Thermal Behavior of Dispersed Systems

THERMAL BEHAVIOR OF DISPERSED SYSTEMS

edited by Nissim Garti The Hebrew University of Jerusalem Jerusalem, Israel

Marcel Dekker, Inc.

New York • Basel

TM

Copyright © 2000 by Marcel Dekker, Inc. All Rights Reserved.

ISBN: 0-8247-0432-0 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 or 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

SURFACTANT SCIENCE SERIES

FOUNDING EDITOR

MARTIN J. SCHICK 1918–1998 SERIES EDITOR

ARTHUR T. HUBBARD Santa Barbara Science Project Santa Barbara, California

ADVISORY BOARD

DANIEL BLANKSCHTEIN Department of Chemical Engineering Massachusetts Institute of Technology Cambridge, Massachusetts

ERIC W. KALER Department of Chemical Engineering University of Delaware Newark, Delaware

S. KARABORNI Shell International Petroleum Company Limited London, England

CLARENCE MILLER Department of Chemical Engineering Rice University Houston, Texas

LISA B. QUENCER The Dow Chemical Company Midland, Michigan

DON RUBINGH The Procter & Gamble Company Cincinnati, Ohio

JOHN F. SCAMEHORN Institute for Applied Surfactant Research University of Oklahoma Norman, Oklahoma

BEREND SMIT Shell International Oil Products B.V. Amsterdam, The Netherlands

P. SOMASUNDARAN Henry Krumb School of Mines Columbia University New York, New York

JOHN TEXTER Strider Research Corporation Rochester, New York

1. Nonionic Surfactants, edited by Martin J. Schick (see also Volumes 19, 23, and 60) 2. Solvent Properties of Surfactant Solutions, edited by Kozo Shinoda (see Volume 55) 3. Surfactant Biodegradation, R. D. Swisher (see Volume 18) 4. Cationic Surfactants, edited by Eric Jungermann (see also Volumes 34, 37, and 53) 5. Detergency: Theory and Test Methods (in three parts), edited by W. G. Cutler and R. C. Davis (see also Volume 20) 6. Emulsions and Emulsion Technology (in three parts), edited by Kenneth J. Lissant 7. Anionic Surfactants (in two parts), edited by Warner M. Linfield (see Volume 56) 8. Anionic Surfactants: Chemical Analysis, edited by John Cross 9. Stabilization of Colloidal Dispersions by Polymer Adsorption, Tatsuo Sato and Richard Ruch 10. Anionic Surfactants: Biochemistry, Toxicology, Dermatology, edited by Christian Gloxhuber (see Volume 43) 11. Anionic Surfactants: Physical Chemistry of Surfactant Action, edited by E. H. Lucassen-Reynders 12. Amphoteric Surfactants, edited by B. R. Bluestein and Clifford L. Hilton (see Volume 59) 13. Demulsification: Industrial Applications, Kenneth J. Lissant 14. Surfactants in Textile Processing, Arved Datyner 15. Electrical Phenomena at Interfaces: Fundamentals, Measurements, and Applications, edited by Ayao Kitahara and Akira Watanabe 16. Surfactants in Cosmetics, edited by Martin M. Rieger (see Volume 68) 17. Interfacial Phenomena: Equilibrium and Dynamic Effects, Clarence A. Miller and P. Neogi 18. Surfactant Biodegradation: Second Edition, Revised and Expanded, R. D. Swisher 19. Nonionic Surfactants: Chemical Analysis, edited by John Cross 20. Detergency: Theory and Technology, edited by W. Gale Cutler and Erik Kissa 21. Interfacial Phenomena in Apolar Media, edited by Hans-Friedrich Eicke and Geoffrey D. Parfitt 22. Surfactant Solutions: New Methods of Investigation, edited by Raoul Zana 23. Nonionic Surfactants: Physical Chemistry, edited by Martin J. Schick 24. Microemulsion Systems, edited by Henri L. Rosano and Marc Clausse 25. Biosurfactants and Biotechnology, edited by Naim Kosaric, W. L. Cairns, and Neil C. C. Gray 26. Surfactants in Emerging Technologies, edited by Milton J. Rosen 27. Reagents in Mineral Technology, edited by P. Somasundaran and Brij M. Moudgil 28. Surfactants in Chemical/Process Engineering, edited by Darsh T. Wasan, Martin E. Ginn, and Dinesh O. Shah 29. Thin Liquid Films, edited by I. B. Ivanov 30. Microemulsions and Related Systems: Formulation, Solvency, and Physical Properties, edited by Maurice Bourrel and Robert S. Schechter 31. Crystallization and Polymorphism of Fats and Fatty Acids, edited by Nissim Garti and Kiyotaka Sato

32. Interfacial Phenomena in Coal Technology, edited by Gregory D. Botsaris and Yuli M. Glazman 33. Surfactant-Based Separation Processes, edited by John F. Scamehorn and Jeffrey H. Harwell 34. Cationic Surfactants: Organic Chemistry, edited by James M. Richmond 35. Alkylene Oxides and Their Polymers, F. E. Bailey, Jr., and Joseph V. Koleske 36. Interfacial Phenomena in Petroleum Recovery, edited by Norman R. Morrow 37. Cationic Surfactants: Physical Chemistry, edited by Donn N. Rubingh and Paul M. Holland 38. Kinetics and Catalysis in Microheterogeneous Systems, edited by M. Grätzel and K. Kalyanasundaram 39. Interfacial Phenomena in Biological Systems, edited by Max Bender 40. Analysis of Surfactants, Thomas M. Schmitt (see Volume 96) 41. Light Scattering by Liquid Surfaces and Complementary Techniques, edited by Dominique Langevin 42. Polymeric Surfactants, Irja Piirma 43. Anionic Surfactants: Biochemistry, Toxicology, Dermatology. Second Edition, Revised and Expanded, edited by Christian Gloxhuber and Klaus Künstler 44. Organized Solutions: Surfactants in Science and Technology, edited by Stig E. Friberg and Björn Lindman 45. Defoaming: Theory and Industrial Applications, edited by P. R. Garrett 46. Mixed Surfactant Systems, edited by Keizo Ogino and Masahiko Abe 47. Coagulation and Flocculation: Theory and Applications, edited by Bohuslav Dobiáð 48. Biosurfactants: Production · Properties · Applications, edited by Naim Kosaric 49. Wettability, edited by John C. Berg 50. Fluorinated Surfactants: Synthesis · Properties · Applications, Erik Kissa 51. Surface and Colloid Chemistry in Advanced Ceramics Processing, edited by Robert J. Pugh and Lennart Bergström 52. Technological Applications of Dispersions, edited by Robert B. McKay 53. Cationic Surfactants: Analytical and Biological Evaluation, edited by John Cross and Edward J. Singer 54. Surfactants in Agrochemicals, Tharwat F. Tadros 55. Solubilization in Surfactant Aggregates, edited by Sherril D. Christian and John F. Scamehorn 56. Anionic Surfactants: Organic Chemistry, edited by Helmut W. Stache 57. Foams: Theory, Measurements, and Applications, edited by Robert K. Prud'homme and Saad A. Khan 58. The Preparation of Dispersions in Liquids, H. N. Stein 59. Amphoteric Surfactants: Second Edition, edited by Eric G. Lomax 60. Nonionic Surfactants: Polyoxyalkylene Block Copolymers, edited by Vaughn M. Nace 61. Emulsions and Emulsion Stability, edited by Johan Sjöblom 62. Vesicles, edited by Morton Rosoff 63. Applied Surface Thermodynamics, edited by A. W. Neumann and Jan K. Spelt 64. Surfactants in Solution, edited by Arun K. Chattopadhyay and K. L. Mittal 65. Detergents in the Environment, edited by Milan Johann Schwuger

66. Industrial Applications of Microemulsions, edited by Conxita Solans and Hironobu Kunieda 67. Liquid Detergents, edited by Kuo-Yann Lai 68. Surfactants in Cosmetics: Second Edition, Revised and Expanded, edited by Martin M. Rieger and Linda D. Rhein 69. Enzymes in Detergency, edited by Jan H. van Ee, Onno Misset, and Erik J. Baas 70. Structure-Performance Relationships in Surfactants, edited by Kunio Esumi and Minoru Ueno 71. Powdered Detergents, edited by Michael S. Showell 72. Nonionic Surfactants: Organic Chemistry, edited by Nico M. van Os 73. Anionic Surfactants: Analytical Chemistry, Second Edition, Revised and Expanded, edited by John Cross 74. Novel Surfactants: Preparation, Applications, and Biodegradability, edited by Krister Holmberg 75. Biopolymers at Interfaces, edited by Martin Malmsten 76. Electrical Phenomena at Interfaces: Fundamentals, Measurements, and Applications, Second Edition, Revised and Expanded, edited by Hiroyuki Ohshima and Kunio Furusawa 77. Polymer-Surfactant Systems, edited by Jan C. T. Kwak 78. Surfaces of Nanoparticles and Porous Materials, edited by James A. Schwarz and Cristian I. Contescu 79. Surface Chemistry and Electrochemistry of Membranes, edited by Torben Smith Sørensen 80. Interfacial Phenomena in Chromatography, edited by Emile Pefferkorn 81. Solid–Liquid Dispersions, Bohuslav Dobiáð, Xueping Qiu, and Wolfgang von Rybinski 82. Handbook of Detergents, editor in chief: Uri Zoller Part A: Properties, edited by Guy Broze 83. Modern Characterization Methods of Surfactant Systems, edited by Bernard P. Binks 84. Dispersions: Characterization, Testing, and Measurement, Erik Kissa 85. Interfacial Forces and Fields: Theory and Applications, edited by Jyh-Ping Hsu 86. Silicone Surfactants, edited by Randal M. Hill 87. Surface Characterization Methods: Principles, Techniques, and Applications, edited by Andrew J. Milling 88. Interfacial Dynamics, edited by Nikola Kallay 89. Computational Methods in Surface and Colloid Science, edited by Maùgorzata Borówko 90. Adsorption on Silica Surfaces, edited by Eugène Papirer 91. Nonionic Surfactants: Alkyl Polyglucosides, edited by Dieter Balzer and Harald Lüders 92. Fine Particles: Synthesis, Characterization, and Mechanisms of Growth, edited by Tadao Sugimoto 93. Thermal Behavior of Dispersed Systems, edited by Nissim Garti 94. Surface Characteristics of Fibers and Textiles, edited by Christopher M. Pastore and Paul Kiekens 95. Liquid Interfaces in Chemical, Biological, and Pharmaceutical Applications, edited by Alexander G. Volkov

96. Analysis of Surfactants: Second Edition, Revised and Expanded, Thomas M. Schmitt 97. Fluorinated Surfactants and Repellents: Second Edition, Revised and Expanded, Erik Kissa 98. Detergency of Specialty Surfactants, edited by Floyd E. Friedli 99. Physical Chemistry of Polyelectrolytes, edited by Tsetska Radeva 100. Reactions and Synthesis in Surfactant Systems, edited by John Texter 101. Protein-Based Surfactants: Synthesis, Physicochemical Properties, and Applications, edited by Ifendu A. Nnanna and Jiding Xia 102. Chemical Properties of Material Surfaces, Marek Kosmulski 103. Oxide Surfaces, edited by James A. Wingrave 104. Polymers in Particulate Systems: Properties and Applications, edited by Vincent A. Hackley, P. Somasundaran, and Jennifer A. Lewis 105. Colloid and Surface Properties of Clays and Related Minerals, Rossman F. Giese and Carel J. van Oss 106. Interfacial Electrokinetics and Electrophoresis, edited by Ángel V. Delgado 107. Adsorption: Theory, Modeling, and Analysis, edited by József Tóth 108. Interfacial Applications in Environmental Engineering, edited by Mark A. Keane 109. Adsorption and Aggregation of Surfactants in Solution, edited by K. L. Mittal and Dinesh O. Shah 110. Biopolymers at Interfaces: Second Edition, Revised and Expanded, edited by Martin Malmsten 111. Biomolecular Films: Design, Function, and Applications, edited by James F. Rusling 112. Structure–Performance Relationships in Surfactants: Second Edition, Revised and Expanded, edited by Kunio Esumi and Minoru Ueno

ADDITIONAL VOLUMES IN PREPARATION

Liquid Interfacial Systems: Oscillations and Instability, Rudolph V. Birikh, Vladimir A. Briskman, Manuel G. Velarde, and Jean-Claude Legros Novel Surfactants: Preparation, Applications, and Biodegradability: Second Edition, Revised and Expanded, edited by Krister Holmberg Colloidal Polymers: Preparation and Biomedical Applications, edited by Abdelhamid Elaissari

Preface

Many important everyday materials are known to be colloidal heterogeneous systems. Milk, margarine, ice cream, mayonnaise, cosmetic creams, hand lotions, blood, ink, paint, and other substances are heterogeneous systems that can flow or become solid, and contain structural entities with at least one linear dimension in the size range of several nanometers to tens of microns. Colloidal systems consist of a dispersed phase of particles, droplets, and bubbles in a second continuous phase called the dispersion medium. Dispersed systems are said to be stable if, over a certain period of time, there is little detectable aggregation or settling of particles. In many colloidal systems, a stable thermodynamic state is reached only when all particles or droplets have become united in a single homogeneous lump of dispersed phase and, therefore, any apparent stability must be regarded as purely kinetic phenomenon. Dispersed systems are stabilized by a third component known to have amphiphilic properties and surface activity. The amphiphiles migrate to the interface and modify it to reduce the interfacial free energy and to minimize interactions between particles and droplets. It is obvious that any temperature change will affect the mobility of the amphiphiles from the continuous phase to the interface, and vice versa, and will affect the thermodynamic and geometric parameters of the interface. Therefore, the thermal behavior of dispersed systems is an essential parameter in studying structural and thermodynamic aspects. For generations, attempts have been made to heat and cool foams, emulsions, dispersions, and heterogeneous colloidal systems, and to learn about the stability of the systems through their thermal behavior. Differential scanning calorimetry (DSC) and differential thermo gravimetry (DTG) are classical instruments that iii

iv

Preface

through complex heating-cooling protocols provide important information on the behavior of the components of the dispersions. Dispersions (mostly emulsions and microemulsions) are used as microreactors or nanoreactors for important organic and enzymatic processes, and serve as reservoirs for the solubilization of materials. The behavior of the solubilized matter is also dramatically affected by thermal fluctuations. Hydration or solvation, as well as other interactions of cosolvents, are also studied through thermal treatment. It is therefore important to bring to the reader’s attention the options and the scope, as well as the limitations, of the thermal behavior of dispersed systems. This book calls attention to some of the recent studies that have been carried out on heterogeneous colloidal (dispersed) systems. Chapter 1, by Turco Liveri (Italy), reviews calorimetric investigations on reversed micelles, in which the apolar molecules interact by dispersion forces that are always attracted independently of their relative orientation. The author describes the tendency of the apolar medium in reverse micelles to form a longrange, ordered molecular arrangement in condensed phases. The amphiphilic molecules, characterized by the coexistence of spatially separated polar and apolar moieties, work together to drive the intermolecular aggregation, giving rise to dimensionally limited supramolecular aggregates. From a thermodynamic point of view, self-aggregation of amphiphilic molecules in apolar solvents involves a favorable enthalpic term due to intermolecular bonding counteracted by an unfavorable entropic term as a result of partial loss of molecular translational and rotational degrees of freedom. V. Turco Liveri discusses structural aspects, the state of water and other solutes in reversed micelles, intermicellar interactions and percolation phenomena, solubilization of nonionic solutes, and the reversed micelles as nanoreactors. The second chapter, by D. Vollmer (Germany), brings a quantitative comparison of experimental data and theoretical predictions on thermodynamic and kinetic properties of microemulsions based on nonionic surfactants. Phase transitions between a lamellar and a droplet-phase microemulsion are discussed. The work is based on evaluation of the latent heat and the specific heat accompanying the transitions. The author focuses on the kinetics of phase separation when inducing emulsification failure by constant heating. The chapter is a comprehensive, detailed study of all the aspects related to the phase separation phenomenon in microemulsions. In Chapter 3, Ezrahi et al. (Israel) discuss the use of subzero temperature behavior of water in microemulsions as an analytical tool to enable better understanding of the interfacial behavior of the surfactant. Microemulsions are cooled to subzero temperatures and the water in the internal reservoir freezes. In the heating cycle the thawing of the water is measured. The authors critically discuss the problems related to the use of this technique and the advantages derived from it.

Preface

v

Chapter 4, by Schulz et al. (Argentina and Mexico), describes the use of DSC techniques for studying binary and multicomponent systems containing surfactants. The authors explain how DSC helps to elucidate such properties as type of transition, phase boundaries, enthalpies of phase transition, and heat capacity of systems in heterogeneous states. Fouconnier et al. (France) introduce us in Chapter 5 to dispersed systems that are not stable thermodynamically, such as emulsions and double emulsions, and teach us how to carry out DSC measurements properly in order to obtain valuable information on the stability of the emulsions. Various physical and chemical phenomena that occur during cooling and heating have been pointed out. They may be associated with either the dispersed, the continuous, or the interfacial phase. A tentative description of some of these events is presented, and a correlation was made with the resulting properties of the emulsions themselves. Simple water-in-oil (W/O) or oil-in-water (O/W) emulsions, mixed emulsions, and multiple emulsions can be found during the fabrication process. Their storage and their use are considered. Senatra (Italy), who was a pioneer in the use of DSC as a technique to study interfacial phenomena, offers in Chapter 6 some interesting physical parameters and the essence of these observations. Chapter 7 is an interesting review by Kodama and Aoki (Japan) on the behavior of water in phospholipid bilayer systems. The authors distinguish between nonfreezable interlamellar water and freezable intralamellar and bulk water, and estimate the number of molecules of water in each category. They also examine the relationship between lipid phase transitions and ice-melting behavior in lipidwater systems. The behavior of water is also discussed in the gel phase of systems such as DPPC, DMPE, and DPPG. Part II concentrates on solid–liquid interfaces. Chapter 9, by Kira´ly (Hungary), attempts to clarify the adsorption of surfactants at solid/solution interfaces by calorimetric methods. The author addresses questions related to the composition and structure of the adsorption layer, the mechanism of the adsorption, the kinetics, the thermodynamics driving forces, the nature of the solid surface and of the surfactant (ionic, nonionic, HLB, CMC), experimental conditions, etc. He describes the calorimetric methods used, to elucidate the description of thermodynamic properties of surfactants at the boundary of solid–liquid interfaces. Isotherm power-compensation calorimetry is an essential method for such measurements. Isoperibolic heat-flux calorimetry is described for the evaluation of adsorption kinetics, DSC is used for the evaluation of enthalpy measurements, and immersion microcalorimetry is recommended for the detection of enthalpic interaction between a bare surface and a solution. Batch sorption, titration sorption, and flow sorption microcalorimetry are also discussed. Chapter 10, by De´ka´ny (Hungary), describes the microcalorimetric control of liquid sorption on hydrophilic/hydrophobic surfaces in nonaqueous dispersions.

vi

Preface

The dispersed systems are mostly silicates. The author discusses interparticle interactions as a tool for evaluating the stability of dispersions. Parameters such as heat of immersion at solid–liquid interfaces and adsorption capacity are determined, and the mathematical treatment for determining the enthalpy isotherms is described. The heat of wetting in amorphous silica dispersion and on zeolites is discussed. Fu¨redi-Milhofer (Israel), in Chapter 11, provides a broad overview of the role of thermal analysis techniques in basic and applied studies of the formation and transformation of crystalline dispersions. Crystalline disperisons are formed by a succession of some of the following precipitation processes: nucleation, crystal growth, flocculation, Ostwald ripening, and/or phase transformation. After a brief elaboration of the theories underlying these processes, a review is given of experimental studies on the formation and transformation of ionic precipitates from bulk electrolyte solutions. At relatively high supersaturations, compounds that include hydrophilic cations (such as Ca, Al, Fe, etc.) are likely to form highly hydrated amorphous precipitates via homogeneous nucleation and subsequent flocculation. A number of important crystalline compounds, such as hydroxyapatite or zeolites, are formed by phase transformation via amorphous and/or gel-like precursor phases. Thermal analysis techniques yield information on the amount of incorporated water, and mechanism and strength of bonding, and pore sizes of such amorphous and poorly crystalline materials. In some cases they have been successfully used to detect the initiation of phase transformation, such as the formation of ordered subunits of a quasicrystalline zeolite phase within amorphous alumosilicate precursors. At low and medium supersaturations, hydrophilic cations form different crystal hydrates by heterogeneous nucleation and subsequent crystal growth and phase transformation. Dehydration curves give information on the modes of water incorporation resulting from different modes of crystallization. A useful application of thermal analysis is the analytical approach: by determining the mass loss due to dehydration, it was possible to quantitatively determine the proportion of different calcium oxalate hydrates in mixtures, which have been qualitatively analyzed by other techniques (X-ray powder diffraction, IR spectroscopy, etc.). The method yielded excellent results in studies of the kinetics of phase transformation and has been successfully used to demonstrate the potential of surfactant micelles to control the nature of the crystallizing phase. Chapter 11 also deals with crystallization in O/W emulsions and W/O microemulsions. Filipovic´-Vincekovic´ and Tomasˇic´ (Croatia) have contributed Chapter 12, ‘‘Solid-State Transitions of Surfactant Crystals,’’ which discusses the effect of surfactants on the crystallization of materials in aqueous and nonaqueous solutions. The chapter describes the crystalline structure of surfactant and its thermal

Preface

vii

behavior, and the effects related to its crystallization. Single- and double-chain surfactants are reviewed, and the differences in their thermal behavior are elucidated. Chapter 13 is the only chapter that discusses thermal behavior of real complex systems. Raemy et al. (Switzerland and Israel) in ‘‘Thermal Behavior of Foods and Food Constituents,’’ reveal the complexity of studying such systems using different thermal calorimetric techniques. In conclusion, this book presents only a very small fraction of the options, scope, and limitations of using thermal behavior of dispersed systems as an analytical and physical tool for the evalution of phenomena occurring at the interface between the dispersed phase and the dispersion phase. It must be noted that much more work is required to enable better understanding of complex systems and real dispersions. These systems will be discussed in a separate book that will be devoted to complex dispersion systems that have been converted into commercial products. Nissim Garti

Contents

Preface iii Contributors xi Part I 1. Calorimetric Investigations of Solutions of Reversed Micelles 1 Vincenzo Turco Liveri 2. Thermodynamics and Phase-Separation Kinetics of Microemulsions 23 Doris Vollmer 3. Subzero Temperature Behavior of Water in Microemulsions 59 Shmaryahu Ezrahi, Abraham Aserin, Monzer Fanun, and Nissim Garti 4. DSC Analysis of Surfactant-Based Microstructures 121 Pablo C. Schulz, J. F. A. Soltero, and Jorge E. Puig 5. Effects of Cooling–Heating Cycles on Emulsions 183 B. Fouconnier, J. Avendano Gomez, K. Ballerat-Busserolles, and Daniele Clausse 6. Thermal Analysis of Self-Assembling Complex Liquids 203 Donatella Senatra 7. Water Behavior in Phospholipid Bilayer Systems 247 Michiko Kodama and Hiroyuki Aoki ix

x

Contents

8. Heat Evolution of the Self-Assembly of Amphiphiles in Aqueous Solutions 295 Dov Lichtenberg, Ella Opatowski, and Michael M. Kozlov Part II 9. Calorimetric Methods for the Study of Adsorption of Surfactants at Solid/Solution Interfaces 335 Zolta´n Kira´ly 10. Microcalorimetric Control of Liquid Sorption on Hydrophilic/ Hydrophobic Surfaces in Nonaqueous Dispersions 357 Imre De´ka´ny 11. The Formation and Transformation of Crystalline Dispersions as Studied by Thermal Analysis 413 Helga Fu¨redi-Milhofer 12. Solid-State Transitions of Surfactant Crystals 451 Nada Filipovic´-Vincekovic´ and Vlasta Tomasˇic´ 13. Thermal Behavior of Foods and Food Constituents 477 Alois Raemy, Pierre Lambelet, and Nissim Garti Index 507

