting phenomena. Their study in the laboratory are useful for optimizing the operating conditions of bioreactors in a preparative scale. In addition, they also help to understand better the behavior of enzymatic systems in vivo. For instance, we study here the inﬂuence of the surrounding media on the behavior of two enzymatic reactions in two-phase systems: Lipase (EC 3.1.1.3, triacylglycerol acylhydrolase), both substrate (ester) and product (fatty acid), are poorly water soluble. The reaction occurs at the organic–aqueous interface [8,43,83,84]. Lipoxygenase (EC 1.13.11.12, nonheme iron dioxygenase), the substrate (polyunsaturated fatty acid) is poorly water soluble and the product (hydroperoxy-fatty acid) is hydrophilic. The reaction occurs in the aqueous phase [85,86]. The lipase-catalyzed fatty acid ester hydrolysis and the lipoxygenation of free polyunsaturated fatty acids are involved in the same lipid degradation pathway. They are respectively the ﬁrst and second reaction in the lipoxygenase pathway (Fig. 3) [87–91]. The pathway produces volatile products of considerable importance in food technology including C6 ½92; 93 or C9½9496 aldehydes and alcohols from polyunsaturated fatty

568

Gargouri

FIG. 3 Hydroperoxy-fatty acid synthesis from triacylglycerol with successive lipase-catalyzed hydrolysis and lipoxygenation.

acids by sequential enzyme steps. The hydroperoxides, intermediates in this pathway, are very interesting because of their high reactivity [89]. As previously mentioned, a knowledge of the reaction location and its interaction with mass transfer in the biocatalytic medium is of key importance for the process design. One method to elucidate this is a set of experiments carried out in a deﬁned ﬂat liquid– liquid interface apparatus (Lewis cell) [27,44]. We used a modiﬁed Lewis cell with a welldeﬁned interfacial area between organic solvent and aqueous phase (Fig. 4) [25]. This vessel is made of a cylindrical beaker with two agitation systems: a magnetic stirrer for the bottom layer (aqueous phase) and an impeller for the top layer (organic phase). These mix counterclockwise to each other. In such a device, the rate of mass transfer of substrate from organic to aqueous phase under deﬁned conditions can be measured and a mass transfer coefﬁcient is calculated. The obtained information can be combined with the biocatalyst kinetics to predict the system evolution, which can be compared to experimental results in a biphasic reactor. The approach is valid for a micro-organism- or enzyme-catalyzed biotransformation [25, 27,131] and for a coupled enzyme system [37,63].

A.

Lipase in Two-Phase Systems

The lipases demonstrated very high stability in media partially or totally composed of organic solvent. In such media, the lipases catalyze esteriﬁcation, transesteriﬁcation, and resolution of enantiomers [19,45,75,97–100]. Nevertheless, several biphasic systems (organic–aqueous) are used for hydrolysis of lipid and fats [7,34,101]. Kinetic studies in biphase media or in inverted micelles demonstrate that the lipase behavior is different

Biocatalysis in Liquid–Liquid Biphasic Media

569

FIG. 4 Modiﬁed Lewis cell: macroheterogeneous biphasic medium. (From Ref. 25.)

when it catalyses hydrolysis or esteriﬁcation. In fact, high hydrolytic activity does not necessarily correspond to high synthesis activity [14,102,103]. Several mechanisms have been proposed for lipase-catalyzed reactions. Kinetic studies of hydrolysis [14,15] and esteriﬁcation [50] catalyzed by Pseudomonas cepecia lipase, demonstrate that the enzyme has a ping-pong mechanism. The simplest kinetic model applied to describe lipase catalyzed reactions is based on the classic Michaelis–Menten mechanism [10] (Table 3). To test this model Be´laﬁ-Bako` et al. [58] studied kinetics of lipase-catalyzed hydrolysis of tri-, di-, and mono-olein separately. All these reactions were found to obey the Michaelis–Menten model. The apparent parameters (KM and VM ) were determined for global hydrolysis. In our previous work [63], we studied the hydrolysis kinetics of lipase from Mucor javanicus in a modiﬁed Lewis cell (Fig. 4). Initial hydrolysis reaction rates (vr1 ) were measured in the presence of lipase in the aqueous phase (borate buffer). Initial substrate (trilinolein) concentration (TLi Þ in the organic phase (octane) was between 0.05 and 8 mM. The presence of the interface with octane enhances hydrolysis [37]. Lineweaver–Burk plots of the kinetics curve (1=vr1 ¼ f ð1=TLÞÞ gave straight lines, demonstrating that the hydrolysis reaction shows the expected kinetic behavior (Michaelis–Menten). Excess substrate results in reaction inhibition. Apparent parameters of the Michaelis equation were determined from the curve 1=vr1 ¼ f ð1=TLÞ and substrate inhibition was determined from the curve 1=vr1 ¼ f ðTLÞ: Reaction maximal velocity: VM1 ¼ 9:8 1M= min : Michaelis constant: KM1 ¼ 192 20M: Constant for substrate excess inhibition: Kss1 ¼ 5300 M. The equation for the hydrolysis reaction rate is:

Free lipase from Pseudomonas cepecia Free lipase from Pseudomonas cepecia Free lipase from Mucor javanicus Lipase from C. rugosa entrapped on polyethylene glycol Lipase from C. rugosa entrapped on polypropylene glycol

Enzyme preparation

Olive oil hydrolysis

Iso-octane–water (4/1)

35

62.5 mol/(min g 0.043% of support) w/v

0.043% w/v

41.5 mol/(min g of support)

35

Olive oil hydrolysis

192 M

9.8 M/min

258C

13.563 mM

0.24 mM/min

8.187 mM

KM

Not available

Octane–borate buffer pH 9.6 (1/1) Iso-octane–water (4/1)

Acetone–phosphate buffer pH 7.1 (1.5/8.5)

VM 0.319 mM/min

Asymmetrical hydrolysis of (+)1-chloro-2-acetoxy3-(1-naphthyloxy)-propane Asymmetrical hydrolysis of (+)1-chloro-2-acetoxyl-3(1-naphthyloxy)-propane Trilinolein hydrolysis

Acetone–Phosphate buffer pH 7.1 (1/3)

Tð8CÞ Not available

Catalyzed reaction

Biphasic medium

TABLE 3 Kinetic Parameters of Enzymes in Organic–Aqueous Biphasic Media

—

KSS ¼ 5300 M —

—

—

Other constants

121

121

63

8

8

Reference

570 Gargouri

Biocatalysis in Liquid–Liquid Biphasic Media

571

VM1 TL KM1 þ TL þ TL2 =Kss1

ð6Þ

r1 ¼

The substrate for the reaction is triacylglycerol of polyunsaturated fatty acid, which is not soluble in water, but can be solubilized with high concentration in octane. The lipase converts its substrate at the interface between octane and the aqueous phase. The free fatty acid produced is poorly water soluble. As the majority of enzyme systems in aqueous–organic biphasic media, lipase-catalyzed hydrolysis uses substrates that are insoluble in aqueous media and yield hydrophobic products (Fig. 3). Therefore, the aqueous phase serves as a biocatalyst reservoir.

B.

Lipoxygenase in Two-Phase System

In some systems occurring in biphasic media, one or other of the reactants (substrate or product) can be soluble in the aqueous phase. The lipoxygenase-catalyzed reaction is an excellent example. Since the substrate fatty acid is sparingly water soluble, it is initially concentrated in the organic phase and it transfers slowly to the aqueous phase containing the lipoxygenase. The lipoxygenation takes place in the bulk of the aqueous phase. The produced hydroperoxide is hydrophilic, therefore it remains in the aqueous phase (Fig. 3). The lipoxygenase shows Michaelis–Menten kinetics in an aqueous medium. We previously described [25] the function of soybean lipoxygenase-1 in a biphasic system (modiﬁed Lewis cell) composed of an aqueous phase (borate buffer) and octane. The substrate of the reaction is linoleic acid (LA) and the main product is hydroperoxyoctadecadienoic acid (HP). The system involves two phenomena: LA transfer from the organic to the aqueous phase and lipoxygenase kinetics in the aqueous medium. 1. The Study of Mass Transfer Both substrate and product have suface-active properties and favor mass transfer across the liquid–liquid interface. Their physicochemical properties modulate the behavior of the reaction in the heterogeneous system. Saturating substrate concentration in the aqueous phase (LAaq ) was not constant. It increased when using a high initial concentration of LA (LAt Þ and when the HP concentration increased. The percentage of transferred LA (T ¼ LAaq =LAt Þ depended on LAt and HP concentrations: T ¼ ða LAt þ b LA2t Þ10ðcdLAtÞHP a ¼ 0:0023 b ¼ 0:0013 c ¼ 0:309

ð7Þ

d ¼ 0:019

The rate of LA transfer to the aqueous phase can be described by the following equation: Vt ¼ KL aðLAaq LAaq Þ

ð8Þ

Where KL a is the LA mass transfer coefﬁcient (0.126 min1 Þ; LAaq is the LA concentration in the aqueous phase (mM). When replacing LAaq ¼ T LAt by its function, the expression of the transfer rate becomes: Vt ¼ KL a½½ða LAt þ b LA2t Þ10ðcd LAt ÞHP LAt LAaq

ð9Þ

572

Gargouri

Neither lipase nor lipoxygenase (inactivated enzymes) have an effect on the LA transfer. The presence of TL, 1.3-dilinolein and monolinolein does not affect transfer of LA from organic to aqueous phase. 2. The Study of Lipoxygenation in Aqueous Phase The kinetics of the lipoxygenase was studied in aqueous media [25]. The afﬁnity of the enzyme for its substrate LA is very high. When LA is in excess in the medium it becomes the inhibitor of the reaction [Fig. 5(a)]. HP is also competitive inhibitor. The experimentally determined kinetic constants are: Reaction maximal velocity: VM2 ¼ 10:15 0:4 M/min mg. Catalytic constant: Kcat2 ¼ 16:9 s1 . Michaelis constant: KM2 ¼ 30:15 2 M. Constant for substrate excess inhibition: Kss2 ¼ 11; 240 M. Product inhibition constant: KP2 ¼ 102:3 6 M. The equation for the lipoxygenation rate is: r2 ¼

Kcat ½lipoxygenaseLA KM2 ð1 þ HP=KP2 Þ þ LA þ LA2 =Kss2

ð10Þ

In the biphasic bioreactor, we found that the presence of octane causes an inactivation of lipoxygenase dissolved in the aqueous phase [Eq. (1)]. This loss in activity is more pronounced than that observed in the aqueous system. 3. Lipoxygenation in Lewis Cell According to the preceding results we cannot determine the steady state of the system using the sequential approach suggested by Woodley [27]. This method involves sequential study of two phenomena: reactant transfer in biphasic medium and enzyme kinetics in the aqueous medium. In the steady state, substrate transfer rate is equal to the reaction rate.

FIG. 5 Rate of hydroperoxide production in (a, *) lipoxygenation in pure aqueous medium, (b, *) lipoxygenation in biphasic system, (c, ) two-enzyme (lipase–lipoxygenase) system in two-phase medium, determined experimentally, and (d, &) modeled kinetic of the two enzyme system. (From Ref. 63.)

Biocatalysis in Liquid–Liquid Biphasic Media

573

However, in the two-phase system described here the reaction progress has an inﬂuence on substrate transfer [Eq. (9)] and steady-state changes continually during the evolution of the system. Interaction between the reactant transfer and lipoxygenase-catalyzed reaction is therefore studied in octane–aqueous biphasic medium (modiﬁed Lewis cell). The kinetics of soybean lipoxygenase-1 in a biphasic medium is different from the kinetics in an aqueous system [Fig. 5(a),(b)]. The kinetic curve in the two-phase system has a sigmoid shape, which is due to surface active properties of LA and HP [25]. When initial LA concentration is small in the organic phase (0–5 mM) its transfer is poor and bioconversion in the aqueous phase is slow. When the initial LA concentration is large, the quantity of substrate transferred to the aqueous phase allows the lipoxygenation to progress. This reaction consumes LA and produces HP, which favor the transfer of residual substrate between the two phases. Then catalysis and transfer have a reciprocal inﬂuence on each other. We demonstrated that the use of a non-allosteric enzyme in a compartmentalized medium permits the simulation of a co-operativity phenomenon. The optimal reaction rate in the two-phase system is reached for a high initial LA concentration: 14 mM. Inhibition by substrate excess is observed in two-phase medium. C.

The Kinetic Behavior of a Two-Enzyme System in Biphasic Media: Coupling Lipase and Lipoxygenase

A common characteristic of metabolic pathways is that the product of one enzyme in sequence is the substrate for the next enzyme and so forth. In vivo, biocatalysis takes place in compartmentalized cellular structure as highly organized particle and membrane systems. This allows control of enzyme-catalyzed reactions. Several multienzyme systems have been studied by many researchers. They consist essentially of membrane- [104] and matrix- [105,106] bound enzymes or coupled enzymes in low water media [107]. Recently [63], we studied the behavior of two-enzyme system catalyzing two consecutive reactions in a macroheterogeneous medium (modiﬁed Lewis cell). The system consisted of lipase-catalyzed hydrolysis of trilinolein and subsequent lipoxygenation of liberated fatty acids (Fig. 3). Our approach compared the kinetic behavior of coupled enzymes in the Lewis cell with the sequential study of separated phenomena presented before: Hydrolysis kinetics in two-phase media. LA transfer between the two phases. Lipoxygenation in aqueous media. The system has been modeled by using numerical integration program. TLi used was between 0 and 7.33 mM (equivalent to 22 mM LA). TL initially dissolved in the organic phase, was hydrolyzed in the presence of the lipase at the liquid–liquid interface. Liberated LA transferred to the aqueous phase in which it reacted with lipoxygenase. Enzyme preparations and concentration were the same as those already chosen for determination of kinetic constants. Kinetic behavior of the two-enzyme system (lipase–lipoxygenase) in biphasic media (curve c in Fig. 5) is compared with kinetics of lipoxygenase in the same biphasic medium (b) and in an aqueous medium (a). These curves demonstrated that the conﬁguration of the media inﬂuences the production rate of HP. As previously stated, lipoxygenase in biphasic media has an apparent kinetic behavior different from that in aqueous media (see difference between curves a and b in Fig. 5).

574

Gargouri

Furthermore, in the system with coupled lipase and lipoxygenase, the production rate of HP is governed by the ﬁrst enzymatic reaction and mass transfer. When TLi is small (0 to 1 mM: equiv. 3 mM LA), the kinetic curve has a sigmoid shape due to surface active properties of LA and HP [25]. Hydrolysis of TL and the increase of LAt favor the transfer of LA. Such a transfer allows the lipoxygenase reaction to progress. Since lipoxygenation consumes LA and produces HP, catalysis and transfer demonstrates a reciprocal inﬂuence. When using TLi greater than 1 mM (equiv. 3 mM LA), product appearance seems to be independent of TLi concentration. The presence of the ﬁrst reaction is the major factor limiting the production rate of HP. This system displays a two-enzyme kinetic model in which bioconversion is controlled by the interaction between the two reactions and the mass transfer. This situation offers a more realistic model for the conditions occurring in vivo, in which some pathways of intermediary metabolism consist of linear sequences of reactions. These pathways take place in highly organized compartments. Evolution of the component concentrations in the two phases of the bioreactor are modeled by using an iteractive program (Runge–Kutta). All the kinetic equations and the experimentally determined constants are introduced into the program. The mass balance equation is included. TLi ¼ TL þ LAt with LAt ¼ LAorg þ LAaq þ HP Modeled rates (curve d, Fig. 5) agreed with those determined experimentally. We suggest that the interaction of mass transfer and metabolism consisting of two or several bioreactions in compartmentalized media is an interesting phenomenon, which has not been fully researched to date. The approach presented here can help us better understand the behavior of some enzymatic systems in vivo. It can be useful for optimizing the operating conditions of bioreactors containing chemical species with amphiphilic properties.

VIII.

THE PRODUCTIVITY IN TWO-PHASE MEDIA

The present section deals with the improvement in the performance of biocatalysis when carried out in organic–aqueous biphasic systems. Such systems are very useful in equilibrium reactions and conversion yield where substrates and products can be dissolved and drawn into different phases. Subsequently the synthesis in the reactive aqueous phase is allowed to continue. Several micro-organism- or enzyme-catalyzed reactions are performed in two-phase systems (Table 1 and 4). The examples given illustrate the advantages of the procedure which may be of practical interest in technological applications of biocatalysts. The effect of biphasic mixtures on the productivity includes the contributions of solvent partitioning on enzyme activity and stability. An important activity does not necessarily lead to increased productivity. We must then distinguish between the effect of the environment on activity and productivity.

Biocatalysis in Liquid–Liquid Biphasic Media

A.

575

Lipase

The hydrolytic reaction catalyzed by lipases generally takes place at the oil–water interface. The hydrolytic activity in the presence of triacylglycerols is the basis characteristic of lipases (Table 4). However, hydrolytic activity of different lipases may not always give a good indication of the potential synthesis activity (Table 4). Lipases are able to catalyze many hydrolytic and esteriﬁcation reactions in the presence of different substrates. The type of substrate is a key factor affecting the activity and productivity of lipase-catalyzed reactions. Yang and Russell [7] made comparison of lipase-catalyzed hydrolysis in three different systems: organic, biphasic, and reversed micelles. They afﬁrmed that water content is an important factor that distinctly affects every system. Their results demonstrated that activity of lipase in organic–aqueous biphasic media was lower than that obtained in reversed micelles. However, better productivities were obtained in biphasic media, which were the most suitable environment.

B.

Lipoxygenase

The ability of free or immobilized lipoxygenase to introduce oxygen derived from the air into polyunsaturated fatty acids in media containing organic solvent and aqueous buffer has been investigated [9,56]. The inﬂuence of many parameters was tested upon the degree of oxygenation in biphasic systems [36,108]. The advantage of a two-phase lipoxygenation system lies in three points. They include avoidance of inhibition by the substrate as well as high solubility of the substrate in the organic phase and product recovery in the aqueous phase. Drouet et al. [36] improved the production yield of hydroperoxylinoleic acid at high concentrations of linoleic acid in highly stirred borate buffer-octane biphasic medium.

C.

Bienzymatic Systems

In our previous work [37,38], we have studied productivity of two-enzyme reaction: lipasecatalyzed hydrolysis of triacylglycerol and lipoxygenation of polyunsaturated fatty acids (Fig. 3) in a biphasic microheterogeneous sytem (ratio octane/borate buffer ¼ 1 : 5Þ. By coupling both hydrolysis and lipoxygenation in the same reactor, we are able to perform two different reactions in the same system with the speciﬁc aim of improving the yield of hydroperoxide production from triglycerides. Bioconversion of trilinolein in a bienzymatic reactor not only reduces the number of steps, but increases the total yield when comparing it to lipolysis and lipoxygenation which are achieved separately (Table 4). The presence of the second enzyme in the medium accelerates and increases consumption of the ﬁrst substrate (trilinolein), because lipoxygenase reacts with the second substrate (linoleic acid) produced by lipolysis of trilinolein. Conversion yields in the bienzymatic system have been optimized by using pure substrates (triglycerides) as well as crude vegetable oils (Table 4) rich in a range of polyunsaturated fatty acids (sunﬂower oil or linseed oil). The use of crude reactants approaches a more realistic scenario for the industrial-scale manufacture of hydropexides. Reaction yields depend on the nature of the substrate. Linseed oil contains two polyunsaturated fatty acids: 50% linolenic acid and 18% linoleic acid. The corresponding hydroperoxides are obtained with low yields.

Lipase from porcine pancreas

Lipase from Rhizomucor miehei

Lipase from Chromobacterium viscosum Lipase from Chromobacterium viscosum Lipase from Rhizomucor miehei

Lipase 1 from Candida rugosa

Lipase 1 from Candida rugosa

Lipase from Aspergillus niger

Lipase from Aspergillus niger

Lipase from Aspergillus sp.

Lipase from Aspergillus sp.

Lipase from Aspergillus sp.

Lipase from Aspergillus sp.

Lipase from Aspergillus sp.

Enzyme system

Olive oil hydrolysis (highly unsaturated) Soybean oil hydrolysis (highly unsaturated) Milk fat hydrolysis (rich in saturated fatty acids) Lard hydrolysis (rich in saturated fatty acids) Coconut oil hydrolysis (rich in saturated fatty acids) Esteriﬁcation of 1-butanol and oleic acid Transesteriﬁcation 2-ethyl-1hexanol and rapeseed oil Esteriﬁcation of 1-butanol and oleic acid Transesteriﬁcation 2-ethyl-1hexanol and rapeseed oil Esteriﬁcation of 1-butanol and oleic acid Transesteriﬁcation of 2-ethyl-lhexanol and rapeseed oil Esteriﬁcation of 1-butanol and oleic acid Transesteriﬁcation 2-ethyl-1hexanol and rapeseed oil Esteriﬁcation of 1-butanol and oleic acid

Reaction

92.9

Oil–deionized water (96.6/3.4)

Oil–deionized water (96.6/3.4)

49.7

93.8

97.2

Oil–water (97/3)

Oil–water (97/3)

14.2

99.6

91.4

41.1

Oil–deionized water (96.6/3.4)

Oil–water (97/3)

Oil–deionized water (96.6/3.4)

Oil/water (97/3)

49.7

26.8

Oil–phosphate buffer (1/2) Oil–deionized water (96.6/3.4)

29.9

35.7

47.1

68

Conversion yield (%)

Oil–phosphate buffer (1/2)

Oil–phosphate buffer (1/2)

Oil–phosphate buffer (1/2)

Oil–phosphate buffer (1/2)

Biphasic medium

103

103

103

103

103

103

103

103

103

101

101

101

101

101

Reference

TABLE 4 Yields of Different Enzyme-Catalyzed Reactions in Biphasic Media. 100% Conversion Yield Corresponds to the Total Conversion of Substrate to Product

576 Gargouri

Immobilized soybean lipoxygenase Immobilized soybean lipoxygenase Coupled Mucor javanicus lipase and soybean lipoxygenase Coupled Pseudomonas sp lipase and soybean lipoxygenase Coupled Mucor miehei esterase and soybean lipoxygenase Coupled Mucor javanicus lipase and soybean lipoxygenase Coupled Mucor javanicus lipase and soybean lipoxygenase Coupled Mucor javanicus lipase and soybean ﬂour extract Coupled Pseudomonas sp. lipase and soybean lipoxygenase

Soybean lipoxygenase

Lipase from porcine pancreas

66.4

62.7

Octane–borate buffer pH9 (1/5)

Octane–borate buffer pH 9 (1/5) Octane–borate buffer pH 9 (1/5)

Octane–borate buffer pH 9 (1/5)

Octane–borate buffer pH 9 (1/5)

Octane–borate buffer pH 9 (1/5)

13-Hydroperoxy- acid from trilinolein

13-Hydroperoxy-acid from trilinolein

13-Hydroperoxy-acid from trinolenin

13-Hydroperoxy-linoleic acid from sunﬂower oil

13-Hydroperoxy-linoleic acid from sunﬂower oil

13-Hydroperoxy-linoleic acid from sunﬂower oil

37

77

79.2

42.7

58.5

38

37

37

37

37

38

24

69

87.1

24

23

103

81

35

19.4

Oxtane–borate buffer pH 9 (5/2 at 78C) Octane–borate buffer pH 9; (5/2 at 158c) Octane–borate buffer pH 9 (1/5)

Hexane–borate buffer pH 6.5 (1/1)

Oil–water (97/3)

Transesteriﬁcation 2-ethyl-1hexanol and rapeseed oil 9-Hydroperoxy-acid from -linolenic acid 13-Hydroperoxy-acid from linoleic acid 13-Hydroperoxy-acid from linoleic acid 13-Hydroperoxy-acid from trilinolein

Biocatalysis in Liquid–Liquid Biphasic Media 577

578

Gargouri

The major fatty acid that exists in sunﬂower oil is linoleic acid (>60% molar). The bienzymatic system produces exclusively hydroperoxylinoleic acid with high yields. Crude powder or immobilized lipases were coupled with pure soybean lipoxygenase-1 or aqueous extract of soybean ﬂour (10% w/v). In the bioreactor, the interface between the two liquid phases signiﬁcantly restricts the transfer to the aqueous phase of intermediates appearing during hydrolysis (diacylglycerols, monoacylglycerols); thus, their oxidation is very limited and lipoxygenase acts exclusively on free fatty acid. Evolution of hydroperoxides in the two-enzyme system has an optimal rate between 150 and 200 min. At 300 min, production becomes much slower because lipoxygenase is inactivated at the octane–borate buffer interface [38]. The two reactions are achieved in only one step without altering the product quality. The inhibition of enzymes by excess of intermediate components is reduced in this system. The presence of an organic solvent in the medium allows a high solubility of acylglycerols and a well-controlled partition of the components in the reactor. At the end of the reaction, hydroperoxide can be easily recovered in the aqueous phase (98–99%) after its separation from the organic phase and precipitation of the enzymes. The hydroperoxides obtained are highly reactive molecules [109]. They are intermediate compounds in the lipoxygenase pathway in plants, precursors for the synthesis of hydroxy-fatty acids (i.e., (+)-coriolic acid [38,110], and regulators of the prostaglandins biosynthesis [111–113]. This approach can easily be extended to a large scale to produce hydroperoxy-fatty acids from high concentrations of triacylglycerols with facile extraction.

IX.

BIPHASIC BIOREACTORS

Many interesting biocatalytic reactions involve organic components that are poorly watersoluble. When using organic-aqueous biphasic bioreactor, availability of poorly watersoluble reactants to cells and enzymes is improved, and product extraction can be coupled to the bioreaction. Many applications in two-phase media can use the existing standardtype bioreactors, such as stirred-tank, ﬂuidized-bed, and column reactors with minor adjustments. A.

Stirred-Tank Reactors

The stirred batch reactors are easy to operate and their conﬁgurations avoid temperature and concentration gradient (Table 5). These reactors are useful for hydrolysis reactions proceeding very slowly. After the end of the batch reaction, separation of the powdered enzyme support and the product from the reaction mixture can be accomplished by a simple centrifugation and/or ﬁltration. Rofﬂer et al. [114] investigated two-phase biocatalysis and described stirred-tank reactor coupled to a settler for extraction of product with direct solvent addition. This basic experimental setup can lead to a rather stable emulsion that needs a long settling time. B.

Membrane Reactors

Different enzymes – particularly lipases – immobilized in membrane reactors have been studied in the presence of two-liquid phases (Table 5). Organic and aqueous phases containing respectively hydrophobic and hydrophilic reactants are separated by a solid mem-

Batch reactor Membrane reactor Hollow-ﬁber membrane reactor Membrane reactor Packed-bed reactor Liquid-impelled loop reactor Fluidized-bed reactor Continuous extraction loop reactor Continuous stirred-tank reactor Continuous stirred-tank reactor

Stirred-tank reactor

Bioreactor

TABLE 5 Biphasic Bioreactors

Alcoholysis of 1-phenyl ethyl butyrate and 1heptanol Production of acetone and butanol from glucose Ethyl laurate hydrolysis Hydrolysis of sunﬂower oil Synthesis of monoglycerides Hydrolysis of olive oil Production of anthraquinones Epoxidation of propene Ethanol production with glucose fermentation Hydrolysis of milk fat Hydrolysis of olive oil

Reaction

Clostridium acetobutylicum Candida rugosa lipase Lipase from Rhizopus sp. Lipase from Candida rugosa Lipase from porcine pancreas Plant cell culture Mycobacterium cells Saccharomyces cerevisiae Lipase from Rhizopus delemar Lipase from Candida cylinderacea

Lipase from Candida cylindracea

Biocatalyst

129 116 122 75 123 124 125 126 127 115

120

Reference

Biocatalysis in Liquid–Liquid Biphasic Media 579

580

Gargouri

brane in which enzyme is trapped or adsorbed. The ﬂow of liquid phases is tangential when both phases ﬂow parallel to the membrane in either cocurrent or countercurrent fashion. If ﬂow is normal to the membrane, one of the phases is pumped through whereas the other remains stationary. The organic phase containing the hydrophobic product is then separated by simple centrifugation. Lipase-catalyzed esteriﬁcation was performed in a membrane bioreactor [75]. The system catalyses esteriﬁcation of glycerol and fatty acids and produces monoglycerides with an inline column which adsorbs the product preferentially. C.

Fixed-Bed Reactors

Fixed-bed reactors employed for lipase-catalyzed hydrolysis and interesteriﬁcation reactions are highly efﬁcient and have been used on a large scale (Table 5). The two phases may ﬂow through the reactor in the opposite or same directions. If no solvents are used, the effect of viscosity of some substrates (i.e., oil) may be minimized by employing high temperatures which lead to faster rates of inactivation of lipases. D.

Fluidized-Bed Reactors

Applications of the organic solvents in ﬂuidized-bed reactors have also been investigated, particularly with immobilized cells (Table 5). This type of reactor has several advantages over a ﬁxed-bed reactor, namely, reduced coalescence of the emulsion particles, lower pressure at high ﬂow rate, and less channeling and plugging. E.

Continuous Stirred-Tank Reactors

A continuous stirred tank reactor has been reported for the hydrolysis of the triglycerides existing in vegetable oil in the presence of the aqueous phase and for synthesis reactions (Table 5). A microﬁlter can be used to prevent the immobilized enzyme from leaving the reactor. Kawano et al. [115] investigated the hydrolysis of olive oil in octane with Candida cylindracea lipase in aqueous solution in a ‘‘Vibro Mixer’’ reactor containing vibration plates connected to the crankshaft of a motor and oscillated with ﬁxed rates.

X.

CONCLUDING REMARKS

As proven in this review and other papers, organic–aqueous biphasic media have been useful in many areas of biocatalysis applications. We summarize the potential advantages in carrying out biocatalysis in biphasic systems: High reactor substrate and/or product concentrations. Efﬁcient bioconversion of sparingly water-soluble substrates. Reduction in inhibition with substrate and/or product. Possibility of signiﬁcant equilibrium shift in the desired direction. Thermodynamically unfavorable reactions become possible. Ease of product recovery. Biocatalyst (especially when immobilized) can be separated after the reaction and used for a long period of time. Microbial contamination is limited in the presence of the organic solvent.

Biocatalysis in Liquid–Liquid Biphasic Media

581

Nevertheless, development of processes for commercial purposes is still limited, particularly with interfacial effects: the loss of activity of the biocatalyst, the slow coalescence, the biocatalyst aggregation, and accumulation of medium components at the interface. The study of compartmentalized media and interaction of the mass transfer and metabolism can help us to better understand the behavior of some enzymatic systems in vivo. The cell is not a homogeneous medium but it is composed of compartments between which reactants are distributed according to their physicochemical properties. In living cells, there are highly organized particle and membrane systems. The spatial metabolic organization in these heterogeneous media cannot be explained by the homogeneous enzymology. However, the study of enzymatic pathways in multiphasic bioreactors provides a useful alternative, which approaches the genuine natural systems. Current research is in progress in our laboratory on biocatalysis in two-phase media with -glycosidases, yeast, and enzymes of the lipoxygenase pathway.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

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24 Design of Biocompatible Ion Sensors KEIICHI KIMURA Department of Applied Chemistry, Faculty of Systems Engineering, Wakayama University, Wakayama, Japan

I.

INTRODUCTION

Potentiometric ion sensors such as ion-selective electrodes are compact and convenient tools for ion assay in solution. Speciﬁcally, much attention has been focused on neutralcarrier-type ion sensors owing to their high ion selectivities. Solvent-polymeric membranes are generally required as their ion-sensing membranes. A most popular ion-sensing membrane material for neutral-carrier-type ion sensors is plasticized poly(vinyl chloride) (PVC). The solvent-polymeric ion-sensing membranes, however, have some drawbacks. The ion-sensing membranes need high volume percentages of a special plasticizer, which is easy to exude from the membranes to aqueous (sample) phases and thereby to deteriorate. Not only the plasticizers but also the neutral carriers are often toxic, and PVC itself is becoming an issue in environmental science due to the chlorinated compound. Also, plasticized-PVC membranes do not seem to be very biocompatible because they tend to adsorb bio-organic compounds such as proteins on serum metal-ion assay. Sometimes, neutral-carrier-type PVC-membrane ion-selective electrodes may give some negative errors on metal-ion assay in biological systems. It is therefore quite difﬁcult to apply ion sensors based on neutral-carrier-type PVC membranes to in-vivo metal-ion assay such as in-situ ion monitoring at a bedside. In another aspect, plasticized- PVC membranes are not very suitable for ion-sensitive ﬁeld-effect transistors (ISFETs) mainly due to the poor adhesion to the FET gate surface. Considerable efforts are therefore required for alleviating the toxicity and promoting the biocompatibility of the neutral-carrier-type ion sensors, in order to obtain biocompatible ion sensors that are applicable in-vivo ion sensing in biological systems, especially in clinical systems. One of the efforts is in material selection for the support polymers of the ion-sensing membranes. That is to say, materials that are compatible with biological systems such as human blood should be applied as the membrane support. Another effort is in chemical bonding of active materials such as neutral carriers to the membrane supports and avoidance of special plasticizers. They would diminish the toxicity of membrane components considerably by preventing the exudation of neutral carriers from the membranes to aqueous (sample) phases. This chapter is concerned with the recent research concerning the design of biocompatible ion sensors, especially the results of our research group.

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II.

MEMBRANE MATERIALS SELECTION

A.

Poly(oxyethylene)-Containing Polymers

Poly(oxyethylene) (POE) is thought to have some blood compatibility by reducing protein adsorption [1]. Even PVC, if it contains PEO, shows some effect on alleviating protein adsorption in blood, and the polymer was therefore applied as an outer membrane for an enzyme electrode [2]. Poly(urethane) derivatives containing oligo(oxyalkylene) units, which are called segmented poly(urethane)s, are known to have some nonthrombogenic property, so their use as a material for artiﬁcial human organs was investigated. Crosslinked polyether-urethane was used as a coating agent to obtain blood electrolyte sensors [3]. A pHISFET was mounted on a catheter, which was then dipped into a prepolymer of segmented poly(urethane) for the coating. The coating polymer can pick up water and Hþ easily, so the pH-ISFET can work in blood with some blood compatibility. Segmented poly(urethane) was also applied as a membrane support for ion-selective electrode [4]. A poly(urethane) prepolymer as well as an ion-sensing material was dissolved in tetrahydrofuran (THF) and then the THF solution was cast on a glass substrate. The poly(urethane) membranes containing a quaternary ammonium salt and a Naþ ionophore yielded ion-selective electrodes for Cl and Naþ , respectively. The ion-sensing membranes based on poly(urethane) gave better nonthrombogenic property than those based on PVC. Surface modiﬁcations of segmented poly(urethane)-based ion-sensing membranes with crosslinked PEO brings about marked nonthrombogenic property, that is, remarkably alleviated blood platelet adsorption [5]. Potentiometric ion electrodes based on the membrane composite doped with valinomycin and quaternary ammonium salts retained good response properties for Kþ and anion sensors, essentially equivalent to the corresponding untreated membranes. B.

Poly(dimethylsiloxane)

An alternative membrane material to PVC for ion-selective electrodes is crosslinked poly(dimethylsiloxane), which is generally called room temperature vulcanizing-type (RTV) silicone rubber. Formation of crosslinked poly(dimethylsiloxane) (RTV silicone rubber) consists of two processes: (1) the hydrolysis of active end groups (alkoxy, acetoxy, oxime, amino, amido groups, and so forth) of dimethylsiloxane oligomers, and (2) crosslinking by condensation of the active end groups with the resulting silanol groups. Silicone rubber has several advantages: (1) easy fabrication at ambient temperature, (2) high elasticity at ambient temperature, (3) excellent adhesive property, especially for inorganic materials, (4) excellent electrical property, (5) chemical inactivity, and (6) low toxicity. Silicone rubber is, therefore, an excellent candidate for membrane materials of ion sensors. The material was ﬁrst applied to heterogeneous precipitate-based membranes for silver ion-selective electrodes [6]. Since the polymer material is highly elastic at ambient temperature, neutral-carrier-type ion-sensing silicone-rubber membranes do not necessarily require special plasticizers to endow a neutral carrier with mobility enough for ion exchanges. This eliminates deterioration of the sensing membranes caused by the plasticizer exudation. Most importantly, silicone-rubber-membrane ion-selective electrodes are also expected to show some biocompatibility on practical use in biological systems [7–11]. Moreover, the excellent adhesive property of silicone rubber to inorganic materials is very advantageous on its use as ionsensing membranes for ISFET. These characteristics of silicone rubber become great advantages on the application of the silicone-rubber-membrane ion sensors to clinical analyses. Simple encapsulation or dispersion of neutral carriers in silicone rubber is an easy way to fabricate silicone-rubber ion-sensing membranes based on neutral carriers.

Design of Biocompatible Ion Sensors

587

However, there seems to be some drawback in the solubility or dispersibility of ion-sensing material in silicone rubber. This is mainly because silicone rubber does not contain a large quantity of plasticizer as the membrane solvent, in which neutral carriers can be dissolved easily, unlike in plasticized-PVC ion-sensing membranes. This issue is serious, especially with silicone-rubber membranes containing neutral carriers that show high crystallinity. Valinomycin, a typical Kþ ionophore, seems applicable to silicone-rubber-based Kþ -selective electrodes [7,8,12–14]. Conventional crown-ether-based neutral carriers are also quite soluble in silicone rubber. Calix[4]arene derivatives carrying carbonyl linkages at the lower rim [15] are excellent neutral carriers for plasticized-PVC membrane Naþ -selective electrodes [16–19]. We have also designed high-performance Naþ -ISFETs based on calix[4]arene neutral carriers. Most calix[4]arene neutral carriers are quite soluble in the plasticized membranes, but they are not necessarily soluble and applicable in silicone rubber. Silicone-rubber-based ion-sensing membranes possess relatively high electrical resistivity, which often brings about unstable EMF readings. The issue for the poor dispersibility in membrane is serious especially in ionsensing membranes containing electrically neutral ion-exchanger, that is, neutral carriers. Highly soluble calix[4]arene neutral carriers should, therefore, be designed for the application in silicone-rubber membranes. Most calix[4]arene neutral carriers incorporating four ester or amide linkages show high crystallinity and high melting points because of their structural symmetry. The symmetrical structure results in comparably high molecular cohesion, and therefore the calix[4]arene neutral carriers are generally not very easy to dissolve in polymeric matrices, even in plasticized PVC. The solubility of calix[4]arene neutral carriers is generally worse in silicone-rubber membranes than in plasticized-PVC membranes. Incorporation of unsymmetrical structures into calix[4]arene neutral carriers improves their solubility in silicone rubber. So, an unsymmetrical calix[4]arene neutral carrier was designed which possesses three ethyl-ester linkages and an amide linkage with longer alkyl chains at the phenoxy positions, (1) [20]. As compared to a symmetrical calix[4]arene neutral carrier such as (2), the unsymmetrical one possesses only low symmetry and is therefore amorphous. Two other calix[4]arene neutral carriers with different unsymmetrical moieties were also synthesized for comparison with (1). Calixarene neutral carrier (3), which carries an amide carbonyl linkage without a long aliphatic chain, turns out to be an amorphous glass by melting, followed by cooling to room temperature. Compound (4) has a dodecyl group as the long aliphatic chain and an ester carbonyl linkage and is still unsymmetrical only with the aliphatic chain.

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Figure 1 shows a typical potential response of a Naþ -ISFET based on a siliconerubber membrane containing 10 wt% unsymmetrical calix[4]arene neutral carrier (1). A Nernstian response to Naþ activity changes was attained in the range of 1 104 to 1 M with the silicone rubber/(1) membrane. The potential response is very fast with a response time (t90 ) of about 2 s for a tenfold Naþ -activity increase. However, silicone-rubber membranes of symmetrical calix[4]arene neutral carrier (2), when applied for Naþ ISFETs, exhibit only poor response to Naþ activity changes. The silicone-rubber membrane of (2) is very different in the ISFET response from the corresponding plasticizedPVC membrane. This poor response of the silicone-rubber membrane (2) is derived mainly from its low solubility in silicone rubber. Scanning electron microscopy (SEM) afforded some information about the solubility of (2) in silicone rubber. Microcrystals of (2), which were not very compatible with silicone rubber, were found on the silicone-rubber membrane of (2), while the corresponding (1) membrane possesses a smooth surface. This implies good compatibility of the unsymmetrical calix[4]arene neutral carrier with silicone rubber. Calixarene neutral carrier (3) is also quite soluble in silicone rubber. In Naþ ISFETs with (3)/silicone-rubber membranes, a Nernstian response was attained in the range of 1 104 to 1 101 M Naþ , but the sensitivity was decreased more or less at higher Naþ activities. On the contrary, calixarene neutral carrier (4), although also unsymmetrical, bears only poor solubility in the polymer matrix. Serious phase separation was observed in the (4)–silicone-rubber membranes, thus resulting in poor ISFET sensitivity. The high solubility of (1) in silicone rubber and thereby high ISFET sensitivity are, therefore, ascribable mainly to the unsymmetrization of calixarene neutral carriers by the incorporation of an amide carbonyl group. There also seems to be some contribution of the unsymmetrization based on the incorporation of a long aliphatic chain to the solubility enhancement. The highly dispersible calix[4]arene neutral carriers can also improve the durability for neutral-carrier-type ion sensors. Time-course changes in both sensitivity (slope for Naþ calibration graph) and selectivity (selectivity coefﬁcient for Naþ with respect to Kþ ) were followed in the Naþ -ISFETs based on ion-sensing membranes of silicone rubber–(1), plasticized PVC–(1), and plasticized PVC–(2) (Fig. 2). Deterioration proceeded quite quickly in the Naþ -ISFETs of plasticized PVC–(2); both the Naþ sensitivity and selectivity

FIG. 1 Potential response to Naþ activity changes of ISFETs based on silicone-rubber membranes of calixarene neutral carriers (1)(*), (2) (*), (3) (&), and (4) (~). (From Ref. 20.)

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FIG. 2 Time-course changes of sensitivity (a) and selectivity (b) for Naþ -ISFETs based on silicone rubber – (1) (90/10 wt%) membrane (*), PVC–DOS–(1) (30/60/10 wt%) membrane (&), and PVC– DOS–(2) (30/60/10 wt%) membrane (~). (DOS is 2-ethylhexyl sebacate.) (From Ref. 20.)

were drastically decreased in about 30 days. This occurred because the plasticizer and neutral carrier (2) dissolved out from the membrane into the aqueous phases. In the Naþ ISFETs of plasticized PVC–(1) membranes, a marked deterioration started at about 50 days, that is, more gradually than in the plasticized PVC–(2) system. This implies that the unsymmetrical calix[4]arene (1) is very superior to the symmetrical one (2) in solubility even in plasticized PVC. Nevertheless, leaching of the plasticizer out from the plasticized PVC–(1) membrane resulted in such ISFET deterioration. The Naþ -ISFETs containing silicone rubber–(1) membranes, on the other hand, showed an excellent durability. In these ISFETs, their high Naþ sensitivity and selectivity remained unchanged even after 120 days. Silicone rubber is a polymer consisting of siloxane units, as mentioned above. It is therefore expected that incorporation of oligosiloxane moiety to calix[4]arene neutral carriers increases their afﬁnity to silicone rubber and thereby to enhance their solubility or dispersibility in the polymer matrix. Oligosiloxane-modiﬁed calix[4]arene neutral carriers have been designed which are unsymmetrical and symmetrical ones (5) and (6) [21]. In the unsymmetrical oligosiloxane-modiﬁed calixarene neutral carrier (5), one may also expect dispersibility enhancement derived from its structural asymmetry. Dispersibility of oligosiloxane-modiﬁed calixarene neutral carriers (5) and (6) in silicone rubber was ﬁrst checked by microscopic observation. In the SEM photographs, the silicone-rubber membranes of (5) exhibit smooth surface, which suggests high dispersibility of the oligosiloxane-modiﬁed calixarene neutral carriers in silicone rubber. This is also the case with the (6)-containing silicone-rubber membranes. Membrane impedance (resistivity), obtained by AC impedance measurements in Naþ aqueous solutions, also provided important information concerning the membrane dispersibility of the calixarene neutral carriers

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FIG. 3 Comparison of membrane impedance among silicone-rubber-based ion-sensing membrane containing calixarene neutral carriers (5) (*), (6) (*), and (2) (~). (From Ref. 21.)

(Fig. 3). The silicone-rubber membranes containing the oligosiloxane-modiﬁed calix[4]arene neutral carriers, especially (5), possess extremely low resistivity as silicone-rubber-type ion-sensing membranes. On the contrary, high resistivity was found with the membrane of (2), which is equivalent to or even higher in the resistivity than silicone-rubber membranes not containing any neutral carrier. This fact strongly supports that both (5) and (6) are highly dispersible in silicone rubber, thus undergoing active cation diffusion in the membrane. Thus, the Naþ -ISFETs of (5) and (6) exhibit high sensitivity with a Nernstian slope in a wide Naþ activity range, which is very similar to that for (1) as shown in Fig. 1. The time–response proﬁle indicated that the potential response is quite fast in the Naþ -ISFETs based on the oligosiloxane-modiﬁed calixarene neutral carriers, and their response time being about 1 s. The potential response of the Naþ sensors is fast enough for their practical use. Figure 4 summarizes the selectivity coefﬁcients for Naþ with respect to other ions in the Naþ -ISFETs based on calixarene neutral carriers (1), (2), and (5). The Naþ sensors

FIG. 4 Selectivity comparison among silicone-rubber-membrane Naþ -ISFETs based on calixarene neutral carriers (1), (2), and (5).

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based on nonsymmetrical calixarene neutral carrier (1) and oligosiloxane-modiﬁed one (5) are similar to that based on (2) in the Naþ selectivity against Kþ . The selectivity coefﬁcient for Naþ with respect to Kþ for the ISFET of (1) and (5) is about 3 103 , being sufﬁcient of Naþ assay in blood serum. Silicone rubber is also applicable to membrane supports for neutral-carrier-type ionselective electrodes. The problem of membrane impedance is, however, more serious in the ion-selective electrodes than in the ISFETs. High membrane impedance often leads signiﬁcantly to the low sensitivity and slow potential response in the ion-selective electrodes. The silicone-rubber membrane based on oligosiloxane-modiﬁed calix[4]arene neutral carrier (5) still exhibits high performance when used for Naþ -selective electrodes [22]. Figure 5 shows a typical potential response for a silicone-rubber-membrane Naþ -selective electrode based on calixarene neutral carrier (5), together with those for (2) and a well-known Naþ neutral carrier, bis[(12-crown-4)methyl] dodecylmethylmalonate [bis(12-crown-4)] [23]. The silicone-rubber membrane of (5) afforded high electrode sensitivity with a Nernstian slope in the wide Naþ activity range of 3 105 to 1 M. On the other hand, both the silicone-rubber membrane electrodes based on (2) and bis(12-crown-4) possess only poor sensitivity to Naþ activity changes and even anion response in the high NaCl concentration range. Obviously, the poor dispersibility of neutral carriers (2) and bis(12-crown-4) in silicone rubber and therefore the high electrical resistivity of their silicone-rubber membranes lead to the low sensitivity of their Naþ -selective electrodes. A marked difference in response time was also found among Naþ -selective electrodes with silicone-rubber membranes of the three neutral carriers (Fig. 6). Fast response [2 s of response time (t90 Þ was attained in the electrodes with silicone-rubber membranes of (5). The electrode response is, however, sluggish in the silicone-rubber membrane system of (2) and bis(12-crown-4). The response times in both the silicone-rubber membrane systems of (2) and bis(12-crown-4) are in the order of 1 min. Thus, high dispersibility of oligosiloxane-modiﬁed calixarene neutral carrier (5) in silicone rubber is reﬂected more remarkably in the performance of siliconerubber membrane Naþ -selective electrodes than the corresponding ISFETs. C.

Sol–Gel-Derived Membranes

Sol–gel chemistry enables us to design hybrid inorganic–organic materials, allowing us to fabricate glasses and ﬁlms with novel properties and functionalities [24]. The low reac-

FIG. 5 Potential response of silicone-rubber-membrane Naþ -selective electrodes based on neutral carriers (5) (*), (2) (*), and bis(12-crown-4) (~). (From Ref. 22.)

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FIG. 6 Time-course changes of potential response for silicone-rubber-membrane Naþ -selective electrodes based on neutral carriers (5), (2), and bis(12-crown-4) on changing Naþ concentration from 1 103 to 3 103 M. (From Ref. 22.)

tion temperature on sol–gel processing facilitated incorporation of functional organic compounds into inorganic materials. Sol–gel-derived membranes are therefore promising candidates for sensing membrane materials for ion sensors mainly due to their physical stability and chemical inactivity. Sol–gel-derived membranes encapsulating enzymes have already been applied to amperometric biosensors [25,26]. For potentiometric ion sensors, we have tried to apply sol–gel-derived membranes containing valinomycin and a bis(12crown-4) derivative to ion-sensing membranes for Kþ - and Naþ -ISFETs, respectively [27]. Tetraethoxysilane (TEOS) is often used for fabrication of sol–gel-derived materials by its hydrolysis followed by condensation of its resulted silanols. However, the sol–gel processing of TEOS itself affords brittle glassy products, which may not be suitable for ion-sensing membranes due to the poor mechanical strength. An idea to alleviate the brittleness of sol–gel-derived membranes for neutral-carrier-based ion-sensing membranes is to decrease the crosslinking degree by using mixtures of TEOS and diethoxydimethylsilane (DEDMS) as starting alkoxysilanes. Solutions containing DEDMS and TEOS mixtures with DEDMS/TEOS ratios of 1, 2, and 3 and also a small quantity of neutral carriers were, therefore, tested for the sol–gel-derived membranes for neutralcarrier-type ISFETs. It takes too long to solidify the ion-sensing membranes in the higher DEDMS/TEOS ratios than 3. The potential response to Kþ activity changes for the Kþ -ISFETs based on valinomycin-encapsulated sol–gel-derived membranes depends on the DEDMS/TEOS ratios (Fig. 7). Only poor sensitivity was attained in

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FIG. 7 Potential response of Kþ -ISFETs based on valinomycin-encapsulated sol–gel-derived membranes fabricated with initial DEDMS/TEOS ratios of 1 (~), 2 (&), and 3 (*). (From Ref. 27.)

the ISFETs of sol–gel-derived membranes fabricated with the lower DEDMS/TEOS ratios. On the other hand, the Kþ -ISFETs of the membrane with a DEDMS/TEOS ratio of 3 can afford a Nernstian response in the wide Kþ -activity range. The poor sensitivity in the membrane systems with the lower DEDMS/TEOS ratios is probably due to the high degree of crosslinking in their resulted sol–gel-derived membrane, which in turn leads to the low mobility of the neutral carrier encapsulated in membrane. The response time of the ISFETs also depends remarkably on the initial DEDMS/ TEOS ratios for sol–gel processing. The ISFETs with the initial DEDMS/TEOS ratios of 1 exhibited slow potential response and the response time (t90 ) is in the order of minute. The higher DEDMS/TEOS ratios allowed rapid responses. The response time is ten or more seconds for the membrane system with the ratio of 2 and only a few seconds for that with the ratio of 3. The response times for the higher DEDMS/TEOS ratios, especially with the ratio of 3, are acceptable for practical use of ion sensors. The initial DEDMS/ TEOS ratio of 3, therefore, seems to be suitable for the fabrication of sol–gel-derived membranes encapsulating valinomycin, at the viewpoint of the membrane mechanical strength, sensor sensitivity, and response time. Sol–gel-derived membranes encapsulating a bis(crown ether) derivative [bis(12crown-4-ylmethyl) 2-dodecyl-2-methylmalonate] [28] were also fabricated with an initial DEDMS/TEOS ratio of 3 for Naþ -ISFETs. The Naþ -ISFETs showed a Nernstian response to Naþ activity changes in the activity range of 1 104 to 1 M and a short response time of 2 s. Employment of a polythiophene interlayer improved the potential instability and the lower detection limit in both of the Kþ - and Naþ -ISFETs based on the sol–gel-derived membranes with the initial DEDMS/TEOS ratio of 3 (Fig. 8). Selectivity coefﬁcients values for Kþ - and Naþ -ISFETs with the optimized ion-sensing membranes encapsulating valinomycin and bis(12-crown-4) are summarized in Fig. 9. The selectivity coefﬁcient for Kþ with respect to Naþ in the Kþ -ISFET is 2 104 and that for Naþ with respect to Kþ in the Naþ -ISFET is 3 103 . The selectivity coefﬁcient values are similar to those for the ISFETs and ion-selective electrodes with the previous membrane materials containing the same neutral carriers. The high sensitivity and selectivity for the neutral-carrier-type ISFETs based on sol–gel-derived membranes can last for at least 3 weeks.

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FIG. 8 Potential response of Kþ - and Naþ -ISFETs based on optimized sol–gel-derived membranes of valinomycin (*) and bis(12-crown-4) (*) with interlayer of polythiophene [27]. The initial DEDMS/TEOS ratio for sol–gel processing is 3.

Adsorption of blood proteins on the sol–gel-derived membrane containing a neutral carrier was tested to obtain some information about biocompatibility of the ion-sensing membranes and therefore the resulted ISFETs on blood ion assay. For comparison, plasticized-PVC membranes containing the same neutral carrier were also employed for the biocompatibility check. Comparison in the SEM photographs between a sol–gelderived membrane and its corresponding plasticized-PVC membrane indicates a striking difference in the blood protein adsorption (Fig. 10). The sol–gel-derived membrane hardly adsorbs blood proteins, whereas the plasticized-PVC one adsorbs a large amount of proteins. This suggests that the sol–gel-derived ion-sensing membranes are superior to the corresponding plasticized-PVC membranes in the biocompatibility. The adsorption of organic components in blood on plasticized-PVC ion-sensing membranes often causes some negative errors on blood ion assay by the resulted membrane ion sensors [8,29]. The serious protein adsorption also makes it difﬁcult to use plasticized-PVC membrane ion sensors for in-vivo ion monitoring. Conversely, the alleviated protein adsorption on the

FIG. 9 Selectivity coefﬁcients for Kþ - and Naþ -ISFETs based on optimized sol–gel-derived membranes of valinomycin (a) and bis(12-crown-4) (b) with polythiophene interlayer. (From Ref. 27.)

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FIG. 10 SEM photographs for sol–gel-derived (a) and plasticized-PVC (b) membranes encapsulating bis(12-crown-4) after protein adsorption test. (From Ref. 27.)

sol–gel-derived membrane suggests a possibility for intra-arterial use of the neutral-carrier-type ISFETs based on the membrane.

D.

Other Biocompatible Materials

Heparin is often utilized for preventing blood coagulation. When ion-selective electrodes are used in vivo, supplying heparin to the bloodstream suppresses ﬁbrin formation on the surface of the ion-sensing membranes [9]. The heparin treatment to patients on in-vivo measurements, is however, a serious disadvantage. This induced the covalent bonding of heparin to the ion-sensing membrane surface [30]. Heparin was bonded covalently to the surface of cellulose triacetate (CTA) membrane effectively by carbonyldiimidazole activation of the cellulose hydroxyl groups. The heparin-immobilized membrane, which is biologically active, was combined with an unmodiﬁed CTA membrane containing valinomycin. The heparin modiﬁcation by covalent bonding does not affect signiﬁcantly the original electrode property such as sensitivity and selectivity for the Kþ -selective electrode. Nitric oxide is recently becoming well known due to its biological action. Nitric oxide exhibits antiaggregation property of blood platelet [31] as well as vasodilating property [32]. Therefore, if ion-sensing membranes can emit low levels of nitric oxide gradually, the ion sensor must be blood-compatible. For instance, piperizine–PVC copolymer/N2 O2 (diazeniumdiolate) adducts can produce NO gas by its hydrolysis. The NOevolving polymer was dispersed as a solid particle in plasticized PVC or segmented poly(urethane) membranes containing tridodecylamine or valiomycin, in order to obtain bloodcompatible pH- or Kþ -sensing membranes [33]. The ion-sensing membranes are capable of generating NO gas for several days on exposing aqueous samples and thereby hardly adsorb blood platelets. As a result, excellent biocompatibility was attained for the ionselective electrodes without affecting their sensor performance. Alternatively, a low-molecular-weight NO-evolving compound, N; N 0 -dimethylhexanediamine/NO adduct, was dissolved in plasticized-PVC membranes for providing blood compatibility [34,35]. The ionsensing membranes were fabricated as a multilayer ﬁlm; an membrane containing the NOevolving material was sandwiched by two unmodiﬁed ion-sensing ﬁlms containing Hþ or Kþ carrier. NO generation by the hydrolysis of the material with water is slower and therefore the blood compatibility can last a long time.

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Recently, remarkably high blood compatibility was realized in polymers containing phosphorylcholine groups at the side chain (MPC) polymer), which are generally copolymers of methacryloyloxyethyl phosphorylcholine and an alkyl methacrylate [36]. It was proved that they possess higher thrombogenic property as compared to conventional blood-compatible materials such as poly(dimethylsiloxane) and poly(urethane). They are now being tested for their usefulness as artiﬁcial internal organs [37]. The MPC polymer is also a material candidate for biocompatible ion sensors. MPC polymers were applied as blood-compatible layers for amperometric sensors [38,39]. Enzyme-based glucose sensors generally have a membrane on which glucose oxydase is immobilized on an H2 O2 amperometric electrode. On glucose assay in blood samples, the enzyme membranes are apt to adsorb proteins. The protein adsorption on the enzyme membrane often results in the sensor deterioration. Coating of the enzyme membrane with an MPC polymer prevents protein adsorption and thereby increases the sensor lifetime. We have applied MPC polymers for biocompatible potentiometric ion sensors. Modiﬁcation of neutral-carrier-based PVC membranes by an MPC polymer has improved thrombogenic properties markedly, with the original sensor property of the PVC membrane remaining unchanged [40].

III.

CHEMICAL MODIFICATION WITH ION-SENSING COMPONENTS

A.

PVC-Based Membrane

The exudation of neutral carriers and plasticizers from ion-sensing membranes results in deterioration of the ion sensors and contamination in environmental and biological systems. In order to prevent the outﬂow of neutral carriers from ion-sensing membranes, attempts have been made to immobilize neutral carriers to PVC membranes by covalent bonding [41–43]. However, unless the neutral-carrier-type PVC membranes are plasticized like the conventional PVC-based ion-sensing membranes, they do not seem to show very good electrode properties, i.e., non-Nernstian response and slow potential response. It is probably because PVC and the chemically modiﬁed PVC themselves do not allow enough mobility for the chemically bonded neutral carriers to exchange cations due to their high glass-transition temperatures (at least higher than room temperature). High contents of membrane plasticizers in the PVC-based ion-sensing membranes may also lead to the toxicity and deterioration of the resulting ion sensors due to their exudation to aqueous sample solutions. It is still difﬁcult for the plasticized-PVC membranes modiﬁed chemically with neutral carriers to be biocompatible. B.

Poly(dimethylsiloxane)

Poly(dimethylsiloxane) (silicone rubber) membranes are fabricated by hydrolysis of alkoxysilyl terminal groups of silicone-rubber precursors [oligo(dimethylsiloxane) derivatives and crosslinking agents], followed by condensation. Covalent bonding of neutral carriers carrying an alkoxysilyl group to silicone rubber is, therefore, feasible by simple reaction of the silicone-rubber precursor with alkoxysilylated neutral carriers, as schematically shown in Scheme 1 [44]. As neutral carriers for the chemical modiﬁcation, 16-crown-5 and calix[4]arene derivatives possessing a triethoxysilyl group (7) and (8) were designed for Naþ sensors. Triethoxysilylethyl-16-crown-5(7) was then mixed with a silicone-rubber precursor for the membrane fabrication accompanying covalent bonding of the neutral carrier. Comparison of IR spectra before and after extraction of the nonbonded neutral carrier

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SCHEME 1 Mechanism for chemical modiﬁcation of poly(dimethysiloxane) (silicone rubber) membranes with ion-sensing active material.

with benzene conﬁrmed the covalent bonding of the 16-crown-5 derivative to siliconerubber membranes. In the IR spectrum for the silicone-rubber membranes fabricated using the ethoxysilylated 16-crown-5, a signiﬁcant peak assigned to C–H deformation vibration for its 16-crown-5 ring was observed around 1350 cm1 even after benzene extraction of (7) from the membranes for a whole day. It is obvious that a considerable amount of 16-crown-5 moiety was bonded covalently to the silicone-rubber membranes fabricated using (7). IR spectroscopy of the silicone-rubber membranes obtained using an alkoxysilylated calixarene (8) also supported the covalent bonding of the calix[4]arene neutral carrier to silicone-rubber membranes.

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The Naþ -selective electrodes of the silicone-rubber membranes containing (8) without any other additive exhibited a very curious potential response, especially in the Naþ activity changes between 1 105 to 1 102 M (Fig. 11). It is probably because the chemical modiﬁcation of silicone-rubber membranes with a calixarene neutral carrier results in high membrane impedance. Sodium tetrakis[3,5-bis(triﬂuoromethyl)phenyl]borate (TFPB) was, therefore, used to improve the electrode response. The TFPB addition to the silicone-rubber membranes reduces the membrane impedance to about one-third of the initial values, thus the membranes allow high sensitivity with a Nernstian slope in the Naþ activity range of 1 105 to 1 M. TFPB is still easy to dissolve out from the membrane because it is not bonded covalently to silicone rubber. For further durability enhancement and toxicity alleviation of the ion-sensing membranes, sodium triphenyl-4-[3-triethoxysilyl)propyloxy]phenylborate (9), together with the calixarene neutral carrier, was also used for the immobilization of an anion excluder on silicone-rubber membranes by covalent bonding. A decreased membrane impedance was again attained in the silicone-rubber membranes incorporating both calixarene neutral carrier (8) and anion excluder (9). The potential response proﬁle for the membrane system containing both (8) and (9) is quite similar to that for the conventional membrane system of calixarene neutral carriers and TFPB that are not bonded covalently, showing a Nernstian response to Naþ activity changes in the wide activity range. Response time was also improved with Naþ -selective electrodes based on the silicone-rubber membranes modiﬁed chemically by calixarene neutral carrier (8) and an anion excluder TFPB or alkoxysilylated sodium tetraphenylborate (9). Another way to immobilize neutral carriers to silicone rubber by covalent bonding may be copolymerization of a vinyl-modiﬁed polysiloxane and neutral-carrier vinyl monomers induced by UV-light irradiation and the resulting neutral-carrier-based membranes were applied to Kþ - and Naþ -sensitive ﬁeld-effect transistors (ISFETs) [45–47]. The neutral-carrier-modiﬁed silicone-rubber membranes often experience anomalous electrode response, unless the ion-sensing membrane contains a lipophilic salt to overcome their high membrane impedance. The design of an oligomeric neutral carrier with a medium molecular weight and its blending with a silicone rubber might alleviate the demerits of the silicone-rubber membranes modiﬁed chemically by a neutral carrier. The mediummolecular-weight neutral carrier may improve the poor mobility of the covalently bonded

FIG. 11 Potential response of Naþ -selective electrodes based on silicone-rubber membranes modiﬁed chemically by triethoxysilylated calix[4]arene (8) (*) without anion excluder; (*) with TFPB; (&) modiﬁed chemically by triethoxysilylated tetraphenylborate (9) as well. (From Ref. 44.)

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neutral carriers and its outﬂowing from the membrane owing to its relatively high molecular weight. For obtaining a medium-molecular-weight calixarene neutral carrier, calix[4]arene tetra-allyl ester was incorporated into an oligo(methylhydrosiloxane) to yield oligosiloxane-modiﬁed calix[4]arene neutral carrier (10) [48]. The oligosiloxane backbone is expected to enhance the solubility or dispersibility of the resulting calixarene neutral carrier in silicone-rubber membranes containing dimethylsiloxane repeating units. Calixarene oligomer (10) carries two or three calixarene units and possesses a molecular weight of several thousands. The Naþ -selective electrodes based on siliconerubber membranes containing the oligomeric calixarene neutral carrier (10) in 10 wt% exhibit a Nernstian response to tenfold Naþ activity changes in the wide activity range. Such a curious potential response as shown in Fig. 11 was not found in the silicone-rubber membranes containing the oligomeric calixarene neutral carrier (10). This means that the calixarene moiety itself is more mobile and it is easier to exchange Naþ in the siliconerubber membranes encapsulating an oligomeric calixarene neutral carrier than in those modiﬁed chemically with a calixarene moiety. There is another signiﬁcant difference in the sensor response time between the membranes containing oligomeric calixarene neutral carrier (10) and incorporating a calixarene moiety by chemical bonding. The response time (t90 ) is no shorter than 3 min in the system of the calixarene-bound membranes. In the present membrane system containing oligomeric calixarene neutral carrier (10), on the other hand, the response time is below 1 min. Thus, the employment of the silicone-rubber membranes containing oligomeric calixarene neutral carrier (10) instead of the calixarenebound membranes can improve the electrode potential response and the response time owing to its enhanced mobility of the calixarene moiety in the membranes. Of course, the oligomeric calixarene neutral carrier (10) is much more insoluble in water than monomeric calix[4]arene neutral carriers and is still not easy to exude from the membrane to aqueous phases.

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Sol–Gel-Derived Membranes

Appropriate fabrication of sol–gel-derived membranes encapsulating neutral carriers such as valinomycin can afford an excellent type of neutral-carrier-type ion-sensing membranes for ISFETs [27] as already mentioned. The simple encapsulation of neutral carriers in sol– gel-derived membranes, however, has a drawback: the encapsulated neutral carriers are still apt to exude from the membranes into aqueous sample solutions, which thereby makes the resulting ion sensors less durable and more toxic. Incorporation of neutral carriers to sol–gel-derived membranes by covalent bonding is desirable. Sol–gel-derived membranes are generally made by hydrolysis of an alkoxysilane such as tetraethoxysilane (TEOS), followed by condensation of the resulted silanol. So, an easy way to incorporate a neutral carrier to sol–gel-derived membranes by covalent bonding is sol–gel processing of the alkoxysilane together with an alkoxysilylated neutral carrier [49]. Triethoxysilylated 16-crown-5 and bis(12-crown-4) derivatives (7) and (11) were selected as the crown-ether neutral carriers. The corresponding triethoxysilylated derivative of sodium tetraphenylborate (9) was chosen as an anion excluder. Since sol–gel-derived membranes made from solutions containing only TEOS are very brittle [27] sol–gelderived ion-sensing membranes were fabricated by using solutions containing TEOS and diethoxydimethylsilane (DEDMS) with a 1:3 ratio. IR-spectral measurements indicated that the neutral carrier and anion excluder can be covalently bonded to the membranes to a great extent, by the present sol–gel processing using the alkoxysilyl-substituted neutral carrier and anion excluder. Typical proﬁles for the potential response of Naþ -ISFETs based on the sol–gelderived membranes modiﬁed chemically by alkoxysilylated 16-crown-5 (7) and bis(12crown-4) (11), together with anion excluder (9) show that both of the Naþ -ISFETs have high sensitivity with a Nernstian response to Naþ activity changes in wide activity ranges of 3 105 to 1 M (Fig. 12). The potential response is quite fast in the Naþ -ISFETs in spite of the covalent bonding of the neutral carriers to the ion-sensing membranes, as exempliﬁed in the membrane system of the bis(12-crown-4) (11). Some mobility of the chemically bonded neutral carriers can probably be maintained in the present sol–gelderived membranes. The response time (t90 Þ is several seconds for both of the Naþ -

FIG. 12 Potential response to Naþ activity changes of Naþ -ISFETs based on sol–gel-derived membranes modiﬁed chemically by alkoxysilyl-substituted neutral carriers (7) (*) and (8) (*), together with anion excluder (9). (From Ref. 49).

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ISFETs based on the sol–gel-derived membranes of (7) and (11), being almost comparable to that for similar ISFETs based on sol–gel-derived membranes simply encapsulating bis[(12-crown-4-)ylmethyl]2-dodecyl-2-methylmalonate [27]. Selectivity coefﬁcients for Naþ with respect to interfering cations which exist in biological and environmental systems were determined for the Naþ -ISFETs based on sol–gel-derived membranes incorporating neutral carriers (7) and (11) by covalent bonding (Fig. 13). In the ISFETs of the 16-crown-5 membrane system, the Naþ selectivities against Hþ , Liþ , NH4 þ , Mg2þ , and Ca2þ are quite good, but the selectivity against Kþ is not high enough, especially for Naþ assay in biological systems such as blood. On the contrary, high Naþ selectivity against Kþ as well as the other interfering ions was found in the sensor of the bis(crown ether) membrane system. This ion sensor is of practical use in biological systems from the standpoint of the ion selectivity. An advantage of the ion-sensing membranes modiﬁed chemically by a neutral carrier and an anion excluder over those simply encapsulating them is high durability of the ionsensing membranes and therefore of the resulted ion sensors. In the ISFETs of the membranes simply encapsulating bis[(12-crown-4-)ylmethyl]2-dodecyl-2-methylmalonate and NaTFPB, an abrupt decrease in the sensitivity was observed after 30 days (Fig. 14), probably due to their easy extrusion from the membrane to sample solutions. In the ISFETs of the membranes modiﬁed chemically by (11) and (9), on the other hand, the high sensitivity of a Nernstian response was kept even after 100 days. The long lifetime for the ISFETs of the membranes modiﬁed chemically by the neutral carrier and anion excluder is desirable on practical applications. The high sensor durability also means that the active materials for ion-sensing membranes hardly exude out from the membrane to aqueous sample solutions during ion assay. This also implies the low toxicity of the ion sensors for use in biological systems. Quaternary alkylammonium salts are generally water-soluble surfactants. The sol– gel-derived anion-sensing membranes encapsulating a quaternary alkylammonium salt, especially with high contents, are easy to deteriorate due to the exudation of the cationic site from the membrane to aqueous sample phases. Moreover, another issue concerning the dispersibility of ammonium salts in sol–gel-derived membranes may happen when high

FIG. 13 Selectivity comparison between Naþ -ISFETs based on sol–gel-derived membranes modiﬁed chemically by alkoxysilyl-substituted neutral carriers (7) and (11). (From Ref. 49.)

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FIG. 14 Time-course changes of sensitivity (slope of calibration plots) for Naþ -ISFETs based on sol–gel-derived membranes incorporating bis(12-crown-4) by covalent bonding using (11) (*) and by encapsulation of bis[(12-crown-4-)ylmethyl] 2-dodecyl-2-methylmalonate (*). (From Ref. 49.)

contents of quaternary alkylammonium salt are applied to membranes. Chemical modiﬁcation of sol–gel-derived membranes by an alkoxysilylated quaternary ammonium chloride (12) was therefore attempted to improve the durability and dispersibility of ammonium salts in the membranes [50]. The alkoxysilylated derivative of quaternary ammonium salt can take part in the sol–gel reaction to allow the covalent bonding of its ammonium sites to sol–gel-derived membranes. For the sol–gel-derived membranes modiﬁed chemically by the anion exchanger, the initial TEOS/DEDMS ratio of 1:1 and (12) content of 30 wt% are the best with respect to the sensor sensitivity and membrane stability. The ISFETs exhibit a Nernstian response in the wide Cl -activity range (Fig. 15). The high sensitivity is comparable to the anion sensors based on that of the corresponding membranes simply encapsulating trioctylmethylammonium chloride. The response for the

FIG. 15 Potential response of anion ISFETs based on sol–gel-derived membranes encapsulating trioctylmethylammonium chloride (*) and modiﬁed chemically by alkoxysilylated quaternary ammonium salt (12) (*) to CI -activity changes. (From Ref. 50.)

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anion sensors with sol–gel-derived membranes of (12) is somewhat slower as compared to the sensors of quaternary-ammonium-encapsulating membranes. The response time of >10 s, however, still allows practical use of the sensors based on the chemically modiﬁed membranes without difﬁculty. The anion selectivity order for the ISFETs of (12) also follows the Hofmeister series, being the same as those of quaternary-ammonium-encapsulating membranes (Fig. 16). The selectivity difference among the anions seems to be more remarkable in the former anion sensors than the latter ones. SEM photographs showed that the anion-sensing sol–gel-derived membranes modiﬁed chemically by (12), are superior to the corresponding membranes simply encapsulating trioctylmethylammonium chloride in the dispersibility of quaternary ammonium salts in membranes and the protein-adsorption property.

IV.

APPLICATIONS TO BIOLOGICAL ION ASSAY

A.

Poly(dimethylsiloxane)

Applicability in biological ion assay is an important factor for biocompatible potentiometric ion sensors. Attempts were made to determine Naþ concentrations in human blood sera by using silicone-rubber membrane Naþ -ISFETs based on (5) [Fig. 17(a)] [29]. The found values for Naþ concentration in undiluted, 10-fold diluted, and 100fold diluted serum samples are in good agreement with the Naþ calibration plots. Even in the undiluted serum samples, only a slight potential shift was observed from the calibration. This indicates that the calixarene-based silicone-rubber-membrane Naþ ISFETs are reliable on serum Naþ assay. For comparison with the silicone-rubber membrane, Naþ -ISFETs with corresponding plasticized-PVC membrane containing (2) or (5) were also tested for the Naþ assay. The found values of Naþ concentration

FIG. 16 Selectivity coefﬁcients for CI with respect to other anion ISFETs based on sol–gelderived membranes (a) encapsulating trioctylmethylammonium chloride (b) modiﬁed chemically by (12). (From Ref. 50.)

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FIG. 17 Naþ calibration graphs and Naþ concentrations in sera obtained by Naþ -ISFETs based on (a) silicone-rubber membrane of calixarene (5) and (b) plasticized-PVC membrane of (2). (*) Naþ calibration plots: (~) found values for Serum I (145 mM Naþ and 4.1 mM Kþ ); (&) found values for Serum II (124 mM Naþ and 6.5 mM Kþ ). (From Ref. 29.)

in the serum samples, obtained by the PVC-membrane Naþ -ISFET, deviate considerably from the Naþ calibration [Fig. 17(b)]. The negative potential shift from the Naþ calibration was observed in any of the serum samples. However, there is hardly any signiﬁcant deviation in the Naþ -concentration found value for the dummy samples containing the same concentrations of Naþ and Kþ without any organic components such as proteins. Obviously, the negative potential shift of the serum samples from the calibration graphs is not ascribable to interference by Kþ and by organic components (proteins) in sera. Also, for the Naþ assay in human urine samples, the calixarenebased silicone-rubber membranes are superior to the corresponding plasticized-PVC ones as ion-sensing membranes for Naþ -ISFETs. Thus, the silicone-rubber membrane Naþ -ISFETs based on calixarene neutral carrier (5) are quite useful for Naþ assay in human sera and urine, whereas the corresponding plasticized-PVC membrane ISFETs are likely to cause signiﬁcant errors on the assay. Adsorption of blood protein on the silicone-rubber membranes containing a neutral carrier was tested to obtain some information about biocompatibility of the ion-sensing membranes and therefore the resulted ISFETs on Naþ assay in blood. Comparison in the SEM photographs for a silicone-rubber membrane and its corresponding plasticized-PVC membrane indicates a striking difference in the protein adsorption. The silicone-rubber membrane hardly adsorbs blood proteins, whereas a large amount of proteins can be seen on the plasticized-PVC membrane. This indicates that the silicone-rubber ion-sensing membranes are superior to the corresponding plasticized-PVC membranes in the blood compatibility. The adsorption of blood organic components on plasticized-PVC ion-sensing membranes often causes some negative errors on blood Naþ assay by the resulted membrane ion sensors. The serious protein adsorption also makes it difﬁcult to use plasticized-PVC membrane ion sensors for in-vivo ion monitoring. On the contrary, this is not

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the case with the silicone-rubber membranes that can alleviate markedly the protein adsorption. The Naþ -selective electrodes based on silicone-rubber membranes modiﬁed chemically by (8) and (9), were also investigated for Naþ assay in control serum and urine [22]. The found values for the Naþ concentrations in both of the serum and urine samples are in good agreement with their corresponding actual values with a relative standard deviation of about 1%. These results suggest that the Naþ -selective electrodes based on siliconerubber membranes modiﬁed chemically by calix[4]arene neutral carrier (8) are reliable on assay in human body ﬂuid.

B.

Sol–Gel-Derived Membranes

The sol–gel-derived membrane ISFETs based on bis(12-crown-4) and valinomycin were applied for Naþ and Kþ assay in blood sera [27]. For reproducibility checking, the metalion assay was carried out ten times for each sample, using two different control sera. The ISFETs gave reliable data both in Naþ and Kþ assay. The coefﬁcient of variation ranges between 0.45 and 0.78%, thus indicating excellent reproducibility in the serum cation assay with the ISFETs of neutral-carrier-type sol–gel-derived membranes. The results for real blood sera for normal human for the cation assay showed relative errors within 2% for the Naþ assay and within 4% for the Kþ assay. The sol–gel-derived membranes incorporating the alkoxysilylated bis(crown ether) (11) by covalent bonding were tested for their thrombogenic property. Any signiﬁcant adsorption of blood platelets was hardly observed on the membranes, as is the case with sol–gel derived membranes encapsulating a neutral carrier [27]. Such excellent thrombogenic property of the sol–gel-derived membranes modiﬁed chemically by a bis(crown ether) suggests a high possibility of their application to Naþ assay in blood sera. The results for Naþ assay in human blood serum with the Naþ -ISFETs are given in Fig. 18, showing that the found values for Naþ concentrations are in good agreement with the corresponding actual values.

FIG. 18 Correlation between actual and found values of Naþ concentrations on serum assay with ISFETs based on sol–gel-derived membranes of bis(12-crown-4) (11). (From Ref. 49.)

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CONCLUSION

The design of biocompatible (blood compatible) potentiometric ion sensors was described in this chapter. Sensing membranes fabricated by crosslinked poly(dimethylsiloxane) (silicone rubber) and sol–gel-derived materials are excellent for potentiometric ion sensors. Their sensor membrane properties are comparable to conventional plasticized-PVC membranes, and their thrombogenic properties are superior to the PVC-based membranes. Speciﬁcally, membranes modiﬁed chemically by neutral carriers and anion excluders are very promising, because the toxicity is alleviated drastically. The sensor properties are still excellent in spite of the chemical bonding of neutral carriers on membranes. The biocompatible potentiometric ion sensors have been successfully applied for ion assay in biological systems such as human blood. They might be used in in-vivo cation assay in biological systems such as intra-arterial assay in the near future.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

20. 21. 22. 23.

Y. Mori, S. Nagaoka, H. Takiuchi, N. oguchi, H. Tanzawa, and Y. Noishiki. Trans. Am. Soc. Artif. Intern. Organs 28:459 (1982). M. Kyrolainen, S. M. Reddy, and P. M. Vadgama. Anal. Chim. Acta 353:281 (1997). M. Karakelle and R. J. Zdrahala, U. S. Patent 4,816,130 (1989). K. Hiiro, T. Tanaka, A. Kawahara, S. Wakita, M. Yamane, N. Yamamoto, and I. Yamashita, Japanese Patent 63,229,356 (1995). C. Espadas-Torre and M. E. Meyerhoff. Anal. Chem. 67:3108 (1995). E. Pungor, J. Havas, K. Toth, and G. Mandarasz, French Patent 140,235 (1965). W. Crowe, A. Mayevsky, and L. Mela. Am. J. Physiol. 233:C56 (1977). H.-B. Jenny, C. Riess, D. Ammann, B. Magyar, R. Asper, and W. Simon. Mikrochim. Acta, 1980 II: 309 (1980). M. E. Collison, G. V. Aebli, J. Petty, and M. E. Meyerhoff. Anal. Chem. 61:2365 (1989). M. Mascini and G. Marrazzaa. Anal. Chim. Acta, 231:125 (1990). G. Marrazza and M. Mascini. Electroanalysis 4:41 (1992). J. Pick, K. Toth, and E. Pungor. Anal. Chim. Acta 64:477 (1973). L. A. Mostert, P. Anker, H.-B. Jenny, U. Oesch, W. E. Morf, D. Ammann, and W. Simon. Mikrochim. Acta 1885 I: 35 (1985). O. H. LeBlanc and W. T. Grubb. Anal. Chem. 48: 1658 (1976). A. Arduini, A. Pochini, S. Reverberi, R. Ungaro, G. D. Andreetti, and F. Ugozzoli. Tetrahedron 42:2089 (1986). D. Diamond, G. Svehla, E. M. Seward, and M. A. McKervey. Anal. Chim. Acta 204:223 (1988). K. Kimura, T. Miura, M. Matsuo, and T. Shono. Anal. Chem. 62:1510 (1990). R. J. Forster, A. Cadogan, M. T. Diaz, D. Diamond, S. J. Harris, and M. A. McKervey. Sens. Actuators B 4:325 (1991). F. Arnaud-Neu, G. Barrett, S. Cremin, M. Deasy, G. Ferguson, S. J. Harris, A. J. Lough, L. Guerra, M. A. McKervey, M. J. Schwing-Weill, and P. Schwinte. J. Chem. Soc. Perkin Trans. 2 1992:1119 (1992). K. Kimura, T. Matsuba, Y. Tsujimura, and M. Yokoyama. Anal. Chem. 64:2508 (1992). Y. Tsujimura, M. Yokoyama, and K. Kimura. Electroanalysis 5:803 (1993). Y. Tsujimura, M. Yokoyama, and K. Kimura. Anal. Chem. 67:2401 (1995). T. Shono, M. Okahara, I. Ikeda, K. Kimura, and H. Tamura. J. Electroanal. Chem. Interfacial Electrochem. 132:99 (1982).

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24. L. L. Hench and J. K. West, Chemical Processing of Advanced Materials, Wiley, New York, 1992. 25. B. C. Dave, B. Dunn, J. S. Valentine, and J. I. Zink. Anal. Chem. 22:1120A (1994). 26. J. Wang, P. V. A. Pamidi, and K. R. Rogers. Anal. Chem. 70:1171 (1998). 27. K. Kimura, S. Sunagawa, and M. Yokoyama. Anal. Chem. 69:2379 (1997). 28. K. Kimura, M. Yoshinaga, K. Funaki, Y. Shibutani, K. Yakabe, T. Shono, M. Kasai, H. Mizufune, and M. Tanaka. Anal. Sci. 12:67 (1996). 29. Y. Tsujimura, M. Yokoyama, and K. Kimura. Sens. Actuators B 22:195 (1994). 30. K. A. Brooks, J. A. Allen, P. W. Feldhoff, and L. G. Bachas. Anal. Chem. 68:1439 (1996). 31. B. T. Mellion, L. J. Ignarro, E. H. Ohlstein, E. G. Pontecorvo, A. L. Hyman, and P. J. Kadowitz. Blood 57:946 (1981). 32. M. W. Radomski, M. J. Palmer, and S. Moncada. Br. J. Pharmac. 92:639 (1987). 33. K. A. Mowery, M. H. Schoenﬁsch, and M. E. Meyerhoff. Polym. Mater. Sci. Eng. 79:33 (1998). 34. C. Espadas-Torre, V. Oklejas, K. Mowery, and M. E. Meyerhoff. J. Am. Chem. Soc. 119:2321 (1997). 35. K. A. Mowery, C. Espadas-Torre, V. Oklejas, and M. E. Meyerhoff. Polym. Mater. Sci. Eng. 76:562 (1997). 36. K. Ishihara, N. Nakabayashi, K.Nishida, M. Sakakida, and M. Schichiri. Chemtech 1993:19 (1993). 37. K. Ishihara and N. Nakabayashi. Artiﬁcial Organs. 19:1215 (1995). 38. C.-Y. Chen, E. Tamiya, K. Ishihara, Y. Kossugi, Y.-C. Su, N. Nakabayashi, and I. Karube. Appl. Biochem. Biotechnol. 36:211 (1992). 39. K. Nishida, M. Sakakida, Y. Hashiguchi, M. Uehara, T. Uemura, T. Kajiwara, M. Schichiri, K. Ishihara, and N. Nakabayashi. Jinko Zoki 22:1090 (1993). 40. S. Yajima, K. Suzuki, and K. Kimura, 6th National Meeting of the Chemical Society of Japan, Abstr. No. 3E215, 1999. 41. J. Tietje-Girault, I. MacInnes, M. Schroder, G. Tennant, and H. H. Girault. Electrochim. Acta 35:777 (1990). 42. S. Daunert, and L. G. Bachas. Anal. Chem. 62:1428 (1990). 43. G. G. Cross, T. M. Fyles, and V. V. Suresh. Talanta 41:1589 (1994). 44. Y. Tsujimura, T. Sunagawa, M. Yokoyama, and K. Kimura. Analyst (London) 121:1705 (1996). 45. D. N. Reinhoudt, J. F. J. Engbersen, Z. Brzozka, H. H. v. d. Vlekkert, G. W. N. Honig, H. A. J. Holterman, and U. H. Verkerk. Anal. Chem. 66:3618 (1994). 46. J. A. J. Brunink, R. J. W. Lugtenberg, Z. Brzozka, J. F. J. Engbersen, and D. N. Reinuoudt. J. Electroanal. Chem. 378:185 (1994). 47. R. J. W. Lugtenberg, R. J. M. Egbernk, A. v. d. Berg, J. F. J. Engbersen, and D. N. Reinhoudt. J. Electroanal. Chem. 452:69 (1998). 48. K. Kimura, Y. Tsujimura, M. Yokoyama, and T. Maeda. Bull. Soc. Chem. Jpn. 71:657 (1998). 49. K. Kimura, T. Sunagawa, S. Yajima, S. Miyake, and M. Yokoyama. Anal. Chem. 70:4309 (1998). 50. K. Kimura, H. Takase, S. Yajima, and M. Yokoyama. Analyst (London) 124:517 (1999).

25 The Oscillation of Membrane Potential or Membrane Current KOHJI MAEDA and SORIN KIHARA Institute of Technology, Kyoto, Japan

I.

Department of Chemistry, Kyoto

INTRODUCTION

The oscillation of membrane current or membrane potential is well-known to occur in biomembranes of neurons and heart cells, and a great number of experimental and theoretical studies on oscillations in biomembranes as well as artiﬁcial membranes [1,2] have been carried out from the viewpoint of their biological importance. The oscillation in the membrane system is also related to the sensing and signal transmission of taste and olfaction. Artiﬁcial oscillation systems with high sensitivity and selectivity have been pursued in order to develop new sensors [3–8]. The mechanisms of the oscillations in biomembranes have been explained based on the gating of membrane protein called an ‘‘ion channel,’’ and enormous efforts have been made to elucidate the gating process, mainly by reconstitution of channel proteins into bilayer membranes [9–11]. The oscillations observed with artiﬁcial membranes, such as thick liquid membranes, lipid-doped ﬁlter, or bilayer lipid membranes indicate that the oscillation can occur even in the absence of the channel protein. The oscillations at artiﬁcial membranes are expected to provide fundamental information useful in elucidating the oscillation processes in living membrane systems. Since the oscillations may be attributed to the coupling occurring among interfacial charge transfer, interfacial adsorption, mass transfer, and chemical reactions, the processes are presumed to be simpler than the oscillation in biomembranes. Even in artiﬁcial oscillation systems, elementary reactions for the oscillation which have been veriﬁed experimentally are very few. The oscillation at a liquid–liquid interface or a liquid membrane is the most popular oscillation system. Nakache and Dupeyrat [12–15] found the spontaneous oscillation of the potential difference between an aqueous solution, W, containing cetyltrimethylammonium chloride, CTAþ Cl , and nitrobenzene, NB, containing picric acid, Hþ Pic . They explained that the oscillation was caused by the difference between the rate of transfer of CTAþ controlled by the interfacial adsorption and that of Pic controlled by the diffusion, taking into consideration the dissociation of Hþ Pic in NB. Yoshikawa and Matsubara [16] realized sustained oscillation of the potential difference and pH in a system similar to that of Nakache and Dupeyrat. They emphasized the change of the surface potential due to the formation and destruction of the monolayer of CTAþ Pic at the interface. It is 609

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difﬁcult, however, to explain the characteristics of the oscillation, such as the amplitude, period, or pulse width based on these mechanisms, indicating that further investigations are required on elementary reactions which control the oscillation process, such as the interfacial ion transfer and the interfacial adsorption. The voltammetry for ion transfer at an interface of two immiscible electrolyte solutions, VITIES, which is a powerful method for identifying the transferring ion and for determining the amount of ion transferred, must be helpful for the elucidation of the oscillation process [17–19]. The VITIES was also demonstrated to be useful for ion transport through a membrane, considering that the membrane transport of ions is composed of the ion transfers at two aqueous–membrane interfaces and the mass transfers and/or chemical reactions in three phases [2,20,21]. In this chapter, novel oscillations observed with liquid membrane systems by the present authors [22–25] will be introduced, and the mechanisms for the oscillation are clariﬁed by using VITIES, taking into consideration ion transfer reactions and adsorptions at two aqueous–membrane interfaces. The mechanism of the spontaneous potential oscillation in a liquid membrane system proposed by Yoshikawa et al. is also discussed brieﬂy.

II.

NOVEL MEMBRANE OSCILLATIONS ACCOMPANIED BY ION TRANSPORT

A.

Oscillation of the Membrane Potential Difference Under an Applied Current [22,23]

1. Characteristics of Potential Oscillation Two aqueous phases separated by a liquid membrane, LM, of nitrobenzene, NB, were layered in a glass tube, which was equipped with Pt counterelectrodes in W1 and W2 and reference electrodes in three phases as in Eq. (1). Reference electrodes set in W1 and W2 were Ag/AgCl electrodes, SSE, and those in LM were two tetraphenylborate ion selective electrodes [26,27], TPhBE, of liquid membrane type. The membrane current, IW1-W2 , was applied using two Pt electrodes. The membrane potential, VW1-W2 recorded as the potential of SSE in W2 vs. that in W1. When a constant current of 25 A cm2 was applied from W1 to W2 in the cell given as Eq. (1), the oscillation of membrane potential was observed as shown in curve 1 of Fig. 1. The oscillation of VW1-W2 continued for 40 to 60 min, and ﬁnally settled at ca. 0:40 V.

ð1Þ

Here, TPAþ and TPhB denote tetrapentylammonium ion and tetraphenylborate ion, respectively.

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FIG. 1 Time courses of VW1-W2 , VW1=LM , and VLM=W2 under an applied current of 35 A cm2 in the direction for the transfer of a positive charge from W1 to W2 to the cell of Eq. (1). (From Ref. 22.)

Time courses of the potential difference between W1 and LM, VW1=LM , and that between LM and W2, VLM=W2 , recorded simultaneously with VW1-W2 are given as curves 2 and 3 in Fig. 1, respectively. The VW1=LM and VLM=W2 were recorded as the potential of TPhBE vs. SSE in W1 and that of SSE in W2 vs. TPhBE, respectively. The amplitude, period and the pulse width in curve 3 coincide with those in curve 1, whereas practically no oscillation appears in curve 2. The coincidence suggests that the oscillation of VW1-W2 is attributed to that of VLM=W2 . Equation (2) holds among VW1-W2 , VW1=LM , and VLM=W2 , suggesting that the membrane potential is determined by potential differences at two interfaces [20,21]: VW1-W2 ¼ VW1=LM þ VLM=W2

ð2Þ

The characteristics of the oscillation of VLM=W2 depended on the concentration of Csþ TPhB , cCsTPhB , and that of TPAþ TPhB , cTPATPhB , in LM, since the concentrations of these salts inﬂuence the equilibrium of the ion pair formation of Csþ TPhB in NB as well as vary the activity of dissociated Csþ , aCsþ , and that of Csþ TPhB , aCsTPhB . The activities were calculated based on the ion pair formation constants which were determined by conductivity measurements according to the Shedlovsky method [28]. Figure 2 shows the dependence of aCsþ and aCsTPhB in organic solvents containing 4 104 M Csþ TPhB on cTPATPhB . The induction time until the beginning of the oscillation and the period of the oscillation depended strongly on aCsþ and these lengthened with an increase of aCsþ . The oscillation was not observed at any applied current when cCsTPhB was less than 104 M and cTPATPhB was less than 0.01 M. This fact and the ion pair formation equilibrium as shown in Fig. 2 indicate that an appreciable activity of Csþ TPhB is indispensable to realize the oscillation. The amplitude and the pulse width are almost independent to both aCsþ and aCsTPhB . There existed a certain range of applied current in order to get the sustained oscillation, and the upper limit of the range was affected by aCsTPhB and lowered with a decrease

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FIG. 2 Dependence of aCsþ and aCsTPhB in organic solvents containing 4 104 M Csþ TPhB on cTPATPhB . (1–3) aCsþ ; (1 0 –3 0 ) aCsTPhB . (1, 1 0 ) Nitrobenzene; (2, 2 0 ) 1,2-dichloroethane; (3, 3 0 ) onitroanisole. (From Ref. 22.)

of aCsTPhB . When a current smaller than the lower limit was applied, the oscillation did not occur within 60 min after applying the constant current. When the applied current was larger than the upper limit, the potential shifted to the negative limit immediately after applying current and did not return to the original potential. When 1,2-dichloroethane, DCE ( ¼ 10:37), or o-nitroanisole, o-NA ( ¼ 5:23), was employed instead of nitrobenzene ( ¼ 34:78), the induction time and period with o-NA were obviously less than those with NB or DCE. It should be noted that, in case of o-NA, the sustained oscillation was observable even with cTPATPhB of less than 0.01 M, though the oscillation was not observed with NB or DCE. The result suggests that aCsTPhB is the essential factor for the appearance of the oscillation, taking into account that the ion pair formation is more serious in o-NA than in NB or DCE. When Csþ in Eq. (1) was replaced by tetramethylammonium ion, TMAþ , the positive limit of the amplitude shifted to more negative potentials and the amplitude decreased to be 0.28 V as compared to 0.40 V with Csþ . Employing tetraethylammonium ion, TEAþ , instead of Csþ , the oscillation was not observed regardless of the magnitude of the applied current and the concentration of TEAþ TPhB or TPAþ TPhB . Replacing the TPAþ of the supporting electrolyte in LM by tetrabutylammonium ion, TBAþ , or tetrapropylammonium ion, TPrAþ , the negative limit of the oscillation shifted positively and the amplitude decreased to 0.28 V or 0.20 V, respectively.

2. Ion Transfer Voltammograms at the LM/W2 Interface The ion transfer voltammogram was recorded at the LM/W2 interface of Eq. (1) in order to understand the oscillation mechanism of VLM=W2 . Curve 1 in Fig. 3 is the voltammogram obtained by scanning the potential toward the negative direction. The negative current peak and the ﬁnal descent correspond to the transfer of Csþ and that of TPAþ from LM to W2, respectively. Though the negative current at around 0:4 V was con-

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FIG. 3 Voltammograms for the transfer of Csþ from LM of NB to W2 with various supporting electrolytes. LM: nitrobenzene containing 4 104 M Csþ TPhB þ 0:05 M (1) TPrAþ TPhB , (2) TBAþ TPhB , or (3) TPAþ TPhB . W2: 2 M MgSO4 . Scan rate: 0.01 V s1 . (From Ref. 22.)

ﬁrmed to be controlled by the diffusion of Csþ in LM, the current peak was much larger than the current controlled by diffusion. A negative current peak also appeared upon reversing the scan direction at potentials identical with those for the peak. Taking into account these results together with the drop time–potential curves mentioned later, the negative peak is considered to be the maximum current caused by the interfacial adsorption of the ion pair of Csþ TPhB . Here, it is obvious from the voltammogram that the range of applied current available for the oscillation is between the maximum peak current and the diffusion-controlled current at around 0:4 V. The voltammetric maxima were measured with various cCsTPhB and cTPATPhB , considering aCsþ and aCsTPhB . The maximum current increased depending on aCsþ rather than aCsTPhB , which suggests that the main process of the maximum current may be due to the interfacial reactions consisting of the adsorption of the ion pair at the W/NB interface and the transfer of Csþ from NB to W. The maximum current recorded with o-NA was much smaller than that with NB or DCE because of the lower dissociation of Csþ TPhB in o-NA (cf. Fig. 2). The voltammogram recorded with TMAþ TPhB instead of Csþ TPhB in Eq. (1) also exhibited the maximum current corresponding to the transfer of TMAþ from LM to W2, and the peak potential shifted to less positive potentials around 0:3 V. When TEAþ was used in place of Csþ , the maximum current was not observed, and the voltammogram was that for the reversible transfer of TEAþ . When TBAþ or TPrAþ was adopted as a cation of the supporting electrolyte in LM in place of TPAþ , the ﬁnal descent of the voltammogram shifted to more positive potentials depending on their transfer energies, as illustrated as curves 2 and 3 in Fig. 3. 3.

Drop Time – Potential Curves at the W/NB Interface

The dependence of the interfacial tension at the W/NB interface on the interfacial potential difference [29,30] was investigated by using an aqueous solution dropping electrode [26,31]. In this investigation, the aqueous solution was forced upward dropwise in NB and the drop time of W was measured as a function of potential difference applied at the W/ NB interface. When W contained 1 M MgSO4 and NB contained 4 104 M Csþ TPhB

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FIG. 4 Drop time–potential curves at the interface between W containing 1 M MgSO4 and NB containing various concentrations of Csþ TPhB and TPAþ TPhB . aCsþ : (a–d) 4 105 (e) 2 105 , (f) 6 105 M; aCsTPhB : (a) 3:4 104 , (b) 2:5 104 , (c, e, f) 1:5 104 , (d) 8 104 M. Curve 1 (solid): in the presence of Csþ TPhB , curve 2 (broken): in the absence of Csþ TPhB . (From Ref. 22.)

and 0:05 M TPAþ TPhB , the drop time–potential curve was as curve 1 in Fig. 4(a). Curve 2 in Fig. 4(a) was obtained in the absence of Csþ TPhB in NB. Comparing curves 1 and 2 in Fig. 4(a), it is obvious that there existed a depressed part in curve 1 suggesting the interfacial adsorption of chemical species relative to Csþ in the potential range between 0:1 V and the potential of zero charge, PZC, at around 0:25 V. The depression in the drop time–potential curves measured under the condition of constant aCsþ was more conspicuous with an increase of aCsTPhB , as demonstrated in Figs. 4(a)–(d), whereas the depression was indifferent to aCsþ as seen in Figs. 4(c), (e), and (f). These results suggest that the adsorbed species responsible for the maximum current is the ion pair, Csþ TPhB .

4. Amplitude of the Potential Oscillation The positive limit and negative limit of the amplitude in the oscillation of VLM=W2 (cf. curve 3 in Fig. 1) agreed with the potential of the maximum wave (indicated by A) and that of the ﬁnal descent (indicated by B), respectively, at 35 A cm2 in the voltammogram (Fig. 3). When TMAþ was used instead of Csþ , the positive limit of the oscillation amplitude was ca. 0.12 V more positive than that with Csþ . The difference corresponds to that in the potential difference of the maximum wave between TMAþ and Csþ . The negative limit of the amplitude observed when TBAþ or TPrAþ was employed in place of TPAþ was more positive than that with TPAþ , since the ﬁnal descent due to the transfer of TBAþ or TPrAþ from LM to W2 is more positive than that for TPAþ transfer, as in Fig. 3. These results suggest that the amplitude of the potential oscillation is determined by the transfer energy Gtr , of the objective ion causing the voltammetric maximum at the

The Oscillation of Membrane Potential

615

LM/W2 interface and that of the coexisting ion (the supporting electrolyte ion in this study). 5. Mechanism for the Potential Oscillation The mechanism of the oscillation generated by the transfers of Csþ and TPAþ will be discussed by referring to Fig. 3. When a constant current available for the transfer of cations from W1 to W2 is applied to the membrane system of Eq. (1), Csþ transfers at the LM/W2 interface, since Gtr of Csþ from NB to W is much smaller than that of TPAþ . It is clear from drop time–potential curves in Fig. 4 that the adsorption of Csþ TPhB at the LM/W2 interface takes place at potentials more positive than the PZC where Csþ transfers, and the adsorption generates the stirring of solutions in the vicinity of the interface. The ion pair adsorbed will be represented by Csþ TPhB ip , hereafter. The stirring enhances the ion transfer at the interface resulting in a current maximum which is much larger than the ordinary current due to the ion transfer being controlled by the diffusion. Hence, when a current larger than the diffusion-controlled current but smaller than the maximum current is applied, VLM=W2 is settled at a potential in the region where the maximum appears (e.g., A in Fig 3 when the objective ion is Csþ and applied current is 35 A cm2 ). Due to the enhanced transfer of Csþ , the concentration of Csþ in LM near to the interface decreases more extensively than that in the case of the diffusioncontrolled ion transfer. The adsorption continues during the transfer of Csþ , although the change of the interfacial tension caused by the adsorption of Csþ TPhB ip becomes smaller and the stirring becomes weaker when an appropriate amount of Csþ TPhB ip is accumulated and the LM/W2 interface approaches the state saturated with Csþ TPhB ip . As the results of the consumption of Csþ and the weakened stirring, the ﬂux of Csþ to the interface from the bulk of LM decreases, becoming too small to undertake the applied current. Then, the coexisting supporting electrolyte cation, TPAþ , which requires more energy to transfer at the interface than Csþ may participate in carrying a part of the applied current. At this time, VLM=W2 shifts to a potential more negative (B in Fig. 3) than the original A. At B, which is more negative than PZC, Csþ TPhB ip which has been adsorbed desorbs from the interface toward LM, as expected from the drop time–potential curve. Owing to the þ desorption and dissociation of Csþ TPhB ip , the concentration of Cs in LM near to the interface may be restored sufﬁciently to undertake the applied current. At this time, VLM=W2 returns to A, where the adsorption of Csþ occurs. These processes are then repeated to realize the oscillation of VLM=W2 . The oscillation of VLM=W2 leads to that of VW1-W2 , since Eq. (2) holds among VW1-W2 , VW1=LM , and VLM=W2 . Here, VW1=LM is kept almost constant during the oscillation because the applied current at the W1/LM interface is carried by the transfer of Csþ , which exists in W1 in high concentration. Adopting the above-mentioned mechanism, the induction time or period is considered to be determined by the time required to consume dissociated Csþ near the interface in LM. The following facts support this consideration. That is, the induction time and period increase with a decrease of the applied current or with an increase of aCsþ , and the period was shortened when o-NA was used as an organic solvent of LM. 6. Lower and Upper Limits of the Range of Applied Current Available for Oscillation The lower limit of the applied current range for the oscillation is determined by the diffusion of Csþ in LM as demonstrated by comparing the range with the ion transfer

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voltammogram. If the applied current is less than the diffusion-controlled current, VLM=W2 stays at the potential for the transfer of Csþ , since the applied current is undertaken by the transfer of Csþ from the bulk of LM. The upper limit of applied current for the oscillation was less than the maximum current in the voltammogram. If the applied current exceeding the maximum is applied, VLM=W2 is determined by the transfer of TPAþ . When the applied current is slightly lower than the maximum, VLM=W2 shifts to the potential for the transfer of TPAþ within a fairly short time after applying the current, and does not come back to the original potential. In this condition, the recovery of dissociated Csþ due to the dissociation of the desorbed Csþ TPhB in the vicinity of the interface is not enough to undertake the applied current and for the shift of VLM=W2 to the potential for the transfer of Csþ : When the applied current was much less than the maximum current and more than the diffusion-controlled current, the sustained oscillation was observed. B.

Oscillation of Membrane Current Under an Applied Membrane Potential [24,25]

1. Characteristics of Current Oscillation Curve 1 in Fig. 5 gives an example of the oscillation of membrane current observed with the liquid membrane system as in Eq. (3) by applying a constant VW1-W2 of 0:48 V and measuring the time course of the current through the LM, IW1-W2 . The cell used was the same as that used for the measurement of the potential oscillation, except a tetraphenylarsonium ion selective electrode [26,27], TPhAsE, was employed as a reference electrode in LM of NB:

ð3Þ

Here, TPhAsþ and DPA denote tetraphenylarsonium ion and dipicrylaminate ion, respectively. The oscillation lasted for more than 2 h. Curves 2 and 3 show time courses of VW1=LM and VLM=W2 observed simultaneously with curve 1. From these curves, it is obvious that the current oscillation occurs with the oscillations of VW1=LM and VLM=W2 , though the amplitudes are not large (about 0.08 V). Here, it is notable that the amplitude of the oscillation of VW1=LM is the same as that of VLM=W2 . The range of applied VW1-W2 available for the current oscillation was between 0:40 and 0:55 V. When VW1-W2 was more negative in the range, the amplitude of the oscillation was larger and the period was longer as follows: amplitude was 53, 38, or 22 A cm2 and period was 2.1, 1.8, or 1.6 min when VW1-W2 was 0:53, 0:48, or 0:43 V, respectively.

The Oscillation of Membrane Potential

617

FIG. 5 Time courses of membrane current (curve 1), VW1=LM (curve 2), and VLM=W2 (curve 3) observed by applying a membrane potential of 0:48 V to the cell of Eq. (3). The membrane potential was applied as a potential of SSE in W2 with respect to of SSE in W1. (From Ref. 25.)

The oscillation of VW1-W2 ¼ 0:48 V was not observed with 2 h, when cNaDPA was less than 104 M or more than 2 103 M (cTPhAsDPA : 0.02 M) and when cTPhAsDPA was less than 0.01 M or more than 0.07 M (cNaDPA : 4 104 M). The dependence of the oscillation on the activity of dissociated Naþ , aNaþ , and that of associated Naþ with DPA , aNaDPA , in LM (NB) were examined by varying cNaDPA or cTPhAsDPA . The amplitude of the current oscillation strongly depended on aNaþ , but little on aNaDPA .

2. Induction or Inhibition of the Current Oscillation Similarly to the induction or the inhibition of the current oscillation at a biomembrane with a ‘‘sodium channel,’’ the current oscillation at the liquid membrane (without any channel proteins) caused by the transfer of Naþ can be induced by acetylcholine ion, Achþ , or inhibited by such rather hydrophobic ions as alkylammonium and glutamate ions. The current oscillation was induced by adding 2 104 M Achþ into W1 of the membrane system as Eq. (3), to which VW1-W2 of 0:30 V had been applied instead of 0:48 V. Here, 0:30 V is not the VW1-W2 effective for the oscillation in the absence of Achþ . The lifetime of the induced current oscillation was much shorter than that observed by applying 0:48 V to the system in the absence of Achþ , and was from 20 to 40 min. The concentration range of Achþ effective for the induction was from 7 105 to 3 104 M. The lifetime was longer with higher concentration of Achþ as follows: 5 to 15, 10 to 25, 20 to 40, or 30 to 45 min when concentration was 7 105 , 1:2 104 , 2 104 , or 3 104 M, respectively: The amplitude was larger with higher concentration of Achþ as follows: about 25, 33, 45, or 50 A cm2 when concentration was 7 105 , 1:2 104 , 2 104 , or 3 104 M, respectively. The current oscillation observed by applying VW1-W2 ¼ 0:48 V was inhibited when one of the rather hydrophobic ions such as TEAþ , TBAþ or glutamate ion was added to W1 to more than 103 M or when more than 106 M of bovin serum albumin, BSA, was added to W2.

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3. Voltammograms for the Ion Transfer Through LM and at W1/LM and LM/W2 Interfaces The voltammograms for the ion transfer through LM and at the W1/LM and LM/W2 interfaces were investigated in order to understand the processes involved in the oscillations. Curve 1 in Fig. 6 is a voltammogram recorded with the cell of Eq. (3) by scanning VW1-W2 and measuring IW2-W2 . Curves 2 and 3 are voltammograms at the W1/LM and LM/W2 interfaces recorded simultaneously with curve 1, measuring VW1=LM and VLM=W2 as a function of IW1-W2 . An extremely large current peak appeared in voltammograms 1 and 3. The peak current was about 12 times larger than the ordinary diffusion-controlled current for the transfer of Naþ from NB containing 4 104 M Naþ to W. Comparing with voltammograms at the W/NB interface recorded under various conditions, the negative current peak in voltammogram 3 was attributed to the maximum due to the transfer of Naþ from LM to W2 enhanced by interfacial adsorption (which will be discussed later). The ﬁnal rise and the ﬁnal descent in voltammogram 2 or 3 were conﬁrmed to be due to transfers of TPhAsþ from LM to W1 and Naþ from W1 to LM or DPA from LM to W2 and TPhAsþ from LM to W2, respectively. As demonstrated in work on the ion transport through a membrane [20,21], the relation among VW1-W2 in curve 1, VW1=LM in curve 2, and VLM=W2 in curve 3 at a deﬁnite current value can be approximated by Eq. (2), when W1, W2, and LM contain sufﬁcient concentrations of ions as in the case of Eq. (3). This equation suggests that the membrane potential in the presence of sufﬁcient electrolytes in W1, W2, and LM is

FIG. 6 Voltammograms for ion transfer through a membrane (curve 1), at the W1/LM interface (curve 2) and at the LM/W2 interface (curve 3) recorded with the cell of Eq. (3). (From Ref. 25.)

The Oscillation of Membrane Potential

619

primarily determined by potential differences at the two interfaces in the membrane system, which depend on ion transfer reactions at the interfaces. Taking into account the relation of Eq. (2), the negative current peak in voltammogram 1 in Fig. 6 is considered to be composed of the peak in voltammogram 3 due to the enhanced transfer of Naþ from LM to W2 and the ﬁnal descent in voltammogram 2 due to the transfer of Naþ from W1 to LM. The maximum peaks in voltammograms 1 and 3 in Fig. 6 were not observed when cNaDPA was less than 104 M and cTPhAsDPA was 0.02 M. The dependence of the maximum peak on aNaþ or aNaDPA was examined under the condition that aNaDPA or aNaþ was constant, respectively. The magnitude of the maximum peak depended strongly on aNaþ , although it was practically independent of aNaDPA . The maximum observed with the transfer of Naþ at the LM/W2 interface was suppressed completely by the addition of 106 M BSA into W2. The above-mentioned results on the voltammograms indicate that the condition available for the oscillation of the membrane current resembles closely that for the appearance of the maximum. 4. Drop Time–Potential Curves at the W/NB Interface The drop time–potential curve was measured with an aqueous solution dropping electrode [26,31], as mentioned in Section II.A.3, at the interface between W containing 1 M MgSO4 and NB containing 4 104 M Naþ DPA and 0.02 M TPhAsþ DPA . In the curve, there existed a depressed part as compared with the curve in the absence of Naþ DPA , suggesting the interfacial adsorption of chemical species relative to Naþ . Assuming that W and NB in the polarographic measurement correspond to W2 and LM, respectively, in the membrane system of Eq. (2), the potential range for the depression resembles that available for both the transfer of Naþ from LM to W2 and the appearance of the maximum peak at the LM/W2 interface (cf. voltammogram 3 in Fig. 6). Here, the potential range for the depression lies at more positive potentials than PZC of the interface at around 0.2 V, and hence W is polarized to be positive in the potential range. Taking into account that both the voltammetric maximum and the depression in drop time–potential curves were affected by the ion pair formation equilibrium of Naþ DPA in LM, it is concluded that Naþ which has been transferred from NB to W may be adsorbed at the interface from the side of W inducing the adsorption of DPA as a counterion from the NB side. At the interface, the adsorbed Naþ may exist as an ion pair, which is denoted as Naþ DPA ip , hereafter. The possibility of the interfacial ion pair formation between a hydrophobic cation (or anion) in an organic phase and a hydrophilic anion (or cation) in an aqueous phase has been proposed by Girault and Schiffrin [32], and Kakiuchi et al. [33]. 5. Mechanism of the Current Oscillation The mechanism will be discussed by referring to the voltammograms in Fig. 6. The oscillation of the membrane current is brought about by the mutually dependent ion transfer reactions at the W1/LM and LM/W2 interfaces. When VW1-W2 in the range effective for the maximum in curve 1 of Fig. 6 is applied to the membrane system of Eq. (3), VLM=W2 settles at a potential (B) available for both the transfer of Naþ from LM to W2 and the adsorption of Naþ DPA ip at the LM/W2 interface, and VW1=LM at a potential (A) in the ﬁnal descent due to the transfer of Naþ from W1 to LM. Here, it should be reminded that the relation of Eq. (2) holds among VW1-W2 , VW1=LM , and VLM=W2 ,

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and magnitudes of current ﬂowing across the W1/LM and LM/W2 interfaces, IW1=LM and ILM=W2 , are of the same magnitude. At VLM=W2 of B, Naþ transfers from LM to W2, and the Naþ transferred to W2 is adsorbed at the LM/W2 interface as Naþ DPA ip . The adsorption generates stirring of the solution in the vicinity of the interface because the adsorption induces a change in the interfacial tension at the LM/W2 interface. Since the stirring enhances the transfer of Naþ at the interface, ILM=W2 grows to the maximum current. At the same time, IW1=LM grows along the ﬁnal descent of the voltammogram at the W1/LM interface (see curve 1 in Fig. 6), causing the negative shift of VW1=LM to A 0 . The negative shift of VW1=LM results in the positive shift of VLM=W2 to B 0 because of the relation of Eq. (2). The adsorption at B 0 may be stronger than that at the original VLM=W2 , B, since B 0 is a potential more remote from PZC than B, and hence the polarization of the LM/W2 interface is more signiﬁcant at B 0 than that at B. The duration of the adsorption brings about the saturation of Naþ DPA ip at the interface and reduction of the stirring. Because of the reduced stirring and the consumption of Naþ in LM near to the interface owing to the enhanced transfer of Naþ , ILM=W2 decreases. Simultaneously, IW1=LM decreases, accompanying the positive shift of VW1=LM to around A and the negative shift of VLM=W2 to around B [cf. Eq. (2)]. At the VLM=W2 around B, which is nearer to PZC than B 0 , Naþ DPA ip which has been adsorbed at the LM/W2 interface is desorbed into LM, because the adsorption at this VLM=W2 (around B) is weaker than that at the positive VLM=W2 (around B 0 ) and Naþ DPA ip is hydrophobic rather than hydrophilic. þ The desorption followed by the dissociation of Naþ DPA ip restores the activity of Na in LM in the vicinity of the interface. Hence, the current increases again, causing the positive shift of VLM=W2 . These processes may repeat to realize the oscillation of the membrane current. In this regard, the shift of VW1=LM and VLM=W2 accompanied with the current oscillation were clearly observed, as shown as curves 2 and 3 in Fig. 5. 6. Mechanism of Induction or Inhibition of the Current Oscillation It is noteworthy that the current oscillation was induced or inhibited by the addition of Achþ or TEAþ , respectively, into W1 although the W1/LM interface is not directly related to the voltammetric maximum essential for the oscillation. The induction of the oscillation of the membrane current by the addition of Achþ can be understood with the aid of ion transfer voltammograms at the W1/LM and LM/

FIG. 7 Voltammetric explanation for the induction of the oscillation by acetylcholine ion (Achþ ) under the membrane potential of 0:30 V. Curves 1 and 2: schematic illustration of curves 2 and 3 in Fig. 6. Curve 3: voltammogram recorded at the W1/LM interface in the presence of 2 104 M Achþ in W1. (From Ref. 25.)

The Oscillation of Membrane Potential

621

W2 interfaces (Fig. 7). Curves 1 and 2 in Fig. 7 are schematic illustrations of voltammograms 2 and 3 in Fig. 6, and curve 3 in Fig. 7 is the voltammogram for the transfer of Achþ from W1 to LM. When 0:30 V is applied as VW1-W2 to the cell of Eq. (3) in the absence of Achþ , VW1=LM and VLM=W2 settle at potentials indicated as C and D, respectively, and satisfy the relation of Eq. (2). The potential D is not effective for the adsorption of Naþ DPA ip and hence for the maximum current. When Achþ is added into W1 to become 2 104 M (cf. curve 3), VW1=LM shifts to a less negative potential C 0 , because IW1=LM is undertaken by the transfer of Achþ from W1 to LM. At the same time, according to the relation of Eq. (2), VLM=W2 shifts to a potential D 0 less positive than D and effective for the adsorption 0 þ of Naþ DPA ip . At D , ILM=W grows to the maximum current since the transfer of Na from LM to W2 is enhanced by the stirring caused by the adsorption. With the growth of ILM=W2 , IW1=LM due to the transfer of Naþ as well as Achþ from W1 to LM increases. The same processes similar to those for the oscillation of the membrane current in the absence of Achþ mentioned previously may succeed, and the oscillation induced by Achþ may be realized. The lifetime of the induced current oscillation is considered to be determined by the concentration of Achþ , and the oscillation may terminate when the concentration of Achþ in W1 is decreased owing to its transfer from W1 to LM, which explains the result that the lifetime was shorter with lower concentrations of Achþ . The higher concentration limit of Achþ effective for the induction can be understood by considering the following. When Achþ of concentration higher than 3 104 M is added to W1, the positive shift of VW1=LM due to the transfer of Achþ is too large and causes a negative shift of VLM=W2 to a potential less positive than the range for the maximum current. Therefore, the oscillation cannot be induced when the concentration of Achþ is higher than 3 104 M.

FIG. 8 Voltammetric explanation for the inhibition of the oscillation by TEAþ . Curves 1, 2, and 3: schematic illustration of curves 1, 2, and 3 in Fig. 6. Curves 1 0 and 2 0 : voltammograms recorded under the same conditions for curves 1 and 2, but in the presence of 0.01 M TEAþ in W1. (From Ref. 25.)

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The inhibition of the oscillation by tetra-alkylammonium ions can be explained by referring to the voltammograms in Fig. 8. In the following, the inhibition by 0.01 M TEAþ will be adopted as an example. Curves 1, 2, and 3 in the ﬁgure schematically illustrate voltammograms 1, 2, and 3 in Fig. 6, respectively. Curves 1 0 and 2 0 are voltammograms observed under the same conditions as that for curves 1 and 2, but adding 0.01 M TEAþ to W1. Since the ﬁnal descent in the voltammogram at the W1/LM interface in the presence of 0.01 M TEAþ in W1 (curve 2 0 ) lies at much more positive potentials than those in the absence of TEAþ (curve 2), the maximum in the voltammogram for the transfer of Naþ through the LM in the presence of TEAþ (curve 1 0 ) appears at more positive potentials than that in the absence of TEAþ (curve 1) for the sake of the relation of Eq. (2). Therefore, the VW1-W2 value necessary to observe the current oscillation in the absence of TEAþ (e.g., 0:48 V) is too negative to continue the oscillation after the addition of TEAþ . The inhibition by BSA is attributable to the strong adsorption of BSA on the LM/ W2 interface. The drop time–potential curve was measured with an aqueous solution dropping electrode by dropping W containing 106 M BSA and 1 M MgSO4 into NB containing 4 104 M Naþ DPA and 0.02 M TPhAsþ DPA . The drop time was extremely short over a wide potential range, indicating that BSA is adsorbed on the W/NB interface in the potential range on both sides of PZC as pointed out by Vanysek and Sun [34]. The current oscillation does not appear because the interface is occupied by the adsorbed BSA, and hence Naþ cannot be adsorbed there.

III.

CONDITIONS REQUIRED FOR THE OSCILLATION AT THE LIQUID–LIQUID INTERFACE

In order to elucidate the general features of the oscillation of VW1-W2 or IW1-W2 , NBmembrane systems have been investigated from the viewpoint of ion transfer reactions. The systems examined are Eqs. (4) to (15) which are classiﬁed into four types: (1) transfer of a cation from LM to W2, (2) transfer of an anion from LM to W2, (3) transfer of a cation from W2 to LM, and (4) transfer of an anion from W2 to LM. 1.

transfer of Naþ , Csþ , TMAþ , or TPrAþ from LM to W2: ½W2 ½W1 ½LM; NB 4 þ 2 M MgSO4 ðSEÞ 0:1 M NaCl 4 10 M Na DPA þ 1 M MgSO4 ðSEÞ 0:02 M TPhAs DPA ðSEÞ

ð4Þ

4 104 M Csþ TPhB 2 M MgSO4 ðSEÞ 1 M MgSO4 ðSEÞ 0:05 M THexAþ TPhB ðSEÞ

ð5Þ

0:1 M TMAþ Cl 4 104 M TMAþ TPhB 2 M MgSO4 ðSEÞ 1 M MgSO ðSEÞ 0:05 M THexAþ TPhB ðSEÞ

ð6Þ

0:01 M TPrAþ Cl 5 104 M TPrAþ TPhB 2 M MgSO4 ðSEÞ 1 M MgSO ðSEÞ 0:05 M THexAþ TPhB ðSEÞ

ð7Þ

0:1 M CsCl

4

4

The Oscillation of Membrane Potential

2.

623

transfer of I , Br , or Pic from LM to W2: 0:1 M NaI 5 104 M THexAþ I 2 M MgSO4 ðSEÞ 1 M MgSO4 ðSEÞ 0:05 M THexAþ TPhB ðSEÞ

ð8Þ

5 104 M THexAþ Br 2 M MgSO4 ðSEÞ 1 M MgSO4 ðSEÞ 0:05 M THexAþ TPhB ðSEÞ

ð9Þ

0:1 M Naþ Pic 5 104 M THexAþ Pic 2 M MgSO4 ðSEÞ 1 M MgSO ðSEÞ 0:05 M THexAþ TPhB ðSEÞ

ð10Þ

0:1 M NaBr

4

3.

transfer of TPAþ or TMAþ from W2 to LM: 1 M MgSO4 ðSEÞ 0:05 M THexAþ TPhB ðSEÞ 2:5 104 MðTPAþ Þ2 SO2 4 2 M MgSO4 ðSEÞ (11) 1; M MgSO4 ðSEÞ 0:05 M THexAþ TPhB ðSEÞ 5 104 M TMAþ Cl 2 M MgSO ðSEÞ

ð12Þ

4

4.

transfer of Pic , ClO 4 , or Br from W2 to LM: 1 M MgSO4 ðSEÞ 0:05 M THexAþ TPhB ðSEÞ 5 104 M Naþ Pic 2 M MgSO ðSEÞ

ð13Þ

4

1 M MgSO4 ðSEÞ 0:05 M THexAþ TPhB ðSEÞ 5 104 M NaClO4 2 M MgSO ðSEÞ

ð14Þ

1 M MgSO4 ðSEÞ 0:05 M THexAþ TPhB ðSEÞ 5 104 M NaBr 2 M MgSO ðSEÞ

ð15Þ

4

4

Here, THexAþ denotes tetrahexylammonium ion. It has been found that the oscillation of VW1-W2 or IW1-W2 could be realized by employing the membrane systems of Eqs. (4), (5), (6), (8), (9), (11), and (13). When membrane systems such as Eqs. (7), (10), (12), (14), and (15) were examined, however, the oscillation was not observed at any applied current or membrane potential. All oscillations of VW1-W2 observed were conﬁrmed to be due to the oscillation of VLM=W2 , but not due to VW1=LM . Since the voltammetric maximum due to the adsorption was essential for the oscillations, as mentioned previously, voltammograms (polarograms) were investigated by using an aqueous solution dropping electrode and employing W and NB of which the compositions were the same as those of W2 and LM, respectively, in systems of Eqs. (4) to (15). The polarograms observed are illustrated in Fig. 9. Though potential differences in the measurements were applied as potentials of SSE in W vs. TPhAsE or TPhBE in NB, they were converted into the TPhE scale according to the previous paper [26,27], and plotted as the abscissa in Fig. 9. In the TPhE scale, 0 V corresponds to Gtr ¼ 0 and lies at around PZC.

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FIG. 9 Polarograms for transfers of various ions at the W/NB interface. Concentration of objective ion in W or NB; 5 104 M. Supporting electrolytes: 1 M MgSO4 in W and 0.05 M THexAþ TPhB in NB. Curves 1, 2, 3, 4, 5, 6, 7; transfer of Naþ , Csþ , TMAþ , TPrAþ , I , Br , or Pic , respectively, from NB to W. Curves 8, 9, 10, 11, 12; transfer of TPAþ , TMAþ , Pic , ClO 4, or Br , respectively, from W to NB. Curve 13; residual current. (From Ref. 25.)

As is clear from Figs. 3, 6, and 9, the voltammetric maxima were observed at the LM/W2 interface of Eqs. (4), (5), (6), (8), (9), (11), and (13). In these cases, the positive current ﬂows in a potential range more negative than PZC [Eqs. (8), (9), and (11)] or the negative current ﬂows in a potential range more positive than PZC [Eqs. (4), (5), (6), and (13)]. On the other hand, currents without maxima were observed at the LM/W2 interface of Eqs. (7), (10), (12), (14), and (15). In these cases, the positive current ﬂows in a potential range more positive than PZC [Eqs. (10) and (12)] or the negative current ﬂows in a potential range more negative than PZC [Eqs. (7), (14), and (15)]. Drop time–potential curves recorded under the same conditions as those for the polarographic measurements indicated that all polarographic maxima observed were caused by the adsorption of transferring ions at W/NB interfaces. The above-mentioned results demonstrate that the voltammetric maximum due to the adsorption of the transferring ion at one of two LM/W interfaces is requisite for the oscillation of VW1-W2 or IW1-W2 . However, the oscillation was not always realized with systems which gave maximum currents. The recovery of the concentration of the objective ion in the interfacial region of one phase from which the objective ion transfers to another is necessary in order to get the oscillation. If the ion pair which has been accumulated at the interface is desorbed to the phase to which the ion transfers, the oscillation cannot be realized. Taking into account this circumstance, the fact that the oscillation was not observed when SO2 in Eq. (11) was replaced by Br can be explained as follows. 4 þ When TPA transfers from W2 to LM, TPAþ is adsorbed on the interface as an ion pair irrespective that a counteranion is SO2 4 or Br . The hydrophobicity of ion pair adsorbed at the interface depends on the nature of the counterion, and the more hydrophobic ion pair is desorbed more easily into LM. In the presence case, TPAþ Br is desorbed to LM rather than to W2, but ðTPAþ Þ2 SO2 4 is desorbed to W2 rather than to LM, which means the concentration of TPAþ in the interfacial region of W2 cannot be recovered when Br is adopted as a counteranion, but the concentration can be recovered

The Oscillation of Membrane Potential

625

2 when SO2 4 is adopted. Therefore, the oscillation was realized with SO4 , but not with Br . The above-mentioned consideration in this section suggests that not only the nature of the ion transferring at the interface but also the nature of the counterion with which the ion transferred forms the ion pair at the interface is important for the understanding of the oscillation mechanism.

IV.

SPONTANEOUS OSCILLATIONS OF MEMBRANE POTENTIAL WITHOUT APPLIED CURRENT

The oscillation of membrane potential with the membrane system as in Eq. (16) has been extensively investigated as a typical example of spontaneous oscillations.

ð16Þ

As mentioned in the introduction, it is difﬁcult to explain the characteristics of the oscillation based on the mechanisms which have been proposed so far for the potential oscillations with systems similar to Eq. (16) [4,7,35–38]. A precise investigation on individual ion transfers and adsorptions at two interfaces is necessary for the elucidation of the oscillation mechanism, although the spontaneous oscillation might be realized by the combination of a much larger number of ion transfer reactions and adsorptions than those in the case of the oscillation under the applied potential or current. Adopting Eq. (16) as representative of the system, ion transfer reactions and adsorptions of respective ions participating in the oscillation were investigated individually at two aqueous–membrane interfaces in the system of Eq. (16) by use of VITIES, and as a result the mechanism of the oscillation was elucidated almost quantitatively. The mechanism can be summarized as follows [39]. The independent measurements of time courses of VW1=LM and VLM=W2 indicated that the oscillation of VW1-W2 observed with the system of Eq. (16) was attributable to the oscillation at the LM/W2 interface. Since W1 contained a high concentration of CTAþ Cl and the distribution of Cl from W1 to LM proceeds with CTAþ as a counterion at the W1/LM interface through the whole time including the induction and oscillation time, VW1=LM is determined to be constant (ca. 0:1 V as a potential of TPAþ ion selective electrode, TPAE, vs. SSE) by the composite transfer of CTAþ and Cl from W1 to LM. During the induction time before the start of the oscillation, VLM=W2 stayed at ca. 0.4 V as a potential of SSE vs. TPAE, and hence VW1-W2 stayed at ca. 0.3 V [cf. Eq. (2)]. The VLM=W2 coincided with the interfacial potential where the current is zero in the ion transfer polarogram recorded at the interface between W containing 1 M MgSO4 and NB containing 4 104 M Hþ Pic , 2 104 M CTAþ Cl , and supporting electrolyte (curve 1 in Fig. 10). Here, it should be

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noted that VW1=LM , VLM=W2 , and VW1-W2 for the spontaneous oscillation correspond to those at zero current, since any currents or potentials are not applied to the system. The polarogram of curve 1 is proved to be caused by the composite of transfers of Hþ , Pic , and Cl from LM to W2 by referring to the ion transfer polarograms for transfers of individual ions. The transfer of Hþ from LM to W2 gave a maximum current suggesting the interfacial adsorption of Hþ Pic . As time passes, the concentration of Cl in LM increases because of the distribution from W1, and the positive current due to the transfer of Cl from LM to W2 increases. Simultaneously, the negative maximum current due to the transfer of Hþ decreases owing to the consumption of Hþ and the saturation of adsorption of Hþ Pic . Therefore, the potential difference at zero current at the LM/W2 interface does not stay at ca. 0.4 V and shifts to more negative potentials. Postulating this circumstance, the polarogram shown as curve 2 in Fig. 10 was recorded under the same conditions as for curve 1 but changing the concentration of CTAþ Cl in NB from 2 104 M to 5 104 M. The potential difference at zero current in curve 2 lies at ca. 0.1 V vs. TPAE which is determined by the composite transfer of Hþ and Cl from LM to W2. The potential agreed well with VLM=W2 at the top of the oscillation impulse. The difference between this VLM=W2 (ca. 0.1 V) and VLM=W2 during the induction time (ca. 0.4 V) was identical with the amplitude of the oscillation of VW1-W2 . Since VLM=W2 passes over PZC of the W/NB interface in the shift from 0.4 V to 0.1 V, the ion pair which has been adsorbed is desorbed to LM and dissociated. The recovery of the concentration of Hþ because of the dissociation of Hþ Pic causes the shift of VLM=W2 to ca. 0.4 V and the negative maximum current is regenerated. These processes repeat to realize the oscillation.

V.

CONCLUSION

The electrical oscillations at the aqueous–organic interface or at membranes in the absence of any substances relative to the ‘‘channel’’ or ‘‘gate’’ were introduced. These oscillations might give some fundamental information on the electrical excitability in living organisms. Since the ion transfer at the aqueous–organic or aqueous–membrane interface and the interfacial adsorption are deeply concerned in the oscillation, it has been stressed that the voltammetry for the ion transfer at an interface of two immiscible electrolyte solutions is

FIG. 10 Composite polarograms recorded at the W/NB interface. W: 1 M MgSO4 , NB: 0.05 M TPAþ TFPB þ 4 104 M Hþ Pic þ 2 104 M (1) or 5 104 M (2) CTAþ Cl . TFPB : tetrakis[3,5-bistriﬂuoromethyl]phenylborate ion.

The Oscillation of Membrane Potential

627

very useful in the elucidation of the mechanism of membrane oscillations realized by applying membrane potential or current (cf. Section II) as well as the mechanism of spontaneous oscillation realized by the coupling of the plural ion transfer reactions (cf. Section IV). The voltammetric method and concept are expected to be applicable also to the analysis of the oscillation at a very thin membrane such as a bilayer lipid membrane, since even the ion transfer through a bilayer lipid membrane can be observed as a voltammogram and interpreted by the way similar to that for a liquid membrane [20,21].

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.

R. Larter. Chem. Rev. 90:355 (1990). S. Kihara and K. Maeda. Prog. Surf. Sci. 47:1 (1994). K. Yoshikawa and Y. Matsubara. J. Am. Chem. Soc. 106:4423 (1984). K. Yoshikawa, T. Omochi, and Y. Matsubara. Biophys. Chem. 23:211 (1986). K. Yoshikawa, M. Shoji, S. Nakata, and S. Maeda. Langmuir 4:759 (1988). S. Iiyama, K. Toko, and K. Yamafuji. Sens. Materials 3:1 (1991). K. Arai, S. Fukurama, F. Kusu, and K. Takamura. Electrochim. Acta 40:2913 (1995). A. Higuchi and M. Hara. J. Phys. Chem. 100:2183 (1996). B. Sakmann and E. Neher, Single-Channel Recording, Plenum Press, New York, 1983. C. Miller, Ion Channel Reconstitution, Plenum Press, New York, 1986. S. Numa. Harvley Lectures 83:121 (1989). M. Dupeyrat and E. Nakache. Bioelectrochem. Bioenerg. 5:134 (1978). M. Dupeyrat and E. Nakache. Bioelectrochem. Bioenerg. 9:583 (1982). E. Nakache and M. Dupeyrat. J. Colloid Interface Sci. 94:187 (1983). E. Nakache and M. Dupeyrat. Faraday Discuss. Chem. Soc. 77:189 (1984). K. Yoshikawa and Y. Matsubara. J. Am. Chem. Soc. 105:5967 (1983). H. H. J. Girault, and D. J. Schiffrin, Electroanalytical Chemistry, (A. J. Bard, ed.), vol. 15, Marcel Dekker, New York, 1989, pp. 1–141. M. Senda, T. Kakiuchi, and T. Osakai. Electrochim. Acta 36:253 (1991). Liquid–Liquid Interfaces. Theory and Methods, A. G. Volkov and D. W. Deamer, eds.), CRC Press, New York, 1996. O. Shirai, S. Kihara, Y. Yoshida, and M. Matsui. J. Electroanal. Chem. 389:61 (1995). O. Shirai, Y. Yoshida, M. Matsui, K. Maeda, and S. Kihara. Bull. Chem. Soc. Jpn. 69:3151 (1996) K. Maeda, S. Kihara, M. Suzuki, and M. Matsui. J. Electroanal. Chem. 295:183 (1990). S. Kihara, K. Maeda, M. Suzuki, Y. Yoshida, and M. Matsui. Anal. Sci. 7(suppl.): 601 (1991). S. Kihara, K. Maeda, O. Shirai, Y. Yoshida, and M. Matsui, Bioelectroanalysis 2 (E. Pungor, ed.), Akademiai Kiado, Budapest, 1993, pp. 331–342. K. Maeda, W. Hyogo, S. Nagami, and S. Kihara. Bull. Chem. Soc. Jpn. 70:1505 (1997). S. Kihara, M. Suzuki, K. Maeda, K. Ogura, S. Umetani, M. Matsui, and Z. Yoshida. Anal. Chem. 58:2954 (1986). S. Kihara, M. Suzuki, K. Maeda, K. Ogura, and M. Matsui. J. Electroanal. Chem. 210:147 (1986). T. Shedlovsky and R. L. Kay. J. Phys. Chem. 60:151 (1956). T. Kakiuchi, M. Kobayashi, and M. Senda. Bull. Chem. Soc. Jpn. 60:3109 (1987). Z. Yoshida and S. Kihara. J. Electroanal. Chem. 227:171 (1987). S. Kihara, Z. Yoshida, and T. Fujinaga. Bunseki Kagaku 31:E297 (1982). H. H. J. Girault and D. J. Schiffrin. J. Electroanal. Chem. 170:127 (1984). T. Kakiuchi, M. Kobayashi, and M. Senda. Bull. Chem. Soc. Jpn. 61:1545 (1988). P. Vanysek and P. Sun. Bioelectrochem. Bioenerg. 23:177 (1990).

628 35. 36. 37. 38.

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T. Kawakubo and K. Fukunaga. Ferroelectrics 86:257 (1988). K. Yoshikawa, S. Maeda, and H. Kawakami. Ferroelectrics 86:281 (1988). S. Sha, T. Nakamoto, and T. Moriizumi. Jpn. J. Appl. Phys. 30:L1774 (1991). K. Miyamura, H. Yoshihisa, K. Hirai, and Y. Gohshi. J. Chem. Soc. Faraday Trans. 91:895 (1995). 39. K. Maeda, S. Nagami, Y. Yoshida, H. Ohde, and S. Kihara. J. Electroanal. Chem. in press.

26 Selective Ion Transfer of Alkali and Alkaline Earth Metal Ions Facilitated by Naphtho-15-Crown-5 Across Liquid^ Liquid Interfaces and a Bilayer Lipid Membrane HIDEKAZU DOE Japan

I.

Department of Chemistry, Osaka City University, Osaka,

INTRODUCTION

Early in the 20th century the ﬁrst electrochemical study at an ITIES (interface of two immiscible electrolyte solutions) on ion transfer across a water–phenol interface was reported by pioneers Nernst and Riesenfeld [1]. However, it was about 70 years before the start of the many interesting electrochemical studies of ITIESs, which successfully continue today. Various types of research are carried out on ITIESs nowadays. These studies are modeled on electrochemical techniques, theories, and systems. Studies of ion transfer across ITIESs are especially interesting and important because these are the only studies on ITIESs. Many complex ion transfers assisted by some chemical reactions have been studied, to say nothing of single ion transfers. In the world of nature, many types of ion transfer play important roles such as selective ion transfer through biological membranes. Therefore, there are quite a few studies that get ideas from those systems, while many interests from analytical applications motivate those too. Since the ion transfer at an ITIES is closely related with the ﬁelds of solvent extraction and ion-selective electrodes, these studies mainly deal with facilitated ion transfer by various kinds of ionophores. Since crown ethers as ionophores show interesting selectivity, a lot of derivatives are synthesized and their selectivities are evaluated in solvent extraction, ion-selective systems, etc. Of course electrochemical studies on ITIESs are also suitable for the systems of ion transfer facilitated by crown ethers and have thrown new light on the mechanisms of selectivity exhibited by crown ethers. It was reported that neutral ionophore naphtho-15-crown-5 (N15C5, see Fig. 1) gives an excellent selective response to Kþ ion over Naþ ion when it is doped into an ion-selective electrode [2,3]. This result is very interesting considering the hole size of the crown. Ishibashi and coworkers studied the mechanisms of that selectivity using the technique of solvent extraction into 1,2-dichloroethane (DCE) where picrate anion was used as a counterion [4]. Their result is also interesting because Naþ is extracted as a 629

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FIG. 1 Chemical structure of naphtho-15-crown-5.

monocomplex with N15C5 but Kþ makes a bis-complex (metal-to-ligand ratio of 1 : 2 sandwich type complex) producing much stability in DCE. There are not so many systems where speciﬁc selectivity is produced by a difference in composition; at least, such systems never have been electrochemically studied at the ITIES. Therefore, various facilitated ion transfers by N15C5 have been ﬁrst studied electrochemically and some results have been interestingly compared with those from the solvent extraction study. On the other hand, electrospray ionization mass spectrometry (ESMS) has been ﬁrst combined with electrochemistry at ITIES in order to conﬁrm the stoichiometry of a complex ion transferred into an organic phase directly. ESMS is now becoming a popular and powerful technique not only in chemistry but also in biology, pharmacy, medical science, etc. Electrospray (ES) ionization is exceedingly effective resource for producing gas-phase ions from various solutions which contain any kinds of ion. Thus, ESMS can sometimes give us highly useful information in comparison with electrochemical results.

II.

EXPERIMENTAL ASPECTS

Polarography (current-scan) with an electrolyte-dropping electrode and cyclic voltammetry with an aqueous gel electrode were employed to study the ion transfer. Nitrobenzene (NB) was used as an organic phase in the polarographic measurements and 1,2-dichloroethane (DCE) in the cyclic voltammetric ones. The supporting electrolyte in the aqueous phase was MgSO4 and in the organic phase was tetraheptylammonium tetraphenylborate (THATPB). Naphtho-15-crown-5 (N15C5) was synthesized by Pedersen’s procedure [5,6]. The electrochemical cell for the polarographic measurements had a four-electrode conﬁguration equipped with a microsyringe, and was connected to a computer-assisted data-acquisition system [7]. On the other hand, the cyclic voltammetric measurements that are also assisted by a computer data-acquisition system were carried out using a gel electrode that contains the aqueous phase [8]. The cell structure was as follows:

Selective Ion Transfer of Metal Ions

631

where NaTPB denotes sodium tetraphenylborate. All electrode potentials were referred to the half-wave potential of the transfer of tetraethylammonium ion (TEAþ ) from the aqueous to the organic phase. Sample solutions for electrospray ionization mass spectrometry (ESMS) measurements were the organic DCE phases, in which there were metal ions extracted by N15C5 from the aqueous solutions with almost the same composition as those in the electrochemical measurements [9]. NB was not used in the ESMS measurements because of its high viscosity. The ESMS spectra were obtained on a sector-type mass spectrometer, JEOLD300, equipped with a laboratory-made electrospray (ES) interface. The ES ion source was similar to that designed by Fenn [10]. A sample solution is sprayed at the tip of a needle applied at 3.5 kV higher than a counterelectrode. Heated N2 gas at 70 C is ﬂowed between the needle and the counterelectrode in order to dry the charged ES droplets. Then the desolvated ions (dried ES droplets) enter in the vacuum system through the ﬁrst (10 Torr) and second (0.1 Torr) skimmers. Before entering the main slit, the ion beam is focused by a lens system 20 cm long where it is pumped down to a typical pressure of 2 106 Torr. The voltage of the second skimmer determines the translational energy of ions in the mass spectrometer which has been 2 keV. The details are described elsewhere [11].

III.

RESULTS AND DISCUSSION

A.

Transfers of Na+ and K+

The facilitated transfers of Naþ and Kþ into the NB phase were observed by the currentscan polarography at an electrolyte-dropping electrode [12]. In the case of ion transfers into the DCE phase, cyclic voltammetry was measured at an aqueous gel electrode [9]. Both measurements were carried out under two distinctive experimental conditions. One is a N15C5 diffusion-control system where the concentration of N15C5 in the organic phase is much smaller than that of a metal ion in the aqueous phase. The other is a metal ion diffusion-control system where, conversely, the concentration of metal ion is much smaller than that of N15C5. Typical polarograms measured in the both experimental systems are shown in Fig. 2. In the case of Naþ transfer, there appears one polarographic wave (see the polarogram shown by a symbol * in Fig. 2) caused by the facilitated ion transfer in the N15C5 diffusion-control system. In the Naþ diffusion-control system, however, no obvious wave is observed (symbol *), because the positive end of potential window shifts to decrease the window’s width. This shift becomes the more prominent, the higher the organic bulk concentration of N15C5, [N15C5o is. Hence, it is expected that the aqueous supporting cation Mg2þ is also facilitated by N15C5. In the case of Kþ transfer differing from the case of Naþ an outstanding wave appears in the Kþ diffusion-control system (symbol ! in Fig. 2), but no wave in the N15C5 diffusion-control system (symbol !). Although in the latter case there may be a small wave near the positive window’s end, it is clear that a large shift of its end puts the wave behind. This positive end is current caused by the transfer of Kþ itself and moves toward a negative potential with an increase of Kþ aqueous bulk concentration [Kþ ]. According to the comprehensive analysis of those waves [12], the facilitated wave of Naþ has been attributed to the transfer of 1 : 1 monocomplex ion, NaðN15C5Þþ , and that of Kþ to the transfer of 1 : 2 bis-complex ion, KðN15C5Þþ 2 . Since the wave for the KðN15C5Þþ transfer appears at more negative potential than that for the NaðN15C5Þþ 2

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FIG. 2 Current-scan polarograms of Naþ and Kþ ion transfers facilitated by N15C5 at the water ð½MgSO4 ¼ 0:125 MÞ–NB ð½THATPBo ¼ 0:10 M) interface: *, ½N15C5o ¼ 2:00 104 M and ½Na2 SO4 ¼ 2:00 102 M; *, ½N15C5o ¼ 2:00 102 M and ½Na2 SO4 ¼ 5:00 105 M; !, ½N15C5o ¼ 2:00 102 M and ½K2 SO4 ¼ 4:08 105 M; !, ½N15C5o ¼ 2:00 104 M and ½K2 SO4 ¼ 1:00 101 M.

þ transfer in Fig. 2, it is inferred that KðN15C5Þþ 2 is more stable than NaðN15C5Þ in the NB phase. Typical cyclic voltammograms of the N15C5 diffusion-control systems are shown in Fig. 3; the organic phase is DCE in these measurements. Clear waves of facilitated ion transfers are observed in both cases of Naþ and Kþ . In DCE as well as in NB, a facilitated wave of Kþ appears at a more negative potential than that of Naþ ; that is, the transfer of Kþ will also be more strongly facilitated into the DCE phase by N15C5 than that of Naþ . As described elsewhere [9], it has been concluded that the ions transferred to the DCE phase are the 1 : 1 complex NaðN15C5Þþ and the 1 : 2 complex KðN15C5Þþ 2 in the respective cases. This conclusion is clearly shown in the voltammograms of Fig. 3 already; the peak currents for the Kþ transfer are just a half of those for the Naþ transfer at the same ½N15C5o . Since those are the N15C5 diffusion-control systems, this means the transfer of one Kþ ion needs twice as many N15C5 molecules as that of one Naþ ion. The values of diffusion coefﬁcients and thermodynamic parameters on the interfacial ion transfer are determined and summarized in Tables 1 and 2. The diffusion coefﬁcients of Naþ and Kþ are of the values in the aqueous solutions of ½MgSO4 ¼ 0:125 M and those of N15C5 are of ones in the NB and DCE solutions of ½THATPB ¼ 0:10 and 0.010 M, respectively. The value of Naþ in NB is not evaluated because any clear polarographic wave has not been observed in the Na+ diffusion-control system. The values of Kþ are

Selective Ion Transfer of Metal Ions

633

FIG. 3 Cyclic voltammograms of Naþ and Kþ ion transfers facilitated by N15C5 at the Water ð½MgSO4 ¼ 0:125 MÞ–DCE ð½THATPBo ¼ 0:010 MÞ interface. Aqueous phase: 2:0 102 M M2 SO4 . Organic phase: (1) 1:0 104 (2) 3:0 104 (3) 7:0 104 (4) 1:0 103 M N15C5. Scan rate, 0:050 V s1 .