Contributors

Hiroyuki Aoki Department of Biochemistry, Okayama University of Science, Okayama, Japan Abraham Aserin Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel K. Ballerat-Busserolles UTC–De´partment Ge´nie Chimique, Laboratoire Ge´nie des Proce´de´s, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Proce´de´s Industriels, Compieg`ne, France Daniele Clausse UTC–De´partment Ge´nie Chimique, Laboratoire Ge´nie des Proce´de´s, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Proce´de´s Industriels, Compieg`ne, France Imre De´ka´ny Department of Colloid Chemistry, University of Szeged, Szeged, Hungary Shmaryahu Ezrahi Materials and Chemistry Department, The Ordnance Corps, Israel Defense Forces, Ramat Gan, Israel Monzer Fanun Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel Nada Filipovic´-Vincekovic´ Department of Physical Chemistry, Ru
er Bosˇkovic´ Institute, Zagreb, Croatia xi

xii

Contributors

B. Fouconnier UTC–De´partment Ge´nie Chimique, Laboratoire Ge´nie des Proce´de´s, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Proce´de´s Industriels, Compieg`ne, France Helga Fu¨redi-Milhofer Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel Nissim Garti Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel J. Avendano Gomez UTC–De´partment Ge´nie Chimique, Laboratoire Ge´nie des Proce´de´s, CNRS UPRES A 6067, Equipe Thermodynamique et Physicochimie de Proce´de´s Industriels, Compieg`ne, France Zolta´n Kira´ly Department of Colloid Chemistry, University of Szeged, Szeged, Hungary Michiko Kodama Department of Biochemistry, Okayama University of Science, Okayama, Japan Michael M. Kozlov Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel Pierre Lambelet

Nestle´ Research Center, Nestec Ltd., Lausanne, Switzerland

Dov Lichtenberg Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel Ella Opatowski Department of Physiology and Pharmacology, Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel Jorge E. Puig Departamento de Ingenierı´a Quı´mica, Universidad de Guadalajara, Guadalajara, Mexico Alois Raemy Nestle´ Research Center, Nestec Ltd., Lausanne, Switzerland Pablo C. Schulz Departamento de Quı´mica e Ingenieria Quı´mica, Universidad Nacional del Sur, Bahı´a Blanca, Argentina Donatella Senatra Department of Physics—INFM Group, University of Florence, Florence, Italy

Contributors

xiii

J. F. A. Soltero Departamento de Ingenierı´a Quı´mica, Universidad de Guadalajara, Guadalajara, Mexico Vlasta Tomasˇic´ Department of Physical Chemistry, Ru
er Bosˇkovic´ Institute, Zagreb, Croatia Vincenzo Turco Liveri lermo, Palermo, Italy

Department of Physical Chemistry, University of Pa-

Doris Vollmer Institute for Physical Chemistry, University of Mainz, Mainz, Germany

1 Calorimetric Investigations of Solutions of Reversed Micelles VINCENZO TURCO LIVERI Department of Physical Chemistry, University of Palermo, Palermo, Italy

I. Introduction II.

Reversed Micelles as Nanocontainers: The State of Water and Other Solutes Within Reversed Micelles

1 8

III. Intermicellar Interactions and Percolation

12

IV. Water-Containing Reversed Micelles as Nanosolvents: The Solubilization of Nonionic Solutes

13

V. Reversed Micelles as Nanoreactors

17

VI. Conclusion

19

References

20

I. INTRODUCTION Apolar molecules interact by means of dispersion forces, which are always attractive independently of their relative orientation, and for this reason they display little tendency to give a long-range ordered molecular arrangement in condensed phases. On the other hand, polar molecules interact also by means of dipole– dipole interactions, which are attractive or repulsive depending on the relative orientation of the molecules. It follows that these molecules display a more marked tendency to give a three-dimensionally unlimited ordered molecular arrangement. In the case of amphiphilic molecules, characterized by the coexistence of spatially separated apolar (alkyl chains) and polar moieties, both these parts 1

2

Turco Liveri

concur to drive the intermolecular aggregation giving rise to dimensionally limited supramolecular aggregates. In particular, when dissolved in apolar solvents, as a consequence of both dispersion and dipole–dipole interactions triggered by steric hindrance and thermal agitation, amphiphilic molecules self-assemble, forming a more or less wide spectrum of dynamical structures that differ in aggregation number, shape (linear, cyclic, three-dimensional), and lifetime [1]. Some examples of two-dimensional aggregates of ‘‘amphiphilic molecules’’ (obtained by combining rubber pipette bulbs and magnetic stir bars) oriented according to dipole–dipole interactions are shown in Fig. 1. From a thermodynamic point of view, self-aggregation of amphiphilic molecules in apolar solvents involves a favorable enthalpic term due to intermolecular bonding counteracted by an unfavorable entropic term due to a partial loss of molecular translational and rotational degrees of freedom. Using vapor pressure osmometry, for example, it has been found that the enthalpies of formation of molecular aggregates of dodecylammonium propionate in benzene and cyclohexane are ⫺83.4 kJ/mol and ⫺57.4 kJ/mol, whereas the entropy changes for the same processes are ⫺0.23 kJ/mol and ⫺0.14 kJ/mol, respectively [2]. It is generally agreed that the equilibrium concentrations of monomers and aggregates are well described by a multiple equilibrium model [3,4]. The relative populations of these aggregates are maintained in thermodynamic equilibrium by fast breaking and re-forming processes of labile intermolecular interactions and are controlled by some internal (nature and shape of the polar group and of the apolar molecular moiety of the amphiphile) and external (concentration of the amphiphile, temperature, etc.) parameters. Within a more or less restricted range of these parameters some amphiphilic molecules self-assemble in apolar solvents,

FIG. 1 Examples of linear and cyclic two-dimensional aggregates of ‘‘amphiphilic molecules’’ (obtained by combining rubber pipette bulbs and magnetic stir bars).

Solutions of Reversed Micelles

3

forming globular aggregates called reversed micelles, which are structurally characterized by an internal polar core constituted by opportunely arranged hydrophilic headgroups surrounded by the alkyl chains of the amphiphile (see Fig. 2) [5]. This kind of aggregation involves the formation of ‘‘supermolecules,’’ which appear from the outside as apolar objects dispersed in the apolar solvent. Many amphiphilic substances are able to form reversed micelles. Certainly, the most studied is sodium bis (2-ethylhexyl) sulfosuccinate (AOT) [6]. From this salt, other interesting surfactants able to form reversed micelles have been derived by simply changing the counterion [7]. Other frequently used surfactants are didodecyldimethylammonium bromide [8], benzyldimethylhexadecylammonium chloride, lecithin [9], tetraethylene glycol monododecyl ether (C 12 E 4) [10], decaglycerol dioleate [11], and dodecylpyridinium iodide [12]. With extensive aggregation, a number of translational and rotational degrees of freedom of surfactant molecules are converted into translational, rotational, and internal degrees of freedom of the entire aggregate. In the case of a reversed micelle, its dynamics are characterized by a wide variety of processes such as diffusion of a surfactant molecule within the aggregate, conformational dynamics of the polar and apolar molecular moieties, micellar shape fluctuation, exchange of surfactant molecules between bulk solvent and micelle, structural collapse of the aggregate leading to its dissolution and vice versa, diffusion and rotation of the entire aggregate, and intermicellar collisions [13–16]. Dry reversed micelles ˚ , exchange of AOT have a mean aggregation number of 23 and a radius of 15 A ⫺6 monomers with the bulk in a time scale of 10 s, and dissolve completely in a time scale of 10 ⫺3 s [17,18].

FIG. 2 Micellar aggregate of ‘‘amphiphilic molecules.’’

4

Turco Liveri

Water, aqueous solutions and many other strongly hydrophilic substances can be solubilized within the micellar core [19,20]. Water solubilization involves hydration of the surfactant headgroup accompanied by an increase in the headgroup area, a micellar swelling, a marked increase in the surfactant aggregation number, and, at constant surfactant concentration, a decrease in the number density of reversed micelles [21]. A representation of a spherical reverse micelle entrapping a polar solubilizate in the core is shown in Fig. 3. Moreover, in the case of ionic surfactants, the addition of water weakens the electrostatic interactions between the counterion and the surfactant ionic head, forming solvent-separated ion pairs. For electrostatic reasons, counterions and ionic heads together with molecules of water of hydration are confined in a restricted interfacial shell. Nearly unperturbed water molecules (‘‘bulk’’ water) exist in the micellar core [22,23]. The size and shape evolution of reversed micelles as a function of the water and surfactant concentrations are system-specific. The micellar size is mainly controlled by the strong tendency of the surfactant to be located at the interface between water and apolar solvent, which involves an enormous value of the interfacial surface and micelles of nanometric size. Spherical micelles result from a minimization of the micellar surface-to-volume ratio, i.e., a minimization of water–surfactant interactions less favorable than water–water and/or surfactant– surfactant interactions, while rodlike micelles, characterized by a greater surfaceto-volume ratio, result from water–surfactant interactions more favorable than

FIG. 3 Micellar aggregate of ‘‘amphiphilic molecules’’ entrapping a ‘‘polar solubilizate.’’

Solutions of Reversed Micelles

5

water–water and/or surfactant–surfactant interactions. In the case of AOT, the radius (r) of nearly spherical and monodisperse reversed micelles increases linearly with the molar ratio R (R ⫽ [water]/[surfactant]; r (nm) ⫽ 1.5 ⫹ 0.175R) and is quite independent of the surfactant concentration [14,24]. With increasing R, the fraction of water molecules located in the core of spherical micelles (or the time fraction spent by each water molecule in the core) increases progressively as a consequence of the parallel increase in the micellar radius. In contrast, lecithin, being able to establish strong hydrogen bonds with water, forms very long rodlike water-containing reversed micelles [25,26]. Solubilization of water within the micellar core transforms reversed micelles from small and labile aggregates to more stable aggregates with a greater persistence in the size and shape of the entire aggregate (even if each molecular component is continuously exchanged with the surroundings), influences the intermicellar interactions, and widens the spectrum of their dynamics [27]. In addition to the dynamics of dry micelles, fast exchange of water molecules between the surface and the center of the hydrophilic core, micellar shape and charge (in the case of ionic surfactant) fluctuations, breaking and re-forming of adhesive bonds between contacting micelles, and intermicellar exchange of material are generally considered. In the case of AOT, less than 1 in 1000 intermicellar collisions leads to micelle coalescence followed by separation and a material exchange process occurring in the microsecond to millisecond time scale [13,28]. The intermicellar exchange of material can also be assisted by the exocytotic–endocytotic mechanism, i.e., through the formation of minimicelles that encapsulate hydrophilic molecules in their interior and their subsequent coalescence with other micelles [15,21]. In spite of the closed structure of reversed micelles, some mechanisms have been suggested to account for their attractive interactions. In the case of watercontaining AOT reversed micelles, it has been suggested that a pivotal role in the intermicellar interactions is played by the surfactant dissociation, which leaves hydrated charged heads at the micellar surface and hydrated counterions in the aqueous core [29]. Then, the continuous jumping of AOT ⫺ anions (hopping mechanism) [30] among neighboring micelles forming oppositely charged micelles is responsible for the attractive intermicellar interactions leading to the formation of extended clusters of reversed micelles and for the conductometric behavior of water–AOT–hydrocarbon microemulsions [29,31]. Another mechanism, postulated to explain the conductometric behavior of these microemulsions, attributes it to the transfer of sodium counterions from one reversed micelle to another through water channels opened by intermicellar coalescence [32,33]. In the case of water-containing lecithin reversed micelles, an enhancement of hydrogen bonding induced by an increase in water and/or micellar concentration has been suggested to account for the huge increase in intermicellar interactions [21,34].

6

Turco Liveri

Interesting properties are observed when the concentration of reversed micelles is increased, the temperature is changed, or suitable solutes are added. In some cases, in fact, a dramatic increase has been observed in some physicochemical properties such as viscosity, conductance, static permittivity, and sound absorption. Two main interpretive pictures have been proposed to rationalize this percolative behavior. One attributes percolation to the formation of a bicontinuous structure [35,36], and the other to the formation of very large transient aggregates of reversed micelles [30]. In this respect, most interesting is the observation that the percolation threshold is dependent on the physicochemical property. As an example, in Fig. 4 the trends of the viscosity and conductance of AOT– n-heptane solutions as a function of the volume fraction of AOT are reported. As can be seen in a range where a divergence of the viscosity is observed, the conductance does not display significant variations. This implies that a deeper understanding of percolation requires a detailed description of the molecular processes involved and, in particular, that different molecular processes are responsible for charge and momentum transfer in these systems [37].

FIG. 4 Viscosity (䊐) and conductivity (■) of AOT–n-heptane solutions as a function of the surfactant volume fraction. (Data from Ref. 37.)

Solutions of Reversed Micelles

7

Temperature or water and surfactant concentrations can influence the intermicellar interactions and/or the micellar number density. Both effects could induce an extensive intermicellar connectivity due to intermicellar interactions or for topological reasons, creating a network able to enhance momentum and/or charge transfer in the system. By considering the viscosimetric behavior of water–AOT– n-heptane microemulsions at various values of R, it can be observed that at very low R values or at R ⬎ 10 these systems behave as suspensions of quite monodisperse hard sphere particles whereas at intermediate R values they interact strongly. This interesting conclusion can be drawn from Fig. 5, where the dependence of the relative viscosity (η/η 0) on the volume fraction (Φ) at various R values is compared with that of a suspension of hard silica spheres in cyclohexane [37,38]. This is consistent with the finding that, in the semidilute region, AOT reversed micelles form micellar clusters in the range 0 ⬍ R ⬍ 10 whereas they do not at R ⬎ 10 [39] and also that the globular structure of reversed micelles persists even at the higher volume fractions of the dispersed phase and bicontinuous structures never set in [40].

FIG. 5 Comparison of the relative viscosity of dispersions of silica hard spheres and water–AOT–n-heptane microemulsions. (䉱) Hard spheres; (䊊) R ⫽ 0; (䊉) R ⫽ 5; (䊐) R ⫽ 10; (■) R ⫽ 20; (䉭) R ⫽ 30; (䉬) R ⫽ 40. (Data from Refs. 37 and 38.)

8

Turco Liveri

A number of investigations have been performed on solubilization of solutes within water-containing reversed micelles to probe micellar structure and dynamics, to define their preferential solubilization site, and to emphasize mutual modifications due to solute–micelle interactions. Electrolytes and strongly polar molecules are obviously solubilized in the micellar core. Adding electrolytes to water containing AOT reversed micelles has an effect that is opposite to that observed for direct micelles, i.e., decreases are observed in the micellar radius and intermicellar attractive interactions [41] owing to the stabilization of AOT ions at the water/surfactant interface. Polar solutes, increasing the micellar core matter, induce an increase in the micellar radius, while amphiphilic molecules, being preferentially solubilized at the water/surfactant interface and consequently increasing the interfacial surface, lead to a decrease in the micellar radius [42,43]. As a consequence of their size and specific interactions, hydrophilic macromolecules or solid nanoparticles cause strong changes in micellar size and dynamics, and their properties are strongly affected [4,44].

II.

REVERSED MICELLES AS NANOCONTAINERS: THE STATE OF WATER AND OTHER SOLUTES WITHIN REVERSED MICELLES

The study of the state of water within reversed micelles has received a lot of attention as it simulates the water confined in biological membranes or tightly bonded to biopolymers, enzymes, and proteins. There has been some controversy over the number of types of water encapsulated within reversed micelles and the appropriate model to describe the distribution among them. In the case of AOT reversed micelles, three main states can be hypothesized: water hydrating the sodium counterion, water hydrating the surfactant anionic headgroup, and water in the core. Some contributions to the measured physicochemical property could arise from the small fraction of water dispersed monomerically in the bulk solvent. Taking into account the spatial distribution of water molecules within the reversed micelles and assuming a nearly constant ratio between the numbers of water molecules hydrating the headgroup and the counterion, only two types of water can be hypothesized, ‘‘interfacial’’ water interacting with surfactant headgroups and counterions and ‘‘bulk-like’’ water in the micellar core. These types of water exchange on the nanosecond time scale (a time scale greater than the infrared window) and can be considered in a continuous equilibrium or existing above a critical molar ratio R below which only interfacial water exists. Several authors have investigated the energetic state of water in reversed micelles by calorimetry [45–50]. To emphasize the information gained on this subject by use of calorimetry, the enthalpies of solution of water in AOT or in lecithin reversed micelles as a

Solutions of Reversed Micelles

9

function of the molar ratio R are reported in Fig. 6 [51,52]. These values, strongly different from the enthalpy of solution of water in apolar organic solvents (⫹33.1 kJ/mol) [53,54], immediately indicate that water is practically totally encapsulated in the micellar core. Incidentally, it must be pointed out that the heat effect arising from the very small fraction of water that dissolves monomerically in the organic solvent must be taken into account in order to avoid misinterpretations of the calorimetric data, especially at the lower R values [54]. The continuous variation of the enthalpy of solution of water for both systems is consistent with a continuous model of water partitioned between the micellar core and the interface of a reversed micelle, which swells with R. The small and positive values of enthalpies of solution of water in AOT reversed micelles indicate that the energetic state of the water is only slightly changed and that water solubilization (unfavorable from an enthalpic point of view) is mainly driven by a favorable change in entropy (the water state at the interface and its dispersion as nanodroplets could be prominent contributions) [48,51]. In contrast, the solubilization of water in lecithin is a relatively strong exothermic process. This has been taken as an indication that water interacts favorably

FIG. 6 Enthalpy of solution of water in AOT (■, left-hand scale) or lecithin (䉱, righthand scale) reversed micelles as a function of R. (Data from Refs. 51 and 52.)

10

Turco Liveri

with the zwitterionic headgroup of lecithin, promoting the formation of strong intermolecular hydrogen bonds, which can account for the rodlike structure of lecithin reversed micelles (i.e., micelles with a surface-to-volume ratio greater than that of spherical micelles) [52,55]. Both thermodynamic and spectroscopic properties of ‘‘core’’ water in AOT reversed micelles are similar to those of pure water. This indicates that the penetration of counterions in the micellar core is negligible. From differential scanning calorimetric measurements a marked cooling–heating cycle hysteresis has been observed, showing that water encapsulated in AOT reversed micelles is only partially freezable and that the freezable fraction displays marked supercooling behavior as a consequence of the very small size of the micellar core. The nonfreezable fraction has been identified as the water hydrating the AOT ionic heads [56,57]. The state of water within AOT reversed micelles has also been probed indirectly through measurements of the specific heat of water–AOT–n-heptane microemulsions [54,58]. An analysis of these data made it possible to calculate the apparent specific heat (C AOT ) of AOT (see Fig. 7). The observed decrease of C AOT

FIG. 7 Apparent specific heat capacity of AOT (C AOT ) in the micellar phase as a function of R. (Data from Ref. 54.)

Solutions of Reversed Micelles

11

with R (i.e., by decreasing the AOT concentration in the micellar phase) was explained in terms of the breakdown of the water structure by the hydration of AOT ionic heads. Other strongly hydrophilic substances such as methanol, formamide, n-methylformamide, and ethylenediamine solubilized in dry AOT reversed micelles are able, like water, to create their own micellar core [20,59,60], whereas amphiphilic solubilizates such as 1-pentanol and cholesterol are partitioned between the micellar palisade layer and the bulk organic solvent. As an example of the evolution of the partitioning process of an amphiphilic solubilizate as its concentration increases, the molar enthalpy of solution of 1-pentanol in the AOT–n-heptane system is shown in Fig. 8 as a function of the alcohol molality at various AOT concentrations [61]. An analysis of these data showed that at infinite dilution of the alcohol, following a Poisson distribution, 1-pentanol molecules distribute between AOT reversed micelles and the continuous organic phase, whereas at finite alcohol concentration, given the ability of alcohol to self-assemble in the apolar organic solvent, a coexistence between reversed micelles (solubilizing

FIG. 8 Enthalpy of solution of 1-pentanol in AOT–n-heptane solutions as a function of the alcohol molal concentration (m PentOH ) at various AOT concentrations. (■) [AOT] ⫽ 0 mol/kg; (䊉) [AOT] ⫽ 0.049 mol/kg; (䉱) [AOT] ⫽ 0.0986 mol/kg; (䉲) [AOT] ⫽ 0.196 mol/kg; (䉬) [AOT] ⫽ 0.292 mol/kg. (Data from Ref. 61.)

12

Turco Liveri

1-pentanol) and alcoholic aggregates (incorporating AOT molecules) is realized. The observed humps have been qualitatively explained in terms of two opposite effects. The first (predominant at low alcohol concentrations and responsible for the initial increase in ∆H ) was ascribed to the decrease in the binding constant with 1-pentanol concentration and attributed to rapid saturation of the binding sites of AOT reversed micelles or to alcohol-induced changes in the AOT reversed micelle structure. The second effect (predominant at high alcohol concentrations and responsible for the decrease in ∆H ) was attributed to the self-association of the alcohol molecules by intermolecular hydrogen bonds.

III. INTERMICELLAR INTERACTIONS AND PERCOLATION With a high degree of approximation, solutions of reversed micelles can be described as solutions of supramolecular objects that display more or less strong intermicellar interactions. By changing the concentration of these aggregates one can attain different physical conditions corresponding to various physical phenomena. In particular, above threshold values of the concentration of reversed micelles, a dramatic increase in static viscosity can be observed, leading to the formation of systems, called organogels, that are particularly interesting for industrial applications (biocatalysis, biomembrane mimetic systems, extraction processes, and preparation of nanoparticles) [62]. Using calorimetry, it has been observed that the enthalpy of dilution of water– AOT–n-heptane microemulsions and the apparent specific heat capacity of the micellar phase vary monotonically with the micellar concentration without any change in rate during the crossover of the percolation threshold [54]. The observed trends suggested that even at the highest values of the volume fraction of the dispersed matter (Φ), the microemulsions are made up of water-containing reversed micelles dispersed in the hydrocarbon and that the intermicellar interactions decrease as R increases, vanishing when R ⬎ 10. This hypothesis is in agreement with the observation that the percolation threshold of these microemulsions at R ⬎ 10 occurs at a Φ value of approximately 0.5, a value that corresponds to the packing fraction of a cubic array of contacting spheres. Moreover, it is consistent with the viscosimetric behavior of these microemulsions reported above. Whereas the dilution of solutions of AOT reversed micelles at R ⬎ 10 is an athermal process (clustering results from topological effects), the dilution of water–lecithin reversed micelles is a strongly endothermic process [52,54]. This has been attributed to a strong dependence of the micellar size upon the lecithin

Solutions of Reversed Micelles

13

reversed micelle concentration involving the breakage of many hydrogen bonds with dilution.

IV.