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TABLE 1 The Diffusion Coefﬁcients of Naþ and Kþ in the Aqueous Phase (½MgSO4 ¼ 0:125 M), and those of N15C5 in the Organic Phase 105 D ðcm2 s1 Þ

NBa DCEb a b

Naþ

Kþ

N15C5

— 1.04

1.03 1.28

0.16 0.54

½THATPBo ¼ 0:10 M: ½THATPBo ¼ 0:010 M:

TABLE 2 Thermodynamic Parameters on the Facilitated Ion Transfers Determined Under the TPATPB Assumption NaðN15C5Þþ FE 0 =RT NB DCE

5:3b 8:3 –11:5b c

KðN15C5Þþ 2

log Kall

a log Kex

FE 0 =RT

log Kall

a log Kex

1.37 1:58

— 1:24

3:5b 8:1b

5.31 4.43

— 4.41

a

Reference 4. Reference 14. c Reference 15. See the text for the meaning of parameters. b

different between NB and DCE systems, although these should have been determined in the same aqueous solutions. The most possible cause is a mutual dissolution between the aqueous and the organic phases [13]; that is, the aqueous phase contains a small amount of NB or DCE. Another cause may be that the surface of a gel electrode is small (its surface area was 0:011 cm2 ) and not so ﬂat. The thermodynamic parameters summarized in Table 2 have been determined in an EC mechanism where the complexation between the metal ion and N15C5 occurs at the organic interphase (the organic side of an interface) just after the metal ion transfer across the interface. Therefore, the standard potential E 0 in Table 2 is that of the ion transfer of a metal ion itself. The E 0 values are cited from two representative studies [14,15]. The larger this value is, the more energy the cation transfer from the aqueous to organic phase needs. The equilibrium constant Kall stands for an equilibrium Mþ ðaqÞþaN15C5ðorgÞ Ð þ MðN15C5Þþ a ðorgÞ: It contains two steps of the interfacial M -transfer and the complexation in the organic phase. Thus, the Kall corresponds to the solvent extraction constant Kex . The Kall values are evaluated under the TPATPB assumption [16,17], and those for the DCE system are of a concentration constant in those aqueous ð½MgSO4 ¼ 0:125 MÞ and organic ð½THATPB ¼ 0:010 MÞ electrolytic solutions. The Debye–Hu¨ckel second approximation has been adopted in the calculation of formal ion-transfer potentials [9]. The stability constants of complexation are simply calculated by the following relation: ln ¼ ln Kall þ FE 0 =RT

Selective Ion Transfer of Metal Ions

635

The Kex values in Table 2 are calculated from those obtained in the solvent extraction study [4], where these complex ions are extracted as ion pairs with a picrate anion MðN15C5Þa pic. The ion-association constants of the ion pairs NaðN15C5Þpic and KðN15C5Þ2 pic in DCE were reported to be 5.1 and 3.2 on the logarithmic scale, respectively [4]. Thus, the Kex and Kall in Table 2 are the constants of the identical equilibrium, but their values have been determined by different measurements. It should be very interesting that these values agree well, and this should indicate the high reliability of both measurements. However, it may be of importance that our study has not taken an ion-pair formation with the organic supporting TPB into account. The ESMS measurements have been ﬁrst carried out in a positive ion mode to get direct identiﬁcation of transferred species. DCE solutions for the ESMS measurements were prepared by solvent extractions with an aqueous and the DCE solutions that were the same as those used in the electrochemical studies except ½THATPBo . Small ½THATPBo was used in the ESMS measurements in order to avoid extremely high signal intensity of THAþ compared with those of objective ions. Some typical spectra are shown in Fig. 4. A spectrum inserted in the spectrum (a) is of a supporting electrolyte system, ½THATPBo ¼ 1:0 106 M and ½MgSO4 ¼ 0:125 M. Therefore, the signal assigned to THAþ appears very strongly. Although, unexpected weak signals þ are assigned to NaðN15C5Þþ 2 and KðN15C5Þ2 , these should probably originate in þ þ impurities of Na and K which MgSO4 salt usually contains in a very small quantity. Every spectrum in Fig. 4 showed no anion signals, because only positive ions were sprayed. The results from the ESMS measurements have given us several remarkable facts. To begin with, the signal of NaðN15C5Þþ appears only in the system of Naþ transfer as shown by spectra (a) and (b) in Fig. 4. The intensity of that signal seems not to increase with an increase of ½Naþ [since the spectrum (b) is of the N15C5 diffusioncontrol system, its ½Naþ is 100 times larger than that of the spectrum (a) which is of the metal ion diffusion-control system], but the intensity for NaðN15C5Þþ 2 is somewhat increased. Hence, the formation of NaðN15C5Þþ may have occurred in the course of 2 spraying. However, there is no adequate explanation for the detection of NaðN15C5Þþ 2 now, which should be also detected electrochemically if its complex ion transfers to the DCE phase. On the other hand, it is very interesting that only the signal of þ KðN15C5Þþ 2 has been observed with strong intensities in the K -transfer system. It should also indicate something important that the intensity of that signal remains unaltered between ½Kþ ¼ 2:0 105 and 2:0 103 M. Anyway, this result seems to be just consistent with the electrochemical one. Furthermore, it may also be true that the high intensity of KðN15C5Þþ 2 signal is caused by its easier transfer than that of NaðN15C5Þþ into the DCE phase. Thus, the ESMS will also become a powerful measurement in this ﬁeld. Several attempts are being carried out in our laboratory to measure this selective ion transfer across a bilayer lipid membrane (BLM) that contains N15C5. One example of the selective ion transfer is presented in Fig. 5. A BLM is formed across a hole in a Teﬂon partition using a small brush [18]. As shown in Fig. 5, a pair of clear waves has been observed only in the Kþ -transfer system. These waves are not affected only by [N15C5] in the BLM, but also by the concentration of tetra-alkylammonium salt as a supporting electrolyte in the BLM to some extent. Moreover, the BLM is not stable enough to get quantitative data. Therefore, this study is being executed carefully to conﬁrm this selectivity now, since the selective transfers through BLMs are extremely attractive phenomena.

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FIG. 4 ESI-MS spectra of Mþ –N15C5 systems. (a,c) ½N15C5o ¼ 1:0 103 M and ½Mþ ¼ 2:0 105 M; (b,d) ½N15C5o ¼ 1:0 104 M and ½Mþ ¼ 2:0 103 M; where Mþ is Naþ (a,b) or Kþ (c,d). Inset shows the spectrum of supporting electrolyte system; ½THATPBo ¼ 1:0 106 M and ½MgSO4 ¼ 0:125 M.

B.

Transfers of Ca2+, Sr2+, and Ba2+

The facilitated ion transfers of some alkaline earth metals have been also studied in the DCE systems by the cyclic voltammetry. These systems perhaps have not been studied by any solvent extraction methods yet. Typical voltammograms in the N15C5 diffusioncontrol systems are shown in Fig. 6. The aqueous supporting electrolyte was MgCl2 instead of MgSO4 in these measurements because BaSO4 precipitated. It is very clear in Fig. 6 that the waves for the Ca2þ transfer shift to a very negative potential compared with those for the Sr2þ and Ba2þ transfers. Also only the peak currents of Ca2þ waves are small (half currents of Sr2þ and Ba2þ waves). According to the same account as the alkali metal systems, it is concluded that only the transfer of Ca2þ is facilitated by N15C5 selectively over those of Sr2þ and Ba2þ (of course over the transfer of Mg2þ too); only Ca2þ forms a stable bis-complex CaðN15C5Þ2þ 2 in order to transfer into the DCE phase such as Kþ . The waves of Sr2þ and Ba2þ are assigned to the transfer of monocomplex. The cathodic waves of Sr2þ are considerably broad. Since those waves correspond to the reverse transfer of SrðN15C5Þ2þ from the DCE to the aqueous phase, this may indicate slow decomposition of its complex ion. The half-wave potentials of the transfers of BaðN15C5Þ2þ and SrðN15C5Þ2þ are 161 and 183 mV, respectively. From these values, the half-wave potential of mono CaðN15C5Þ2þ -transfer

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637

FIG. 5 Cyclic voltammograms of Naþ and Kþ ion transfer through a bilayer lipid membrane (phosphatidylcholine þ cholesterol þ N15C5 þ ðC7 H15 Þ4 Nþ ½ðCF3 Þ2 Ph4 B Þ. Aqueous phase: 2:0 103 M M2 SO4 and 0:125 M MgSO4 . Scan rate, 0:040 V s1 .

is expected to be around 200 mV if it would also transfer. As shown in the voltammograms of the Ca2þ system (Fig. 6), there possibly appear the traces of some waves near the positive end of potential window. If so, the transfer of CaðN15C5Þ2þ may also take place to a certain extent. ESMS measurements have been carried out for these systems. According to these spectra, the obvious signal of CaðN15C5Þ2þ was observed, though its intensity was not so strong; and the one of CaðN15C5Þ2þ 2 was very weak, but it can be recognized. This is a tendency different from the Naþ system where the signal of a bis-complex ion was rather 2þ prominent. On the other hand, no signals of SrðN15C5Þ2þ a and BaðN15C5Þa were detected from the DCE solutions extracted under the same conditions as those of electrochemical measurements. These interesting results have not been well understood. The electrospray process still contains several unsolved mechanisms. Therefore, it is necessary to compile much more data not only from ESMS studies, but also from electrochemical ones in order to discuss those in detail.

C.

Transfers of Some Transition Metals

Some divalent transition and post-transition metal ions, Co2þ , Ni2þ , Cu2þ , Zn2þ , and Cd2þ , have been studied in the same way, but these systems need a pH-control in order to avoid any precipitation. Although measurements have not been completed yet, a pair of waves has been observed only in the Cu2þ system that is somewhat irreversible (100 to 50 mV of the half-wave potential). In the other systems, any waves except ambiguous broad ones could not be obtained. While analyzing some waves, Cu2þ seems to be facili-

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FIG. 6 Cyclic voltammograms of Ca2þ , Sr2þ , and Ba2þ ion transfers facilitated by N15C5 at the water ð½MgCl2 ¼ 0:125 MÞ–DCE ð½THATPBo ¼ 0:010 M) interface. Aqueous phase: 1:0 102 M MCl2 . Organic phase: (a) 1:0 104 , (b) 2:0 104 , (c) 3:0 104 , (d) 4:0 104 M N15C5. Scan rate, 0:050 V s1 .

tated by forming a tris-complex ion CuðN15C5Þ2þ 3 depending on conditions. The broad wave may mean that several complex ions with consecutive metal-to-ligand ratio transfer one after another. Anyway these complicated systems need further experiments.

Selective Ion Transfer of Metal Ions

IV.

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CONCLUSIONS

Taking advantage of interesting reports from the studies of solvent extraction and ionselective electrodes, various metal ion transfers facilitated by N15C5 have been studied by electrochemistry at the ITIES (organic phases are NB and DCE) and ESMS, and also through BLM. Since it is very important to compare these results with those from the solvent extraction study, the transfers of Naþ and Kþ in particular have been investigated in detail. The electrochemical study is not able to specify elementary steps through which the ion transfer takes place. Therefore the elementary steps introduced in the solvent extraction study have been employed in this electrochemical study and each parameter has been determined. Interestingly, the extraction constants have been well consistent with each other. The difference in the structure of complex ions between Naþ and Kþ , which is a direct cause of the difference in selectivity between them, has been evidently conﬁrmed by the electrochemical and ESMS measurements; that is, Kþ gets the ability to selectively þ transfer as the bis-complex ion KðN15C5Þþ 2 over the monocomplex ion NaðN15C5Þ . Such a structural effect has also been observed among the facilitated ion transfers of alkaline earth metals. It is a result that the transfer of bis CaðN15C5Þþ 2 ion is better facilitated than those of mono SrðN15C5Þþ and BaðN15C5Þþ ions. On the other hand, BLM doped by N15C5 also shows evidence of the selectivity between Naþ and Kþ . Comprehensive studies of selectivity like ours are really attractive and important not only in the ﬁeld of analytical chemistry but also biochemistry.

ACKNOWLEDGMENT The help of Dr. Md A. Rahman (Ministry of Education Scholarship Student in Japan, now Senior Scientiﬁc Ofﬁcer, Institute of Glass and Ceramic Research and Testing, Bangladesh Council of Scientiﬁc and Industrial Research), Dr. M. S. Bakshi (JSPS Postdoctoral Fellow in Japan), and the other coworkers has been invaluable in these studies. My special thanks to Ryuich Arakawa (Professor, Department of Applied Chemistry, Kansai University, Japan) for his assistance with ESMS measurements must be expressed. The support by Grant-in Aid for Scientiﬁc Research (No. 07804049, 08454240, and 97468 from the Ministry of Education, Science and Culture, Japan, and from Osaka City, Japan) is gratefully acknowledged.

REFERENCES 1. 2. 3. 4.

W. Nernst and E. H. Riesenfeld. Ann. Phys. 8:600 (1902). M. Yamauchi, A. Jyo, and N. Ishibashi. Anal. Chim. Acta 136:399 (1982). T. L. Blair, S. Daunert, and L. G. Bachas. Anal. Chim. Acta 222:253 (1989). M. Yamauchi, T. Imato, M. Katahira, Y. Inudo, and N. Ishibashi. Anal. Chim. Acta 169:59 (1985). 5. C. J. Pedersen. J. Am. Chem. Soc. 89:7017 (1967). 6. S. Z. Perry and H. Hibbert. Canad. J. Res. [B] 14:77 (1936). 7. H. Doe, K. Yoshioka, and T. Kitagawa. J. Electroanal. Chem. 324:69 (1992). 8. M. A. Rahman and H. Doe. J. Electroanal. Chem. 424:159 (1997). 9. M. A. Rahman, H. Doe, M. Okamoto, and R. Arakawa. Electrochim. Acta 44:39 (1998). 10. M. Yamashita and J. B. Fenn. J. Phys. Chem. 88:4451 (1984).

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11. R. Arakawa, L. Jian, A. Yoshimura, K. Nozaki, T. Ohno, H. Doe, and T. Matsuo. Inorg. Chem. 34:3874 (1995). 12. H. Doe, Y. Yamada, and M. A. Rahman. Anal. Sci. 13:531 (1997). 13. H. Doe, M. Hoshiyama, and L. Jian. Electrochim. Acta 40:2947 (1995). 14. Z. Samec and P. Papoff. Anal. Chem. 62:1010 (1990). 15. Z. Samec, V. Marecek, and M. P. Colombini. J. Electroanal. Chem. 257:147 (1988). 16. A. J. Parker. Chem. Rev. 69:1 (1969). 17. A. J. Parker. Electrochim. Acta 21:671 (1976). 18. T. Hanai, in Shin-Jikken Kagaku Koza vol. 18 (Chem. Soc. Japan, ed.), Maruzen, Tokyo, 1978, pp. 476–497.

27 Langmuir and Langmuir^Blodgett Films of Chlorophyll a and Photosystem II Complex ROGER M. LEBLANC and VEERANJANEYULU KONKA Chemistry, University of Miami, Coral Gables, Florida

I.

Department of

INTRODUCTION

Photosynthesis is a process through which green plants convert light energy into chemical energy in a complex organelle, called chloroplast. Chloroplast is a membraneous organelle enclosing lipid bilayer membranes embedded with supramolecular polypeptide assemblies. These lipid bilayers are called thylakoid membranes, which are responsible for light energy conversion into reductant power, which is necessary to reduce carbon dioxide into carbohydrates. Thylakoid membranes of higher plants consist of four major protein complexes: photosystem (PS) II, PS I, cytochrome b6 =f, and proton-ATPase complex. Among these protein complexes, PS II is involved in the process of light absorption, energy transfer, charge separation, and evolution of molecular oxygen [1,2]. PS II complex is a multisubunit protein complex with a total molecular mass of 890 kDa, and is composed of the PS II reaction center, chlorophyll a=b binding proteins of CP 47 and CP 43, extrinsic proteins of 33, 24, and 17 kDa, LHC II, and some smaller protein components [2,3]. The minimum PS II complex capable of evolving oxygen consists of seven major intrinsic proteins – D1, D2, cyt b559 and subunits, CP 47, CP 43, and one extrinsic protein 33 kDa, with a total molecular mass of about 230–250 kDa [3,4]. Because of its importance in the photosynthetic process, understanding the structure and the functions of the PS II complex has been the subject of intense investigations over many years [1,3,5–7]. Due to the structural complexity of the PS II complex, the morphological basis for its physiological functions has been difﬁcult to determine. So, it is desirable, methodologically, to extract and isolate each functional subunit, and to study them either individually or collectively by reconstructing the membrane in a controlled fashion. The Langmuir technique provides a promising approach in this regard because it allows a ﬁne control of molecular constituents and their relative orientation that are similar to those found in natural membranes. In addition, this technique permits us to study the effects of environmental parameters such as temperature, pH, and ionic strength as well as to use those parameters to control the desirable formation of ﬁlms. Nevertheless, to utilize this technique with conﬁdence, optimization of the Langmuir technique for PS II and the development of systematic methods for ﬁlm formation is required. 641

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LANGMUIR FILMS OF PHOTOSYSTEM II

Using the Langmuir technique we investigated the surface pressure and surface potential properties of monolayers of PS II membranes and PS II core complex as well as the mixed monolayers of the PS II core complex and supporting lipid (MGDG) formed at the air–water interface. Optimization of the Langmuir technique to the PS II systems is essential for further investigations using surface spectroscopy and atomic force microscopy [8]. A.

Surface Pressure Studies

The surface pressure as function of molecular area, or –A curve, as the sample at the air–water interface being compressed, is an important indicator of the quality of the monolayer. A sudden change in surface pressure usually signals the formation or collapse of a stable layered structure. Although the PS II membrane proteins possess a pair of hydrophobic and hydrophilic parts, which are appropriate for forming a monolayer at the air–water interface, the ability of the membrane to form a stable monolayer structure is hindered by its massive size and density. The complex structure of the PS II membrane and the interactions among its subunits further complicate the interpretation of its –A curve. The –A curve of PS II membrane proteins, although quite typical of other proteins (Fig. 1), lacks some sharp features that are representative of those more rigid and well-structured materials such as pure lipids. Nevertheless, the fact that stable –A curves can be produced with reliability and repeatability supports the fact that a stable monolayer of PS II membranes can be formed reliably at the air–water interface. It is also interesting to note that only a fraction of PS II membrane protein forms a stable monolayer structure and the rest of them fall into the water subphase. This can be seen directly by the naked eye during the compression. Furthermore, if we use the total amount of PS II membrane protein to calculate the average particle size from the –A curve, we obtain an area of about 200 nm2 . This value is very small when compared with that of the PS II core complex (320 nm2 , as discussed in the subsequent section), which is a smaller subunit of the PS II membranes. A PS II membrane fragment contains PS II core complex and several LHC II proteins, and is much larger in size than a PS II core complex

FIG. 1 Surface pressure–area isotherm of PS II membrane. Subphase, 2 mM CdCl2 , 2 mM ascorbate, and 2 mM MES/NaOH, pH 6.5. Temperature, 23:0 0:5 C.

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particle. Using the actual particle size along with the –A curve, we can estimate that only a fraction of PS II membrane protein stays on the surface and forms a stable monolayer structure. Compression of the PS II membrane monolayer shows that the monolayer collapses at a relatively low surface pressure, at around 20 mN/m. This can be attributed to the formation of a multilayered structure [8] and some of PS II membrane fragments diffuse into the subphase. This observation further indicates that PS II membranes can only marginally stay at the air–water interface and one must be very careful in choosing the experimental parameters. In the case of PS II membrane proteins, as discussed above, the hydrophobic and hydrophilic pairs of attached lipids can partially support the protein complex at the air– water interface, despite their large size and density. However, in the case of PS II core complex, the detergent strips the attached lipids and some extrinsic proteins. The remaining protein complex is water soluble. It is very difﬁcult to prepare a stable monolayer of water-soluble proteins with the Langmuir method. Indeed, it is hard to directly prepare a stable monolayer of PS II core complex because of its water solubility as well as density. One possible solution is to change the density and ionic strength of the subphase [9]. We studied the surface pressure–area isotherms of PS II core complex at different concentrations of NaCl in the subphase (Fig. 2). Addition of NaCl solution greatly enhanced the stability of monolayer of PS II core complex particles at the air–water interface. The –A curves at subphases of 100 mM and 200 mM NaCl clearly demonstrated that PS II core complexes can be compressed to a relatively high surface pressure (40 mN/m), before the monolayer collapses under our experimental conditions. Moreover, the average particle size calculated from –A curves using the total amount of protein complex is about 320 nm2 . This observation agrees well with the particle size directly observed using atomic force microscopy [8], and indicates that nearly all the protein complexes stay at the water surface and form a well-structured monolayer. However, one must also be careful when using a high concentration of salt to increase the density of the water subphase. Two disadvantages of using high-concentration salt solution as subphase are: (1) high concentration of salt in the subphase can change the protein conformation at the air–water interface; (2) the salt particles can be deposited

FIG. 2 The surface pressure–area isotherms of PS II core complex with different concentrations of salt in the subphase. Subphase, 10 mM tris-HCl, pH 8.0, 2 mM sodium ascorbate and concentrations of 100, 200, and 500 mM NaCl. Temperature, 23:0 0:5 C.

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together with the protein complex monolayer onto the substrate when we prepare LB ﬁlms [9]. An optimal condition must be attained in order to use this technique effectively. We noticed that there are little differences in the –A curves of 100 and 200 mM of NaCl in the subphase. However, for 500 mM of NaCl in the subphase, the average particle size calculated from the –A curve decreases when compared with that of 100 and 200 mM of NaCl in the subphase. This indicates that the conformation of the PS II core complex has been altered by the presence of a high concentration of salt solution. We chose the 100 mM NaCl concentration in the subphase for our work. We also noticed that the initial surface pressure is relatively high for all subphase compositions. This is due to the fact that we used a rather small Langmuir trough and the presence of residual detergent in the sample. The –A isotherm is nonreproducible during the compression and expansion. In the sample solution, the hydrophobic regions of protein subunits are covered by the detergent molecules. Once the PS II samples are spread onto the air–water interface, the detergent molecules separate from the protein particles and a mixed monolayer of protein and detergent molecules is formed. However, the detergent molecule has a fairly short hydrophobic chain, which cannot form a stable monolayer at the air–water interface (data not shown). After compression to relatively high pressures, detergent molecules are ejected from the monolayer to the subphase and the surface concentration of detergent molecules is decreased due to the formation of micelles [10–12]. The presence of detergent molecules resulted in nonreproducibility of –A isotherms during compression and expansion. We also noticed that the molecular area decreases gradually when the surface pressure is held at a certain value. Two possible explanations for this are: (1) there may be some leakage of protein molecules from the surface into the subphase, since the protein is water soluble; (2) protein denaturation may be taking place at the air– water interface. Our studies on the surface pressure–area isotherms of MGDG and the mixture of PS II core complex and MGDG indicate the presence of both PS II core complex and MGDG in the monolayer. MGDG molecules diluted the PS II core complex concentration in the monolayer. MGDG lipid functions as a support for the protein complex and the resulting mixture forms higher-quality ﬁlms than PS II core complex alone. B.

Surface Potential Studies

The surface potential as function of particle area (V–A isotherm) is another indicator of the quality of the monolayer structure. The surface potential at the air–water interface changes as the ﬁlm-forming molecules reorient themselves during the compression process. For a closely packed monolayer, the surface potential is directly proportional to the surface dipole moment (? ) by [13]: V ¼ 12? =A where V is the surface potential change in millivolts when a monolayer is spread at the air–water interface, A is the molecular area in A˚2 /molecule, and ? is the surface dipole in millidebye (mD) units. As the surface area is compressed from 400 to 175 nm2 , the surface potential remains at a constant value, whereas the surface pressure increases slightly from 6.5 to 10 mN/m (Fig. 3). Further compression results in a decrease in the surface potential and a sharp increase in the surface pressure. Both the decrease in surface potential and the sharp

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FIG. 3 The surface pressure–area (–A) and surface potential–area (V–A) isotherms of PSII membranes.

increase in surface pressure after 175 nm2 clearly indicate the collapse of the monolayer structure and the formation of a multilayer at surface pressures larger than 10 mN/m. The formation of the multilayered structure partially cancels out the molecular dipole moment of the PS II membrane protein and results in the decrease in surface potential. Independent AFM studies conﬁrmed that the monolayer structure of PS II membrane protein collapses under the high surface pressure [8]. From the V–A curve of PS II membrane protein, we can calculate the surface dipole moment to be about 1:58 105 mD. The V–A isotherm of PS II core complex is rather different from that of PS II membrane (Fig. 4). The surface potential of a monolayer of PS II core complex increases slightly as the molecular area is compressed from 600 to about 150 nm2 , while surface pressure changes from 5 to 35 mN/m. Further compression results in a sharper increase in surface potential. The surface potential starts to decrease only after the surface area is compressed to about 80 nm2 or surface pressure becomes larger than 40 mN/m. This is consistent with the previous discussion that PS II core complexes form a more ordered monolayer structure at relatively high surface potential and will not form multilayered

FIG. 4 The surface pressure–area (–A) and surface potential–area (V–A) isotherms of PS II core complex particles.

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aggregates until the surface pressure is larger than 40 mN/m. At a surface area of 320 nm2 , the dipole moment of the PS II core complex monolayer can be calculated from the corresponding surface potential as about 2:38 105 mD. In summary, our studies demonstrate that both PS II membranes and PS II core complex particles from higher plants can form a monolayer structure at the air–water interface. Surface pressure–area and surface potential–area isotherms indicate that PS II membrane proteins can form a stable monolayer directly at the air–water interface, although a large fraction of protein diffuses into the aqueous subphase. As for the water–soluble protein PS II core complex, it is hard to form a monolayer directly at the air–water interface. However, addition of a moderate concentration of NaCl (100 mM) into the subphase greatly enhances the ﬁlm-forming ability of PS II core complex and quality of the resulting monolayer. We also demonstrated that the addition of lipid MGDG to PS II core complex also greatly enhances ﬁlm-forming ability and the mixture monolayer shows good miscibility at all surface pressures. These results conﬁrm that lipid MGDG can function as supporting material in the mixture monolayer.

III.

ORGANIZATION OF CHLOROPHYLL MOLECULES

In photosynthetic pigment protein complexes, the chlorophyll a molecules are organized with a well-ordered spacing and orientation for the gathering of light energy and for the efﬁcient transfer of absorbed energy to the site of charge separation [14]. This charge separation occurs in the reaction centers of photosystems. In the PS II reaction center, charge separation occurs at a specialized chlorophyll a molecule called P680. The oligomeric nature of P680 in vivo is a matter of considerable interest. Some studies suggest that P680 is composed of one molecule of chlorophyll a [15–17], while others propose it as a dimer [18–20]. Absorption and ﬂuorescence spectra of dry Langmuir–Blodgett (LB) multilayers of chlorophyll a present similarities with those observed for the P680 [21]. As mentioned, LB ﬁlms have the potential to assemble individual molecules into a highly ordered architecture [22]. This exciting aspect has motivated researchers to simulate the models of natural membranes [23]. With the development of scanning probe microscopy, attempts have been made to understand the organization of LB ﬁlms of molecules at a nanoscale level [24,25]. In order to understand the oligomeric nature of the chlorophyll a molecules in PS II reaction centers, we have developed mono- and multilayers of chlorophyll a molecules and observed their topography using scanning probe microscopy. We recorded the images of chlorophyll a molecules in multilayers using scanning tunneling microscopy (STM) and atomic force microscopy (AFM). The images show that ﬁlms undergo a reconstruction process following their fabrication and transfer onto the substrate in order to reach a more stable state. Although the reconstruction differs from one ﬁlm to another, the repeated unit in the reorganization of the ﬁlms is always found to be a dimer of chlorophyll a. Our results with chlorophyll a multilayers are in good agreement with the observations on monomolecular layer [26]. In the literature, LB ﬁlms of chlorophyll a have been investigated by many techniques [21,27,28]. In particular, Chapados et al. [29] have studied the aggregation state of chlorophyll a in LB ﬁlms with electronic and infrared spectroscopies. Their results suggest many points. First, immediately after the fabrication of the ﬁlm (time zero) the ketone — O of one chlorophyll a molecule links to the magnesium of an adjacent chlorgroup C — ophyll a molecule to form a dimer. Each dimer interacts via water with another dimer to

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form an oligomeric structure. With time some water molecules leave the ﬁlm causing the collapse of the overall structure of the ﬁlm. This results in a more stable organization of the ﬁlm. This organization differs slightly from one ﬁlm to another although the same kind of substrate was used. Finally, the results obtained by Chapados et al. [29] imply that after the collapse, the ﬁlm is mainly composed of dimers of chlorophyll a. Our STM observations on LB ﬁlms of chlorophyll a are essentially in agreement with those of Chapados et al. [29]. The LB ﬁlms of chlorophyll a undergo a transformation following their fabrication and this transformation may differ from one sample to another. — O of the ﬁfth ring of a chlorophyll a molecule is In this ﬁnal conformation, the ketone C — linked by co-ordination to the Mg atom of a neighboring molecule to form a dimer as shown in the model of Chapados et al. [29]. The orientation of chlorophyll a molecules in the dimer must change from one ﬁlm to another since the tip–sample interaction differs with the sample. Again, this fact shows that the chlorophyll a dimer is the natural state in a closely packed environment. However, contrary to the interpretation of Chapados et al. [29], our results show a ﬁlm composed exclusively of dimers. These dimers interact with each other to build up into a more complex structure. Because spectroscopic data of LB ﬁlms present similarity with those found in P680 [21], we suggest that P680 is composed of a chlorophyll a dimer. Numerous attempts have been made to model the arrangements of chlorophyll a to rationalize its high energy conversion efﬁciency. One model [30] proposed for the primary electron donor of PSI describes the formation of a chlorophyll a dimer held together via water bridges. In this model, the oxygen of one water molecule is co-ordinated to the magnesium of a chlorophyll a molecule, while its hydrogen bonds to the ketocarbonyl group of a second chlorophyll a molecule. A second water molecule completes the dimer in the same way. This results in a structure where the distance between the Mg centers is 0.89 nm, and the interplanar separation between the macrocycles is 0.36 nm. In an effort to obtain direct structural information on the aggregation of chlorophyll a in thin ﬁlms, we have examined monolayers of chlorophyll a transferred onto freshly cleaved graphite by STM and AFM. The images showed a well-organized grain-structured LB ﬁlm with grains packed into a rectangular lattice. Considering the rectangular shape and size of the grains, we consider the grains as dimers with (anti-) parallel transition moments of the constituent monomers. In this dimer, the macrocycles are tilted toward each other by 30 with respect to the substrate surface. We observed an average distance of 3.20 nm between the two nearest maxima and this distance is within the range of the grain width. This average distance is in the range of the center-to-center distance (3.00 nm) calculated using transient absorption difference spectroscopy of the reaction center of PSII [31]. It also should be noted that the 3.00 nm distance corresponds to the proposed distance between the chlorophyll a accessory and P680. On the other hand, the distance between the Mg centers (1.20 nm) within the dimer agrees with the calculated distance (1.00 nm) between centers of chlorophyll a, identiﬁed as a special pair P680. It is possible that the distance between the Mg centers, in the compressed monolayer at the air–water interface, is smaller than 1.20 nm. Considering the orientation angle estimated at the air–water interface (62:5 ), the distance calculated between the Mg centers (0.70 nm) corresponds to the gap estimated between the macrocycle. Our observations suggest formation of chlorophyll a dimer in the monolayer compressed at 20 mN/m and it may be a suitable model for the organization of P680. The packing of chlorophyll a dimers may be appropriate for producing systems with uniform charge density distribution. In summary our studies with mono- and multilayer LB ﬁlms of chlorophyll a present strong evidence for the dimeric nature of chlorophyll a in vivo. The model presented

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explains the high energy transfer efﬁciency in the pigment protein complexes of photosystems of photosynthetic apparatus.

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H. J. Michel. Mol. Biol. 158:567 (1982). M. Ikeuchi. Bot. Mag. Tokyo 105:327 (1992). E. Haag, K. D. Irrgang, E. J. Boekema, and G. Renger. Eur. J. Biochem. 189:47 (1990). M. Ikeuchi and Y. Inoue. Arch. Biochim. Biophys. 247:97 (1986). M. Roger, J. P. Dekker, E. J. Boekema, and H. T. Witt. FEBS Lett. 219:207 (1987). A. Holzenburg, M. C. Bewley, F. H. Wilson, V. Nicholson, and R. C. Ford. Nature 363:470 (1993). E. J. Boekema, B. Hankamer, D. Bald, J. Kruip, J. Nield, A. Boonstra, J. Barber, and M. Ro¨gner. Proc. Natl. Acad. Sci. USA 92:175 (1995). L. Shao, V. Konka, and R. M. Leblanc. J. Colloid Interface Sci. 215:92 (1999). V. Erokhin and L. A. Feigin, Progr. Colloid Polymer Sci. 85:47 (1991). S. Yu, N. A. Kalabina, V. P. Zubov, E. P. Lukashev, A. A. Kononenko, and R. A. Uphaus. Thin Solid Films 210/211:723 (1992). Y. Lvov, V. Erokhin, and S. Zaitsev. Biol. Membr. 4:1477 (1991). R. A. Hann, in Langmuir–Blodgett Films (G. G. Roberts, ed.), Plenum, New York, 1990, pp. 17–92. G. L. Gaines Jr., Insoluble Monolayers at Liquid–Gas Interfaces, Wiley Interscience, New York, 1996. W. Kuhlbrandt and D. A. Wang. Nature 350:130 (1991). A. Trebst. Z. Naturforsch. 41C:240 (1986). A. Michel and J. Deisenhofer. Biochemistry 27:1 (1988). S. I. Allakhverdiev, A. Ahmed, H. A. Tajmir-Riahi, V. V. Klimov, and R. Carpentier. FEBS Lett. 339:151 (1994). R. Van der Vos, P. J. Van Leeuwen, P. Braun, and A. J. Hoff. Biochim. Biophys. Acta 1140:184 (1992). V. L. Tetenkin, B. A. Gulyaev, M. Seibert, and A. B. Rubin. FEBS Lett. 250:459 (1989). V. A. Shuvalov, U. Heber, and U. Schreiber. FEBS Lett. 258:27 (1989). S. Krawczyk, R. M. Leblanc, and L. J. Marcotte. Chim. Phys. 85:1073 (1988). A. Ulman, An Introduction to Ultrathin Organic Films, Academic Press, San Diego, 1991. G. G. Roberts, Langmuir–Blodgett Films, Plenum, New York, 1990. J. De Rose and R. M. Leblanc. Surf. Sci. Reports 22:73 (1995). L. Shao, N. J. Tao, and R. M. Leblanc. Chem. Phys. Lett. 273:37 (1997). S. Boussaad, A. Tazi, and R. M. Leblanc. Proc. Natl. Acad. Sci. USA 94:3504 (1997). C. Chapados and R. M. Leblanc. Biophys. Chem. 17:211 (1983). A. Desormaux and R. M. Leblanc. Thin Solid Films 132:91 (1985). C. Chapados, D. Germain, and R. M. Leblanc. Biophys. Chem. 12:189 (1980). L. L. Shipman, T. M. Cotton, J. R. Norris, and J. J. Katz. Proc. Natl. Acad. Sci. USA 73:1791 (1976). J. P. M. Schelvis, P. I. Van Noort, T. J. Aartsma, and H. J. van Gorkom. Biochim. Biophys. Acta 1184:242 (1994).

28 Interfacial Electrical Phenomena in Green Plants: Action Potentials ALEXANDER G. VOLKOV and JOHN MWESIGWA Chemistry, Oakwood College, Huntsville, Alabama

I.

Department of

INTRODUCTION

The processes of life have been found to generate electric ﬁelds in every organism that has been examined with suitable and sufﬁciently sensitive measuring techniques [1,2]. The electrochemical conduction of electrochemical excitation must be regarded as one of the most universal properties of living organisms. It arose in connection with the need for transmission of a signal about an external inﬂuence from one part of a biological system to another. The study of the nature of regulatory relations of the plant organism with the environment is a basic bioelectrochemical problem, one that has a direct bearing on tasks of controlling the growth and development of plants. Any living cell continuously receives information about its surroundings. Its surface membrane has numerous protein receptors, which interact with practically all vitally important molecules. Plants have a speciﬁc property, which is excitability [1–3]. This property is used by cells, tissues, and organs to change their internal condition and external reactions under the action of various environmental factors, referred to as irritants. The high sensitivity of protoplasm and all cell organelles to any natural and electrochemical effects is the basis for excitability. According to Goldsworthy [4], electrochemical signals that look like nerve impulses exist in plants at all levels of evolution. Gunar and Sinyukhin [5] proposed the idea that the excitation waves or action potentials in higher plants could be information carriers in intercellular and intracellular communication in the presence of environmental changes. The irritability of plants developed during their evolution and improved with adaptation to changes in their environment and to the increasingly complicated organization of plants. It has acquired complex forms among the modern higher plants. A plant consists of interconnected cells, tissues, and organs, and its integral organism can be maintained and developed in a continuously varying environment only if all cells, tissues, and organs function in concordance. Plants are continuously balancing with the external world. The co-ordination of internal processes and their balance with the environment are connected with the excitability of plant cells. The huge amount of experimental material testiﬁes that the main laws of excitability, such as the inducement of nonexcitability after excitation and the summation of subthres649

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hold irritations were developed in the vegetative and animal kingdoms in protoplasmatic structures earlier than the morphological differentiation of nervous tissues. These protoplasmatic excitable structures consolidated into the organs of a nervous system and adjusted the interaction of the organism with the environment. Volkov and Haack [6,7] studied the role of electrical signals induced by insects in long-distance communication in plants and conﬁrmed the mechanism by which electrical signals can directly inﬂuence both biophysical and biochemical processes in remote tissues. Mechanical, physical, or chemical external irritants act not only at the place of occurrence, but the excitation can be also transferred along the whole plant [3,6–21]. The speed of transfer depends on many factors, such as the intensity of the irritation, temperature, chemical treatment, or mechanical wounding; it is also inﬂuenced by previous excitations. The excitation reaction travels in both directions, from the top of a stem to roots and conversely, but not always at identical rates. The transfer of excitation has a complicated character accompanied by an internal change in cells and tissues. Bose [9,22–25] has established the availability of a reﬂex arch in plants such as Mimosa pudica. When plants are excited, sensory cells generate impulses which terminate at motor cells. The character of their distribution depends upon the physiological condition of the plants. The signal from a beam of the sun is transmitted to the tissues of a stem at an extremely high speed and consequently the stem will curve toward the source of light. After excitation, the illuminated top of a stem causes an impulse to be distributed among the tissues. When the impulse reaches motor cells, the stem bends. Thus, after electrochemical signals have reached the cell, deep cytophysiological reactions occur. The phloem consists of two types of conducting cells, known as sieve-tube elements and companion cells [Fig. 1(a)]. Sieve-tube elements are elongated cells that have end walls perforated by numerous minute pores through which dissolved materials can pass. Such sieve-tube elements are connected in vertical series known as sieve tubes. Sieve-tube elements are alive at maturity, although their nuclei disintegrate before the element begins its conductive function. Companion cells, which are small, have nuclei at maturity and are living; they are found adjacent to the sieve-tube elements and are believed to control the process of conduction in the sieve tubes. Conductive bundles of vegetative organisms not only facilitate the movement of substances, but also actuate the transfer of bioelectrochemical impulses [26–56]. This phenomenon underlies the co-ordination of processes of the vital activity of vegetative organisms. These bioelectrical impulses arise under the inﬂuence of various chemical compounds (herbicides, pollutants, salts, water, plant growth stimulants) and physical factors such as mechanical wounding, electromagnetic or gravitational ﬁelds, and temperature effects. The most rapid methods of long-distance communication between plant tissues and organs are bioelectrochemical or electrophysiological signals [1,6,7]. The effectiveness of such long-distance communication is clear, since plants can rapidly respond to external stimuli (e.g., changes in temperature or osmotic environment, illumination level, wounding, cutting, mechanical stimulation, or water availability). These changes can be detected in distant parts of the plant soon after the injury [3,19,20]. Wounding stress is accompanied by the rapid long-distance propagation of electrochemical signals [6,57– 60], known as action potentials, which switch on the membrane enzymatic systems that realize biochemical reactions, accelerate ethylene synthesis, increase the concentration of proteinase inhibitor, and decrease or increase formation of polysomes and protein synthesis. Action potentials have been induced in higher plants by cold or heat shock, wounding, chemical treatment, and by changing of orientation of gravitational or magnetic ﬁelds [61–70].

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The velocities of the propagation of electrical signals that have values from 0.0005 to 40 m/s are sufﬁciently high to facilitate rapid long-distance communication and account for the rapid response phenomena observed in plants. Both the speed of propagation and the duration of action potential depend on the type of external stimulus. The action potential propagates rapidly throughout the plant. A potential pathway for transmission of this electrical signal might be the phloem sieve-tube system, since it represents a continuum of plasma membranes. A phloem is an electrical conductor of bioelectrochemical impulses over long distances. From an electrochemical point of view, structures of phloem and axon can be pictured as tubes ﬁlled with electrolyte solutions (Fig. 1). The length of an axon or phloem can be several meters and their diameters a few micrometers. At the cellular level in plants, electrical potentials exist across membranes, between cellular compartments, and within speciﬁc compartments. Ions such as Kþ , Ca2þ , Hþ , Naþ , and Cl represent electrolytic species involved in the establishment and modulation of electrical potentials. Electrical potentials have been measured at the tissue and whole plant level. Since electrical potential differences are expressed spatially within biological tissue and are modulated over time, many investigators have postulated the involvement of electrical potentials in inter- and intracellular communication and thus in the regulation of such physiological plant processes as phloem unloading. Action potentials represent the primary candidate for signaling between cells since they can be rapidly induced and transmitted within plant tissue. Speciﬁcity of the signal communication can be achieved through modulation of the amplitude, the duration, the direction of the polarity change, and the rate of propagation of the electrical potential signal. The problem of action and resting potentials in plants has a rich and dramatic history, which has been discussed by Bose [9,22–25], Bois-Reymond [32], Pickard [40], and Sinyukhin [16–18]. The response reactions of plant tissues and organs can be local or transmitted from cell to cell over long distances via the plasmodesmata. Excitation functions as a carrier of information about changes in environmental conditions. Action potentials are signals caused by the depolarization of plasma membrane. Bose [22,23] tried to examine the coordinating theme of response reactions of so-called sensitive plants, such as Mimosa pudica. He noticed that response reactions of these plants to external effects are not as slow, as seemed from ﬁrst sight. Bose registered the quickly transmitted reactions by electrophysiological equipment without causing rough damage to the plants. The generation and propagation of action potentials and electrical impulses between the tissues of higher plants can be measured by reversible nonpolarizable electrodes. Impulses take an active part in the expedient character of response reactions of plants as a reply to external effects. These impulses transfer a signal about the changes of conditions in a conducting bundle of a plant from the root system to the point of growth and conversely. Action potentials are now found in many plants, such as: beans, bindweed, Solanaceae, tomato, cucumber, potato, buckwheat, and others. The generation of action potentials is used for the transfer of information which produces a response impellent reaction: the leaf folds up and lowers under the inﬂuence of the appropriate external effect. A number of plants can eat insects. These plants are called insectivorous plants. Examples include the Drosera, Dionaeva, Venus-ﬂytrap, pitcher plants, sundew, and bladderworts. Insectivorous plants are most often found in moist and nutrient-poor habitats. The insects, which the plants trap, provide mineral nutrients. The amazing speeds of electrical impulses are illustrated by the capture of insects by insect-eating plants and during the tropism. Action potentials in the plants not processing motor activity are similar in their characteristics to the action potentials of ‘‘sensitive’’ plants of the

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FIG. 1 Structures of (a) phloem [71] and (b) neuron.

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Mimosa pudica and insectivore type, Drosera rotundifolia, Dionaea muscipula, and the cells of algae Nitella and Chara [62,63]. Physiological mechanisms for rapid long-distance communication between plant tissues and organs, particularly in response to external stimuli, are poorly understood. The translocation of phytohormones or other endogenous organic and inorganic compounds has been traditionally viewed as the primary means of signalling between stimulated and speciﬁc remote tissues in the plant where physiological responses are observed. A signiﬁcant limitation of communication systems involving the transport of chemical compounds is the relatively slow response kinetics. Many systemic physiological responses within higher plants are known to occur within seconds of treatment with speciﬁc stimuli.

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Fromm and Bauer [36] found that action potentials in maize sieve tubes change phloem translocation. Using macro- and microautoradiography in mature leaves of maize, Fromm and Bauer [36] studied the inhibition of phloem translocation caused by electric and cold shock. They stimulated the leaf tip with ice water and found that the velocity of signal transmission was 3–5 cm=s. Upon stimulation, the microelectrode recorded a basipetally propagating action potential with a depolarizing amplitude of 80 mV in the sieve tubes (Fig. 2). During electrical stimulation, the action potential was measured in the sieve-tube system with a speed of 5 cm/s. The ability of a given stimulus to elicit electrical signals in plants and perhaps even the receptor tissue responses to the electrical signal are inﬂuenced by the physiological condition of the plant and the plant species. Zawadski et al. [67,68] suggest that many electrophysiological parameters are highly variable within higher plants including the excitability state, the excitability threshold, the velocity of impulse movement, and the length of the refractory period. Mizuguchi et al. [72] found out that the application of DC voltage to the cultured solution accelerates a plant growth rate by 30%. The effect of voltage-dependent plant growth acceleration was observed only under illumination. Bean sprouts were cultured in an aqueous culturing bath, a pair of PT electrodes being located at both sides of the bath and separated from the seedling compartment by agar walls. Several types of potential, namely DC, sinusoidal AC, square wave, and spike pulse, were applied to the electrode. During the application, root length, epicotyl length, leaf growth, as well as lateral root shootings were all found to be accelerated at an appropriate condition. The acceleration was not restricted to bean, but effective for monocotyledonous plants of maize as well. The authors considered such an accelerating effect to be related to the stimulation of the ion pumps for a growth metabolism.

FIG. 2 Measurements of intracellular potentials in sieve tubes of maize via severed aphid stylets. Stimulation by ice water (above) and electric shock (below) evoked action potentials which were propagated with a velocity of 3–5 cm s1 in a basipetal direction. (From Ref. 36.)

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The plant cell is controlled by a molecular stochastic computer (MC), which operates with molecule words (DNA, RNA, proteins) according to the program recorded in DNA and RNA. In the cell, the main programs are written in the molecules of DNA by a fourletter code. Operations are produced by molecular devices operating with molecule words, recorded on molecules themselves, which are read off by ribosomes [3,73]. MC operates with molecular words having deﬁnite addresses. Green plants measure many parameters in order to have orientation in the outer medium. The plant cell continuously receives information on the environment. Its surface membrane has numerous protein receptors, which interact with nearly all the vitally important molecules. Wounding of plants inﬂuences gene expression [74].

II.

ELECTROCHEMICAL CIRCUITS, CHAINS, AND ELECTRODES

The ends of a correctly constructed electrochemical circuit measuring electrical potential difference must always have metals or conductors with identical chemical composition. It is usually reached by simple connection of two metals by copper wires. The inclusion between two metal conductors of a third metal conductor according to Volta’s law does not change the difference of potentials at the output of a circuit. The difference of potentials in an electrochemical circuit at equilibrium is caused by the change of Gibbs free energy during the appropriate electrochemical reaction: E ¼ G=nF

ð1Þ

where F ¼ 96,500 C is the Faraday constant and n is the number of electrons. The difference of electrical potentials of an electrochemical circuit at equilibrium (E) is the electromotive force (EMF). The value of nFE characterizes the maximum electrical work that can be received through an electrochemical circuit. Equation (1) is the basis for the calculation of the Gibbs free energy for different electrochemical reactions. The electrode potential at a given temperature and pressure is determined by the magnitude of the standard electrode potential and the activities of the substances taking part in the electrode reaction. The standard potential is a constant, which is speciﬁc for each electrode, while the activities of the reacting species may be different, depending on the concentration of the reaction medium. The classiﬁcation of electrodes is based upon the chemical nature of the substances participating in the electrochemical process [75]. Electrodes of the ﬁrst type are systems in which the reduced forms are metals of electrodes and oxidized forms are ions of the same metal. Electrodes of second type are systems in which the metal is covered by a layer of low soluble salts (or oxide), and the solution contains anions of these salts (for oxide–OH ions). The Nernst equation for electrodes of the second type can be written as: E ¼ E0

RT ln aAz nF

ð2Þ

where E 0 is the standard potential of an electrode of the second kind. It follows from Eq. (2) that electrodes of the second kind are anion reversible. The potential of an electrode of the second kind depends on the anionic activity of the sparingly soluble compound of the electrode material. The values of the potentials of electrodes of the second kind are readily reproducible and stable. These electrodes are often employed as standard half-cell or reference electrodes with respect to which the potentials of other electrodes are

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measured. Of greatest interest in practice are silver–silver chloride, calomel, mercury– mercurous sulfate, mercury–mercuric oxide, and antimony electrodes. Silver–silver chloride electrodes are reversible or nonpolarizing [75]. Ag/AgCl electrodes consist of a piece of silver wire covered with a layer of silver chloride and immersed in an electrolyte solution containing chloride ions. Ag/AgCl electrodes are initially unstable. However, stabilization can be accomplished by placing two electrodes for 24 h in 0.05 M KCl solution and connecting a short circuit between them. Ag/AgCl electrodes should be stored in the dark and protected from light while in use. Ag/AgCl and saturated calomel electrodes are sensitive to temperature (Fig. 3) and should be maintained at constant temperature.

III.

MEASURING OF ACTION AND RESTING POTENTIALS IN PLANTS

Two distinct classes of cell bioelectrochemical potential measurements exist. The intracellular action potential is measured with one electrode placed inside a cell while the reference electrode is situated in the conducting medium surrounding the cell. The extracellular action potential is measured with both electrodes in contact with the conducting tissue embodying larger groups of cells. In the latter case the signal observed is due to the depolarization–repolarization process in a group of cells. Abundant measurements of these two types have been made in animal electrophysiology. The well-known methods such as electromyograms (EMG), electrocardiograms (EKG), and electroencephalograms (EEG) are based upon measurements of the summed bioelectrical activity in large groups of cells.

FIG. 3 Temperature dependence of the standard potential of the saturated calomel electrode (1) and Ag/AgCl electrode (2).

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An example of the experimental setup for the measuring of extracellular action and resting potentials is shown in Fig. 4. All electrochemical measurements can be conducted at constant temperature inside a Faraday cage mounted on a vibrationstabilized table in a laboratory (Fig. 4). Ag/AgCl electrodes were connected to a voltmeter/pH meter [Cole Palmer Microcomputer pH-vision Model 05669-20, Fig. 4(a)] with high input impedance or a programmable electrometer/ampliﬁer [Keithley2000/20, Keithley-6517, or Keithley-6514, Fig. 4(b)]. An IBM-compatible microcompu-

FIG. 4 Apparatus for measuring electrical signals in green plants. Frequency of scanning is up to 5000 (a) or 1000 (b) samples per second.

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ter with a multi-I/O plug-in data acquisition board (DAS-801, Keithley MetraByte) was interfaced with the voltmeter (Cole Palmer Microcomputer pH-vision Model 05669-20) and used to record the digital data. A programmable electrometer/ampliﬁer (Keithley) was interfaced with a PC using RS232 cable or GPIB card (Keithley). The measuring signals were recorded as ASCII ﬁles using software (ASO-801, EASYEST AG or Keithley-2000) tool kits for fast startup and an automatic data acquisition application (Keithley). A fundamental rule of sampled data systems is that the input signal must be sampled at a rate greater than twice the highest frequency component in the signal. This is known as the Shannon sampling theorem, and the critical sampling rate is called the Nyquist rate. Stated as a formula, it says that fs =2 > fa , where fs is the sampling frequency and fa is the maximum frequency of the signal being sampled. Violation of the Nyquist criterion is called undersampling and results in aliasing. The maximum sample rate is speciﬁed in samples per second, rather than hertz. The generation and propagation of action potentials and electrical impulses between the tissues in higher plants can be measured by reversible nonpolarizable electrodes [1]. Since both Ag/AgCl electrodes are identical, we decided to call them reference and working electrodes as shown in Fig. 4. The reference electrode ðÞ was usually inserted in the stem or in a root of a soybean plant, and the upper (working) electrode ðþÞ inserted in the stem or a leaf of the plant. Ag/AgCl electrodes were inserted in the plant at different positions. Following insertion of the electrodes, the plants were allowed to rest until a stable potential difference was obtained between the measuring and reference electrodes. Insertion of electrodes in plants induces action potentials across the stem and slow ﬂuctuations of the resting potential (Fig. 5). After approximately 1–2 h, the resting potential stabilizes and action potentials induced by wounding disappear (Fig. 6).

IV.

ATMOSPHERIC ELECTROCHEMISTRY: EFFECTS OF THE ELECTRICAL DOUBLE LAYER OF THE EARTH AND ACID RAINS

The existence of ions in the atmosphere is the fundamental reason for atmospheric electricity. The voltage between the earth’s surface and ionosphere is about 40 kV with an electrical current of about 2000 A and a current density of about 5 pA=m2 . The earth is an electrode immersed in a weak gaseous electrolyte, the naturally ionized atmosphere. The earth’s surface absorbs anions and has a negative charge. The electrostatic ﬁeld strength at the earth’s surface is about 110–220 V/m and depends on time of day. Usually it is about 110 V/m, but at 7 p.m. Greenwich time the electrostatic ﬁeld strength is about 220–250 V/m [76]. Oceans, lakes, and rivers cover a signiﬁcant part of the earth and their surface is also charged negatively against the atmosphere. Electrical polarity in soybean, potato, tomato, and cacti coincides with the electrical ﬁeld of the electrical double layer of the earth, negative in roots and positive at the top of the plants. Atmospheric change of the electrostatic ﬁeld strength at 7 p.m. Greenwich time does not induce action potentials or change the resting potential of soybean or potato plants. Chemical reactions involving aerosol particles in the atmosphere derive from the interaction of gaseous species with the liquid water associated with aerosol particles and with dissolved electrolytes. For example, the generation of HONO from nitrogen oxides

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FIG. 5 Potential difference between two Ag/AgCl electrodes in the stem of a soybean plant after insertion of the electrodes. Distance between electrodes was 8 cm. Volume of soil was 0.5 L. The plants were given water every other day and kept at 24 C. Frequency of scanning was 1000 samples per second.

take place at the air–water interface in seawater aerosols or in clouds. Clouds convert between 50% and 80% of SO2 to H2 SO4 . This process contributes to the formation of acid rain. About 70% of the acid in rain is sulfuric acid, with nitric acid contributing about 30%. Acid rain exerts a variety of inﬂuences by greatly increasing the solubility of different compounds and by directly or indirectly affecting many forms of life. Acid rain is the most serious environmental problem and has an impact on agriculture, forestry, and human health. Acid rain has a pH below 5.6. Sulfuric and nitric acids are the two predominant acids in acid rain. Spraying soybean plants with an aqueous solution of H2 SO4 in pH region from 5.0 to 5.6 does not induce action potentials or variations of the resting potential [Fig. 7(a)]. Spraying the plant (0.1 mL) or deposition of 10 L drops of aqueous solution of H2 SO4 or HNO3 in the pH region from 0 to 4.9 on leaves induced action potentials in soybean [Fig. 7(b), (c)]. The duration of single action potentials, after treatment by HNO3 and H2 SO4 , was 0.2 s and 0.02 s, respectively. Action potentials were generated in a soybean plant with a speed of propagation of 55 5 cm=s if the pH of the soil was acidiﬁed even without spraying the plant (Fig. 8). The action potential induced by acid rain reaches a working electrode in the soybean plant, which changes its potential relative to the reference electrode. Hence, it is possible to measure the peak potential of the working electrode compared to the reference electrode. The action potential propagates along the stem and reaches the reference electrode, which gives a mirror image of the potential peak with an opposite sign from that of the ﬁrst peak (Fig. 8) because during this process the potential of the reference electrode changes relative to that of the working electrode. The speed of

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FIG. 6 Potential difference between two Ag/AgCl electrodes in the stem of a soybean plant before any treatment of the plant. Distance between electrodes was 5 cm. (b) and (c) show short time intervals of (a). Volume of soil was 0.5 L. Frequency of scanning was 1000 samples per second. The plants were given water every other day and kept at 24 C.

propagation of the action potential does not depend on the location of the working electrode in the stem of the plant, the leaves, or the distance between the working and reference electrodes. The cells of many biological organs generate an electrical potential that may result in the ﬂow of electric current. Electrical impulses may arise spontaneously or they may result from stimulation. Once initiated, they can propagate to adjacent excitable cells. The change in transmembrane potential creates a wave of depolarization, or action potential, that affects the adjoining, resting membrane. Thus, when the phloem is stimulated at any point, the action potential is propagated over the entire length of the cell membrane and along the phloem with a constant voltage. The propagation of each impulse is followed by the absolute refractory period during which the ﬁber cannot transmit a second impulse. The high sensitivity of the protoplasm and all cell organelles to any natural and chemical effects is the basis for excitability. The integral organism of a plant can be maintained and developed in a continuously varying environment only if all cells, tissues, and organs function in concordance. Plants are continuously balancing with the external world.

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FIG. 7 Potential difference between two Ag/AgCl electrodes in the stem of a soybean plant: (a) after single spraying with 0.1 mL of H2 SO4 at pH 5.0; (b) action potential after single spraying with 0.1 mL of HNO3 at pH 3.0; (c) action potential after single spraying with 0.1 mL of H2 SO4 at pH 3.0. The plants were given water every other day and kept at 24 C. (From Ref. 3.)

V.

EFFECTS OF PESTICIDES, POLLUTANTS, UNCOUPLERS, AND PROTONOPHORES

A.

2,4-Dinitrophenol (DNP)

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FIG. 8 Potential difference between two Ag/AgCl electrodes in the stem of a soybean plant measured after adding to soil H2 SO4 . pH of soil was 3.0. Distance between Ag/AgCl electrodes was 5 cm. The plants were given water every other day and kept at 24 C. (From Ref. 3.)

2,4-Dinitrophenol is a member of the aromatic family of pesticides, many of which exhibit insecticide and fungicide activity. DNP is considered to be highly toxic to humans, with a lethal oral dose of 14 to 43 mg/kg. Environmental exposure to DNP occurs primarily from pesticide runoff to water. DNP is used as a pesticide, wood preservative, and in the manufacture of dyes. DNP is an uncoupler, or has the ability to separate the ﬂow of electrons and the pumping of Hþ ions for ATP synthesis. This means that the energy from electron transfer cannot be used for ATP synthesis [75,77]. The mechanism of action of DNP is believed to inhibit the formation of ATP by uncoupling oxidative phosphorylation. DNP induces fast action potentials and decreases the resting potential to zero in soybeans [20,78]. Addition to the soil of an aqueous solution of DNP induces fast action potentials in soybean (Figs. 9, 10). After treatment of the soil by an aqueous solution of DNP, resting potential, measured between two Ag/AgCl microelectrodes in the stem of a soybean plant, slowly decreased from 80–90 mV (negative in a root, positive at the top of the plant) to zero during 48 h. Figures 9(c) and 10(a) show that positive and negative spikes appear during measurement of the electrical potential difference between two reversible silver chloride electrodes. High-resolution analysis of short intervals shows that these spikes are action potentials [Figs. 9(c) and 10(b), (c)]. The action potential induced by DNP reaches a working electrode in the soybean plant, which changes its potential relative to the reference electrode. Hence, it is possible to measure the peak potential of the working electrode compared to the reference electrode. The action potential propagates along the stem and after a few milliseconds reaches the reference electrode, which gives a mirror image of the potential peak with an opposite sign from that of the ﬁrst peak [Figs. 9(c) and 10(b), (c)] because during

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FIG. 9 Potential difference between two Ag/AgCl electrodes in the stem of a soybean plant 24 h after adding 50 mL of 103 M 2,4-dinitrophenol to soil. Distance between electrodes was 5 cm. The plants were given water every other day and kept at 24 C. Volume of soil was 0.5 L.

this process the potential of the reference electrode changes relative to that of the working electrode. The distance between the Ag/AgCl electrodes divided by the time between positive and negative mirror spikes corresponds to the speed of action potential propagation. The duration of single action potentials 24 h after treatment by DNP from 3 s to 0.02 s [Fig. 9(a)–(c)]. The amplitude of action potentials is about 60 mV. The maximum speed of action potential propagation is 1 m/s [Fig. 9(c)]. Figure 4 shows action potentials in soybean 24 h after treatment of soil by DNP. During the second day, action potentials in the soybean plant reach an amplitude of about 60 mV, duration time 0.02 s, and propagation speed of 1 m/s [Fig. 10(b)] and 2 m/s [Fig. 10(c)]. After two days the resting potential stabilized at zero, fast action potentials with an amplitude of about 60 mV, duration time 0.02 s, and propagation speed of 2 m/s was generated. Fromm and Spanswick [79] studied inhibiting effects of DNP on the excitability of willow by recording the resting potential of the phloem cells. In willow, 104 M DNP rapidly depolarized the membrane potential by about 50 mV.

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FIG. 10 Potential difference between Ag/AgCl electrode in the stem and Ag/AgCl electrode in a root of a soybean plant measured 70 h after adding 50 mL of 103 M 2,4-dinitrophenol to soil. Distance between Ag/AgCl electrodes was 5 cm. The plants were given water every other day and kept at 24 C. Volume of soil was 0.5 L. (From Ref. 78.)

B.

Pentachlorophenol (PCP)

PCP is commonly used as a wood preservative having both antifungal and insecticide properties. It has also been used in a range of areas for antifungal, antibacterial, general herbicide, and slime prevention in both industrial and consumer applications. Chronic exposure to PCP has effects on the liver, kidneys, and immune system. PCP also has the potential to cause reproductive problems and has been listed as a probable carcinogen.

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PCP has a negative effect on a number of aquatic life forms. Since 1987 PCP has been banned for herbicide and consumer uses, though it continues to be used for industrial applications, most notably as a wood preservative. Since 1992 the maximum contaminant level for drinking water has been set at 1 ppb. Pentachlorophenol is known as a protonophore or uncoupler of oxidative phosphorylation in bioenergetics, a pollutant, and one of the largest chemical sources of dioxins to the environment, a herbicide, an insecticide (termite control), a fungicide (wood preservation and seed treatment), and a molluscicide (snail control). PCP is a member of the substituted halogenated aromatic family of pesticides, many of which exhibit insecticide and fungicide activity. In addition, PCP and its products are toxic to plants, making them useful as defoliants and general herbicides. Primary uses of PCP include protection of timber from fungal rot and wood-boring insects. PCP is one of the largest chemical sources of dioxins to the environment. Addition of PCP to the soil induces fast action potentials in soybean [Figs. 11(a)–(c)] [20,21]. Figures 11(a) and (b) show that positive and negative spikes appear during measurement of the electrical potential difference between two reversible silver chloride electrodes. High-resolution analysis of more short intervals shows that these spikes are action potentials (Figs. 11 and 12). The action potential induced by PCP reaches a working electrode in the soybean plant, which changes its potential relative to the reference electrode. Hence, it is possible to measure the peak potential of the working electrode compared to the reference electrode. The action potential propagates along the stem and after a few milliseconds reaches the reference electrode, which gives a mirror image of the potential peak with an opposite sign from that of the ﬁrst peak (Figs. 11–13). During this process the potential of the reference electrode changes with regard to the working electrode. The duration of single action potentials, after treatment by PNP, is 2 ms. The amplitude of action potentials is about 60 mV. After treatment of soil by an aqueous solution of PNP, the resting potential, measured between two Ag/AgCl microelectrodes in the stem of a soybean plant, slowly decreased from 75–85 mV (negative in a root, positive at the top of the plant) to zero during 48 h. Figure 11 shows action potentials in soybean after the ﬁrst 24 h of treatment with pentachlorophenol. During the second day, action potentials reached an amplitude of about 60 mV, duration time 2 ms, and propagation speed of 12 m/s was generated. After 48 h resting potential stabilized at zero and fast action potentials with amplitude at about 60 mV, duration time of 2 ms, and a propagation speed of 30 m/s was generated [Figs. 12(b)–(d)]. The duration of action potentials and speed of excitation propagation does not depend on the distance between working and reference electrodes. The speed of propagation of action potentials was measured as the distance between Ag/AgCl electrodes divided by the time between positive and negative peaks of action potentials (Fig. 13). C.

Carbonylcyanide-4-triﬂuoromethoxyphenylhydrazone (FCCP)

Carbonylcyanide-4-triﬂuoromethoxyphenylhydrazone is known as a protonophore or uncoupler of oxidative phosphorylation in bioelectrochemistry because it disrupts the tight coupling between electron transport and the ATP synthase. Uncouplers act by dis-

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FIG. 11 Potential difference between two Ag/AgCl electrodes in the stem of a soybean plant 24 h after adding 50 mL of 5 104 M pentachlorophenol to soil. Distance between electrodes was 8 cm. The plants were given water every other day and kept at 24 C. Volume of soil was 0.5 L. (b) and (c) show short time intervals of (a). (From Ref. 19.)

sipating the proton gradient across a membrane created by the electron transport system. Uncouplers share two common features: hydrophobic character and a dissociable proton. Uncouplers, soluble in both water and lipids, permeate the lipid phase of a membrane by diffusion and transfer a proton across the membrane, thus eliminating a proton concentration gradient or a membrane potential, respectively. In the presence of an uncoupler, due to the absence of the proton gradient, protons are transported by ATP synthase from the stroma to the thylakoid lumen at the expense of ATP which is hydrolyzed to ADP and phosphate. This is the reason why uncouplers cause ATP hydrolysis. FCCP is a weak acid and diffuses in the undissociated protonated form from the compartment with a high proton concentration through the membrane into the compartment with a low proton concentration and dissociates there into a proton and the FCCP anion. The proton remains and the FCCP anion returns by diffusion to the other compartment, where it is protonated again. Addition to the soil of aqueous solution of FCCP induces action potentials in soybean (Figs. 14–16). After treatment of the soil with an aqueous solution of FCCP, resting potential, measured between two Ag/AgCl microelectrodes in the stem of a soy-

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FIG. 12 Potential difference between Ag/AgCl electrode in the stem and Ag/AgCl electrode in a root of a soybean plant measured 70 h after adding 50 mL of 5 104 M pentachlorophenol to soil. Distance between Ag/AgCl electrodes was 9 cm. The plants were given water every other day and kept at 24 C. Volume of soil was 0.5 L. (b), (c) and (d) show short time intervals of (a). (From Ref. 19.)

bean plant, slowly decreased from 80–90 mV (negative in a root, positive at the top of the plant) to zero during 20 h [80]. Figures 15(a) and 16(a) show that positive and negative spikes appear during measurement of the electrical potential difference between two reversible silver chloride electrodes. High-resolution analysis of short intervals shows that these spikes are action potentials [Figs. 15(b), (c), 16(b), and (c)]. The action potential induced by FCCP reaches a working electrode in the soybean plant, which changes it potential relative to the reference electrode. Hence, it is possible to measure the peak potential of the working electrode compared to the reference electrode. The action potential propagates along the stem and after a few milliseconds it reaches the reference electrode, which gives a mirror image of the potential peak with an opposite sign from that of the ﬁrst peak (Figs. 15 and 16) because during this process the potential of the reference electrode changes relative to that of the working electrode.

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FIG. 13 Determination of the speed of action potentials in soybean by measuring of potential differences between two Ag/AgCl electrodes in the stem of a soybean plant 24 h after adding 50 mL of 5 104 M pentachlorophenol to soil. Distance between electrodes was 8 cm. The plants were given water every other day and kept at 24 C. Volume of soil was 0.5 L. (a) and (b) were taken from Fig. 11(a). (From Ref. 19.)

The distance between Ag/AgCl electrodes, divided by the time between positive and negative mirror spikes, corresponds to the speed of action potential propagation. The duration of single action potentials during the ﬁrst 20 h after treatment by FCCP varies from 2 s to 2 ms (Fig. 13). The amplitude of action potentials is about 60 mV [Fig. 14(b)]. The maximum speed of action potential propagation during the ﬁrst 20 h is 10 m/s [Fig. 14(b)]. Figure 14(b) shows action potentials in soybeam 20 h after treatment of the soil with FCCP. After 100 h, action potentials with amplitude about 60 mV, duration time 0.3 ms, and propagation speed of 40 m/s (Figs. 15 and 16) are generated in a soybean plant. The speed of propagation, duration, and amplitude of action potentials is independent of the location of the working electrode in the stem, root, or leaves of the plant, or on the distance between the working and reference electrodes. Action potentials take an active part in the expedient character of response reactions of plants in a reply to external effects. These impulses transfer a signal about the changes of conditions in a conducting bundle of a plant from the root system to the point of growth, and conversely. The fastest velocity reported for transmission of action potentials in green plants was 0.2 m/s in Dionaea ﬂytrap [11]. Action potentials induced in soybean by FCCP are 200 times

Interfacial Electrical Phenomena in Green Plants

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FIG. 14 Potential difference between two Ag/AgCl electrodes in the stem of a soybean plant 4 h (a) and 20 h (b) after adding 30 mL of 106 M FCCP to soil. Distance between electrodes was 7 cm. The plants were given water every other day and kept at 24 C. Volume of soil was 0.5 L. (From Ref. 3.)

faster (Figs. 15 and 16). The automatic measurements of the electrical potential difference can be effectively used in environmental plant electrophysiology, for studying the molecular mechanisms of transport processes, and the inﬂuence of external stimuli on plants.

VI.

ACTION AND RESTING POTENTIALS IN POTATO PLANTS (Solanum tuberosum L.)

Action potentials, induced by mechanical wounding, have been measured by Volkov and Haack [6,7] in the stem tissue of potato plants using a few Ag/AgCl electrodes and an ampliﬁer-recording system. Action potentials and resting potentials were measured [6,7] in potato plants (Solanum tuberosom L.) under different physiological conditions. External stimuli (e.g., changing temperature, wounding or exposing plant leaves or soil to certain chemical compounds) cause an action potential to be generated and change the resting potential from the original steady-state level. Amplitude, polarity, and speed of the action

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FIG. 15 Potential difference between two Ag/AgCl electrodes in the stem of a soybean plant 100 h after adding 30 mL of 106 M FCCP to soil. Frequency of scanning was 5000 samples per second. Distance between electrodes was 8 cm. The plants were given water every other day and kept at 24 C. Volume of soil was 0.5 L.

potential propagation depend on the type of external stimuli or stress. The kinetics and amplitude of the resting potential also change depending on the nature of the external stimuli. Two hours after the insertion of reversible Ag/AgCl electrodes in the stem of a potato plant, the difference of electrical potentials between electrodes separated by a distance of 5–10 cm was equal to 30 5 mV. Insertion of electrodes in stem, leaf or tuber, pinching of a young terminal leaf [Fig. 17(a)] and application of a thermal shock to the terminal leaﬂet using a ﬂame [Fig. 17(b)] resulted in propagation of an action potential along the stem, probably via the phloem. The amplitude, duration, and velocity of the propagation of action potentials depend on the external stimulus. Production of the action potential ceased 2 h after mechanical wounding of plants by inserting electrodes in the stem because a steady state was established. The potential difference in the potato stem remains stable for many hours if experimental conditions such as temperature, humidity, or illumination are not changed. In the absence of illumination at night the resting potential dropped to a level of 15–20 mV, but returned to the level of 30 mV in the morning. If

Interfacial Electrical Phenomena in Green Plants

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FIG. 16 Potential difference between two Ag/AgCl electrodes in the stem of a soybean plant 100 h after adding 30 mL of 106 M FCCP to soil. Frequency of scanning was 5000 samples per second. Distance between electrodes was 5 cm. The plants were given water every other day and kept at 24 C. Volume of soil was 0.5 L. (From Ref. 3.)

artiﬁcial illumination was used during the night, the steady-state potential difference did not drop. The speed of the propagation of action potentials in potato plants also depends on the external stimuli. The speed of action potential induced by pinching the terminal leaﬂet of a potato plant is equal to 7 2 cm=s [6,7]. The speed of propagation of the action potential induced in the terminal leaﬂet by thermal shock is equal to 0:7 0:2 cm/s [7]. Plants require all the essential ingredients of photosynthesis to construct the necessary compounds and structures. Water is especially important, because cell enlargement is a result of internal water pressure (turgor) extending the walls. In periods of drought, plants tend to have smaller leaves. Water generally moves into a plant through its roots. The water inside a plant creates a pressure against the cell walls called turgor. Most plants require large quantities of water in order to grow and reproduce. Turgor causes expansion of the cell wall and stimulates cell growth. It also keeps cells rigid and so enables the plant to remain upright. Loss of water, and consequently of turgor, from plant cells causes the entire plant to wilt.

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FIG. 17 Resting and action potentials of a potato plant after (a) pinch along the midrib in the center of the young terminal leaﬂet by forceps; (b) thermal shock of terminal leaﬂet leaf by a ﬂame. The plants were given water every other day and kept at 20 C. Distance between Ag/AgCl electrodes: (a) 5 cm, (b) 5 cm, and (c) 9 cm. (From Ref. 7.)

If the soil is sufﬁciently wet, further addition of water to the soil or spraying of water on the leaves does not result in the generation of action potentials or any essential changing of the resting potential. If the soil has not been watered for a few days, the water stress of the plant was observed. After adding water to soil surrounding the plant or spraying of 0.3 mL of water on the leaves, action potentials were generated over a period of 20–30 min. [6]. The speed of propagation of electrical signals is sufﬁciently high to facilitate rapid long-distance communication and account for the rapid response phenomena observed in plants.

Interfacial Electrical Phenomena in Green Plants

VII.

673

INSECT-INDUCED BIOELECTROCHEMICAL SIGNALS IN POTATO PLANTS

Volkov and Haack [6,7] were the ﬁrst to afford a unique opportunity not only to investigate the role of electrical signals induced by insects in long-distance communication in plants, but also to conﬁrm the mechanism by which electrical signals can directly inﬂuence both biophysical and biochemical processes in remote tissues. Action and resting potentials were measured in potato plants (Solanum tuberosum L.) in the presence of leaf-feeding larvae of the Colorado potato beetle [Leptinotarsa decemlineata (Say); Coleoptera: Chrysomelidae]. When the larvae were allowed to consume upper leaves of the potato plants, after 6–10 h action potentials with amplitudes of 40 10 mV were recorded very 2 0:5 h during a two-day test period. The speed at which insect-induced action potentials moved downward through the stem is about 0.05 cm/s. The resting potential decreased from 30 mV to a steady-state level of 0 5 mV. Figure 18 shows that positive spikes and negative humps appear during measurement of electrical potential difference between two reversible silver chloride electrodes. High-resolution analysis of more short time intervals shows that these spikes are action potentials (Figs. 19 and 20). The action potential induced by the Colorado potato beetle in potato plants propagates slowly and hence the speed of propagation can be measured with two Ag/AgCl electrodes. The action potential propagates from plants leaves with Colorado potato beetles down the stem [Figs. 19(a)–(c)] to the potato tuber [Figs. 19(d) and (20)]. The action potential induced by the Colorado potato beetle on the terminal young leaf reaches a working electrode in the plant stem and changes its potential relative to the reference electrode. Hence it is possible to measure the peak potential of the working electrode

FIG. 18 Potential difference between two Ag/AgCl electrodes in the stem of a potato plant in the presence of ﬁve Colorado beetles on leaves of the plant. Frequency of scanning is 0.07 samples per second. Distance between Ag/AgCl electrodes was 10 cm. The plants were given water every other day and kept at 20 C. (From Ref. 7.)

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FIG. 19 Action potential in the stem of a potato plant in the presence of Colorado beetles on young terminal leaves of the plant. Distance between electrodes: (a) 3.5 cm, (b) 12 cm, (c) 22 cm, and (d) 20 cm. The plants were given water every other day and kept at 20 C. The reference Ag/AgCl electrode was inserted in stem between cotyledons. The working Ag/AgCl electrode was inserted in stem (a, b, c) or in potato ‘‘seed’’ (d). (From Ref. 7.)

compared with the reference electrode. The action potential slowly propagates along the stem and after some time reaches the reference electrode, which gives a mirror image of the potential peak with the opposite sign to that of the ﬁrst peak (Figs. 18–20), since during this process the potential of the reference electrode changes relative to that of the working electrode.

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FIG. 20 Potential difference between two Ag/AgCl electrodes in the presence of ﬁve Colorado beetles on leaves of a potato plant. The reference Ag/AgCl electrode ðþÞ was inserted in the stem of the plant, the second Ag/AgCl electrode was immersed in potato ‘‘seed.’’ The plants were given water every other day and kept at 20 C. Frequency of scanning is 0.07 samples per second. Distance between Ag/AgCl electrodes was 10 cm. (From Ref. 7.)

The speed of propagation of the action potential does not depend on the location of a working electrode in the stem of the plant [Figs. 19(a)–(c)] or in the tuber [Figs. 19(d) and 20], or on the distance between the working and reference electrodes (Fig. 21). The speed of propagation of the action potential induced by the Colorado potato beetle can be determined from the slope of the dependence of the time interval between peaks on the distance between electrodes (Fig. 21) and is about 0.05 cm/s.

VIII.

ELECTRICAL ACTIVITY OF EXCITABLE MEMBRANES

Nerve cells in animals and phloem cells in plants share one fundamental property: they possess excitable membranes through which electrical excitations in the form of action potentials can propagate. These propagating excitations are modeled theoretically as traveling wave solutions of certain parameter-dependent nonlinear reaction–diffusion equations coupled with some nonlinear ordinary differential equations. These traveling wave solutions can be classiﬁed as single and multiple loop pulses, fronts and backs of periodic waves, with different wave speed. This classiﬁcation is matched by the classiﬁcation of the electrochemical responses observed in plants. The experimental observations also show that under inﬂuence of various pathogens, the shapes and wave speeds of the electrochemical responses undergo changes. From the theoretical perspective, the changes in the shapes and wave speeds of the traveling waves can be accounted for by appropriate changes in parameters in the corresponding nonlinear differential equations. In a moving co-ordinate system, the traveling wave equations typically reduce to a system of parameterized nonlinear ordinary differential equations. The solutions of this system corresponding to pulses and fronts for the original reaction–diffusion equation are called homoclinic and heteroclinic orbits, correspondingly, or just connecting orbits.

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FIG. 21 The time dependence between positive and negative peaks of action potential induced by Colorado potato beetles on the distance between electrodes. The plants were given water every other day and kept at 20 C. A few electrodes were immersed in potato ‘‘seed’’ and different parts of the plant stem 2 h before measurements of the potential difference. (From Ref. 7.)

Mathematically, these are trajectories connecting equilibrium points of a system of autonomous ordinary differential equations. Hodgkin and Huxley [81] formulated a membrane model that accounts for Kþ , Naþ , and ion leakage channels in squid giant axons [Fig. 22(a)]. The membrane resting potential for each ion species is treated like a battery and the degree to which the channel is open is modeled by a variable resistor. Fromm and Spanswick [79] found that electrical stimulation of a plant is followed by ion shifts which are most striking in the phloem cells. While their content of potassium and chloride was diminished after stimulation, the amount of cytoplasmic calcium increased slightly (Table 1). These displacements lead to the conclusion that Ca2þ inﬂux as well as Kþ and Cl efﬂux are involved in the propagation of action potentials. The main difference between propagation of action potentials in animals and plants is that in an axon there is the Kþ =Naþ transmembrane transport but in phloem cells the Kþ =Caþ channels are involved in this process [Fig. 22(b)]. The Hodgkin–Huxley (HH) equations model action potentials in membranes. Variants of these equations are used in most models for electrical activity of excitable membranes and have been studied by many authors. Space-clamped (HH) equations relate the difference in electrical potential across the cell membrane (V) and gating variables (0 m; n; h 1), for ion channels to the stimulus intensity (Ia ) and temperature (T), as follows: V 0 ¼ Gðm; n; hÞ þ Ia m 0 ¼ ðTÞ½ð1 mÞm ðVÞ m m ðVÞ n 0 ¼ ðTÞ½ð1 nÞm mðVÞ n m mðVÞ h 0 ¼ ðTÞ½ð1 nÞm ðVÞ n m ðVÞ

ð3Þ

Interfacial Electrical Phenomena in Green Plants

677

FIG. 22 The Hodgkin–Huxley equivalent for an axon (a) and the modiﬁed HH circuit for sieve tubes in phloem (b).

where x 0 stands for dx=dt and is given by ðTÞ ¼ 3ðT6:3Þ=10 . The other functions involved are ð4Þ Gðm; n; hÞ ¼ g Na m3 h V V Na þ g K n4 V V K þ g L V V Na and the equations modeling the membrane permeability are: V V þ 25 m ðVÞ ¼ 4e18 m ðVÞ ¼ 10 V V þ 10 m ðVÞ ¼ 0:125e80 n ðVÞ ¼ 0:1 10

Vþ30 1 V þ 10 h ðVÞ ¼ 0:1 m ðVÞ ¼ 1 þ e 10 10 with

( ðxÞ ¼

x ex 1 1

if

x 6¼ C

if

x¼0

ð5Þ

ð6Þ

The FitzHugh–Nagumo (FHN) model [82] is a simpliﬁcation of the HH model and involves a tunnel diode (Fig. 23).

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TABLE 1 Concentration of Kþ , Cl , and Ca2þ in Twigs of Nonstimulated Willow Plants. Emitted X-ray Signals Are Given as Peak : Background Ratio. The Data Are Mean Values of 20 Measurements Taken from Three Plants with a Standard Error Lower than 0.5 for Kþ , 0.2 for Ca2þ and 0.9 for Cl Concentration (counts per second) Nonstimulated

Cortex Kþ Caþ Cl Phloem parenchyma Kþ Caþ Cl Companion cell Kþ Caþ Cl Sieve tube Kþ Caþ Cl Cambium Kþ Caþ Cl Xylem parenchyma Kþ Caþ Cl Pith Kþ Caþ Cl

Cytoplasm

Cell walls

Cytoplasm

Cell walls

4.7 0.1 7.6

2.0 4.2 4.7

3.0 0.7 3.9

2.1 4.1 5.5

6.0 0.1 8.3

3.5 2.2 7.0

3.2 1.2 4.7

3.3 2.2 6.7

5.7 0.5 10.8

3.0 1.6 6.8

2.0 0.9 6.5

3.0 1.6 7.0

6.5 0.3 0.1

2.6 1.5 6.5

3.6 1.4 5.2

2.9 1.5 7.6

3.7 0.1 8.4

2.4 1.6 8.2

2.7 0.8 5.5

2.7 1.7 8.0

5.7 0.4 7.6

3.7 1.5 7.6

2.6 1.5 3.1

3.5 1.2 5.5

8.9 0.1 9.2

6.5 7.2 4.9

8.7 3.6 5.4

6.7 6.0 5.8

Source: Ref. 79.

FIG. 23

Stimulated

The FitzHugh–Nagumo equivalent circuit.

Interfacial Electrical Phenomena in Green Plants

IX.

679

CONCLUSIONS

The automatic measurement of the extracellular and intracellular electrical potential difference can be effectively used in plant electrophysiology for studying the molecular interfacial mechanisms of ion transport, the inﬂuence of external stimuli on plants, and for investigating the bioelectrochemical aspects of the interaction between insects and plants. Green plants interfaced with a computer through data acquisition systems can be used as fast biosensors for monitoring the environment and to detect effects of pollutants, pesticides, defoliants, for prediction and monitoring of climate changes, and in agriculture for direct and fast control of conditions inﬂuencing the harvest. Action potentials in green plants and animals have similar speed of propagation of excitations and duration. The use of new computerized methods provides opportunities for detection of fast action potentials in green plants in real time. Uncouplers induce action potentials in soybean plants with speed of excitation waves propagation up to 40 m/s.

ACKNOWLEDGMENTS Financial support from the National Science Foundation is gratefully acknowledged.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.

9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

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29 Voltammetric Study of Drugs at Liquid^ Liquid Interfaces MITSUGI SENDA, YUKO KUBOTA, and HAJIME KATANO Bioscience, Fukui Prefectural University, Fukui, Japan

I.

Department of

INTRODUCTION

Ion-transfer voltammetry of organic compounds, including those of biological importance, such as neurotransmitters [1–3], drugs [4–17], pesticides and uncouplers [18,19], at the interface of two immiscible electrolyte solutions or, in short, the organic solvent or oil–water (O/W) interface has been studied by many authors. These organic compounds or drugs are frequently ionizable and present as neutral or charged species or both in physiological-pH media. Thus, the electrochemical or voltammetric study of these organic compounds at the O/W interface should give important information on physicochemical properties of biological interest; the partition coefﬁcients between an organic solvent and water of neutral and charged species and the dissociation constants in organic and aqueous media [14–18], which provides a new approach to studying biological effects of drugs, such as the quantitative structure–activity relationship, mode of action, and others [20]. Recently, Girault and his coworkers presented a theory of the ionic partition diagram [21,22]; the ionic partition diagram or lipophilicity proﬁle of drugs as a function of pH and O/W-interfacial potential is constructed on the basis of the transfer potential of related ions, which in turn is derived from the experimental half-wave potential of the ion-transfer voltammogram of drugs at the O/ W interface. In this chapter, the voltammetric study of local anesthetics (procaine and related compounds) [14–16], antihistamines (doxylamine and related compounds) [17,22], and uncouplers (2,4-dinitrophenol and related compounds) [18] at nitrobenzene (NB)–water (W) and 1,2-dichloroethane (DCE)–water (W) interfaces is discussed. Potential step voltammetry (chronoamperometry) or normal pulse voltammetry (NPV) and potential sweep voltammetry or cyclic voltammetry (CV) have been employed. Theoretical equations of the half-wave potential vs. pH diagram are derived and applied to interpret the midpoint potential or half-wave potential vs. pH plots to evaluate physicochemical properties, including the partition coefﬁcients and dissociation constants of the drugs. Voltammetric study of the kinetics of protonation of base (procaine) in aqueous solution is also discussed. Finally, application to structure–activity relationship and mode of action study will be discussed brieﬂy. 683

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II.

VOLTAMMETRIC THEORY OF ORGANIC BASES AND ACIDS AT O/W INTERFACE

A.

Ion-Transfer Voltammetry of Bases [16,17,23]

Procaine, doxylamine, and their related compounds are organic dibases and hence can be present in the forms of neutral molecule (B), protonated, univalent (BHþ ), and divalent cations (BH2þ 2 ) in both W and O phases. We consider the partition or transfer of a dibase between O and W phases in the forms of either B, BHþ , or BH2þ 2 , as expressed, respectively, by BðOÞ ¼ BðWÞ

ð1Þ

BHþ ðOÞ ¼ BHþ ðWÞ

ð2Þ

2þ BH2þ 2 ðOÞ ¼ BH2 ðWÞ

ð3Þ

These transfer reactions are interrelated by two successive protonation reactions in both O and W phases, as expressed by BðÞ þ Hþ ðÞ ¼ BHþ ðÞ

ð ¼ O; WÞ

BHþ ðÞ þ Hþ ðÞ ¼ BH2þ 2 ðÞ

ð4Þ ð5Þ

In deriving theoretical equations of the current–potential (or time) curves of ion-transfer voltammetry of a dibase we shall make the following assumptions: 1.

2.

3. 4.

We consider a plane diffusion model; the O/W interface is taken as the origin of co-ordinates (x ¼ 0) and the O and W phases are placed in the regions 1 x 0 and 0 x þ1, respectively. Supporting electrolytes at sufﬁciently high concentration are present in both O and W phases. For the sake of simplicity, we assume that the diffusion coefﬁcients of relevant species in the phase ( ¼ O; W) have the common value D . The W phase is well-buffered, whereas the O phase contains no buffer component. The rates of protonation and deprotonation reactions are sufﬁciently large in comparison with corresponding diffusion rates, so that it can be assumed that these reactions are at equilibrium even when current is ﬂowing, that is, the following equations are valid everywhere at t 0, t being the time: cBHþ =cB cHþ ¼ B1 ¼ 1=KB1

ð ¼ O; WÞ

cBH22þ =cBHþ cHþ ¼ B2 ¼ 1==KB2

5.

ð6Þ ð7Þ

where ci is the concentration of i species (i ¼ Hþ , B, BHþ , BH2þ 2 ) in the phase, and KB2 the formal B1 and B2 are the formal formation constants, and KB1 dissociation constants of the ﬁrst and second protonation–deprotonation reactions, expressed by Eqs. (4) and (5), respectively, in the phase. The rates of the transfer reactions of all relevant species across the O/W interface are sufﬁciently large [13] in comparison with the corresponding diffusion rates, so that the following Nernst equations are valid for the transfer of relevant species, as expressed by Eqs. (1)–(3), at x ¼ 0 and t > 0:

Voltammetric Study of Drugs o O o W cB = cB

¼ PB

o O cBHþ =o cW BHþ

685

ð8Þ

¼ PE;B1 ¼ exp ðF=RTÞð o O cBH22þ =o cBH22þ ¼ PE;B2 ¼ exp ð2F=RTÞð oBH22þ Þ

6.

oBHþ Þ

ð9Þ ð10Þ

where o ci ( ¼ O; W) is the surface concentration, that is, o ci ¼ ½ci x¼0 , of þ species i [i ¼ B, BHþ ; BH2þ 2 , and H in Eq. (12) below] in the phase, and PB , PE;B1 , and PE;B2 are the partition coefﬁcients of B, BHþ , and BH2þ 2 , respectively, between organic (O) and aqueous (W) media. PE;B1 and PE;B2 , which may be called the ionic partition coefﬁcients, are dependent on the potential difference across the O/W interface, , deﬁned by ¼ W O , ð ¼ O; W) being the Galvani potential of the phase and the formal potentials, og , of ion þ g [g ¼ BHþ , BH2þ 2 , and H in Eq. (12) below], as expressed by Eqs. (9) and (10), respectively. We also consider the transfer of a proton, Hþ , across the O/W interface: Hþ ðOÞ ¼ Hþ ðWÞ

ð11Þ

which is assumed to proceed with sufﬁciently high rate so that the Nernst equation o O o W cHþ = cHþ ¼ PE;Hþ ¼ exp ðF=RTÞð oHþ Þ ð12Þ is valid at x ¼ 0 and t > 0. O O W and KB2 are related to KB1 In view of Eqs. (8)–(10) and (12), it can be shown that KB1 W and KB2 , respectively, according to Eqs. (6) and (7) by O W KB1 ¼ KB1 PB exp ðF=RTÞð oBHþ oHþ Þ ð13Þ O W KB2 ¼ KB2 exp ðF=RTÞð2 oBH22þ oBHþ oHþ Þ ð14Þ

The diffusion problems of B, BHþ , and BH2þ 2 species in both the O and W phases can be solved under the assumptions 1–6 to give equations of the reversible current– potential curves or voltammograms of dibases in NPV and CV [17,23]. Thus, it can be predicted that, in general, one or two (depending on pH of W phase) waves or steps in NPV or one or two (depending on pH of W phase) pairs of anodic and cathodic peak currents in CV are to be observed. For the sake of simplicity we assume in the following þ þ that o cW Hþ ¼ ½H , ½H being the activity of hydrogen ion in the bulk of the W phase and that the pH of the W phase is given by pH ¼ log½1=½Hþ . The theoretical half-wave against pH 0 of the W potentials, 1=2 ’s of the predicted voltammograms are plotted W W0 W and pH pKB1 [where pKW phase, that is, against pH pKB2 B1 ¼ pKB1 þ O W 1=2 o p½1 þ ðD =D Þ KB , see Eq. (17)], for example, in Fig. 1 where B ¼ ðF=RTÞð BH22 W W oBHþ Þ ¼ 8 and pKB1 B2 > 5. The half-wave potential, which is deﬁned and determined in NPV, can also be obtained by the midpoint potential, m , deﬁned by m ¼ ð pa þ pc Þ=2, pa and pc being the anodic and cathodic peak potentials, respectively, in CV, that is, we can take that 1=2 ¼ m . In Fig. 1, plot (a) represents the half-wave potential of divalent ion transfer or two-proton transfer assisted by B that may 2þ be expressed by BH2þ 2 ðOÞ=BH2 ðWÞ and plot (c)–(d) represents that of univalent ion transfer or (the ﬁrst) one-proton transfer assisted by B that may be expressed by þ BHþ ðOÞ=BH2þ 2 ðWÞ and/or BH ðWÞ, whereas plot (b) represents that of (the second) þ one-proton transfer assisted by B that may be expressed by BH2þ 2 ðOÞ=BH ðWÞ. Also,

686

Senda et al.

0 FIG. 1 Theoretical half-wave potential, 1=2 ¼ ðF=RTÞð 1=2 1=2;BH þ Þ ¼ ðF=RTÞðE1=2 W W0 E1=2;BHþ Þ, plotted against (pH pKB2 Þ and ðpH pKB1 Þ when ¼ ðF=RTÞð oBH22þ oBHþ Þ W0 W =8: pKB1 ¼ pKB1 þ p½1 þ ðDO =DW Þ1=2 KB :

plot (e)–(f) represents univalent ion transfer or one-proton transfer assisted by B that may be represented by BHþ ðOÞ=BHþ ðWÞ and/or B(W) [but see Eqs. (35–37) below]. These plots can be expressed by 0 þ ðaÞ: 1=2;1þ2 ¼ 1=2;BH22

ðbÞ: 1=2:2 ¼ ðcÞðdÞ: 1=2;1 ¼

0 2 1=2;BH22 þ 0 1=2;BH þ

0 þ ðeÞðfÞ: 1=2;1 ¼ 1=2;BH

0 1=2;BH þ

W KB2 =½Hþ

ð15Þ

þ ðRT=FÞ ln ð16Þ þ W þ ðRT=FÞ ln 1 þ ½H =KB2 ð17Þ h

i W þ ðRT=FÞ ln 1 þ KB1 =½Hþ 1 þ DO =DW Þ1=2 PB

ð18Þ with 0 o þ ¼ BH22þ þ ðRT=2FÞ ln 1=2;BH22 0 1=2;BH þ

¼

oBHþ

DW =DO

1=2

1=2 W O þ ðRT=FÞ ln D =D

ð19Þ ð20Þ

Note that Eq. (16) is an approximate equation [23] that may be applied to analyze the experimental results observed in most cases, including those discussed below in this chapW W ter. Equations (17) and (18) may be combined when pKB1 and pKB2 are reasonably separated to give 0 þ 1=2;1 ¼ 1=2;BH

1=2 W þ W þ O W þ ðRT=FÞ ln ½H =KB2 þ 1 þ KB1 =½H 1 þ D =D PB

ðcÞðdÞ ¼ ðeÞðfÞ:

ð21Þ

Voltammetric Study of Drugs

687

W When ð1 þ ðDO =DW Þ1=2 PB Þ 1 in addition to ðKB1 =½Hþ Þð1 þ ðDO =DW Þ1=2 PB Þ 1, Eq. (18) is reduced, in view of Eq. (13), to give h i O þ ðRT=FÞ ln 1=½H þ ð22Þ ðfÞ: 1=2;1 ¼ oHþ þ ðRT=FÞ ln KB1

B.

Ion-Transfer Voltammetry of Acids [18]

Phenols are weak acids and hence can be present in the forms of neutral molecule (AH) and univalent anion (A ). We consider the transfer of acid across the interface between an organic solvent (O) and water (W) in the forms of a neutral molecule and a univalent ion, respectively, AHðOÞ ¼ AHðWÞ

ð23Þ

A ðOÞ ¼ A ðWÞ

ð24Þ

which are interrelated by the proton dissociation–association reactions in both O and W phases, AHðÞ ¼ A ðÞ þ Hþ ðÞ

ð ¼ O; WÞ

ð25Þ

In deriving theoretical equations of the current–potential (or time) curves of ion transfer of an acid we shall make essentially the same assumptions as the assumption 1–6 above. It is noted here that theoretical equations of the more general case, that is, of a dibasic acid, such as expressed by AH2 ¼ AH þ Hþ , AH ¼ A2 þ Hþ , can be derived [24], but are not included here, to save space. The formal formation constant, A1 , and formal disso , in the phase is deﬁned by ciation constant, KA1 cAH =cA cHþ ¼ A1 ¼ 1=KA1

ð ¼ O; WÞ

ci

ð26Þ

þ

where is the concentration of species i ði ¼ AH, A , H ) in the phase. Also, the partition or transfer equilibrium at the O/W interface for Eqs. (23)–(24) is expressed by o O cAH =o cW AH o O o W cA = cA

¼ PA

ð27Þ

¼ PE;A1 ¼ exp½ð1ÞðF=RTÞð oA Þ

ð28Þ

where o ci ( ¼ O; W) is the surface concentration of species i (i ¼ AH, A , Hþ ), PA and PE;A1 the partition coefﬁcients of AH and A , respectively, og the formal potential of g ion ðg ¼ A ; Hþ ). We also have in view of Eqs. (26)–(28) the following relationship, O W ¼ KA1 ð1=PA Þ exp ðF=RTÞð oA oHþ Þ ð29Þ KA1 The diffusion problem can be solved to predict that one wave in NPV or one pair of anodic and cathodic peak currents in CV are to be observed; the half-wave potential is expressed by

1=2 þ 0 W O W þ ðRT=FÞ ln 1 þ ½H =K 1=2;1 ¼ 1=2;A 1 þ D =D PA ð30Þ A1 with 0 1=2;1

¼

oA

þ ðRT=FÞ ln

D =D W

O

1=2

ð31Þ

688

Senda et al.

W Equation (30) predicts that at sufﬁciently high pH where ð½Hþ =KA1 Þð1 þ ðDO =DW Þ1=2 PA Þ 0 1, 1=2;1 approaches to the pH-independent value of 1=2;1 deﬁned by Eq. (31) and W Þð1 þ ðDO =DW Þ1=2 PA Þ 1, 1=2;1 shifts to that at sufﬁciently low pH so that ð½Hþ =KA1 0 more positive potential linearly with increasing pH; the pH of the inﬂection point, pKA1 , of 0 W O W 1=2 the 1=2;1 vs. pH plot is given by pKA1 ¼ pKA1 þ log½1 þ ðD =D Þ PA . Furthermore, W Þð1 þ ðDO =DW Þ1=2 PA Þ 1, we have when ðDO =DW Þ1=2 PA 1 in addition to ð½Hþ =KA1 h i O 1=2;1 ¼ oHþ þ ðRT =FÞ ln KA1 ðRT=FÞ ln ½Hþ ð32Þ

in view of Eq. (29).

III.

EXPERIMENTS

The applied potential, that is, the observed potential, E, is related to the potential difference across the O/W interface, by E ¼ þ Eref

ð33Þ

where Eref is determined by the reference electrode system constructing the electrochemical cell used in electrochemical measurements. Potential step voltammetry (chronoamperometry) or normal pulse voltammetry (NPV) and potential sweep or cyclic voltammetry (CV) were employed for investigating drugs at the NB/W or DCE/W interface. A thin O-layer cell [15,16,23] was used to realize the partition equilibrium of neutral species (that is, B) at the O/W interface initially at t ¼ 0 within a reasonably short time. All measurements were carried out at 25 C. Experimental details should be consulted in the references cited.

IV.

VOLTAMMETRY OF PROCAINE AND RELATED COMPOUNDS [14,15,23]

Procaine gives a single wave in NPV and a pair of anodic and cathodic peak currents in CV in the pH range tested, that is, pH ¼ 0:9–9.6. Figure 2 shows a cyclic voltammogram of 0.2 mM procaine (W) at 0.1 M TPenATPB (NB)–0.1M LiCl, 10 mM acetate buffer, pH 4.06 (W) interface at the potential scan rate, ¼ 20 mV=s. TPenATPB stands for tetrapentylammonium tetraphenylborate. The voltammograms at pH 4.06 have proved to be of reversible or Nernstian nature; the anodic peak height is proportional to the square root of between ¼ 5–100 mV/s; the observed midpoint potential, Em , deﬁned by Em ¼ ðEpa Epc Þ=2, Epa and Epc being the observed anodic and cathodic peak potentials, respectively, was independent from , whereas the observed peak potential separation, Ep , deﬁned by Ep ¼ Epa Epc , when extrapolated to ¼ 0, was determined to be 0:058 0:002 V, indicating that the voltammograms can be assigned to a reversible univalent ion transfer or one-proton transfer assisted by B that may be expressed by BHþ ðOÞ= BHþ ðWÞ at pH 4.06. The diffusion coefﬁcient of procaine was determined to be DW ¼ ð5:6 0:1Þ 106 cm2 s. Similarly, the reversible or quasireversible character of the cyclic voltammograms of procaine obtained at pH 0.9–9.6 has also been veriﬁed, indicating that the midpoint potentials obtained from the voltammograms can be considered to be equal to the reversible half-wave potentials, E1=2 , of procaine at the NB/W interface in the pH range studied.

Voltammetric Study of Drugs

689

FIG. 2 Cyclic voltammograms of (a) 0.2 mM procaine (W) at 0.1 M TPenATPB (NB)–0.1 M LiCl, 10 mM acetate buffer, pH 4.06 (W) interface, (b) base current, and (c) ðaÞ ðbÞ. ¼ 20 mV/s.

Figure 3 shows the Em vs. pH plot of procaine at the NB/W interface. Procaine gives a single wave in the pH range tested, indicating that the half-wave potentials corresponding to plots (a) and (b) in Fig. 1 [see Eqs. (15)–(16)] should lie at such a positive potential that they are not observed within the potential window of the NB/W interface examined and that the E1=2 vs. pH curve should correspond to plots (c)–(d)=(e)–(f) in Fig. 1 [see Eq. (21)]. Thus, the pH-independent half-wave potential of procaine corresponding to plots 0 0 þ . was determined to be E1=2;BHþ ¼ 0:266 V. Also, the experimental half(d)=(e), E1=2;BH wave potential of tetramethylammonium ion (TMAþ ) at the NB/W interface, E1=2;TMAþ , was determined to be E1=2;TMAþ ¼ 0:369 V using the same electrochemical cell system as 0 used in the determination of E1=2;BH þ . In view of Eq. (33) we have the relationship

FIG. 3 The midpoint potential, Em , of procaine at 0.1 M TPenATPB (NB)–0.1 M LiCl, 10 mM buffer (W) interface plotted against pH.

690

Senda et al. 0 o o E1=2;BH þ E1=2;TMAþ ¼ BHþ TMAþ

ð34Þ

W 1=2 can be considered to be nearly constant, independent of since in most cases ðDO i =Di Þ ionic species. On taking oTMAþ ¼ 0:035 V [24], the formal potential of BHþ (here, protonated procaine) can be determined to be oBHþ ¼ 0:068 V. Furthermore, the Em vs. pH W ¼ 2:45 by Eq. (17) and the Em vs. pH plot in the plot in the acidic-pH range gives pKB2 W ¼ 8:98 [26] and neutral to basic-pH range gives pPB ¼ 2:0 by Eq. (18), where pKB1 O W 1=2 O ðD =D Þ ¼ 0:75 [14] are taken, and ﬁnally pKB1 ¼ 13:8 is obtained according to Eq. (13) where oHþ ¼ 0:335 V at the NB/W interface [25] is taken. The results are summarized together with those of the other local anesthetics studied in Table 1.

V.

VOLTAMMETRY OF DOXYLAMINE AND RELATED COMPOUNDS [17,23]

Doxylamine gives one or two waves in NPV and one or two pairs of anodic and cathodic peak currents in CV, depending on the pH of the W phase, at the NB/W interface. Figure 4 shows cyclic voltammograms of 0.2 mM (except at pH 9.87) doxylamine in the W phase at 0.01 M THexATC1PB (NB)–0.1 M Li2 SO4 , 10 mM buffer (W) interface at ¼ 50 mV=s. THexATC1PB stands for tetrahexylammonium tetrakis(4chlorophenyl)borate. The voltammograms have been shown to be of reversible or quasireversible nature. Therefore, the observed midpoint potential, Em , can be equated to the reversible half-have potential of doxylamine at the NB/W interface. Figure 5 shows the Em vs. pH diagram of doxylamine at the NB/W interface. At pH < 2:0 where one pair of anodic and cathodic peak currents is observed, the voltammograms can be assigned to divalent ion transfer or two-proton transfer assisted by B that may be 2þ 2þ ion in W expressed by BH2þ 2 ðNBÞ=BH2 ðWÞ; the diffusion coefﬁcient of BH2 W 5 2 (pH 1.16) phase was calculated to be D ¼ 0:26 10 cm =s (from NPV) and 0:8 105 cm2 /s (from CV). At pH 5–6, the voltammograms can be assigned to univalent ion transfer or one-proton transfer assisted by B which may be expressed by BHþ (NB)/BHþ (W); the diffusion coefﬁcient of BHþ ion in the W (pH 6.05) phase was calculated to be DW ¼ 0:20 105 cm2 =s (from NPV) and 0:6 105 cm2 =s1 (from CV). Thus, the Em vs. pH plots of Fig. 5 were ﬁtted to Eqs. (15–21) in the similar way to

TABLE 1

Physicochemical Properties of Local Anesthetics at the NB/W Interface

Drugs Ester-linked Procaine Tetracaine Oxybuprocaine Amide-linked Prilocaine Mepivacaine Lidocaine Bupivacaine Dibucaine a

Ref. 26.

oBHþ (V)

pPB

Wa pKB1

W pKB2

NB pKB1

0:068 0:165 0:187

2.0 2.8 3.7

8.98 8.33 8.79

2:45 2:70 2:40

13.8 13.8 14.0

0:002 0:050 0:057 0:123 0:169

2.1 1.9 2.5 3.6 2.7

7.95 7.79 7.86 8.29 8.30

— — — — 1:92

11.5 12.4 10.2 12.5 14.1

Voltammetric Study of Drugs

691

FIG. 4 Cyclic voltammograms, corrected for base current, of 0.2 mM (except at pH 9.87) doxylamine (W) at 0.01 M THexATC1PB (NB)–0.1 M LiCl, 10 mM buffer (W) interface. ¼ 50 mV=s:

FIG. 5 The midpoint potential, Em , of doxylamine at 0.1 M THexATC1PB (NB)–0.1 M LiCl, 10 mM buffer (W) interface plotted against pH.

692

Senda et al.

that of procaine stated above, giving the values of oBH22þ , oBHþ , and pPB (when p w w is given) of doxylamine at the NB/W interface, and pKB2 of doxylamine in the W KB1 O O phase; and pKB2 and pKB1 of doxylamine in the NB phase according to Eqs. (13)–(14). They are summarized together with those of pheniramines in Table 2. Doxylamine and pheniramines also give at the DCE/W interface one or two waves in NPV and one or two pairs of anodic and cathodic peak currents in CV, depending on the pH of the W phase. Figure 6 shows the Em vs. pH plots of doxylamine at 0.01 M THexATC1PB (DCE)–0.1 M Li2 SO4 , 10 mM buffer (W) interface. As seen in Fig. 6, a voltammogram attributable to divalent ion transfer or two-proton transfer assisted by B was not observed within the potential window of the DCE/W interface even at pH 1.0 but two waves or pairs of anodic and cathodic peak currents, each corresponding to one0 þ can be proton transfer, were observed at pH 1.0 to 3. Then, the value of E1=2;BH22 calculated from the midpoint potential of the second, more positive wave on the basis of Eq. (16). The E1=2 vs. pH plots at pH 1.0 to 11.0 were analyzed in the similar way to that of procaine or doxylamine at the NB/W interface stated above, giving physiochemical properties of doxylamine at the DCE/W interface. The results are included in Table 2, where oHþ ¼ 0:546 V at the DCE/W interface [28] is taken. Comparison of the results at the DCE/W interface with those at the NB/W interface is interesting. The study is continuing.

VI.

VOLTAMMETRY OF 2,4-DINITROPHENOL AND RELATED COMPOUNDS [18,24]

2,4-Dinitrophenol (DNP) gives a single wave in NPV and a pair of anodic and cathodic peak currents in CV at the NB/W interface in pH range studied. Figure 7 shows a cyclic voltammogram of 0.6 mM DNP (NB) at 0.1 M TPenATPB (NB)–0.1 M LiCl, 50 mM phosphate buffer, pH 6.3 (W), that can be assigned to one-proton transfer assisted by A present in NB. The E1=2 vs. pH plot is shown in Fig. 8, in which the results obtained with

TABLE 2

Physicochemical Properties of Doxylamine and Pheniramines

Drugs Nitrobenzene–water interface Doxylamine Pheniramine Bromopheniramine Chloropheniramine 1,2-Dichloroethane– water interface Doxylamine Pheniramine Bromopheniramine Chloropheniramine a b

oBHþ (V)

oBH22þ (V)

pPB

W pKB1

W pKB2

O pKB1

O pKB2

0:168 0:137 0:209 0:200

0:016 0:028 0:003 0:020

2.4 2.1 38 37

9:2a 9:29 a 9:21 b 9:16 a

4:11 3:71 3:72 3:84

15.3 15.2 14.7 14.5

6.5 6.6 5.8 5.8

0:072 0:040 0:089 0:082

0:203 0:246 0:225 0:230

3.2 25 40 36

9:2 a 9:29 a 9:21 b 9:16 a

4:16 4:19 4:00 4:10

16.4 16.7 16.0 16.2

5.3 4.4 4.1 4.2

Ref. 27. Determined by the titration method.

Voltammetric Study of Drugs

693

FIG. 6 The midpoint potential, Em , of doxylamine at 0.1 M THexATC1PB (DCE)–0.1 M Li2 SO4 , 10 mM buffer (W) interface plotted against pH.

other uncouplers, 2,4,6-trinitrophenol, cabonylcyanide p-triﬂuoromethoxyphenylhydrazone (FCCP) and 3,5-t-butyl-4-hydroxybenzylidenemalononitrile (SF6847) are also shown. The plots (a) and (b) can be ﬁtted to Eq. (30) to ﬁve the values of oA and W NB is given), and then pKA1 according to Eq. (29). The plots (c) and (d) are pPA (when pKA1 not able to be ﬁtted to Eq. (30) because the oA ’s of these compounds lie at a potential too positive (> 0:1 V) to be observed within the potential window of the NB/W interface. NB ’s. Furthermore, However, the plots (c) and (d) can be ﬁtted to Eq. (32) to give their pKA1

FIG. 7 Cyclic voltammograms of (a) 0.6 mM DNP (NB) at 0.1 M TPenATPB (NB)–0.1 M LiCl, 50 mM phosphate buffer, pH 6.3 (W) and (b) base current. ¼ 5 mV=s. (From Ref. 18.)

694

Senda et al.

FIG. 8 Dependence of the half-wave potential, E1=2 , on pH of (a) 2,4,6-trinitrophenol, (b) DNP, (c) FCCP, and (d) SF6847 at the NB/W interface. (From Ref. 18.)

the oA ’s of these uncouplers can be calculated using Eq. (29) if their pPA ’s are determined independently, for instance, by the ﬂask-shaking method. The results obtained with several uncouplers are summarized in Table 3.

VII.

KINETICS OF ASSISTED PROTON TRANSFER AT LIQUID–LIQUID INTERFACE [14–16]

We shall consider the voltammetric behavior of a base at the O/W interface. In the discussion stated above it is assumed that the transfer process of drugs at the O/W interface is of reversible nature (see the assumptions 1–6 above). With increasing pH of the W phase, particularly in basic solutions, however, the rate of protonation in the W phase, that is, BðWÞ þ Hþ ðWÞ ¼ BHþ ðWÞ should rapidly decrease, resulting in decreasing of the current associated with the transfer of BHþ ion across the O/W interface. This has actually

TABLE 3 Physicochemical Properties of Uncouplers at the NB/W Interface Uncouplers

oA ðVÞ

2,4,6-Trinitrophenol 2,4-Dinitrophenol Pentachlorophenol FCCP SF6847

0:069 0:059 0:041 0:154 0:190

a b

Ref. 29. Ref. 30.

pPA

W pKA1

NB pKA1

2:34 2:45 4:68 3:51 5:82

0:7a 4:1b 4:8b 6:2b 6:8b

7.6 13.3 14.5 12.8 15.1

Voltammetric Study of Drugs

695

been observed in CV of procaine at hydrophilic membrane-covered NB/W interface [5,6] and later studied quantitatively using a polarographic technique with dropping electrolyte electrode. More recently it has been shown that kinetics of the protonation reaction at the O/W interface can advantageously be studied using NPV or chronoamperometry at a stationary O/W interface (see also Ref. 31). The results of these studies show that the mechanism of the proton transfer assisted by procaine at an O/W interface is the homogeneous or chemical transfer of protons (mainly from the acid component of buffer Aj , Aj H, to procaine, B, in the W phase, kB;AjH BðWÞ þ Aj HðWÞ

¼

BHþ ðWÞ þ A j ðWÞ

ð35Þ

which is followed by the electrochemical transfer of BHþ ion across the O/W interface, BHþ ðWÞ ¼ BHþ ðOÞ

ð36Þ

When procaine is initially present in the O phase, the transfer of B across the O/W interface, BðOÞ ¼ BðWÞ

ð37Þ

which is supposed to be very fast, should precede Eq. (35). The rate constants of the protonation reaction of procaine with buffers have been determined (Table 4). The validity of the Broensted relationship has been suggested.

VIII.

STRUCTURE–ACTIVITY RELATIONSHIP AND MODE OF ACTION OF DRUGS

The physicochemical properties of a drug are of prime importance for its biological effects, and the hydrophobicity or lipophilicity is perhaps one of the most signiﬁcant [19–22]. Biomembranes have complex structure. The organic solvent–water system is nevertheless used as an artiﬁcial model to assess hydrophobicity. Voltammetric study of drugs at the O/ W interface can provide information on hydrophobicity or lipophilicity of drugs, such as the partition coefﬁcients between O and W phases of both neutral and charged species and the dissociation constants in the O as well as W phase. From the viewpoint of the ionic partition diagram theory [21,22], the half-wave potential vs. pH plot, such as illustrated in Figs. 1, 3, 5, 6, and 8, represents (by taking (DO =DW Þ1=2 ¼ 1) the ionic partition diagram,

TABLE 4 Rate Constants of Proton Transfer, kB;Aj H , Between Procaine (B) and Acid Component of Buffer (Aj H) According to Eq. (35) at pH 8.0 in 0.1 M LiCl Buffer (Aj ) TAPSO EPPS TAPS

pKAWj

kB;Aj H ð106 dm3 =mol=sÞ

7.7 8.0 8.4

5:4 2:1 0:85

TAPSO: N-tris(hydroxymethyl)methyl-2-hydroxy-3-aminopropanesulfonic acid. EPPS: N-2-hydroxyethylpiperazine-N 0 -3-propanesulfonic acid. TAPS: N-tris(hydroxymethyl)methyl-3-aminopropanesulfonic acid.

696

Senda et al.

stating for a dibase, for example, between BHþ or BH2þ 2 species in the O phase and the species in the W phase, plus B species in the O phase. sum of B, BHþ , and/or BH2þ 2 Neither protonation nor deprotonation in the O phase, as represented by BðOÞ þ Hþ ðOÞ ¼ BHþ ðOÞ, should occur in any appreciable amount in the cases illustrated. In electrochemical experiments, NB and DCE are mainly used for the O phase, which are different from the solvents traditionally used in hydrophobicity measurements of drugs (n-octanol and alkanes [20]). Comparative study of the partition coefﬁcients at DCE or NB/W systems with those at n-octanol or alkanes–water systems is interesting [7,32–34]. Partitioning of local anesthetics between n-octanol and aqueous buffer (SAM: 0.15 M NaCl, 5 mM Good’s buffer) and the correlation of hydrophobicity with potencies of the drugs on isolated nerve have been the subject of recent studies [35,36]. A conventional ﬂask-shaking method was used to determine the hydrophobicity of the drugs. Both the dissociation of charged species (BHþ ) and the protonation to neutral species (B) in the O phase should be negligibly small as indicated by the voltammetric study, whereas the ionic form has been suggested to be active in mode of action; the hydrophobicity of the charged species could be of prime interest. An excellent linear correlation of log½50% block dose] vs. log½P0E;B1 ], where P0E;B1 ¼ ðF=2:303RTÞð oBHþ Þ [see Eq. (9)], has been found with four amide-linked local anesthetics, prilocaine, mepivacaine, lidocaine, and bupivacaine [23]. A relationship correlating the weak acid uncouplers’ activity with their oA , pKAO , and pKAW has been presented on the basis of protonophoric theory of uncoupling activity, in which the concentration of anionic ionophore (A ) within a biomembrane is supposed to be controlled by the ionic partition of A at the biomembrane–solution interface according to Eq. (28) [19]. The biomembrane–solution interface could be polarized or electrogenic [37]. Experimental results on the activities of uncouplers on rat liver mitochondria [30] have been explained reasonably [19,24]. Electrochemical study of biologically active compounds at the O/W interface provides information on physiochemical properties of the compounds at the O/W interface and in the O and W phases or, in short, hydrophobicity or lipophilicity of biologically active compounds, which seems essential to understand their biological effects, including mode of action, structure–activity relationship, delivery, and others.

ACKNOWLEDGMENT This work was supported by Fukui-ken University Science Foundation, to which the author (M.S.) is very grateful.

REFERENCES 1.

2. 3. 4.

D. Homolka, L. Q. Hung, A. Hofmanova, M. W. Khalil, J. Koryta, V. Marecek, Z. Samec, S. K. Sen, P. Vanysek, J. Weber, M. Brezina, M. Janda, and I. Stibor. Anal. Chem. 52:1606 (1980). P. Vanysek and M. Behrendt. J. Electroanal. Chem. 130:287 (1981). D. Homolka, V. Marecek, Z. Samec, K. Base, and H. Wendt. J. Electroanal. Chem. 163:159 (1984). Z. Yu and E. Wang. Chinese Anal. Chem. 17:34 (1989).

Voltammetric Study of Drugs 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

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Y. Yamamoto, T. Osakai, and M. Senda, in 51st Symposium on Analytical Chemistry, Saga, Japan, 1990, Abstract, pp. 347–348. Y. Yamamoto. Studies on Amperometric Ion-Selective Electrode Sensors. PhD Thesis, Kyoto University, Kyoto 1991. K. Kontturi and L. Murtomaki. J. Pharm. Sci. 81:970 (1992). K. Arai, M. Ohsawa, F. Kusu, and K. Takamura. Bioelectrochem. Bioenergetics 31:65 (1993). K. Arai, F. Kusu, N. Tsuchiya, S. Fukuyama, and K. Takamura. Denki Kagaku 62:840 (1994). K. Arai, S. Fukuyama, F. Kusu, and K. Takamura. Bioelectrochem. Bioenergetics 31:159 (1994). F. Reymond, G. Steyaert, P.-A. Carrupt, B. Testa, and H. H. Girault. Helv. Chim. Acta 79:101 (1996). F. Reymond, G. Steyaert, A. Pagliara, P.-A. Carrupt, B. Testa, and H. H. Girault. Helv. Chim. Acta: 79:1651 (1996). Z. Samec, J. Langmaier, A. Trojanek, E. Samcova, and J. Malek. Anal. Sci. 14:35 (1998). Y. Kubota, H. Katano, and M. Senda. Electrochim. Acta 44:109 (1998). Y. Kubota, H. Katano, and M. Senda. Rev. Polarogr. (Kyoto) 44:165 (1998). Y. Kubota, Ion-Transfer Voltammetry of Organic Compounds at Organic Solvent/Water Interface. Study on Partition of Organic Compounds between Organic Solvent and Water, MS thesis, Fukui Prefectural University, Fukui 1998. Y. Kubota, H. Seto, H. Katano, and M. Senda. Rev. Polarogr. (Kyoto) 45:154 (1999). T. Ohkouchi, T. Kakutani, and M. Senda. Bioelectrochem. Bioenergetics 25:71 (1991). T. Ohkouchi, T. Kakutani, and M. Senda. Bioelectrochem. Bioenergetics 25:81 (1991). C. Hansch and A. Leo, Exploring QSAR. Fundamentals and Applications in Chemistry and Biology. American Chemistry Society, Washington, DC, 1995. F. Reymond, G. Steyaert, P.-A. Carrupt, B. Testa, and H. H. Girault. J. Amer. Chem. Soc. 118:11951 (1996). F. Reymond, V. Chopineaux-Courtois, G. Steyaert, G. Bouchard, P.-A. Carrupt, B. Testa, and H. H. Girault. J. Electroanal. Chem. 462:235 (1999). Y. Kubota, H. Katano, and M. Senda, in preparation. Y. Kubota, H. Katano, and M. Senda, in preparation. J. Koryta, P. Vanysek, and M. Brezina. J. Electroanal. Chem. 75:211 (1977). D. D. Perrin, Dissociation Constants of Organic Bases in Aqueous Solution, IUPAC, Butterworths, London, 1965. N. G. Lordi and J. E. Christina. J. Am. Pharm. Assoc. Sci. Ed. 45:300 (1956). A. Sabela, V. Marecek, Z. Samec, and R. Fuoco. Electrochim. Acta 37:231 (1992). G. Kortuem, W. Vogel, and K. Andrussow, Dissociation Constants of Organic Acids in Aqueous Solution, IUPAC, Butterworths, London, 1961. H. Terada and Y. Shinohara. Biochim. Biophys. Acta 639:225 (1981). H. Katano and M. Senda. Bull. Chem. Soc. Jpn. 72:2085 (1999). G. Steyaert, G. Lisa, P. Gaillard, G. Boss, F. Reymond, H. H. Girault, P.-A. Carrupt, and B. Testa. J. Chem. Soc. Faraday Trans. 93:401 (1997). V. Chopineaux-Coutois, F. Reymond, G. Bouchard, P.-A. Carrupt, B. Testa, and H. H. Girault. J. Amer. Chem. Soc., accepted. S. Sawada and T. Osakai. Phys. Chem. Chem. Phys. 1:4819 (1999). V. Sanchez, G. R. Arthur, and G. R. Strichartz. Anesth. Analg. 66:159 (1987). G. R. Strichartz, V. Sanchez, G. R. Arthur, R. Chafetz, and D. Martin. Anesth. Analg. 71:158 (1990). S. Ohki, in Comprehensive Treatise of Electrochemistry, Vol. 10, Bioelectrochemsitry (S. Srinivasan, Yu. A. Chizmadzhev, J. O’M. Bockris, B. E. Conway, and E. Yaeger, eds.), Plenum Press, New York, 1985, p. 1.

30 Electrical Potential Oscillation Across a Water^Oil^Water Liquid Membrane in the Presence of Drugs KENSUKE ARAI and FUMIYO KUSU Department of Analytical Chemistry, Tokyo University of Pharmacy and Life Science, Tokyo, Japan

I.

INTRODUCTION

There is diverse drug pharmacological activity on biomembranes [1], which in any one case may be biologically important. Biomembranes function to recognize chemical substances and bring about conversion of chemical information into electrical signals, selective transportation of chemical substances, and energy conversion, and to protect organs from chemical poison and dryness. In many cases, the pharmacological action of a structurally speciﬁc drug is triggered through chemical recognition followed by conversion of chemical information into electric or chemical signals. Thus, the study of such functions is a considerable pharmacological importance. The structures of biomembrane are complicated and artiﬁcial membranes with simple structures should be made available to simplify the clariﬁcation of the mechanisms of pharmacological drug activity. This study directs attention to immiscible oil–water interfaces as a biomembrane model. Spontaneous oscillation occurs in biological systems as cardiac rhythm and nerve impulse, and thus spontaneously oscillating phenomena at immiscible oil–water interfaces would be a signiﬁcant aspect of a functional model of a biological system. In 1978, Dupeyrat and Nakache [2] discovered irregular dynamic ﬂuctuation at immiscible oil– water interfaces in the presence of a surfactant, the oil of which was nitrobenzene or nitroethane. In 1983, this system was expanded by Yoshikawa and Matsubara [3] to a liquid membrane of nitrobenzene interposed between two aqueous solutions, one containing a surfactant (nitrobenzene membrane) and showing spontaneous oscillation of electrical potential difference between the two aqueous solutions. Arai et al. [4] proposed a novel mechanism for potential oscillation across this membrane. Kawakubo et al. [5,6], Miyamura et al. [7–9], Sha et al. [10–12], and Yoshidome et al. [13], reported potential oscillation across a nitrobenzene membrane. Igawa et al. [14] reported potential oscillation across a water–polyoxyethylene p-nonylphenylether–water liquid membrane system. Nakajo et al. [15] noted the frequency and amplitude of potential oscillation across a nitrobenzene membrane to be affected by diethyl ether, a volatile anesthetic. Svirschevsky et al. [16] tested the effects of local anesthetics on potential oscillation across a liquid membrane of nitrobenzene–propanol comprising two aqueous solutions. Arai et al. [17,18] developed a liquid membrane of water–1-octanol–water system (octanol mem699

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brane) and found this oscillation to be altered by hypnotic [19], local anesthetic [19], adrenergic [20], antiadrenergic [20], cholinergic [20], anticholinergic [20], antitussive [21,22], antimalarial [21], bitter stomachic [21], antibiotic [21,23], and sweetening agents [21–23] added to an octanol membrane system. These effects on oscillation may possibly arise from interactions between drug molecules or ions and surfactant ions adsorbed at one octanol–water interface. Consequently, the surfactant ion layer at the interface may behave essentially as a biomembrane. This chapter presents research on electrical potential oscillation across a liquid membrane from pharmaceutical and bioelectrochemical viewpoints. The mode of potential oscillation was found to change in response to drugs dissolved in one aqueous phase of this membrane and to be related to pharmacological activity.

II.

SPONTANEOUS OSCILLATION OF ELECTRICAL POTENTIAL ACROSS A LIQUID MEMBRANE

A.

Systems

1. Water–Nitrobenzene–Water System Yoshikawa and Matsubara [3] ﬁrst observed the spontaneous oscillation of an electrical potential across a liquid membrane. The explanation previously given for the oscillation was the repetitive formation and destruction of a monolayer structure of surfactant ions adsorbed at one interface between the nitrobenzene solution and aqueous solution to which the surfactant had previously been added. The present authors [4] observed a nitrobenzene membrane during measurement of potential oscillation under conditions essentially the same as those used by Yoshikawa and Matsubara. A solution (4 ml) of nitrobenzene containing 1.5 mM 2,4,6-trinitrophenol (picric acid) was introduced onto the bottom of a U-shaped glass cell. Ten milliliters of each aqueous solution were poured simultaneously into both arms of the cell on the nitrobenzene solution with care so as to avoid their mixing with each other. One aqueous solution contained 5 mM cetyltrimethylammonium bromide (CTAB) and 1.5 M ethanol and the other, 0.1 M sucrose. The potential of the aqueous solution to which no surfactant had yet been added was measured in reference to the other aqueous solution with a high input-impedance potentiometer (10 M) connected to a pair of Ag/AgCl electrodes via KCl salt bridge. All measurements were conducted at room temperature. Figure 1 shows typical oscillation across the nitrobenzene membrane and schematically illustrates yellowish substances diffusing within the U-shaped cell. Amplitude (difference between upper and lower potentials of oscillation) was ca. 300 mV for the ﬁrst pulse, which subsequently decreased. The oscillatory period (period between two pulses) was 1–2 min and gradually increased. The induction period (from time of solution contact to ﬁrst pulse) was 6 min. Immediately following contact of the nitrobenzene solution with the two aqueous solutions, light yellowish substances formed at the interface between the nitrobenzene and aqueous solutions containing a surfactant and then diffused to the nitrobenzene phase. Diffusion of picric acid from the octanol to the other aqueous solution was also observed. Just when the yellowish substances reached the other interface, electrical oscillation began. After a sudden drop in potential, a small area of the yellowish substances at the interface between the nitrobenzene solution and aqueous solution with surfactant collapsed. Takahashi et al. [24] observed similar aggregation at a nitrobenzene–water interface containing surfactant and noted the aggregation to occur and diminish synchronously with potential oscillation.

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FIG. 1 Electrical potential oscillation across the nitrobenzene membrane and schematically illustrated features of the diffusion of yellowish substances in the U-shaped cell: (a) potentiometer, (b) aqueous phase, (c) nitrobenzene phase, (d) KCl salt bridge, and (e) Ag/AgCl reference electrode. (Ref. 4.)

Potential differences between the nitrobenzene and aqueous phases at the interfaces in the presence [Fig. 2(B)] and absence of surfactant (C) were measured simultaneously. KCl salt bridges were inserted into the octanol phase to monitor potential. Oscillation measurement data across the nitrobenzene membrane are given in Fig. 2(A) for comparison. The oscillation mode in Fig. 2(C) is virtually the same as that in (A) with respect to oscillatory period and amplitude but quite different with that in (B). Although the potential across the nitrobenzene membrane (A) was not recorded simultaneously with that between nitrobenzene–water phases (B) and (C) but successively, it was noted that the algebraic sum of (B) and (C) should be essentially the same as (A). This is an indication that potential oscillation across the nitrobenzene membrane is likely generated at the interface between the nitrobenzene phase and aqueous phase initially containing no surfactant.

2. Water–Octanol–Water System Though potential oscillation of the nitrobenzene membrane became more continuous and regular in contrast to the Dupeyrat–Nakache system, the establishment of a reproducible

FIG. 2 Electrical potential oscillation across the nitrobenzene membrane (A) and between nitrobenzene and aqueous phases on the left (B) and right (C): (a–d) Ag/AgCl reference electrodes, (e–h) KCl salt bridges. (Ref. 4.)

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mode of potential oscillation for practical use still remains difﬁcult due to use of nitrobenzene as an organic phase. In the Yoshikawa system, both aqueous phases ﬂoat on the organic phase and oil–water interfaces are situated at the bend of the U-shaped glass tube. The former causes mercurial stability in the oil–water interfaces and the latter, low reproducibility of the area and geometry of the interface. Miyamura et al. [7,8] solved the latter problem by replacing the U-shaped cell with a hollow glass tube inserted into a glass beaker so that the location of the interfaces could be adjusted. The former still remains to be solved. Thus, in this study, attention was directed to the organic solvent with speciﬁc gravity less than water and which would be required for creating potential oscillation with high reproducibility using 1-octanol as the solvent. The apparatus for measuring potential oscillation across an octanol membrane is shown in Fig. 3. One milliliter each of water (phase w1) and aqueous solution containing a surfactant and 5.0 M ethanol (phase w2) was placed at the bottom of each arm of an inverted U-shaped cell made of poly(chlorotriﬂuoroethylene). Two milliliters of an octanol solution containing an electrolyte (phase o) were carefully layered on the top of the aqueous solutions. The potential of phase w2 was measured in reference to phase w1. All measurements were made at room temperature. Figure 4 shows typical potential oscillation in the presence of 8 mM sodium dodecyl sulfate (SDS) as surfactant in phase w2 and 5 mM tetrabutylammonium chloride (TBACl) as electrolyte in phase o [19]. Amplitude was ca. 250 mV for the ﬁrst pulse, which subsequently decreased. The oscillatory period was 1 min at minimum and gradually increased. The induction period was 15–30 min. The potential oscillation continued for several hours. With 2 mM CTAB as the surfactant instead of SDS and 3 mM picric acid instead of TBACl, pulse direction was opposite that when using SDS [20]. Other characteristics such as amplitude and oscillatory and induction periods remained basically the same as those with SDS. To produce a regular and reproducible mode of potential oscillation, a cell for measuring potential oscillation across an octanol membrane was designed [25]. An inverted U-shape facilitated the pouring of two aqueous solutions into the arms of the cell and then layering octanol solution on the top of each of these aqueous solutions. A pair of reference electrodes made of Ag/AgCl was connected to the two aqueous solutions by a pair of salt bridges on each arm of the cell. A salt bridge across an octanol–water

FIG. 3 Apparatus for measuring electrical potential oscillation across the octanol membrane: (a) octanol phase, (b) aqueous phase, (c) Ag/AgCl reference electrode, (d) KCl salt bridge, (e) saturated KCl, and (f) potentiometer.

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FIG. 4 Electrical potential oscillation across the octanol membrane of an octanol solution containing 5 mM tetrabutylammonium chloride comprising two aqueous solutions, one containing 8 mM sodium dodecyl sulfate and 5 M ethanol. (Ref. 19.)

interface reduced reproducibility of the oscillation mode and thus salt bridges should be inserted into the aqueous solutions from the bottom of each cell arm. The shape, size, and material of the cell were found to affect the reproducibility of the oscillation mode, such as with respect to the amplitude and oscillatory and induction periods. Effects of the shape of each section of a cell arm on potential oscillation were examined (Fig. 5). A 10:0 10:0 mm square is ideal for achieving oscillation reproducibility rather than a 5:0 5:0 mm square, a 15:0 15:0 mm square, and a circle 10.0 mm in diameter. Poly(chlorotriﬂuoroethylene) gave better reproducible oscillation than polystyrene with respect to solvent resistance. With a quartz glass cell instead of poly(chlorotriﬂuoroethylene) cell, the aqueous solution edge of the interface between the octanol solution and aqueous solution initially containing no surfactant moved up the inner wall of the cell, possibly causing slight mixing of the two aqueous solutions with consequently less reproducibility. Poly(chlorotriﬂuoroethylene) was easier to process than poly(tetraﬂuoroethylene) (teﬂon). Thus, the poly(chlorotriﬂuoroethylene) cell with a 10:0 10:0 mm square section of each arm should prove most ideal for establishing a reproducible potential oscillation mode. This cell design evidently appeared to provide greater reproducibility of oscillation and this in turn facilitated the examination of electrical response of the octanol membrane to various chemical compounds. Potential oscillation across the octanol membrane was conﬁrmed to be generated at the interface between the octanol phase and aqueous phase having no previous surfactant. Potential differences between the octanol and aqueous phases at the two interfaces were measured simultaneously [26]. Figure 6 shows these differences at interfaces o/w1 (B) and o/w2 (C). Oscillation across the octanol membrane is given in (A) for comparison. The oscillation mode in (B) is virtually the same as that of (A). The algebraic sum of (B) and (C) was found to be basically the same as (A). Potential oscillation across the octanol membrane was thus shown to occur at interface o/w1. Consequently, electrolytes were added to phase w1 so that the added electrolytes would act on interface o/w1. Though potential oscillation under the above conditions occurred at interface o/w1, the concentrations of surfactant and ethanol were found to determine the particular interface at which potential oscillation occurs. Figure 7 shows the potential at interfaces o/w1

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FIG. 5 Electrical potential oscillation across the octanol membrane with (A–D) poly(chlorotriﬂuoroethylene), (E) polystyrene, and (F) quartz glass cells. Section of each arm: (A) 10.0 mm dia. circle, (B, E, F) 10:0 10:0 mm square, (C) 15:0 15:0 mm square, and (D) 5:0 5:0 mm square. (Ref. 25.)

FIG. 6 Electrical potential oscillation across the octanol membrane with sodium dodecyl sulfate as surfactant (A) and between octanol and aqueous phases (B and C). All data were obtained using the inverted U-shaped cell: (a1) water, (a2) 8 mM sodium dodecyl sulfate and 5 M ethanol, (b) octanol containing 8 mM tetrabutylammonium chloride, (c) Ag/AgCl electrode, (d) KCl salt bridge, and (e) saturated KCl. (Ref. 26.)

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FIG. 7 Potentials at the interfaces between the octanol phase (phase o) and aqueous phases in the absence (phase w1) and presence (phase w2) of surfactant of the octanol membrane at various concentrations of SDS and ethanol. Octanol phase contains 5 mM tetrabutylammonium chloride. SDS concentrations: (A) 8 mM, (B) 3 mM, (C) 0 mM, and (D–F) 1 mM. Ethanol concentrations: (A– D) 5 M, (E) 0.5 M, and (F) 0 M. (Ref. 27.)

and o/w2 at various concentrations of SDS and ethanol [27]. Potential oscillation was generated at interfaces o/w1 and/or o/w2. Based on their nitrobenzene membrane system study, Yoshihisa et al. [28] concluded potential oscillation to be generated at the interface between the organic phase and aqueous phase initially containing a surfactant. In the present study, however, potential oscillation across the nitrobenzene membrane and octanol membrane was generated at the interface between the organic phase and aqueous phase initially containing no surfactant. This inconsistency may possibly arise from different experimental conditions such as the particular cell design and surfactant and ethanol concentrations used. B.

Various Factors of Oscillation

1.

Organic and Inorganic Compounds

To clarify the relation between potential oscillation and features of interface o/w1, potential oscillation at the interface was measured in the presence of inorganic and organic electrolytes in phase w1, and potential oscillations in the octanol membrane system were compared with interfacial potential between octanol and aqueous solutions of a two-phase octanol–water system with and without surfactant [27]. Figure 8 shows potential oscilla-

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FIG. 8 Potential oscillation at interface o/w1 with SDS as surfactant with (A) no electrolyte, (B) with 100 mM NaCl, (C) 100 mM KCl, (D) 100 mM CsCl, (E) 100 mM MgCl2 , (F) 100 mM CaCl2 , (G) 100 mM BaCl2 , (H) 100 mM FeCl3 , (I) 100 mM NaF, (J) 100 mM NaBr, (K) 100 mM NaI, (L) 100 mM sodium acetate, (M) 100 mM sodium propionate, (N) 100 mM sodium n-butyrate, (O) 100 mM sodium n-valerate, (P) 100 mM tetramethylammonium chloride, (Q) 20 mM tetraethylammonium chloride, (R) 20 mM tetrapropylammonium chloride, and (S) 20 mM tetrabutylammonium chloride in phase w1. Phase w2 contains 8 mM SDS and 5 M ethanol and phase o contains 5 mM tetrbutylammonium chloride. (Ref. 27.)

tion at interface o/w1 in the presence of sodium chloride, potassium chloride, cesium chloride, magnesium chloride, calcium chloride, barium chloride, iron(III) chloride, sodium ﬂuoride, sodium bromide, sodium iodide, sodium acetate, sodium propionate, sodium n-butyrate, sodium n-valerate, tetramethylammonium chloride, tetraethylammonium chloride, tetrapropylammonium chloride, and tetrabutylammonium chloride in phase w1. The potential of phase o was measured in reference to phase w1. Oscillation mode change in amplitude and oscillatory and induction periods were noted to differ according to electrolyte. Change in amplitude was noted to be a remarkable clariﬁcation of the effects of the electrolyte on upper and lower potentials and thus provide clear indication of the properties of the interface. When no electrolyte was present in phase w1, the upper potential of the ﬁrst oscillation (EA;SDS ) was 120 mV and the lower potential (EB;SDS ), 130 mV. EA;SDS and EB;SDS for various electrolytes were determined and mean potential values of EA;SDS and EB;SDS for two experimental runs are shown in Fig. 9 (A). EA;SDS differed greatly according to the inorganic or organic anion. It was hardly affected by inorganic or organic cations. EA;SDS shifted to more negative potentials in the order, ﬂuoride < chloride bromide < iodide and acetate < propionate < n-butyrate < nvalerate. The effects of electrolytes on EA;SDS differed considerably from those on EB;SDS . EB;SDS was greatly affected by organic cations, slightly so by inorganic cations and hardly at all by inorganic or organic anions. EB;SDS slightly shifted to more positive potentials with increase in inorganic cation charge and greatly so to more positive potentials in the order, tramethylammonium < tetraethylammonium < tetrapropylammonium < tetrabutylammonium.

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FIG. 9 Upper potential values, EA;SDS and lower potential values, EB;SDS , of the ﬁrst oscillation at the interface between phases o and w1 of the octanol membrane (A), interfacial potential of a twophase octanol–water system in the absence of SDS, EC;SDS (B) and those in the presence of 10 mM SDS (in the case of inorganic electrolyte, 1 mM), ED;SDS (C). TMACl: tetramethylammonium chloride; TEACl: tetraethylammonium chloride; TPACl: tetrapropylammonium chloride; TBACl: tetrabutylammonium chloride; AcNa: sodium acetate; PrNa: sodium propionate, BuNa: sodium nbutyrate; VaNa: sodium n-valerate. (Ref. 27.)

Figure 9 (C) and (B) show interfacial potential of the two-phase system in the presence of SDS and inorganic and organic electrolytes in the aqueous phase and tetrabutylammonium chloride in the octanol phase, ED;SDS , and interfacial potential in the absence of SDS, EC;SDS , respectively. The potential of the octanol phase was measured in reference to the aqueous phase. The effects of electrolytes on EC;SDS and ED;SDS were the same for the most part as those on EA;SDS and EB;SDS , respectively, and differences between EC;SDS and ED;SDS were essentially as much as those between EA;SDS and

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EB;SDS . Figure 10(A) shows interfacial potential of the two-phase system in the presence of SDS at various concentrations. At high concentrations of SDS, the potential reached 140 mV, a value quite close to EB;SDS with no electrolyte in phase w1. The potential greatly changed at 1–10 mM, close to the critical micelle concentration (CMC) of SDS. EB;SDS would thus quite likely arise from interface o/w1 in the presence of surfactant ions at interface o/w1. At low SDS, the potential was 170 mV, this being close to EA;SDS with no electrolyte in phase w1. EA;SDS should thus derive from interface o/w1 with tetrabutylammonium and chloride ions but with no or only a small amount of surfactant ion. Cationic surfactant was used for comparing the effects of surfactant charge on potential at the interface. With 2 mM CTAB as the surfactant instead of SDS and 3 mM picric acid instead of TBACl, the oscillation mode varied according to inorganic and organic electrolyte added to aqueous phase w1 (Fig. 11). Pulse direction was opposite that of SDS owing to the different electric charges. When no electrolyte was present in phase w1 (A), the lower potential of the ﬁrst oscillation (EA;CTAB ) was 120 mV and the upper potential (EB;CTAB ), 120 mV, EA;CTAB was greatly affected by organic cations but hardly so by inorganic or organic anions. On using a different inorganic cation EA;CTAB remained the same, except for FeðIIIÞ. EA;CTAB shifted to more positive potentials in the order, tetramethylammonium tetraethylammonium < tetrapropylammonium < tetrabutylammonium. The effects of an electrolyte on EB;CTAB clearly differed from those on EA;CTAB , EB;CTAB was greatly affected by organic ions and inorganic anions. EB;CTAB shifted to more positive potentials in the order, tetramethylammonium < tetraethylammonium tetrapropylammonium < tetrabutylammonium and to more negative potentials in the order, ﬂuoride < chloride < bromide iodide and acetate < propionate < nbutyrate < n-valerate. The effects of electrolytes on the interfacial potential of the two-phase system with CTAB, ED;CTAB , markedly differed from the case without CTAB, EC;CTAB [Fig. 11(B) and (C)]. The effects of electrolytes on EC;CTAB and ED;CTAB were basically those on EA;CTAB and EB;CTAB , respectively and differences between EC;CTAB and ED;CTAB were essentially as much as those between EA;CTAB and EB;CTAB . The interfacial potential of the two-phase system with CTAB at high concentrations reached 180 mV [Fig. 10(B)]. EB;CTAB thus quite likely results from interface o/w1 in the presence of surfactant ions. The potential changed quite considerably at 1 mM, the CMC of CTAB. At low concentrations of CTAB, the potential was at 120 mV. It follows then that the interfacial potential of the two-phase system greatly changes due to

FIG. 10 Effects of concentrations of SDS (A) and CTAB (B) on interfacial potential of a two-phase octanol–water system. (Ref. 27.)

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FIG. 11 Lower potential values, EA;CTAB , and upper potential values, EB;CTAB , of the ﬁrst oscillation at interface o/w1 of the octanol membrane (A), interfacial potential of a two-phase octanol– water system in the absence of CTAB, EC;CTAB (B), and those in the presence of 10 mM (in the case of inorganic electrolyte, 0.1 mM) CTAB, ED;CTAB (C). Abbreviations the same as in Fig. 9. (Ref. 27.)

CTAB at about the CMC. EA;CTAB should thus be determined by interface o/w1 with tetrabutylammonium and chloride ions but with no or only a small amount of surfactant ion.

2.