WATER-CONTAINING REVERSED MICELLES AS NANOSOLVENTS: THE SOLUBILIZATION OF NONIONIC SOLUTES

Solutions of water-containing reversed micelles are systems characterized by a multiplicity of domains: apolar bulk solvent, oriented alkyl chains of the surfactant, hydrated surfactant headgroup region at the water/surfactant interface, and ‘‘bulk’’ water in the micellar core. Many polar, apolar, and amphiphilic substances, which are preferentially solubilized in the micellar core, in the bulk organic solvent, and in the domain comprising the alkyl chains and the hydrated surfactant polar heads, henceforth referred to as the palisade layer, respectively, may be solubilized in these systems at the same time. Moreover, it is possible that (1) local concentrations of solubilizate are very different from the overall concentration, (2) molecules solubilized in the palisade layer are forced to assume a certain orientation, (3) solubilizates are forced to reside for long times in a very small compartment (compartmentalization, quantum size effects), (4) the structure and dynamics of the reversed micelle hosting the solubilizate as well as those of the solubilizate itself are modified (personalization). All these peculiarities have been exploited by using these systems as useful solvent and reaction media for technological applications. Also, some resemblance between these systems and biological environments has been the driving force to employ solutions of reversed micelles to model or to mimic biological processes or to realize pharmaceutical preparations [63]. Knowledge of the solubilization site in microemulsions and the interaction forces driving the partitioning of a solute between the different microregions is fundamental to the rationalization of many complex phenomena. Among the various techniques, calorimetry has been used to determine the complete set of thermodynamic parameters of the partitioning process and also to gain information on the solubilization site and on the mutual changes following the solubilization process [59,60]. The quantity experimentally determined is the thermal effect accompanying the mixing in the calorimetric cell of a solubilizate–organic solvent solution with a water–surfactant–organic solvent microemulsion at a given surfactant concentration ([S]). This thermal effect, corrected for the enthalpy of dilution of both solutions and referred to 1 mole of the solubilizate, corresponds to the enthalpy of transfer (∆H t) of the solubilizate from the organic to the micellar phase. In order to analyze the calorimetric data (∆H t, [S]), it is also necessary to develop

14

Turco Liveri

a suitable model. Here I report briefly on a simple one that has been proven to explain consistently the experimental data of nonionic solubilizates. Using a Nernstian approach to the partitioning of solubilizates among three different microdomains (organic continuum, micellar palisade layer, and micellar aqueous core), the following distribution constants may be defined: Kp ⫽

mp mo

(1)

Kw ⫽

mw mo

(2)

where m p , m w , and m o are the equilibrium molal concentrations of the solubilizate in the palisade layer, aqueous core, and organic continuum, respectively. K p is the distribution constant of the solubilizate between the organic continuum and the micellar palisade layer, and K w is the distribution constant of the solubilizate between the organic continuum and the micellar aqueous core. Using Eqs. (1) and (2), it can be easily shown that the fraction of molecules bonded to the micelles, X b (X w to the micellar core and X p to the palisade layer), is given by Xb ⫽ Xw ⫹ Xp ⫽

K[S] 1 ⫹ K[S]

(3)

where K ⫽ KpPS ⫹ KwPwR

(4)

and P s and P w are the molecular weights of surfactant and water (expressed in kilograms), respectively. The last equation is important because from the dependence of K and R the solubilization site of the solubilizate can be defined. Taking into account that ∆H t is related to the fractions of solubilizate molecules transferred to the aqueous core (X w) and to the micellar palisade layer (X p) by the equation ∆H t ⫽ X p ∆H°t,p ⫹ X w ∆H°t,w

(5)

where ∆H°t,p and ∆H°t,w are the enthalpies of transfer from the organic solvent to the palisade layer and to the aqueous core, respectively, and combining Eqs. (3)– (5), it can also be found that ∆H t ⫽

K ∆H°t [S] 1 ⫹ K[S]

(6)

Solutions of Reversed Micelles

15

where ∆H°t is given by the equation ∆H°t ⫽

K p P s ∆H°t,p ⫹ K w P w ∆H°t,w KpPs ⫹ KwPwR

(7)

Then an analysis of the calorimetric data (∆H t , [S]) by Eq. (6) and using Eqs. (4) and (7) allow us to obtain the complete set of thermodynamic parameters for the transfer process. In order to show the information gained through calorimetric investigations on the partitioning of nonionic solubilizates, Table 1 lists the thermodynamic parameters for the transfer process of some amphiphilic solubilizates from the organic continuum to the micellar palisade layer or the micellar aqueous core. The standard free energies of transfer were obtained from the equations ∆G°t,p ⫽ ⫺RT ln K°p

(8)

and ∆G°t,w ⫽ ⫺RT ln K°w

(9)

where K°p and K°w are the K p and K w values converted to the molarity scale as suggested by Ben-Naim [64]. A perusal of the data reported in Table 1 shows that the distribution constants K w decrease with increases in the hydrophobic character of the solubilizate while the opposite is true for K p and that for the more hydrophilic solubilizates the preferential solubilization site changes as the water content of reversed micelles increases. It can also be observed that in terms of standard free energies the additivity rule holds for the transfer between microdomains. The enthalpies of transfer from the apolar solvent to the micelles are exothermic, and, in principle, changes in the micellar structure and/or preferential orientation of the solubilizate in the palisade layer also contribute to their values [59]. It can also be observed that the standard enthalpies of transfer from the organic continuum to the palisade layer are between ⫺26 and ⫺20 kJ/mol whereas the corresponding quantities for the transfer from the organic continuum to the aqueous core are in the range of ⫺45 to ⫺21 kJ/mol. This indicates that in the palisade layer the solubilizates are forced to be oriented such that only one polar group of a diamine interacts with a hydrophilic head of AOT, whereas this does not happen in the aqueous core, where both polar groups of the diamines can be hydrated [60]. In the case of Kryptofix 221D, a cryptand able to complex the alkali metal cations [65], it has been observed that it is solubilized mainly in the palisade layer of the AOT reversed micelles, and from an analysis of the enthalpy of transfer of this solubilizate from the organic to the micellar phase it has been established that the driving force of the solubilization is the complexation of the sodium counterion. Moreover, the enthalpy values made it possible to show the

41 22 20 48 17 1.4 25

Methanol n-Propanol n-Pentanol Ethylenediamine N,N-Dimethylaminoethylamine N,N,N′,N′-Tetramethylenediamine Cholesterol

Source: Refs. 59 and 60.

Kp

Solubilizate 187 20 — 1990 319 17 —

Kw 21 24 24 25 22 20 26

⫺∆H°t,p (kJ/mol) 22 21 — 45 41 35 —

⫺∆H°t,w (kJ/mol)

10 9.0 8.7 11 8.3 2.1 9.2

⫺∆G°t,p (kJ/mol)

14 8.4 — 20 15 8.0 —

⫺∆G°t,w (kJ/mol)

TABLE 1 Thermodynamic Parameters for the Transfer of Some Nonionic Solubilizates from the Organic Continuum to the Micellar Palisade Layer or the Micellar Aqueous Core

16 Turco Liveri

Solutions of Reversed Micelles

17

peculiar solvation state of sodium counterions and demonstrate that they are essentially located near the water/AOT interface [66].

V. REVERSED MICELLES AS NANOREACTORS The small size of water-containing reversed micelles together with their stability in form but not in constituent molecules (persistence of shape accompanied by fast material exchange dynamics) suggests the use of these systems as peculiar nanoreactors. It can be expected that reaction rates, reaction mechanisms, and equilibrium constants can be affected significantly compared to the same processes occurring in bulk [67]. Preferential solubilization involves local concentrations different from the analytical values and catalytic effects. In addition, since reversed micelles share some fundamental features of biomembranes (dominance of interfacial effects, ordered arrangement of amphiphilic molecules), water-inoil microemulsions have also been proposed as advantageous reaction media for the investigation of biochemical reactions. A calorimetric investigation of the substitution reaction [Pd(bipy)(en)] 2⫹ ⫹ en → [Pd(en) 2] ⫹ bipy (where bipy ⫽ 2,2′-bipyridine and en ⫽ ethylenediamine) performed in water– AOT–n-heptane microemulsions demonstrated that with increases in R the reaction becomes less exothermic and its rate constant decreases, approaching the value observed in water. These features were rationalized in terms of the peculiar solvation state of reactants inside the AOT reversed micelles and/or the peculiar physicochemical properties of the micellar core [68]. Another field recently opened is the use of water-in-oil (W/O) microemulsions as reaction media for the synthesis of solid nanoparticles. The interest in synthesizing nanoparticles in solutions of reversed micelles is due to their important technological applications as catalysts for redox reactions [69] or their use to model or mimic processes occurring in geological or biological environments [70]. Some calorimetric investigations have shown that the enthalpy of formation of metallic nanoparticles and the molar enthalpy of precipitation of inorganic salts become more negative with increasing R (i.e., increasing micellar radius) and level off at higher R values. This experimental evidence has been rationalized in terms of the formation of nanoparticles dimensionally controlled by the micellar radius [70–73]. Typical behavior is shown in Fig. 9, where the enthalpy of formation of AgCl nanoparticles in AOT reversed micelles is reported as a function of the molar ratio R at various salt concentrations. As can be seen, the enthalpies become more exothermic as R increases. The small ∆H values at lower R, corresponding to

18

Turco Liveri

FIG. 9 Enthalpy of formation of AgCl nanoparticles in water–AOT–n-heptane microemulsions as a function of R at various concentrations (C ) of the reagent salts in the aqueous microphase. (■) C ⫽ 0.005 mol/kg; (䊉) C ⫽ 0.03 mol/kg; (䉱) C ⫽ 0.05 mol/ kg. (Data from Ref. 66.)

lower values of the micellar radii, indicate the formation of smaller microcrystals with higher surface-to-volume ratios and consequently in a higher energetic state. In the synthesis of ZnS nanoparticles in various W/O microemulsions, further effects have been revealed [74]. In Fig. 10 the molar enthalpy of precipitation of ZnS nanoparticles in some W/O microemulsions is reported as a function of R. The continuous line indicates the molar enthalpy for the same process performed in water. As can be seen, with increases in R the molar enthalpy value becomes more negative, and in the case of AOT it tends to level off at higher R values. Moreover, these molar enthalpies are always less negative than the corresponding value in water. This is consistent with an increase in the nanoparticle size with R. By comparing the enthalpies at the same R value it can be noted that these quantities are in the order DDAB ⬎ C 12 E 4 ⬎ lecithin ⬎ AOT. Moreover, since the enthalpies of precipitation of ZnS at the same nanoparticle radius were different for the various microemulsions, it was also concluded that some

Solutions of Reversed Micelles

19

FIG. 10 Enthalpy of formation of ZnS nanoparticles in W/O microemulsions [(■) DDAB; (䊉) C 12 E 4; (䉱) AOT; (䉲) lecithin] as a function of R. The continuous line indicates the enthalpy of formation of bulk ZnS in water. (Data from Ref. 74.)

enthalpic contributions arise from interactions between nanoparticles and the water/surfactant interface.

VI.

CONCLUSION

In this chapter I have attempted to present a panoramic view of the contributions of calorimetry to the study of solutions of reversed micelles. In particular, it has been shown that it is possible with calorimetry to obtain information on the energetic state of water and that of other solubilizates within reversed micelles, the complete set of thermodynamic parameters for the solubilization process, and the preferential solubilization site as well as information on the intermicellar interactions and the energetic state of solid nanoparticles entrapped in the micellar core. All these data together with those obtained by other techniques help to better and better define the structural and dynamical picture of solutions of reversed micelles and to exploit their potential technological applications.

20

Turco Liveri

Finally, it must be remarked that in spite of the importance of the information that can be gained by calorimetry, the numbers of calorimetric investigations on solutions of reversed micelles and relative to other experimental techniques are still very small.

ACKNOWLEDGMENTS Financial support from CNR, MURST 60%, and MURST 40% (cofin MURST 97 CFSIB) is gratefully acknowledged.

REFERENCES 1. N Muller. J Phys Chem 79:287–291 (1975). 2. FY Lo, BM Escott, EJ Fendler, ET Adams, RD Larsen, PW Smith. J Phys Chem 79:2609–2621 (1975). 3. JB Nagy. In: Solution Behavior of Surfactants, Vol. 2 (KL Mittal, EJ Fendler, eds.), Plenum Press, New York 1982, pp. 743–766. 4. PL Luisi, LJ Magid. CRC Crit Rev Biochem 20:409–474 (1986). 5. N Muller. J Colloid Interface Sci 63:383–393 (1978). 6. HF Eicke. Topics Curr Chem 87:85–145 (1980). 7. J Eastoe, TF Towey, BH Robinson, J Williams, RH Heenan. J Phys Chem 97:1459– 1463 (1993). 8. J Eastoe, RK Heenan. J Chem Soc Faraday Trans I 90:487–492 (1994). 9. R Scartazzini, PL Luisi. J Phys Chem 92:829–833 (1988). 10. A Merdas, M Gindre, R Ober, C Nicot, W Urbach, M Waks. J Phys Chem 100: 15180–15186 (1996). 11. AB Mandal, B Unni-Nair. J Chem Soc Faraday Trans I 87:133–136 (1991). 12. GR Seely, XC Ma, RA Nieman, D Gust. J Phys Chem 94:1581–1598 (1990). 13. PDI Fletcher, BH Robinson. Ber Bunsenges Phys Chem 85:863–867 (1981). 14. PDI Fletcher, AM Howe, BH Robinson. J Chem Soc Faraday Trans I 83:985–1006 (1987). 15. J Lang, A Jada, A Malliaris. J Phys Chem 92:1946–1953 (1988). 16. A D’Aprano, G D’Arrigo, M Goffredi, A Paparelli, V Turco Liveri. J Phys Chem 93:8367–8370 (1989). 17. M Wong, JK Thomas, T Nowak. J Am Chem Soc 99:4730–4736 (1977). 18. M Kotlarchyk, JS Huang, SH Chen. J Phys Chem 89:4382–4386 (1985). 19. PL Luisi, M Giomini, MP Pileni, BH Robinson. Biochim Biophys Acta 947:209– 246 (1988). 20. V Arcoleo, F Aliotta, M Goffredi, G La Manna, V Turco Liveri. Mater Sci Eng C5: 47–53 (1997). 21. V Turco Liveri. In: Current Topics in Solution Chemistry, Vol 2. (JE Desnoyers, F Franks, G Gritzner, LG Hepler, H Ohtaki eds.), Research Trends, Trivandrum, 1997, pp. 143–156. 22. P Linse. J Chem Phys 90:4992–5004 (1989).

Solutions of Reversed Micelles

21

23. G Giammona, F Goffredi, V Turco Liveri, G Vassallo. J Colloid Interface Sci 154: 411–415 (1992). 24. R Day, BH Robinson, J Clarke, J Doherty. J Chem Soc Faraday Trans I 75:132– 139 (1979). 25. PL Luisi, R Scartazzini, G Hearing, P Schurtenberger. Colloid Polym Sci 268:356– 374 (1990). 26. G Cavallaro, G La Manna, V Turco Liveri, F Aliotta, ME Fontanella. J Colloid Interface Sci 176:281–285 (1995). 27. G D’Arrigo, A Paparelli, A D’Aprano, ID Donato, M Goffredi, V Turco Liveri. J Phys Chem 93:8367–8370 (1989). 28. J Clarke, J Nicholson, K Regan. J Chem Soc Faraday Trans I. 81:1173–1182 (1985). 29. V Arcoleo, M Goffredi, V Turco Liveri. J Solution Chem 24:1135–1142 (1995). 30. MW Kim, JS Huang. Phys Rev A 34:719–722 (1986). 31. H Mays. J Phys Chem B 101:10271–10280 (1997). 32. MA Van Dijk, G Casteleijn, JGH Joosten, Y Levine. J Chem Phys 85:626–631 (1986). 33. Y Feldman, N Kozlovich, I Nir, N Garti, V Archipov, Z Idiyatullin, Y Zuev, V Fedotov. J Phys Chem 100:3745–3748 (1996). 34. YA Shchipunov, EV Shumilina. Prog Colloid Polym Sci 106:228–231 (1997). 35. PG De Gennes, GJ Taupin. J Phys Chem 86:2294–2304 (1982). 36. M Borkovec, HF Eicke, H Hammerich, B Dasgupta. J Phys Chem 92:206–211 (1988). 37. A D’Aprano, G D’Arrigo, A Paparelli, M Goffredi, V Turco Liveri. J Phys Chem 97:3614–3618 (1993). 38. C G de Kruif, EMF van Iersal, A Vrij. J Chem Phys 83:4717–4725 (1985). 39. M Hirai, R Kawai-Hirai, S Yabuki, T Takizawa, T Hirai, K Kobayashi, Y Amemiya, M Oya. J Phys Chem 99:6652–6660 (1995). 40. SH Chen, JS Wang. Phys Rev Lett 55:1888–1891 (1985). 41. B Bedwel, E Gulari. J Colloid Interface Sci 102:88–100 (1984). 42. MP Pileni, T Zemb, C Petit. Chem Phys Lett 118:414–420 (1985). 43. PDI Fletcher, BH Robinson, J Tabony. J Chem Soc Faraday Trans I 82:2311–2321 (1986). 44. PL Luisi. Angew Chem 97:449–460 (1985). 45. J Rouviere, JM Couret, A Lindheimer, M Lindheimer, B Brun. J Chim Phys 76: 297–301 (1979). 46. M Nakamura, GL Bertrand, SE Friberg. J Colloid Interface Sci 91:516–524 (1983). 47. G Olofsson, J Kizling, P Stenius. J Colloid Interface Sci 111:213–222 (1986). 48. G Haandrikman, GJR Daane, FJM Kerkhof, NM van Os, LAM Rupert. J Phys Chem 96:9061–9068 (1992). 49. G Gu, W Wang, H Yan. J Colloid Interface Sci 167:87–93 (1994). 50. K Mukherjee, DC Mukherjee, SP Moulik. J Colloid Interface Sci 187:327–333 (1997). 51. A D’Aprano, A Lizzio, V Turco Liveri. J Phys Chem 91:4749–4751 (1987). 52. V Arcoleo, M Goffredi, G La Manna, F Aliotta, ME Fontanella. J Thermal Anal 50:823–830 (1997).

22

Turco Liveri

53. R De Lisi, M Goffredi, V Turco Liveri. J Chem Soc Faraday Trans I 76:1660–1662 (1980). 54. F Goffredi, V Turco Liveri, G Vassallo. J Colloid Interface Sci 151:396–401 (1992). 55. YA Shchipunov, EV Shumilina. Mater Sci Eng C3:43–50 (1995). 56. C Boned, J Peyrelasse, M Moha-Ouchane. J Phys Chem 90:634–637 (1986). 57. H Hauser, G Haering, A Pande, PL Luisi. J Phys Chem 93:7869–7887 (1989). 58. JP Morel, N Morel-Desrosiers, C Lhermet. J Chim Phys 81:109–112 (1984). 59. A D’Aprano, ID Donato, F Pinio, V Turco Liveri. J Solution Chem 18:949–955 (1989). 60. G Pitarresi, C Sbriziolo, ML Turco Liveri, V Turco Liveri, J Solution Chem 22: 279–287 (1993). 61. A D’Aprano, A Lizzio, V Turco Liveri. J Phys Chem 92:1985–1987 (1988). 62. P Terech, RG Weiss. Chem Rev 97:3133–3159 (1997). 63. JH Fendler. Chem Rev 87:877–899 (1987). 64. A Ben-Naim. J Phys Chem 82:792–803 (1978). 65. JM Lehn, JP Sauvage. J Am Chem Soc 75:6700–6707 (1975). 66. A D’Aprano, ID Donato, F Pinio, V Turco Liveri. J Solution Chem 19:589–595 (1990). 67. JH Fendler. Membrane Mimetic Chemistry, Wiley, New York, 1982. 68. ML Turco Liveri, V Turco Liveri. J Colloid Interface Sci 176:101–104 (1995). 69. A Sobczynski, AJ Bard, A Campion, MA Fox, T Mallouk, SE Webber, JM White. J Phys Chem 91:3316–3320 (1987). 70. V Arcoleo, M Goffredi, V Turco Liveri. Thermochim Acta 233:187–197 (1994). 71. A D’Aprano, F Pinio, V Turco Liveri. J Solution Chem 20:301–306 (1991). 72. V Arcoleo, G Cavallaro, G La Manna, V Turco Liveri. Thermochim Acta 254:111– 119 (1995). 73. F Aliotta, V Arcoleo, S Buccoleri, G La Manna, V Turco Liveri. Thermochim Acta 265:15–23 (1995). 74. V Arcoleo, M Goffredi, V Turco Liveri. J Thermal Anal 51:125–133 (1998).