Characteristics and Behavior of Surfactants at Oil–Water Interfaces

To monitor the movement of surfactant ions in the octanol membrane visually, electrical potential oscillation across the octanol membrane was measured with eriochrome black T (EBT) as colored surfactant in phase w2 [20]. Migration of EBT from interface o/w2 toward bulk phase o could be seen during the induction period of oscillation. After EBT reached interface o/w1, the ﬁrst pulse of oscillation started. Thus, surfactant ions at interface o/w1 are indispensable for oscillation. Considerable convection in phase o and

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dynamic ﬂuctuation in interface o/w1 were evident during potential change from lower to upper potential of oscillation. When ion adsorption occurs in the ion-transfer voltammetry at the polarized oil–water interface, considerable convection of a bulk solution and dynamic ﬂuctuation in the interface may take place and polarographic maxima emerge on the voltammogram [29]. Considerable convection in phase o and dynamic ﬂuctuation in interface o/w1 should be indication of the absorption of surfactant ions on interface o/ w1. The transfer of EBT from phase o to phase w1 was seen during potential change from lower to upper potential of oscillation. Surfactant ions thus transfer across interface o/w1 and diffuse into phase w1 during potential change. Potential oscillation is induced by surfactant ions at an octanol–water interface and thus the features of surface active substances may determine whether or not potential oscillation occurs. Figure 12 shows potential across the octanol membrane in the presence of anionic surface active substances (SDS and sodium oleate, SO), a cationic surface active substance (CTAB), carboxylic acid (oleic acid), alkylphosphate (dioctyl phosphate, DOPH), alkylamine (oleylamine), phospholipid (dioctanoylphosphatidylcholine, PC), and alcohols (decanol and cholesterol) with ethanol in phase w2 [30]. On using SDS, CTAB, and SO as surface active substances, spontaneous potential oscillation with large amplitude was observed and continued for a few hours. The oscillation mode for SO was essentially that for SDS. The pulse direction for CTAB was opposite that for SDS or SO. SDS is an anionic surfactant and CTAB, a cationic surfactant. The electric charge of a surfactant thus determines the direction of the pulse. For oleic acid, DOPH and PC, only irregular pulses were observed, and pulse reproducibility was in all cases poor and the amplitude was quite small. Oscillation diminished rapidly subsequent to the ﬁrst pulse. With oleylamine, decanol, and cholesterol, no oscillation could be detected and only chaotic ﬂuctuation was observed. Surfactant molecules thus require charge on the hydrophilic group to be sufﬁciently dissociated and there must be sufﬁcient stability of the surface active substance layer. Transfer of charged surfactant ions across interface o/w1 can be controlled by external electrical force. Application of constant current to interface o/w1 facilitates or inhibits surfactant transfer and thus also changes the mode of potential oscillation. Figure 13 shows the apparatus for measuring potential at interface o/w1 with application of constant current to interface o/w1 by a conventional galvanostat connected to three Ag/ AgCl electrodes inserted into phases o, w1, and w2. Transfer of positive charge from phase o to phase w1 occurred through application of positive current, and that from phase w1 to phase o, negative current. Figure 14 shows potential oscillation with application of current at 0, þ2, þ10, 2, and 10 A. The potential of phase o was measured in reference to phase w1. Amplitude and oscillatory period were affected by applied current. Amplitude greatly increased in the order, 0 < 2 < 10 A. Application of þ2 and þ10 A caused a slight increase in amplitude. Oscillatory period increased in the order, þ10 < þ2 < 0 < 2 < 10 A. A negative current inhibits negative charge transfer from phase o to phase w1 and consequently inhibits dodecyl sulfate (DS) ion transfer. With negative current, DS ions should accumulate on this interface, with consequently longer induction period. Negative charge on the interface is concentrated by this accumulation and interfacial potential in the presence of the adsorption layer thus shifts to more negative values, causing negative shift in the lower potential. Accordingly, amplitude, the difference in upper and lower potentials, increases with negative current. In contrast, positive current facilitates the transfer of DS ions across interface o/w1, leading to a shorter oscillatory period. No accumulation of DS ion occurs at the interface and the structure of the electrical double layer at the interface is only slightly affected by positive current and thus, amplitude slightly so by positive current.

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FIG. 12 Electrical potential oscillation across the octanol membranes containing (A) 8 mM sodium dodecyl sulfate, (B) 2 mM cetyltrimethylammonium bromide, (C) 8 mM sodium oleate, (D) 8 mM oleic acid, (E) 8 mM dioctyl phosphate, (F) 10 mM dioctanoylphosphatidylcholine, (G) 8 mM oleylamine, (H) 8 mM decanol, and (I) 8 mM cholesterol, and 5 M ethanol in phase w2, and (A, C–I) 5 mM tetrabutylammonium chloride, or 3 mM picric acid (B) in the octanol phase. (Ref. 30.)

With application of positive current, the entire potential shifted to much more negative values and with positive current, to more negative values. These shifts should be the result of ohmic drop induced by electrical resistance of the octanol solution. There arises the question as to what causes the upper and lower potentials. The upper potential was found to be the potential of interface o/w1 in the presence of tetrabutylammonium chloride in phase o as well as the potential during the induction period. The upper potential should thus derive from a mixed Galvani potential of the transfer of

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FIG. 13 Apparatus for measuring electrical potential oscillation across the octanol membrane with application of current through the interface between phases o and w1: (a) octanol phase, (b) aqueous phase, (c) Ag/AgCl reference electrode, (d) KCl salt bridge, and (e) saturated KCl.

tetrabutylammonium and chloride ions. Inorganic and organic ions in phase w1 affect this mixed potential. The mechanism by which lower potential is generated would appear more complicated The following possibility is proposed: according to Gouy and Chapmann, when water containing a 1 : 1-type electrolyte comes into contact with a charged surface, the potential of the charged surface, ES , is 2kT 1 A pﬃﬃﬃﬃ sinh ES ¼ e C

ð1Þ

FIG. 14 Electrical potential oscillation across the octanol membrane with application of current at (A) 0, (B) þ2, (C) þ10, (D) 2, and (E) 10 A to the interface between phases o and w1.

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where k is the Boltzmann constant, T absolute temperature, e electric charge of electrolytes, surface charge density, and C, bulk concentration of electrolytes in the aqueous phase. A ¼ ð8N0 r kTÞ1=2 , where N is Avogadro’s number, r dielectric constant of the solvent, and 0 permittivity of free space. Assuming the formation of an adsorption layer of DS ions at the octanol–water interface, where is 0.01 A˚, C 100 mM, and r 78.3 (value for water), ES becomes 111 mV, which is in agreement with the potential obtained at the octanol–water interface of the two-phase system of an octanol–water in the presence of SDS, as seen in Fig. 10(A), though the actual system composition is complex. Cations that bind to surfactant ions present in phase w1 neutralize surface negative charge due to surfactant ions adsorbed at this interface and decrease in in Eq. (1). This decreases ES . Charge density at the interface decreases with increase in the strength of counterion binding. Counterion binding becomes stronger with greater cation charge or size. EB;SDS and ED;SDS in the presence of organic and inorganic cations thus were quite clearly noted in this study to increase with cation charge and size, as is apparent from Fig. 9. No interactions occurred between the surfactant ion and inorganic or organic anion in phase w1 and thus these ions had no effect on EB;SDS and ED;SDS . It follows from the above that the mechanism for electrical potential oscillation across the octanol membrane in the presence of SDS would most likely be as follows: dodecyl sulfate ions diffuse into the octanol phase (State I). Ethanol in phase w2 must be available for the transfer energy of DS ions from phase w2 to phase o to decrease and thus, facilitates the transfer of DS ions across this interface. DS ions reach interface o/w1 (State II) and are adsorbed on it. When surfactant concentration at the interface reaches a critical value, a surfactant layer is formed at the interface (State III), whereupon, potential at interface o/w1 suddenly shifts to more negative values, corresponding to the lower potential of oscillation. With change in interfacial tension of the interface, the transfer and adsorption of surfactant ions is facilitated, with consequent ﬂuctuation in interface o/ w1 and convection of phases o and w1 (State IV). Surfactant concentration at this interface consequently decreased. Potential at interface o/w1 thus takes on more positive values, corresponding to the upper potential of oscillation. Potential oscillation is induced by the repetitive formation and destruction of the DS ion layer adsorbed on interface o/w1 (States III and IV). This mechanism should also be applicable to oscillation with CTAB. Potential oscillation across the octanol membrane with CTAB is induced by the repetitive formation and destruction of the cetyltrimethylammonium ion layer adsorbed on interface o/w1. Potential oscillation is induced at interface o/w1 and thus drugs were previously added to phase w1 so as to cause changes in oscillation mode in the present study. Maeda et al. [29,31] studied the mechanism of potential oscillation across the nitrobenzene membrane by ion-transfer voltammetry. In spite of the different liquid membranes used in this study, their methods for clarifying the oscillation mechanism should be useful for obtaining more detailed information on the octanol membrane. This matter will be considered in a future article.

III.

ELECTRICAL RESPONSE OF THE LIQUID MEMBRANE TO DRUGS

A.

Hypnotics

Hypnotics induce states of drowsiness and facilitate the onset and continuation of sleep resembling natural sleep [32]. Central nervous system (CNS) functions, in addition to the maintenance of wakefulness, are usually depressed by these drugs. Barbiturates, clinically

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prescribed as hypnotic drugs, reversibly depress CNS. Possibly, they interact with central nerve cell membranes and exert a pharmacological effect. In this study, potential oscillation was measured in the presence of 100 mM sodium salts of barbital, allobarbital, phenobarbital, and amobarbital in phase w1 [19]. Their chemical structures are shown in Fig. 15. Amplitude and the oscillatory and induction periods were noted to depend on the particular hypnotic used. Amplitude decreased in the order, barbital > allobarbital > phenobarbital > amobarbital. The oscillatory period increased in the order, barbital < allobarbital < phenobarbital < amobarbital. Induction period increased in the order, barbital < allobarbital < phenobarbital < amobarbital. These parameters changed depending on drug concentration. Hypnotics at less than 5 mM had virtually no effect on the oscillation mode. Hypnotic ions in phase w1 should dissolve in the surfactant ion layer adsorbed on interface o/w1 owing to their hydrophobicity, which causes the charge density at interface o/w1 to change. Upper or lower potential of oscillation changes accordingly and thus also amplitude. The order of partition coefﬁcients was barbital < allobarbital < phenobarbital < amobarbital [33]. This should sufﬁce as an explanation for amplitude decrease in the order, barbital > allobarbital > phenobarbital > amobarbital. Hypnotic ions should be adsorbed at interface o/w1 with consequent decrease in interfacial tension. Interface geometry thus becomes ﬂat and the time required for surfactant ions to travel through the octanol phase increases, consequently making longer induction and oscillatory periods. Drug hydrophobicity and adsorption at an oil–water interface may thus be expected to affect amplitude and induction and oscillatory periods. The mode of potential oscillation thus provides drug permeability to cell membranes and drug adsorptive activity on receptors of cell membranes or other objective organs, and these parameters then determine drug pharmacological activity.

B.

Local Anesthetics

Local anesthetics interact with peripheral nerve cell membranes and exert a pharmacological effect [34]. Potential oscillation was measured in the presence of 20 mM hydrochlorides of procaine, lidocaine, tetracaine, and dibucaine (structures shown in Fig. 16) [19]. Amplitude and the oscillatory and induction periods changed, the extent depending on the

FIG. 15 Chemical structures of (a) sodium barbital, (b) sodium allobarbital, (c) sodium phenobarbital, and (d) sodium amobarbital.

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FIG. 16 Chemical structures of (a) procaine hydrochloride, (b) lidocaine hydrochloride, (c) tetracaine hydrochloride, and (d) dibucaine hydrochloride.

particular local anesthetic. Amplitude decreased in the order, procaine > lidocaine > tetracaine > dibucaine. The oscillatory period increased in the order, procaine lidocaine tetracaine < dibucaine. Induction period increased in the order, lidocaine < tetracaine < dibucaine. Amplitude and the oscillatory and induction periods were also determined by drug concentration. Local anesthetic ions in phase w1 are adsorbed at interface o/w1 owing to strong surface activity to alter amplitude and induction and oscillatory periods as also noted for hypnotics. The anesthetic activity of local anesthetics and hypnotic activity of barbiturates becomes greater with solubility in the hydrophobic phase in a biological system. These drugs are called ‘‘structurally nonspeciﬁc’’ [1]. Mode change in potential oscillation was found closely correlated with drug activity and consequently, attention was directed to the relationship between pharmacological activity and oscillation mode. Pharmacological activity increased with less amplitude, longer oscillatory period, and longer induction period [19]. The oscillation mode varied according to pharmacological activity and hence, measurement of potential oscillation across the liquid membrane should prove useful for studying quantitatively structure–activity relationships (QSAR) [35].

C.

Adrenergic and Antiadrenergic Agents

Drugs with pharmacological activity equivalent to that caused by adrenergic nerve stimulation are called adrenergic agents [36]. Epinephrine is representative of such drugs. Drugs that inhibit adrenergic nerves and block adrenergic receptors are antiadrenergic agents [37]. The pharmacological activity of adrenergic and antiadrenergic agents strongly depends on stereochemical structure rather than physicochemical properties and thus may be referred to as ‘‘structurally speciﬁc’’ [1]. These evidently differ from hypnotics and local anesthetics. Potential oscillation was measured in the presence of adrenergic agents (epinephrine hydrochloride, dopamine hydrochloride, isoproterenol hydrochloride and phenylephrine hydrochloride) and antiadrenergic agents (tolazoline hydrochloride, oxyprenlol hydrochloride, alprenolol hydrochloride and propranolol hydrochloride) in phase w1 [20]. Their structures are shown in Fig. 17. Within each drug group, the mode of potential oscillation in most cases was independent of pharmacological activity, though decrease in amplitude at higher pharmacological activity was apparent in some instances. A compar-

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FIG. 17 Chemical structures of (a) epinephrine hydrochloride, (b) dopamine hydrochloride, (c) isoproterenol hydrochloride, (d) phenylephrine hydrochloride, (e) tolazoline hydrochloride, (f) oxyprenolol hydrochloride, (g) alprenolol hydrochloride, and (h) propranolol hydrochloride.

ison of oscillation modes of adrenergic and antiadrenergic agents indicated the amplitude of antiadrenergic agents to apparently be less than that of adrenergic agents. Mode change reﬂects drug hydrophobicity, and less amplitude for antiadrenergic agents should be indication of greater hydrophobicity of antiadrenergic agents than adrenergic agents. Antiadrenergic agent association with receptors must occur through hydrophobic interactions between drug ions and a receptor so that association of adrenergic ions with a receptor is blocked owing to this greater hydrophobicity.

D.

Cholinergic and Anticholinergic Agents

Cholinergic agents primarily function to excite autonomic effector cells innervated by postganglionic parasympathetic nerves [38]. Anticholinergic agents inhibit acetylcholine on autonomic effectors innervated by postganglionic cholinergic nerves [39,40]. Cholinergic and anticholinergic agents are ‘‘structurally speciﬁc drugs’’ as in the case of adrenergic and antiadrenergic agents [1]. Potential oscillation was measured in the presence of cholinergic agents (acetylcholine chloride, carbamylcholine chloride, carbamyl- -methylcholine chloride, and acetyl- methylcholine chloride) and anticholinergic agents (tetramethylammonium chloride, tetraethylammonium chloride, succinylcholine chloride, hexamethonium chloride, scopolamine hydrobromide, atropine sulfate, homatropine hydrochloride, and tubocurarine chloride)

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in phase w1 [20]. Their structures are shown in Fig. 18. For each drug group, the mode of potential oscillation was generally independent of pharmacological activity. Amplitude of anticholinergic agents was less than that of cholinergic agents. Mode change reﬂects hydrophobicity of drugs, thus indicating the hydrophobicity of anticholinergic agents to exceed that of cholinergic agents. Anticholinergic agent association with receptors may possibly occur through hydrophobic interactions between drug ions and a receptor with consequent blockage of the association of cholinergic agents with receptors, on account of the greater hydrophobicity. E.

Antibiotics

Antibiotics are used to treat bacterial infection [41]. Some antibiotics act directly on cell membranes of micro-organisms, with consequent alteration of permeability and leakage of intracellular components. Antibiotics affect cell membranes and thus also the liquid membrane, with the possibility of change in oscillation. Antibiotics may be classiﬁed by chemical structure. Erythromycin, chloramphenicol, ampicillin, cefpodoxime proxetil, and doxycycline hydrochloride are antibiotics whose primary structures differ from each other (Fig. 19). Figure 20 shows potential oscillation across the octanol membrane in the presence of erythromycin at various concentrations [23]. Due to the low solubility of antibiotics in water, 1% ethanol was added to phase w1 in all cases. Antibiotics were noted to shift EB;SDS to more positive values. Other potentials were virtually unaffected by the antibiotics. On oscillatory and induction periods, there were antibiotic effects but reproducibility was poor. Detailed study was then made of EB;SDS . Figure 21 (a)–(d) shows potential oscillation in the presence of chloramphenicol, ampicillin, cefpodoxime proxetil, and doxycycline hydrochloride [21,23]. EB;SDS differed according to the antibiotic in phase w1 and shifted to more positive values with concentration. No clear relationship between activity and oscillation mode due to complexity of the antibacterium mechanism could be discovered but at least it was shown possible to recognize or determine antibiotics based on potential oscillation measurement. F.

Antitussives

Dextromethorphan hydrobromide [Fig. 22(a)] acts primarily on CNS components of the cough reﬂex [42]. Papaverine hydrochloride (b) acts directly on the bronchial tracts and exerts antitussive activity. Figure 23 (a) and (b) show potential oscillation in the presence of 0.7 mM dextromethorphan hydrobromide and 1 mM papaverine hydrochloride [21,22]. Compared to oscillation without substances in phase w1 (Fig. 4), EB;SDS shifted to more positive values with these drugs. EB;SDS resumed a very positive value upon exceeding 0.1 mM. Antitussives must have great hydrophobicity in order to interact with receptors on central nerve cell membranes or end organs and exert a pharmacological effect. A shift in EB;SDS at as low as 0.1 mM is possibly owing to the great hydrophobicity of antitussives. G.

Antimalarial Agent

Quinine hydrochloride [Fig. 22(c)], an antimalarial agent, acts primarily as a schizontocide, affecting sporozoites or preerythrocytic forms of malarial parasites [43]. Figure 23(c) shows potential oscillation with 1 mM quinine hydrochloride [21]. EB;SDS became very

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FIG. 18 Chemical structures of (a) acetylcholine chloride, (b) carbamylcholine chloride, (c) carbamyl- -methylcholine chloride, (d) acetyl- -methylcholine chloride, (e) tetramethylammonium chloride, (f) tetraethylamonium chloride, (g) succinylcholine chloride, (h) hexamethonium chloride, (i) scopolamine hydrobromide, (j) atropine sulfate, (k) homatropine hydrochloride, and (l) tubocurarine chloride.

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FIG. 19 Chemical structures of (a) erythromycin, (b) chloramphenicol, (c) ampicillin, (d) cefpodoxime proxetil, and (e) doxycycline hydrochloride.

FIG. 20 Electrical potential oscillation across the octanol membrane in the presence of (a) 0.1, (b) 1, and (c) 10 mM erythromycin and 1% ethanol in phase w1. Phase w2 and o the same as in Fig. 8. (Ref. 23.)

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FIG. 21 Electrical potential oscillation across the octanol membrane in the presence of (a) 0.1 mM chloramphenicol, (b) 0.1 mM ampicillin, (c) 0.1 mM cefpodoxime proxetil, and (d) 0.1 mM doxycycline hydrochloride and ethanol in phase w1. Phases w2 and o the same as in Fig. 8. Ethanol concentration: (a–c) 1%, (d) 0%.

much more positive at 0.1–10 mM, this being an indication that antimalarial agents can be recognized or determined based on potential oscillation measurement.

H.

Bitter Stomachic

Berberine chloride [Fig. 22(d)] is a medicinally effective ingredient of Phellodendri cortex and Coptidis rhizoma expressing astringent activity toward the mucous membrane as well as sterilizing activity toward gastrointestinal tracts [44]. It may thus be considered a membrane-acting drug. Figure 23(d) shows potential oscillation with berberine chloride [21]. EB;SDS became very much more positive with 0.1–10 mM berberine chloride. Though antitussives, antimalarial agent, and bitter stomachic have no direct effect on the physiochemical properties of biomembranes, they did so on the octanol membrane and altered the oscillation mode. Thus possibly, these drugs may be recognized or determined by measuring potential oscillation. The taste of bitter stomachic is indication of astringency. Antibiotics, antitussives, and antimalarial agent have bitterness, as well as bitter stomachic. The bitter taste of drugs is undesirable from a clinical standpoint, making oral administration difﬁcult, especially for babies and small infants. Thus, a method should be established for assessing drug bitter taste. The oscillation mode across the octanol membrane was changed by bitter drugs, and thus a study was made to evaluate the bitter taste of these drugs with a sweetening agent.

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FIG. 22 Chemical structures of (a) dextromethorphan hydrobromide, (b) papaverine hydrochloride, (c) quinine hydrochloride, and (d) berberine chloride.

I.

Sweetening Agents

Sugars are the most popular sweetening agents and their effects on oscillation mode were examined. Figure 24 shows potential oscillation with 100 mM sucrose, glucose, and maltose [21,22]. All sugars at 10 mM–1 M decreased EA;SDS . Potential during the induction period slowly changed to more negative values. Potential just after the contact of the aqueous and octanol solutions, E1 , and EB;SDS remained essentially unchanged. The sugars had hardly any effect on EB;SDS , since their chemical structures are without any charge. Sugar molecules slowly penetrate a lipid membrane [45] and may slowly become distributed within phase o near the interface during induction, affecting the physicochemical properties of the interface, with consequent change in potential with time. Thus potential during the induction period slowly changes to more negative values. The artiﬁcial sweeteners erythritol, sodium saccharin, and aspartame (Fig. 25) were also studied. Figure 26 shows potential oscillation in the presence of these artiﬁcial sweeteners [22]. The oscillation modes of these substances differed considerably. For erythritol above 10 mM, EA;SDS slightly shifted to more negative potentials. E1 and EB;SDS were essentially unaffected by this sweetener. Erythritol thus induces change in the oscillation mode in much the same way as sugars. At 1 mM–1 M sodium saccharin, E1 and EA;SDS shifted to more negative values with increase in its concentration. For aspartame at less than 10 mM, there was no change in potential.

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FIG. 23 Electrical potential oscillation across the octanol membrane in the presence of (a) 0.7 mM dextromethorphan hydrobromide, (b) 1 mM papaverine hydrochloride, (c) 1 mM quinine hydrochloride, and (d) 1 mM berberine chloride in phase w1. Phases w2 and o the same as in Fig. 8.

FIG. 24 Electrical potential oscillation across the octanol membrane in the presence of (a) 100 mM sucrose, (b) 100 mM glucose, and (c) 100 mM maltose in phase w1. Phases w2 and o the same as in Fig. 8.

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FIG. 25 Chemical structures of (a) erythritol, (b) sodium saccharin, and (c) aspartame.

Mode differences and similarities in this study were due to chemical structures. Erythritol is a sugar alcohol with structure very much like those of sugars and thus the oscillation mode was basically the same as that in the case of sucrose, glucose, and maltose. Aspartame is an amino acid ester having no charge and thus its effect on the octanol membrane may possibly be essentially the same as those of sugars, though the decrease in EA;SDS at high concentrations is still unknown, since aspartame at above 10 mM cannot dissolve in water. Aspartame at less than 10 mM thus causes no change in potential. For sodium saccharin, amplitude decreased even at low concentration, as in the case of bitter substances. An aqueous solution of 1 M sodium saccharin exhibits bitterness rather than sweetness, though a low concentration of saccharin solution has a sweet taste [46]. This

FIG. 26 Electrical potential oscillation across the octanol membrane in the presence of (a) 10 mM erythritol, (b) 10 mM sodium saccharin, and (c) 10 mM aspartame in phase w1. Phases w2 and o the same as in Fig. 8. (Ref. 22.)

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similarity in oscillation mode for sodium saccharin and bitter substances is a point of considerable signiﬁcance. Though no quantitative assessment of the strength of sweetness with change in oscillation mode was made in this study, the mode was found to reliably reﬂect taste difference. Figure 27 shows potential oscillation in the presence of quinine hydrochloride and sucrose as a mixture [21]. The mean value of low potentials of the initial ﬁve pulses was taken as EB;SDS . In the presence of 1 mM quinine hydrochloride without sucrose, in contrast to oscillation without any substance in phase w1, EB;SDS was more positive by 56 mV and E1 and EA;SDS , slightly more negative. This change was due only to quinine hydrochloride. With sucrose in addition to quinine hydrochloride, EB;SDS shifted to more negative values. With 1 mM quinine hydrochloride and 500 mM sucrose, the oscillation mode was basically the same as with only 500 mM sucrose. The taste of aqueous quinine hydrochloride solution with and without sucrose was examined in four volunteers (males, aged 23–28). All considered 1 mM quinine hydrochloride quite bitter, 1 mM quinine hydrochloride and 100 mM sucrose bitter-sweet, and 1 mM quinine hydrochloride and 500 mM sucrose sweet though bitter. Sucrose is thus shown to lessen the bitterness of quinine hydrochloride solution, as generally already known. Quinine hydrochloride and sucrose are bitter and sweet substances, respectively, and thus a sweet substance may alter oscillation, when a bitter substance is present, to that corresponding to a sweet substance. Other drugs in combination with a sweetening agent were also studied, dextromethorphan hydrobromide [21], doxycycline hydrochloride [21], erythromycin [23], chloramphenicol [23], ampicillin [23] and cefpodoxime proxetil [23] as bitter drugs and simple syrup (2.5 M sucrose solution, used as a ﬂavoring agent prescribed by The Japanese Pharmacopoeia) as sweetening agent. The most probable mechanism for electrical potential oscillation across the octanol membrane in the presence of a bitter drug and simple syrup is proposed as follows:

FIG. 27 Electrical potential oscillation across the octanol membrane in the presence of 1 mM quinine hydrochloride and sucrose at (a) 0, (b) 100, and (c) 500 mM in phase w1. Phases w2 and o the same as in Fig. 8. (Ref. 21.)

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potential oscillation is induced by the repetitive formation and destruction of the DS ion layer adsorbed at interface o/w1. EB;SDS corresponds to the potential in State II. Bitter drug molecules having high hydrophobicity penetrate the DS ion layer and/or are adsorbed onto the interface and neutralize the charge or reduce the charge density of this layer, thus making EB;SDS more positive. With the previous addition of sucrose or simple syrup to phase w1, sucrose molecules penetrate this layer in spite of the much lower hydrophobicity of sucrose and expel bitter drug molecules, being present in much greater number. A sweet substance thus restores EB;SDS , causing the oscillation mode to be essentially the same as with only sucrose. The bitterness of a mixture of 1% ethanol and erythromycin, chloramphenicol, ampicillin, and cefpodoxime proxetil at 0.1, 1, and 10 mM was assessed by eight volunteers (males and females, aged 21–25) [23]. The score for a mixture of 1 mM chloramphenicol and 1% ethanol was deﬁned at 3, and that of 1% ethanol, 0. The score of 10 mM erythromycin was greatest and that of 0.1 mM ampicillin, smallest. At 1 mM, bitterness becomes greater in the order, cefpodoxime proxetil ¼ ampicillin < chloramphenicol < erythromycin. Figure 28 shows EB;SDS plotted against the bitterness score. For the same antibiotic, EB;SDS was more positive with increase in bitterness score and thus, potential oscillation would appear to depend on the degree of bitterness. Variation in EB;SDS in the absence of antibiotic or ethanol in phase w1 was within 4.4 mV (n ¼ 5) [21]. All values of antibiotic EB;SDS differed, the extent in any case exceeding the above value of 4.4 mV and thus should be considered signiﬁcant. The extent of bitterness is closely correlated with hydrophobicity [47]. Drug hydrophobicity may possibly affect the mode of potential oscillation. The mode of potential oscillation thus provides drug bitterness. An EB;SDS –

FIG. 28 Correspondence of the lower potential of the ﬁrst pulse, EB;SDS , in the presence of antibiotics to bitterness scores of aqueous solution containing antibiotics and 1% ethanol in phase w1: (*) ampicillin, (&) erythromycin, (~) chloramphenicol, and (!) cefpodoxime proxetil. Phases w2 and o the same as in Fig. 8. (Ref. 23.)

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bitterness score curve such as in Fig. 28 may serve as a calibration curve of bitterness and be useful for evaluating drug bitterness.

IV.

CONCLUSIONS

The features of the octanol membrane are described in terms of drug response. This membrane was found useful for evaluating drug features such as pharmacological activity and bitter taste, possibly owing to its solubility in a lipid phase such as a biomembrane and adsorption at a biomembrane receptor, both these parameters determining drug afﬁnity toward a biomembrane. Measurement of potential oscillation across the octanol membrane may thus be applicable for clarifying what interactions occur between a drug and biomembrane, studying structure–activity relationships and designing new drugs. Measurement of potential oscillation may accordingly be expected to serve as a new and highly effective method for pharmaceutical analysis.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.

J. J. Zimmerman and S. Feldman, in Principles of Medicinal Chemistry (W. O. Foye, ed.), Lea and Febiger, Philadelphia, 1974, pp. 8–52. M. Dupeyrat and E. Nakache. Bioelectrochem. Bioenerg. 5:134 (1978). K. Yoshikawa and Y. Matsubara. Biophys. Chem. 17:183 (1983). K. Arai, F. Kusu, and K. Takamura. Chem. Lett. 1990:1517 (1990). T. Kawakubo and K. Fukunaga. Ferroelectrics 86:257 (1988). H. Suzuki and T. Kawakubo. Biophys. Chem. 45:153 (1992). K. Miyamura, H. Morooka, K. Hirai, and Y. Gohshi. Chem. Lett. 1990:1833 (1990). K. Miyamura, H. Yoshihisa, K. Hirai, and Y. Gohshi. J. Chem. Soc. Faraday Trans. 91:895 (1995). S. Sutou, H. Yoshihisa, K. Miyamura, and Y. Gohshi. J. Coll. Interface Sci. 187:544 (1997). S. Sha, P. J. Abatti, K. Iko, T. Nakamoto, and T. Moriizumi. Jpn. J. Appl. Phys. 30:L1435 (1991). S. Sha, T. Nakamoto, and T. Moriizumi. Jpn. J. Appl. Phys. 30:L1774 (1991). S. Sha, T. Nakamoto, and T. Moriizumi. Jpn. J. Appl. Phys. 32:L151 (1993). T. Yoshidome, T. Higashi, M. Mitsushio, and S. Kamata. Chem. Lett. 1998:855 (1998). M. Igawa, K. Ohtani, S. Horiguchi, and H. Okochi. Chem. Lett. 1997:923 (1997). N. Nakajo, K. Yoshikawa, M. Shoji, and I. Ueda. Biochem. Biophys. Res. Commun. 167:450 (1990). S. Svirschevsky, O. Iordache, and P. T. Frangopol. Rev. Roum. Biochim. 28:11 (1991). K. Arai, F. Kusu, and K. Takamura. Denki Kagaku 58:665 (1990). K. Arai, F. Kusu, and K. Takamura. Bunseki Kagaku 41:775 (1990). K. Arai, S. Fukuyama, F. Kusu, and K. Takamura. Bioelectrochem. Bioenerg. 33:159 (1994). K. Arai, F. Kusu, and K. Takamura, in Liquid–Liquid Interfaces: Theory and Methods (A. G. Volkov and D. W. Deamer, eds.), Marcel Dekker, New York, 1996, pp. 375–400. K. Arai, S. Fukuyama, F. Kusu, and K. Takamura. Denki Kagaku 63:1183 (1995). K. Arai, F. Kusu, and K. Takamura. Anal. Chim. Acta 365:279 (1998). K. Arai and F. Kusu. Trans. IEE Japan 119-E:544 (1999). S. Takahashi, I. Tsuyumoto, T. Kitamori, and T. Sawada. Electrochim. Acta 44:165 (1998). K. Arai, K. Watanabe, and F. Kusu. Bunseki Kagaku 47:1093 (1998). K. Arai. Bunseki Kagaku 45:41 (1996). K. Arai, S. Fukuyamna, F. Kusu, and K. Takamura. Electrochim. Acta 40:2913 (1995).

Electrical Potential Oscillation 28. 29. 30. 31. 32. 33. 34.

35. 36. 37. 38. 39. 40. 41.

42.

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727

H. Yoshihisa, K. Miyamura, and Y. Gohshi. Nippon Kagaku Kaishi 1995:95 (1995). K. Maeda, S. Kihara, M. Suzuki, and M. Matsui. J. Electroanal. Chem. 295:183 (1990). K. Arai, F. Kusu, and K. Takamura. Denki Kagaku 65:452 (1997). K. Maeda. Rev. Polarogr. 46:35 (2000). S. C. Harvey, in The Pharmacological Basis of Therapeutics, (A. G. Gilman, L. S. Goodman, T. W. Rall, and F. Murad, eds.), 7th edn. Macmillan, New York, 1985, pp. 339–371. C. Hansch and S. M. Anderson. J. Med. Chem. 10:745 (1967). J. M. Ritchie and N. M. Greene, in The Pharmacological Basis of Therapeutics (A. G. Gilman, L. S. Goodman, T. W. Rall, and F. Murad, eds.), 7th edn. Macmillan, New York, 1985, pp. 302–321. C. Hansch, in Drug Design (E. J. Arie¨ns, ed.), Academic Press, New York, 1971, pp. 271–342. N. Weiner, in The Pharmacological Basis of Therapeutics (A. G. Gilman, L. S. Goodman, T. W. Rall, and F. Murad, eds.), 7th edn. Macmillan, New York, 1985, pp. 145–180. N. Weiner, in The Pharmacological Basis of Therapeutics (A. G. Gilman, L. S. Goodman, T. W. Rall, and F. Murad eds.), 7th edn. Macmillan, New York, 1985, pp. 181–214. P. Taylar, in The Pharmacological Basis of Therapeutics (A. G. Gilman, L. S. Goodman, T. W. Rall, and F. Murad eds.), 7th edn. Macmillan, New York, 1985, pp. 100–109. P. Taylar, in The Pharmacological Basis of Therapeutics (A. G. Gilman, L. S. Goodman, T. W. Rall, and F. Murad eds.), 7th edn. Macmillan, New York, 1985, pp. 110–129. N. Weiner, in The Pharmacological Basis of Therapeutics (A. G. Gilman, L. S. Goodman, T. W. Rall, and F. Murad eds.), 7th edn. Macmillan, New York, 1985, pp. 130–144. M. A. Sande and G. L. Mandell, in The Pharmacological Basis of Therapeutics (A. G. Gilman, L. S. Goodman, T. W. Rall, and F. Murad eds.), 7th edn. Macmillan, New York, 1985, pp. 1066–1094. J. H. Jaffe and W. R. Martin, in The Pharmacological Basis of Therapeutics (A. G. Gilman, L. S. Goodman, T. W. Rall, and F. Murad eds.), 7th edn. Macmillan, New York, 1985, pp. 491– 531. L. T. Webster, in The Pharmacological Basis of Therapeutics (A. G. Gilman, L. S. Goodman, T. W. Rall, and F. Murad eds.), 7th edn. Macmillan, New York, 1985, pp. 1029–1048. T. Sollman, in A Manual of Pharmacology and Its Application to Therapeutics and Toxicology, 8th edn. W. B. Saudners, Philadelphia, 1957. S. Iiyama, K. Toko, K. Hayashi, and K. Yamafuji. Agric. Biol. Chem. 53:675 (1987). H. R. Moskowitz and L. Klarman. Chem. Senses Flavor 1:411 (1975). H. D. Belitz, W. Chen, H. Jungel, H. Stepﬂ, R. Treleano, and H. Wieser. Chem. Ind. 1983:23 (1983).

31 Transfer Mechanisms and Lipophilicity of Ionizable Drugs FRE´DE´RIC REYMOND Laboratoire d’Electrochimie, De´partement de Chimie, Ecole Polytechnique Fe´de´rale de Lausanne, Lausanne, Switzerland

I. A.

INTRODUCTION Lipophilicity and Drug Action

The action of a drug, when administered to animals or humans, is usually divided into two phases: the pharmacokinetic phase and the pharmacodynamic phase [1]. The pharmacokinetic phase comprises all processes of absorption, distribution, metabolism, and clearance [2]. The pharmocodynamic phase includes all biological processes involved in the interaction of the drug with its target (receptor, enzyme, etc.) [3]. In other words, the pharmacokinetic phase is concerned with the effects exerted by a drug upon a biological system, whereas the pharmacodynamic phase represents the effects exerted by a biological system upon a drug [4,5]. It is the balance of the performances of a compound in these two phases that determines the success of a drug. Whereas attention is often focused on the interaction of a drug with its receptor, the signiﬁcance of drug delivery has been largely underestimated. Due to the complex structure of membranes [6–8], the mechanisms of their interactions with bioactive compounds may be more intricate than those governing ligand–receptor interactions [9,10]. Indeed, before it can exert its effects, a drug must reach its target site in a concentration sufﬁcient to permit its biological activity. Actually, it should ﬁrst dissolve (when formulated in a solid form), then avoid being metabolized or blocked during its displacement and cross over several barriers, such as biological membranes. Furthermore, if it needs to be transported by blood, the drug may undergo metabolism, protein binding, or clearance, and must be able to desorb from blood proteins. These numerous obstacles limit the permeation of drugs into cellular barriers and thus their delivery to the target site [11]. Generally speaking, the properties that govern the behavior of a drug in the pharmacokinetic phase can be broadly divided into its physiochemical properties and its actual chemical structure. The determination of drug–biological membrane interactions and the measurements of physicochemical properties, particularly lipophilicity, serve to model many aspects of drug disposition [12]. They are essential to overcome the delivery problems that limit the efﬁciency of a drug [13–15], and constitute the gist of the present chapter.

Current afﬁliation: DiagnoSwiss, Monthey, Switzerland. 729

730

B.

Reymond

Membrane Transport

Because they act as semipermeable barriers controlling movement into and out of cells, biological membranes [16] play a central role in the structure and functions of all living organisms (e.g., reception and transfer of information, energy transformations, maintenance of salt composition and acid–base equilibrium, regulation of biochemical processes and removal of metabolic products from the cell) [17,18]. Such control results in highly signiﬁcant differences between intra- and extracellular concentrations of numerous solutes. The resultant concentration gradient is of major importance in membrane transport, and it also leads to an electrochemical polarization of the membrane (with the inside of the cell being negatively charged compared to the outside). Except the special case of large particles and proteins that enter the cell by endocytosis [19], the transport of molecules across biomembranes can be divided into two categories [20]: active and passive transport. 1. Active Transport Active transport uses metabolic energy to move molecules against their electrochemical gradient, and it it always mediated by carrier proteins (‘‘carrier-mediated’’ transport). The carrier proteins bind their substrate outside the cell membrane, inducing a conformational change which allows the substrate to pass through the protein and out through a newly created opening into the cell [21]. Nevertheless, when this process does not require any metabolic energy, the carrier-mediated transport is not an activated process and, hence, it enters into the passive transport category. For clarity, Fig. 1 differentiates between these various types of transport. A well-known example of active transport is the sodium–potassium pump that maintains the imbalance of Naþ and Kþ ions across cytoplasmic membranes. Here, the movement of ions is coupled to the hydrolysis of ATP to ADP and phosphate by the ATPase enzyme, liberating three Naþ out of the cell and pumping in two Kþ [21–23]. Bacteria, mitochondria, and chloroplasts have a similar ion-driven uptake mechanism, but it works in reverse. Instead of ATP hydrolysis driving ion transport, Hþ gradients across the membranes generate the synthesis of ATP from ADP and phosphate [24–27].

FIG. 1 Differentiation between active and passive transport. (Adapted from Ref. 46.)

Transfer Mechanisms and Lipophilicity

731

Otherwise, the energy stored in ion gradients drive many active transport systems. The free energy released during the movement of an organic ion down its electrochemical gradient is used as the driving force to pump other solutes uphill, against their own electrochemical gradient [28–30]. The regulation of the intracellular pH is made in most cells by proteins which use the energy stored in the Naþ gradient to reduce the proton concentration [31–34]. Either Hþ is directly transported out of the cell or HCO 3 is brought into the cell to neutralize Hþ . In intestinal cells, the transcellular transport of glucose follows a similar mechanism [35,36]. Likewise, such a process is used in the red blood cell membrane to exchange Cl for HCO 3 conditioning deeply the movement of CO2 in the blood [37,38]. Nevertheless, active transport is mainly restricted to endogeneous compounds. 2.

Passive Transport

Unlike in active transport, a species moves down its electrochemical or concentration gradient in passive diffusion processes. No metabolic energy is expended and the transfer often operates thanks to channel proteins. These proteins form a water-ﬁlled pore which allows the ion to pass inside it through the membrane. Such pores are usually closed by a ‘‘gate’’ which opens in response to a stimulus to the membrane, such as a change in membrane potential (voltage-gated channels) a mechanical stress (mechanically gated channel), or the binding of a ligand (ligand-gated channels) [39–45]. These channels are responsible for the electrical excitability of muscle cells, and they mediate most forms of electrical signaling in the nervous system. Either they convert chemical signals to electrical signals, or the reverse. However, the most common ion channels are those that are permeable mainly to Kþ [46]. They consist of simple pores that do not need to be stimulated and are found in almost all animals cells. By letting Kþ diffuse inside the cell, the role of these channels is to maintain the membrane potential and to balance the negative charges carried by the organic molecules that are conﬁned inside the cell. Besides, these negative charges prevent the Kþ ion from leaking out down its concentration gradient, so that a thermodynamic equilibrium is reached, which can be quantitatively expressed by the Nernst equation at the ITIES [see Section II.B, Eq. (9)]. The transport of exogenous chemical (xenobiotics) and thus of the majority of common drugs is a passive process. Consequently, the transmembrane ﬂux depends on the pKa of the drug, on the pH and on the overall concentration gradient across the membrane. It is then governed mainly by lipophilicity [10] and, hence, lipophilicity is the major factor in determining drug disposition characteristics. Nevertheless, drug transport may be conditioned in a very complicated manner by various membrane interactions, among which the following have been recently reported: speciﬁc interactions with the membrane’s interior [47]; dynamic control of solute–membrane interactions [9]; the inﬂuence of pH [48] on the formation of solute-membrane complexes, either by shift in ionization constants [49–51] or by modiﬁcations of the membrane’s permeability [52]; and the interaction of solutes with ion channels [53]. Whereas the relationship of solute permeability with lipophilicity has been studied in a large number of in vivo systems (including intestinal absorption models [54,55], blood– brain [56–58] and blood–nerve [59] barrier models, and cell culture models [60–62], to name just a few), numerous in vitro model systems have been developed to overcome the complexity of working with biological membranes [63–66]. Apart from oil–water systems that are discussed here, the distribution of a solute between a water phase and liposomes is

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the simplest model used to explore the ability of a drug candidate to cross biological membranes [67–71]. Multicompartment models are used to study the kinetics of drug transfer between two immiscible phases [72–74]. Phopholipid bilayers, phospholipid vesicles, biomembrane vesicles, and suspensions of organelles such as mitochondria or chloroplasts have all been used to study the electrical properties of biological membranes [75,76]. The latter studies [18] demonstrate that organic ions can partition into the bilayer core as a result of their hydrophobic character and their large size [77,78]. However, until recently [79–81], the concept of organic ionic species partitioning was largely underestimated. As will be described in detail below, solute distribution in biphasic systems can be modulated by application of a Galvani potential difference across the interface, thereby leading to the transfer of species from one phase to the other. Therefore, in electrochemical terms, passive transfer simply means the partition across an interface, mediated by a potential-driven process.

C.

Importance of Ion Partitioning

In the passive transport mechanism, it is traditionally assumed that highly water-soluble molecules and, in particular, organic ionic species can only cross biological membranes in their nonionized form. If this accepted dogma has been veriﬁed many times, recent studies have yielded unexpected results suggesting the possibility of a signiﬁcant passive transfer of organic ions [82–85]. Furthermore, recent studies [86–88] reveal the pharmacological relevance of drug partitioning in their ionized form by measurements in the water–octanol system. Indeed, three different aspects should be put forward: 1.

2.

3.

In particular, for basic compounds, ionized at physiological pH, ion-pair formation may be favored by charge–charge interactions with the acidic phospholipid headgroups in many tissue membranes [5], as for amlodipine [89,90] (a dihydropyridine calcium channel blocker), azithromycin [91] (an antibiotic) or disobutamide [92] (an antiarrhythmic). Likewise, the extent of tissue distribution may be affected by drug binding to plasma proteins [93]. This is notably the case of the lipophilic base zamifenacin [94] (an antimuscarinic agent) or of acidic drugs which bind to plasma albumin [95]. Similarly, the binding of antigenic peptides to antibodies has been explored by molecular dynamic calculations [96]. All the above interactions induce a pKa shift of pharmacological and biochemical signiﬁcance [49,97–99]. Ion-partitioning may favor drug transport. This has been recently demonstrated for the anti-inﬂammatory drug azapropazone [86], which is taken here as example. Due to the very low value of its acidic pKa , it exists as a zwitterion at stomachic pH and as a mixture of anion and zwitterion at physiological pH. The log Poct of the zwitterion is 1.78, suggesting that azapropazone can permeate the gastric mucosa. Molecules of zwitterionic nature could then be an approach towards the design of highly permeable drugs. Ionization may be used to counteract disregulation of pH levels (which is maintained through the concerted action of Naþ =Hþ antiporters, Cl =HCO 3 exchangers, and other channels and/or transporters that exist within the plasma membrane of eucaryotic cells [32,100,101]). Indeed, it has been shown that ionophores (such as nigericin [102]) can lower the intracellular pH, while weak acids (such as propionic acid) can promote acidiﬁcation. Likewise, nonsteroidal anti-

Transfer Mechanisms and Lipophilicity

733

inﬂammatory drugs (NSAIDs), such as azapropazone or piroxicam [86,103], and antirheumatic agents, such as chloroquine [104] or tenidap [105,106], can modulate intracellular pH. From the latter studies, it has been concluded that the net effect of the drug (which is actually an alkalinzation of the extracellular ﬂuids in the present case ) is dependent on the pKa of the molecule, on the partition coefﬁcient of the free acid species and on the afﬁnity of the anion for its transporter [107], as illustrated by the model shown in Fig. 2. In summary, the deﬁnitive way of deciding if either the neutral or one of the ionized forms of a drug is biologically active is to study their comparative activity as a function of pH [108]. However, the pharmacological and biochemical interpretation that can be deduced from quantitative structure–activity relationship (QSAR) [109,110] studies of ionizable drugs is often hampered by the limited understanding of the partitioning and permeation of ionic compounds. Consequently, it is now necessary to reject the hypothesis of nonpartitioning of ions, as well as to better understand the transfer mechanisms of ionizable drugs and their regulation processes in cells and tissues. The present chapter therefore describes the experimental methodologies enabling one to overcome these shortcomings and outlines the lipophilicity parameters that are used nowadays to assess the biological behavior of drugs.

II.

THEORETICAL BACKGROUND

A.

Lipophilicity

Lipophilicity is a molecular property expressing the relative afﬁnity of solutes for an aqueous phase and an organic, water-immiscible solvent. As such, lipophilicity encodes most of the intermolecular forces that can take place between a solute and a solvent, and represents the afﬁnity of a molecule for a lipophilic environment. This parameter is commonly measured by its distribution behavior in a biphasic system, described by the partition coefﬁcient of the species X, PX . Thermodynamically, PX is deﬁned as a constant relating the activity of a solute in two immiscible phases at equilibrium [111,112]. By convention, PX is given with the organic phase as numerator, so that a positive value for log PX reﬂects a preference for the lipid phase:

FIG. 2 Model explaining the ability of tenidap to lower intracellular pH. Step 1: drug dissociation dictated by its pKa value; Step 2: entry of the conjugate acid of tenidap into the cell by diffusion, followed by reestablishment of the acid–base equilibrium; Step 3: transport of tenidap anion out of the cell, activated by an anion transporter. (Reprinted from Ref. 107.)

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Reymond

PX ¼

aoX Xo coX ¼ awX Xw cwX

ð1Þ

where X is the activity coefﬁcient of compound X, and where PX can be approximated by the concentrations in dilute solutions [113]. On the other hand, the ratio of total concentrations of ionized and nonionized species between both phases is named ‘‘distribution coefﬁcient’’ (symbolized as D). It is often referred to as an effective or apparent partition coefﬁcient and, in concentration terms, it is mathematically deﬁned as: n X

D¼

coXtot cwXtot

¼

coXz0þi

i¼0

n X

ð2Þ cwXz0þi

i¼0 z0

where X represents the most acidic (or deprotonated) form of the substance X and Xzn its most basic (or protonated) form. Log D varies considerably with pH, because it determines the degree of ionization of the solute, causing its redistribution between the two phases. In the pH region where a substance is neutral, D ¼ PX , and the substance is usually maximally partitioning in the organic phase. However, as the afﬁnity of a charged species is generally greater for the aqueous phase (because of hydrogen-bonding and dipolar stabilization), D decreases upon ionization, while PX remains the same. As schematically illustrated in Fig. 3 for a weak monobase, the log D vs. pH plot is normally a sigmoid curve (although deviating behaviors have been reported [114–116]). Of course, the shape of the lipophilicity proﬁles becomes much more complicated for molecules with multiple ionized forms. Nevertheless, the partition coefﬁcients may be calculated from the distribution coefﬁcient using the general equation [113]: log D ¼ log PX þ correction term

ð3Þ

FIG. 3 Calculated distribution proﬁle (log D þvs. pH) for a generic monobase B with þ pKaw ¼ 9; log PB ¼ 2; log PBH ;0 ¼ 3, and ðlog PBH B;0 Þ ¼ 5 (bold plain line). The distribution proﬁle when the partitioning of the charged species is neglected is also given for comparison (dashed line).

Transfer Mechanisms and Lipophilicity

735

General equations may be derived to express the above correction term, and it is easy to demonstrate that, in the case of a monoprotic substance, the lipophilicity proﬁle on the entire pH range reads:

w w ð4Þ log D ¼ log PX þ PXH 10ðpKa pHÞ log 1 þ 10ðpKa pHÞ where XH stands for the neutral form of an acid, but for the protonated form of a base, and where the dissociation constant is deﬁned as: c c þ ð5Þ Ka ¼ base H cacid Hence, two drugs of similar log PX may differ greatly in log D at physiological pH, with profound consequences for their pharmacological activity. As a consequence, log PX values of ionizable compounds are often quoted at pH 7.4, and equations similar to those above are used in pH-metric techniques [117–124] to determine either log PX or log D. A compilation of the principal relationships linking partition and distribution coefﬁcients is available in Refs. 125 and 126. Experimentally, the most commonly used system for determining lipophilicity of drug molecules is the buffered water–octanol partition system. Using n-octanol (OCT) as a model for biological membranes is viewed as the best all-round compromise readily available [127]. However, since octanol is able to accept hydrogen bonds almost as well as water, hydrophilicity may not be expressed by partitioning in OCT. Consequently, octanol gives higher lipophilicity values than reﬂected in membrane partitioning and disposition characteristics. Other solvents such as alkanes or 1,2-dichloroethane (DCE) can yet provide insights into these processes. Apart from the above considerations, the distribution of a solute between two immiscible phases is always dependent upon temperature [128–130], solubility [131,132], resistance to degradation [133–135], solvent purity [130], and phase composition [136,137] (several reviews [130,132,138] give full details about the impact of these parameters on log PX determination). Nevertheless, ionization often complicates the measurement and interpretation of partition coefﬁcient because of the charge distribution it generates across the interface. It is therefore necessary to brieﬂy recall the fundamentals of partition thermodynamics at the ITIES. B.

Partition Equilibrium of Ions in Biphasic Systems

When an aqueous phase (noted w) is brought in contact with a second immiscible phase (noted o), the different species dissolved in one or the two phases spontaneously distribute depending on their hydrophilic–lipophilic balance until the thermodynamic equilibrium is reached. The distribution of the charged species generates an interfacial region, in which the electrical ﬁeld strength differs from zero, so that an electrical Galvani potential difference, wo , is established across the interface: wo ¼ w o

ð6Þ

where is the inner (or Galvani) potential of the respective phase. At constant pressure and temperature, after the building up of the interface, thermodynamic equilibrium is obtained when the electrochemical potentials for each component distributed between the two phases are equal:

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Reymond

~ oI ¼ ~ wI

ð7Þ

This equation can further be developed into: w w 0;o o o 0;w I þ RT ln aI þ zI F ¼ I þ RT ln aI þ zI F

ð8Þ

0I

representing the standard chemical potential and aI the activity of I in its respecwith tive phase. The Galvani potential difference across the ITIES is thus: o o 0 RT a RT c ð9Þ wo ¼ wo 0I þ ln wI ¼ wo 0I þ ln wI zI F zI F aI cI 0

where cI is the concentration of the ion I in both phases, and where wo 0I and wo 0I are called the standard and formal transfer potentials, respectively. This equation is often called the Nernst equation for the ITIES, and the term wo 0I is 0;w!o expressed on a potential scale, since, in fact the standard Gibbs energy of transfer Gtr;I 0;w!o is equal to the difference between the standard Gibbs energy of by deﬁnition, Gtr;I solvation I0;o and the standard Gibbs energy of hydration 0;w I : 0;w!o Gtr;I 0;o 0;w I ¼ I ð10Þ wo 0I ¼ zI F zI F Moreover, as the ratio aoI =awI is by deﬁnition the partition coefﬁcient of I, PI , this parameter can be deﬁned by putting into evidence the ratio of the ion activities in the Nernst equation: z F w z F wo 0I ¼ log PI;0 þ I w

log PI ¼ I ð11Þ 2:3RT o 2:3RT o where log PI;0 is the standard partition coefﬁcient of I. This equation shows that, contrary to the partition of neutral species for which log PN is a unique quantity related by Eq. (12) to its standard Gibbs energy of transfer, the partition of ionic species is potential dependent, and log PI;0 represents the proportion of ions present in each phase if the interface is not polarized: log PN ¼

0;w!o Gtr;N RT

ð12Þ

This fundamental parameter quantiﬁes the relative afﬁnity of an ion in the two phases, but it is not directly accessible experimentally because it is associated with a single ionic 0;w!o component. Therefore, to make Gtr;I or log PI;0 amenable to direct measurement, an extrathermodynamic assumption must be introduced such as the Grunwald or TATB assumption [139], which states that the cation and the anion of tetraphenylarsonium tetraphenylborate (TPAsþ TPB or TATB) have equal standard Gibbs energies for any pair of solvents [140,141]: 1 0;w!o 0;w!o 0;w!o Gtr;TPATPB Gtr;TPAs þ ¼ Gtr;TPB ¼ 2

ð13Þ

This allows us to ﬁx the zero of the absolute Galvani potential scale and then to deduce 0;w!o . Gtr;I It is important to notice that the standard Gibbs energy of transfer refers to the transfer from pure w to pure organic o. It is therefore different from the Gibbs energy of partition, which refers to the transfer between mutually saturated solvents. Nevertheless, in the case of solvents of low miscibility such as water–DCE or water–nitrobenzene, the transferred ion is practically not hydrated by water present in the organic phase, so that

Transfer Mechanisms and Lipophilicity

737

the ionic standard Gibbs energy of transfer is considered equal to the ionic standard Gibbs energy of partition [142]. Consequently, both terms will be used without differentiation in the above solvent systems.

C.

Thermodynamics for the Partition of Ionizable Compounds

The amperometric determination of the partition coefﬁcient of an ion at the ITIES is achieved with an electrochemical cell in which electrolytic salts have been preliminarily dissolved in both phases in order to conduct the current. As these electrolytes are in excess compared to the ion of interest, they are the principal contributors to the Galvani potential difference across the interface at equilibrium, and they condition the distribution of the ion under study, which follows the Nernst equation for the ITIES. In practice, this ion is forced to transfer by applying an external potential difference across the interface, which displaces the previously established equilibrium. The ionic distribution across the interface subsequently changes until a new equilibrium is reached. When the transfer of the ion is very fast, the reaction is called reversible in the electrochemical nomenclature, and the establishment of the new equilibrium is considered instantaneous. In this case, the Nernst equation is valid whatever the applied potential, and the transfer reaction is controlled not by the reaction rate, but by the diffusion of the transferring species. Cyclic voltammetry, where the applied potential is swept linearly between the two limiting values where the electrolyte ions begin to transfer, stems from this characteristic, and it is the methodology most commonly used to study charge transfer reactions at the ITIES. When ionizable compounds are concerned, the situation is complicated by the fact that all the species present may transfer from one phase to the other depending on the interfacial potential difference, so that the transfer process of the solute is entirely determined by the thermodynamic cycle described in Fig. 4. The application of a potential also modiﬁes all the acid–base equilibria in the vicinity of the interface, which, in turn, establishes a reaction layer on both sides of the interface. However, the bulk composition of each phase remains unchanged on the short experimental time scale, and the dissociation equilibria are maintained during a potential sweep.

FIG. 4 Thermodynamic equilibria for the interfacial distribution of a solute X which can be ionized n times, Xz0 and Xzn being its most acidic (or deprotonated) and its most basic (or protonated) forms, respectively. Kaiw and Kaio are the dissociation constants in the aqueous and organic phase, respectively, and Pi is the partition coefﬁcient of the various species between the two phases.

738

D.

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Danger of Neglecting Ion Partitioning

Most drugs are organic molecules with one or more groups that confer them acid, basic, or amphoteric properties. Many drugs, perhaps a majority, are then partly or largely ionized at physiological pH. As a consequence, even if only the neutral form of these drugs could cross biological membranes, their concentration at the target site as well as their receptorbinding may be deeply affected by their ratio of ionization, which in turn inﬂuences their ability to exert their pharmacological activity [132]. If this undeniable fact is totally accepted (since distribution coefﬁcients D replace partition coefﬁcient to quantify the lipophilicity of ionizable compounds), most of the models used [74,113] assume that the ionized form of a drug is conﬁned in the aqueous phase without being able to transfer. It follows that, up to now, the distribution coefﬁcients have always been simply estimated by: log D ¼ logðxN PN Þ

ð14Þ

where xN is the molar fraction of the neutral species at the experimental pH. However, recent studies on the variation of the distribution coefﬁcient of ionizable drugs as a function of pH (pH-lipophilicity proﬁles) shows that the partitioning of charged species cannot be neglected [143]. In other words, the general relationship between distribution and partition coefﬁcients [Eq. (15)] cannot be simpliﬁed.

X log D ¼ log xN PN þ ð15Þ xI PI where I stands for the various ionized forms of the neutral species N (I ¼ A for anions and I ¼ C for cations). As illustrated in Fig. 5, large errors on log PN are produced when approximated by Eq. (14). Indeed, in the pH region where the ionized species dominate, the proportion of neutral molecules in the aqueous phase becomes rapidly negligible. The ions are then liable to partition into the organic phase provided they form an ion pair with an electrolyte present in the aqueous phase or a species of equal charge crosses the interface in the opposite direction in order to maintain electroneutrality.

III.

MONITORING DRUG TRANSFER AND MEASURING ION LIPOPHILICITY

A.

Lipophilicity of Neutral Compounds

1. Conventional Measurements of Partition Coefﬁcients Despite their very simple deﬁnition, the measurement of partition coefﬁcients is not as easy as one would expect. The variety of recently introduced techniques tends to show that this experimental failure has not been fully overcome yet. The simplest technique is the shakeﬂask method [128,144–146], which consists of dissolving the solute under study in one phase (or in the two until saturation is reached separately) and then shaking them together before separation and analyzing each phase composition. The most realistic range of measurable log PN is from 3 to þ3 [147], although log PN values as high as 8.3 have been reported for measurements with a shake-ﬂask technique [135]. This error is about 510% towards log PN ¼ 0, but approaches 100% at the extremes of the range, because the analytical methods (UV, GLC, HPLC) cannot measure such ratios with sufﬁcient accuracy. Although extreme values of log PN may be partially compensated by changing the phase volume ratio [130] or by using a potentiometric titration method to correct for the distribution of ions [130,148], the shake-ﬂask method become unreliable beyond the

Transfer Mechanisms and Lipophilicity

739

FIG. 5 pH–lipophilicity proﬁles (on the left) and errors (curves in bold on the right) made by using the simpliﬁed Eq. (14) instead of the complete Eq. (15) when estimating log PN . The calculation is made for a monobase (top), a monoacid (middle), and a zwitterion (bottom) with a difference of three units between log PN and log PI . (Adapted from Ref. 143.)

above limits. Nevertheless, it remains the primary standard and no other method can be valid without calibration this way. Alternatives are then used to assess lipophilicity of organic compounds. Chromatographic methods such as reversed-phase high-performance liquid chromatography (RP-HPLC) [149–151], thin-layer chromatography (TLC) [149,152–154] and centrifugal partition chromatography (CPC) [155–158] become increasingly popular in replacing the shake-ﬂask method [157]. In both RP-HPLC and TLC, the organic phase serves as the stationary phase, which is stuck to an inert support [159–164], and the main problem of

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this technique is to distinguish between partition and adsorption [150]. In CPC however, the organic phase is used as the mobile phase and no solid support is needed because the stationary phase is maintained by centrifugal forces [165,166]. Although the initial systems were not able to use octanol because of its viscosity, which generated too high pressure in the chromatograph [167,168], measurements may now be carried out with this solvent [166] and with various others, such as chloroform, dibutyl ether [169], alkanes [117,170], and DCE [171], which allows one to investigate the different structural information encoded in partition coefﬁcients [172] (see Section IV.C). Most of the problems inherent in the shake-ﬂask method (such as precision of the phase volume ratio, the (im)purity of the solvent and solutes used, the volatility and adsorption of solutes, or the formation of microemulsions) do not affect the chromatographic methods, and they have the advantage of necessitating much less time and amounts of sample. The range of measurable log PN is approximately the same with CPC as with the shake-ﬂask [147,173], but more lipophilic compounds may be measured by RP-HPLC [149], TLC [174], or indirect methods [175,176]. Numerous other techniques have been used to obtain lipophilicity parameters (see Ref. 177 for a review), among them the following must be quoted: ﬁlter probe methods [178–180], which include a phase splitter to separate the two phases; the AKUFVE method [181,182], which is an automated version of the shake-ﬂask method used for examining effect of temperature, pH, or ionic strength; ﬂow-injection extraction [183], where the aqueous solution is directly introduced into the organic phase; the microscale partitioning method [184], which requires only 10 mg of sample; the generator column method [185,186], which allows one to measure the solubility ratio of highly lipophilic compounds; the dialysis method [187], where tubing of a given cutoff separates water from the octanol phase containing the analyte, allowing one to prevent the problem of emulsions; and the pH-metric method which will be explained in detail below. Nevertheless, the chromatographic methods are probably the methods of choice at present, thanks to their reproducibility and rapidity, and to their ability to provide data relating various solvent systems. 2. Calculation of Neutral Partition Coefﬁcients Although experimental partition coefﬁcients are the values of reference, drug design often necessitates log PN evaluations before the compound has been synthesized. Consequently, various methods have been developed to predict lipophilicity [188], and they generally apply only to neutral compounds in the water–OCT system. The ﬁrst attempt for calculating log PN was proposed by Hansch and Fujita [189] who considered partition coefﬁcients as an additive–constitutive property. This means that lipophilicity of a given compound is given by that of the unsubstituted ‘‘parent’’ compound plus a term representing the difference in partition coefﬁcient between a particular substituent X and the hydrogen atom which it replaces: X ¼ log PRX log PRH

ð16Þ

This implies that the X increments are independent of the molecule to which the constituent X belongs [190], and that H ¼ 0 (which is actually a serious ﬂaw of this theory, since it has been measured that log PH ¼ 0:45 [191]). A very large number of X values are collected in a data bank [192,193], but numerous correction factors are necessary to account for structural features such as multiple bonds, branching, ring-joining and for intramolecular interactions [194]. These shortcomings prompted Rekker [195–199] and

Transfer Mechanisms and Lipophilicity

741

later Leo and Hansch [191,200] to develop fragmental methods that calculate log PN by considering the two-dimensional (2D) geometry of a compound. In the former method, a molecule is decomposed into fragments, and the partition coefﬁcient of this molecule is the sum of the lipophilicity increments fj of all the fragments: log PN ¼

n X

ð17Þ

nj f j

j¼1

where nj is a numerical factor indicating the occurrence of each fragment in the structure. In this model, there is no reference to a chemical operation (such as substitution for the substituent model), but only results from mentally segmenting a molecule into pieces. Here also, the fj values must often be corrected to account for intramolecular interactions, and the correction factors are all multiple of a constant called the ‘‘magic constant.’’ Numerous speculations have been made about the signiﬁcation of this constant, and this method is fastidious because the fragmentations and the number of magic constants are not unique. Leo and Hansch’s model is based on the same ideas as Rekker’s, but instead of dividing logPN into fragments, partition coefﬁcients are calculated from small molecules ðH2 ; O2 ; N2 ; lower alkanes, etc.), the logPN of which are averaging to constitute fragto larger molecules by ‘‘construction’’ of mental constants fj and which are in turn adapted 0 a set of correction factors symbolized by Fj , expanding Rekker’s equation to: log PN ¼

n X j¼1

nj f j 0 þ

m X

mj Fj

ð18Þ

j¼1

Basically, the Fj concern bonds on one hand and polar effects on the other hand, as clearly treated by various authors [190,194,200–202]. Here, the fragmentation follows simple rules, but the number of Fj factors renders it impossible to use manually. A program called CLOGP has been developed [190,202–204], providing an easy way of calculating log PN with good agreement with experimental data. If the above fragmental approaches have proved their utility, they do not always predict partition coefﬁcients accurately, and this is due to the fact that lipophilicity is not a strictly additive property. Indeed, the lipophilicity contributions of most fragments vary from one compound to another, because a large spectrum of molecular properties (isomerism, tautomerism, folding, ionization, inter- and intramolecular H-bonds, etc.) are ignored in the 2D-additivity scheme. Therefore, three-dimensional and even four-dimensional appraoches are now used to calculate partition coefﬁcients (the former taking account of the 3D topology of a molecule and the latter adding a dynamic dimension, e.g., the variation of lipophilicity over a given conformational space). These methods of calculations are based on theoretical parameters (the solvent-accessible surface area, the semiempirical molecular orbital method, the decomposition of lipophilicity into parameters associated with atoms) or on molecular ﬁelds (molecular lipophilicity potential (MLP) or comparative molecular ﬁeld analysis) for the 3D approach and on an ensemble of conformers or on direct computation for the 4D approach. These sophisticated methods are beyond the scope of the present chapter, and further details can be obtained in systematic and complete overviews [132,188,205,206]. Otherwise, prediction of partition coefﬁcient from the known physical properties of the solute and solvents have been developed by Taft, Abraham, Kamlet, and coworkers [207–210]. They have introduced ‘‘solvatochromic parameters’’ to assess the intermolecular forces governing the partition mechanisms of neutral organic solutes: nonspeciﬁc

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dipolarity/polarizability and speciﬁc hydrogen-bond complex formation, which is subdivided into solute hydrogen-bond donor acidity and solute hydrogen-bond acceptor basicity . Taking account that a volume term to allow cavity formation is also required (such as the van der Waals volume Vw ), and by assuming that linear solvation energy relationships (LSER) exist between each contributing term and the observed solvent effects, it is deduced that the partition coefﬁcient for a solvent pair may be factorized as [211–213]: log PN ¼ vVw þ p þ a þ b þ c

ð19Þ

where v, p, a, and b are the regression coefﬁcients which reﬂect the contribution of each solute parameter to the partition coefﬁcient. This equation has been ﬁtted to log PN values of numerous solutes in various solvent systems, yielding the correlations given in Table 1. The relative contributions of each parameter vary accordingly to the properties of the solvent used. For instance, Table 1 shows that the polarizability and the H-bond donating acidity of the solutes have only a minor inﬂuence on their partitioning in the water–OCT system [212]. Therefore, solutes with different or cannot be differentiated by their log PN oct values. Similarly, the partitioning between DCE and water is mainly governed by hydrophobic interactions, and by hydrogen bonding in the water phase. As the same considerations apply for the water–heptane system, and as experimental measurements are often hampered by the low alkane solubility of many compounds, DCE has been proposed to replace the water–alkane system to characterize the H-bonding capacity of solutes [147,171]. Otherwise, the water–OCT system is not always suitable to interpret lipophilicity in pharmacokinetics terms. Indeed, penetration into the brain [214,215] or into lipid membranes [216] does not always correlate well with log PN OCT values. Likewise, for many drugs, log PN OCT is not a good predictor of biodistribution, presumably because of the negligible contributions of , which is known to play a major role in membrane penetration and biological selectivity [217–220]. To give a greater weight to hydrogen-bonding properties, the difference between the water–OCT and the water–alkane or water–DCE systems (noted log PN ) has been introduced [117,214,215,221,222], which is generally used when the difference of intermolecular interactions encoded in the partition coefﬁcients obtained in two solvent systems needs to be quantiﬁed. It has further been proposed to use the quartet of solvents given in Table 1 (with DCE replacing HEP) to fully express

TABLE 1 Solvatochromic Parameters Taken from the Literature for the Determination of log PN in Various Solvent Systems (oct Stands for Octanol, dce for 1,2-Dichloroethane, hep for Heptane, chf for Chloroform, and dbe for Dibutylether)

log PN oct [212] log PN dce [171] log PN hep [172] log PN chf [172] log PN dbe [220] a b

102 v

p

a

b

c

na

r2b

þ3:10 þ3:40 þ6:78 þ3:70 þ4:02

0:60 — 1:02 0:14 0:86

þ0:16 2:44 3:54 3:20 0:80

4:14 4:21 5:35 2:87 5:89

þ0:26 0:13 0:06 0:16 þ0:24

248 44 75 60 43

0.97 0.90 0.95 0.95 0.95

Number of compounds used for the regression. Correlation coefﬁcient.

Transfer Mechanisms and Lipophilicity

743

the recognition forces accounting for membrane partitioning and biological selectivity [146,220,223]. B.

Lipophilicity of Ionizable Compounds

1.

Electrochemistry at ITIES

Various electrochemical methodologies can be used to study drug transfer reactions at the ITIES, but the most widely used technique is cyclic voltammetry. In practice, it is very common to use cylindrical glass vessels to support the ITIES and a four-electrode potentiostat comprising two reference electrodes to polarize the interface and two counterelectrodes to provide the current and monitor the charge transfer reaction [224,225]. For experimental facilities and interpretation simplicity, numerous studies are achieved at a large ITIES without renewal of the interface, but polarography [142,226,227], where a drop of aqueous solution is introduced into the organic phase from the tip of a capillary, is also highly appreciated because it decreases the risk of contamination of the interface [228]. In both cases, the electrochemical cells commonly used for ion transfer studies at polarizable ITIES are constituted as follows:

SCHEME 1 where A1 B1 and A1 B2 are electrolytic salts, e.g., tetrabuylammonium chloride (TBACl) and tetrabutylammonium tetrakis(4-chlorophenyl)borate (TBATPBCl). As mentioned above, the distribution of the various species in the two adjacent phases changes during a potential sweep which induces the transfer of an ion I across the interface when the potential approaches its standard transfer potential wo 0I . This ﬂux of charges across the interface leads to a measurable current which is recorded as a function of the applied potential. Such curves are called voltammograms and a typical example for the transfer of pilocarpine [229] is shown in Fig. 6, illustrating that cyclic voltammograms produced by reversible ion transfer reactions are similar to those obtained for electron transfer reactions at a metal–electrolyte solution interface. As reversible ion transfer reactions are diffusion controlled, the mass transport to the interface is given by Fick’s second law, which may be directly integrated with the Nernst equation as a boundary condition (see, for instance, Ref. 230–232). A solution for the interfacial concentrations may be obtained, and the maximum forward peak IpFWD may then be expressed as a function of the interfacial area A, of the potential scan rate , of the w bulk concentration of the ion under study cw I and of its diffusion coefﬁcient DI . This leads to the Randles–Sevcik equation [233]: rﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃwﬃpﬃﬃﬃ FWD w zi F ð20Þ Ip ¼ 0:4463zI FA cI DI RT By varying the scan rate, this equation allows then the evaluation of the diffusion coefﬁcient of the transferring ion. With the determination of the formal transfer potential of an ion and thus of its Gibbs energy of transfer by application of Eq. (10), this is the most important application of cyclic voltammetry.

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Reymond

FIG. 6 Typical cyclic voltammogram obtained for the transfer of pilocarpine hydrochloride at the water–DCE interface. The organic phase contains 0.01 M tetrabutylammonium tetrakis(4-chlorophenyl)borate, the aqueous solution is 0.01 M HCl þ 0.2 mM pilocarpine hydrochloride, and the sweep rate is ﬁxed at 10, 25, 75, 100, and 150 mV/s. (Reprinted from Ref. 229.)

For reversible transfer reactions of a simple ion, wo 0I may be expressed in terms of the half-wave potential, wo 1=2 , by direct transposition from the case of reversible electron transfer at a metal electrode–electrolyte solution interface [234]: w RT D ln Io wo 1=2 ¼ wo 0I þ ð21Þ 2zI F DI where the ratio DwI =DoI is generally approximated by the inverse ratio of the solvent viscosities using Walden’s rule [233]. However, the half-wave transfer potential is not a constant when ionizable compounds are concerned, because their transfer behavior depends on their degree of dissociation and hence on the pH of the aqueous phase. For instance, with a basic drug B that can be protonated once to give BHþ , it has been shown [230] that wo 1=2 is related to wo 0BHþ by: w ! RT DBHþ RT PB Kaw DoB 1=2 w w 0 þ ln o ln 1 þ w o 1=2 ¼ o I þ ð22Þ 2zI F zI F DBHþ cHþ DwB which can be approximated by Eq. (21) when pH < pKaw logðPB ðDoB =DwB ÞÞ and by: ! w RT DBHþ RT PB Kaw w w 0 o 1=2 ¼ o I þ ln o ln þ ð23Þ 2zI F zI F DBHþ cwHþ when pH > pKaw logðPB ðDoB =DwB ÞÞ.

Transfer Mechanisms and Lipophilicity

745

Such a behavior was ﬁrst observed with 1,10-phenanthroline [235,236] and bromophenol blue [237], and the above relationships were conﬁrmed by measuring the voltammograms of various drugs as a function of pH [238–240]. Experimentally, wo 1=2 is generally considered equal to the midpeak potential, and is then directly deduced from the voltammograms. This does not generate experimental errors, since an ion of known standard transfer potential (for instance, tetramethyl ammonium, TMAþ ) must be used as an internal reference to transpose the experimental potential scale (noted E) to the absolute Galvani potential scale, so that wo 0I is obtained by: wo 0I ¼ wo 0TMAþ E1=2;TMAþ þ E1=2;I

ð24Þ

Therefore, the partition coefﬁcient of an ion can be assessed from cyclic voltammetry experiments, and the half-wave transfer potential is a direct measure of drug lipophilicity. In other words, the standard transfer potential of an ion can be regarded as its lipophilicity expressed on a potential scale. wo 0I is normalized by the charge, which renders it more convenient than log PI;0 when comparing the lipophilicity of ions of different charges. Indeed, as drug permeation by passive diffusion is driven by the transmembrane Galvani potential difference, ions with different charges but with equal log PI;0 values do not have the same afﬁnity for the organic phase and thus do not permeate similarly, because the electrical work required by a singly charged ion to reach a given distribution is twice that required by a doubly charged species. Therefore, wo 0I is the key parameter to evaluate the lipophilicity of ions [241]. A large variety of drugs have been examined by various voltammetric techniques at polarizable ITIES. The most popular are cyclic voltammetry and dropping electrolyte electrodes, which have been used to determine the transfer potentials of amines [242– 246], 1,10-phenanthroline [235,236,247], acetylcholine [248–251], arenediazonium ions [252], antibiotics [253–256], vasodilators [241,257,258], and anti-inﬂammatory [103,259], antimalarial [231,260–263], and anesthetic [264,265] drugs, as well as for a series of hypnotic, anesthetic, cholinergic, and adrenergic agents [240,266,267]. Drug transport across the ITIES has also been clariﬁed by differential pulse stripping voltammetry [242] and potential step amperometry [238,268]. Furthermore, modiﬁed interfaces with phospholipid monolayer [269–272] or bilayer lipid membranes [273,274] have been used, as well as potential oscillation at ITIES [267,275–277]. Dealing only with charged species, cyclic voltammetry at the ITIES is particularly well suited to measure lipophilicity of ions, but, as will be described in detail below, log PN can also be deduced from the evolution of the standard transfer potentials over a pH domain encompassing the pKaw of the drug substance. However, the major drawback of cyclic voltammetry is the fact that it is restricted to well-polarizable solvent systems. Therefore, solvents conventionally used in pharmaceutical research, such as water–OCT or water-alkanes, cannot be employed, which drastically limits the biological interpretations from cyclic voltammetric data. Indeed, as described in Section III.A.2, such interpretations require knowledge of what information is encoded in the partition coefﬁcients measured in a given solvent system, which can be obtained through solvatochromic analysis. Up to now, solvatochromic analysis of polarizable solvent systems has only been achieved for water–DCE [171], revealing its ability to evaluate the H-bonding properties of solutes. Therefore, it would be proﬁtable to expand this methodology to other solvent systems, which preliminarily necessitates investigation of their solvatochromic characteristics. With this respect, nitrophenyloctyl ether (NPOE) would be worth exploring thanks to the similarity of its structure with biomembranes. As it also resembles octanol, it is

746

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likely to provide similar informations, which would assuredly extend the use of electrochemistry at the ITIES in medicinal chemistry. 2. Potentiometry The potentiometric technique relies on the use of a pH electrode to measure the aqueous pH as a function of the volume of acid or base added during the titration of the drug substance under study. In a ﬁrst step, the titration is carried out in the aqueous phase only, which allows for the conventional determination of the various pKaw of the substance. After completion of this ﬁrst titration, a certain volume of water immiscible organic solvent is added to the aqueous solution, and the dual-solvent mixture is titrated back to the starting pH [see Fig. 7(A)]. In the mixture, the apparent pKaw (called p0 Kaw ) is shifted from the value observed in the absence of organic phase due to the partition of the various forms of the drug substance. The extent of this shift is related to its log P, which is obtained from the evolution of the aqueous pH with the number of base or acid equivalents added to the system [see Fig. 7(B)] or from the Bjerrum difference curve [148,278,279] (i.e., the plot of the average number of bound protons n Hþ as a function of pH [see Fig. 7(C)] through an iterative least squares procedure.

FIG. 7 The four steps towards the pH-metric determination of the pH–lipophilicity proﬁle of a monoacid, illustrated by the example of benzoic acid for which pKaw ¼ 3:99, log PAH oct ¼ 1:96, and log PA ¼ 1:23. (a) Titration curve (pH vs. volume of titrant): to a 10 mL 0.1 M KNO3 solution oct containing 1 mg benzoic acid, 0.3 mL 0.5 M HCl was added to lower the pH to 2; the solution was then titrated with 0.5 M KOH to pH 11 (left curve) at which point 1 mL octanol was added before the solution was titrated with 0.5 M HCl back to pH 2 (curve ending on the right). (b) Titration curve, pH vs. base equivalents. (c) Bjerrum plot, number of bound protons n Hþ vs. log cwHþ . (d) pH–lipophilicity proﬁle, log D vs. pH. (Reprinted from Ref. 361. With permission from Sirius Analytical Instruments Ltd.)

Transfer Mechanisms and Lipophilicity

747

When both the neutral and the n different charged forms of a compound partition into the organic phase, a minimum of ðn þ 1Þ titrations with different phase volume ratios is necessary to determine the partition coefﬁcient of each species. For a monoprotic substance, for instance, p0 Kaw can be related to pKaw by an empirical equation [119]: " " # # ðcwX þ coX Þ cwHþ þ coHþ 1 þ r PX w w w p0 Ka ¼ log ¼ pKa log ð25Þ 1 þ r PXH cXH þ coXH where the partitioning of the protons is neglected and the phase volume ratio r is deﬁned as: r¼

Volume of organic phase Vo ¼ w Volume of aqueous phase V

ð26Þ

Although Eq. (25) has no physical meaning and although its simpliﬁcation is not valid thermodynamically, since the condition of electroneutrality in both phases is not fulﬁlled if the proton cannot partition, it agrees very well with experimental data, which justiﬁes its use. In fact, computerized ﬁtting procedures correct for this error in commercial twophase titrators, so that the experimental value of p0 Kaw can directly be introduced in Eq. (25). The pH–metric technique used to determine partition coefﬁcients was ﬁrst used in the 1950s in solvent extraction of metal complexes [280–282], but it is in pharmaceutical research that it is most widely used thanks to the recent development of a fully automated and computer-controlled apparatus [125,283]. The potentiometric approach has been validated in various solvent systems [284–287], and it has become a relevant and expanding experimental technique to obtain lipophilicity descriptors [257,287–289]. The major limitations of the pH–metric approach are similar to those encountered in cyclic voltammetry at the ITIES and concern nonionizable compounds, acids with pKaw < 2, bases with pKaw > 11:5, and hydrophilic solutes with log PN smaller than 0:5 [126]. However, due to the generally low lipophilicity of ions, the technique often fails in measuring log PI . It is indeed more difﬁcult to obtain reliable potentiometric values of log PI in water–DCE than in water–OCT, because the afﬁnity of ions for DCE is smaller than for octanol due to the larger solubility of water in OCT and to the higher H-bonding capacity of OCT [257,290]. It must be stressed that, thanks to the fact that it works by displacement of the thermodynamic equilibrium in the vicinity of the interface, cyclic voltammetry at the ITIES is more convenient to assess log PI , the range of which being only limited by the available potential window and thus to values between 0 and 10. Furthermore, cyclic voltammetry at the ITIES gives access to standard thermodynamic values, whereas results obtained by potentiometry depend strongly on the experimental conditions. Indeed, the nature of the base electrolytes, the ionic strength of the solutions, and the phase volume ratio may nonnegligibly affect partition coefﬁcient values [126], and it has been shown [291,292] that this inﬂuence is due to the change of the distribution potential across the interface.

IV.

APPLICATIONS

A.

pH–Lipophilicity Proﬁles

In the past, numerous studies were limited to the measurement of log D at physiological pH, but, as pH is not uniform in the body, it is generally more relevant to know the

748

Reymond

evolution of the lipophilicity of a compound over the entire pH range (pH–lipophilicity proﬁle) [143]. In the shake-ﬂask method, log D is measured directly [293], and log PN , log PI , and pKaw are derived if the measurements are achieved at several judiciously selected pH values. Conversely, in both potentiometric and cyclic voltammetric techniques, the pH-lipophilicity proﬁles are calculated from the partition coefﬁcients values obtained experimentally, which necessitates measurements over the whole pH range. Changes in aqueous pH modify the degree of ionization of the substance under study, thereby displacing all the thermodynamic equilibria given in Fig. 4. Potentiometry deduces the lipophilicity of a substance from pKaw shifts during titration, and constitutes then a direct method of measuring pKaw with indirect determination of the various log PI . On the other hand, the current peaks obtained in cyclic voltammetry depend on the charge and nature of the species present in both phases, and the halfwave transfer potentials are directly related to the log PI of the transferring species. As an example, Fig. 8 compares the results obtained by cyclic voltammetry for the transfer of quinidine to the Bjerrum plot obtained for quinine, two compounds of very similar structures. The two inﬂection points in Fig. 8(a) clearly indicate that quinine possesses two pKaw , but it is quite difﬁcult to evaluate the lipophilicty of its singly and doubly charged forms from this plot, and these values are only valid at the experimental base electrolyte concentration. On the other hand, the current waves obtained in cyclic voltammetry [Fig. 8(B)] show that the doubly charged species transfers at relatively higher potentials compared to that of the singly charged one, that it requires more energy to cross the interface and hence that it is much less lipophilic. However, the half-wave transfer potential is not constant over the entire pH range. This has been evidenced in various studies as already shown by Eqs. (21) and (23). What happens is the following: in the pH region where the drug can be considered completely ionized, the ionic form transfers into the organic phase upon application of a potential difference, and the corresponding half-wave transfer potential is constant. When pH approaches values where the majority of the drug is in its neutral form, a current is still measurable, but the half-wave potential now depends on the aqueous pH. This current results from the displacement of the thermodynamic equilibria upon applied potential, which necessitates the passage of a proton across the interface. In this region, we thus have an assisted proton transfer reaction where the neutral drug plays the same role as the ionophore in interfacial complexation of metal ions. When acidic compounds are concerned, the neutral drug deprotonates at the interface releasing the anionic form in the organic phase, which is similar to a transfer by interfacial decomplexation (TID) mechanism [294]. In the case of bases, the modiﬁcation of the thermodynamic equilibrium forces the neutral form to protonate, thereby necessitating the transfer of a proton coming from the adjacent phase, which corresponds to a transfer by interfacial complexation (TIC) mechanism. In both cases, the half-wave potential shifts by RT=ðzI FÞ mV per pH unit, and a typical example of such a behavior is given in Fig. 9 for the transfer of two acidic diketones at the water–nitrobenzene interface. These results were unexpected, since a current wave is measured at a pH where the compound of interest is by a very large majority neutral, but they in fact represent the typical behavior of ionizable compounds at the ITIES and prove that the interfacial potential and the transfer of protons plays a key role for the distribution in biphasic systems. It should ﬁnally be mentioned that cyclic voltammetry at the ITIES allows for a precise discrimination between compounds of different charges, since the position of the peak currents depends directly on lipophilicity, since their intensity varies with z3=2 [Eq. I

Transfer Mechanisms and Lipophilicity

749

FIG. 8 (a) Bjerrum plot for quinine based on water–OCT titrations at various volume ratios: (1) 0.25 mL octanol: 20 mL 0.15 M KCl, (2) 0,5:20, (3) 5:15, and (4) 10:10. The obtained physicochemw and QHþ ) are: pKa1 ¼ 4:24, ical parameters for the two protonated forms of quinine2þ (QH2þ 2 QH2 QHþ w pKa2 ¼ 8:55, log PQ ¼ 3:47, log P ¼ 0:87, and log P ¼ 0:21 at 0.15 M KCl. (Reprinted oct oct oct from Ref. 126.). (b) Calculated voltammograms for the transfer of the two protonated forms of þ quinidine (QH2þ 2 and QH ) across the water–DCE interface at various pH of the aqueous phase. The total quinidine concentration cQinit is taken equal to 1 mM, and the parameters used for the w w ¼ 4:43, pKa2 ¼ 8:66, log PQ calculation are those obtained experimentally, namely [262]: pKa1 dce ¼ þ

0

0

0

QH2þ ;0 0

;0 ¼ 1:37), and wo 0QH2þ ¼ 162 mV (so that log Pdce 2 2.5, wo 0QHþ ¼ 80 mV (so that log PQH dce 2 w w 5:54Þ, with DQH2þ estimated equal to DQHþ ¼ 1:23 106 cm2 =s. (Adapted from Ref. 231.)

¼

2

(20)] and since the peak-to-peak separation is given by RT=ðzI FÞ. On the other hand, the pH-metric method does not allow one to determine the nature of the partitioning species. Indeed, all the ionic forms of a molecule must be treated as a unique entity, because the two–phase titration differentiates only poorly between, for instance, a doubly charged and two singly charged species. This often prevents potentiometry from attributing partition coefﬁcient values to each ionic form separately. In this respect, cyclic voltammetry is very likely to rapidly become an interesting alternative to potentiometry.

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FIG. 9 Half-wave potential dependence on aqueous pH for the transfer of thenoyltriﬂuoroacetone (dots, left curve) and 1-phenyl-3-methyl-4-octadecenoyl-5-pyrazolone (crosses, right curve) at the water–nitrobenzene (nb) interface supported in a microhole of 10 mm in diameter. The anionic form of these compounds (L ) was dissolved in the organic phase as a bis(triphenylphosphoranylidene)ammonium (BTPPA+) salt, and the electrochemical cell used was: Ag|AgCl|1 mM BTPPAþ Cl |1 mM BTPPAþ TPBCl + 5 104 M BTPPAþ L k10 mM phosphatejAgCljAg. The physicochemical parameters obtained for thenoyltriﬂuoroacetone and, respectively, 1-phenyl3-methyl-4-octadecenoyl-5-pyrazolone are the following: pKaw ¼ 6:23 and 6.64, log PN nb ¼ 2:0 and I ;0 0 2.0, and log Pnb ¼ 4:52 and 2:46. (Reprinted from Ref. 362.)

B.

Ionic Partition Diagrams

As can be deduced from the above paragraph, the main advantage of cyclic voltammetry over other techniques is the mechanistic information it provides, and this is of prime importance for the understanding of drug transport across biomembranes, because it does not only depend on the distribution coefﬁcient at the pH of interest but also on the chemical nature of the permeating compound, since movement of ions in biology is also driven by a potential difference. In biomimicking systems like ITIES, it is therefore of interest to know which form of a compound dominates at the interface depending on the aqueous pH. This led us to develop the ‘‘ionic partition diagram’’ methodology [263], which is a transposition to biphasic systems of the well-known Pourbaix’s diagrams [295]. These diagrams are established by drawing the boundary lines representing the geometrical locus where the mole numbers nI of two adjacent species are equal, with nI being deﬁned as: nI ¼ V cI

ð27Þ

These boundary lines are thus determined by solving the various equilibria for these particular conditions, and, for clarity, we brieﬂy describe the methodology to follow in

Transfer Mechanisms and Lipophilicity

751

the case of a monoprotic substance like methyl orange [296]. When the mole number of the deprotonated form (noted MO ) is equal in both phases, the Nernst equation [Eq. (9)] reduces to: 0

wo ¼ wo 0I

RT ln r zI F

when nwI ¼ noI

ð28Þ

As shown in Fig. 10, Eq. (28) does not depend upon pH, and the predominance domain of the two ionic species in both phases [denoted MO ðwÞ and MO ðoÞ] are thus separated by a horizontal line, indicating that a simple ion transfer reaction occurs upon a change of wo (MO transfers across the interface). The position of this boundary line indicates the energy required for this transfer and hence directly reﬂects the lipophilicity of the ion. There are three possibilities of letting the neutral species appear in the ionic partition diagram. Indeed, as the partition coefﬁcient of the neutral species is neither potential- nor pH-dependent, the variable can be either the neutral species in the aqueous phase or that in the organic phase. However, to account for the experimental reality, it is more convenient to introduce the total mole number of neutral species [297], deﬁned as: nNtot ¼ nwN þ noN

ð29Þ

In this manner, the boundary line between Ntot and IðwÞ is directly deduced from the deﬁnition of the dissociation constant [Eq. (5)], which can be rewritten as: pH ¼ pKaw zI logð1 þ rPN Þ

when nwI ¼ nNtot

ð30Þ

FIG. 10 Ionic partition diagram of methyl organe at 258C in water–DCE. The circles and squares denote the experimental values of the standard transfer potentials deduced from the voltammograms obtained at a phase volume ratio of r ¼ 1, while the boundary lines (bold) are the equiconcentration lines between two adjacent species that determine the domain of predominance of: (I) neutral methyl orange (MOH), (II) deprotonated methyl orange in water [MO ðwÞ], and (III) deprotonated methyl orange in DCE [MO ðoÞ]. These boundary lines were calculated with the values obtained experi 0 0 ;0 mentally, namely pKaw ¼ 3:37, log PMOH ¼ 0:80, and log PMO ¼ 1:32 (wo 0MO ¼ 78 mV). dce dce Lines a and b denote the experimental domain, which is limited here by the transfer of Liþ and Cl at high and low potentials, respectively. (Adapted from Ref. 296.)

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This time, the boundary line is independent of the Galvani potential difference across the interface, and the corresponding pH value can be regarded as the effective dissociation w , which appears experimentally due to the partitioning of the neutral constant, pKaeff w species. For a monoprotic substance, pKaeff can thus be deﬁned as: w ¼ pKaw zI logð1 þ rPN Þ pKaeff

ð31Þ

The partition coefﬁcient of the neutral species can then be deduced from the pH-shift w between pKaw and pKaeff , but no reliable value can be obtained with poorly lipophilic w compounds because pKaeff corresponds to pKaw in this case (see Fig. 10 for the case of methyl orange). Finally, introduction of the Nernst equation [Eq. (9)] into Eq. (5) leads to a relation between noI and nNtot , which, at the boundary between Ntot and IðoÞ, simpliﬁes to: 0

wo ¼ wo 0I

2:3RT 2:3RT w pKaeff þ zI log r þ pH F F

when noI ¼ nNtot

ð32Þ

This line is both potential and pH dependent, and it represents the zone where an assisted proton transfer reaction occurs. As a matter of fact, an oblique line in the ionic partition diagram always relates to such a mechanism, the slope indicating the number of protons exchanged at the interface. As can be deduced from Eqs. (28), (30), and (32), the ionic partition diagrams are inverted according to the sign of the charge of the ionic species: the domain of predominance of IðwÞ appears within the upper part of the diagram in the case of acids (see Fig. 10), but within its lower part in the case of bases. The ionic partition diagram representation has thus the advantage of taking the electrochemical process into account, since the cations are forced towards the organic phase upon increase of wo , whereas the anions are restrained within the aqueous phase. If the shape of the ionic partition diagrams complicates with multiprotic substances, the various boundary lines can always be easily deduced from the expressions of the thermodynamic equilibria. In a general manner, two species of equal charge are separated by a horizontal line, which is indicative of the simple transfer of this ion across the interface. Similarly, the various species in water are separated by vertical lines which simply accounts for a proton exchange in the aqueous phase (dissociation equilibria). On the other hand, two species of different charges are separated by an oblique line, of which the absolute value of the slope indicates the number of protons that need to transfer to fuﬁll the reaction and the sign of which indicates the direction of the transfer (positive for water to oil and negative for oil to water). Therefore, the ionic partition diagrams offer a direct view of the dominating species as a function of potential and pH, of the lipophilicity of the various species and of the mechanisms governing their distribution. This representation also allows us to understand how protons can transfer from an aqueous phase to another medium like cellular membranes, and how the presence of neutral drug can facilitate this process by decreasing the Gibbs transfer energy of the proton. This process is of great importance in pharmacology, because the proton concentration is tightly regulated in functional biological systems (see also Section I.B). Dysfunction of pH regulation is at the origin of numerous pathologies; various recent studies have shown that the pharmacological activity of compounds like chloroquine [104], nigericin [102], tenidap [105–107], piroxicam [103], azapropazone [287], or trimetazidine [241] are linked to their ability to modulate pH in biological environments, thereby correcting for this dysfunction.

Transfer Mechanisms and Lipophilicity

C.

753

Effects of Intramolecular Interactions on Lipophilicity

Inter- and intramolecular interactions can drastically affect the lipophilicity of a compound and, hence, its pharmacokinetic behavior. Unfortunately, values of partition (or distribution) coefﬁcients do not yield direct insights into these effects because they are global values. Comparison between different lipophilicity data can give access to such effects that are generally assessed by difference parameters. These descriptors can be divided into two classes, namely those expressing the difference between the partition coefﬁcient values of a compound at a given electrical state obtained in two different solvent systems (named log P) and those derived from the difference of partition coefﬁcient values obtained in the same solvent system [named diff ðlog PÞ]. As already mentioned in Section III.A.2, numerous studies demonstrate that log P affords an expression of polar intermolecular interactions and it is mainly used to identify H-bonding between solute and solvent [172,221,222]. The diff ðlog PÞ parameters may refer either to the difference between experimental and calculated values ½diff ðlog PXexpXcalc Þ, to a pair of congeners [generally a metabolite and its parent, diff ðlog PMetaboliteParent Þ] or to two distinct electrical states of a compound [generally the neutral species and one of its charged form, diff ðlog PNI;0 Þ, where the superscript denotes that the partition coefﬁcient of the ion is its standard value]. Depending on their nature, the diff ðlog PÞ parameters can thus be inﬂuenced either by inter- or by intramolecular interactions. As described below, all the above parameters have been successfully used to evaluate and interpret these effects, and this is what gives them such a value. 1. Difference of Lipophilicity Between Two Solvent Systems As shown in Table 1, the various contributions of each solvatochromic parameter to the LSER model indicate what are the principal forces governing the partitioning of a solute. Therefore, the log P parameters quantify the difference of intermolecular interactions encoded in the two solvent systems under study. Generally, these interactions are evaluated by plotting log PN oct for an optimized set of compounds as a function of the partition coefﬁcients obtained in the second solvent system [171,220,298]. A linear function is found for all the solvent systems given in Table 1, the Y-intercept representing the average log P. However, as the partitioning in each solvent system depends on various contributions, linear correlations can only emerge with solutes possessing the same solvatochromic property. In the case of the water–DCE system shown in Fig. 11(a), the H-bond donors ð > 0Þ and non-H-bond donor solutes ð ¼ 0Þ must be examined separately [171]. In water-DBE however, this distinction is not required [see Fig. 11(b)], because is only a minor contributor to log PN dbe [220]. The effects of intramolecular interactions on the lipophilicity of a compound can then be assessed by comparing its position in these graphs to its chemical structure. This has, for instance, been achieved with a series of b-blockers [290] that have the common structural elements of one or more aromatic rings and a b-aminoethanol or a 3-amino-2hydroxypropoxy side chain, which gives them a positive H-bond donor character. As shown in Fig. 11(a), only four compounds in the series are positioned on the ideal line, the intermediate position of the other compounds between the two regression lines suggesting that their H-bonding properties are not fully expressed in water–DCE, probably due to the formation of intramolecular H-bonds between the OH and the neutral NH group of the 3-amino-2-hydroxypropoxy side chain. It is only when additional H-bond donor substituents are present that the solutes behave as regular H-bond donors. In water–DBE, however, the formation of internal H-bonds in this side chain is not favored,

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N N FIG. 11 Evolution of log PN oct as a function of (a) log Pdce and (b) log Pdbe . The correlation lines are obtained with a well-distributed series of model compounds [171,220] that must be divided into Hbond donor solutes (*) and non-H-bond donor solutes (*) with DCE. The partition coefﬁcient values obtained for a series of b-blockers (*) are added to both graphs, showing that only acebutolol (1), atenolol (3), carazolol (5), and pindolol (11) behave as regular H-bond donors in water– DCE, the other compounds deviating due to the presence of intramolecular H-bonds, whereas only atenolol (for unknown reasons) is an outlier in water–DBE. (Reprinted from Ref. 290.)

which renders the substituents available for intermolecular interactions with the solvent, so that these b-blockers behave as regular H-bond donors. Similar studies have been performed for a series of nitrophenols [299], showing the ability of the log P parameter to identify the presence of intramolecular H-bonds in a series of congeners. This is of pharmaceutical relevance, since, as mentioned above, it is often recognized that the log P parameter is a good predictor of biodistribution and passive diffusion [215,300]. This approach is as yet restricted to neutral species, because of the difﬁculty in establishing LSER for ions. It would yet be of great interest to enlarge the spectrum of LSERs to this ﬁeld. 2. Difference of Lipophilicity Between Two Forms of a Compound The presence of intramolecular interactions can be checked by comparing calculated and experimental log P values. Such identiﬁcation can yet only be obtained for the water–OCT system, since computed lipophilicity values have only been derived for this solvent pair. Due to its simplicity and its easy adaptation to complex structures, Rekker’s calculation method is often appreciated, but more sophisticated approaches like that evaluating log P using the molecular lipophilicity potential (MLP) has also been employed.

Transfer Mechanisms and Lipophilicity

755

These calculation methods have been used to compare HPLC-derived lipophilicity indexes to Rekker’s calculated log P values for a series of xanthines [301], showing that experimental lipophilicity was lower than predicted due to a folding of the conformers that are stabilized by hydrophobic and van der Waals forces and by a partial masking of their nonpolar surface. In a study of the lipophilicity of nucleosides [302], it has been shown that none of the calculation methods used was able to assess correctly the partition coefﬁcients of these polar compounds, showing the importance of using 4D approaches to take conformational ﬂexibility and intramolecular interactions into account. Comparison between several predicted partition coefﬁcients has, for instance, been applied for two morphine glucoronides [303], allowing one to demosntrate that these compounds may become more polar in polar solvents and more lipophilic in nonpolar solvents due to hydrophobic and/ or hydrophilic folding [304,305], explaining their high penetration into the brain [306–308]. The diff ðlog PXexpXcalc Þ parameter has ﬁnally been used to identify intramolecular effects in the above mentioned series of b-blockers [290], as well as in sulﬁnpyrazone, sulindac, and their metabolites [287]. The good agreement between calculated and experimental data indicated that no strong intramolecular effect operates for the neutral b-blockers and sulindac in the water–OCT system. However, large values of diff ðlog PXexpXcalc Þ were obtained for sulﬁnpyrazone and its metabolites, showing that conformation and tautomeric equilibria affected the lipophilicity of the neutral form, whereas only conformational effects inﬂuence the lipophilicity of anions. The effects of metabolic transformations on lipophilicity can also be addressed using the difference in log P between metabolites and their parent compounds, i.e., using the diff ðlog PMetaboliteParent Þ parameter. It has usually been considered [5,309–311] that the effect of metabolism (i.e., liberation of functional groups of hydrolysis of the drug or addition of functional groups to it by oxidation or reduction, followed by conjugation to endogeneous compounds [309,312]) was to increase drug solubility in water, thereby facilitating its elimination. Various studies yet showed that metabolic reactions lead to an increase in lipophilicity [313]. If the literature is very scarce on this topic despite its pharmacokinetic signiﬁcance [314], the global inﬂuence of N-oxidation [315,316] and glucoronation [304,317] on lipophilicity has recently been studied, demonstrating that the values of diff ðlog PMetaboliteParent Þ varied markedly with the electronic interactions and H-bond acceptor basicity of the substituents in the para position of the N-oxide function and with masking of polar groups by folding in glucoronides. Of particular interest when considering ionizable compounds is the difference of lipophilicity between the neutral species and one of its ionic forms, because ionization dramatically alters intramolecular interactions (such as electronic conjugation, internal ionic and hydrogen bonds, polarity, hydrophilic folding, and shielding). In a given solvent system, diff ðlog PNI;0 Þ is approximately constant for compounds with similar chemical structure, and it has been shown that the value obtained for a monoprotic substance is about 3 in water–OCT [109] and about 5 in water–DCE [257,318]. These averages are in good agreement with Born’s solvation model, from which the diff ðlog PNI;0 Þ can be estimated by [257]: diff ðlog PNI;0 Þ ¼

GoIS GwIS z2I e2 NA "wr "or ¼ RT ln 10 8"0 r "wr "or

ð33Þ

where GIS is the Gibbs energy of ion–solvent interaction (i.e., the chemical potential difference between one mole of ions and one mole of neutral molecules of equal size), e is the charge of the proton, NA is the Avogadro constant, r the radius of the molecule, "0 is

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the vacuum permittivity, and "r is the dielectric constant of each phase, which is equal to 78 for water and to 10 for both OCT and DCE). It must be stressed that models taking account of short-range ion–solvent interactions like the dielectric saturation can improve the calculated Gibbs transfer energies [319–321], but Born’s model already provides a useful approximation of diff ðlog PNI;0 Þ. Indeed, the difference of the mean diff ðlog PNI;0 Þ values signiﬁes that the molecular radius of ions is approximately 1:2 A larger in OCT than in DCE. This result perfectly agrees with the fact that ions keep more water molecules when they transfer into OCT than in a less polar solvent like DCE, because of the larger solubility of water in OCT and of its H-bonding capacity, which is almost as large as in water [since the term of its solvatochromic equation (see Table 1) is nearly zero]. Speciﬁc intramolecular interactions can thus be identiﬁed by a diff ðlog PNI;0 Þ deviating from the above average values. As schematically described in Fig. 12, four categories must be distinguished: a low diff ðlog PNI;0 Þ can arise from a neutral form less lipophilic than expected (case a) or from an increased lipophilicity of the ionic form (case b), whereas high diff ðlog PNI;0 Þ values may be due either to a large lipophilicity of the neutral form (case c) or to a smaller lipophilicity of the ion (case d). These differences have been identiﬁed for two main classes of interactions, namely intramolecular H-bonding and charge delocalization. It has, for instance, been shown for N-(p-methylbenzyl)hexylamine in water–DCE that its diff ðlog PNI;0 Þ is 4.51, which is smaller than 5 due to the binding of the alkyl chain which masks the ammonium group, thereby diminishing its molecular electrostatic potential and hence avoiding a strong destabilization of the cation in the organic phase (above case b) [259,322]. In contrast, this effect does not appear with lauric acid despite its long alkyl chain, since its diff ðlog PNI;0 Þ has been measured as 6.64, suggesting that the terminal position of the protolytic

FIG. 12 Effects of intramolecular interaction on diff ðlog PNI;0 Þ: (a) diff ðlog PNI;0 Þ smaller than predicted because of an increased hydrophilicity of the neutral form; (b) diff ðlog PNI;0 Þ smaller than predicted because of an increased lipophilicity of the ionized form; (c) diff ðlog PNI;0 Þ larger than predicted because of an increased lipophilicity of the neutral form; (d) diff ðlog PNI;0 Þ larger than predicted because of an increased hydrophilicity of the ionized form.

Transfer Mechanisms and Lipophilicity

757

function in an alkyl chain is not favorable and that the delocalization of a carboxylate group does not improve the solvation in the organic phase. An increased lipophilicity of the ionic species has also been evidenced for the bblockers acebutolol, carvedilol, and oxprenolol, which form an H-bond between the protonated amine and their ortho-oxygen on the aromate ring [290]. This effect is yet even stronger upon incorporation of the protolytic group within an aromatic cycle. In protonated pyridine, for instance, the high electron density of the aryl group can efﬁciently delocalize the charge, so that it is less exposed to ion–dipole interactions, which explains why its diff ðlog PNI;0 Þ value is only 4.54 although neutral pyridine is only weakly lipophilic ðlog PN ¼ 0:72Þ [259]. However, the introduction of an aromatic function in a molecule does not necessarily imply a diff ðlog PNI;0 Þ value higher than predicted. This can only result from a delocalization of the charge, as has been exempliﬁed with substituted anilines [257]. Otherwise, in many compounds, both intramolecular H-bonding and charge delocalization can affect lipophilicity. In the case of (di)nitrophenols for instance [299], the neutral ortho-substituted compounds are stabilized by H-bonding between the nitro and the alcoholic functions, which renders them more lipophilic than their meta and parasubstituted congeners. Once charged, however, this H-bonding disappears, and lipophilicity varies in accordance to the delocalization of the charge, which is better with the orthoand para-substituted anions due to higher resonance equilibria. This explains why 2,4dinitrophenolate is signiﬁcantly more lipophilic than the other anions in the series, which is in good agreement with their skin and stratum corneum permeabilities. This result also conﬁrms the key role played by H-bonding capacity in membrane permeation, as encoded N in log PN dce and not in log Poct . With multiprotic substances, the scheme of Fig. 12 must be expanded to all forms, which further complicates it. Nevertheless, doubly charged species are of course much less lipophilic than singly charged ones, since the Gibbs energy2þ of solvation varies with the square of the charge [see Eq. (33)], and typical diff ðlog PNI ;0 Þ values are about 11 [259]. However, if the distance between the charged sites of a molecule is large, the doubly charged species may be much more lipophilic than expected, because this ion does not behave as a dication but as twice a monocation. This has been evidenced by comparing the various partition coefﬁcient values obtained for trimetazidine and quinine in water–DCE and the electric ﬁeld around the doublyþ charged species (see Fig. 13). This study revealed 2þ that diff ðlog PNI ;0 Þ 2diff ðlog PNI ;0 Þ in the case of quinine because the charges are sufﬁciently far apart [241,257]. Finally, the diff ðlog PNI;0 Þ parameter has been used to identify intramolecular effects in zwitterions, compounds that attracted a special interest due to their totally singular pharmacokinetic behavior [86,323–326]. Despite the fact that they are globally neutral compounds, zwitterions are often less lipophilic than their respective cationic and anionic forms, so that their lipophilicity proﬁle exhibits a U shape. However, intramolecular interactions can deeply stabilize these charges, so that these proﬁles become bellshaped. High log PZ can result from neutralization through - or -bonds or through an internal ionic bond, and these effects have recently been reviewed [143]. The distribution proﬁles are not necessarily symmetrical because the anion and the cation may have different partition coefﬁcients. For both types of proﬁles, however, zwitterionic compounds have an approximately constant value of lipophilicity in the region around their isoelectric pH, so that they behave as ‘‘lipophilicity buffers’’ between their two pKaw values [143,327].

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FIG. 13 Electrostatic potential surrounding the doubly charged forms of trimetazidine (left) and quinine (right). The electrostatic potential was obtained by AM1 semiempirical calculations (Spartan 5.0, Wavefunction Inc., Irvine, USA), and it increases linearly from white to black. The physicow w chemical parameters of quinine and trimetazidine are respectively: pKa1 ¼ 4:48 and 4.54, pKa2 ¼ 8:51 0 I2þ N Iþ ;0 0 2 ;0 and 9.14, log Pdce ¼ 2:41 and 1.04, log Pdce ¼ 1:44 and 2:74, and log Pdce ¼ 5:31 and 9:84. (Reprinted from Ref. 257.)

It should ﬁnally be noted that the amount of the neutral and zweitterionic forms of a compound in solution is determined by its tatuomeric equilibrium constant, deﬁned as KZ ¼ cZ =cN . Therefore, the neutral species and the zwitterion coexist around the isoelectric pH, and membrane permeation is conditioned by KZ and by the partition coefﬁcient values of both tautomers.

D.

Relationships Between Physicochemical and Pharmaceutical Parameters

In the drug discovery process, the ﬁnal aim of partition coefﬁcient measurements is to ﬁnd a relationship between lipophilicity and the biological activity of a drug. Indeed, in the early 1960s, Hansch and coworkers [328–330] showed that bioactivity could be correlated with physicochemical properties such as lipophilicity by a linear regression analysis [331– 334]. This was a real breakthrough in pharmacochemistry, which lead to the development of what is now called ‘‘quantitative structure-activity relationships’’ (QSAR) [109,110]. Following the correlations between oil–water partition coefﬁcients and the potencies of narcotic drugs found by Meyer [335] and Overton [336] at the turn of the century, the era of QSAR started in the early 1960s with Hansch and coworkers [328] who showed that the effects of a series of phenoxyacetic acids on the growth of Avena plant cell cultures could be described by a quadratic function of hydrophobicity. This quadratic dependence has been observed in many systems, and the dominance of lipophilicity in controlling activity reﬂects its importance in transport [74]. Nevertheless, the biological response (BR) of a series of compounds (which is often expressed by the inverse of the drug concentration) may also involve an electronic (E) and/or a steric ðSÞ contribution. Hence, QSARs have been mostly constructed using the generalized Hansch equation [337]: 2 log BR ¼ a log PN þ b log PN þcE þ dS þ e

ð34Þ

Transfer Mechanisms and Lipophilicity

759

Such a parabolic relation has the following incidence on drug delivery: a molecule with a low partition coefﬁcient will partition slowly from water into a lipid membrane. If the receptor is within or beyond that membrane, such a molecule will have a low probability of reaching it in the time interval under study. Conversely, molecules which are highly lipophilic will readily partition into the ﬁrst of a series of lipid membranes, but will be held there and thus slowed down in their random walk to their site of action. Hence, optimal transport conditions are clearly achieved by drugs of intermediate partition coefﬁcient, with no transfer step being too low. Nevertheless, numerous QSARs involve other lipophilicity dependencies to model biological activity of drugs, among which Kubinyi’s bilinear relationship must be quoted [338] (see Ref. 109 for a review). However, the database collected by Hansch’s group showed in 1993 [339] that only 15% of the biological QSARs do not imply any lipophilicity term. Hence, lipophilicity is clearly a major determinant of biological activity [340]. If the lipophilicity of numerous neutral compounds has been correlated with their biological activity, literature is very scarce on QSARs taking account of the ionic forms of a drug. Actually, despite the increasing number of studies on ionizable drug transfer (see Refs 234, 267, and 341–343 for reviews), only very few lipophilicity data have been interpreted in terms of QSARs. Good agreement between the pharmaceutical activity of drugs and the lipophilicity of their ionic forms has only been qualitatively demonstrated for anaesthetics [265] and phosphorylation uncouplers [238,258,299], and few attempts have been made to relate the ionic partition diagrams of several drugs to their transport through biological membranes [241,257,259,263]. To our knowledge, only one systematic study provides quantitative relationships between ion lipophilicity and biological activity [266]. As shown in Fig. 14, good correlations have been established for compounds belonging to various pharmaceutical groups, showing linear relationships between the half-wave transfer potentials and their pharmacological activity expressed here as the median inhibiting concentration ID50 [344], the median effective concentration ED50 [345], or the intrinsic activity I [346]. QSARs based on ionic compounds have thus been dramatically restricted due to the neglect of ion partitioning, which consequently meant that no technique was dedicated to such measurements and that modeling never took account of ionic species. To become fully accepted, potentiometry and electrochemistry at the ITIES need now to prove interesting in QSARs. As numerous lipophilicity data of ionizable compounds become available, one can expect that solvatochromic equations for ions will soon be developed in various solvent systems, which would greatly facilitate QSAR studies.

V.

CONCLUSION

Encouraged by its fantastic success at discovering drugs, the pharmaceutical industry has become ever more ambitious in the type of biologically active compounds that it develops. Whereas two decades ago the majority of drug targets were enzymes, the advances in molecular and cell biology have opened the way to cell-membrane receptors and their ligands, ion channels, intracellular signaling molecules, and even nuclear targets such as transcription factors. However, the very complex mechanisms of action of these drugs and the pressure on the industry to diminish research and development costs require rapid advancements in the knowledge of the pharmaco- and physicochemical interactions of organic compounds with

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FIG. 14 Relationships between the half-wave potential and the pharmacological activity of: (a) hypnotic drugs, (b) local anesthetic drugs, (c) cholinergic drugs, (d) anticholinergic drugs, (e) adrenergic drugs, and (f) antiadrenergic drugs. The values of the median inhibiting concentration ID50 , the median effective concentration ED50 , and the intrinsic activity I were taken from the literature. (Reprinted from Ref. 266.)

biological features and call for an increasing number of studies and technologies (e.g., high-throughput screening [347], structure-based drug design [348,349], and combinatorial chemistry [350]) before bringing new drugs on to the market. Physicochemical parameters and, in particular, lipophilicity are an absolute must in the drug discovery process, which explains why this ﬁeld is the object of such intense study worldwide. If pharmacological research has so far been limited to neutral compounds because of lack of experimental techniques, the interest of the pH–lipophilicity proﬁles for the discovery of novel lead compounds will certainly force medicinal chemists to pay more attention to ion partitioning. In this respect, the pH-metric technique and the electrochemical methodologies at the ITIES afford a large amount of highly reliable physicochemical and mechanistic information, as exempliﬁed by the assessment of partition coefﬁcients, dissociation constants, and difference parameters. Each technique possesses its own advantages (e.g., the possibility of using a water–OCT system for the former and direct access to standard thermodynamic values for the latter). These experimental techniques are completed by the ionic partition diagram representation, which compiles all the measured data in a kind of description card. The simplicity of this representation and its efﬁciency in predicting lipophilicity and transfer mechanisms render it very attractive for most applications in biphasic systems, and it promises extensive use in pharmacokinetic studies. To reach this aim, however, it still requires automation and systematic biological validation.

Transfer Mechanisms and Lipophilicity

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If the electrochemical methodology improves lipophilicity measurements of ionizable compounds, since it overcomes the main limitation of the neglect of ion partitioning, the implications of the currently available experimental results on drug transport, delivery, and design remain unexplored. Also, the individual steps composing the global transfer mechanisms (i.e., solvation–desolvation of ions, adsorption, and association–dissociation equilibria in the bulk and in the vicinity of the interface) have not been examined yet. To complete the above work, a variety of fundamental investigations should now be performed, for instance in the ﬁelds of the kinetics of drug transfer across model biological membranes (e.g., by use of potential modulated techniques [351]), of the process of drug adsorption at interfaces (e.g., by surface tension measurements [341,351] or surface second harmonic generation (SSHG) [353–357]) or of the establishment of quantitative structureproperty relationships [174] (e.g., by using standard techniques of computational chemistry [358–360]).

ACKNOWLEDGMENTS We want to express our gratitude to Prof. Hubert H. Girault of the Laboratoire d’Electrochmie of the Ecole Polytechnique Fe´de´rale de Lausanne as well as to Prof. Bernard Testa and Dr. Pierre-Alain Carrupt of the Institut de Chimie The´rapeutique of the Universite´ de Lausanne (Switzerland) for their fruitful collaboration, insightful discussions, and valuable comments on this manuscript. We are also indebted to the Swiss National Science Foundation for its support. Laboratoire d’Electrochimie is part of the European Training and Mobility Network on Organization Dynamics and Reactions at Electriﬁed–Liquid Interfaces (ODRELLI).

ABBREVIATIONS AND ACRONYMS Roman Alphabet a: activity A: interfacial area B: base BR: biological response c: concentration CHF (chf): chloroform D: diffusion coefﬁcient, or distribution coefﬁcient DBE (dbe): dibutylether DCE (dce): 1,2-dichloroethane diff ðlog PÞ: difference between two partition coefﬁcients in the same solvent system e: charge of the proton E: applied potential at a metal–electrolyte solution interface eff : effective f : Rekker’s fragmental constant f 0 : Leo and Hansch’s fragmental constant F: Faraday constant Fj : Leo and Hansch’s correction factor FWD: forward potential scan G: Gibbs energy

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HEP (hep): heptane i: species i or serial number i I: ionic species (cation or anion) I: current ITIES: interface between two immiscible electrolyte solutions KZ : tautomeric equilibrium constant between the zwitterionic and the neutral forms of a compound LSER: linear solvation energy relationship MLP: molecular lipophilicity potential n: mole number N: neutral species nj : numerical factor indicating the occurrence of a fragment in a structure nHþ : average number of bound protons NA : Avogadro number NSAID: nonsteroidal anti-inﬂammatory drug o: organic phase OCT (oct): n-octanol p: peak P: partition coefﬁcient pKa : acidic dissociation constant p0 Ka : apparent acidic dissociation constant QSAR: quantitative structure–activity relationship r: phase volume ratio R: universal gas constant T: temperature TATB: tetraphenylarsonium tetraphenylborate TIC: transfer by interfacial complexation TID: transfer by interfacial decomplexation TMA: tetramethyl ammonium tot: total tr: transfer V: volume Vw : van de Waals volume w: van der Waals or water phase x: molar fraction X: compound X z: charge number Z: zwitterion Greek Alphabet : solute hydrogen-bond donor acidity, or phase : solute hydrogen-bond acceptor basicity or phase : activity coefﬁcient 0;! Gtr;i : Gibbs transfer energy of an ion i from phase to GIS : Gibbs energy for ion–solvent interaction in phase log P: partition coefﬁcient difference between two solvent systems : Galvani potential difference between and phases wo 1=2 : half-wave potential

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wo p : potential difference between forward and reverse peak current "0 : vacuum permittivity "r : dielectric constant : solvent viscosities : chemical potential ~ : electrochemical potential : potential sweep rate : square root of the ratio of the diffusion coefﬁcients in two adjacent phases : Hansch’s substitutent constant, or number pi : dipolarity/polarizability term

: inner (or Galvani) potential Superscripts *: bulk or initial value 0: standard 0 0 : formal

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32 NMR Studies on Lipid Bilayer Interfaces Coupled with Anesthetics and Endocrine Disruptors EMIKO OKAMURA and MASARU NAKAHARA Research, Kyoto University, Kyoto, Japan

I.

Institute for Chemical

INTRODUCTION

Molecules which are composed of hydrophilic (polar or ionic) and hydrophobic (nonpolar) moieties are called amphiphiles. When amphiphilic compounds are dissolved into water, their dual nature avoids the macroscopic phase separation and spontaneously forms vesicles, micelles, and emulsions depending on the thermodynamic conditions and the hydrophile–lipophile balance (HLB). A wide variety of interfaces or membranes are constructed by the self-organization of amphiphilic molecules to separate the molecular ﬁeld composed of nonpolar interior and polar interfaces from the aqueous exterior. The self-assembling phenomenon is of great importance in aqueous biological systems. Biological membranes are highly organized with a composite structure, as schematically pictured by the ﬂuid mosaic model by Singer and Nicolson [1]. The existence of biomolecules conﬁned to membranes is a necessary condition for the appearance of vital activities. Drug delivery (DD) from an aqueous medium into biomembranes is crucial as a primary step of the bioactivity. When a drug is delivered to membranes, both drugs and membranes are perturbed. Thus the DD process should be monitored on both sides of drugs and membranes. This can be done by sensitive high-resolution NMR. In particular, direct information on the drug side is needed to elucidate the DD mechanism. The equilibrium concentration of the drugs in membranes is, however, rather low and the detection has been very difﬁcult for commercially available samples. In this situation attention has been paid to the membrane side of membrane–drug interactions. Now the application of the highly developed NMR method to both sides of drugs and membranes is expected to make a signiﬁcant contribution to advances in the DD study. DD can be monitored by a variety of experimental techniques. They involve thermodynamic, dilatometric, and spectroscopic procedures. Molecular dynamics (MD) simulations also become applicable to self-assembled systems to some extent; see the review in Ref. 2. Spectroscopic methods provide us with molecular parameters, as compared with thermodynamic ones on the macroscopic level. The ﬂuorescence probing method is very sensitive (mM to nM; M ¼ mol dm3 ) and informs us of the molecular environment around the probes. However, ﬂuorescent molecules are a kind of drug and the membrane 775

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may be perturbed by their injection. In contrast, NMR sepctroscopy is a noninvasive method and provides site-selective information. Although the sensitivity is rather low (>100 mM), NMR enables us to determine static and dynamic properties of both drugs and membranes. Here we review the molecular level DD research carried out by NMR. The drugs discussed are summarized in Table 1. The structures of the drugs, which are classiﬁed into anesthetics and endocrine disruptors, are shown in Fig. 1. Anesthetics, which induce general and local anesthesia, are examples of the most popular drugs clinically used. The anesthetic mechanisms have been extensively discussed over the past century in view of the Meyer–Overton correlation [3] proposed just at the end of the 19th century. However, the mechanism has not yet been fully understood. The molecular mechanism still remains unsolved. On the other hand, endocrine disruptors are concerned with the most recent and sensational problems of the endocrine damage of wildlife. They are hydrophobic organic compounds exhibiting a high afﬁnity with lipid membranes [4]. They are environmental pollutants and exogeneous chemicals that interfere with the endocrine system of intact organisms. They include bisphenol A, alkylphenols, and alkylbenzenes. Molecular study of lipid bilayer interfaces is necessary for a better understanding of the membrane–drug interaction and DD into biomembranes. The points to be clariﬁed are: (1) How can we determine DD sites at the bilayer interface? (2) What kind of method is advantageous? (3) Is it possible to unambiguously specify the bilayer interfacial portion coupled with drugs? (4) What are most important characteristics of DD at the bilayer interface? In order to answer these important questions, this chapter has been planned. We will emphasize the signiﬁcance of the molecular level information obtainable from NMR studies. In the 1970s the structure and dynamics of lipid bilayer membranes were extensively investigated by NMR. The principles of the NMR spectroscopy applied to the study of biomembranes are reviewed in Ref. 5, together with the fruitful achievements in the early stage. In the 1980s the NMR biomembrane research was carried out mainly by applying the solid-state NMR techniques [6–11]. Generally, the solid-state spectra are of low reso-

TABLE 1

List of Drugs Discussed

Anesthetics

Endocrine disruptors

General anesthetics

Alkanols Halothane Enﬂurane Isoﬂurane Halogenated cyclobutanes Xenon

Local anesthetics

Dibucaine Procaine Tetracaine Lidocaine Benzyl alcohol

Bisphenol A Alkylbenzenes

Benzene Toluene Ethylbenzene Propylbenzene

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FIG. 1 Molecular structures of the drugs examined in the delivery study: the general anesthetics, alkanols (I), halothane (II), enﬂurane (III), isoﬂurane (IV), halogenated cyclobutane (V); the local anesthetics, dibucaine hydrochloride (VI), procaine hydrochloride (VII), tetracaine hydrochloride (VIII), lidocaine hydrochloride (IX), benzyl alcohol (X); the endocrine disruptor, bisphenol A (XI), and alkylbenzenes, benzene (XII), toluene (XIII), ethylbenzene (XIV), and propylbenzene (XV).

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lution due to the dipole–dipole interactions. Now the spectral resolution has been improved to a large extent by the combined application of cross polarization (CP) and magic angle spinning (MAS). In the case of solid-state NMR, high signal-to-noise ratios are obtained usually with the aid of labeled 2 H, 13 C, and 15 N nuclei; enriched samples are, however, expensive. High-resolution solution NMR is more informative and can be used for the study of biomimetic membranes for the following reasons: membrane lipids are rapidly ﬂuctuating under physiological conditions. Vital functions of biomembranes are actually associated with large ﬂuctuations of the membrane components. The larger the surface curvature, the larger the ﬂuctuations. Surface curvatures are often related to biomembrane function and integrity. For example, the synaptic vesicles in axons involve the highest membrane curvatures in eucaryotic cells [12]. It is well-known that plasma lipoproteins regulate apolipoprotein binding by controlling their surface curvatures; the average diameters of the aggregates range from 200 to 10 nm in the lipid metabolism processes [13]. For the case of these biological membrane systems with large ﬂuctuations, therefore, it is of great interest to apply the solution NMR with high-sensitivity and high-resolution, using low-cost and naturally abundant samples. The scope of this review is to summarize the recent development of the solution NMR to DD from aqueous phase to lipid bilayer membranes on the basis of our recent NMR work. Relevant physicochemical and computational aspects of the membrane DD are also referred to here.

II.

CHARACTERIZATION OF LIPID BILAYER INTERFACES

Before going to the discussion of DD, we ﬁrst summarize the general features of lipid bilayer structures and dynamics.

A.

Methods

Physicochemical techniques so far applied to the study of structural and dynamical properties of phospholipid bilayers are the following: x-ray diffraction [14–17], neutron scattering [18], infrared (IR) and Raman scattering [19–25], nuclear magnetic resonance (NMR) [5,15,26–30], electron spin resonance (ESR) [31–33], ﬂuorescence [34], calorimetry [35–37], dilatometry [38–40], and molecular dynamics (MD) simulations [2,41–44]. These methods are listed for comparison in Table 2. Each method provides structural information averaged on a characteristic length scale and dynamical information on a characteristic time scale. NMR is a versatile noninvasive technique. It can provide information not only on microscopic structure at an atomic scale but also dynamics in a range from picoseconds to seconds. Low-sensitivity problems have nowadays been overcome by the introduction of the Fourier transform (FT) technique, the dramatic improvement of the computerized instrumentation, and the stable and homogeneous generation of the high magnetic ﬁeld. Recent progress in 13 C NMR enables us to obtain reliable site-selective information on membrane structure and dynamics without labeling nuclei. Unlike neutron scattering and IR absorption, no solvent peaks of water can interfere with the membrane and drug signals in the 13 C NMR spectra.

b

a

Atom ð126Þ Static Dynamic

Atom–Atom (14–12) Static

IR/Raman

Electron microscopy. Molecular dynamics simulation.

Scale Log(time/s) Probe Information

NMR

Molecule 1 Static

EMa

Molecule (11–9) þ Dynamic

ESR

Molecule (10–6) þ Static Dynamic

Fluorescence

Molecule (14–12) Static

Neutron scattering

TABLE 2 Physicochemical Techniques for the Characterization of Lipid Bilayers

Atom–Atom >2 Static

X-ray

Calorimetry 1 >2 Static

Light scattering 1 2 Static Dynamic

Atom (12–9) Static Dynamic

MDb

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Static and Dynamic NMR

One of the most important advantages of the NMR method is the selectivity of the atomic site of interest. NMR spectroscopy enables us to investigate the structure and dynamics of lipid bilayers at each atomic site. The static and dynamic parameters of lipid bilayers obtainable from NMR are the chemical shift, , the spin coupling constant, J, the linewidth, 1=2 , the longitudinal relaxation time, T1 , the transverse relaxation time, T2 , and the self-diffusion coefﬁcient, D. These are summarized in Table 3 to show the characteristic information. The chemical shift is the most popular parameter that reﬂects the molecular environment of an atom; it gives sensitive and detailed information about the molecular structure [45]. The spin coupling constant also gives the structural or geometrical information via nuclear spin interactions through one or more bonds. Since the position and the orientation of molecules ﬂuctuate with time, the chemical shift and the coupling constant are observed as averaged values. Linewidth can be broadened dynamically and statically; the dynamic and static broadenings are due to a decrease in the motional narrowing effect and an increase in inhomogeneity, respectively. Linewidth and two relaxation times reﬂect the molecular and molecular-assembly motions. The self-diffusion coefﬁcient also reﬂects the translational mobility of molecules. Two-dimensional (2D) NMR tells us about the average atom–atom distances. Atomic nuclei often used for the NMR study of lipid bilayers are 1 H, 2 H, 13 C, 14 N, 15 N, and 31 P; natural and model lipid membranes are usually composed of these atomic nuclei. Magnetic properties of these nuclei are summarized in Table 4. 1 H is the most sensitive, the chemical shift being reliable within 0:001 ppm. 2 H is useful to specify the hydrogen atom position by the isotope labeling on enrichment. Hydrophilic and hydrophobic moieties of bilayers are usually composed of carbon atoms, so 13 C can give us sharp information about structure and dynamics of bilayers. It is a unique nucleus for probing ester carbonyls, which are important as a DD site in lipid bilayer interfaces. The sensitivity has been improved by the proton-decoupling technique and the nuclear Overhauser effect (NOE). 2 H and 14 N are quadrupolar nuclei, which can provide local and short-range information on functional motions and microenvironments around the probed nuclei; these are to be compared with such dipolar (half-spin) nuclei as 1 H, 13 C, 15 N, and 31 P. 17 O, 19 F, 23 Na, and 35 Cl are sometimes used to investigate DD from aqueous phase to lipid bilayers.

TABLE 3 High-Resolution NMR Parameters Providing Static and Dynamic Information on Lipid Bilayers Parameter

J 1=2 T1 ; T2 D

Information Molecular structure Environment (electron density, hydrogen bonding, solvent effect, hydration etc.) Conformations Segmental motions, order parameters, exchange rates Segmental motions, relaxation rates Atomic, molecular, and aggregate motions

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TABLE 4 Magnetic Properties of Atomic Nuclei Used for the NMR Study of Lipid Bilayers and Drug Delivery Nucleus 1

H H 13 C 14 N 15 N 17 O 19 F 23 Na 31 P 35 Cl 2

Ia

Abundanceb

Sensitivityc

Frequencyd

Site selectivity

1/2 1 1/2 1 1/2 5/2 1/2 3/2 1/2 3/2

99.98 0.015 1.108 99.63 0.37 0.0037 100.00 100.00 100.00 75.53

1.00 0.0097 0.016 0.0010 0.0010 0.029 0.83 0.093 0.066 0.0047

100.00 15.35 25.14 7.22 10.13 13.56 94.08 26.45 40.48 9.80

Zone I, II, III Zone I, IIe , III Zone I

Zone I

a

Nuclear spin. Natural abundance in percent. c Sensitivity relative to 1 H NMR. d Frequency in MHz in the case of the external magnetic ﬁeld, 2.35 T. e13 — O in zone II. C NMR is the only method to probe ester C — b

C.

Classiﬁcation of Zones of Lipid Bilayers

Biomembranes mainly consists of phospholipid matrices, and the major component is phosphorylcholines (PC). PC is an amphiphile consisting of hydrophilic headgroup and hydrophobic long chains. In view of the amphiphilic feature of PC, we can divide hydrated lipid bilayers into the three zones, I, II, and III. The zone model, which has been used in a recent NMR study of DD [46–48], is illustrated in Fig. 2. Zone I is the hydrophilic part of the bilayer. It includes the polar headgroup consisting of positively charged choline ammonium group and negatively charged phosphate

FIG. 2 A zone model of bilayer vesicles consisting of amphiphilic lipid molecules.

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group. Electrostatic interactions between PNþ dipoles and the PNþ and water dipoles are important in this zone. Water can easily come into this part; strong hydration is always the case. Zone II is the interfacial region between the hydrophilic and the hydrophobic parts of the lipid. Glycerol and ester carbonyl groups belong to this region. This region is most sensitive to the bilayer curvature or the aggregate size. In this region the water penetration also depends on the curvature. Zone III is the hydrocarbon chain region and composes the bilayer core. This region is nonpolar, and it is dominated by the hydrophobic interactions of the chains. Thus water rarely penetrates into this core region. It is to be noted that the zone boundary in Fig. 2 is an averaged one; it usually ﬂuctuates due to the molecular, segmental, and overall aggregate motions. Lipid bilayer membranes can cover a wide range of polarity in a limited colloidal or mesoscopic space as shown in Fig. 3. Corresponding to the zone model in Fig. 2, it is schematically illustrated how the dielectric constant " and the water density ðH2 OÞ distribute in the layer. In the hydrophilic zone I, " and ðH2 OÞ are very close to the bulk in the aqueous phase due to the substantial hydration. A marked decrease in " and ðH2 OÞ with a large gradient is characteristic of the interfacial zone II. No substantial hydration is recognized in the hydrophobic zone III. Thus, zone II is expected to play a key role in connecting the hydrophilic and hydrophobic microenvironments in a short range. Zone II can be a gate interface for various biological functions and DD (cf. the ion channel). D.

Phase Behavior of Lipid Bilayers

Polymorphic phase behavior of hydrated lipid bialyers can be one of the controlling factors of DD, because DD depends on the dynamical features of the bilayer which abruptly change upon phase transition. The most typical transitions of biological signiﬁcance are the thermotropic transition [the gel (G) to liquid–crystalline (LC) phase transition] and the barotropic transition [49]. The overview of the phase transition phenomena is beyond the scope of this review; see Refs. 37, 49, and 50. Most extensively investigated is the phase transition behavior of 1,2-dipalmitoyl-sn-glycero-3-phosphorylcholine (DPPC), the lipid component occurring frequently in natural membranes. A phase diagram of fully hydrated DPPC bilayers is shown in Fig. 4 [50]. At ambient pressure, gel ðL 0 Þ, rippled gel ðP 0 Þ, and liquid-crystalline ðL Þ phases usually appear with increasing temperature. At

FIG. 3 A schematic representation of the variation of the dielectric constant " and water density ðH2 OÞ in the water medium (bulk) and three zones of lipid bilayers.

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FIG. 4 Phase diagram of fully hydrated DPPC bilayers. Different phases found are also schematically shown: L 0 , gel; P 0 , rippled gel; L I, interdigitated gel; and L , liquid crystalline phases. (From Ref. 50. Copyright # 1999 The Japan Society of High Pressure Science and Technology.)

high pressures, the interdigitated gel phase ðL IÞ is formed as a result of high molecular packing. 1 H, 2 H, 13 C, and 31 P NMR are valuable for the elucidation of structural and dynamical aspects of the phase behavior on the molecular level, as reviewed in Refs. 5 and 26. 13 C NMR spectroscopy is advantageous because of its ability to distinguish the individual carbon atom site in the bilayer. It enables us to probe all carbon atoms of cholines in zone I, glycerol and carbonyls in zone II, and alkyl chains in zone III simultaneously. 31 P NMR tells us only headgroup information in zone I; see Table 4. There has been, however, relatively few number of reliable 13 C NMR studies due to the low sensitivity in the case of natural-abundance samples. Using a large-size NMR tube (10 mm o.d.) we have succeeded in observing high-resolution 13 C NMR spectra of DPPC membranes over a wide temperature range encompassing the G/LC phase transition [51]. Using the chemical shifts, we have examined the continuity and discontinuity of their temperature dependence, as summarized in Table 5. The nature of the ﬁrst-order transition is most pronounced with respect to ðCH2 Þn in the hydrophobic core. It has been proved that the ester carbonyl group in zone II is most susceptible to the change in hydration induced by the transition. This ﬁnding is relevant to the DD mechanism because DD into bilayer membranes from aqueous phase often affects the hydration of the bilayer interface and drugs. 14 N is a unique quadrupole nucleus for probing the choline ammonium of the hydrophilic headgroup of DPPC in zone I. It is interesting to examine the phase transition behavior of DPPC bilayers also by 14 N NMR [52]. Contrasting features have been disclosed by the comparison between the 14 N and the 13 C NMR spectra of the choline group in DPPC bilayers and analogous lysoPC micelles as a function of temperature. As shown in Fig. 5, 14 N NMR spectra are strikingly sensitive to the temperature and the surface curvature of the membrane, whereas the 13 C signals of the choline methyl ðÞ are almost independent of these parameters. Difference in the sensitivity between the quadrupolar 14 N and the dipolar 13 C is interesting because choline nitrogen and methyl carbons are close to each other. In other words, 14 N NMR specra provide more local and short-ranged information on the segmental motion and microenvironments of nitrogen atoms, as com-

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TABLE 5 NMR Characterization of Thermal Phase Transition in Zones I–III of Phospholipid Bilayers Zone I

II

III

Site

Type of transition

Choline N(CH3 Þ3 CH2 N POCH2 Phosphatea

Continuousc Continuous Constantd Almost continuous

Glycerol CH2 OP CHORb CH2 OR Carbonyl

Constant Constant Constant Almost continuous

Alkyl chain (CH2 Þn CH3

Discontinuouse Almost continuous

a

From Ref. 26. R ¼ acyl. c Monotonous change against temperature. d Independent of temperature. e Abrupt change against temperature. b

pared with such dipolar nuclei like 1 H, 13 C, and 15 N. Quite similar trends have been found in small and large unilamellar vesicles of egg yolk phosphatidylcholine (EPC). 14 N NMR study is useful to the DD study, because the hydrophilic phosphoyrlcholine in zone I is the ﬁrst contact site of DD from aqueous phase and directly affected by the ﬁrst step of the DD process.

III.

BASIC CONCEPTS OF DRUG DELIVERY

As a primary step of the biological action, both anesthetics and endocrine disruptors are delivered into lipid bilayer membranes from the aqueous phase. The delivery site of drugs in membranes is closely related to the subsequent action mechanism. It is thus important and valuable to directly determine the DD sites and orientation of drugs in membranes. Most recently, we have succeeded in specifying the DD site in small unilamellar vesicles (SUV) of EPC with a diameter of 50 nm, by taking advantage of the atomic site selectivity of NMR [46]. As model membranes, EPC SUV are useful to investigate DD by high-resolution solution NMR because of the large ﬂuctuation of the EPC molecules.

A.

Drug Delivery Sites and Membrane–Drug Interactions

Here the basic concepts and the method for strictly determining DD sites in lipid bilayer membranes are viewed, together with some examples of their applications.

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FIG. 5 14 N NMR (left) and 13 C NMR spectra (right) of the small and large unilamellar vesicles, SUV and LUV, of DPPC at various temperatures. For comparison, the spectra of palmitoyl lysophosphatidylcholine micelles at 308C are given by trace a. Traces b and c denote the spectra of the DPPC SUV with a diameter of 55 nm at 30 and 508C, respectively; trace d represents the spectra of the DPPC LUV with 100 nm diameter at 508C. Saturated KNO3 in D2 O was used as an external reference for the 14 N NMR spectra. In the 13 C NMR spectra, the signal assignment is also shown; , , and denote the choline methylene and methyl carbons POCH2 , CH2 N, and N(CH3 Þ3 , respectively. Asterisks (*) indicate the CH and two CH2 signals of the glycerol group.

1.

Categories of Drug Delivery Sites

DD sites have been classiﬁed into the three categories, as illustrated in Fig. 6 [46]. Category I is where drugs are adsorbed on the hydrophilic surfaces of bilayer membranes, zone I in Fig. 2, by Coulombic interactions or hydrogen bonding. In this case, drugs are generally polar and water-soluble; for example, procaine hydrochloride (VII) in Fig. 1. No signiﬁcant effect of drugs is induced in the membrane interior, zone III. Category II is the case where drugs slightly penetrate into and are trapped at the interfacial site of the membranes, zone II. These drugs are less hydrophilic than those of category I, such as alkanols (I), dibucaine hydrochloride (VI), lidocaine hydrochloride (IX), benzyl alcohol (X), bisphenol A (XI), and benzene (XII) in Fig. 1. These drugs do not signiﬁcantly perturb the inner hydrophobic chains in zone III. Membrane structure is perturbed mainly at the interfacial glycerol and carbonyl sites of phospholipids in zone II. Category III is where drugs deeply penetrate into the hydrophobic chain region of the membranes. These drugs are ethylbenzene (XIV) and propylbenzene (XV) in Fig. 1; almost insoluble in water, nonpolar, and highly lipophilic. In this case, the membrane interior, zone III, can be most remarkably perturbed.

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FIG. 6 Classiﬁcation of drug delivery sites in lipid bilayers.

In order to distinguish the two membrane-trapped states of categories II and III, we have paid attention to the membrane curvature difference between inner and outer layers [46]. When drugs are trapped at the interfacial site (category II), the NMR signal splitting can be recognized due to the curvature difference. There is, however, no effect when drugs are incorporated deeply into the hydrophobic membrane interior (category III). Since drugs penetrate into the outer layer of the membrane and are ﬁnally transported to the inner layer, the distinction of these two layers plays an important role in monitoring the DD processes.

2. Noninvasive Determination of Drug Delivery Sites by NMR In this section, we focus on how to determine DD sites by NMR. The speciﬁcation of the DD sites in bilayers can be done by utilizing the NMR signals of both drugs and membrane lipids. An example of the delivery site determination is given for the case of two benzene derivatives, propylbenezene (PrBe) and benzyl alcohol (BzOH) in egg phosphatidylcholine (EPC) bilayers [46]. Alkylbenzenes are suspected to be endocrine disruptors, and BzOH is one of the local anesthetics. (a) Changes of Molecular Environments of Drugs. In order to determine the trapped site of drugs at the atomic-site level from their direct NMR signals, we have followed the empirical rule that the NMR signals largely shift to a higher ﬁeld when molecules are dehydrated in the nonpolar environment [46]. Here we call it the hydration chemical shift (HCS) rule. According to this simple and powerful rule, the NMR signals of the trapped drugs should shift to a higher ﬁeld in the order, category I
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that the drug categories determined by the HCS rule correspond well to the solvent polarity dependence of the drug solubility as discussed in Section VI. Propylbenzene. We have succeeded in observing the high-resolution NMR spectra of aqueous propylbenzene (PrBe) solution, as shown in Fig. 7(a) [46]. The ring proton NMR signal of PrBe is the strongest at 7.41 ppm in the aqueous environment. It is of great signiﬁcance in detecting the reliable NMR signal of PrBe in water, because PrBe is sparingly soluble in water; it is at a sub-mM level. The delivery of PrBe from water to EPC bilayers induces typical changes in NMR spectra, as shown in Figs. 7(b) and (c) [46]. A broad signal and relatively sharp ones appear at 0.05 and 0.2–0.4 ppm higher ﬁelds than those in water, respectively. The signal of PrBe in water disappears; it means that the delivery of PrBe occurs from aqueous phase. The high-ﬁeld shift (0.05 ppm) of the broad signal is not large. According to the empirical HCS rule, this is due to the PrBe molecules located near the polar environment. We can acribe this signal to the PrBe adsorbed on the SUV surface in zone I of Fig. 2. The broad linewidth, which indicates the restricted molecular motion, also supports the adsorption of PrBe at the aqueous surface. On the other hand, the high-ﬁeld shifts (0.2–0.4 ppm) of the relatively sharp signals are large and due to the PrBe molecules in considerably hydrophobic surroundings. Thus we have ascribed this to the PrBe deeply penetrating into the hydrophobic core of the membrane interior, zone III. The assignment is also supported by the agreement of the signal with that of PrBe in n-hexane shown in Fig. 7(d). It has been also proved that there is no particular restriction to the motion of PrBe in the membrane core, zone III, because of the appearance of the sharp signal due to the motional narrowing effect. It is noteworthy to simultaneously distinguish the two different delivery sites for the DD process. The disappearance of the broad signal and the simultaneous increase of the sharp signals from (b) to (c) (shown by the dashed arrow) indicates that the PrBe,

FIG. 7 Ring proton region in the 1 H NMR spectrum of PrBe. (a) In D2 O, (b) immediately, and (c) 3 d after injection of EPC SUV. The 1 H NMR spectrum of PrBe in n-hexane solution is also shown in (d). (From Ref. 46. Copyright # 1999 American Chemical Society.)