2 Thermodynamics and PhaseSeparation Kinetics of Microemulsions DORIS VOLLMER Institute for Physical Chemistry, University of Mainz, Mainz, Germany

I. Introduction II.

Phase Behavior of Microemulsions A. Microemulsions B. Phase diagrams C. Characteristic size of droplets D. Specific heat E. Free energy F. Latent heat G. Step in the specific heat

24 27 27 27 29 31 34 39 41

III. Phase Separation Kinetics A. Energy barrier B. Experimental observation of oscillations C. Mechanism of phase separation D. Temperature dependence of the droplet–droplet distance

43 43 45 47 48

IV. Conclusion

54

References

56

23

24

Vollmer

I. INTRODUCTION Mixtures containing surfactants and hydrophilic (for instance, water) and hydrophobic (for instance, alkanes) components show a fascinating thermodynamic and kinetic behavior. Gaining an understanding of this behavior poses a large variety of interesting physical and chemical challenges, which have been a focus of fundamental research in colloid science throughout recent decades. In addition to this interest from a statistical physics point of view, this research is also strongly stimulated by applications. Surfactants are ingredients of various products such as pharmaceuticals, lubricants, and cosmetics [1]. They are of importance for tertiary oil recovery and for emulsion polymerization. To improve production capacities, a better understanding of the varying forces of interaction between the surfactant molecules and the other ingredients in the course of production is desirable. In this review, we highlight recent insights into the driving forces of phase transitions and their kinetics in these mixtures that have been made possible by microcalorimetric studies. Binary and ternary mixtures of water, alkanes, and surfactants show a rich variety of phases [2–4]. At room temperature, they are typically organized on the scale of a few tens of nanometers, so that mesoscopic water and oil domains are separated by a surfactant monolayer. The domains can have various structures. Nearly monodisperse droplets or disordered cylindrical structures, lamellar arrangements of alternating water and oil layers, and spongelike structures have been observed. For several model systems, the approximate extent of these structures in the phase diagram is known [5–12]. There can be as many as five transitions between structures with vastly different mechanical properties in temperature intervals of only 10 K, and there are extended two-phase (2Φ) and three-phase (3Φ) regions, where these structures coexist with each other or with water- or oil-rich excess phases. Analysis of the underlying microstructures and understanding of the origin of the phase transitions between the structures have received a lot of attention (see Ref. 13 for a review). The improved experimental characterization of the phase behavior formed a basis for theoretical and computational modeling of phase diagrams [13–24]. In recent years the relevant parameters entering into the equilibrium free energies have been identified. However, their precise values, as well as their dependence on components, temperature, and composition, are still under debate [23,25–31]. Fascinating kinetics is observed when the systems are driven out of equilibrium. Typically, this is accomplished by mechanical treatment, by a sudden change of composition, or by a temperature jump. The most intensively studied mechanically induced transition is the formation of multilamellar vesicles (‘‘onions’’), which occur on shearing of a lamellar phase [32–36]. A sudden change of composition may lead to the formation of myelins [36–39]. Mechanical pinch-

Microemulsions

25

ing of a cylindrical vesicle might lead to a pearling instability, where the cylinder disintegrates into a row of equidistant droplets [40,41]. Temperature jump experiments have been performed to investigate the phase separation of bicontinuous, sponge, lamellar, or droplet phases into one or several coexisting phases of different morphologies [42–44]. Unlike the thermodynamics of surfactant mixtures, their kinetics is poorly understood. A main problem in modeling the kinetics is that, typically, temporal changes of the thermodynamic properties have to be combined with a complex hydrodynamics. In this chapter we argue that differential scanning microcalorimetry (DSC) is an outstanding method for investigating the thermodynamic and kinetic properties of surfactant mixtures [29,30,45–47], since it is highly sensitive to small changes in the surfactant monolayer. This is demonstrated for a three-component mixture of water, octane, and the nonionic surfactant C 12 E 5, i.e., CH 3 (CH 2) 11 (OCH 2 CH 2) 5 OH, where we focus on two structural transitions. This restraint allows us to compare quantitative predictions on the behavior of the mixtures with detailed experimental data. We investigate the thermodynamics of the temperature-induced phase transitions between a lamellar phase and a droplet phase and of the failure of water droplets to emulsify all water in a sample when the temperature is increasing (emulsification failure) [48]. A schematic drawing of the varying microstructure for the phase sequence lamellar–droplet–2Φ is given in Fig. 1. The values for the latent heat of the transition between a lamellar and a droplet phase and for the height of a step in the specific heat at emulsification failure are determined. Both are compared with predictions for the equilibrium free energies describing the mixtures. This permits identification of the important contributions to the free energy. An application of DSC to study the kinetics of phase separation is demonstrated for the case of the phase separation of a droplet phase microemulsion. When heated across the emulsification boundary the droplets tend to decrease in size (Fig. 1c). However, due to the small mutual solubility of the components this is hindered by the conservation of the area of the internal interface between water and oil and of the partial volumes of water, oil, and surfactant. As a consequence, the droplet size changes only when, with considerable overheating (or after exceedingly long times), large droplets are formed. They can be viewed as nuclei of the coexisting water-rich phase [43,49] that grow quickly by taking up excess water of small droplets and merging with larger ones (Fig. 1d). This leads to a fast decay of their number and average distance. Eventually, the distance between large droplets becomes so large that the diffusive transport of water from small to large droplets becomes inefficient. Under constant heating, the small microemulsion droplets (Figs. 1d, 1e, or 1b) are overheated again until another wave of nucleation sets in (Fig. 1d). To emphasize this step-

26

Vollmer

FIG. 1 Schematic drawing of the temperature-dependent microstructure of a mixture of water, oil, and a nonionic surfactant. The temperature-induced phase sequence from lamellar to droplet phase microemulsion to two-phase microemulsion is shown. In the 2Φ region constant heating leads to a decrease in the average size of droplets in a stepwise manner. This is due to the process of repeated nucleation and growth, as indicated by the arrow below the schematically drawn test tubes. The mechanism is discussed in detail in Section III.

wise change in the droplet size, we term this phase separation ‘‘cascade nucleation’’ [50]. This chapter is organized as follows. In Section II we concentrate on a discussion of the thermodynamics of microemulsions. After a definition (Section II.A), special emphasis is put on a description of the temperature-dependent phase behavior (Section II.B) and typical length scales (Section II.C). In Section II.D we discuss the temperature-dependent specific heat of phase transitions. After a discussion of various contributions to the free energy (Section II.E), a quantitative comparison between experimentally determined values and theoretical estimates for the latent heat (Section II.F) and for the step in the specific heat accompanying emulsification failure (Section II.G) is carried out. In Section III we discuss the kinetics of emulsification failure. The parameter dependence of the energy barrier preventing phase separation is discussed in Section III.A. This is followed up by a discussion of oscillations in the specific heat that are induced by cascade nucleation (Section III.B). In Section III.C the mechanism of cascade nucleation is described, and in Section III.D we point out that a slight nonmonotonous dependence of the period of oscillation is due to the dependence of the diffusion length between small droplets on composition. Finally, in Section IV the main results are summarized.

Microemulsions

II.

27

PHASE BEHAVIOR OF MICROEMULSIONS

A. Microemulsions Water and oil are immiscible. A sample containing water and oil will phase separate into macroscopic water and oil domains, since the surface tension of the interface between water and oil tends to minimize the interfacial area. However, when surfactant molecules are added, the interfacial tension between the water and oil domains may decrease by several orders of magnitude [27,31,51–53]. These molecules have a water-soluble polar headgroup and an oil-soluble apolar tail, separating the water and oil domains by a liquid-like monolayer of fixed average area per surfactant molecule [54]. In the case of very low interfacial tension, morphologies requiring a large interfacial area may be thermodynamically stable. Schulmann et al. [55] defined microemulsions as mixtures of water, oil, and surfactant that are thermodynamically stable, isotropic, and of low viscosity. In the present review, we follow this convention and denote the system as an ‘‘amphiphilic mixture’’ when we wish to also include lamellar and other locally ordered structures of higher viscosity.

B. Phase Diagrams At present, amphiphilic mixtures containing surfactants of the type C i E j (alkylpolyglycol ether) are most completely characterized. Their phase behavior has been extensively studied by Kahlweit, Olsson, Strey, and coworkers, and detailed knowledge of the temperature- and composition-dependent morphology of such amphiphilic mixtures is available [2,11,22,23,31,53,54,56–58]. In view of this, the majority of theoretical work aiming at a comparison with experiments focuses on these mixtures.

1.

Gibbs Phase Triangle

Figure 2 schematically shows an isothermal cut through the Gibbs phase prism. Depending on composition, the mixture may be single-phase (1Φ), two-phase (2Φ), or three-phase (3Φ). 1Φ: In the single-phase region, the microemulsion solubilizes all water and oil. The mixture is macroscopically homogeneous. Its microstructure depends, however, on temperature and composition. Oil droplets in water, oil cylinders in water, bicontinuous and lamellar morphologies, water cylinders in oil, and water droplets in oil* have been observed.

* Oil and water droplets are also called swollen and reversed swollen micelles, respectively.

28

Vollmer

FIG. 2 Schematic drawing of the Gibbs phase triangle for a mixture of water, alkane, and nonionic surfactant (C i E j ). 1Φ, 2Φ, and 3Φ stand for a single-phase microemulsion, a microemulsion coexisting with a water- or oil-rich phase, and a microemulsion coexisting with a water-rich phase and an oil-rich phase.

2Φ: In the two-phase region, there is a microemulsion phase containing almost all amphiphile, which coexists with an oil-rich (2Φ, Winsor I [59]) or with a water-rich (2Φ, Winsor II [59]) phase [56]. 3Φ: If the mixture separates into three phases (Winsor III [59]), the amphiphile is mainly dissolved in the middle phase, which coexists with phases containing predominantly water and oil, respectively [56]. The extent of the 1Φ, 2Φ, and 3Φ regions in the Gibbs phase triangle depends on composition, on temperature, and on the choice of the components [2,13,53].

2.

Fish Cut

Nonionic surfactants of the type of C i E j show a strongly temperature-dependent phase behavior. In the present chapter we restrict ourselves to mixtures of water, octane (Merck, Darmstadt, Germany), and C 12 E 5 (Nikko Chemicals, Tokyo, Japan). These intensively studied mixtures show extended droplet phases [10,11,31,54,58,60]. Sample compositions are given by the volume fractions of water φ w, octane φ o, and surfactant φ s. Figure 3a shows a section through the phase prism as a function of temperature and surfactant concentration. The ratio φ w /φ o of the volume fractions of water and oil is fixed. Because of its characteristic fishlike shape, this section is called a ‘‘fish cut’’ [57]. The phase diagram is to a good approximation mirror symmetrical with respect to the phase inversion temperature T, where the value for T depends only on the choice of components and takes the value T ⫽ 305.6 K for

Microemulsions

29

the investigated mixtures. For T ⱕ T the surfactant monolayer is curved on the average toward oil, whereas for T ⱖ T it is curved toward water. For φs ⱕ 0.05 a three-phase region (3Φ) is formed close to T ⫽ T, whereas for higher surfactant concentrations the mixture becomes single-phase. For still higher surfactant concentrations a lamellar phase (lam), i.e., an alternation of water–surfactant–oil– surfactant layers is found (see Fig. 3a). The lamellar phase is birefringent and may be of high viscosity. It is bounded in the phase diagram by two clear microemulsion phases, enclosing oil (L 1) or water (L 2). The L 1 and L 2 phases are separated from the lamellar phase by a two-phase region whose width is not shown in Fig. 3. For φ w ⬍ φ o the microstructure in the L 2 region conforms to water droplets embedded in an oil matrix. Analogously, in the microemulsion channel L 1 oil droplets are formed for φ o ⬍ φ w. Even further from T, the single-phase microemulsion phase separates. The corresponding phase boundaries are called the water (for L 2 to 2Φ) and oil (for L 1 to 2Φ) emulsification boundaries. For temperatures sufficiently above the water emulsification boundary (i.e., well inside the 2Φ region), a water droplet microemulsion is in equilibrium with a water-rich phase. With increasing temperature the average size of the droplets decreases, leading to an increase in the volume fraction of the coexisting waterrich phase. A schematic drawing of a water droplet covered by a surfactant monolayer is given in Fig. 3b. The average radius of the hydrophilic part of the water droplet is given by R 1Φ, and l s denotes the average thickness of the monolayer. For simplicity, the hydrophilic headgroup [OCH 2 CH 2] j OH is drawn as a circle. The microstructure of the chain is similar to its hydrophobic counterpart H[CH 2] i .

C. Characteristic Size of Droplets For microemulsions containing various types of nonionic or ionic surfactants, the composition- and temperature-dependent size of microemulsion droplets was determined by highly sensitive scattering experiments [10,31,58]. These studies permit a determination of the average droplet size and of the effective thickness of the surfactant monolayer with relative errors of roughly 10%.

1.

The One-Phase Region

In the 1Φ region the droplet size is determined by composition. To a good approximation it does not depend on temperature. The average radius R 1Φ of the droplets is determined by the conservation of their enclosed volume, 4πNR 31Φ /3 ⫽ Vφ d, and of their surface area, 4πNR 21Φ ⫽ Vφ s /l s, from which one finds

R 1φ ⫽

冦

3l s φ d φs

where

φd ⯝ φw ⫹

φs 2

for water droplets

3l φ ⫺ s d φs

where

φd ⯝ φo ⫹

φs 2

for oil droplets

(1)

30

Vollmer

2F

(a)

(b)

Microemulsions

31

To distinguish water from oil droplets, we take water droplets to have a positive radius and oil droplets to have a negative radius. The enclosed volume φ d is the sum of the interior phase volume, i.e., water or oil, and the volume of the respective water- or oil-soluble part of the surfactant molecules. N denotes the number of droplets in a volume element V [11,31,58]. The effective thickness of the surfactant monolayer has been determined to be l s ⬇ 1.3 nm [54]. Depending on composition, the droplet radius is on the order of 2–20 nm, the total oil/water interfacial area is on the order of 100 m 2, and 10 16 –10 18 droplets are formed per cubic centimeter.

2.

The Two-Phase Region

In the 2Φ region only the surface area of the droplets is preserved; their volume can be adjusted so that the droplets take their optimum size R opt , i.e., a radius that locally minimizes the interfacial free energy. R opt depends only on temperature; it is independent of composition [23]. At the emulsification boundary R opt ⫽ R 1Φ, whereas in the 2Φ region |R opt | ⬍ |R 1Φ |. For temperatures sufficiently below those corresponding to the micellar size and several degrees away from T, the optimum radius has been determined by small-angle neutron scattering (SANS) experiments to vary as [31] R opt (T) ⯝

1 a(T ⫺ T )

(2)

˚ ⫺1. where a ⫽ 1.2 ⫻ 10 ⫺3 K ⫺1A

D. Specific Heat The specific heat is measured by using a differential scanning microcalorimeter (VP-DSC, Microcal Inc.). This microcalorimeter measures the difference in the

FIG. 3 (a) Section through the phase prism for mixtures of water, octane, and C 12 E 5 for varying volume fractions of surfactant and nearly equal volume fractions of octane and water (φ o ⫽ 0.95φ w). The filled squares show experimentally determined values for the phase boundaries. L 1 and L 2 denote single-phase microemulsions, lam denotes a lamellar phase, 2Φ denotes a microemulsion phase in equilibrium with a water-rich (2Φ) or an oil-rich (2Φ) phase, and 3Φ denotes a microemulsion phase in equilibrium with a waterrich phase and an oil-rich phase. At sufficiently high temperatures, the microstructure close to and above the water emulsification boundary corresponds to water droplets in oil, as indicated by the circles. The variation in the size of the circles shows the composition and temperature dependence of the droplet size in the 2Φ region. The increase in the volume fraction of the water-rich phase with increasing temperature is indicated by the size of the shaded area in the ‘‘test tubes.’’ (Data points taken from Ref. 31.) (b) Schematic drawing of a surfactant-covered water droplet.

32

Vollmer

specific heat between the sample and a suitably chosen reference system. By this means it provides a very accurate description of the variation of the specific heat C rel V (T) relative to a baseline set by the reference sample. A more detailed description of the application of this technique to microemulsions is given in Ref. 45.* Figure 4a shows the thermogram of a heating and cooling scan performed on a sample of equal volume fractions of water and oil (φ w ⫽ φ o ⫽ 0.40; φ s ⫽ 0.20). A heating rate of υ s ⬇ 5 K/h and a cooling rate of υ s ⬇ ⫺5 K/h were chosen. The solid line indicates the variation of the signal for the specific heat due to heating, while the dashed line shows the variation of C rel V (T) due to cooling. For convenience, the optically determined phase transition temperatures between single- and two-phase microemulsions are marked by arrows below the thermograms. Immediately after the start of the heating scan (solid line) at 294 K, i.e., slightly above the 2Φ → L 1 phase boundary, the signal for the specific heat shows a peak at T ⫽ 296.5 K. For T ⬍ 296.5 K the mixture is clear and gel-like, whereas in the L 1 region for T ⬎ 296.5 K the mixture remains clear and is of a lower viscosity. After going through a minimum, C rel V (T) increases sharply. It passes a very narrow peak, which is immediately followed by a large and relatively broad one. From a comparison with the phase diagram it can be concluded that the mixture is lamellar. The test probe appears slightly turbid and birefringent. According to the C rel V (T) signal, the mixture shows a single-phase lamellar region with a width of only 3 K, which is followed by another large peak (307–311 K). Comparison with the optically determined phase boundaries suggests that the latter is due to the phase transition of the lamellar phase into the L 2 channel. Before the signal has dropped toward the value it had in the lamellar phase, C rel V (T) increases again and starts to oscillate. The origin and parameter dependence of these oscillations is discussed in detail in Section III. The cooling scan (dashed line) starts in the L 2 channel. Both, the L 2 → lam and the lam → L 1 phase boundaries give rise to a peak in the specific heat. Due to hysteresis, the peaks are shifted toward slightly lower temperatures compared to the boundaries observed during the heating scan. A broad peak in the L 1 channel is visible. We attributed this peak to a structural transition accompanying an appearance of local ordering in the L1 region. Passing the L 1 → 2Φ phase boundary leads to a small peak in C rel v (T). Within the range 288 K ⬍ T ⬍ 293 K the signal for the specific heat is nearly constant; it increases only at T ⱗ 285 K, where another large peak is visible. From optical investigations it is expected that the peak at T ⫽ 293.5 K is due to the entrance into the 2Φ region. However, the mixture is metastable. Close to T ⫽ 293.5 K the mixture remains clear, and

* The difference between the MC2-MicroCal described in Ref. 45 and the VP-DSC is that the latter has a cell volume of 0.519 cm 3 and better baseline reproducibility.

(a)

(b) FIG. 4 A heating scan (solid line) and a cooling scan (dashed line) for the specific heat relative to a reference mixture containing appropriate amounts of water and oil. The vertical bars indicate the optically determined phase boundaries for the compositions. The numbers above the bars denote the optically determined phase transition temperatures. (a) φ s ⫽ 0.2, φ w ⫽ φ o ⫽ 0.4; (b) φ s ⫽ 0.2, φ w ⫽ 0.15, and φ o ⫽ 0.65. The inset in (b) shows the low temperature region on an enlarged scale.

34

Vollmer

it is several hours before a macroscopic phase separation is observed. Below T ⱗ 285 K the mixture immediately becomes turbid.* Finally, we point out that the width of a peak gives a measure for the width of the two-phase region separating the two single-phase regions. It has been checked that the width does not depend on scan speed. The area under a peak corresponds to the heat absorbed during a phase transition; i.e., in first-order phase transitions it is a measure of the latent heat of the transition. As required by thermodynamics, all transitions are endothermic for up scans and exothermic for down scans. A more detailed discussion of the structure of the thermograms and the peak shape is given in Ref. 30. For equal-volume fractions of oil and water, the peaks related to the transition from a lamellar into an L 1 or L 2 phase, respectively, are broad and look similar. Note, however, that the transition lam → L 1 gives rise to two peaks that are very close to each other. The differences between the high and low temperature regions become even more apparent upon entry into the 2Φ or 2Φ region. This is interesting to note, since the phase diagram (see, e.g., Fig. 3a) gives the impression that the microstructure and the thermodynamic properties do not change when T is replaced by 2T ⫺ T and water and oil are simultaneously interchanged. Therefore, the C 12 E 5 –water–octane system is called a symmetrical microemulsion [31]. The influence on the thermograms of changing the water-to-oil ratio is demonstrated in Fig. 4b, where C rel V (T) is shown for a sample with φ w ⫽ 0.15, φ o ⫽ 0.65, and φ s ⫽ 0.2. For both the heating (solid line) and cooling (dashed line) scans, a heating rate of | υ s | ⬇ 6 K/h is used. In comparison to Fig. 4a, the spectrum looks strongly asymmetrical. In contrast, the transition lam → L 2 gives rise to a narrow large peak, whereas the transition lam → L 1 is accompanied by a small peak at T ⬇ 292 K. A second small peak is visible when the 2Φ region is entered. Also, in the L 1 channel, C rel V (T) does not remain constant, but the signal shape suggests that in the L 1 channel the microstructure changes with temperature (inset in Fig. 4b). On the other hand, C rel V (T) is nearly constant in the L 2 channel, and, again, passing the water emulsification boundary leads to a step in the specific heat.

E. Free Energy To describe the phase behavior, contributions to the free energy arising from the bending of the interfacial monolayer, F b; from undulations of the lamellae, F u ; and from the entropy of mixing of water and oil domains, F mix , are discussed in

* Similar behavior was observed by Olsson and coworkers [42], who investigated the turbidity after quenching the mixture into the 2Φ region.

Microemulsions

35

the literature for mixtures of water, alkane, and surfactant [14–17,19,21–24]. Since in the present review we deal solely with nonionic surfactants, electrostatic contributions to the free energy need not be considered. The surfactant film is treated as an incompressible, tensionless two-dimensional fluid. In addition, it is assumed that all surfactant molecules are located at the interface and that water and octane are immiscible. Both assumptions hold to within a few percent for this model system, and the corrections can be incorporated into the theory when the deviations become more significant. The free energy per unit area arising from the bending of the interfacial monolayer was introduced by Helfrich [61] and applied to amphiphilic mixtures by various authors [15,19,23,30];

冤

κ 1 1 ⫹ ⫺ 2c o Fb ⫽ 2 R1 R2

冥 ⫹ κ R 1R 2

1

(3) 2

Here, R 1 and R 2 denote the local radii of curvature [30]. The bending modulus κ, the Gaussian modulus κ, and the spontaneous curvature* c 0 (T) are empirical material constants; κ and κ describe the elastic energy needed to curve the interface away from its preferred curvature. According to Refs. 22 and 29, they take the values κ ⫽ 0.8k B T and κ ⫽ ⫺0.4 k B T. For monodisperse spheres of radius R, the local radii of curvature identically fulfill R 1⫺1 ⫽ R 2⫺1 ⫽ R ⫺1. In that case, the bending free energy per unit volume becomes Fs ⫽

冢 冣冢

φ s 2κ ls R2

[1 ⫺ Rc o (T)] 2 ⫹

κ 2κ

冣

(4)

where R ⫽ R 1Φ in the single-phase region and R ⫽ R opt in the 2Φ region and ⫺1 c 0 (T) ⫽ R opt (1 ⫹ κ/2κ) [63]. The factor φ s /l s R 2 corresponds to the interfacial area per unit volume. For a flat lamellar phase one has R 1⫺1 ⫽ R 2⫺1 ⫽ 0, yielding φ F lam ⫽ 2κ s c o (T) 2 ls

(5)

It will be assumed that the linear dependence of c 0 (T) on temperature, c 0 (T) ⫽ ⫺1 R opt (1 ⫹ κ/2κ), still holds. Equations (4) and (5) do not account for fluctuations

* The relationship between the spontaneous curvature and the optimum radius is still under debate. The relationship used here is a good approximation for the investigated mixture if (1) the microstructure conforms to droplets and (2) the droplets are sufficiently larger than micelles.

36

Vollmer

of the interface. Undulations of the lamellae are expected to give important contributions to the free energy of lamellar structures [17,20]. To account for this, Helfrich’s result [62] for the free energy of undulating lamellar liquid crystals has been generalized heuristically [17]: F u ⫽ (k B T ) 2

冢 冣冢

χ φ 3s κ 4l 3s

冣冢

1 1 ⫹ 2 2 φo φw

冣

1 φo ⫹ φw

(6)

Following Ref. 17 we choose χ ⫽ 0.05. The free energy is positive and represents the entropic repulsions between fluctuating sheets that cannot cross. Additional contributions to the free energy result from equivalent possibilities to realize surfaces with a given structure in space. In particular, there are many different possibilities to distribute a given set of droplets in space, giving rise to a free energy of mixing [17],

冮

F mix ⫽ ⫺ S dT

F mix ⫽

冦

(7)

k B T φ 3s [φ d log φ d ⫹ (1 ⫺ φ d) log(1 ⫺ φ d)] 6 3 l 3s φ 3d (1 ⫺ φ d) 3

1Φ channel

k B T φ 3s {φ d (T ) log φ d (T ) ⫹ [1 ⫺ φ d (T )] log [1 ⫺ φ d (T )]} 6 3 l 3s φ d (T ) 3 [1 ⫺ φ d (T )] 3

2Φ channel

(8)

In the 1Φ region, F u and F mix depend only on temperature owing to the factor k B T. After crossing the emulsification boundary, the volume fraction of droplets φ d becomes temperature-dependent, φ d (T) ⬅ φ (opt) ⫽ d

φs φs R opt (T) ⫽ 3l s 3l s a(T ⫺ T)

(9)

leading to a second temperature-dependent term in F mix . In that case Fmix ≠ ⫺TS. Figure 5a shows a survey of the temperature dependence of the bending free energies per unit volume according to Eqs. (4) and (5) for the case φs ⫽ 0.2 and φ w ⫽ φ o ⫽ 0.4. The indices o and w on the symbol for the free energies distinguish between morphologies, where the average curvature of the monolayer is toward oil and water, respectively. F oopt and F wopt denote the free energy for an oil and water droplet phase microemulsion, respectively, where the droplets take their optimum radius. The dashed lines visualize the evolution of the free energies for a lamellar structure F lam and those of oil F os and water droplets F ws. The solid line

Microemulsions

37

shows the temperature evolution of the thermodynamic free energy. By definition, it follows the lowermost of these curves, provided the constraints of conservation of the respective partial volumes can be fulfilled. It has different branches crossing over between morphologies. The free energy follows F opt except for a temperature window around T, where there is too little water or oil to let the droplets assume their optimum size. Consequently, the temperature of the intersection between every two such energies can serve as an estimate for the phase transition temperature. The resulting calculated phase diagrams agree within a few degrees with experiment [22].* In Fig. 5b, the influence of F u and F mix on the previously discussed energies is shown. The composition of the sample is kept the same. Fu leads to a significant increase in the free energy of the lamellar phase. The entropy of mixing F mix opt leads to a comparatively smaller decrease in free energy. Close to T ⫽ T, F mix (T) is not defined. After all, the optimum size of the droplets diverges in such a manner that the constraints due to the conservation laws can no longer be fulfilled. [This is underlined by the divergence of φ d (T) ⫽ φ s /[3l s a(T ⫺ T)], although, clearly, φ d (T ) may never exceed 1.] Note that the entropy of mixing does not affect the position of the emulsification boundary, since R 1Φ ⫽ R opt at that boundary. In contrast, both F mix and F u decrease the range of stability of a lamellar morphology, so the phase boundary between the droplets and the lamellar phase moves closer toward T. The influence of the water-to-oil ratio on the temperature dependence of the free energies is demonstrated in Fig. 5c, where the bending free energies F s, F lam , and F opt are shown for φ s ⫽ 0.2, φ w ⫽ 0.15, and φ o ⫽ 0.65. Note that F opt and F lam remain the same since their values are affected only by φ s; they do not depend on φ w and φ o . In contrast, this change in composition strongly changes the free energies for the droplet structures; F os depends on φ o, and F ws depends on φ w. In comparison with Fig. 5a, the slope of F ws (T) has increased around T, and its minimum is shifted toward lower energies. This implies that the intersection of F ws (T) and F lam (T) and that of F ws (T) and F wopt (T) are shifted toward higher temperatures. In contrast, the slope of F os (T ) decreases close to T, and its minimum increases. Note that for this composition and temperature interval, F os (T ) does not correctly describe the morphology, since it has been shown to be cylindrical or bicontinuous for T ⬍ T [54]. Surprisingly, although an incorrect morphology is considered, the temperatures of the intersections of the free energies deviate from the experimentally determined ones (see Fig. 4b) by only a few degrees [22].

* Taking the intersection of the free energies as the position of the phase transition does not account, however, for the width of the 2Φ region, which can be calculated by evaluating the components’ chemical potentials in the respective coexisting phases (cf. Refs. 17,21,20).

38

Vollmer

FIG. 5 Survey of different contributions to the free energy. (a) The bending free energy for nonfluctuating interfaces of oil droplets (F os, F oopt), water droplets (F ws, F wopt), and a lamellar morphology (Flam). (b) Free energies when undulations of lamellae F u and the entropy of mixing Fmix are included. For these parts the composition is φ w ⫽ φ o ⫽ 0.4 and φ s ⫽ 0.2. (c) Influence of composition on the temperature-dependent bending free energy; φ w ⫽ 0.15, φ o ⫽ 0.65, and φ s ⫽ 0.2.

Microemulsions

39

(c)

F.

Latent Heat

The experimentally determined values for the heat absorbed during a transition, ∆Q exp, can be compared directly to theoretical estimates ∆Q th. The value for the latent heat of a first-order phase transition can be calculated from the free energy, yielding ∆Q th ⫽

冮

T⫹

T⫺

冢

冮

dT C υ (T) ⫽ ⫺

⫽ ⫺ T⫹

∂F (T) ∂T

冷

T⫹

T⫺

⫺ T⫺ T⫹

dT T ∂F (T) ∂T

∂ 2 F (T) ∂T 2

冷 冣 ⫹ F (T ) ⫺ F (T ) ⫹

⫺

(10)

T⫺

⬅ ⫺F′(T ⫹) ⫹ F′(T ⫺) ⫹ F(T ⫹) ⫺ F(T ⫺) where the last equation was obtained by partial integration and we defined F′(T) ⬅ T ∂F(T)/∂T. Note that this expression for ∆Q th contains only the values for the free energy and its first derivative with respect to temperature, evaluated at the borders T ⫺ and T ⫹ of the coexistence region. Figure 6 gives a survey of the contributions to the latent heat due to the temperature derivatives F′ ⬅ ⫺TS(T ) of the free energies F opt, F s, F lam , and F mix . The

40

Vollmer

FIG. 6 Dependence of the heat ⫺TS ⫽ T ∂F/∂T ⬅ F′ on temperature for φ s ⫽ 0.2 and φ w ⫽ φ o ⫽ 0.4.

composition is again (cf. Figs. 5a and 5b) φ s ⫽ 0.2 and φ w ⫽ φ o ⫽ 0.4. The heat o w quantities F′s o, F′sw, F′lam, F′mix , and F′mix show a linear temperature dependence. o w F′s , F′s , and F′lam have slopes of a comparable magnitude. However, they are shifted relative to each other. The slope of F′opt is of comparable magnitude but has the opposite sign. F′mix almost vanishes in the single-phase region and in the 2Φ region. F′u is not shown, since it almost vanishes in the relevant parameter range, too. All heat curves depend explicitly on surfactant concentration. In addition, the slopes of F′s o and F′sw depend on the water-to-oil ratio. The contribution of the difference F(T ⫹) ⫺ F(T ⫺) of the free energies to the latent heat [see Eq. (10)] can in general be neglected, since it is much smaller than the difference F′(T ⫹) ⫺ F′(T ⫺) (note the vastly different scales of the y axes of Figs. 5 and 6). Using Eq. (10) and the experimentally determined values of T ⫹ and T ⫺, the values for the latent heat of a phase transition can be read off from Fig. 6 by taking the difference of the respective values belonging to T ⫹ and T ⫺.

1.

Lamellar to L 2 Transition

We now evaluate the values for the latent heat for the transition of a lamellar phase into a microemulsion phase of water droplets. According to Eq. (10), the latent heat is given by

Microemulsions

冢

∆Q th ⬇ ⫺ T ⫹

41

冷

冷

∂F ws (T) ∂F (T) ⫹ T ⫹ mix T⫹ ∂T T ⫹ ∂T

⫺ T⫺

(11)

冷 冣

冷

∂F lam (T) ∂F (T) ⫺ T⫺ u T⫺ ∂T ∂T T ⫺

where we have already dropped the contribution F ws (T ⫹) ⫹ F mix (T ⫹) ⫺ F lam (T ⫺) ⫺ F u (T ⫺) to ∆Q th. Moreover, for narrow and large peaks, the value for the latent heat is dominated by the temperature derivative of the bending free energy evaluated at T ⫹ ⬇ T ⫺ ⬇ T peak , where T peak corresponds to the temperature of the maximum of the corresponding peak in C rel V (T ) (see Fig. 6). Inserting Eqs. (4) and (5) into Eq. (11) yields [29,30] ∆Q th ⫽

冢 冣冢

4aκT peak φ2s 3l 2s φd

1⫹

κ 2κ

冣

(12)

Figure 7 shows experimental data (squares) and the corresponding theoretical predictions (solid line) for the values of the latent heat for the lam → L 2 transition for varying surfactant concentrations and a fixed ratio of water and octane, φ o /φ w ⫽ 5.67. We find close agreement between the theoretical curve and the experimental results, both in absolute magnitude and in the dependence on the surfactant volume fraction. The errors for the calculated values for the latent heat depend strongly on the width-to-height ratio of the peak [30]. For the samples studied the peaks are comparatively narrow, leading to errors for ∆Q th on the order of 10% when Eq. (12) is applied rather than Eq. (11).

G. Step in the Specific Heat According to Fig. 4, there is a step in the specific heat C rel V when the emulsification boundary is passed. In Fig. 8, the height ∆C step V of the step in the specific heat is plotted for different sample compositions. The different data points for a single surfactant concentration denote repeated measurements at different heating rates between 8 and 50 K/h. In evaluating the height of the step, it should be kept in mind that the values for ∆C rel V may depend on υ s . Within experimental accuracy no scan speed dependence is observed for ∆C step V when the measurement is started in the L 2 channel and the L 2 channel is entered during the cooling and stirring of a mixture that was previously in a 2Φ region or when it is started in the L 1 channel and the L 1 channel is entered during the heating and stirring of a mixture that was previously in the 2Φ region. The thermodynamic value for the height of the step, i.e., ∆C step th , can be calculated from the free energies via Eq. (4):* * In principle, the entropy of mixing [cf. Eq. (8)] will also contribute to the step. It has been checked that in general this contribution is much smaller than the one resulting from the bending free energy [47]. Therefore, we neglect it in the following.

42

Vollmer

FIG. 7 The latent heat ∆Q per cubic centimeter of sample volume for the transition lam → L 2 is plotted as a function of φ s at a fixed ratio φ o /φ w ⫽ 5.67. The squares are obtained from the calorimetric spectra, and the solid line is the prediction of Eq. (12) for the heat changes obtained from the interfacial model [29]. The inset shows the location of the sample compositions in the Gibbs phase triangle.

冤∂ F∂T(R ) 冷 4κT φ a κ 1⫹ ⫽ 冢 l 2κ冣 2

∆C step th ⫽ ⫺T e

s

opt

2

e

s

2Φ,T⫽T e

⫺

∂ 2 F s (R 1Φ) ∂T 2

冷

1Φ,T⫽T e

冥

(13)

2

s

The predicted value increases linearly with surfactant concentration. It is in remarkably good agreement with the experimental data shown in Fig. 8. We stress that the good agreement between calculated and calorimetrically determined data is found without fitting parameters. This underlines the dominant role that the bending free energy, Eq. (3), plays in the description of the equilibrium behavior of the mixtures. Entropic contributions determine the width of the coexistence regions between different morphologies [13,20]. However, for a first prediction of the topology of the phase diagram, the positions of phase boundaries, and connected anomalies in the specific heat, they are of minor importance.

Microemulsions

43

FIG. 8 Dependence of the height of the step in the specific heat ∆C Vstep on surfactant concentration φ s . The squares correspond to φ o /φ w ⫽ 5.67, and the crosses to φ o /φ w ⫽ 0.35 [47]. To a good approximation the height of the step depends linearly on φ s , as predicted by the theory (solid line).

III. PHASE SEPARATION KINETICS To explore the origin of the oscillations in the signal for the specific heat (see e.g., Fig. 4a) we first discuss the parameter dependence of the energy barrier preventing the formation of smaller droplets coexisting with a water-rich phase. This oscillating phase separation involves a complex collective nucleation process, which will be identified as the origin of the stepwise phase separation.

A. Energy Barrier The formation and growth of a nucleus, i.e., of a droplet having a radius larger than the optimum radius, is energetically hindered by the unfavorable bending energy of that droplet. On the other hand, because of volume and surface conservation, large droplets must be formed to allow the majority of small droplets to attain their optimum size. The height of the energy barrier the microemulsion droplets have to pass in order to be able to form a single large droplet is the maximum value of the difference ∆F s between the bending free energy F s (N, R)

44

Vollmer

of the supersaturated state of N monodisperse droplets of radius R (cf. Fig. 1c) and that of the state F s (N′, R′) ⫹ F s (1, ρ) (see Fig. 1d), where N′ droplets of radius R′ (R ⬎ R′ ⲏ R opt) coexist with a single large droplet of radius ρ [49]: ∆F s ⫽ F s (N′, R′) ⫹ F s (1, ρ) ⫺ F s (N, R)

(14)

As soon as ∆F s ⬍ 0, it is energetically favorable to form N′ droplets of radius R′ and a single big droplet of radius ρ. For a system with initially 1000 monodisperse droplets, Fig. 9 shows the dependence of ∆F s on the reduced size of the large droplet, (ρ ⫺ R 1Φ)/ρ, at different degrees of overheating, τ ⬅ R 1Φ /R opt ⬀ (T ⫺ T ). The monodisperse state corresponds to (ρ ⫺ R 1Φ)/ρ ⫽ 0, whereas (ρ ⫺ R 1Φ)/ ρ → 1 for ρ ⬎⬎ R 1Φ. Thermodynamically stable monodisperse systems are characterized by values for τ less than 1, while τ ⬎ 1 corresponds to the two-phase system. For a system with a finite number of particles N, the phase transition can occur only at τ ⬎ 1, and it only requires the production of a finite size excess

FIG. 9 Dependence of the energy difference ∆F s separating a system of monodisperse droplets (radius R 1Φ) from a phase-separated state of smaller droplets coexisting with a single large droplet of radius ρ. The initial number of droplets is fixed at N ⫽ 1000. The different curves correspond to different degrees of overheating, τ. (Dashed line: τ ⫽ 1.1; solid line: τ ⫽ 1.15; dotted line: τ ⫽ 1.22.)

Microemulsions

45

droplet. For small values of τ (τ ⫽ 1.1, dashed line), the energy difference ∆F s always increases as the reduced size of the large droplet increases. The monodisperse system is still stable, showing that more than 1000 droplets are needed to form a phase-separated state. As the overheating increases, a second minimum shows up. For τ ⬇ 1.15, the energy difference can become negative for the first time (solid line). In this case, the mixture has to pass an energy barrier ∆F max s the order of 10 k B T to reach phase separation, and the excess droplet takes on a reduced size larger than (ρ ⫺ R 1Φ)/ρ ⬇ 0.75, i.e., ρ ⬇ 4R 1Φ. Its volume exceeds that of the microemulsion droplets by more than a factor of 50. For even greater rapidly decreases, becoming only a few k B T for τ ⫽ 1.22, overheating, ∆F max s where it becomes negative for (ρ ⫺ R 1Φ)/ρ ⬇ 0.55, i.e., for ρ ⬇ 2R 1Φ (dotted line). The height of the energy barrier depends only slightly on the number of droplets. However, due to the conservation of volume and total interfacial area, a minimal number of droplets are required to build a sufficiently large droplet for ∆F s to become negative (Fig. 9). Energy barriers of a few k B T require values for R 1Φ /R opt ⬇ 1.2 in accordance with experimental observations [46]. In this case, a few hundred droplets participate in nucleating a large droplet. Consequently, the nucleation of large water droplets is a strongly collective process.

B. Experimental Observation of Oscillations In the last paragraph we observed that the conservation of volume and interfacial area is essential for the occurrence of the energy barrier. In contrast to classical nucleation processes [65,66], it is energetically unfavorable for a single large droplet to be formed and to grow. Large droplets form only in order to decrease the free energy of the whole system. This novel feature can modify the phase separation kinetics significantly. This comes to light when the system is driven into the 2Φ region by constant heating. Constant heating may lead to periodic clouding and clearing of the mixture [46,49,64]. The repeated appearance of clouding is due to strong threshold behavior in the formation of aggregates (i.e., water-rich domains) larger than the wavelength of light, which is reflected in an oscillating variation of the turbidity [46,64]. Two to four periods of clouding can be discerned optically for most compositions and heating rates. More detailed information about the kinetics of this phase separation can be achieved from microcalorimetric measurements [46]. In contrast to optical measurements, which are sensitive to large particles in the system, the DSC signal is affected by all droplets. After all, it measures changes in the average curvature of the interface (see Section II.E and Ref. 29). In particular, it is therefore governed by the vast majority of small droplets. As a consequence, the values for the specific heat contain less noise. They even show an oscillating signal when

46

Vollmer

nothing can be discerned any longer in the optical data. Up to 20 oscillations can clearly be dissolved. Due to their favorable signal-to-noise ratio, the microcalorimetric data allow us to quantitatively investigate the oscillations. Figure 10 shows the temperature-dependent variation of the microcalorimetric signal for the specific heat C rel V (T ) for different heating rates υ s . All thermograms show about 15 oscillations. From the scan speed dependence it is clear that the thermograms do not resemble the equilibrium values for the specific heat. Rather, they reflect aspects of the phase separation kinetics. To stress this nonequilibrium nature of the data we denote them as ‘‘apparent specific heat.’’ In agreement with expectations from thermodynamics, the onset of the oscillations shifts to higher values for increasing surfactant concentration. The time lag ∆T between two succeeding maxima (cf. inset of Fig. 10) increases with increasing υ s. In Refs. 46 and 50 it is shown that ∆T ⬃ υ 1/2 s .

FIG. 10 Temperature-dependent variation of the apparent specific heat C Vrel (T ) while entering the 2Φ region by constant heating for φ s ⫽ 0.1 and φ w ⫽ 0.33 and different heating rates. Top to bottom: υ s ⫽ 4 K/h, solid line; υ s ⫽ 14 K/h, dotted line; υ s ⫽ 27 K/h, crosses. The respective baselines are chosen in such a way that thermograms do not cross. The inset shows the definition of the height of a peak ∆C v and of the period of oscillation ∆T.

Microemulsions

47

The time lag ∆T between the peaks of C rel V changes nonmonotonously with the number of oscillations, i.e., with the temperature. This dependence is most evident when the signal for the apparent specific heat also shows a pronounced superimposed structure. An explanation of the dependence of ∆T on the number of oscillations will give a hint about a relevant process to understand the kinetics of this phase separation.

C. Mechanism of Phase Separation We now further discuss Fig. 1, in order to clarify the origin of cascade nucleation in more detail (also see Refs. 49 and 50). To this end, we observe that for a small degree of supersaturation (Fig. 1c, τ ⱗ 1.15), nucleation is strongly suppressed for energetic and kinetic reasons, while it becomes fast for larger values of τ, leading locally to a structure such as the one shown in Fig. 1d. Typically, a large droplet is nucleated from a few thousand small ones. Nevertheless, in a very short time, a macroscopic number of nuclei (ⲏ10 12) appear in the sample (note that there are 10 16 –10 18 droplets per cubic centimeter). They are homogeneously distributed with typical distances of less than a few hundred nanometers between them, so they induce rapid relaxation of the size distribution of droplets to a state close to equilibrium. At the same time, the nuclei grow in size and merge into water-rich domains, whose mutual distance soon exceeds 10–100 µm. By that time, a typical neighborhood of a water-rich domain contains a few thousand small droplets. It looks very much like those sketched in Fig. 1b. Due to the large distance between the water-rich domains and typical neighborhoods of small droplets, water transport—no matter whether by molecular diffusion of water through the oil or by diffusion and collisions of droplets—from small droplets of a to the water-rich domains is negligible on the time scales ∆T/υ s ⬃ υ ⫺1/2 s single oscillation. Consequently, the droplets cannot change in size upon heating, leading again to supersaturation (Fig. 1c) and eventually to nucleation (Fig. 1d), but now for droplets with a slightly different radius and density. This possibility for repeated bursts of nucleation is hinted at in Fig. 1 by the arrow pointing back from parts (d) and (e) to part (b). The stepwise decrease in the droplet size is hence due to an alternation between long periods of slow heating and a comparatively rapid relaxation after nucleation arises in the system. As a consequence, cascade nucleation involves at least two, typically quite different, time scales t 1 and t 2: The time scale t 1 ⬃ (a R opt υ s) ⫺1 characterizes the change in the optimum radius of droplets due to heating. The time scale t 2 ⬃ γ ⫺1 is set by the inverse of the decay rate γ of the number of big droplets in the system due to coalescence. When the Stokes–Einstein law is applied, t 2 depends on the distance between large droplets D big and on their diffusion velocity Ᏸ diff like t 2⫺1 ⬃ γ ⬃ Ᏸ diff /D 2big.

48

Vollmer

For a theoretical discussion of this picture from a more general point of view, we refer to Ref. 50. Here, we remark only that the bottom line of the arguments presented in that paper is that the time ∆T/υ s between subsequent bursts of nucleation scales as the geometric mean of the time scales t 1 and t 2. This leads to

冢 冣 υs ∆T

2

⫽

1 Ᏸ ⬃ a R opt υ s diff t1 t2 D 2big

(15)

Moreover, the distance D big between large droplets can be related to the composition of the microemulsion by equating D 3big with the volume occupied by N small droplets in the region of the sample containing only a single large droplet, D 3big ⫽

4π R 3opt N 3 φ d(opt)

(16)

Combining Eqs. (15) and (16) leads to the prediction ∆T 2 ⬃

R

φ

opt (opt) 2/3 d

υs

(17)

when one assumes that Ᏸ diff and N can be considered constant. For the first oscillations after crossing the emulsification boundary the radius of droplets is still very close to its value in the single-phase region, R opt ⬇ R 1Φ. In this situation, the prediction of Eq. (17) agrees remarkably well with experimental data, as demonstrated in Fig. 11. When ∆T is plotted against (υ s R 1Φ φ ⫺2/3 ) 1/2 on a log-log scale, the data for a variety of compositions and scan d speeds converge to a single line with a slope of 0.5, as predicted by Eq. (17).

D. Temperature Dependence of the Droplet–Droplet Distance In Fig. 11, the dependence of ∆T on (υ s R 1Φ φ ⫺2/3 ) 1/2 is shown only for the respecd tive first oscillations. This is the most accurate test of the theoretical prediction, because there are only small errors in the composition, which is still very close to the one in the 1Φ region. On the other hand, it leaves the question open as to how to explain the evolution of ∆T with the number of oscillations. As shown in Fig. 10, the specific heat may show a pronounced superimposed structure. To shed light on this behavior, one has to keep track of the temperature dependence of the volume fraction and radius of the microemulsion droplets. According to Eq. (2), the radius of the droplets decreases with increasing temperature. Accompanying the decrease of R opt (T), the volume fraction of droplets decreases also. To a good approximation, the small droplets account for all the interface in the sample, φ s V ⫽ 4πN R 2opt l s, and they occupy the volume φ d(opt) V ⫽ 4πN R 3opt /3.

Microemulsions

49

FIG. 11 Dependence of the period of the first oscillation log(∆T ) on log(υ s R 1Φφ ⫺2/3 ). d The symbols show the results of microcalorimetric measurements on nine different compositions and typically three different heating rates per sample. The straight line is a fit through the data points with a slope of 0.5. Sample compositions: (䉮) φd ⫽ 0.096, R ⫽ 5.8 nm; (⫹) φ d ⫽ 0.094, R ⫽ 16 nm; (䉭) φ d ⫽ 0.19, R ⫽ 5.8 nm; (䊉) φ d ⫽ 0.19, R ⫽ 6.8 nm; (䉫) φ d ⫽ 0.19, R ⫽ 15 nm; (䉭) φ d ⫽ 0.38, R ⫽ 6.0 nm; (■) φ d ⫽ 0.37, R ⫽ 8.2 nm; (䊐) φ d ⫽ 0.38, R ⫽ 11 nm; (⫻) φ d ⫽ 0.38, R ⫽ 15 nm.

In the 2Φ region φ (opt) depends on the temperature and on surfactant concentrad tion, φ (opt) ⫽ φ s /[3l s a(T ⫺ T )] according to Eq. (9). Figure 12 shows the variation d in the period of ∆T for different heating rates and two surfactant concentrations. However, now ∆T is plotted as a function of the scaling variable υ s R opt φ (opt)⫺2/3 . d The open triangles correspond to φ s ⫽ 0.1 and the filled squares to φ s ⫽ 0.05. The heating rate increases from the left (v s ⬇ 1 K/h) to the right (v s ⬇ 31 K/ h). The data points still follow the scaling of ∆T with (υ s R opt φ (opt)⫺2/3 ) 1/2. However, d in all cases one clearly discerns a superimposed nonmonotonous behavior of ∆T; . In view of it first increases and then decreases under increasing υ s R opt φ (opt)⫺2/3 d this observation, we conclude that the nonmonotonous dependence of the oscillation amplitude may be caused by a variation of the period of the oscillations due to an adiabatic change of composition. For larger ∆T also the amplitude of the oscillations increases, since the system is driven further into the metastable region and hence more heat is released when nucleation sets in.