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adsorbed at the bilayer surfaces, is ﬁnally trapped in the hydrophobic core due to the much stronger afﬁnity with the hydrophobic lipid phase. Benzyl alcohol. We have demonstrated that all benzyl alcohol (BzOH) molecules dissolved in water are also immediately transported and trapped in the lipid bilayer phase, when it is mixed with EPC bilayer [46]. The trapped site of BzOH, however, differs from that of PrBe. As shown in Fig. 8, the ring proton signal of BzOH in water is at ﬁrst broadened and shifted to a higher ﬁeld [from (a) to (b)]; then the signal is split into two (c). As pointed out in Section III.A.1, we have utilized the membrane curvature difference between inner and outer layers, to interpret the NMR signal splitting. From the similarity of the signal splitting observed for the 13 C NMR signal of the interfacial carbonyl site of the EPC SUV [54,55], we have explained that, unlike the case of PrBe, BzOH is immediately trapped near the carbonyl site of EPC at the interfacial zone II, and assigned the doublet of the ring proton signal to BzOH trapped in the outer (shown by the asterisk) and the inner layer of the bilayer, respectively. In order to conﬁrm the assignment described above, we have utilized the lanthanideinduced shift, LIS. Since neither the polar site in the inner layer nor the hydrophobic site can make contact with the lanthanide ions in the bilayer, the NMR signal shifted by LIS can be assigned to the hydrophilic site in the outer layer. We have mixed two kinds of the paramagnetic lanthanide reagents (YbCl3 and PrCl3 ) with the sample from the outer aqeuous phase side [46]. LIS can be observed in the asterisked ring proton signal of BzOH in the presence of Yb3þ and Pr3þ [Fig. 8(d) and (e), respectively], while the other signal essentially remains constant (see the dashed line). It is therefore clear that BzOH is preferentially trapped at the interfacial site of the bilayer, zone II. In order to evaluate the DD site semiquantitatively, we have analyzed the chemical shift change of the ring proton signals of PrBe and BzOH on the delivery from water to

FIG. 8 Ring proton and methylene signals in the 1 H NMR spectra of BzOH. (a) In D2 O, (b) immediately, and (c) 15 min after injection of EPC SUV. Asterisks (*) indicate the ring proton signal of BzOH delivered to the outer layer of the SUV. The dashed line denotes the position of the BzOH signal trapped into the inner layer of the SUV. The 1 H NMR spectra of BzOH–SUV system in the presence of the 12 mM Yb3þ and 70 mM Pr3þ are also given in (d) and (e), respectively. (From Ref. 46. Copyright # 1999 American Chemical Society.)

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bilayer phases [46]. As shown in Table 6, of BzOH is small (0:03 and 0:05 ppm). In contrast, the absolute value of the of PrBe is relatively large (0:36 ppm). On the basis of the HCS rule, the drugs deeply penetrate into the bilayer interior in the order PrBe>BzOH, which is in accord with the sequence of the insolubility in water. (b) Membrane Pertubation. As pointed out before, DD sites can also be demonstrated by analyzing values of the NMR signals of the bilayers during the delivery process. The membrane side of the NMR signal is most perturbed at the DD site by the ring current effect of the drug. We have compared the site dependence of the 1 H NMR ring current effect between PrBe and BzOH [46]. As shown in Table 7, the ring current effect by PrBe is small for the choline methyl proton in zone I. The effect is, in contrast, large in the chain methylene and methyl signals in the bilayer core, zone III; values are gradually shifted to a higher ﬁeld with time. On the other hand, BzOH induces the remarkable signal perturbation of the hydrophilic choline methyl proton in zone I, whereas the effect is relatively small in the hydrophobic chains in zone III. In order to specify the DD site, we have also analyzed the change in the 13 C NMR spectra [46]. All results of the 13 C NMR spectra are consistent with the DD sites determined by 1 H NMR. In Table 8, we can clearly specify carbon atom sites of EPC; the most prominent change is induced by the delivery of BzOH. Large ’s are observed at the choline methyl, glycerol C2, and carbonyl sites in zones I and II; signiﬁcant change is recognized also in the chain and methylenes, the two sites most adjacent to the headgroup. The values at the other sites are within the experimental error. (c) Delivery Sites and Orientations. The delivery sites of PrBe and BzOH have been determined as illustrated in Fig. 9 [46]. PrBe is penetrated into the hydrocarbon tail region in zone III of the bilayer. The alkyl chain of PrBe has a strong afﬁnity with this region. It is thus clear that PrBe belongs to categroy III in Fig. 6. The delivery site of BzOH is the interfacial region, zone II, near the carbonyl group of EPC. The delivery site determination of BzOH by the NMR signal splitting is novel and unique. Combining the 1 H and 13 C NMR, we have demonstrated that BzOH belongs to category II. The orientation of BzOH trapped at the interfacial site can also be determined; the aromatic ring of BzOH cannot penetrate deeply into the bilayer because of the bulkiness, and the methylene group of BzOH is oriented toward the inside of the bilayer compared to the aromatic ring [46].

TABLE 6 Chemical Shift Difference of the Ring Proton Signals of PrBe and BzOH Delivered to the EPC SUV from the Water Phase a in D2 O PrBe BzOH a

7.41 7.39

in EPC SUVb 7.05 7.36 (Out) 7.34 (In)

c 0:36 0:03 0:05

Chemical shift in ppm for the strongest signal. Chemical shift after the drug injection. c Chemical shift difference in ppm. Negative values mean upﬁeld shifts. Source: Ref. 46. Copyright # 1999 American Chemical Society. b

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TABLE 7 Change in the Value of the 1 H NMR Signals of the EPC SUV Associated with the Drug Delivery a

Choline CH3

Chain (CH2 Þn

Chain CH3

EPC only +PrBe +BzOH

3.24

EPC only +PrBe +BzOH

1.25

EPC only +PrBe +BzOH

0.87

5 min after

3 d after

3.22 3.15

3.22 3.15

1.23 1.26

1.20 1.26

0.85 0.87

0.84 0.87

a

Chemical shift in ppm. Source: Ref. 46. Copyright # 1999 American Chemical Society.

TABLE 8 Carbon Atom Site of the EPC SUV Affected by the Delivery of BzOH, Together with Its Chemical Shift Difference Observed in the NMR Signal a Choline CH3 Glycerol CH Carbonyl Chain -CH2 Chain -CH2

0:07 0:08 0:09 (out) þ0:03 (in)b 0:07 0:09

Chemical shift difference (ppm) with an uncertainty of 0:01 ppm. Negative values designate upﬁeld shifts. b For the two components of the carbonyl signal, see the text. Source: Ref. 46. Copyright # 1999 American Chemical Society. a

B.

Dynamic Aspects of Drugs in Bilayer Membranes

Dynamic aspects of drugs delivered into lipid bilayer membranes are signiﬁcant in discussing bioactivities and the mechanism of the drug–membrane interactions. So far, however, the dynamic properties of drugs in the membrane interior have not been well understood. No systematic NMR experiments have been carried out because of the low concentration of the bilayer interior. In this section, we illustrate how to obtain dynamic features of drug molecules trapped in membranes by NMR. As described in Section II.B, NMR is a powerful method for providing dynamic information. When signals of interest can be measured with a sufﬁcient signal-to-noise ratio at different frequencies, the two relaxation times, the longitudinal relaxation time,

NMR Studies on Lipid Bilayer Interfaces

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FIG. 9 Schematic representation of the delivery sites of PrBe (left) and BzOH (right) in the EPC SUV determined by the NMR chemical shift difference. (From Ref. 46. Copyright # 1999 American Chemical Society.)

T1 , and the transverse relaxation time, T2 , which reﬂect the dynamics of molecules and aggregates, can be solved to obtain correlation times relevant to the dynamics [56]. We can characterize the dynamic features of drugs trapped in the bilayer on the basis of the line broadening (linewidth) of the drug signal. Dynamically, the NMR signal broadens for the following two reasons: the reduced motional narrowing, and a fast exchange between different states. Imagine a two-state model (states A and B) for the drug. States A and B may be two different environments or different trapped sites in the bilayer. A single NMR signal is detected when the exchange rate between states A and B is faster than the chemical shift difference between these states. The mean lifetime (the inverse exchange rate), , may be deﬁned by ¼ A B =ðA þ B Þ where A and B are the lifetimes of the drug in states A and B, respectively. According to the rapid exchange model applied to the Bloch equation, the lifetimes of states A and B are obtainable from the observed time of the system, T2 . In contrast, two sets of peaks are observed when the exchange rate is slow. The situation is similar to the exchange between the monomer and the micellar states. Usually, the exchange between the monomer and the micellar states is fast. The spectra at surfactant concentrations above CMC, therefore, consist of a single set of peaks whose chemical shifts are averaged between the monomer and micellar states. Such an example is shown by spherical micelles formed by lithium perﬂuoro-octylsulfonate (FOS )

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studied by 19 F NMR [57]. When the hydrophilic counterion is replaced by the hydrophobic tetraethylammonium (TEA) ion, huge, threadlike micelles are formed, and two sets of peaks appear in the 19 F NMR spectrum of FOS at concentrations above CMC. This is due to the coexistence of monomer and micellar species with sufﬁcient lifetimes. The self-diffusion coefﬁcient ðDÞ of drugs trapped in the bilayer membrane can be obtained by the FT pulse-gradient spin-echo (PGSE) technique [58,59], when high-quality NMR signals of drugs in bilayers are measurable. The D values of surfactants decrease by a factor of 5–10 when they are transformed into spherical micelles and by two orders of magnitude when the threadlike micelles are formed. It is therefore expected that the D values drops by one to two orders of magnitude when amphiphiles are assembled into SUV. The reduction of the D value of a drug trapped in the bilayer would be in the broad range depending on the zone deﬁned in Fig. 2.

IV.

LIPID BILAYER INTERFACES COUPLED WITH ANESTHETICS

It has been generally accepted that anesthetics interact with membrane lipids as a primary step of anesthesia. The detailed mechanism of the anesthetic action is, however, still controversial. This is mainly due to the absence of speciﬁc information on delivery sites in membranes. The NMR data for the delivery site of drugs in membranes are of great use. General anesthetics are usually small solutes with relatively simple molecular structure. As overviewed before, Meyer and Overton have proposed that the potency of general anesthetics correlates with their solubility in organic solvents (the Meyer–Overton theory) almost a century ago. On the other hand, local anesthetics widely used are positively charged amphiphiles in solution and reversibly block the nerve conduction. We expect that the partition of both general and local anesthetics into lipid bilayer membranes plays a key role in controlling the anesthetic potency. Bilayer interfaces are crucial for the delivery of the anesthetics. A.

Delivery Sites of Local Anesthetics in Membranes

Local anesthetics are positively charged amphiphiles in solution. We have selected hydrochlorides of dibucaine (DBCHþ ), procaine (PRCHþ ), tetracaine (TTCHþ ), and lidocaine (LDCHþ ). All of these drugs are structurally similar; they consist of the substituted benzene ring and tertiary amine moieties, as shown by (VI)–(IX) in Fig. 1. The presence of the positive charge increases the solubility in water and in consequence, the anesthetic efﬁciency. Despite the structural similarities, the drugs have different anesthetic potency. DBCHþ has the strongest and longest-lasting anesthetic effect, although it is the most toxic. PRCHþ has the mildest anesthetic action. Information on the delivery sites of these drugs is required to explain the potency difference. A few papers have investigated the membrane–local anesthetic interaction by 1 H, 2 H, and 31 P NMR [60–72]. Although the 13 C NMR spectroscopy is powerful in distinguishing each carbon atom site of both membranes and anesthetics, no progress has been made in this ﬁeld. We should ﬁnd a correlation between the DD sites and the anesthetic potency by NMR measurements. Most recently, we have applied 13 C and 1 H NMR to the delivery of local anesthetics from water to phospholipid bilayer membranes [48]. Preferential locations of the four drugs DBCHþ , PRCHþ , TTCHþ , and LDCHþ in EPC SUV have been speciﬁed and compared. To specify the delivery sites of drugs on the atomic-site level from their

NMR Studies on Lipid Bilayer Interfaces

793

NMR signals, we have applied the empirical HCS rule described in Section III.A.2(a) that the NMR signals largely shift to a higher ﬁeld when molecules are dehydrated in the nonpolar environment. Delivery sites are also conﬁrmed by the membrane structure perturbation summarized in Section III.A.2(b), which can be monitored by the ring current effect of drugs on phospholipid NMR signals. We have discussed the contribution of the partial discharging of the anesthetics at the bilayer surface. We have also paid attention to the dynamics of the local anesthetics in membranes, to elucidate the molecular mechanism of the anesthetic potency and the toxicity. As already pointed out in Section III.A.2(b), the perturbation on the membrane side should be protruding near the trapped site of the drugs. Signiﬁcant changes in the chemical shifts and linewidths are expected near the delivery site. We have compared the chemical shift changes of the 13 C NMR signals of EPC after the injection of the two anesthetics, DBCHþ and PRCHþ [48]. The result of the EPC carbon atom sites perturbed is shown in Fig. 10. The upﬁeld chemical shifts are induced by DBCHþ at the carbon atom sites of glycerol CH (C2), ester carbonyl, and - and -methylenes most adjacent to the headgroup. All of these sites reside in the interfacial region of EPC between the hydrophilic headgroup and the hydrophobic carbon chains, zone II. Neither the carbon atom sites around the headgroup nor those in the bilayer core are signiﬁcantly modiﬁed by the injection of DBCHþ . The modiﬁcation of the EPC interface by DBCHþ is prominent and site speciﬁc, as compared with the modiﬁcation caused by the injection of BzOH [46]. Similar membrane perturbation is found for the ring current effect of DBCHþ in the 1 H NMR spectra of EPC; note that the 1 H NMR speciﬁes the atom site less clearly than the

FIG. 10 Chemical shift change of the 13 C NMR signals of EPC induced by the injection of DBCHþ and PRCHþ with a molar ratio of 1/1. Negative value means an upﬁeld shift.

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C NMR. The membrane perturbation by PRCHþ is found to be relatively smaller than DBCHþ . The ring current effect on the EPC 1 H NMR signal is not substantial at any site. Only signiﬁcant 13 C NMR downﬁeld shift is noticed in the carbonyl site, as shown in Fig. 10. The difference in the perturbation effect between DBCHþ and PRCHþ supports the difference in the trapped site in bilayers and that in the anesthetic mechanism between the two drugs. The 13 C and 1 H NMR spectral changes on the drug side signal are consistent with the delivery site mentioned above. From the 13 C NMR signals of the drug side, we have found that DBCHþ is delivered from the aqueous phase into a medium polarity region of lipid bialyers, the polarity almost similar to acetone or methanol. The line broadening of the drug signal has been observed after the mixing with bilayers. On the other hand, PRCHþ resides in the polar enviromment without any speciﬁc trap at the bilayer interface; neither the line broadening nor the chemical shift change can be observed in the 13 C and 1 H NMR of PRCHþ . From both sides of NMR signals of drugs and membranes, we have determined that DBCHþ is preferentially located in the regions of the bilayer interfacial glycerol, ester carbonyl group in zone II, and two chain methylenes in zone III most adjacent to zone II. It is thus appropriate to classify the delivery site of DBCHþ into category II. The delivery site of PRCHþ can be classiﬁed into category I. This is consistent with the difference in the hydrophilicity; PRCHþ produces no micelles, whereas DBCHþ forms them at high concentrations [69]. The delivery site determination has also been applied to two other anesthetics, LDCHþ and TTCHþ , by using 13 C NMR. As shown in Fig. 11, the preferential delivery site of LDCHþ , which is most popularly administered as a local anesthetic, is the two chain methylenes most adjacent to zone II in the bilayer. In contrast, TTCHþ is rather widely distributed from the interfacial glycerol and carbonyl regions in zone II to the middle region of the hydrocarbons in zone III. The chain tail in the bilayer core is, however, not signiﬁcantly perturbed. All these ﬁndings are in favor of the general concept that most of the local anesthetics selectively perturb the interfacial site of the membrane.

13

FIG. 11 Chemical shift change of the 13 C NMR signals of EPC induced by the injection of LDCHþ with a molar ratio of 1/1. Negative value means an upﬁeld shift.

NMR Studies on Lipid Bilayer Interfaces

795

It is interesting that the different delivery sites of the drugs can provide a variety of anesthetic potencies. For example, the strongest and long-lasting anesthetic effect of DBCHþ can be combined with the speciﬁc trap in zone II. The penetration of DBCHþ into the hydrophobic bilayer interior, zone III, can be a cause of the toxicity. In contrast, PRCHþ , preferentially adsorbed on the hydrophilic surface of the bilayer, zone I, and easily desorbed in the aqueous phase, cannot induce the long-lasting anesthetic effect and toxicity. It should be emphasized that the ester carbonyl group in the interfacial zone II is most crucial and susceptible to the anesthetic action of the drugs. In our 13 C NMR study, we have found that the ester carbonyl site in zone II is particularly susceptible to the extent of hydration [51]. Above the G/LC transition temperature, the carbonyl is the innermost site where the water can penetrate. The strong perturbation of the 13 C NMR signal of the carbonyl shown in Fig. 10 suggests that DBCHþ induces signiﬁcant dehydration and restricts the motion of the carbonyl group [48]. According to the HCS rule, the upﬁeld chemical shift indicates the dehydration around the atomic site. In the case of PRCHþ and TTCHþ , the downﬁeld chemical shifts mean that the ester carbonyl site in zone II is more hydrated. LDCHþ has almost no effect on the carbonyl group. We can imagine that (1) the trap of DBCHþ in the bilayer competes with the penetrating water at the bilayer interface, zone II, and that (2) DBCHþ is trapped as a result of the special afﬁnity with the bilayer interface. The trap of DBCHþ induces dehydration at the bilayer interface. The strongest anesthetic effect of DBCHþ is therefore due to the dehydration and the restricted segmental ﬂuctuation in the most susceptible site, zone II; recall the steep difference in the polarity and water density in zone II shown in Fig. 2. Here we propose the general concept that the carbonyls in zone II play a key role in biological functions. The hypothesis is supported by the results shown later in the case of general anesthetics and endocrine disruptors. 1.

Dynamics of Anesthetics in Membranes

We have evaluated the dynamic features and the orientation of DBCHþ trapped in the bilayer, based on the line broadening effect of the 13 C and 1 H NMR signals of DBCHþ [48]. As described in Section III.B, the signal broadening is generally due to two reasons: (1) the reduced motional narrowing and (2) the fast exchange of molecules between different states. We have observed the most distinct line broadening of the carbonyl and quinoline ring carbons of DBCHþ . The site speciﬁcity of the broadening effect in the rigid planar quinoline ring excludes the ﬁrst reason, because the segmental motion of the rigid ring is united and the motional narrowing effect is common to all sites in the ring. We therefore ascribe the signal broadening to the fast exchange of the DBCHþ molecules trapped in the different polarity of the bilayer. As mentioned above, the signal broadening is site speciﬁc. These facts indicate that the DBCHþ molecules are not tightly bound to the bilayer but ﬂuctuating at the bilayer interface. The orientation of the DBCHþ ring is not parallel but vertical to the bilayer interface, because no site dependence is expected for the parallel orientation. We estimate that DBCHþ molecules are located just at the bilayer interface, that is, the boundary between the hydrophilic headgroup and the hydrophobic alkyl chains. The vertical ﬂuctuation of the molecules at the bilayer interface means that DBCHþ ﬂuctuates between the hydrophilic and the hydrophobic surroundings in the bilayer. Thus it is most likely that the NMR signal broadening is due to the wide distribution of the polarity around the carbon atom site. In the case of PRCHþ , all ﬁndings are thus consistent with the fast exchange of the drug molecules adsorbed at

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the hydrophilic bilayer surface, zone I, and those in the aqueous solution. This is due to the hydrophilic property of the PRCHþ molecules, as already referred to. 2. Discharging of Anesthetics in Membranes It has been proposed that local anesthetics pass nerve membrane by neutral species despite the clinical adminsitration of the cationic form. Experimental molecular information is required for a better understanding of the mechanism. Thus the NMR information can be useful to the anesthetic discharging in membranes. It is expected that the neutral species of the anesthetics can penetrate more deeply into the hydrophobic bilayer interior than the cationic ones. From the 1 H and 13 C NMR, we have demonstrated that the neutral species, DBC and PRC, are trapped deeply in the bilayer; DBC can penetrate into the hydrophobic core of the bilayer, zone III, and PRC can penetrate into the inside of the bilayer preferentially trapping from zone II to the middle of zone III [48]. This information is valuable in the sense that it is difﬁcult to observe the NMR signal of the neutral species in water because of the extremely low solubility. The preferential location is in accordance with the solubility in water; the neutral species of DBC and PRC, sparingly soluble in water, are expected to favor the hydrophobic bilayer interior. We have shown that the cationic species are almost dominant and only a small portion of the cationic species is neutralized (discharged) when they are trapped at the bilayer interface. The discharging of the small portion of the cationic species DBCHþ in membranes is conﬁrmed by the pH change study [48]. The proton should be released into the aqueous phase in the discharging process of DBCHþ at the membrane surface. In fact, the pH of the solution is decreased to a small extent after the addition of the EPC SUV. This means that only a small portion of the DBCHþ molecules is discharged: the pH value is not decreased to the value of the complete discharging. The fraction of the DBC neutralized at the bilayer surface is estimated to be smaller than 1% of the total amount. The predominance of the cationic species of DBCHþ in membranes is consistent with the NMR spectra. If the neutral species are substantially increased in membranes, NMR signals of the neutral species can be observed in addition to the cationic species due to the difference in the delivery sites with a large barrier height in membranes. No independent NMR signals of the neutral species of DBCHþ can be detected after the addition of the EPC SUV; this indicates that the cationic species are dominant also in the hydrated membranes. To conﬁrm the universality of the discharging of the small portion of the anesthetics in membranes, we have examined whether PRCHþ is also neutralized at the membrane surface [48]. Combining the pH change and NMR studies, we have conﬁrmed that the þ discharging of a small portion of the cationic PRCH is also the case; the fraction of PRC discharged in the bilayer is found to be smaller than that of DBC in membranes. Although the contribution is rather small, the partial discharging of the anesthetics in membranes can be important in the mechanism of the anesthetic action. The most plausible mechanism can be summarized as: only a small portion of the cationic species are neutralized (deprotonated) at the bilayer surface and the neutral species are deeply penetrated and widely distributed in the hydrophobic bilayer interior, while the cationic species still remain at the hydrophilic bilayer surface where the hydration is signiﬁcant. The discharging is closely related to the most optimum anesthetic effect. For strong and efﬁcient anesthetic potency, the neutral forms of the drugs are suitable because they

NMR Studies on Lipid Bilayer Interfaces

797

can easily partition into the bilayer; for example, the partition coefﬁcient of PRC is estimated to be 20 times larger than that of PRCHþ [67]. However, cationic forms are favorable to reduction of the anesthetic duration and toxicity. The most efﬁcient anesthesia is induced by only a small amount of discharged species. When we stop the injection of the anesthetics, the cationic species are gradually released to the aqueous phase from the bilayer in accordance with the concentration gradient. It is extremely difﬁcult to release the neutral species deeply penetrating into the hydrophobic bilayer interior. Therefore we can conclude that the reversible and the optimum anesthetic potency is based on the miraculous combination of the cationic and the neutral forms of the drugs.

B.

Delivery Sites of General Anesthetics in Membranes

Recently, a wide variety of NMR studies have focused on the preferential location of general anesthetics in membranes. Most of the studies have suggested that the amphiphilic site of membranes is the most preferable delivery site of general anesthetics, which is similar to the sites of the local anesthetics stated in Section IV.A. The method includes 2 H NMR using deuterated lipids [73,74] and 19 F NMR of ﬂuorinated anesthetics [73,75]. Xu et al. have investigated the delivery site of anesthetic and nonanesthetic ﬂuorine compounds by 19 F NMR, and demonstrated that the anesthetic compounds are preferentially distributed in the region of the bilayer that permits easy contact with water [75]. The region corresponds to categories I and II in Fig. 6. They have also reported that nonanesthetic ﬂuorine compounds are solubilized deeply into the lipid core, category III in Fig. 6. Intermolecular 1 H–1 H nuclear Overhauser effects (NOE) have been measured betweed lipid and anesthetic halothane protons [73]. The preferential location of halothane at the interfacial region of the bilayer, category II in Fig. 6, has been reported [76]. 124 Xe–1 H intermolecular NOE in the xenon–EPC system has also suggested the importance of amphiphilicity (category II in Fig. 6) in association with anesthetic action [76]. Xu et al. have recently pointed out that the nature of the sites of anesthetic action, whether in lipids or proteins, must be amphiphilic [77]. We have investigated the delivery of ethanol into EPC membranes by 13 C NMR [78]. 13 The C NMR signals of EPC demonstrate that both glycerol and the ester carbonyl groups are affected by the incorporation of ethanol. The NMR signal of ethanol itself shows that the ethanol is still located in the relatively hydrophilic environment; only one set of signals is observed despite the presence of ethanol in membrane and aqueous phases. The preferential location of ethanol in membranes can be therefore classiﬁed into categories I–II, the bilayer interfacial region, and a more shallow trap than the local anesthetics described before. These results are consistent with the locations of the other general anesthetics investigated by NMR. MD simulations have been performed to study general anesthetics [79,80]. Volumetric properties of anesthetics are almost available [81]. Most of these anesthetics reside preferentially in the amphiphilic interfacial region of the lipids, supporting the NMR results mentioned above. Thus category II is most relevant to the general anesthetic action. In Section IV.A, we have demonstrated that the interfacial site of the bilayer is important for the local anesthetic action. It is interesting that all of the NMR, MD, and volumetric data demonstrate that the interfacial region of the bilayer in category II is the most relevant to the site of general anesthetic actions. This means a slight deviation from the Meyer–Overton theory.

798

V.

Okamura and Nakahara

LIPID BILAYER INTERFACES COUPLED WITH ENDOCRINE DISRUPTORS, BISPHENOL A, AND ALKYLBENZENES

As an example of suspected endocrine disruptors (EDs), studies of the estrogenic action of bisphenol A (BPA) have been in progress in medical, physiological, and biological ﬁelds. In this situation, physicochemical approaches are required to get the structural information of BPA trapped in biomembranes. Most recently, we have determined the site and the orientation of BPA trapped in phospholipid vesicles by NMR, using the HCS rule [47]. In particular, we have succeeded in monitoring the 13 C NMR spectral changes of phospholipid vesicles, which are induced by the BPA delivery. In Fig. 12(a), we show the ring proton region of the 1 H NMR spectra of aqueous solution of BPA at a remarkably low concentration of 0.2 mM. The spectrum consists of two symmetrical doublets at 7.2 and 6.8 ppm typical of para-disubstituted benzene; the former signal can be assigned to the meta protons against the phenolic OH group, the latter to the protons at the ortho site [82]. When BPA is mixed with EPC vesicles, its spectra are changed as shown in Fig. 12(b). The chemical shifts of the ring protons of BPA are shifted to a higher ﬁeld; the shift is larger for the meta site as compared to the ortho site. The upﬁeld chemical shift of the ring protons means that the aromatic protons of BPA are in the nonpolar environment. There are no BPA signals remaining in the aqueous phase; BPA is trapped in the bilayer from the aqueous phase. The signal broadening occurs in the BPA– EPC system; the broadening is prominent in the meta site. This is due to the fact that the BPA molecules are bound to the bilayer, in agreement with the chemical shift changes [47]. The DD site can be ensured by the chemical shift changes of the BPA signals. The chemical shift differences of the ring proton signals of BPA on the delivery from water to bilayer phases are 0:04 and 0:11 ppm for the ortho and meta sites, respectively. Negative values mean upﬁeld shifts; recall the HCS rule. It is concluded that both benzene rings of BPA are trapped in the bilayer from the water phase and the meta site penetrates more deeply into the hydrophobic interior. The ring current effect on the 1 H NMR signals of EPC can be used to conﬁrm the solubilization of BPA in the vesicles. As expected, the most signiﬁcant upﬁeld shift is observed for the EPC atomic site much closer to the BPA molecules trapped in the bilayer

FIG. 12 Ring proton region in the 1 H NMR spectra of BPA in D2 O (a) and 1 d after mixing with EPC SUV (b). (From Ref. 47. Copyright # 1999 American Chemical Society.)

NMR Studies on Lipid Bilayer Interfaces

799

interior. In Fig. 13 are summarized changes in the chemical shift of the EPC 1 H NMR signals induced by BPA. Signiﬁcant changes are noticed at the choline methyl and two methylene protons of the headgroup, the glycerol methylene, and chain -methylene protons most adjacent to the interface. The change is relatively small for the chain methylene and methyl protons. These indicate that BPA is inserted as far as the hydrophobic chain region most adjacent to the bilayer surface. Figures 14(a)–(d) represent the 13 C NMR spectral changes of the respective carbon atom sites of the EPC SUV caused by the BPA delivery at a low EPC concentration (12 mM) [47]. BPA induces the most prominent changes at the EPC carbon atom sites of the — (b), glycerol CH and CH2 (c), and chain -CH2 — CHCH2 CH — carbonyl (a), oleﬁnic — adjacent to the interface (d). These carbon atom sites are in good agreement with those speciﬁed by the 1 H NMR. Thus these results provide complementary evidence that BPA is preferentially trapped in the bilayer interface. As shown in Table 9, the delivery site of BPA is also conﬁrmed by the chemical shift change of the EPC 13 C NMR signals. The most remarkable upﬁeld shifts are observed at the chain - and -methylenes of EPC, the chain region most adjacent to the headgroup. The perturbation of these sites by BPA is more prominent than BzOH [46], although the mixing molar ratio, BPA/EPC is much lower than BzOH/EPC. BPA speciﬁcally perturbs the EPC chains most adjacent to the headgroup, as a result of the intercalation in the bilayer. The two components of the ester carbonyl signal, assigned to the outer and the inner layers of the SUV [46] merge in the presence of BPA; see Table 9. On the basis of the 1 H and 13 C NMR, we have pictured the delivery site of BPA as illustrated in Fig. 15. There is trapped BPA between the lipid headgroup and hydrocarbon chain region most adjacent to the interface, with two methyl groups oriented toward inside

FIG. 13 Chemical shift change of the EPC 1 H NMR signals induced by the ring current effect of BPA. Negative value means upﬁeld shift. (From Ref. 47. Copyright # 1999 American Chemical Society.)

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FIG. 14 13 C NMR spectra of the EPC SUV in the presence and the absence of BPA, at the EPC atom sites of (a) carbonyl, (b) oleﬁnic, (c) choline and glycerol, and (d) methylene and methyl carbons. In each spectral region, the upper trace represents the EPC spectrum before the addition of BPA, while the lower is that after the BPA delivery. Asterisks denote the signals of the reference, DSS. (From Ref. 47. Copyright # 1999 American Chemical Society.)

TABLE 9 Chemical Shift Changes of the EPC Induced by the Delivery of BPAa

13

C NMR Signals

b

BPA c

BzOH d

Choline CH3 CH2 N CH2 OP

56.68 68.65 62.11

þ0:02 þ0:03 þ0:03

0:07 0:05 0:05

Glycerol CH

73.27

þ0:07

0:08

176.03 175.77

e

þ0:01

0:09 þ0:03

36.71 27.71

0:17 0:16

0:07 0:09

Carbonyl (Out) (In) Chain -CH2 -CH2

Chemical shifts and their changes (ppm) with an uncertainty of 0:02 ppm. Chemical shift (ppm) relative to the reference DSS. c Chemical shift change (ppm) induced by the BPA delivery. Positive and negative values mean downﬁeld and upﬁeld shifts, respectively. d Chemical shift change (ppm) induced by BzOH [46]. Negative values mean upﬁeld shifts. e The two components of the carbonyl signal completely merge. See the text. Source: Ref. 47. Copyright # 1999 American Chemical Society. a

b

NMR Studies on Lipid Bilayer Interfaces

801

FIG. 15 Schematic representation of the delivery site of BPA in the EPC SUV determined by the NMR chemical shift difference. (From Ref. 47. Copyright # 1999 American Chemical Society.)

the bilayer. It is found that two phenolic OH groups are directed to the hydrophilic headgroup. The ortho ring protons are trapped in the less hydrophobic site, similar to the trapped site of ring protons of BzOH [46]. Signiﬁcant perturbation is also observed for the phospholipid glycerol, ester carbonyl, and two methylenes of the hydrocarbon chain most adjacent to the bilayer interface. BPA is more deeply penetrated into the bilayer than BzOH. We have also determined the delivery sites of alkylbenzenes by NMR. As already described in Section III.A, PrBe are deeply transported to the chain tail region in the bilayer core and the delivery site can be classiﬁed into category III [46]. Benzene, however, cannot deeply penetrate into the hydrophobic core, zone III, but is trapped preferentially at the interfacial site of the bilayer, zone II; the delivery site can be classiﬁed into category II. Although benzene is generally considered to be hydrophobic, the delivery site of benzene determined by NMR is reasonable in the sense of the -electrons with some afﬁnity for the hydrophilic sites of the bilayer. Both drug and lipid sides of the 1 H NMR spectra show that alkylbenzenes can deeply penetrate into the bilayer interior in the order PrBe>ethylbenzene>toluene>benzene, which is consistent with the sequence of the insolubility in water.

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CORRELATION BETWEEN DRUG DELIVERY SITES AND SOLVENT POLARITY

It should be noted that the delivery sites of drugs determined by NMR are closely related to their afﬁnity for solvents with different polarities. Drugs of category I are substantially hydrophilic. High afﬁnity for the polar solvents like water opposes transportation to the hydrophobic lipid bilayer; zone I is the most preferential delivery site. The interesting phenomenon is that some of the drugs classiﬁed into category II do not have such high afﬁnity either for water or the hydrophobic solvents; these drugs favor the solvents with intermediate polarities, as shown schematically in Fig. 16. Typical examples are DBCHþ and BPA. The solubility proﬁle of DBCHþ is represented by curve (a) in Fig. 16. As described before, DBCHþ is soluble in water (" ¼ 79) but it forms micelles at high concentrations. It is highly soluble in acetone (" ¼ 21) and chloroform ð" ¼ 5Þ. Surprisingly, however, DBCHþ has low solubility in alkanes (" ¼ 2). The neutral species DBC, extremely less soluble in water, is not so much soluble in alkanes; it is more soluble in acetone and chloroform [83], as shown in curve (b). The solubility proﬁle of BPA is similar; BPA has a high afﬁnity for alcohol with a medium polarity, despite less solubility in water and alkanes [curve (b)]. From this it is reasonable that these drugs most favor zone II in the bilayer. PrBe is highly soluble in nonpolar solvents, although it is sparingly soluble in water. The preferential location in zone III of the bilayer is reasonable in view of this solubility feature. The systematic information on the solubility of drugs thus enables us to predict the most suitable DD sites in membranes.

VII.

CONCLUDING REMARKS AND FUTURE PERSPECTIVES

Basic concepts and the methods for determining DD sites in lipid bilayer membranes have been developed by NMR on the atomic site level. Lipid bilayer interfaces as delivery sites can be speciﬁed by taking advantage of the site selectivity of NMR. DD sites can be generally classiﬁed into the three categories in Fig. 6. The distinction is based on the difference in the micropolarity in membranes around the drug. It has been brieﬂy mentioned how to evaluate dynamic properties of drugs in membranes.

FIG. 16 Solubility proﬁles of drugs in solvents with varying dielectric constant ". For curves (a) and (b), see the text.

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The method introduced here can be widely applied to a variety of drugs, such as anesthetics and EDs. For example, most of the EDs have ring protons and are highly lipophilic. The NMR method developed here should make a signiﬁcant contribution to elucidating the molecular mechanism of the ED delivery into the lipid bilayer as a primary step of the membrane disrupting action. The present method can be also powerful in monitoring the decomposition and the release of EDs accumulated in the membrane interior. For the purposes of detoxication and prevention of the ED accumulation, molecular-level research is now in progress in our group. The method utilizing 1D NMR is simple and convenient. Hence the NMR method discussed here can be applied to the systematic investigation of the membrane–drug interactions, closely related to the vital function in biomembranes. It is expected that the application can be extended to the lipid–peptide interaction and protein uptake. We are now applying the method to apolipoprotein binding with lipid bilayers and emulsions. Preferential protein binding sites in membranes can be speciﬁed by NMR on the molecular level. One of the most interesting subjects to be investigated is the effect of the phase transition behavior of membrane lipids on the partitioning of drugs in membranes. Lipid matrices of biomembranes are usually in the LC state. As described in our NMR phase transition study of DPPC bilayers [51,52] in Section II.D, the hydrocarbon chains of the lipid components are ﬂexible. Hydrophobic interaction is still dominant in the chain region. Hydrophilic headgroups containing dipoles are essential to retain the bilayer structure. Headgroups, however, ﬂuctuate considerably in the LC state. The information on the bilayer phase transition effect on DD is valuable because various portions of biomembranes are microscopically inhomogeneous; the gel-like structure locally appears for an instant, although the bilayers are macroscopically in the LC state. We are now studying the temperature dependence and phase transition effect on the delivery of DBCHþ and BPA from water to bilayers. Although the drug delivery to the lipid bilayer membrane is just the ﬁrst step for bioactivities and phopholipid vesicles are rather simple in view of the composite structure of biomembranes, the unambiguous speciﬁcation of the preferential location of the drug is essential; the successive processes of the action are expected to be induced via the delivery site in membranes. We expect more advances in the dynamic NMR study, so that we can get insight into the mechanism of DD in membranes.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

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10. A. Watts. Biochim. Biophys. Acta 1376:297 (1998). 11. J. A. Urbina, B. Moreno, W. Arold, C. H. Taron, P. Orlean, and E. Oldﬁeld. Biophys. J. 75:1372 (1998). 12. T. Brumm, K. Jorgensen, O. G. Mourtisen, and T. M. Bayerl. Biophys. J. 70:1373 (1996). 13. D. M. Small, in Plasma Lipoproteins and Coronary Artery Disease (R. A. Kreisberg and J. P. Segrest, eds.), Blackwell Scientiﬁc Publications, London, 1992, pp. 57–91. 14. M. J. Janiak, D. M. Small, and G. G. Shipley. Biochemistry 15:4575 (1976). 15. H. Hauser, I. Pascher, R. H. Pearson, and S. Sundell. Biochim. Biophys. Acta 650:21 (1981). 16. M. C. Wiener, R. M. Suter, and J. F. Nagle. Biophys. J. 55:315 (1989). 17. J. F. Nagle, R. Zhang, S. Tristrarn-Nagle, W. J. Sun, H. I. Petrache, and R. M. Suter. Biophys. J. 70:1419 (1996). 18. G. Bu¨ldt, H. U. Gally, A. Seelig, J. Seelig, and G. Zaccai. Nature 271:182 (1978). 19. B. P. Gaber and W. L. Peticolas. Biochim. Biophys. Acta 465:260 (1977). 20. H. L. Casal and H. H. Mantsch. Biochim. Biophys. Acta 779:381 (1984). 21. P. T. Wong, D. J. Siminovitch, and H. H. Mantsch. Biochim. Biophys. Acta 947:139 (1988). 22. M. T. Devlin and I. W. Levin. J. Raman Spectrosc. 21:441 (1990). 23. E. Okamura, J. Umemura, and T. Takenaka. Biochim. Biophys. Acta 1025:94 (1990). 24. E. Okamura, J. Umemura, and T. Takenaka. Vibrational Spectrosc. 2:95 (1991). 25. P. T. Wong. Biophys. J. 66:1505 (1994). 26. J. Seelig. Biochim. Biophys. Acta 515:105 (1978). 27. P. R. Allegrini, G. van Scharrenburg, G. H. de Haas, J. Seelig. Biochim. Biophys. Acta 731:448 (1983). 28. G. Lindblom, in Advances in Lipid Methodology (W. W. Christie, ed.), Oily Press, Dundee, UK, 1996, pp. 133–209. 29. D. Huster, K. Arnold, and K. Gawrisch. J. Phys. Chem. B 103:243 (1999). 30. Z. Zhou, B. G. Sayer, D. W. Hughes, R. E. Stark, and R. M. Epand. Biophys. J. 76:387 (1999). 31. M. Ge, D. E. Budil, and J. H. Freed. Biophys. J. 66:1515 (1994). 32. R. H. Crepeau, S. Saxena, S. Lee, B. Patyal, and J. H. Freed. Biophys. J. 66:1489 (1994). 33. D. Marsh and L. I. Horvath. Biochim. Biophys. Acta 1376:267 (1998). 34. M. Ameloot, H. Hendrickx, W. Herreman, H. Portel, F. van Cauwelaert, and W. van der Meer. Biophys. J. 46:525 (1984). 35. J. M. Sturtevant. Ann. Rev. Phys. Chem. 38:463 (1987). 36. M. Kodama, T. Miyata, and Y. Takaichi. Biochim. Biophys. Acta 1169:90 (1993). 37. C.-h. Huang and S. Li. Biochim. Biophys. Acta 1422:273 (1999). 38. D. A. Wilkinson and J. F. Nagle. Biochemistry 18:4244 (1979). 39. Y. Kita, L. J. Bennet, and K. W. Miller. Biochim. Biophys. Acta 647:130 (1981). 40. Y. Kita and K. W. Miller. Biochemistry 21:2840 (1982). 41. T. R. Stouch. Mol. Simul. 10:335 (1993). 42. K. Tu, J. Tobias, and M. L. Klein. Biophys. J. 69:2558 (1995). 43. K. Tu, J. Tobias, J. K. Blaise, and M. L. Klein. Biophys. J. 70:595 (1996). 44. W. Shinoda, N. Namiki, and S. Okazaki. J. Chem. Phys. 106:573 (1997). 45. C. J. Jameson. Ann. Rev. Phys. Chem. 47:135 (1996). 46. E. Okamura and M. Nakahara. J. Phys. Chem. B 103:3505 (1999). 47. E. Okamura, R. Kakitsubo, and M. Nakahara. Langmuir 15:8332 (1999). 48. E. Okamura, R. Kakitsubo, and M. Nakahara, to be published. 49. R. Koynova and M. Caffrey. Biochim. Biophys. Acta 1376:91 (1998). 50. S. Kaneshina, H. Matsuki, and H. Ichimori. Rev. High Pressure Sci. Technol. 9:213 (1999). 51. E. Okamura, Y. Tsujii, T. Miyamoto, and M. Nakahara, to be published. 52. E. Okamura, C. Wakai, N. Matubayasi, and M. Nakahara. Chem. Lett. 1997:1061 (1997). 53. H. Konishi, N. Matubayasi, and M. Nakahara, to be published. 54. J. A. Hamilton and D. M. Small. Proc. Natl. Acad. Sci. 78:6878 (1981). 55. P. J. Spooner and D. M. Small. Biochemistry 26:5820 (1987). 56. G. Lipari and A. Szabo. J. Am. Chem. Soc. 104:4546 (1982).

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33 Lipid Bilayers in Cells: Implications in Drug and Gene Delivery T. MARJUKKA SUHONEN, PEKKA SUHONEN, and ARTO URTTI Department of Pharmaceutics, University of Kuopio, Kuopio, Finland

I.

INTRODUCTION

Lipid bilayers have important structural and functional roles in the human physiology. The lipids for the bilayers are synthesized in the cells by the biosynthetic pathways and their synthesis is biochemically regulated. Basically the lipid bilayers and the membrane proteins constitute the membranes bordering the cells and the intracellular organelles. In general, the lipid bilayer is able to maintain the important gradients of ions and many other biochemicals across the membranes by preventing their free diffusion. Therefore, the lipid bilayers are a crucial part of the cell physiology. This role is based on the barrier properties of the lipids and on their ability to embed membrane proteins that have an active role in transport and signaling of the cells. These basic functions affect also the pharmcokinetic role of the lipid bilayers: they are the barriers limiting drug permeation and, conversely, the proteins in the membranes regulate the processes of active transport and efﬂux. Biomembranes act as selective barriers of drug permation and, therefore, they have a profound impact on pharmacokinetics and pharmcodynamics at several levels.

II.

ROLE OF CELLULAR MEMBRANES IN PHARMACOKINETICS

Targets of drug action are usually proteins, such as enzymes, transporters, and receptors [1]. For activity, drugs must be able to reach these targets. Most targets are cellular proteins that are located either in the membranes in the cell membrane or in the intracellular organelles. Even those drugs that are targeted to the cell surface receptors must be able to permeate through several lipid bilayers in the body, because they should get across the cellular barriers between different compartments of the body (e.g., the cellular barriers between blood circulation and tissues). Obviously, in the case of intracellular targets, such as nuclear receptors or intracellular viruses, the drug must diffuse through many lipid bilayer barriers. The simplest case of pharmacokinetics is intravenous injection [1]. In this case the drug is injected directly into the bloodstream. The drug may permeate to different tissues depending on its ability to get across the blood vessel walls and the cellular barriers in the particular tissue targets (Fig. 1). If the drug has small molecular weight and adequate 807

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FIG. 1 Schematic presentation of pharmacokinetics in the human body. The arrows indicate possible routes of drug adminsitration and the direction of the blood ﬂow in the circulation.

lipophilicity it diffuses through the cellular barriers to tissues like the brain. Such drugs may be distributed to a large apparent volume in the body and they may be stored for a long time in the tissues. This leads to a long half-life of drug elimination. Intravenously injected drug is eliminated from the body usually by metabolism (predominantly in the liver) or excretion (mostly via kidney) [1,2] (Fig. 1). The ability of the drug to permeate through the cell membranes affects the metabolism and excretion processes. Metabolic enzymes in the liver are located in the cells (hepatocytes) and the drug must be able to pass through the cell membrane in order to reach the enzymes for the metabolic reaction. Renal excretion of drugs depends on two main processes: glomerular ﬁltration and tubular reabsorption. Glomerular ﬁlteration is simple ﬁltration with an approximate molecular size cutoff of 40,000 daltons: only smaller molecules are able to ﬁltrate from blood to the urine [2]. After the ﬁltration the drug may be reabsorbed into the blood through the lipid bilayers of the tubular cells in the kidney. Therefore, those drugs that are able to permeate across the membranes can be reabsorbed and their excretion is slower than that of the hydrophilic drugs. The reader should note that after injection there are many processes going on simultaneously: protein binding in plasma, distribution to various tissues, metabolism, and excretion. In such situations it is not easy to predict the impact of a single physicochemical parameter on the pharmacokinetics on the scale of the whole body. Most drug treatment is exercised by using extravascular routes of drug administration. In these cases, the drug is given to other sites than blood circulation (Fig. 1) [2]. Common examples are per oral, nasal, pulmonary, and transdermal routes of drug delivery. After extravascular administration, the drug must be absorbed into the blood circulation before it can distribute to the tissues. Different routes of drug administration have their own particular features that are out of the scope of this review (see Ref. 3). There are some generic determinants that affect drug absorption. For example, long retention of the drug at the site of absorption and a large membrane surface for drug absorption tend to

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increase drug absorption. Those properties of the drug that favor the diffusion across the lipid bilayer naturally increase drug absorption. Those features of lipid bilayers and drugs are discussed in more detail later in this review. Lipid bilayers affect all phases of pharmacokinetics: absorption, distribution, metabolism, and excretion (Fig. 1). Cells may form monolayers or multilayered structures between the body compartments [4]. These structures, endothelia and epithelia, limit drug transport between macroscopic body compartments during drug absorption, distribution, and elimination. For example, the blood–brain barrier of the brain capillary vessel walls limits access of exogenous compounds to the brain [5]. Similarly, the blood retinal barrier (BRB) prevents the entry of harmful agents to the retina of the eye [6]. The physiological role of these barriers is to prevent the acess of harmful agents and to facilitate transport of nutrients and other vital compounds to the tissues. This protective role makes drug delivery more difﬁcult. Important nutrients and other constituents are shuttled through the body by active transport mechanisms (Fig. 2). Active transport is based on membrane proteins, transporters, that have an extracellular domain (that is recognized by the ligand), a membrane spanning part, and an intracellular cytoplasmic domain [4]. For transport the drug should bind in speciﬁc manner to the transporter and, therefore, the drug must have a structural resemblance to the endogenous ligand of the transporter. There are carriers in the body for several amino acids, nucleosides, sugars, monocarboxylic acids, oligopeptides, and phosphates [7,8]. Efﬂux proteins are membrane proteins that affect the pharmocokinetics by efﬂuxing drugs from the cytoplasm of the cell to the extracellular space (Fig. 2). These proteins include multiple drug resistance (MDR) gene products like P-glycoprotein [9]. They limit absorption and distribution of drugs for those compounds that are ligands to these fairly nonspeciﬁc proteins. New transporters and efﬂux proteins are found continuously in the Human Genome Project and it seems that they are much more important in the pharmacokinetics than was previously thought.

FIG. 2 Mechanisms of drug transfer in the cellular layers that line different compartments in the body. These mechanisms regulate drug absorption, distribution, and elimination. The ﬁgure illustrates these mechanisms in the intestinal wall. (1) Passive transcellular diffusion across the lipid bilayers, (2) paracellular passive diffusion, (3) efﬂux by P-glycoprotein, (4) metabolism during drug absorption, (5) active transport, and (6) transcytosis [251].

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Drugs may pass cellular membranes by passive diffusion along the thermodynamic electrochemical gradient. Drugs may diffuse either through or between the cells (Fig. 2). Paracellular diffusion (between the cells) is limited by the molecular size and the limited porosity (i.e., small surface area) of the intercellular space [4,10]. For drug discovery scientists the ideal drug should pass through the cells by transcellular passive diffusion. Drugs that are able to diffuse effectively through the lipid bilayers of the cells have usually adequate bioavailability and distribution in the body to reach their targets. Understanding drug permeation across the lipid bilayers is important because it may help to choose the best candidate molecules for further development. During recent years the rapid progress in combinatorial chemistry, automated synthesis, and high throughput screening of the drug candidates have shifted the bottleneck of the drug discovery process to the early pharmacokinetic screening. Since about 40% of the drug discovery projects fail for biopharmaceutical and pharmacokinetic reasons, the drug discovery ﬁeld badly needs ways to predict permeation of new drug candidates across the lipid bilayers and, subsequently, to predict drug absorption. Understanding of the drug diffusion in lipid bilayers should augment the development of high throughput methods for early prediction of drug absorption. Another great challenge in modern drug discovery is related to the difﬁcult delivery of biotechnological drugs, like peptides, proteins, and gene-based drugs (oligonucleotides, genes). Special delivery systems are needed in order to deliver these large and often hydrophilic compounds across the lipid bilayers. This review gives an overview of the structure of the lipid bilayers and their role in limiting drug delivery.

III.

PERMEATION OF SMALL MOLECULES ACROSS LIPID BILAYERS: ROLE OF BILAYER STRUCTURE

A.

Bilayer Lipids

Lipids may be deﬁned as a large group of molecules with a substantial portion of aliphatic or aromatic hydrocarbon. Included are molecules with diverse chemical characteristics, such as the hydrocarbons, soaps, detergents, acylglycerols, steroids, phospholipids, sphingolipids, and fat-soluble vitamins, and, subsequently, with diverse physical behavior. One of the most important characteristics of lipids from a biological aspect is their behavior in aqueous environments, as all cells exist in an aqueous milieu. In this respect, the lipids range from almost total insolubility to nearly complete solubility. The hydrocarbon portion of the lipid molecule may be saturated [Fig. 3(A)] or unsaturated [Fig. 3(B),(C)]. The moelcules may be unsubstituted or substitution of an atom or chemical group, e.g., carboxylic acid or alcohol, for a hydrogen can occur anywhere along the hydrocarbon chain [Fig. 3(D)]. Several fatty acids are the building blocks of all complex lipids present in membrane lipids. In these compounds, they are esteriﬁed with alcohols (e.g., with glycerol), sphingosine, or cholesterol. Phospholipids, the main constituents of cellular membranes, have a glycerol backbone. A fatty acid is esteriﬁed to two of the hydroxyl groups and the third is esteriﬁed by a phosphate group and a nitrogenous compound (choline, ethanolamine, or serine) [Fig. 3(E)]. One family of phospholipids contains inositol, a six-carbon sugar-alcohol. Phospholipids isolated from natural sources vary in their fatty acids.

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FIG. 3 Representative structures of lipid molecules.

In sphingolipids, an amino alcohol with a long side chain, sphingosine, is amide bonded to a fatty acid forming a ceramide, the precursor of the sphingolipids [Fig. 3 (F)]. Sphingophospholipids are found in large quantities in the brain and in nervous tissue. Sphingomyelin, the most important sphingolipid has a phosphocholine grouping attached to the terminal hydroxyl of the ceramide [Fig. 3(G)], whereas the glycolipids, cerebrosides, and gangliosides contain no phosphorus but have a sugar or a chain of sugars attached to this hydroxyl terminus [Fig. 3(H)]. Glycolipids are present in all tissues on the outer surface of the plasma membrane.

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Cholesterol, a polycyclic alcohol [Fig. 3(I)] is present in all animal tissues. It is a major constituent of cellular membranes, where it contributes to the ﬂuidity of the membrane. The storage and transport forms of cholesterol are its esters with fatty acids.

B.

Phase Behavior of Membrane Lipids

All major lipids in membranes are amphipathic, i.e., they contain both hydrophilic (headgroups) and hydrophobic (acyl chains) regions. These molecules assume a variety of structures in aqueous dispersions depending on the shape of the molecule, i.e., the relative effective sizes of the polar headgroup and the acyl chain region (Fig. 4). The shape of a lipid molecule is an outcome of a variety of molecular forces [11] and, thus, the lipids organize themselves into a form that thermodynamically satisﬁes both ends of the molecule. Speciﬁc conditions are needed for bilayer formation as the nature of the phase depends on lipid species, lipid concentration, temperature, pH, and ionic strength [12]. In particular, the region of the hydrated headgroups needs to create an area large enough to accommodate the acyl chains. 1. Lipid Phases (a) Crystalline and Gel Phases. Lipids can exist in solid crystalline structures in a hydrated state at relatively low temperatures. These structures are densely packed stacked bilayers with their acyl chains either tail to tail or partially interdigitating at the bilayer center [13,14]. Due to differences in molecular shape there is a considerable variation in molecular packing patterns in the bilayer structures (Fig. 5). Crystalline phases pack into two distinct classes of subcells depending on chemical structure and environmental factors. The ﬁrst class is characterized by speciﬁc chain–chain

FIG. 4 shape.

Schematic representation of various lipid phase structures inﬂuenced by lipid molecular

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FIG. 5 Schematic representation of packing arrangements of natural amphipathic double-chain lipids with different headgroup size in crystalline bilayers. The small ﬁlled circles indicate the accommodation of spacer molecules, such as water or ions. (Reprinted by permission from Ref. 14, copyright 1992, Elsevier Science.)

interactions [15]. On a plane through the hydrocarbon chains perpendicular to their axes, two types of two-dimensional lattices may be found: rectangular or oblique (Fig. 6). With increasing temperature the hydrated lipid crystals revert into a more expanded gel phase [13]. In gel phases, the hydrocarbon chains remain in ordered bilayers, and essentially in the all-trans conﬁguration. This second class of crystalline chain packing includes the hexagonal lattice and hexagonal or quasihexagonal subcells [13,15] (Fig. 6). The individual carbon atoms, however, are allowed to rotate a few degrees within the lattice as the chains lose some of their speciﬁc interactions. Both the volume per — CH2 — group and the area per hydrocarbon chain are greater than in tightly packed crystals [15]. At a pretransition temperature, the lipid headgroup mobility as well as interfacial area per molecule increase substantially and the membrane adopts a rippled appearance, in which it is transformed from a planar to an undulating surface with fairly long, regular periodicity [13,16]. (b) The Liquid Crystalline Phase. At the main ‘‘gel-to-liquid crystalline’’ transition temperature, Tm , there is a drastic increase in acyl chain mobility, and, subsequently, an abrupt increase in the area per hydrocarbon chain and the volume per — CH2 — group [15]. The transition temperature is inﬂuenced by the amount of water present, by the length of the acyl chains, and by the number of double bonds and other substituents [15]. Membrane lipids can exhibit many different liquid-crystalline phases (Fig. 7) consisting of aggregates with different shapes such as spheres, rods, or lamellae [11]. These units are geometrically arranged to form lamellar, hexagonal (of the normal or reversed type), or cubic phases. (c) Nonlamellar Phases. Some lipids prefer to pack in nonbilayer structures such as the inverted hexagonal HII (Fig. 4) or cubic phases. In addition to the rapid axial rotations of

FIG. 6 The three types of two-dimensional lattices of hydrocarbon chains.

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FIG. 7 Structures of various liquid-crystalline phases of membrane lipids. (A) Normal hexagonal phase (HI ); (B) lamellar phase; (C) inverted hexagonal phase ðHII ). Cubic phases consisting of (D) spherical, (E) rod-shaped, and (F) lamellar units. The hydrocarbon regions are shaded and the hydrophilic regions are white. (Reprinted by permission from Ref. 11, copyright 1984, Kluwer Academic Publishers.)

a phospholipid about its long axis exhibited by the bilayer structures, additional motional averaging occurs owing to the ability of the lipids to diffuse laterally around the cylinders with the polar headgroups pointing inwards, characteristic of the HII phase [17]. Whereas bilayers arrange in planar structures, inverted nonlamellar phases exhibit a curved morphology due to the larger cross-sectional area available for the acyl chains relative to the small headgroups [18]. In the HII phase and in the inverted micellar cubic phase, the water associated with the polar headgroups is trapped inside a ring structure and is not in rapid exchange with bulk water [18]. In a bicontinuous cubic phase, however, there is a continuous network of aqueous channels. An increase in temperature above the gel-to-liquid crystalline phase transition can cause a transition from lamellar liquid crystalline phase to an inverted cubic or an HII phase [19]. A higher population of gauche isomers (Fig. 8) is introduced into the hydrocarbon chains leading to more wedge-shaped molecules and reduced packing ability. Isothermally, a variety of factors may induce the transition to inverted nonlamellar phases. For a more thorough review the reader is referred to, e.g., Refs. 11, 20, and 21. Brieﬂy, among glycerolipids, increased acyl chain unsaturation, especially cis-double

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FIG. 8 Schematic representation of the ordering/disordering of acyl chains within a bilayer. Note the strong disordering effect of a gauche conformer.

bonds, increased acyl chain length, and reduction of the size of the headgroup are conditions which favor the HII phase and transition from a lamellar to an HII phase occurs at a lower temperature. The phase structure formed by ionic lipids can be affected by a change in pH of the surrounding water phase. A transition from a lamellar to an HII phase may take place due to reduction of the electrostatic repulsive forces between the headgroups, which in turn decreases the surface area occupied by the hydrocarbon–water interface. Cations such as Ca2þ , Mg2þ , and Mn2þ have been found to trigger a transition from a lamellar to an HII phase for the anionic lipids at a neutral pH. At neutral pH, the polar headgroups of these lipids are negatively charged. Introduction of the divalent cations neutralizes the negative charge leading to a reduction of surface area. Dehydration of the polar headgroups has a similar effect on the phase behavior of lipid molecules [22]. 2.

Polymorphism of Membrane Lipids

Although biomembranes contain a substantial amount of nonbilayer-forming lipids [23], the membrane is maintained as a bilayer. It has turned out that the amount and structure of these nonbilayer-forming lipids are precisely regulated [24,25], implying that the effects of the nonbilayer-forming lipids on the membrane are of biological importance [26]. Nonbilayer phase formation has been found to play an important role in membrane transport, fusion, and exo- and endocytosis [23,27,28]. In addition, the presence of peptides and proteins promotes the formation of nonbilayer phases [29,30], which may be needed to keep them in a functional state [18,31].

C.

Bilayer Lateral Structure and Lipid Domains

According to the Singer–Nicolson ﬂuid-mosaic model of the structure of biological membranes [32] the lipids form a ﬂuid bilayer in which the incorporated proteins as well as the lipids themselves are randomly distributed and free to diffuse laterally. To date, it is established that membranes are not laterally homogeneous but formation of domains with distinct lipid and protein composition is a major driving force in membrane organization [33,34]. There are recent data indicating that the membrane components tend to adopt regular distributions, superlattices, in ﬂuid, mixed bilayers (for a recent review, see Ref. 35). The superlattices represent the energetically most favorable packing of the membrane components and they are in dynamic equilibrium with randomly arranged domains or with superlattices of different composition.

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Lipid mixtures may separate into distinct domains due to differences in their structures and phase behavior [12]. The domains sustained may be liquid–liquid, liquid–solid, or solid–solid in character. Lateral phase separation may be induced among charged lipid mixtures by the introduction of ions such as Ca2þ [12,36]. Charged lipids repel each other electrostatically, and thus they will be homogeneously distributed throughout the model membrane. The ions introduced would crosslink the headgroups and thereby induce clustering. Phase separation may also be encouraged by dehydration [37], by the addition of cholesterol (e.g., Ref. 38), or a solute such as alcohol [39] or by the insertion of proteins and peptides [40,41] (Fig. 9).

D.

Transverse Structure and Fluidity of Lipid Bilayers

As illustrated in Fig. 10 the lipid bilayer consists of several layers of chemically different microenvironments [42,43]. The perturbed water region protruded by lipid dipolar headgroups plays a crucial role in the interaction of the membrane with other membranes or with proteins. The total water density decreases sharply and the lipid density reaches its maximum in the hydrated headgroup interface region including the ester–ether linkages between the headgroups and upper parts of the acyl chains. Therefore, the diffusion coefﬁcients of water and other small molecules are lowest in this region of the bilayer. The ordered acyl chain region is characterized by low free volume and is recognized as the main barrier to the permeation of small molecules. A region of relatively disordered acyl chain segments near the bilayer center occupies about one-half of the ﬂuid bilayer thickness [44]. It is characterized by a low density and a high fraction of free volume, which allows for incorporation of larger molecules [42]. Due to its hydrophobicity this region favors the solution of hydrophobic molecules. The polarity of the lipid bilayer displays appreciable variation with position along the hydrocarbon chain and probably reﬂects the degree of water penetration into the bilayer [45,46]. The acyl chains form a hydrophobic core of the bilayer with a low polarity. Macroscopic approaches have yielded dielectric constant values of around 2–4 for this region, comparable to those found in alkanes [47]. The polar headgroup region, therefore, represents a region with a high gradient of polarity with measured dielectric constant values in the range 10–45, ﬁnally reaching a value of 80 at the bulk water region. The degree of molecular order obtained by NMR as a function of bilayer depth is relatively constant between carbons 1 and 9 and then falls signiﬁcantly for positions deeper

FIG. 9 A scheme representing lateral phase separation for anionic lipids from zwitterionic lipids in a mixed lipid bilayer induced by the peptide antibiotic, polymyxin-B. (Reprinted by permission from Ref. 41, copyright 1998, Elsevier Science.)

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FIG. 10 Top: The polarity proﬁle of a microsomal lipid bilayer from calf liver as derived from spinlabel ESR experiments [45]. Center: A scheme representing the different regions in lipid bilayers. (Center: reprinted by permission from Ref. 88, copyright 1998, Springer-Verlag GmbH & Co. KG.) Bottom: Fourier synthesis of electron density distribution across a lecithin bilayer. The solid curve is the spectrum for the wet state; the dashed curve is that for the dry state. (Reprinted by permission from Ref. 252, copyright 1968, Macmillan Magazines Ltd.)

in the bilayer, reaching a minimum at the center [48,49]. Similar results have been obtained by moelcular dynamics calculations [50]. The value at the minimum is about threefold smaller than the value at the surface of the bilayer. The trend parallels increased mobility of the acyl chains towards the interior of the bilayer (Fig. 11) [12]. A decrease in the motional order, i.e., an increase in ﬂuidity of the acyl chains, may be taken to correspond to an increase in the conformational freedom, i.e., the rate and extent of acyl chain

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FIG. 11 Order parameter variation along acyl chains in red cell ghosts (&), small unilamellar vesicles of egg phosphatidylcholine (r), and parafﬁn oil (þ), as determined by the ﬂuorescence anisotropy decay of the n-anthroyloxy fatty acid probes. (Reprinted by permission from Ref. 12.)

excursion away from some initial chain orientation [51]. This is often associated with an increase in trans–gauche isomerization by individual lipid molecules and an increase in ‘‘kink’’ concentration representing mobile, small free volumes in the hydrocarbon phase of the membrane [52]. Major determinants of membrane ﬂuidity may be grouped within two categories [53]: (1) intrinsic determinants, i.e., those quantifying the membrane composition and phase behavior, and (2) extrinsic determinants, i.e., environmental factors (Table 1). In general, any manipulation that induces an increase in the molal volume of the lipids, e.g., increase in temperature or increase in the fraction of unsaturated acyl chains, will lead to an increase in membrane ﬂuidity. In addition, several intrinsic and extrinsic factors presented in Table 1 determine the temperature at which the lipid molecules undergo a transition from the gel state to liquid crystalline state, a transition associated with a large increase in bilayer ﬂuidity. Biological membranes often exhibit asymmetry in the ﬂuidity of apical and basolateral membranes (for a review, see Ref. 53). There are also differences in the ﬂuidity of cell types of different origin [54,55]. Both of these phenomena may be associated with variations in the cholesterol content of the membranes, as cholesterol has been recognized to ﬂuidize gel phase liquids and to cause an ordering effect on the liquid-crystalline phase lipids [56]. Moreover, the ﬂuidity state of the plasma membranes is dependent on physiological [53,57–59] and pathological [53,60–62] conditions. The addition of exogenous compounds such as drugs or solvents also alters the ﬂuidity of biological [63–72] and artiﬁcial [67,68,72–76] membranes. Alterations in cell membrane ﬂuidity in turn are associated with marked changes in various transport systems, such as Naþ , Kþ -ATPase, Nadependent glucose transport, and Na-dependent phosphate transport, due to the sensitivity of proteins to their lipidic environment [53].

Lipid Bilayers in Cells TABLE 1

819

Major Determinants of Membrane Fluidity [53] Extrinsic

Parameter Temperature Pressure Cell volume Cations (divalent) [Hþ ] a b

Intrinsic

Effect on ﬂuiditya " # " #b #b

Parameter Cholesterol Sphingomyelin Protein/lipid Satur./unsatur. Chain length

Effect on ﬂuiditya # # # # #

The arrows indicate the effect of increase in the corresponding parameter on ﬂuidity. Depends on membrane phospholipid composition (headgroups negatively charged).

E.

Molecular Dynamics of Bilayer Lipids

Lipid membranes may be depicted as structured ﬂuids forming highly dynamic systems [77]. The various molecular motions of phospholipids organized in a bilayer structure depend strongly on temperature and are likely to be restricted by the amphiphilic nature of the molecules with the polar headgroups being anchored at the aqueous interface. Above the gel-to-liquid crystalline phase transition temperature the lipid hydrocarbon chains undergo rapid rotational motion about their long axis [16]. The rotational diffusion coefﬁcient at the terminal end of the acyl chains is similar to that in n-alkanes, but at the center of the chain, the movement is signiﬁcantly more restricted [78]. In addition to internal rotations, lipid molecules undergo two kinds of translational movements: (1) lateral diffusion, or the exchange of molecules that lie next to each other in a single leaﬂet of a bilayer; and (2) ﬂip-ﬂop, or movement of molecules from one bilayer leaﬂet to another involving the polar moiety passing through the hydrophobic region of the bilayer (Fig. 12). Lateral diffusion rates of phospholipids in bilayers are dependent on the physical state of the bilayer and are much more rapid in the liquid crystalline phase than for those in the gel state. The transbilayer movement rates of different phospholipids in bilayers vary over a considerable range. Generally, the rates show a maximum in the temperature range at which the gel-to-liquid crystalline phase transition occurs. Transversely, mammalian biomembranes exhibit a general pattern for preferential localization of choline-containing phospholipids [such as phosphatidylcholine (PC) and

FIG. 12 Different types of motions of lipid molecules in bilayers. (Reprinted by permission from Ref. 78, copyright 1986, Kluwer Academic Publishers.)

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sphingomyelin (SM)] and aminophospholipids [such as phosphatidylserine (PS) and phosphatidylethanolamine (PE)] in an outer and inner membrane bilayer leaﬂet, respectively (see Ref. 79 for a review). In addition, cholesterol content displays asymmetry between the two leaﬂets of the bilayer in biomembranes [53,80]. In model membranes, generally, lipids with larger headgroup area are expected to distribute preferentially into the outer monolayer in mixed lipid vesicles with small radius curvature [11]. Hydrogen bonding may play a role in transbilayer lipid distribution as it has been found that interactive lipids such as PS and PE are preferentially localized in the inner leaﬂet of the bilayer in model membranes of small unilamellar vesicles (SUV) in mixtures with PC [81]. The preference of PS and PE for the inner monolayer decreases as the pH is raised indicating the requirement for an interactive charged state rather than a repulsively charged state. In large unilamellar vesicles (LUVs), transbilayer asymmetry of certain ionizable lipids, such as phosphatidylglycerol (PG) and phosphatidic acid (PA), can be induced due to transmembrane pH gradients [82].

F. Transport Across Lipid Bilayers Substances pass through membranes primarily by passive diffusion. In addition, in biological membranes, substances may penetrate through speciﬁc transport mechanisms. The basic ﬂux across the membranes may be related to that across a thin ﬁlm [83]. Fick’s First Law of Diffusion indicates that the total ﬂux of diffusant across a homogeneous membrane, J, is proportional to the concentration gradient of the diffusant: J ¼ Aj ¼ AD

dC dx

ð1Þ

where A is the area across which diffusion occurs, j is the ﬂux per unit area, D is the diffusion coefﬁcient of the diffusant, C is the diffusant concentration, and x is the distance perpendicular to the surface of the membrane. Fick’s Second Law relates the change in diffusant concentration with time, dC=dt, to the change in concentration gradient at a given point in the membrane: dC d 2C ¼D 2 dt dx

ð2Þ

At a steady state, the change in concentration gradient with time at a given point in the membrane equals zero. In a typical experimental situation a membrane is used between two compartments, one containing a drug solution (‘‘donor’’ compartment) and the other sink conditions (i.e., zero concentration; ‘‘receiver’’ compartment). For a homogeneous barrier membrane of thickness h, Fick’s First Law may be written as j¼

dQ DðC1 C2 Þ ¼ dt h

ð3Þ

where Q is the diffusant amount, and C1 and C2 are the diffusant concentrations on the donor and receiver sides of the membrane, respectively. Because exact measurements of C1 and C2 may be difﬁcult, the partition coefﬁcient, Km , relates C1 and C2 to Cd and Cr , the measurable concentrations in the donor and receiver compartments adjacent to the barrier membrane, respectively. Thus, the ﬂux of diffusant per unit area is related to the partition coefﬁcient, the concentration difference, and the membrane thickness:

Lipid Bilayers in Cells

j¼

DKm ðCd Cr Þ h

821

ð4Þ

In most experimental situations, it is practical to determine the permeability coefﬁcient, P, according to P¼

DKm h

ð5Þ

which may be substituted into Eq. (4) to give j ¼ PC

ð6Þ

Thus, the rate of change for the cumulative mass of diffusant passing through a membrane per unit area, or the ﬂux of diffusant, j, may be evaluated from the steady-state portion of the permeation proﬁle of a drug, as shown in Eq. (3). If the donor concentration and the steady-state ﬂux of diffusant are known, the permeability coefﬁcient may be determined. Several models have been proposed for the molecular mechanism of transport of substances across phospholipid membranes, as reviewed by Jin and Hopﬁnger [84]. The most commonly employed model for describing the passive transport of permeants across lipid membranes is the solubility–diffusion model, which relates a given solute’s permeability coefﬁcient to its ability to partition into and diffuse across the lipoidal membrane interior [85]. The permeation process is described in three steps: (1) the molecule dissolving into the membrane; (2) the molecule diffusing through the membrane interior; and (3) the molecule dissolving into the surrounding environment again. The solubility–diffusion theory assumes that solute partitioning from water into and diffusion through the membrane lipid region resembles that which would occur within a homogeneous bulk solvent. Thus, the permeability coefﬁcient, P, can be expressed as P¼

Dhc Khc=w hhc

ð7Þ

where Khc=w is the partition coefﬁcient of the permeant between water and a bulk organic solvent (e.g., a liquid hydrocarbon), hhc is the thickness of the hydrocarbon interior, and Dhc is the diffusion coefﬁcient of the permeant within the membrane, which is approximated by the diffusion coefﬁcient of the permeant in a bulk hydrocarbon solvent [85]. The solubility–diffusion theory, however, is highly oversimpliﬁed, as it fails to take into account the complex properties of real bilayers and biomembranes. Solute permeation in lipid bilayers shows a much steeper dependence on permeant size than on diffusion in bulk solvents [86], and diffusion coefﬁcients calculated from permeability coefﬁcients are orders of magnitude smaller than those obtained in bulk solvents. Recently, chain ordering has been shown to be a major determinant of molecular transport across liquid-crystalline bilayers [87]. Further, changes in bilayer phase structure has been found to alter the location and hydrophobicity of the transport barrier domain and, e.g., the transition from the gel phase to liquid-crystalline phase shifts the barrier domain deeper within the ordered chain region [88,89]. A scaling factor, the permeability decrement f , has been introduced to account for the decrease in permeability coefﬁcient from that predicted by solubility–diffusion theory owing to chain ordering in lipid bilayers [90]: Pm ¼

Dbarrier Kbarrier=water ¼ fP hbarrier

ð8Þ

where Kbarrier=water is the partition coefﬁcient of the permeant between water and the barrier domain; dbarrier is the barrier thickness, and Dbarrier is the diffusion coefﬁcient of

822

Suhonen et al.

the permeant within the barrier domain. It was found that the lipid bilayer permeability can be predicted from the chain-packing properties in the bilayer through a dependence of f on bilayer free-surface area [90]. As discussed above, lipid membranes are dynamic structures with heterogeneous structure involving different lipid domains. The coexistence of different kinds of domains implies that boundaries must exist. The appearance of leaky interfacial regions, or defects, has been suggested to play a role in abrupt changes in solute permeabilities in the twophase coexistence regions [91,92]. Studies of the effect of permeant’s size on the translational diffusion in membranes suggest that a free-volume model is appropriate for the description of diffusion processes in the bilayers [93]. The dynamic motion of the chains of the membrane lipids and proteins may result in the formation of transient pockets of free volume or cavities into which a permeant molecule can enter. Diffusion occurs when a permeant jumps from a donor to an acceptor cavity. Results from recent molecular dynamics simulations suggest that the free volume transport mechanism is more likely to be operative in the core of the bilayer [84]. In the more ordered region of the bilayer, a kink shift diffusion mechanism is more likely to occur [84,94]. ‘‘Kinks’’ may be pictured as dynamic structural defects representing small, mobile free volumes in the hydrocarbon phase of the membrane, i.e., conformational ‘‘kink’’ ðg tg Þ isomers of the hydrocarbon chains resulting from thermal motion [52] (Fig. 8). Small molecules can enter the small free volumes of the kinks and migrate across the membrane together with the kinks.