50

Vollmer

FIG. 12 Log-log representation of the dependence of ∆T on υ s R optφ d(opt)⫺2/3. (䉮) φ s ⫽ 0.1; (■) φ s ⫽ 0.05. The scan speed increases from left to right; (䉮) υ s ⫽ 1.2, 4, 13, and 27 K/h; (■) υ s ⫽ 1.4, 4, 15, and 31 K/h.

To understand this additional temperature dependence of ∆T, the implications of volume and surface conservation for the number of droplets and the average droplet–droplet distance D d–d have to be considered. In contract to the volume fraction of droplets, their number density n increases with increasing temperature, n⬅

N φs a2 φs ⫽ ⫽ (T ⫺ T ) 2 2 V 4πl s R opt 4πl s

(18)

The average droplet–droplet distance in the 2Φ region can be estimated by assuming a locally close-packed arrangement of droplets [67]: D d–d ⯝

冢 冣冢

1 16π √2 3

1/3

冣

2/3 R opt (T) R opt ⬃ 1/3 ⬃ φ ⫺1/3 (T ⫺ T ) ⫺2/3 s (opt) 1/3 φd φs

(19)

where Eqs. (9) and (2) have been used to express φ d(opt) in terms of the conserved quantity φ s and in terms of the droplet radius R opt. D d–d decreases with increasing

Microemulsions

51

temperature and surfactant concentration. For the collision frequency, however, not the average droplet–droplet distance but the diffusion length D 2 between the interfaces of neighboring droplets is relevant. Its square root is given by D ⬅ D d–d (T) ⫺ 2R opt (T) ⫺ l s ⯝ 2(l s R )

2 1/3 opt

冤 冢 冣 冢 冣 冥⫺l 1 2π √2 φ s

1/3

R opt ⫺ ls

1/3

s

(20)

i.e., it comprises the difference of two different power laws in T ⫺ T. As a consequence, D 2 always shows a maximum. The changes in R opt, n, and D d–d with increasing temperature are schematically shown in Fig. 13. (The relationship of the droplet sizes is chosen to reflect the situations at the beginning and end of a typical experiment.) In Fig. 13a, a droplet configuration is given as it might exist close to the emulsification boundary. The droplets take their optimum radius R 1Φ ⬇ R opt (T 1); D(T 1) denotes the average distance between the respective surfaces of neighboring droplets. In Fig. 13b, at T ⫽ T 2, the mixture is deep in the 2Φ region. The size of the droplets has decreased toward R opt (T 2), and the average droplet–droplet distance has decreased toward D d–d (T 2). Due to conservation of the total interfacial area and of the volume fraction of all components, the number of droplets has increased but their total surface area is preserved. The excess water, which is no longer dissolved in the smaller droplets, has been expelled into a water-rich phase formed at the bottom of the test tube. In Fig. 14, the temperature dependence of ∆T (left axis, squares) is compared to the temperature dependence of D (T ) 2 (right axis, solid line). Similar to ∆T, for small values of (T ⫺ T ⫽ T ⫺ 305.6 K ), the distance D(T) increases with

FIG. 13 Sketch of the radius of the droplets R, the average droplet-droplet distance D d–d and the average distance between droplet boundaries D for (a) a mixture at a temperature close to the emulsification boundary T ⫽ T 1, and (b) deep in the 2Φ-region at T ⫽ T 2.

52

Vollmer

FIG. 14 The variation of ∆T and diffusion length D 2 with temperature for φ s ⫽ 0.1 and υ s ⫽ 4 K/h.

increasing temperature, then it passes a maximum at T ⫽ T max , and eventually it decreases with increasing temperature. The nonmonotonous temperature dependence of D(T) 2 arises from a crossover: Close to T, D 2 increases due to the fast decrease of R opt with increasing temperature, until at sufficiently high temperatures the diffusion length D 2 is dominated by the decrease in D d–d , which is caused by an increase in the number of droplets with increasing temperature. Similar to the volume fraction of droplets in the microemulsion phase [cf. Eq. (18)], D 2 depends solely on temperature and on surfactant concentration. On the other hand, the emulsification temperature [solving R 1Φ ⫽ R opt (T) for T ] depends on the overall volume fraction of water φ w in the sample. For sufficiently small φ w and fixed φ s, the emulsification temperature is to the right of the maximum, leading to a monotonously decreasing behavior of ∆T with increasing temperature (as noted in Ref. 46), while for sufficiently high φ w, ∆T can go through a maximum as shown in Figs. 12 and 14. To verify that the temperature-dependent change in the average distance droplet has to diffuse before it can collide with another droplet is the dominant process determining the nonmonotoneous behavior of ∆T, the data for ∆T shown in Fig.

Microemulsions

53

FIG. 15 Dependence of ∆T D ⫺2 υ ⫺1/2 on the number of oscillations N for φ s ⫽ 0.1 and s φ w ⫽ 0.33. The data points correspond to four different scan speeds. (䊐) υ s ⫽ 1.2 K/h; (䉭)υ s ⫽ 4 K/h; (*) υ s ⫽ 13 K/h; (䉫) υ s ⫽ 27 K/h.

12 were replotted. Since the presented argument does not depend on υ s, the observed square root dependence of ∆T on √υ s should remain valid [46]. Figure 15 shows the evolution of ∆TD ⫺2 υ ⫺1/2 with the number of oscillations N, i.e., s with temperature. The different symbols denote different heating rates, while the composition of the mixture is kept constant (φ s ⫽ 0.1 and φ w ⫽ 0.33). Within the margin of error, the data for ∆TD ⫺2 υ ⫺1/2 no longer depend on N, s in contrast to the pronounced maxima for ∆T shown in Fig. 12. The slight deas the heating rate increases may be due to different concencrease in ∆TD ⫺2 υ ⫺1/2 s trations of oil and surfactant in the water-rich phase. This additional change in composition (besides the expulsion of water) is more pronounced for high heating rates, because in that case the water-rich phase has less time to relax to a state close to equilibrium. This leads to more significant changes in the composition of the microemulsion phase. In any case, however, the very weak dependence of ∆TD ⫺2 υ ⫺1/2 on N strongly suggests that the observed nonmonotonous variation s of ∆T with temperature is due to the change in the average distance between droplet boundaries. This dependence of ∆T on the diffusion length supports our earlier assumption that the water transport from small to big droplets is via diffu-

54

Vollmer

sion and mass exchange during collisions of the nanometer-sized microemulsion droplets.

IV.

CONCLUSION

We have surveyed recent experimental and theoretical developments of a thermal characterization of phase transitions and the kinetics of the emulsification failure in water–oil–surfactant mixtures. As a model surfactant, we chose the nonionic surfactant C 12 E 5. Microcalorimetric measurements are demonstrated to be an efficient method to determine phase transitions, the width of the accompanying coexistence regions, and the kinetics of the phase separation. This method traces changes in the average curvature of the surfactant monolayer with a very high sensitivity [29]. Its value as a method that is complementary to more traditional approaches such as optical inspection and scattering techniques is highlighted by three findings. 1. Mixtures of water, octane, and C 12 E 5 are commonly considered as typical symmetrical surfactant mixtures, since under optical inspection the phase behavior is almost unchanged when the volume fractions of water and oil are exchanged and the temperature is varied from T to 2T ⫺ T. Surprisingly, however, for equal volume fractions of water and oil, the thermograms (cf. Fig. 4) are not at all mirror symmetrical under this change of temperature, suggesting that the symmetry does not necessarily hold on the microscopic level. Furthermore, under these conditions, the peaks are especially broad. Although the mixtures appear to be singlephase close to the microemulsion channels L 1 and L 2 , the higher level of the baseline close to the water emulsification boundary (cf. Fig. 4a) strongly suggests that almost always, microstructures of different morphologies coexist on a microscopic scale. This should be kept in mind when setting up other experiments and calculating polydispersities. 2. Microcalorimetry yields a direct measure of the latent heat ∆Q of firstorder phase transitions in the mixtures. Comparing the experimental data with the predictions of various models allows us to identify relevant contributions to the free energy describing the mixture. Quantitative predictions can most easily be performed for a large ratio of peak height to-width. In that case, the theoretical estimate for the latent heat is dominated by the bending free energy. Up to the factor T, it is to a very good approximation the difference between the slopes of the free energy functionals (in mean-field approximation) for the respective structures at their point of intersection. In addition, the latter gives a good estimate of the phase transition temperature. No fluctuations of the interface need to be considered for this. For a small peak height-to-width ratio, the extent of the twophase region has to be taken into account in calculating the latent heat (also cf. Ref. 30). We stress that the good agreement between experiments and predictions

Microemulsions

55

was obtained without fitting any parameters. It requires only a knowledge of the bending rigidities of the surfactant monolayer at the interface between the water and oil microdomains and of its spontaneous curvature. These material constants have been tabulated for many amphiphilic mixtures (e.g., in Ref. 27). Alternatively [29,47], they can be determined by fitting the results of a few independent temperature scans. 3. Crossing the emulsification boundary by means of constant heating leads to an oscillating signal for the specific heat. An alternation between a slow increase in supersaturation due to heating and a fast relaxation at strong supersaturation appears to be the origin of this dynamic instability of the phase separation. The delay of relaxation is caused by an efficient energy barrier, which the droplets have to pass in order to collectively decrease their average radius at the expense of a large droplet taking up the excess water. The height of the energy barrier can be estimated from the bending free energy of the interface. It decreases strongly with increasing degree of overheating. The time lag ∆T between bursts of nucleation depends, like √υ s, on the heating rate υ s. This dependence not only holds for a vast range of compositions but also remains valid throughout the entire phase separation process. An additional variation of ∆T with the number of oscillations is found to be properly described by the temperature-dependent change in the average distance between the surfaces of neighboring droplets, which strongly influences the transport of water from small to large droplets. This distance varies nonmonotonously with temperature due to the interplay of a temperature-induced decrease in the droplet size and increase in the number of droplets. The success of this modeling shows that the bending free energy may also serve as a starting point to describe the local equilibrium of surfactant mixtures driven far outside equilibrium. In conclusion, we point out that the presented measurements strongly suggest that (1) the temperature dependence of the preferred curvature of the surfactant monolayer, (2) the conservation of the total interfacial area, and (3) the conservation of the partial volumes of water and oil are the dominant parameters needed to understand temperature-dependent phase transitions in the considered mixtures. We expect that these are also the crucial parameters needed to describe the equilibrium properties and kinetics in other amphiphilic mixtures.

ACKNOWLEDGMENTS It is a pleasure to thank M. Schmidt for support in performing this work and R. Strey and J. Vollmer for fruitful and pleasant collaborations. Stimulating discussions with B. Du¨nweg, U. Olsson, M. Kahlweit, and M. E. Cates are gratefully acknowledged. This work has been supported by the Deutsche Forschungsgemeinschaft.

56

Vollmer

REFERENCES 1. K Hill, W von Rybinski, G Stoll. Alkyl Polyglycosides, VCH; Weinheim, 1997. 2. M Kahlweit, R Strey, G Busse. Phys Rev E 47:4197 (1993). 3. R Strey, R Schoma¨ker, D Roux, F Nallet, U Olsson. J Chem Soc Faraday Trans 86: 2253 (1990). 4. S-H Chen, S-L Chang, R Strey. J Chem Phys 93:1907 (1990). 5. W Jahn, R Strey. J Phys Chem 92:2294 (1988). 6. M Kotlarchyk, SH Chen, JS Huang, MW Kim. Phys Rev Lett 53:941 (1984). 7. GJM Koper, WFC Sager, J Smeets, D Bedeaux. J Phys Chem 99:13291 (1995). 8. G Porte, J Marignan, P Bassereau, R May. J Phys France 49:511 (1988). 9. F Nallet, D Roux, J Prost. Phys Rev Lett 62:276 (1989). 10. U Olsson, P Schurtenberger. Langmuir 9:3389 (1993). 11. S Clark, PDI Fletcher, X Ye. Langmuir 6:1301 (1990). 12. EW Kaler, KE Bennett, HT Davis, LE Scriven. J Chem Phys 79:5673. EW Kaler, HT Davis, LE Scriven. J Chem Phys 79:5685 (1983). 13. G Gompper, M Schick. In: Phase Transitions and Critical Phenomena, Vol. 16 (C Domb, JL Lebowitz, eds.), Academic Press, London, pp. 1–175. 14. PG De Gennes, C Taupin. J Phys Chem 86:2294 (1982). 15. SA Safran, LA Turkevich, P Pincus. J Phys Lett 43:2903 (1984). 16. B Widom. J Chem Phys 81:1030 (1984). 17. D Andelman, ME Cates, D Roux, SA Safran. J Chem Phys 87:7229 (1987). 18. DH Anderson, H Wennerstro¨m, U Olsson. J Phys Chem 93:4243 (1989). 19. ME Cates, D Andelman, SA Safran, D Roux. Langmuir 4:802 (1988). 20. J Daicic, U Olsson, H Wennerstro¨m. Langmuir 11:2451 (1995). 21. U Schwarz, K Swamy, G Gompper. Europhys Lett 36:117 (1996). 22. D Vollmer, J Vollmer, R Strey. Phys Rev E 54:3028 (1996). 23. U Olsson, H Wennerstro¨m. Adv Colloid Interface Sci 49:113 (1994). 24. P Pieruschka, U Olsson. Langmuir 12:3364 (1996). 25. D Roux, N Nallet, E Freyssingeas, G Porte, P Bassereau, M Skouri, J Marignan. Europhys Lett 17:575 (1992). 26. CR Safinya, EB Sirota, D Roux, GS Smith. Phys Rev Lett 62:1134 (1989). 27. T Sottmann, R Strey. J Chem Phys 106:8605 (1997). 28. F Sicoli, D Langevin, LT Lee. J Chem Phys 99:4759 (1993). 29. D Vollmer, R Strey. Europhys Lett 32:693 (1995). 30. D Vollmer, J Vollmer, R Strey, H-G Schmidt, G Wolf. J Thermal Anal 51:9 (1998). 31. R Strey. Colloid Polym Sci 272:1005 (1994). 32. J Arrault, C Grand, W Poon, M Cates. Europhys Lett 38:625 (1997). 33. O Diat, D Roux, F Nallet. J Phys II 3:1427 (1993). 34. O Diat, D Roux, F Nallet. Phys Rev E 59:3296 (1995). 35. M Bergmeier, H Hoffmann, C Thunig. J Phys Chem B 101:5767 (1997). 36. M Buchanan, J Arrault, ME Cates. Langmuir 14:7371 (1998). 37. K Mishima, K Yoshiyama. Biochim Biophys Acta 904:149 (1987). 38. I Sakurai, T Suzuki, S Sakurai. Biochim Biophys Acta 985:101 (1989). 39. CA Miller, KH Raney. Colloid Surfact A 74:169 (1993). 40. R Bar-Ziv, E Moses. Phys Rev Lett 73:1392 (1994).

Microemulsions 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.

57

RE Goldstein, P Nelson, T Powers, U Seifert. J Phys II France 6:767 (1996). J Morris, U Olsson, H Wennerstro¨m. Langmuir 13:606 (1997). H Wennerstro¨m, J Morris, U Olsson. Langmuir 13:6972 (1997). A Kabalnov, J Weers. Langmuir 12:1931 (1996). D Vollmer, P Ganz. J Chem Phys 103:4697 (1995). D Vollmer, R Strey, J Vollmer. J Chem Phys 107:3619 (1997). D Vollmer, J Vollmer. Physica A 249:307 (1998). SA Safran, LA Turkevich. Phys Rev Lett 50:1930 (1983). J Vollmer, D Vollmer, R Strey. J Chem Phys 107:3627 (1997). J Vollmer, D Vollmer. Faraday Disc 112:51 (1999). D Langevin, J Meunier. In: Micelles, Membranes, Microemulsions, and Monolayers (WM Gelbart, A Ben-Shaul, D Roux, eds.) Springer-Verlag, Berlin, 1994, pp. 485– 519. K Bonkhoff, A Hirtz, GH Findenegg. Physica A 172:174 (1991). M Kahlweit, R Strey, G Busse. J Phys Chem 94:3881 (1990). R Strey, O Glatter, K-V Schubert, EW Kaler. J Chem Phys 105:1175 (1996). JH Schulmann, W Stoeckenius, LM Prince. J Phys Chem 53:1677 (1959). M Kahlweit, R Strey. Angew Chem Int Ed 24:654 (1985). M Kahlweit, R Strey, P Firman. J Phys Chem 90:671 (1986). H Bagger-Jo¨rgensen, U Olsson, K Mortensen. Langmuir 13:1413 (1997). PA Winsor. Trans Faraday Soc 44:376 (1948). M Gradzielski, D Langevin, T Sottmann, R Strey. J Chem Phys 106:8232 (1997). W Helfrich. Z Naturforsch C 28:693 (1973). W Helfrich. Z Naturforsch C 33a:305 (1978). SA Safran. Phys Rev A 43:2903 (1991). D Vollmer, J Vollmer, R Strey. Europhys Lett 39:245 (1997). K Binder. Rep Prog Phys 50:783 (1987). JL Gunton, M San Miguel, PS Sahni. In: Phase Transitions and Critical Phenomena, Vol. 8. (C Domb, JL Lebowitz, eds.), Academic Press, New York, pp. 1–175. NW Ashcroft, ND Mermin. Solid State Physics, Holt-Saunders, Philadelphia, 1976.

3 Subzero Temperature Behavior of Water in Microemulsions SHMARYAHU EZRAHI Materials and Chemistry Department, The Ordnance Corps, Israel Defense Forces, Ramat Gan, Israel ABRAHAM ASERIN, MONZER FANUN, and NISSIM GARTI Casali Institute of Applied Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel

I. Introduction II.

The Behavior of Water Near Surfaces

60 60

III. State of Water

61

IV.

63

Methodology

V. Information Obtained via the Exothermic Scanning Mode A. Structural transitions B. Percolation transitions VI.

VII.

67 67 69

Information Obtained via the Endothermic Scanning Mode A. Ethoxylated alcohols B. Ethoxylated siloxanes C. Sucrose esters D. Phosphatidylcholine

76 76 77 77 80

Results and Discussion A. Variation of water peak temperatures with water content B. Full hydration of the surfactant C. Free water D. Nonfreezable water E. Evaluation of the thickness of the bound water layer F. Alcohol interaction with other constituents

80 80 83 87 89 93 94

59

60

Ezrahi et al.

G. Exothermic peaks H. The problem of phase separation

98 107

VIII. Conclusion

113

References

114

I. INTRODUCTION The purpose of this review is to examine several methodological aspects concerning the use of subzero temperature differential scanning calorimetry (hereafter designated as SZT-DSC), for the study of surfactant–water interactions and to highlight some recent results related to (mostly) nonionic microemulsions. In contrast to the common view that there need not be any a priori relation between properties of hydration measured at low temperatures and those measured at room temperature [1], we shall try to show that if the water–surfactant interaction is defined in terms of a perturbation to the freezing (or melting) of water at about 0°C, then the thermal behavior of microemulsions at ambient temperature is directly related to that at subzero temperatures. It should be stressed that SZT-DSC allows us only a dim glance into the microstructure of microemulsions and an even dimmer glance into its details. Yet the combination of SZT-DSC data and the results of spectroscopic measurements may deepen our understanding of these problems, as will be shown in this review. The review is organized as follows. First we define several states of water in terms of their thermal behavior. Then we compare the exothermic and endothermic modes of SZT-DSC and discuss how to evaluate the relative amounts of free and bound water in a microemulsion sample. After some information obtained via the exothermic scanning mode is demonstrated, we concentrate on the endothermic scanning mode. We analyze the distribution of free and bound water as a function of (total) water content in microemulsion systems. This is followed by a discussion of nonfreezable water and evaluation of the thickness of the bound water layer. The interaction of alcohol with other components of microemulsion systems and the significance of exothermic peaks are also highlighted. Special emphasis is put on the often ignored problem of phase separation during the cooling and freezing of microemulsion samples. Finally, the role of SZT-DSC in the investigation of microemulsions is summarized.

II.

THE BEHAVIOR OF WATER NEAR SURFACES

It is widely known that liquid water departs considerably from its average bulk behavior due to the presence of adjacent interfaces, be they organic, such as biomembranes and proteins, or inorganic, such as clays and ion exchangers [2,3].

Subzero Behavior of Water in Microemulsions

61

The investigation of the interaction between water and such interfaces is relevant to the study of such problems as the behavior of water in living organisms [4,5] and sludge dewatering [6]. Moreover, water enclosed in very small volumes plays a dominant role as the medium that controls structure and behavior near biological membranes, for example, and microemulsions may well serve as model systems for the study of water in confined spaces [2,7,8].

III. STATE OF WATER When describing the state of water in relation to any surface, several distinguishably different types of water, ranging from the most tightly bound (nonfreezable) to free, bulk-like water, may be considered. Besides the general distinction between ‘‘free’’ and ‘‘bound’’ water, more detailed classifications have been suggested. Senatra et al. [9], for example, have used a differentiation based on the difference in melting (freezing) points: 1. ‘‘Free’’ water melts at 0°C. 2. ‘‘Interphasal’’ (or ‘‘interfacial’’ [8]) water melts at about ⫺10°C. 3. ‘‘Bound’’ water melts at temperatures lower than ⫺10°C. The distinction between ‘‘interphasal’’ and ‘‘bound’’ water is based on empirical observations pertinent to specific surfactant-based systems (including some of our model systems, as is shown later on). The melting temperatures of these types of water vary as a function of composition. Two examples will suffice to show our point. Thus, altering the (total) water content may shift the melting point of interphasal water between ⫺15°C and ⫺5°C in some cases. In other cases the shift is only 2–3 degrees. Also, the transition from quaternary systems (containing water, alcohol, oil, and surfactant) to binary systems (containing water and surfactant) shifts the melting point of interphasal water to higher (less negative) temperatures, as is demonstrated later in relation to our model system A (see Section VI.A). The melting temperature, ⫺10°C, is just an arbitrary (and not always sharp) limit between various grades of water–surfactant interactions. Moreover, it should also be emphasized that the attribute ‘‘bound’’ does not refer to covalent binding but rather to dipole–dipole interactions (in nonionic systems) and dipole– ion interactions (in ionic systems). Thus, the degree of order and mobility and the strength of the binding in water–surfactant interactions are lower than might be inferred from the somewhat misleading term ‘‘bound’’ water [10]. Thermograms depicting these three types of water are shown in Fig. 1 for the system dodecane–potassium oleate–water–hexanol [11]. Schulz [8] classified water in microstructured systems in a more descriptive way:

62

Ezrahi et al.

FIG. 1 Typical DSC thermograms of K-oleate–hexanol–dodecane–water microemulsion samples. Surfactant/oil ⫽ 0.2 g/mL; alcohol/oil ⫽ 0.4 ml/mL; water/(water ⫹ oil) ⫽ 0.222–0.4 g/g. Curve a, W/O microemulsion sample; curve b, D 2O/oil microemulsion sample. Endothermic peaks due to the fusion of D 2O (277 K), ‘‘free’’ water (273 K), dodecane and ‘‘interphasal’’ water (263 K), ‘‘bound’’ water (233 K), and hexanol (220 K) were identified. (From Ref. 11.)

1. 2. 3. 4.

Free water Interstitial water, which remains unfrozen at temperatures well below the normal freezing point Surface water—physically and/or chemically adsorbed water Internal water—chemically bound water

The nature of water–substrate interactions and the extent to which water is bound have been investigated using spectroscopic methods such as nuclear magnetic resonance (NMR) [2,12–14], infrared (IR) spectroscopy [15–21], electron spin resonance (ESR) [12], and calorimetric methods, which may be divided into ambient [21–25] and low-temperature [11,12,26,27] measurements. In aqueous solutions of several globular proteins, the degrees of hydration calculated from calorimetric and NMR measurements of frozen samples agree well [28]. In the case of tropocollagen, for instance, hydration numbers of 2.4 and 2.7 mol water per residue were evaluated by using calorimetric and NMR techniques, respectively [29].

Subzero Behavior of Water in Microemulsions

63

Analysis of low-temperature thermal events such as freezing and supercooling is important for understanding the behavior of water in microporous materials, gels, biological tissues, foods, and other microstructured fluids at subzero temperatures [8].

IV.

METHODOLOGY

Low-temperature behavior of surfactant-based systems may conveniently be investigated by utilizing SZT-DSC. Such measurements are usually performed in either the exothermic (i.e., controlled cooling of samples) or endothermic (i.e., controlled heating of previously frozen samples) scanning mode. A characteristic feature of the exothermic mode is the supercooling (or undercooling) phenomenon. Under equilibrium conditions, water freezes at 0°C and ice is the stable phase at subzero temperatures. Usually, in the absence of ice crystallites, water will remain liquid below 0°C. The degree of this supercooling depends on factors such as the volume of water, its purity, and the cooling rate. Once frozen, this unstable, supercooled liquid state cannot be regained directly by heating; the ice must first be melted at 0°C [30]. Actually, the melting of ice in a polycrystalline sample begins at subzero temperatures. The freezing point depression of water between ice crystals is due to the occurrence of hydration forces in thin films of water. These forces cause the chemical potential and freezing point of water to decrease with decreasing film thickness. Thus, the onset of ice melting (as determined by the beginning of the deviation of the endotherm from the baseline) occurs at about ⫺50°C [30]. In a similar way, the separation of ice from the aqueous solution is based on the generation of crystal nuclei, which are capable of growing into macroscopic crystals. Nucleation is a stochastic process caused by random density fluctuations owing to Brownian diffusion of molecules and leading to the formation of a transient embryonic crystallite that has a sufficiently long lifetime for further condensation of molecules to occur. The nucleation probability at any subzero temperature is inversely proportional to the volume of the water droplets [31]. The almost inevitable presence of particulate matter leads to ice formation via a heterogeneous nucleation mechanism at a temperature that depends on the catalytic efficiency of the catalyst particle, its radius of curvature, and its degree of wetting by ice and water. For example, in suspensions of dipalmitoylphosphatidylcholine (hereafter designated as DPPC) vesicles, the formation of ice by such a mechanism occurs first in the extraliposomal space at about ⫺20 to ⫺25°C. The remaining supercooled water will diffuse through the phospholipid bilayers to the ice-containing regions or will form ice between the bilayers via a homogeneous nucleation mechanism at about ⫺45 to ⫺50°C. The slower the cooling rate, the smaller the amount of water that will freeze after homogenous nucleation [30].

64

Ezrahi et al.

In both modes, the calorimeter measures and records the heat flow rate (dH/ dt) of the samples as a function of temperature T, while the samples undergo the aforementioned thermal events (in accordance with the respective scanning mode). The instrument also determines the total heat transferred in the observed thermal processes. The enthalpy changes associated with thermal transitions are evaluated by integrating the area of each pertinent peak [10]. DSC peaks obtained in the exothermic mode are sharper than those of the endothermic mode. This was ascribed to the effect that the substrate had on the melting process, while ice nucleation has preserved its autonomy [32]. Moreover, the overlapping of close peaks, which may occur in the endothermic mode, is not usually observed in the exothermic mode [8] (albeit peak overlap is still problematic in aqueous solutions of polyethylene glycols of sufficiently high molecular weights [33]). Cooling curves were utilized by de Vringer et al. [34]. However, the experimental determination of the enthalpy of fusion is difficult, even if the effect of supercooling is allowed for [33]. On the other hand, it has been argued [35] that the exothermic scanning mode may be used to obtain microstructural information about microemulsions. In our opinion, such information should be treated with caution and be fully corroborated by independent techniques. Even then, we must often settle for something less than a detailed microstructural picture of microemulsions. The endothermic scanning mode is more frequently used to circumvent possible complications from supercooling. In the following, we show some of the results obtained in the endothermic mode for several types of (mostly) nonionic microemulsions. We followed the method used by Senatra et al. [2,9,11,36–39] in which the endothermic scanning mode was applied and the peaks representing various states of water were identified and analyzed. The simple but elegant way by which Senatra and coworkers solved the problem of identifying interphasal water in dodecane-containing systems should be noted. Both interphasal water and dodecane melt at about ⫺10°C, thus leading to overlapping of their fusion peaks. However, the existence of interphasal water may be clearly shown by taking the following into consideration [10]: 1.

The heat of fusion, measured at ⫺10°C, is higher than that required for the known amount of dodecane in the system. By subtracting the enthalpy change due to the dodecane, the contribution of the interphasal water is readily calculated by the equation [10] WI ⫽

∆H I (exp) ⫺ ∆H D f D ⫻ 100 ∆H I

(1)

where W I is the interphasal water concentration (in weight percent); ∆H I (exp) is the measured enthalpy change for the ⫺10°C peak, which includes contributions of interphasal water and dodecane; ∆H D is the heat of fusion

Subzero Behavior of Water in Microemulsions

65

of pure dodecane (191.6 J/g); f D is the dodecane weight fraction; and ∆H I is the heat of fusion of interphasal water. This enthalpy depends on the polymorphic form of ice that is assumed by the interphasal water at its freezing points. Some authors neglect the polymorphism of ice and use the crystallization enthalpy of water without introducing an appreciable error [40]. We followed Senatra et al. [26] and used the corrected enthalpy: ∆H I ⫽ 312.28 J/g. In some systems, part of the oil may be trapped between the alkyl chains of the surfactant. For example, in the system water–AOT (dioctyl sulfosuccinate)–isooctane, only about 50% of the oil contributed to the melting peak [41]. In such a case, an appropriate correction should obviously be applied. 2. The endothermic peak at ⫺10°C remained in the absence of dodecane or when hexadecane was substituted for dodecane [10,26,35,37,38,42] (see Fig. 2). 3. Analysis of samples in which D 2O was used instead of water, with all other components and compositions being the same, showed a typical shift of the D 2O-relevant endothermic peaks toward higher temperatures [2,10,11,35,36,39,41–47] (see Fig. 1). In a similar way, the concentration of free water is calculated, using the equation [8,10] WF ⫽

∆H F (exp) ⫻ 100 ∆H°F

(2)

where W F is the free water concentration (in weight percent), ∆H F (exp) is the measured enthalpy change for the 0°C peak, and ∆H°F is the heat of fusion of pure water, measured at the same experimental conditions. The heat of fusion of freezable water is slightly lower than that of pure water (about 334 J/g). We measured ∆H°F ⫽ 323.72 J/g [10,45]. A similar value (321 J/g) was extrapolated from data derived for the water–polyoxyethylene 1550 system during the heating stage of the DSC cycle [34]. Antonsen and Hoffmann [33] measured ∆H°F ⫽ 307 J/g. For our model system A (a quaternary microemulsion; see below) we obtained [45] ∆H°F ⫽ 308 J/g by a similar extrapolation procedure, in good agreement with our measured ∆H°F ⬃ 324 J/g for pure water [10,45]. Even lower values of ∆H°F were obtained in binary water–polymer systems by extrapolating ∆H I (exp) vs. polymer weight fraction (w 1) plots to w 1 ⫽ 0. Thus, for aqueous solutions of methoxypoly(ethylene glycol) 750 and polyoxyethylene 440, the extrapolated enthalpy of melting for pure water was 280 and 246 J/g, respectively [33]. For a polyoxyethylene 1550–water system investigated in the exothermic mode, the extrapolated ∆H°F was 289 J/g [34]. These rather low values were ascribed to overlapping between peaks of free and interfacial water. The same phenomenon occurs in biopolymers, and it was attributed to the presence of small amounts of solutes in the water [48].

66

Ezrahi et al.

FIG. 2 Differential scanning calorimetric endotherms of the system K-oleate ⫹ hexanol 3: 5 (w/w)–hexadecane (samples a, b, c) or dodecane (sample d)–water. In all samples, the surfactant/oil weight ratio is 0.68 and the water concentration C was expressed as the weight ratio of added water to total sample. C a ⫽ 0.071, C b ⫽ 0.108, C c ⫽ 0.290, C d ⫽ 0.275; dT/dt ⫽ 4 K/min. ∆H x , ∆H b , (∆H w) 263, ∆H d , ∆H w, and ∆H h are the enthalpies of fusion for hexanol, bound water, interphasal water, dodecane, free water, and hexadecane, respectively. Note that the dodecane peak at 263 K superimposes on the peak of interphasal water shown for sample b. (From Ref. 38.)

Neglecting [34] the heat of mixing may also contribute to the decrease in ∆H°F : The area under the endothermic peak about 0°C represents the heat consumed in the melting of ice not to pure water but rather to water in a mixed phase. This contribution is, however, rather small [49]. For example, in 10% polyoxyethylene–90% water solutions, the correction is only 5 J/g [34]; for 50 wt% water–50 wt% polyoxyethylene, this correction is about 6 J/g [34]. When the decrease in the melting point of pure water is significant, the following correction should be applied [50]:

Subzero Behavior of Water in Microemulsions

67

∆H F ⫽ ∆H°F ⫹ (C P,W ⫺ C P,I)(T f ⫺ 273.16)

(3)

where T f is the fusion temperature and C P,W ⫺ C P,I is the difference between the respective specific heats of liquid water and ice, which is usually taken as 2.3 J/(g ⋅ K) [34]. The original designation of the enthalpic terms was changed in order to adjust it to that of Eqs. (1) and (2). The correction for supercooling (including melting point depression) leads to ∆H°F ⫽ 325 J/g, using the exothermic mode for polyoxyethylene 1550–water systems [34]. Another prediction of the enthalpy of the ice–water transition in bulk is based on its lowering by about 1% per 1°C depression. With the addition of surface effects the apparent enthalpy may be lowered to about 200 J/g. Thus, the enthalpy of ‘‘ice’’ melting inside the aqueous spacing between bilayers of DPPC was evaluated as about 173 J/g [32]. An additional method for the determination of the bound water fraction is to use the equation [51] φ⫽1⫺

∆H m f ∆H w

(4)

where φ is the fraction of nonfreezing (bound) water, f is the weight fraction of water present in the sample, ∆H m is the measured enthalpy change, and ∆H w is the heat of fusion of pure water at 0°C (∆H°F in our notation). According to de Vringer et al. [34], the method based on Eq. (4) is very sensitive to small errors in the measured enthalpy changes or in the estimated water fractions for samples with a high water content.

V. INFORMATION OBTAINED VIA THE EXOTHERMIC SCANNING MODE In spite of the aforementioned complications, several studies have used the exothermic scanning mode to obtain more insight into the structure of microemulsions and to identify percolation processes in model systems.

A. Structural Transitions Senatra et al. [35] studied the system H 2O–hexadecane or dodecane–K-oleate– hexanol [with mass ratios K-oleate: hexanol ⫽ 0.6 and (K-oleate ⫹ hexanol): oil ⫽ 0.4]. They argued that the exothermic scanning mode may provide some information about the structural modifications occurring in the system as a function of water content. Typical thermograms recorded in the exothermic mode are shown in Fig. 3. The compositions of all the microemulsions tested lie along the dilution line PP′ (see Fig. 4).

68

Ezrahi et al.

FIG. 3 DSC-exo recordings of the water in hexadecane microemulsion samples with increasing water content C (expressed as the weight ratio of added water to total sample). Concentrations: C a ⫽ 0.069, C b ⫽ 0.087, C c ⫽ 0.105, C d ⫽ 0.138, C e ⫽ 0.169, C f ⫽ 0.25; dT/dt ⫽ 2 K/min. The designation iso.T refers to a 10 min isothermal period that followed the dynamic part of the thermogram. ∆H h , ∆H w, ∆H b , and ∆H x are enthalpy changes relating to hexadecane, water, bound water, and hexanol, respectively. (From Ref. 35.)

The variation of water freezing temperature T wfz with (total) water content C is considered to provide structural information (see Fig. 5). The plateaus in Fig. 5 are thought to indicate microstructural transitions as summarized in Table 1. A basic question that might be raised here concerns whether objective criteria for establishing this quite detailed picture can be ascertained. We can seldom reach this level of description with regard to microstructure of surfactant-based systems when we rely on only calorimetric data. The salient features of such

Subzero Behavior of Water in Microemulsions

69

FIG. 4 Pseudoternary phase diagram of the water in hexadecane system. All measurements were performed in microemulsion samples whose compositions lie on the experimental path PP′. According to Clausse [52], line Γ 1 defines compositions at which all the available surfactant molecules are engaged in shells of W/O micelles possessing a core of ‘‘free’’ water. Line Γ 2 defines compositions at which the system forms nonspherical micelles or, more likely, micellar clusters resulting from the aggregation of spherical micelles that tend to ‘‘flocculate’’ so as to offer the optimum surface-to-volume ratio. Dots on the PP′ line correspond to the composition of the samples at the intersection points between the PP′ line and the W/O microemulsion monophasic domain (dots 1 and 5) as well as between the PP′ line and the curves designated by Γ 1 and Γ 2. LC designates a liquid crystalline phase region. (From Ref. 35.)

structural transitions as those described in Table 1 should obviously be substantiated by more direct evidence. However, since the initial concentration of the surfactant on the dilution line PP′ is relatively high (weight fraction of 0.6 ⫻ 0.4 ⫽ 0.24), spectroscopic methods would fail to give accurate details. As an alternative (albeit similar) interpretation we would suggest that a plateau in a T wfz vs. C plot means that the strength of the water–surfactant interaction is approximately the same within the respective concentration subinterval. The difference between the plateaus just reflects the difference between various grades of such interactions, which may not be directly related to definite microstructures.

B. Percolation Transitions It is known [53–63] that percolation processes are revealed at certain volume fractions of droplets or at specific temperatures (designated here as T P). Senatra

70

Ezrahi et al.

FIG. 5 Water freezing temperature T wfz versus increasing water concentration C for the water in hexadecane system. Values taken from DSC recordings performed at 2 K/min. The first experimental point reported corresponds to the very first exotherm observed at C b ⫽ 0.087. (From Ref. 35.)

et al. [41] showed that the thermal behavior of ‘‘percolative microemulsions’’ could be readily characterized. The first-order exotherms associated with the freezing of the dispersed phase did not show a sharp, well-shaped peak but rather a distribution of thermal events that were not always well separated (Figs. 6–8). They interpreted these typical thermograms by assuming that the nonuniform water clusters (or pools) formed at temperatures close to T p freeze at different temperatures when the system undergoes the exothermic scanning procedure. The smaller the water cluster, the lower its freezing temperature. T p was identified using three methods [41]: 1.

2. 3.

Electrical conductivity measurements as a function of temperature. It is known that at a certain temperature (or volume fraction of droplets) the electrical conductivity increases sharply by several orders of magnitude [56–58]. Heat capacity measurements as a function of temperature [59]. DSC recording (dH/dt vs. dT ). T p is revealed as a peak in the plot.

≠0 ≠0 ≠0

0.122–0.198 0.198–0.273 0.273–0.355

(∆H w) 263

Interphasal water b

∆H h ⫽ ∆H°h ∆H h ⯝ ∆H°h ∆H h ⬍⬍ ∆H°h

∆H h ⫽ ∆H°h ∆H h ⫽ ∆H°h

Hexadecane c — Small ∆H w contribution 1st plateau 2nd plateau 3rd plateau

Enthalpy contribution 1st ∆H w exotherm ∆H w ≠ 0 ∆H w ≠ 0 ∆H w ≠ 0

(∆H w) fz

b

242 249 252

— 234

T wfz

DSC-EXO study d

(Total) water concentration (ⱕ)intervals within which typical thermal events occur. (∆H w) 263 ⫽ enthalpy change of interphasal water. (This type of water melts at 263 K). c ∆H°h ⫽ enthalpy change of pure hexadecane. d (∆H w) fz ⫽ enthalpy change of water at freezing. Source: Ref. 35.

a

— —

Free water

DSC-ENDO study

冧 冧

From monodisperse W/O droplets to the appearance of larger droplets: prolate elipsoids (onset of bicontinuous structure?)

From hydrated soap aggregates to the onset of W/O microemulsions

Type of structure

Thermal Characteristics of W/O Microemulsions in the System Water–Hexadecane–K-Oleate–Hexanol

0.03–0.105 0.105–0.122

∆C a

TABLE 1

Subzero Behavior of Water in Microemulsions 71

72

Ezrahi et al.

FIG. 6 Top: DSC-exo thermogram of the system D 2O–sodium dioctylsulfosuccinate, hereafter designated as Na(AOT)–decane [volume fraction (water ⫹ surfactant)/total ⫽ 0.35; molar ratio of water to surfactant ⫽ 40.7]. The 4 K difference in the D 2O melting temperature with respect to that of H 2O helps to distinguish between the freezing contributions of water and decane (which, due to supercooling, freeze at about the same temperature) and shows the spreading of the exothermic peaks due to the freezing of the dispersed phase. Bottom: The corresponding endo spectrum compared with DSC recording of the system water–Na(AOT)–decane [volume fraction (water ⫹ surfactant)/ total ⫽ 0.35; water/surfactant molar ratio ⫽ 40.8]. The 10 min isothermal period that followed or preceded the dynamic part of the thermogram is also shown. (From Ref. 41.)

The use of SZT-DSC in relation to percolation transitions (which obviously occur at ambient temperatures) requires close scrutiny. The detection of T p is very sensitive to experimental conditions such as the type of surfactant, heating rate, and thermal history [41]. Thus, Senatra et al. could not detect the percolation transition a second time immediately after it had occurred (Fig. 9), implying that

Subzero Behavior of Water in Microemulsions

73

FIG. 7 DSC-exo (top) and endo (bottom) of two samples of the system water– Na(AOT)–isooctane [volume fraction (water ⫹ surfactant)/total ⫽ 0.31; water/surfactant molar ratio ⫽ 37]. The isooctane freezes at 145 K and thus does not influence the thermal behavior of the water phase. Curve 1, T 0 (the temperature at which the samples were kept isothermally at the very beginning of the DSC analysis) ⫽ 313 K; curve 2, T 0 ⫽ 300 K. The small exotherm in the melting curve is due to recrystallization. (From Ref. 41.)

liquid samples first frozen and then thawed maintain the memory of their thermal history. Relying on these data to answer the question of how the microemulsion structure is altered due to freezing is not a simple matter. ‘‘Percolation’’ is a term frequently used to describe microemulsions as having a bicontinuous structure. However, ‘‘bicontinuity’’ describes a situation with dynamic equilibrium structure that results from a particular spontaneous curvature of the surfactant films, with a minor contribution of the volume fraction of the specific solvent. Thus, at the same composition, different systems may have either water droplets, oil droplets, or a bicontinuous structure. ‘‘Percolation’’, on the other hand, describes

74

Ezrahi et al.

FIG. 8 DSC-exo thermograms of the system water–Ca(AOT) 2 –decane. Microemulsions of this system do not percolate. Curve 1, T 0 ⫽ 308 K; curve 2, T 0 ⫽ 298 K; curve 3, T 0 ⫽ 283 K. (From Ref. 41.)

a process conceived as a temporary opening of extended pathways between droplets [64]. The difference between these two concepts was highlighted by using DSC measurements. Vollmer et al. [59] demonstrated that T p does not coincide with the temperature of formation of a single-phase bicontinuous structure, T b . In fact, T p may be several degrees below T b. All this may prima facie be considered not to be connected with SZT-DSC. Yet the very fact that a percolative transition was observed after the microemulsion sample had been frozen (and thawed) in the first thermal cycle and the characteristic thermograms (Figs. 6 and 7) clearly show that the freezing process did not cause the microemulsion to separate into just oil and water bulk phases. This conclusion is further supported by the observation that microemulsion samples that had been quenched in liquid

Subzero Behavior of Water in Microemulsions

75

FIG. 9 (a) DSC recordings of the percolative transition in water–Na(AOT)–decane microemulsions. (1) T 0 (temperature of the isothermal stage at the very beginning of the DSC analysis) ⫽ 303 K, sample mass 18.250 mg; (2) T 0 ⫽ 278 K, mass 13.413 mg; (3) T 0 ⫽ 302 K, mass 10.259 mg. (b) Top: Onset analysis of the transition of curve 3 of part (a). Bottom: Curve 1, an oscillating trend obtained by measuring a second time the higher order phase transition with or without again following the temperature scanning procedure used for the detection of T p . Curve 2, an example of failure recorded on a sample of water–Na (AOT)–decane microemulsion [volume fraction of (water ⫹ surfactant)/total ⫽ 0.35; water/surfactant molar ratio ⫽ 40.8]. If a scan speed of 4 K/min is applied during the scanning procedure used for the determination of T p, the percolative transition escapes detection. (From Ref. 41.)

nitrogen did not phase separate. After several cycles of freezing and thawing, once melted, the samples that were marble white in their frozen state appeared newly isotropic and transparent. Only microemulsions with compositions close to the transition line between the one-phase and two-phase domains were unstable and phase separated [35]. The inability to detect T p in the consecutive thermal cycles may be connected with the presumed mechanism underlying the percolation transition. For example, Vollmer et al. [59] suggested that at room temperature surfactant molecules in the contact area of two droplets may be excited to flip. This entropy-driven mechanism might fail if the heating rate in the thermal cycles were too fast for the water and surfactant molecules to reorganize themselves. More work is certainly needed to clarify this point. An additional underlying cause for this behavior may be the distillation of some free water from the aqueous system onto the lid of the sample pan and its subsequent freezing in the cooling stage of the DSC cycle. This amount of evaporated water (or part of it)

76

Ezrahi et al.

might not participate in the dynamic processes that lead to percolation if the preceding isothermal step, 20 K below T p [41] is too short (only 10 min) [41]. Condensation and subsequent freezing of water on the DSC pan lid were also suggested as an explanation for the appearance of an ice-melting peak at about 0°C during the warming of frozen solutions of polyvinylpyrrolidone and hydroxyethyl starch [65] and in DPPC–water dispersions [30]. In our opinion, this evaporating water is free in the sense that it has virtually no interaction with the surfactant (or polymer) molecules. Such water molecules would melt at about 0°C even if they are not involved in the evaporation and condensation processes. Therefore, the relative distributions of free and bound water do not change. Our argument may prima facie seem to be hardly tenable, since it was found that the endothermic peak at about 0°C did not appear when the samples were covered by oil [30,66]. Yet a three-component [surfactant (or polymer)–water–oil] system does not necessarily have the same structure as the binary [surfactant (or polymer)– water] one. The addition of oil may restrict the mobility of both evaporating and nonevaporating ‘‘free’’ water molecules. The melting peak of ‘‘less free’’ water (for example, in a core of a W/O microemulsion before the inversion to an O/W microemulsion) shifts to lower (more negative) temperatures [10,45]. In such a case, it may merge into the broad endothermic peak of ‘‘bound’’ water. The general problem of phase separation, due to freeze–thaw cycles, is further discussed in the following section VII.H.

VI.