IV.

PERMEATION OF SMALL MOLECULES ACROSS LIPID BILAYERS: ROLE OF PERMEANT STRUCTURE

A.

Partitioning in Membranes

The lipophilicity of a solute affects its permeability in lipid bilayers. Lipophilicity is usually expressed in terms of its partitioning between water and an organic solvent, such as olive oil [95], oleyl alcohol [96], ether [97], or octanol [98]. Partition coefﬁcient (PC) of a compound is expressed as its concentration ratio between organic medium and water at equilibrium: PC ¼ Coctanol =Cwater

ð9Þ

The partition coefﬁcient is a measure of the relative secondary interactions between the solute and each liquid. Partitioning into bilayers is more complicated than homogeneous systems due to the heterogeneity of the lipid bilayers. For this reason the distribution of solutes in the bilayer is not homogeneous [99]. According to the theory of Marqusee and Dill the solutes of differing hydrophilicities will preferentially partition into different bilayer regions [100]. Thus, different solutes may reside in different areas of the bilayer, depending on the nature of the solute. For example, partitioning into bilayers is more selective to branched solutes than partitioning into bulk hydrocarbons. Presumably, this is due to the parallel arrangement of the acyl chains [99]. B.

Methods to Evaluate Solute Partitioning

The log octanol–water partition coefﬁcient ðlog Po=w Þ probably is the most frequently used physicochemical parameter in medicinal chemistry [101–104]. Octanol, with a polar head and a ﬂexible, nonpolar tail, has hydrogen-bonding capabilities and amphilicity similar to

Lipid Bilayers in Cells

823

those of the phospholipids in biological membranes. Therefore, it is used as a predictor for drug partitioning to the lipid bilayers [101]. Despite some good correlations with in vivo pharmacokinetics [105], log Po=w seems to have only a limited performance in predicting brain–blood concentrations (log BB) [106– 109] or oral drug absorption [110]. The octanol–water system still has no serious rival, but alternative partition systems that might give a better description have been suggested and investigated. Notable attempts include the use of cyclohexane–water [111–113] or the use of log P between octanol–water and cyclohexane–water [109,114,115]. In cellular membranes, the principal diffusion barrier consists of the lipid bilayer, a highly anisotropic system, which can be divided into distinct regions such as the polar headgroup–water interface region, and the nonpolar hydrocarbon region (Fig. 10). Deuterium nuclear magnetic resonance (2 H-NMR) [48,116] and neutron diffraction measurements [117] have shown that the order of the hydrocarbon chains is relatively high in the region near the lipid–water interface and decreases strongly towards the bilayer center (Fig. 10). These results show that a bilayer cannot be properly mimicked by an isotropic hydrocarbon phase. Indeed, molecular dynamics simulations show that the rate of diffusion differs considerably even in the membrane hydrocarbon region, being slow in the region of high order and fast in the more disordered central part [118]. Despite the well-established anisotropy of lipid bilayers, the vast majority of investigators still rely on the measurement of partition coefﬁcients between an organic solvent (e.g., octanol, hexane, or cyclohexane) and water to assess the ability of a drug to diffuse through the BBB. Interesting modiﬁcations of this approach are HPLC methods where alkyl chains (e.g., C-18) [119], or carboxyacyl phosphocholine chains [120,121] are covalently attached to silica. These systems show a limited anisotropy. However, the packing density is still dictated by the chemistry of the covalent linkage to silica and is distinctly lower than the lipid packing density of natural membrane [122] or a bilayer model membrane [123]. It is therefore not surprising that octanol–water partition coefﬁcients or lipophilicity parameters obtained from reversed-phase HPLC measurements do not correlate satisfactorily with the ability of a drug to diffuse through a lipid membrane. C.

Membrane Barrier to Solutes

One of the major issues in developing structure–activity relationships for various biological processes and in designing effective drugs and drug delivery systems is the determination of the locations and physicochemical nature of barrier domains in biological membranes for the transport of various molecular agents. Even in the absence of membrane proteins, uncertainty as to the location of the barrier domain arises due to the heterogeneity of transbilayer atomic distributions, reﬂecting a hydrated headgroup interface, the ester–ether linkages between the headgroups and acyl chains, an ordered acyl chain region, and a region of relatively disordered acyl chains near the bilayer center (Fig. 10). This heterogeneity is known to underlie the bell-shaped polarity proﬁle within a bilayer interior as demonstrated in Fig. 10 [45,46]. In the absence of chain ordering effects, the least polar region would impose the highest energetic barrier to the transport of polar permeants. However, chain ordering in bilayers imposes an additional diffusional resistance and an entropic barrier to partitioning, respectively [100,118,124] such that the actual location of the transport barrier domain is determined by the balance of these factors. The degree of success achieved using Hansch parameters, obtained from octanol–water partition coefﬁcients [125], in correlating transport processes in biological membranes support Overton’s suggestion that solute permeability across biological membranes

824

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correlates with corresponding bulk oil–water partition coefﬁcient [126]. However, membranes with different lipid compositions display different chemical selectivity to solute transport. Functional group contributions have shown that the barrier domain for transport across human stratum corneum of the skin (the barrier properties of which are generally attributed to the multiple lamellae of lipid bilayer membranes localized within its intercellular spaces) closely resembles octanol in its selectivity to permeant structure [127,128]. In addition, correlations between octanol–water partition coefﬁcients and transport of solutes across the blood–brain barrier have been established [129,130]. On the other hand, the studies on egg lecithin bilayers have demonstrated a chemical selectivity for this membrane more closely resembling that expected if the barrier domain were hydrocarbon like, with negligible hydrogen-bonding capacity [131,132]. Many natural membranes exist in a highly ordered state either through changes in phase structure or through intercalation of various ordering agents such as cholesterol and sphingomyelin [133]. For example, some natural plasma membranes contain up to 50% mole fraction of cholesterol. Increases in bilayer chain ordering are known to systematically decrease solute permeabilities [87,90]. Some evidence also suggests that the carbonyl dipoles present in most phospholipids have an important effect on polarity within the bilayer interior [134]. However, the effect of the mode(s) of linkage of the hydrocarbon chains to the glycerol moiety in phospholipid on barrier properties has not yet been indicated. Although the linkage is through an ester bond in most phospholipids of biological interest, ether bonded lipids exist in mammalian membranes and other biological membranes and the functional potency of certain lipids is attributed to this ether linkage [135]. Thus, a comparative study of the effects of ester and ether linkages on the chemical selectivity of the barrier domain in phospholipid bilayers would shed light on changes of local polarity as a result of these linkage alterations.

D.

Physicochemical Factors Affecting Structure-Permeability Relationships

The primary physicochemical properties of a drug inﬂuencing its passive absorption across biological membranes are its partition coefﬁcient (PC), extent of ionization, molecular weight, and hydrogen bonding by the drug molecule. The passive transport rates of small molecules across biological membranes are often explained, at least qualitatively, by means of a bulk-phase solubility diffusion model [85,136–138]. This model may be traced to the formulation of Overton’s rules [126]. In general, membrane permeability for a solute increases with increasing partition coefﬁcient, but two exceptions have been found. Highly branched compounds penetrate the membrane more slowly and small polar molecules penetrate the membrane more readily than expected [139,140]. The latter observation resulted in the development of the lipid-sieve membrane concept whereby one envisions aqueous ‘‘pores’’ in the membrane surface. Wright and Diamond postulate that these small, polar, relatively lipid-insoluble compounds penetrate the membrane by following a route lined by the polar groupings of membrane constituents [139,140]. The evaluation of this route would be limited primarily by the molecular size of the compound as a result of steric hindrance. Branched compounds must disrupt the local lipid structure of the membrane and they encounter greater steric hindrance than straight-chain molecules. 1. The Size of the Solute and the Degree of Lipid Chain Packing in Membranes It is well known that the permeabilities across biological membranes and model lipid bilayers strongly depend on both the degree of lipid chain packing in the membranes

Lipid Bilayers in Cells

825

[87,90,141,142] and on the size of the permeating solute [131,143]. The inﬂuence of lipid chain packing on permeability is most clearly demonstrated by the dramatic increase in transmembrane transport rates that appears because of a gel-to-liquid crystalline phase transition [90,144,145]. Membranes that are more ‘‘ordered’’ as a result of polar headgroup composition, or because of increased cholesterol concentrations or lower temperatures, or monolayers under high lateral pressures have greater resistances to permeation than predicted from a bulk solubility diffusion model, often by orders of magnitude [85,146–152]. A steep size selectivity is exhibited by both biological membranes and lipid bilayers by several groups [86,93,128,143,153]. These phenomena cannot be explained by bulk solubility diffusion theory. It has been common to interpret both the effects of chain ordering on permeability [142] and the steep dependence of permeation rates on permeant size [154,155] only in terms of changes in solute diffusivity within membranes. However, large size effects on solute partitioning into interphases are evident from the high resolution attainable on chromatographic separations on the basis of subtle differences in size and shape [156]. Kirjavainen et al. studied the effects of phospholipids on drug partitioning and on ﬂuidity of skin lipid bilayers using steady-state ﬂuorescence anisotropy [157]. They concluded that the increased distribution of drugs into the stratum corneum lipid liposomes (SCLL) was at least partially due to the increased ﬂuidity of SCLL bilayers by phospholipids. Also permeation enhancers may interrupt the rate-limiting lipid domains of the bilayers causing increased permeant diffusivity in this region. Yoneto et al. investigated the inﬂuence of the 1-alkyl-2-pyrrolidones (APs) on permeant partitioning into hairless mouse stratum corneum (SC) under isoenhancement concentration conditions using -estradiol (E2 ) as the model permeant [158]. They suggested that inducing a higher partitioning tendency for E2 into the lipoidal pathway of hairless mouse SC is a principal mechanism of action of the APs in enhancing transdermal transport. It has been investigated both theoretically [100] and experimentally [87,159] that increasing chain ordering within lipid bilayers substantially decreases solute partitioning into bilayers. These effects are particularly evident in the more ordered regions of the bilayer, which were conﬁrmed by neutron diffraction experiments [160] and molecular dynamics simulations [42,161]. Further studies in these laboratories suggest that the size selectivity in partitioning is ampliﬁed with increases in bilayer chain ordering. The structure–transport relationships developed solely on the basis of lipophilicity or hydrogenbonding potential without consideration of molecular size effects and the inﬂuence of bilayer composition (i.e., chain ordering) on these size effects may be misleading. Walter and Gutknecht report that literature data for the incremental free energy changes accompanying the addition of a methylene group to various homologous series of permeants derived from transport studies across a variety of model bilayer and biological membranes were highly variable, ranging from nearly zero up to 900 cal/mol [162]. In addition to the inappropriate treatment of unstirred layer effects in some of these studies pointed out by Walter and Gutknecht, the differences in membrane composition and complexity in terms of lipid chain packing (e.g., gel and liquid-crystalline phases) may also have contributed to the variability in the effects of permeant chain length on permeability. The difﬁculties in investigating the inﬂuence of permeant size on permeability arise from the fact that changes in permeant size are usually accompanied by changes in lipophilicity, with the latter effects often overshadowing the effects of permeant size alone. Xiang and Anderson studied the effects of lipid chain packing and permeant size and shape on permeability across lipid bilayers [163]. They carried out the experiments in gel

826

Suhonen et al.

and liquid-crystalline dipalmitoylphosphatidylcholine (DPPC) bilayers by a combined NMR line-broadening–dynamic light scattering method using short-chain monocarboxylic acids as permeants. They investigated simultaneously the effects of permeant size on permeability in bilayers varying the packing density, which enabled them to establish a model, which combines the effects of bilayer chain packing and permeant size on permeability across lipid bilayer membranes. Previous studies have shown that because of the ordering of lipid molecules in bilayer membranes, solute molecules residing in the bilayer interior are oriented with their long axes preferentially along the bilayer normal (Fig. 13) [164–166]. Theoretically, this alignment minimizes the work required to create a cavity to accommodate the solute molecule in the lipid bilayer. Thus, the resistance to the transbilayer movement of a solute in the bilayer interior due to the partitioning term may depend primarily on the cross-sectional area along the long axis of the solute [163]. A statistical mechanical theory developed by Xiang and Anderson also suggests that solute partitioning into the barrier region of lipid bilayers is disfavored by chain ordering and that the selectivity of the barrier domain for permeant size is ampliﬁed with an increase in surface density (i.e., a decrease in free surface area) (Fig. 13) [164]. These results have been conﬁrmed by molecular dynamics simulations, which have demonstrated a strong size dependence for solute partition coefﬁcients in the order chain region in lipid bilayers and that the size dependence is ampliﬁed at high surface densities [167,168]. 2. Inﬂuence of pH Gradients on the Transbilayer Transport of Drugs Most drug molecules are either weak acids or bases which are ionized to an extent determined by the pKa of the compound and the pH of the biological ﬂuid in which it is dissolved. Because biological membranes are predominantly lipophilic, drugs penetrate these membranes mainly in their undissociated form. Brodie and Hogben were the ﬁrst researchers who applied this principle, the pH-partition hypothesis [169]. The pH-partition principle has been tested in a large number of in vitro and in vivo experiments, but it is only partly applicable in real biological membranes [170]. In many cases, the nonionized form as well as the ionized form partitions into the membranes, and the drug is substan-

FIG. 13 A schematic illustration of the effects of the free surface area of lipid bilayer membranes on the permeation of two permeants with the same molecular volume, but different cross-sectional areas. (a) A lower free surface area. (b) A higher free surface area.

Lipid Bilayers in Cells

827

tially transported across lipophilic membranes. For example, the in vitro permeability coefﬁcient for the ionized form of sulfathiazole may actually exceed that for the nonionized form of the drug. Permeation of the neutral form leads to large transmembrane concentration gradients of certain weak bases or weak acids when transmembrane pH gradients are present, which led to their use to assay pH gradients in cells or organelles [171,172]. These observations for cells and organelles were extended to model membrane liposomal systems [173]. Utilizing the quenching of a ﬂuorescence probe, Deamer et al. demonstrated that gradients of 2–4 pH units (interior acidic) could be established and measured in small unilamellar vesicle (SUV) systems. They extended these results to demonstrate uptake of weak catecholamine bases into liposomes in response to pH gradient [174]. Let us consider uptake of a weak base containing a single amine into an LUV with an acidic interior. [A]o ([AHþ ]o ) and [A]i ([AHþ ]i ) refer to the concentrations of the neutral (protonated) form(s) of the amine on the outside and inside of the vesicle, respectively. Then the total external and internal concentrations of the amine can be written as þ ½Atot i ¼ ½Ai þ ½AH i

ð10Þ

þ ½Atot o ¼ ½Ao þ ½AH o

ð11Þ

We consider the case where the weak base is initially introduced in the external aqueous medium containing the LUVs with an acidic interior (Fig. 14). Assuming that the neutral base is the only membrane permeable form, the rate of uptake of the weak base into the LUVs is given by d½Atot d½Ao o ¼ dt dt

ð12Þ

FIG. 14 A model for the uptake of weakly basic compounds into lipid bilayer membrane (inside acidic) in response to the pH difference. For compounds with appropriate pKa values, a neutral outside pH results in a mixture of both the protonated form AHþ (membrane impermeable) and unprotonated form A (membrane permeable) of the compound. The unprotonated form diffuse across the membrane until the inside and outside concentrations are equal. Inside the membrane an acidic interior results in protonation of the neutral unprotonated form, thereby driving continued uptake of the compound. Depending on the quantity of the outside weak base and the buffering capacity of the inside compartment, essentially complete uptake can usually be accomplished. The ratio between inside and outside concentrations of the weakly basic compound at equilibrum should equal the residual pH gradient.

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N(A) is the number of molecules of the neutral form of the external weak base, PC is the permeability coefﬁcient of the neutral form, Am is the surface of the membrane, and Vo is the external aqueous volume. Then, dNðAÞ ¼ ðPCÞAm ð½Ao ½Ai Þ dt

ð13Þ

The same approach derived for weak bases can also be applied to the uptake of simple weak acids, and to the transbilayer transport of acidic lipids, such as fatty acids and some phospholipids. We consider uptake of a simple weak acid into an LUV with basic interior. Let [AH]o ([A ]o ) and [AH]i ([A ]i ) refer to the concentrations of the neutral (ionized) form(s) of the weak acid on the outside and inside of the vesicle, respectively. Then, the total external and internal concentrations of the weak acid can be written as ½Atot o ¼ ½A o þ ½AHo

ð14Þ

½Atot i ¼ ½A i þ ½AHi

ð15Þ

We consider the case where the weak acid is initially introduced in the external aqueous medium containing the LUVs with a basic interior. Assuming that the neutral (protonated) acid is the only membrane permeable form, the rate of uptake of the weak acid into LUVs is given by d½Atot PAm ½Hþ o tot o ¼ ½Atot o ¼ k½Ao dt Vo Ka

ð16Þ

where Ka ð¼ A o ½Hþ o =½AHo Þ is the dissociation constant of the weak acid, and k ¼ ðPAm ½Hþ o =Vo Ka Þ is the rate constant associated with uptake. We consider only the case where the aqueous interior of the LUV is sufﬁciently well-buffered that the accumulated weak acid does not signiﬁcantly change the interior pH. Then, the uptake will continue until the internal and external concentrations of the neutral form of the weak acid are equal, i.e., until ½AHi ¼ ½AHo . As Ka (inside) ¼ Ka (outside) it follows that ½Hþ o =½Hþ i ¼ ½A i =½A o

ð17Þ

Thus, at equilibrium, the transbilayer concentration gradient of the weak acid reﬂects the inverse of the transbilayer concentration gradient of protons (Fig. 14). For example, a pH difference of 2 units (e.g., internal pH ¼ 9 and external pH ¼ 7) shoud lead to 100-fold higher concentration of weak acid within the vesicle as compared to the external concentration. Many biological membranes exhibit transmembrane pH gradients of 2–3 units. Biological compounds, which are weak bases, such as biogenic amines, are strong candidates for transmembrane accumulation in response to a pH gradient. Although the uptake of biogenic amines such as dopamine into secretory vesicles is usually thought to involve speciﬁc transport proteins [175], pH gradients (acidic interior) exist between these membranes [176,177]. It has been shown that dopamine and catecholamines can be accumulated within LUVs exhibiting such a pH gradient [174]. Thus, at least portion of the uptake into the secretory vesicles would be expected to be protein-independent. One interesting example of the potential importance of intracellular pH gradients is found in the phenomenon of multidrug resistance (MDR). The MDR protein acts as a molecular pump, actively pumping chemotherapeutic agents out of the cell. Tumor cells, which are susceptible to chemotherapeutics have often a lower intracellular pH [178], which would lead to enhanced accumulation of these drugs in response to the pH differ-

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ence. In contrast, the intracellular pH of resistant cells is signiﬁcantly higher than that of nonresistant cells [179,180], giving rise to a reduced pH difference, which would lead to reduced intracellular accumulation of drugs. Thus, it is possible that the proteins responsible for MDR exert at least some of their effect by altering intracellular pH, which then reduces the drug uptake by pH difference. Roepe observed a near-linear relationship between the intracellular pH and the efﬂux of doxorubicin in human myeloma cells [179]. In addition, studies involving systematic alteration in tumor cell intracellular pH reveal that acidiﬁcation of the intracellular pH results in fast accumulation of drug, whereas shifts to alkaline pH result in drug efﬂux [178]. Another important role of transbilayer pH gradients is in the area of membrane lipid asymmetry. Simple lipids such as fatty acids can sequestered to the inner layer of LUVs in response to the pH difference (inside basic) [181], which suggests that fatty acids will be preferentially located in the cytoplasmic monolayer of organelles such as the endoplasmic reticulum, which has an acidic interior [182,183]. The pH-dependent fatty acid transbilayer asymmetry has been observed in adipocytes, where increasing the internal pH leads to accumulation of fatty acids in a manner consistent with passive diffusion of the neutral form [184], which is in good agreement with results using model systems [181]. Similar considerations also apply to other acidic lipids, such as phosphatidic acid (PA) and phosphatidylglycerol (PG), which will also preferentially locate in the monolayer experiencing the highest pH. Alternatively, lipids with amino groups such as sphingosine would be expected to locate in monolayers facing acidic environments. This pH-difference-dependent regulation of transbilayer distributions of lipids could regulate bioavailability and hence modulate metabolic processes. Transmembrane pH gradients cannot account for lipid asymmetry such as observed in erythrocyte membrane, where phosphatidylserine (PS) and phosphatidylethanolamine (PE) are concentrated in the inner leaﬂet, while phosphatidylcholine (PC) and sphingomyeline (SPM) are localized on the external leaﬂet [185], as the neutral form of these lipids is associated with a zwitterionic headgroup resulting in low membrane permeability. There is strong evidence that asymmetrical transbilayer distributions of PE and PS are maintained by an ATP- and Mg2þ -dependent aminophospholipid translocase [79,186]. In summary, pH gradients can play a signiﬁcant role in the transbilayer transport of a wide variety of weak bases and weak acids of biological interest. This has led to a variety of applications, ranging from drug loading of liposomes for drug delivery to the use of LUVs containing electron dense ions as potential contrast-agents in imaging protocols. Studies on lipid asymmetry induced by pH gradients have led to new insights on regulation of such fundamental processes as membrane fusion and factors, which regulate membrane morphology. In addition, pH gradients across organelle membranes may be expected to strongly inﬂuence the intracellular distribution and bioavailability of drugs and certain biological compounds. E.

Alternative Methods to Evaluate Drug Absorption

Using molecular mechanics calculations to assess the three-dimensional shape of a molecule, various surface properties such as polarity and size can be calculated. The dynamic molecular surface properties can be determined from the (low energy) conformation(s) of the drug molecule obtained by molecular mechanics calculations of conformational preferences. The potential advantage of this method is that the calculated surface charactersitics determine numerous physicochemical properties of the molecules including lipophilicity, the energy of hydration and the hydrogen bond formation capacity [187–

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190]. For instance, the surface properties of a molecule that forms an intramolecular hydrogen bond may be less polar, resulting in an enhanced membrane permeability in comparison to a homologous molecule [191]. It can, therefore, be hypothesized that the relative importance of each physicochemical factor will be reﬂected by a single measure such as the polar molecule surface area calculated from low-energy conformations of the drug molecule. However, the inﬂuence of the surface characteristics on each of the physicochemical properties may also vary from one conformation of a drug molecule to another. Thus, it is inappropriate and also misleading to select a single conformer for the calculation of static surface area properties [192]. A dynamic method, which takes into account all preferred (low-energy) conformations, should give a better description of the surface properties than methods that consider only single conformations. Such methods have been available for a long time and are routinely used for the prediction of drug molecule–receptor interactions, i.e., in prediction of structure–activity relationships [193]. Palm et al. compared dynamic surface properties of a series of beta-adrenoreceptor antagonists and drug permeabilities in Caco-2 monolayers and rat intestinal segments in order to predict passive drug absorption [110,194]. Excellent correlations were obtained between the dynamic polar van der Waals surface areas and the permeabilities in Caco-2 cells and rat intestine. The correlations were stronger than those obtained with calculated log Doct values. Moreover, the permeability coefﬁcients were ranked in the correct order in both models using the dynamic polar molecular surface areas, but not using the calculated log Doct values or the number of potential hydrogen bonds. Van der Waterbeemd and Kansy established a relationship between the calculated polar molecular surface areas of drug molecules and blood–brain barrier uptake [195]. The polar molecular surface area of a drug molecule is deﬁned as the sum of the parts of the surface area associated with polar atoms, e.g., oxygen, nitrogen, and hydrogen attached to the polar atoms. Although the criteria for the selection of the molecule conformations used in the calculation of the surface areas were unclear, and no consideration was given to the ﬂexibility of the molecules, a relatively strong correlation was found. Furthermore, Barlow and Satoh have reported a similar relationship between percentage polar surface area of peptide-like molecules and log Doct [187]. Together, these results suggest that molecular surface properties are of potential interest as predictors of drug absorption for conventional drugs (small organic molecules) as well as for slightly larger peptide-like molecules. The decreased permeability of very lipophilic ðlog Poct 4Þ compounds is generally related to their high solubility in the lipophilic cell membranes. Although these drugs distribute rapidly into a cell membrane, their cellular transport is decreased by a slow distribution from the cell membrane into the extracellular (aqueous) ﬂuids [196]. However, Wils et al. [197], who observed a parabolic relationship between permeability in HT29-18-C1 monolayers and log Doct , could not correlate the decreased permeability of the most hydrophobic drugs to an increased cellular uptake. Thus, other factors, such as polarity, could have contributed to the low permeability of the hydrophobic drugs. Palm et al. found that some of the very hydrophobic drugs had larger polar van der Waals surface area than expected [198]. This ﬁnding provides an alternative explanation for the low permeability of the drugs in HT29 cell monolayers [197]. Thus, while the low permeability of some lipophilic drug molecules undoubtedly results from retention in the lipophilic cell membranes [196,199], the low permeability of other lipophilic drugs may be related to their polarity [198]. These results suggest that the dynamic polar surface area can be used as an alternative model for the theoretical prediction of drug absorption.

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F.

831

Membrane Perturbation by Drugs and Excipients

Membrane ﬂuidity determines the rate at which lipids and proteins can diffuse in the membrane. The lipid composition of the membrane, the proteins in the membrane, and the surrounding electrolyte composition of the surrounding solutions inﬂuence the ﬂuidity. Membranes can exist in two phases. The liquid phase is the presumed phase of most membranes under physiological conditions. In the liquid phase, the lipid headgroups are tightly packed, but the hydrocarbon chains have considerable ﬂexibility. As the temperature is lowered, there is a sudden shift in the behavior of the membrane as it undergoes a phase transition to a more solid, or crystalline, phase. In the crystalline phase, the hydrocarbon chains become tightly packed and less ﬂexible. The effect of different membrane components on the phase transition temperature is indicative of their role in modulating membrane ﬂuidity. Biological membranes are complex mixtures of many lipids and proteins, and the role of each of these in the behavior of the membrane is not completely understood. The importance of membrane ﬂuidity is demonstrated by the relationship between the activity of membrane transport protein and the temperature. The result is not a line as would be expected from cytoplasmic enzymes, but a curve with sudden breaks occurring where the phase transition of the membrane occur. Thus, as the membrane undergoes a transition to the crystalline phase there is a sudden drop in the activity of the protein. The molecular mechanisms involved in the pharmacological effects by a variety of drugs upon binding to proteins and lipid membranes is a question of fundamental importance in molecular pharmacology [200]. It is well known that a large number of drugs with different chemical structures and pharmacological effects are able to bind to lipid membranes and alter the physical properties of membranes [201,202]. Examples include general and local anesthetics, nonsteroidal anti-inﬂammatory agents and calcium channel-blocking drugs. In particular, the inﬂuence of local and general anesthetics on lipid membrane structure and dynamics has been extensively studied [105,202,203]. One hypotyhesis relates the molecular action of anesthetics to a change in the lateral pressure proﬁle of the lipid membrane and a subsequent effect on the conformational ﬂexibility and function of membrane-spanning proteins [204]. NMR studies have suggested that the interaction and binding to the interfacial lipid membrane–water interface, which is followed by a disruption of the hydration shell, is involved in the target and action sites for amphilipic agents [205]. In addition, data obtained from infrared, thermal, and ﬂuorescence spectroscopic studies of the outermost layer of skin, stratum corneum (SC), and its components imply enhancer-improved permeation of solutes through the SC is associated with alterations involving the hydrocarbon chains of the SC lipid components. Data obtained from electron microscopy and x-ray diffraction reveals that the disordering of the lamellar packing is also an important mechanism for increased permeation of drugs induced by penetration enhancers (for a recent review, see Ref. 206).

G.

Fusogenic Lipids

Liposomes are vesicles with an aqueous core surrounded by lipid bilayer walls. Drugs may be encapsulated into the liposomes, either in the bilayers or into the aqueous core of the liposomes. Liposomes have been widely investigated by systemic and local drug delivery in different cavities of the body. Interaction of the liposomal lipids with cellular lipid bilayers or other lipid bilayers in the body (e.g. skin lipids) depends on the nature of the lipids in the liposome. In order to

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cause structural changes and subsequently permeability enhancement in the cellular bilayers, the lipids should be able to fuse with the target lipid bilayer. Simple binding and aggregation are not expected to enhance membrane permeability, although liposomal encapsulation affects the drug distribution in the body in macroscopic sense [207]. Upon lipid fusion the contacting lipid bilayers undergo lipid mixing with each other. This takes place, for example, in the viral entry into cells, i.e., viruses utilize lipid fusion in order to enter the cell interior [208]. For lipid fusion to take place, certain structural features of lipids are required. The long-range lipid organization has been discussed in this review earlier. In the case of lipid fusion the most crucial conformation for the lipids is the inverted hexagonal (HII ) conformation (Figs. 4 and 7). Lipids that can adopt hexagonal conformation may facilitate lipid fusion between bilayers [17,209]. In the hexagonal phase (HII ) the lipid headgroups are organized in a highly curved conformation (Figs. 4 and 7), and, therefore, the lipids with small headgroups and cone shape, like phosphatidyl ethanolamine, can form an inverted hexagonal phase easier than the lipids with larger headgroups [209]. The effective size of the polar headgroup is further affected by electrostatic repulsion and hydrogen bonding. The increased length of the alkyl chains as well as their unsaturation favor hexagonal phase formation. Dioleoyl (18:1) phosphatidyl ethanolamine (DOPE) is a commonly used fusogenic lipid. DOPE has structural features required for fusogenicity: small headgroup and unsaturated C-18 acyl chains [209]. Usually fusogenic lipids, like DOPE, do not form stable liposomes as such, but they can be used as a component, i.e., helper lipid, in the liposomes. Fusogenic liposomes are applied for two main purposes: enhancement of membrane permeability and improvement of intracellular drug delivery. Importance of lipid fusion in transdermal liposomal delivery of drugs was demonstrated by Kirjavainen et al. [210]. Nonfusogenic liposomes cannot improve drug delivery through the skin, but rather decrease it. Fushion of liposomal lipids with the skin lipids could be improved by DOPE or ethanol solution [211]. In these cases the lipid fusion was facilitated and, as a consequence of fusion, the lipid order in the skin lipid barrier is decreased as evidenced by ﬂuorescence anisotropy [157]. Such an increase in the ﬂuidity of the lipid bilayers increases both the diffusivity of the drug in the lipid barrier [88] and the partitioning of the drugs in the bilayers [157]. Increased partitioning causes a higher concentration gradient in the membrane at steady state and, therefore, it increases the permeability in the membrane. In contrast, the nonfusogenic saturated lipids do not increase the lipid bilayer ﬂuidity or drug partitioning into the lipid bilayers [157]. In living cells, liposomes are taken up by endocytosis (an active process of internalization in which the cell membrane surrounds the liposome and forms an endocytic vesicle inside the cell) [207]. In many cases drug should escape from the endosome to the cytoplasm and possibly to the nucleus of the cell for activity [212,213]. The endosomal wall is a lipid bilayer with embedded membrane proteins and this wall may prevent the entry of drug into the cytoplasm. For permeabilization of the wall the liposomal lipids should fuse with the endosomal wall. This takes place in the case of the pH-sensitive liposomes that are formed when the stabilizing component has an acidic (e.g., oleic acid or cholesteroyl hemisuccinate, CHEMS) or basic [e.g., cholesterol-(3-imidazol-1-yl propyl) carbamate, DPIm] headgroup with pKa in the neutral range [214–216]. They undergo L ! HII transition and fusion with the endosomal wall when pH is decreasing in the endosomes and the acidic headgroup is neutralized. Lipid fusion may be important also in the intracellular delivery of genes and other gene-based drugs [217,218]. This is discussed later in this chapter.

Lipid Bilayers in Cells

H.

833

Amphipathic Peptides

Amphipathic peptides contain amino acid sequences that allow them to adopt membrane active conformations [219]. Usually amphipathic peptides contain a sequence with both hydrophobic amino acids (e.g., isoleucine, valine) and hydrophilic amino acids (e.g., glutamic acid, aspartic acid). These sequences allow the peptide to interact with lipid bilayer. Depending on the peptide sequence these peptides may form -helix or -sheet conformation [219]. They may also interact with different parts of the bilayer. Importantly, these interactions result in a leaky lipid bilayer and, therefore, these features are quite interesting for drug delivery application. Obviously, many of these peptides are toxic due to their strong membrane interactions. Amphipathic peptides are important for the viruses when they enter the interior. Many viruses have amphipathic peptides on their surface. A classic example is Haemophilus inﬂuenzae [208]. Amphipathic peptide on the viral surface undergoes a conformational change when the endosomal pH is acidiﬁed and, subsequently, this peptide is able to fuse with the endosomal bilayer. Consequently, the virus is able to escape from the endosome to the cytoplasm. Many amphipathic peptides are pH-dependent so that they are activated in the endosomal compartment [219]. Virosomes are virus-mimicking systems that contain liposomal bilayer and pHdependent protein impregnated in the liposomal wall. Virosomes are produced by a detergent dialysis procedure. Many researchers have demonstrated that the virosomes facilitate the leakage of the encapsulated drugs from the endosomes into the cytoplasm. This is, however, complicated technology and, so far, no virosome products are used in the clinical practice.

V.

TRANSPORT OF GENE-BASED DRUGS ACROSS CELLULAR LIPID BILAYERS

A.

Challenge of Gene-Based Drug Delivery

The Human Genome Project will provide in the near future all DNA sequences of approximately 140,000 human genes. Rapid progress of the Human Genome Project, bioinformatics, and biotechnology generates a rapidly increasing number of potential targets for drug and gene therapy. Simultaneously, new diagnostic methods, such as DNA arrays and proteomics technology enable the rapid identiﬁcation of the genes and gene products that are linked to the disease [220–222]. Thus, information about the nucleotide sequences with therapeutic potential increases rapidly, and it is commonly predicted that the number of targets of drug action will increase rapidly from a few hundred to several thousands, even up to 10,000. In disease, the gene product may be expressed at too low or too high level. In both cases the gene-based drugs provide potential treatments. Gene-based drugs are based on the nucleotide chemistry and nucleotide sequences of the target genes [223,224]. Genebased drugs are divided into gene therapy, gene inhibitors, gene correction, and DNA vaccination. In principle, after completion of the Human Genome Project, the function of any human gene could be attenuated or augmented using gene-based drugs. In gene therapy, production of missing or poorly expressed protein is induced by transferring the coding sequence to the cells in plasmid DNA [223]. In principle, the sequence of any protein can be transferred to the cells for protein production. Regulatory elements of DNA, such as cell speciﬁc and inducible promotors, can be

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used to improve the control of gene expression. In DNA vaccination, a gene that is coding for an antigen is transferred to antigen presenting cells to provide immunity. In both cases, DNA-based therapy has signiﬁcant advantages compared to protein therapy. For example, DNA is much more stable, cheaper to produce, and DNA technology allows better control of the gene product localization in the body. Gene inhibition is practiced by using oligonucleotides: single-stranded chains of DNA, RNA, or chemically modiﬁed DNA or RNA [225,226]. They bind selectively to the complementary mRNA or DNA and inhibit either transcription (antigene effect) or translation (antisense, ribozymes), thus inhibiting selectively the function of the target gene. Gene correction is based on chimeric oligonucleotides that correct mutations permanently. Gene-based drugs show great potential in medical treatment. After identiﬁcation of the target gene or gene product, the nucleotide sequence for gene therapy or DNA vaccination is known. Current technology enables rapid identiﬁcation of the targets and the selection of gene-based drug (i.e., sequence) [222]. These advances can be realized in the prevention and treatment of diseases only if the gene-based drugs can be delivered safely and efﬁciently to their target sites in the cells [225]. It is important to note that the sites of action for the gene-based drugs reside inside the cells in the cytoplasm or nucleus. Despite the promising features of gene-based drugs, their delivery to the target sites is not straightfoward due to their high moleculear weights (5000–millions) and negative charges [213]. Each phosphodiester linkage between the nucleotides contains one negative charge. Therefore, a typical oligonucleotide contains about 20 negative charges and their molecular weights are about 5–10 kDa. Oligonucleotides do not diffuse passively across the cell membranes to their sites of action in the cytoplasm (antisense, ribozymes) or in the nucleus (antigene, gene correction) [227]. Oligonucleotides bind to the cell surface, presumably to scavenger receptor for polyanions, and they are internalized [227]. This may not result in good drug activity due to the poor escape of oligonucleotides from the endosomes to the cytoplasm [225]. In gene therapy, plasmid DNA is introduced into the human cells for the production of protein. The aim is to provide a new gene to substitute a mutated gene sequence (e.g., in cystic ﬁbrosis), to increase the production of a therapeutic protein (e.g., in cancer, transplantation), or to render cell susceptible to the defense mechanisms of the body or drug treatment (e.g., suicide genes, DNA vaccination) [223]. In all these cases the required DNA sequences must be transferred efﬁciently and safely to the nucleus of the cells. From the previous discussion on transcellular drug diffusion it is obvious that plasmid DNA with its molecular weight of millions is too big to diffuse through the plasma membrane. Delivery systems for gene-based drugs are needed to fulﬁll their promise in the medical treatment. Interactions of the potential delivery systems with the lipid bilayers are of crucial importance, since the lipid bilayer barrier must be overcome either at the level of plasma membrane or in the endosomes.

B.

Interactions of Some Delivery Systems with Lipid Bilayers

1. Liposomes Liposomes have been investigated in the delivery of the gene-based drugs for more than a decade. The cellular transfer of genes and oligonucleotides is obtained with cationic lipo-

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somes [228]. Some gene transfer is obtained with pH-sensitive liposomes, but their gene transfer efﬁcacy is an order of magnitude less than that of cationic liposomes [215]. The cationic liposomes do not encapsulate DNA in the classical sense of liposomal encapsulation. Instead, the cationic liposomes form a complex with DNA and oligonucleotides electrostatically [229]. Depending on the number of the anionic charges of the oligonucleotide/DNA and the cationic charges of the lipids, different complexes with varying charge ratios and surface charges are formed [230]. Ja¨a¨skela¨inen et al. found out that upon complexation of the oligonucleotides the cationic liposomes ﬁrst aggregate and then fuse together [231]. This was shown by resonance energy transfer experiments in which dilution of the ﬂuorescent lipid probes in the bilayers suggests fusion of the liposomes. Eventually, the liposomal structure may be lost, particularly, if the liposomes contain fusogenic lipid, e.g., DOPE [232]. DOPE is used in cationic liposomes to facilitate the fusion of the liposomes with the endosomal wall, but DOPE affects the complex formation between oligonucleotide/DNA and the liposomes. Freeze-fracture EM pictures show that the cationic liposomes with DOPE are able to adopt tubular hexagonal lipid phases [232]. Furthermore, hexagonal phase formation is more prominent if the complexes are exposed to high ionic strengths (e.g., cell culture medium). Cationic liposomes form complexes with plasmid DNA. Also, in this case DOPE affects the architecture of the complexes. DOTAP liposomes without DOPE are able to condense DNA, while DOTAP/DOPE liposomes do not condense DNA, presumably due to HII -phase formation [230,233]. Interestingly, multivalent cationic liposomes, such as DOGS, can condense DNA more efﬁciently than monovalent cationic liposomes [233]. If the complexation is carried out at high ionic strength the DNA condensation is less prominent than in plain water. Cationic liposomes are most efﬁcient in delivering DNA [217] and oligonucleotides [234] into the cells at positive +/ charge ratios. This coincides with their ability to react with anionic lipid bilayers that mimic the endosomal wall [231]. Positively charged oligonucleotide–liposome complexes could disrupt the anionic liposomal walls during incubation causing release of the encapsulated calcein from the liposomes. Good delivery properties of the positively charged complexes may also be due to the better adherence of the complexes with anionic cell surface and, subsequently, a higher rate of internalization of the complexes. Oligonucleotides and plasmid DNA must be released from the liposomal complexes in the cells. Otherwise, they cannot be activated. Zelphati and Szoka showed by confocal microscopy and resonance energy transfer techniques that oligonucleotide is released from the cationic liposomes at the endosomal wall [235]. They suggested that the cationic surface of the liposome–oligonucleotide complex induces ﬂipping of negatively charged lipids from the outer leaﬂet of the bilayer as illustrated in Fig. 15. Fusogenic liposomes are able to fuse with the endosomal wall and, consequently, the cationic lipids are stripped from the olignucleotide complex, leading to the release of oligonucleotide from the endosome to the cytoplasm. Later Ja¨a¨skela¨inen et al. showed that DOTAP/DOPE liposomes, but not DOTAP, release oligonucleotide in the presence of endosome mimicking liposomes [232]. Accordingly, only those oligonucleotide–lipid complexes that are able to fuse (either due to DOPE or amphipathic peptide) with the endosomal wall could elicit antisense effects in the cells [236]. It is known that free oligonucleotide is able to diffuse freely from the cytoplasm into the nucleus [237]. Therefore, oligonucleotide release at endosomal level should be advantageous for the antisense activity. In the case of plasmid DNA the intracellular target (i.e., transcription machinery) is located in the nucleus. Plasmid DNA is a much larger molecule than oligonucleotides, and

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FIG. 15 Cellular entry and intracellular kinetics of the cationic lipid-DNA complexes. Cationic lipid–DOPE liposomes form electrostatic complexes with DNA, and, in this case, also transferrin (Tf) is incorporated. Cellular uptake by endocytosis and endosomal acidiﬁcation can be blocked with cytochalasin B and baﬁlomycin A1 , respectively. DNA is proposed to be released at the level of endosomal wall after fusion of the carrier lipids with endosomal bilayer. This process is facilitated by the formation of inverted hexagonal DOPE phase as illustrated in the lower corner on the right. After its release to the cytoplasm DNA may enter the nucleus. (From Ref. 253. By permission of Nature Publishing Group.)

therefore, the nuclear entry of plasmid DNA from the cytoplasm to the nucleus is poor [238,239]. Release of plasmid DNA from the cationic lipids in the cells has not been investigated, but Xu and Szoka demonstrated that coincubation with anionic liposomes releases plasmid DNA from the complexes with cationic lipids [240]. In contrast to the oligonucleotides, it appears that the cationic liposomes without DOPE are able to deliver DNA as well or even better than cationic liposomes with DOPE [233]. Several factors may

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be responsible for the difference between the results with oligonucleotides and DNA. One of the reasons may be different lipid interactions with the endosomal lipid bilayer, another possibility being different kinetics in the cytoplasm and nucleus.

2.

Polycations

Plasmid DNA can be complexed electrostatically with cationic polymers. These complexes can be used for gene transfer [241]. Like the complexes of DNA with cationic lipids these complexes adhere to the cell surface with their cationic surface charges. Thereafter, they are internalized, presumably by adsorptive endocytosis. Interactions of the cationic polymer–DNA complexes with endosomal lipid bilayer have not been investigated in detail. There are substantial differences between polycations in terms of their gene transfer efﬁcacy [233], but the reasons for the differences are poorly understood. Anyway, complexation with DNA is not adequate for gene transfer. For example, polyamidoamine dendrimers and polyethylene imine (PEI) show much higher gene delivery than polylysines [233]. The reasons for this are not well understood. Tang et al. [242] and Boussif et al. [243] have suggested that dendrimers and PEI act as proton sponges and swell in the endosomes. These properties may lead to the rupture of the endosomal wall by electrostatic binding and, subsequent stretching of the endosomal membrane. Intensity of DNA binding is also different: PEI releases DNA easier than polylysine [233]. 3. Peptides Peptides have been used for the delivery of gene-based drugs. Several rationales have been utilized. Cationic peptides are used to neutralize the charges of DNA or oligonucleotide. These peptides include polylysines and polyarginines [241,244,245]. They form complexes with DNA or oligonucleotide, thereby resulting in enhanced cellular uptake. The rationale in using amphipathic peptides is to mimic the mechanisms of viral gene transfer. Amphipathic peptides undergo conformational change due to the pH change in the endosomes [246,247]. Subsequently, they form -helical pores in the endosomal bilayer and, eventually, lyse the endosomes and release DNA to the cytoplasm. Among the amphipathic peptides are viral peptides, like INF-7 and JTS-1, and synthetic peptides, like KALA and GALA [248]. Most of these peptides are not cationic, but they can be complexed together with a cationic polymer or cationic liposome. Interestingly, KALA peptide is cationic and amphipathic. Therefore, this peptide is able to complex DNA as such and to mediate transfer of oligonucleotides and DNA into the cells [248]. Several studies have shown that amphipathic peptides are able to augment gene transfer into the cells, but their efﬁcacy in vivo is not as clear. Peptide sequences are important both for viruses and cells in different transfer functions. Some peptide sequences facilitate protein localization in the cells across lipid barriers, while others help viruses to infect cells. These membranes translocating peptides are often hydrophobic. Although a peptide sequence may transfer its protein cargo across the cell membranes efﬁciently [249] it may not function similarly when it is linked to oligonucleotide. Antopolsky et al. conjugated the membrane translocating peptide sequences from Kaposi’s sarcoma ﬁbroblast growth factor to oligonucleotides [250]. The conjugates were taken up preferentially by the cells via endocytic mechanism, but still the conjugate could not exert antisense activity. This was due to the entrapment of the conjugates to the endosomes: they could not escape from the endosomes to the cytoplasm

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as such. After liposomal complexation endosomal escape and antisense effect were observed. Membrane translocating peptides are promising vehicles for the transfer of macromolecules into the tissues. Recent report of Schwarze et al. [249] demonstrated that a signal peptide from HI-virus could transfer betagalactosidase protein to virtually all tissues in rat after intravenous and intraperitoneal injections. In the case of proteins, folding phenomena affect their membrane translocation and these features may be different for gene-based drugs.

VI.

CONCLUDING REMARKS

Lipid bilayers affect drug delivery at several levels of pharmocokinetics, both at macroscopic and microscopic levels. Understanding the structure and function of the bilayers aids in the development of better drug delivery systems. Delivery is particularly important for the success of the gene-based drugs.

ACKNOWLEDGMENTS The authors wish to thank Ms. Anne-Mari Oksman for technical assistance and Dr. Michelle Marra for useful suggestions and discussion. The Academy of Finland is acknowledged for funding.

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Index

Acceptor number, 27 Acid rain, 659–661 Activity coefﬁcient, 3, Adsorption, 83–101 at polarized liquid-liquid interfaces, 118 energy, 235, 359 free energy, 110, 111 Gibbs equation, 415, 416 interfacial, 609 isotherm, 109, 110 Langmuir isotherm, 109, 234–236 nonlocalized model, 539 phenomena, 106 protein, 261, 594 speciﬁc, 3, 4,201 Alternating direction implicit ﬁnite-difference method (ADIFDM), 289 Amphiphilic isotherm, 109 Anesthetics, 690, 775–803 activity, 715 delivery sites, 797 discharging, 796–797 general, 797 local, 715, 792, 796 volumetric properties, 797 Aphid, 654 Assisted proton transfer, 694–695 Atmospheric, electricity, 658 electrochemistry, 658–661 Axon, 651–653 hillock, 653 squid giant, 676

Back-extraction method, 480–481 Berthelot rule, 91 Bienzymatic systems, 575 Biocatalysis, 553–580 Biocatalyst, 558–563, 568 Biocompatibility, 586, 594–596 Bioconversion, 558, 574 Bioreactor, 554, 563, 578 biphasic, 572 Biosensor, 515–530, 592 Biotransformation, 553 Blood-brain barrier (BBB), 809, 824 Boltzmann equation, 454 Born equation, 23, 24, 25, 26, 28, 30 Born model, 25, 134 Butler–Volmer, approximation, 308, 349 equation, 378, 385, 534 law, 175 relationship, 112, 167 Capacitance, 56, 60, 64, 77, 78, 179, 415–435 differential, 179 double layer, 192 interfacial, 206 negative, 62–64 Capillary waves, 172–174, 230, 231, 236 interfacial, 537 frequency, 232, 233, 236, 237 power spectra, 233 Carbonylcyanide-4triﬂuoromethoxyphenylhydrazone (FCCP), 665–669 Carcinogen, 664 845

846 Catalytic reduction, 497 Cell, 656 aggregation, 563 cell signaling, 515 chemical, 10, 11 companion, 650 ,652 concentration, 10, 11 conducting, 650 electrochemical, 689 excitable, 660 galvanic, 9, 10, 14 interfacial, 328 Lewis, 327–328, 349568, 571–573 living, 649 motor, 650 nerve, 675 organelles, 660 phloem, 675 physiology, 807 promoters, 833 rotating diffusion, 331 Schwann, 653 sensory, 650 signaling, 807 structure, 630 voltaic, 10, 14, 15, 16, 17 Centrifugal liquid membrane method (CLM), 337–339, 356 Centrosymmetric particles, 141 Charge transfer, 488, 522, 533–549 mechanism, 325 reaction, 490 Chlorophyll a, 641–647 Chloroplast, 641 Chronoamperometry, 695 Circular Dichroism (CD), 258 Compensating voltage, 16 Communication, intercellular, 651 intracellular, 651 Conductive bundles, 650 Constant-composition model, 291–296 Cooper-Harrison catastrophe, 56–59 Coulomb, ﬂuids, 102 integral, 94, 99 Crowley’s model, 67, 68 Cyclic, voltabsorptogram, 189, 190 voltammetry, 118, 192, 194 voltamogram, 181, 182, 189, 192, 218, 219 Cytoplasm, 652

Index Debye length, 123, 173, 180 Debye-Huckel, approach, 99 charge densities, 103 equation, 94 hole-corrected, 94 limit, 94 theory, 93–95, 99, 102 Dendrite, 653 Density-functional theory, 172 Dielectric relaxation, 138 Dielectric saturation, 25 Difference frequency generation (DFG), 124, 143 Diffusion controlled-electrodeposition, 219 2,4-Dinitrophenol (DNP), 661–664, 694 Distribution coefﬁcient, 4, 8,10, 12, 13 Distribution constant, 8 standard, 8 DNA, 655 based therapy, 834 chemically modiﬁed, 834 delivering, 835 plasmid, 833–837 regulatory elements, 833 replication, 515 single-stranded chain, 834 technology, 834 vaccination, 834 Donor number, 27 Doppler shift, 232 Double layer, 2, 18, 19, 51–79, 115, 118, 123, 153, 192, 454, 543, 658–661, 710 diffuse, 419, 447, 452, 544 dipolar, 2 electrical, 710 ionic, 2, 4,5, 153 relaxation, 209 Drug, 699–726 absorption, 809, 810, 829–831 action, 729 administration, 808 bioavailability, 829 biotechnological, 810 delivery (DD), 729, 775–786, 807–838 gene based, 833–834 diffusion, 810 discovery, 810 disposition, 729 efﬁciency, 729 intracellular distribution, 829 ionizable, 729–761 membrane perturbation, 831

Index [Drug] narcotic, 758 pharmacological effect, 831 structurally nonspeciﬁc, 715 transport, 809, 826 Dynamic condenser method, 15 Elastic capacitor, 51, 54, 63, 64 Elastic dimmer, 51 Elastic stretching, 71 Electric ﬁeld induced second harmonic generation (EFISH), 126, 127 Electrocardiogram, 656 Electrode, antimony, 656 aqueous gel, 631 calomel, 656 classiﬁcation, 655 counter, 631 DNA-modiﬁed, 515–530 dual-pipette, 379–381 electrolyte dropping, 339, 630, 631 ion-selective, 12, 15, 439–466, 586, 595 mercury-mercuric oxide, 656 mercury-mercurous sulfate, 656 nonpolarizable, 651, 655, 658 reference, 658–659, 688 response to DNA-binding protein, 526–527 response to DNA-binding small molecules, 523–525 reversible, 656 rotating disk, 331 second type, 655–656 silver-silver chloride, 656–658 working, 658–670 Electroelastic, instabilities, 51–80 model, 67 phenomena, 52 Electroencephalogram, 656 Electrogenerated chemiluminescence phenomena, 191 Electrolysis, 509 controlled potential, 488, 500, 502, 507 Electromyogram, 656 Electron-transfer (ET), 179–222, 399, 487, 488, 496–499, 503, 504, 542 heterogeneous, 213 kinetics, 179, 196, 307–316 photoinduced, 181–183, 200, 202–208, 212 processes, 200 reaction, 179 Electroporation, 69

847 Electrospay (ES), 630 Energy, activation, 185, 215 cavity formation, 41 chemical solvation, 8 conﬁgurational, 85 density functional, 89 elastic, 70 electrostatic, 23, 95 Fermi, 65 functional, 88 Gibbs, 23, 155, 181–186, 655, 736, 737 hydration, 182 interaction, 30, 57 interfacial, 538 ion hydration, 24 ion solvation, 25, 26 of elastically coupled charges, 53 of transfer of ions, 5, 8,9, 13, 33, 42, 44, 46, 160, 614 of transfer of lipid, 539 potential, 83 reorganization, 170, 185 repulsive interaction, 537 resolvation, 23, 24, 30, 36 resonance, 30 short-range interaction, 39, 47 solar, 179 solvation, 13, 24–28, 32, 200 standard transfer, 11 surface, 52, 158 Endocrine disruptors, 775–803 Enhanced cation transfer, 542 Entropic effect, 90 Entropy, 84, 85 nonlocal, 87, 91 Equilibrium, distribution, 110 electrochemical, 3, 13 interfacial, 10 local interfacial, 15 molecular, 52 Nernst distribution, 8 partition, 15, 20 redox, 14 Excitability, 649, 660, 663 state, 654 threshold, 654 Excitable structure, 650 Excitation, 649–679 function, 651 reaction, 650 wave, 649

848 Excluded volume effect, 83 FCCP, 694 Fermi resonance, 146 Fick’s, First Law, 820 Second Law, 820 Field, electrostatic, 658 gravitational, 650 magnetic, 650 FitzHugh-Nagumo (FHN) model, 677 Fixed-bed reactor, 580 Fluorescence, 259–264, 269, 276, 279 spectroscopy, 259, 260, 265, 269, 279 front-face, 270, 275 Fluorescent probes, 258 Fourier transform infrared (FT-IR), 258 Free-volume model, 822 Frumkin isotherm, 132 Fundamental beam, 126 Fundamental wave, 126, 133 Gene, delivery, 807–838 expression, 655 Generalized van der Waals theory (GvdW), 83–103 Genetic information, 526 Gibbs adsorption equation, 106 Gibbs energy, 2 of adsorption, 131 of transfer, 7, 41, 491 Gibbs isotherm, 17 Goldman-Hodgkin-Katz equation, 490 Gouy-Chapmen (GC), model, 198 space charge layer, 158 theory, 115, 117, 159, 171, 429, 447, 454, 549 Haber’s ion-selective systems, 9 Hamiltonian approach to ion-solvent interactions, 30 Hansch equation, 758 Hartree-Fock wave function, 90 Helmholtz equation, 18 Henderson equation, 490 Henry law, 110 Heparin, 595 Herbicide, antibacterial, 664 antifungal, 664

Index [Herbicide] general, 664 High-speed stirring method (HSS), 356 Hodgkin-Huxley (HH) equation, 676, 677 space-clamped, 676 Human Genome Project, 809 Hydrodynamic approach, 68 Hydrodynamic model, 68 Hydrophilic-hydrophobic balance (HLB), 111, 469, 775 Hyperpolarizability tensor, 144 Hyper-Rayleigh scattering (HRS), 142 Ideal gas law, 84 Immobilization, 516, 517 Impedance, 193–194, 427, 521–522, 524 Insect-induced signal, 673–675 Intensity-modulated photocurrent spectroscopy (IMPS), 211, 213–215 Interactions, acid-base, 26 antigen-antibody, 105 Born-type long-range, 30 casein-fat, 277 chain-chain, 146 Coulomb, 92, 102, 156 dipole-dipole,534 electrostatic, 48, 118, 160, 525, 537 headgroup, 538 hydrophobic, 273 intermolecular, 105, 110 ion-induced dipole, 37 ion-ion, 180 ion-molecule, 37 ion-solvent, 30, 32, 37 Lennard-Jones, 56 long-range, 37 molecular, 258, 533 nonlocal, 88 protein-fat, 275, 277, 279 protein-lipid, 274 repulsive, 88 self-consistent-ﬁeld, 37 short-range, 26, 37, 39, 40, 43 solute-solvent, 26, 358 speciﬁc, 51, 201 water-ion, 407 Interface, 1, 2,9, 12, 86, 105, 123, 180 air-alcohol, 127, 128, 145 air-liquid, 105, 124, 127, 229 air-water, 106, 127, 130, 132, 135, 137–139, 144, 146, 147, 288, 318–321, 536, 540, 642–647

Index [Interface] alkane-water, 139, 145 angular distribution, 130 aqueous-membrane, 487, 499, 511 aqueous-organic, 487, 488, 554, 555 biomembrane-water, 696 blocked, 4 charged, 136 complexation, 359–371 coverage, 234 D2O-CCl4, 147 electriﬁed, 2, 59, 66 electrochemical, 1 fat-water, 265, 266, 270, 274, 276 ﬂat, 194 gas-liquid, 258, 316, 355 heptane-water, 134, 363, 534 hexane-water, 145 ideal polarized, 4 lipid bilayer, 778–784 lipid-water, 261, 263 liquid-liquid, 1, 2,4, 19, 105, 106, 119, 123–148, 153–176, 179–222, 229–238, 259, 283, 288, 289, 293, 307– 316, 325–351, 355–372, 415–435, 461, 462, 540, 549, 554, 555, 683–696 dye-sensitized, 179, 183 membrane-peptide, 79 membrane-water, 76 metal-electrolyte, 130, 136, 197 metal-solution, 159, 487 molecularly deﬁned, 216 nonpolarizable, 107 nonpolar-water, 106 oil-water, 115, 257, 260 polar-nonpolar, 410 polarizable, 12, 106, 107, 188 polarized, 136 polymer-solution, 392 porphyrin-sensitized, 217 rigid, 52 semiconductor-dye, 217 semiconductor-electrolyte, 208, 210, 213 solid-liquid, 105, 147, 258, 288, 325, 355, 409–410 solid-solid, 105 solid-solution, 216 water-benzene, 542 water-DCE, 127, 131, 135, 136, 139, 181, 197, 216, 218–220, 542, 546, 547 water-dichloromethane, 218 water-hydrocarbon, 4

849 [Interface] water-n-dodecane, 536 water-nitrobenzene, 182, 191, 233, 236, 237 water-oil, 4, 259, 263, 346, 534, 536–538, 540, 575, 699–714 water-phenol, 629 water-toluene, 204, 363 irregular dynamic ﬂuctuation, 699 polarized, 710 Interfacial, accumulation, 371 adsorption, 371–372, 609–614 area, 359 boundary, 187 capacitor, 54, 55, 63 capacity, 162, 163, 176 charge transfer, 410, 488 complexation, 168 concentration, 180 dynamics, 136 electrical phenomena in green plants, 649–679 electron transfer, 410 equilibrium, 300 formation, 371 ion pairing, 164 ion transfer, 543, 609, 610 kinetics, 302–306, 327, 333 photoisomerization reaction, 403 reaction, 314, 371, 403 reactivity, 136 region, 371, 547 rotation, 371 solvation, 133 spectroscopy, 179 tension, 106 transfer kinetics, 315 Internal reﬂection ﬂuorescence spectroscopy, 402 Ion-channel concept, 522 Ion-free layer, 186, 197 Ionic partition diagram, 750 Ion-sensitive ﬁeld-effect transistor (ISFET), 585–593, 602–605 Ion transfer, 487, 488, 498, 504, 510, 534, 540–549 coupled, 205, 488, 498, 503 energy, 24 facilitated, 636 reaction, 204, 510–511 selective, 629–639 spontaneous, 495–496 Irritant, 650

850 Irritation, 649, 650 Isomerization, rate, 139 reaction, 139 Isotherm, amphiphilic, 109 Frumkin, 434 Langmuir, 360, 363, 444, 474 pressure-area, 538, 644, 646 water-oil, 534 ITIES (Interface between two immiscible liquids) 1, 13, 15, 20, 136, 179, 183, 193, 210, 218, 219, 222, 286, 289–292, 295–297, 307, 308, 310, 314, 321, 326, 340, 346, 349, 373, 378, 415– 435, 533, 534, 543–548, 629, 639, 735– 759 microhole-supported, 375, 377 Kelvin probe, 15 Kelvin-Zisman probe, 15 Kinematic viscosity, 328 Kink shift diffusion mechanism, 822 Langevin equation, 174 Langmuir, ﬁlm, 641–647 isotherm, 132 method, 643 technique, 641, 642 Langmuir-Blodgett, approach, 541 ﬁlm, 641–647 monolayer, 117 Laplace equation, 71 Latimer diagram, 185 Lattice-gas model, 153–176, 180, 537 Le Hung’s, approach, 5–6 equation, 6, 12 Lennard-Jones ﬂuid, 85, 86, 87, 89, 92 mixtures, 91 model, 84, 88 potential, 89 Linear Circular Dichroism (CD), 130 Liquid jet technique, 334 Liquid-liquid, extraction (LLE), 475–480 bioafﬁnity-based, 479 nonionic surfactant-based, 479 junction, 180, 183, 191–192, 303, 209, 212, 216, 222

Index Local probe, 283 Lorentz-Berhelot rule, 89 Magic angle spinning (MAS), 778 Mass transfer, 326, 553–580 MC simulations, 57 MFA Mean Field Approximation, 57, 83, 154–156, 537 Membrane, 641, 642 apical, 818 artiﬁcial, 1, 609 barrier, 823 basolateral, 818 bilayer lipid, 488, 641 biological, 730, 818, 828 biomimetic, 778 chemically modiﬁed, 603 current oscillation, 609–627 induction, 617–622 inhibition, 617–622 enzyme, 596 excitable, 675–678 heparin-immobilized, 595 ion-exchange resin, 488 ion-sensing, 585, 593–595, 598, 600, 604 liquid, 439–466, 488–491, 610, 627, 799–726 ISE, 440 mammalian, 819 mitochondrial inner, 498 model, 676 natural, 1 ion-sensing, 586 permeability, 824 perturbation, 789 plasma, 651, 652, 818 plasticized-PVC, 585, 587, 596, 604 polyvinyl chloride, 488 potential, 611, 663 potentiometric ion, 603 protein, 807 PS II, 642 quaternary-ammonium-encapsulating, 603 reactor, 578–580 resistance, 491 resting, 660 silicone-rubber, 587–590, 596–599, 603–605 Singer-Nicolson ﬂuid-mosaic model, 815 sol-gel-derived, 591–594, 600–605 solvent-polymeric, 585 surface, 824 thylakoid, 641 transport, 487–511

Index Metropolis algorithm, 156 Meyer-Overton, correlation, 776 theory, 797 Michaelis-Menten mechanism, 569 Micro-ITIES, 373–396 Microelectrochemical measurements at expanding droplets (MEMED), 340–349 Microscopy, atomic force, 642, 646, 647 scanning tunneling (STM), 646, 647 surface, 642 Microstructure effects, 241–254 Milk reconstitution, 264, 265 Mitochondria, 652 Mixed solvent layer, 186 Modiﬁed Verwey-Niessen model (MVN), 419 Molecular capacitor, 56 Molecular dynamics, 180, 229, 358–359, 819, 820 Molecular probe, 439–466 Molecular recognition of DNA, 515–530 Monte Carlo simulations, 95, 153, 156, 157, 160, 162, 172, 180 Motor end plate, 653 Moving-drop method, 335 Multidrug resistance (MDR), 828, 829 protein, 828 Multiple drug resistance (MDR), 809 Myelin, 653 Nernst equation, 9, 110, 181, 736–737, 752 Nernst-Donnan equation, 308, 346 Nernst-Planck equation, 174, 175, 490 Neuron, 609, 652–653 Neurotransmitter, 683 Neutron reﬂectance, 258, Newton’s equation, 180 Nicholson method, 192 NMR, 775–803, 816 combined line-broadening-dynamic light scattering, 826 Nonlinear optics, 123–148 Nonlinear polarization, 125, 126, 127, 141 Non-local electrostatic theory, 25 Nucleus, 652 One-component plasma model, 99 Oligodendrocyte, 653

851 Oligomerization reaction, 219 Orbit, connecting, 675 heteroclinic, 675 homoclinic, 675 Overton’s rule, 824 P680, 646, 647 Pentachlorophenol (PCP), 664–665, 694 Pesticide, 661–669, 683 Pharmacokinetics, 808–809 Phase transition, 534, 537, 538 ﬁrst order, 539 second order, 538 Phloem, 650–679 translocation, 654 unloading, 651 Phospholipid, 533–549 adsorption, 539 zwitterionic, 548 Photocatalysis, 220–222 Photoisomerization, 138–139 Photosynthesis, 641 Photosystem II, 641–647 Photoswitchable ionophore, 439–466 Ping-pong mechanism, 569 Plasmodesmata, 651 Poisson-Boltzmann, equation, 93, 94, 161, 173 theory, 102, 172 Polarized liquid-liquid junction, 179 Polarogram, 631 current-scan, 632 Polarography, 488, 630 Pollutant, 661–669 Polyanions, 28–31 Potential, action, 649–679 adsorption, 1, 17 applied, 688 boundary, 439, 452, 453 chemical, 3, 108, 167, 242–243, 416 Coulomb, 32 dependence, 308 diffusion, 10, 14, 439 distribution, 6, 8,10, 14, 545–546 effective, 31 electrical, 2, 543, 651, 660 electrochemical, 2, 160, 166, 185 electron-transfer, 181, 188 electrostatic, 154, 157, 161 formal, 9, 685, 690

852 [Potential] Galvani, 2, 3,4, 5,7, 8,9, 15, 16, 180, 181, 183, 184, 186, 188, 198–200, 206–212, 214, 220, 415, 416, 536, 543, 547, 548, 685, 711, 732, 752 half-wave, 376, 377, 637, 683 inner, 2, 415 interfacial, 1–20, 200, 707–708 intracellular, 654 ISE, 447 ionic, 14 ionization, 31 ion-transfer, 28, 308 liquid junction, 14 mean force, 165 membrane, 439, 488, 490 oscillation, 609–627 midpoint, 683, 688 mixed, 13, 15 molecular lipophilicity (MLP), 754 observed, 688 operative, 2 oscillation, 699–726 outer, 3, 4 phase boundary, 106, 110, 111, 113 photoinduced, 451 proﬁle, 543 real, 3 redox, 13, 39, 182–184, 188, 189 response, 588, 598 resting, 651 scales, 184 simulated, 547 standard, 181 chemical, 2 equilibrium, 166 ion transfer, ionic, 13 redox, 12 surface, 3, 15, 16, 17, 18, 546, 642–647 transmembrane, 660 window, 116, 631, 693 Volta, 3, 15, 16, 18 Yukawa, 172 zero charge (PZC), 12, 18, 108, 159, 624 zeta, 20 Pourbaix’s diagram, 750 Principal component analysis, 261 Protein, encapsulation, 469–482 extraction, 479

Index [Protein] P, 652 release, 469–482 Proton decoupling, 778 Protonophore, 661–669 Quantitative structure-activity relationship (QSAR), 683, 715, 733, 758–759 Quasielastic light scattering (QELS), 537 Random-mixing approximation, 154 Real-space renormalization group method, 537 Reﬂex arch, 650 Refractory period, 654 Resolvation, 23–48 Reversed micelles, 556, 575 RNA, 655 Rotational dynamics, 403, 405 Rotation motion, 137 Scanning Electrochemical Microscopy (SECM), 283–321, 386, 391–393, 542 feedback, 289, 293, 307 geometry, 289, 292 induced transfer (SECMIT), 285, 286, 289, 301, 304–306 mode, 299–307 operating modes, 289 theory, 289 Scattering, dynamic light, 258 small-angle x-ray, 258 Second harmonic generation (SHG), 124, 125, 138, 140–142, 180, 403, 439–466 Sensor, 609 amperometric, 592, 596 anion, 602–603 bioafﬁnity, 522–525 blood electrolyte, 586 electrochemical, 516 gene, 516, 528–530 chemical, 520 ion biocompatible, 585–606 ion-channel, 520 potentiometric, 585, 606 SF6847, 694 Shannon sampling theorem, 658 Sieve plate, 652 Sieve-tube, 654 element, 650, 654 system, 654

Index Shell-Descartes law, 124, 126, 143 Smectic bilayer model (SBM), 70 Solvation, 2, 23–48 dynamics, 400–411 Solvatochromic parameters, 27 Solvent extraction kinetics, 355–372 Solvent reorganization, 138 Solvophobic interaction, 24 Solubility-diffusion, model, 821 theory, 821 Solute transfer, 540 Spectrometry, electrospray ionization mass (ESMS), 630, 631, 635 Spectroscopy, transient absorption difference, 647 Stirred-tank reactor, 578 Stoke shift, 137 Sum Frequency Generation (SFG), 124, 143–147, 180 Surface, activity, 112 adlayer, 529 coverage, 434 excess, 18, 106–108, 338, 415–418 isotropic, 131 pressure, 534, 642, 644 tension, 18, 24, 83–101 dynamic, 537 tension reducing mechanism, 91 vibrational spectra, 145 viscosity, 231 Synapse, 653 Tension, 78 interfacial, 24, 108, 114–115, 536 surface, 24, 69, 71, 109 Time-domain spectroscopy, 407 Time-resolved, ﬂuorescence spectroscopy, 370–371 ﬂuorescence Stokes shift (TRESS),400 quasielastic laser scattering, 229–238 Transition state theory, 167, 168, 186 Total internal reﬂection (TIR), 123, 357 Transfer energy, 2 standard, 2

853 Tunnel diode, 677 Two-phase, catalysis, 179, 220–222 stopped method, 356–357 Ultramicroelectrode (UME), 340, 373 Uncoupler, 661–669, 683, 693–696 UV-laser photoablation technique, 373 Vacuole, 652 Van der Waals, equation of state, 84 theory, 102 Verwey-Niessen model, 115, 158, 163, 169, 170, 180 modiﬁed, 171, 172 theory, 176 Vibrating plate, 15 Vibrational resonance, 143 Vibrational surface spectroscopy, 146 Vibrational surface spectrum, 144–146 VITIES, 610 Voltammetry, 373–396, 487, 488, 683–696 cyclic, 520–521, 683–696 ion-transfer, 41, 612–613, 683–696 of acids, 687–688 of bases, 684–686 of 2, 4-dichlorophenol, 692–694 of doxylamine, 690–692 of procaine, 688–690 normal pulse, 683 potential step, 683 potential-sweep, 683, 688 Voltammetric elucidation, 488 probe, 285 study of drugs, 683–696 theory, 684–688 Voltammogram, 490, 492–494, 542, 618, 632, 688–696 Volta’s law, 655 Volume-fraction-induced percolation, 244 Walden’s rule, 744 X-ray diffraction, 536