INFORMATION OBTAINED VIA THE ENDOTHERMIC SCANNING MODE

The endothermic scanning mode is more frequently used than the exothermic mode in SZT-DSC measurements. We exemplify the information that can be obtained from such a technique by reviewing some recent results related to several model systems based on various types of nonionic (and zwitterionic) surfactants that we studied with SZT-DSC.

A. Ethoxylated Alcohols System A. Water–pentanol ⫹ dodecane 1:1 (by weight)–octaethylene glycol mono n-dodecyl ether) [hereafter designated as C 12 (EO) 8]. This system was investigated along the water dilution line for which the surfactant/alcohol/ oil weight ratio is 2: 1:1. Henceforth, this dilution line is marked as W5 (see Fig. 10). System B. Water–butanol ⫹ dodecane 1:1 (by weight)–polyoxyethylene [10] oleyl alcohol [hereafter designated as C 18 :1 (EO) 10 or Brij 97]. This system was investigated along the water dilution line for which the surfactant/alcohol/

Subzero Behavior of Water in Microemulsions

77

FIG. 10 Phase diagram for the system dodecane ⫹ pentanol 1: 1 (by weight)–C 12 (EO) 8 – water at 27°C. The dashed line represents the water dilution line W5 along which the dodecane/pentanol/C 12 (EO) 8 weight ratio is 1: 1: 2. LC designates the liquid crystalline phase region. (From Ref. 67.)

oil weight ratio is 4: 3:3. Henceforth, this dilution line will be marked as XB4 (see Fig. 11).

B. Ethoxylated Siloxanes Another group of model systems was based on polymethylhydrogen siloxanes (PHMS) grafted with polyoxyethylene (POE). As a representative of this group we used the surfactant known by its commercial name Silwet L-7607 (molecular weight 1000; EO content 75 wt%). System C. Water–Silwet L-7607–dodecanol. This system was investigated along two water dilution lines for which the oil (dodecanol)/surfactant weight ratios are 1: 1 and 7: 3, respectively [46] (see Fig. 12).

C. Sucrose Esters Sucrose esters have two attractive properties: biocompatibility and temperature insensitivity [68–77]. We are investigating microemulsions based on sucrose esters in order to use them as microreactors for enzymatic and chemical reactions [42,78,79]. SZT-DSC has been applied to model microemulsion systems based on sucrose monostearate (HLB 15, also designated as S-1570). System D. Water–butanol ⫹ dodecane 1: 1 (by weight)–S-1570. The thermal behavior of this system was studied along two dilution lines for which the surfactant/alcohol/oil weight ratios were 0.94: 1:1 and 1.5: 1:1, respectively.

78

Ezrahi et al.

FIG. 11 Phase diagram for the system dodecane ⫹ butanol 1: 1 (w/w)–Brij 97–water at 27°C. Along the XB4 water dilution line, the Brij 97/butanol/dodecane weight ratio is 4: 3: 3. LC designates the liquid crystalline phase region. (From Ref. 67.)

The respective initial concentrations of S-1570 on these dilution lines are about 32 wt% and 43 wt% (see Fig. 13). System E. Water–butanol ⫹ hexadecane 1:1 (by weight)–S-1570. This system was studied along the water dilution line 43 for which the surfactant/alcohol/ oil weight ratio is again 0.94 :1: 1 (see Fig. 14).

FIG. 12 Phase diagram for the system dodecanol–water–Silwet L-7607. Along the water dilution lines 1 and 2 the dodecanol/Silwet L-7607 weight ratios are 1: 1 and 3: 7, respectively. (From Refs. 46 and 47.)

Subzero Behavior of Water in Microemulsions

79

FIG. 13 Phase diagram for the system dodecane–butanol–S-1570–water. No attempt was made to further identify the liquid crystals (not shown) or any other phase within the two-phase area. The dashed lines represent the water dilution lines along which the dodecane/butanol/S-1570 weight ratios are kept constant at 1: 1: 0.94 (dilution line 32) and 1: 1: 1.5 (dilution line 43), respectively. (From Ref. 42.)

FIG. 14 Partial phase diagram for the system hexadecane–butanol–S-1570–water. The dashed line represents the water dilution line 43 along which the hexadecane/butanol/ S-1570 weight ratio is 1:1: 0.94. (From Ref. 42.)

80

Ezrahi et al.

D. Phosphatidylcholine The zwitterionic surfactant phosphatidylcholine (PC) was used for the study of enzymatic hydrolysis reactions in microemulsions [80–82]. The oil used in all the investigated systems was tricaprylin (TC). System F. Tricaprylin ⫹ butanol (60 wt% in varying weight ratios)–PC (25 wt%)–water (15 wt%). System G. Tricaprylin ⫹ alcohol (60 wt%, molar ratio of 1:5, respectively)– PC (25 wt%)–water (15 wt%).

VII. RESULTS AND DISCUSSION In this section we describe some parameters relevant to water behavior at subambient temperatures that were evaluated by using SZT-DSC.

A. Variation of Water Peak Temperatures with Water Content The variation of the temperatures of the midpoints of the peaks related to water (bound, interphasal, and free) as a function of water content followed the same pattern: a gradual increase of the temperature to a less negative value and then a more or less constant temperature. Such behavior was observed for systems A [10], B [45], D [42], and E [42]; for the binary system water–C 12 (EO) 8 [45]; and for aqueous solutions of polymers (here as a function of the sorbed water content) such as poly(4-hydroxystyrene) [40] and mucopolysaccharides [83]. For example, system A has an endothermic peak at about ⫺10°C, which is ascribed to the melting of interphasal water (and dodecane). In fact, it begins at about ⫺12°C, increases in height with increasing water content, and levels off at about ⫺10°C, when (total) water content approaches 30 wt%. For the binary system water ⫹ C 12 (EO) 8, interphasal water melts between ⫺3 and ⫺4°C [45,84]. The case of system E is rather unusual. Increasing its (total) water content from 8 to 16 wt% gradually leads to the merging (or more precisely, superposition) of the melting peaks of the interfacial and free water at ⫺3 ⫾ 1°C (see Figs. 15a and 15b). A similar superposition of water melting peaks was observed for the xanthan– water system [85]. In contrast to system E, in the corresponding system D (where the hexadecane was replaced by dodecane) these melting peaks remain separate even at much higher concentrations [42] (see Figs. 15c and 15d). Two other related differences between systems D and E should be mentioned:

Subzero Behavior of Water in Microemulsions

81

FIG. 15a Thermograms for system E microemulsion samples with varying amounts of water along dilution line 43. Heating rate 5°C/min. (From Ref. 42.)

1. The maximum water solubilization is 80 wt% in system E and only 40 wt% in system D. 2. The first observation of free water is at 14 wt% of (total) water in system D and at 16 wt% (i.e., the concentration at which the water melting peaks merge) in system E [42]. A similar difference in the appearance of free water was shown for the system AOT–isooctane or dodecane–water [27]. Thus, in the case of dodecane, all the water except for the last 6.5 water molecules freezes when the AOT reversed micelles are cooled down to ⫺50°C. The same applies to the isooctane microemulsion, where all the water except for the last 4.5 water molecules freezes when the AOT reversed micelles are cooled down to ⫺50°C. It was suggested that this effect is due to diminished penetration of the longer dodecane within the hydrophobic chains of AOT molecules [27]. On a molecular level, this phenomenon may be interpreted in terms of the Hou and Shah mechanism [86–88].

82

Ezrahi et al.

FIG. 15b Melting temperatures of the interfacial water as a function of water content for system E along dilution line 43. (From Ref. 42.)

The reduced penetration of the oil into the alkyl chains of the surfactant (and the consurfactant) in the palisade layers of ternary (or quaternary) microemulsions tends to cause the interface to become less curved, thereby favoring the growth of the natural (or spontaneous) radius of curvature, R°, and the formation of larger W/O microemulsion droplets [89] as well as increasing the accessibility of the binding sites on the surfactant molecules. The merging of the water melting peaks in system E is yet to be investigated, but it may be associated with the presence of more butanol molecules at the interface relative to system D [42]. The amount of alcohol present at the interface of microemulsion systems increases with the chain length of the oil. Thus, we evaluated [45] the molar ratio of alcohol to surfactant, N A /N S, for the system water–C 12 (EO) 8 ⫹ hexanol (1:1)–oil, using an equation derived by Kunieda et al. [90] for the determination of the surfactant/alcohol weight ratio at the interface (for systems present on the border between Winsor III and Winsor IV). For heptane, N A /N S ⫽ 1.8; for decane, N A /N S ⫽ 2.4; and for hexadecane, N A /N S ⫽ 3.3. The role of alcohol in surfactant-based systems is discussed later in this review. Here it is sufficient to say that alcohol molecules present at the interface of such a system may weaken the association between the surfactant and the outer interfacial water layers, although for the complete detachment of these

Subzero Behavior of Water in Microemulsions

83

FIG. 15c Thermograms for system D microemulsion samples with varying amounts of water along dilution line 43. Heating rate 5°C/min. (From Ref. 42.)

layers—thus transforming them to free water—a critical alcohol concentration is needed [45]. Another possible explanation that may help in understanding this phenomenon of merging melting peaks is that significant microstructural changes must have occurred in view of the intensive water solubilization in system E.

B. Full Hydration of the Surfactant In system A the surfactant becomes saturated with water at N W/EO ⫽ 3, where N W/EO is the number of (interphasal) water molecules per ethylene oxide (EO) group of the surfactant. For this water/surfactant molar ratio, (total) water content is again about 30 wt%. A similar value was determined for the system water/dodecanol ⫹ polydimethylsiloxane 1:4 (by weight) [46,47]. The hydration of EO groups in surfac-

84

Ezrahi et al.

FIG. 15d Melting temperatures of the free water as a function of water content for system D along dilution line 43. (From Ref. 42.)

tants and polymers has been amply investigated. Yet when values of N W/EO obtained in different systems by different techniques are compared, two points should be considered: 1. 2.

N W/EO depends significantly on the method of measurement [91]. The value of N W/EO may be altered owing to factors such as temperature or qualitative and quantitative composition of the system.

Thus, for C 12 (EO) 8, N W/EO values lower than 5 but closer to 2–3 were measured by 17 O relaxation NMR [92], values between 2.6 and 3.3 by sedimentation [93], about 6 by micellar self-diffusion, between 3 and 4 by self-diffusion of water [91], and between 8 and 9 by self-diffusion of water, according to a cell model [94]. SZT-DSC was used for the determination of N W/EO in binary systems. For 70–90 wt% water–30–10 wt% C 12 (EO) 8, N W/EO ⫽ 4.3–3.7 [84]. For water– C 16 (EO) 20 and water–C 12 (EO) 23, N W/EO ⫽ 3.07 [16,44]. Much more attention has been paid to aqueous solutions of polyoxyethylene. For example, values of N W/EO ⫽ 2.3–3.8 (depending on molecular weight) were measured by SZT-DSC [33]; N W/EO ⫽ 2.8 [51]; N W/EO ⫽ 3 in crossed gels (even at 100°C) [95]; and N W/EO ⫽ 2–3 (depending on molecular weight) [96]. Similar values have generally been obtained also by other techniques: N W/EO ⫽ 3 by ESR

Subzero Behavior of Water in Microemulsions

85

and NMR; between 2 and 6 by the relaxation rate of 17 O and 2 H; between 5 and 6 by dielectric measurements; N W/EO ⫽ 6 by SANS; N W/EO ⫽ 2 by NMR and IR; and N W/EO ⫽ 2.9 by molecular simulation [97–100]. To summarize, for polyoxyethylene, N W/EO values ranging between 0.9 and 6 have been determined by using various techniques [97]. The close agreement between system A and the binary systems water–C 16 (EO) 20 and water–C 12 (EO) 23 may, prima facie, lead to the conclusion that the water–surfactant interaction is independent of the length of the hydrophilic headgroup of the ethoxylated surfactant and that the presence of pentanol (and dodecane) does not affect the interaction between water and the EO groups of nonionic surfactants. The picture, however, is not so simple, because long headgroups form coils in which water molecules may become trapped. These molecules do not interact directly with polar atoms of the headgroup, but nonetheless they form part of kinetic unit in the water–surfactant system, thereby increasing N W/EO [44]. Even for the relatively short surfactant C 12 (EO) 8 we find that N W/EO for the binary system water– C 12 (EO) 8 is nearly twice that for the quaternary system (model system A). This observation was interpreted as being the result of the hexagonal liquid crystalline structure of the binary system: A considerable part of the interphasal water is trapped within the voids of the mesophase cylinders without being bound to a specific site on the surfactant headgroup. It should be emphasized that all interfacial (including the trapped) water manifests itself as a distinct endothermic peak at about ⫺3°C. Therefore, from the viewpoint of the intensity of the water– surfactant interaction, these two types of water states (trapped and directly bound to surfactant headgroups) should be treated as though there were no sharp distinction between them in the binary water–C 12 (EO) 8 system. The amount of water thus assigned to each EO group is on average larger than in the case of the quaternary system, leading to N W/EO ⬃ 5.7 [45]. Similar considerations apply to other water binding sites. For example, protein hydration is based on various types of sites: ionic, polar (EOH, ENH, ⬎CO), and apolar (hydrophobic hydration). The perturbation of water by the protein decays as a function of distance, and the decay function depends on the particular hydration site on the polypeptide chain [28]. Franks [28] even thinks that the expression of hydration numbers as the water/organic residue molar (or weight) ratio is ‘‘likely to be meaningless,’’ because some water is trapped randomly within the freeze-concentrated amorphous solid rather than being associated with specific polar sites. In our opinion, the crucial question is whether this trapped water manifests itself as a distinct melting peak during the heating stage of the DSC cycle (see below). The case of zwitterionic surfactants (such as in binary water–PC systems) is instructive. The ‘‘hydration shells’’ around the PC headgroups are reported to include between 1 [101,102] and 25 [103] moles of water per mole of lipid, utilizing various methods such as the isolation of mono- [102] and dihydrate of DPPC [104,105]; adsorption isotherms [106–109] and water distribution data

86

Ezrahi et al.

for two-phase systems [110]; a radiotracer technique using gel filtration [111]; hydrodynamic methods using viscosity [112,113] and ultracentrifugation [114] measurements; X-ray diffraction [102,115–118]; calorimetry [30,32,119–121] with different cooling protocols giving different results; and NMR spectroscopy [101,109,122–132]. This wide range of results extends from tightly bound [‘‘inner shell’’ or ‘‘nonfreezable’’ water (see below)] to weakly bound water intercalated between phospholipid bilayers. The motional characteristics of this ‘‘trapped’’ water approach those of free water. There is also a rapid exchange (⬎10 4 s ⫺1) between trapped and bound water molecules [133]. The different results may reflect different phospholipids (synthetic and natural phosphatidylcholines) or different binding sites (phosphate [101,127,132,133] or trimethylammonium [132,133]; for example, using 2 H NMR relaxation and intensity measurements, it was argued that five to six water molecules reside near the (CH 3) 3 N group and only one or two water molecules are associated with the PO 4 group [132]; and different structures (which may have different cross sections for the headgroups and alkyl chains of the lipids and different degrees of tilt [117] such as anhydrous crystals, small spherical micelles in organic solvents, lamellar liquid crystals, and vesicles [133]. For instance, Nagle and Wiener [118] inferred from various diffraction data that 8.6, 13.6, and 23 water molecules are bound per DPPC molecule in the C (crystal, L c), G (gel, L β′), and F (fluid, L α) phases, respectively. Another problem is the experimentally difficult detection of the onset of phase separation between water and phospholipid units [119]. Yet remarkable agreement was achieved between the various hydration numbers. Based on the different rotational correlation times, it was found that the innermost hydration shell of PC consists of one tightly bound molecule. The main hydration shell consists of 11–12 water molecules per lipid [133]. This is the minimal number of water molecules needed to construct a hydrogen-bonded hydration shell around the phosphorylcholine headgroup according to space-filling molecular models [123]. This hydration number was derived from the results of X-ray diffraction [115], proton NMR [123,124], and 2 H NMR [122,125,130] data and measurements of the diffusion coefficients of 3 H-labeled water [132]. From DSC measurements [102,120,122] a range of 11–15 mol water per mole of lipid is obtained. Hydrodynamic techniques give about 25 mol water/mol lipid as the total hydration, but this hydration number reduces to 12–16 when allowance is made for the water in the core of the lipid aggregate. The water in excess of 24 mol water/mol lipid is free, being outside the phospholipid bilayers and exchanging only slowly (⬍10 2 s ⫺1) with the water (trapped and bound) incorporated within the hydrated bilayers. A ratio of 12 mol water/mol PC was also obtained for the quaternary system F by plotting the free water content as a function of tricaprylin (TC) content in the organic phase of the microemulsion sample and extrapolating it to 100% TC (no butanol) as seen in Fig. 16.

Subzero Behavior of Water in Microemulsions

87

FIG. 16 Variation of free water content as a function of tricaprylin (TC) content in the organic phase of a microemulsion sample containing TC⫹butanol (60 wt% in varying weight ratios), PC (25 wt%), and water (15 wt%).

By subtracting this amount from the fixed water content, the amount of water bound to PC alone is readily evaluated [82].

C. Free Water Free water is usually detected by DSC at higher water/surfactant ratios, i.e., when the surfactant is virtually fully hydrated. Such a behavior was observed for the system AOT–dodecane or isooctane–water [27], for system B [45], for the system PC–TC–butanol–water [82], for model systems D and E [42], and for the related system water–butanol ⫹ medium chain triglycerides (MCT) ⫹ sucrose monostearate (SMS) ⫽ 1: 1:1 (by weight) [79] also using SZT-DSC. In the last case, free water is detected at higher (total) water content when the butanol/ MCT/SMS weight ratio is 3:1:1 and at lower (total) water content when SMS is replaced by glycerol esters, which have far fewer hydroxyl groups available for binding water [79]. However, free water is sometimes formed while the surfactant is still not fully hydrated. The apparent plateau in the plot of interphasal

88

Ezrahi et al.

water content versus (total) water concentration for system A (Fig. 6 in Ref. 10) is a demonstration of this phenomenon [45], which will be treated in more detail elsewhere. The same concurrent formation of free and bound water was shown for the gel phase of the DPPC–water system. A deconvolution analysis of the ice melting peak in the relevant DSC thermograms has indicated that in a ‘‘pre-region’’ for which the water/lipid molar ratio N w is in the range 8 ⬍ N w ⬍ 15, free water is formed together with freezable (i.e., bound) interlamellar water [134]. DPPC becomes fully hydrated at N w ⫽ 15. At this stage, there are five nonfreezable interlamellar water molecules, five freezable interlamellar water molecules, and five free water molecules per lipid [134]. In the sugar ester-based model systems D and E, the binding sites of the surfactant are seven hydroxyl groups, three β etheric oxygen atoms, and one ester group. At saturation, 11–13 water molecules are bound to each surfactant molecule. Assuming that these three types of binding sites are equivalent as far as the formation of hydrogen bonds with water is concerned, the ‘‘bound’’ water/sucrose ester binding oxygen atom molar ratio is approximately 1 [42]. Recently, the same behavior was demonstrated for the system water (NaCl 8%) ⫹ decane 1:1–butanol–N-octylribonamide (C 5 N 8), by using 1 H chemical shift and relaxation time data. At saturation, the molar ratio of ‘‘bound’’ water to OH groups is again about 1 [135]. This is somewhat surprising, as usually the water solubilization behavior revealed by spectroscopic techniques is entirely different. Thus, NMR [14] (Fig. 17), time domain dielectric spectroscopy (TDS) [136], ESR [137], and Fourier transform infrared (FTIR) [15] measurements indicate that upon the addition of even a small amount of water, an equilibrium between free and bound water is established. This apparent discrepancy is readily understood because the spectroscopic techniques sense the water molecules most near the surfactant. On the other hand, DSC ‘‘regards’’ the binding of water molecules (which is conceived of as a restriction imposed on their mobility) in terms of interference with their freezing at 0°C [14]. The formation of a reservoir of free water in systems A and B is accompanied by significant microstructural changes [67,138–141]. The water reservoirs (cores) swell until an inversion from a W/O to an O/W microemulsion occurs at 55– 60 wt% and 60–65 wt% of (total) water for systems A and B, respectively [67]. This conclusion, which was corroborated using electrical conductivity [140], DSC [10], and NMR [14] data for system A and electrical conductivity, DSC, and viscosity data [67] for system B, is at variance with a postulated inversion at 20–30 wt% water for system B, as was suggested (incorrectly in our opinion) by Usacheva et al. [142]. Another type of subzero temperature behavior of water was demonstrated for systems based on oligomeric ethoxylated siloxanes (system C [46,47] and the

Subzero Behavior of Water in Microemulsions

89

FIG. 17 Fraction of bound water (α) as a function of the water/surfactant molar ratio (W o) for system A, along the water dilution line W5. (䊊) DSC data [45]; (䊉) NMR data [14]. (Results based on chemical shift measurements were taken from Fig. 7 in Ref. 14 and reduced to scale. The decrease of α with the increase of W o is slower when α is evaluated from T 1 relaxation time data; see Table 2 in Ref. 14.)

system [143] water–copolymer Ketjenlube 522 ⫹ dimethylaminoethanol (3 :1), respectively, (by weight)–toluene along the water dilution line for which the (surfactant ⫹ cosurfactant)/oil weight ratio is 4:1). These systems, because of geometrical restrictions of the amphiphiles and the nature of their curvature, which prevents inversion, cannot further solubilize water in the surfactant aggregate’s core and phase separation results. A similar phenomenon was observed for systems based on the siloxane surfactant L77-OH [144] and on C 12 (EO) 5 [145,146].

D. Nonfreezable Water Surfactant–water association may lead to the formation of ‘‘nonfreezable water,’’ which can obviously be detected by SZT-DSC only in an indirect manner. This term is often defined too loosely. Sometimes, any water that does not freeze at about 0°C is considered to be nonfreezable, thus obscuring the important distinction between the various types of bound water. A more plausible way to make this distinction is to choose an arbitrary, very low temperature, say ⫺100°C, as

90

Ezrahi et al.

a threshold value. The existence of nonfreezable water in an aqueous system maintained above this temperature may be indicated in two ways: (1) by the absence of water-related DSC peaks or (2) by a significant difference between the total water content of the system and the amounts of free and bound water evaluated from their respective peaks. Two cases may be discerned concerning the inability of DSC to directly detect nonfreezable water: 1.

2.

There are water molecules that interact so strongly with the surfactant headgroups that they cannot undergo a water–ice transition (i.e., they never freeze). Sometimes this strong interaction is due to the formation of a definite, stable hydrate. There are water molecules that might, in fact, crystallize (and melt), but these processes are not revealed by calorimetric techniques. The underlying reason is that such changes in the state of water would be observed at very low temperatures and with very weak enthalpy of transition, leading to such a poor calorimetric signal that it could not be detected [119].

The virtually ultimate limit to freezing is set by the glass transition. As the system is cooled to low temperatures, the water transforms from a fluid whose viscosity rises to very high values via a viscoelastic ‘‘rubber’’ to a brittle solid (‘‘glass’’). ‘‘Glass’’ is, in fact, a very viscous supercooled liquid with a flow rate of 1–10 µm/yr. At this stage, freezing has become so slow that it can no longer be detected on a measurable time scale [31]. In some cases, both NMR and DSC techniques have been used to determine the amount of nonfreezable water. For example, pulsed NMR relaxation data for the hydrated copolymer poly(N-vinyl-2-pyrrolidone/methyl methacrylate) allow one to estimate the relative fractions of three distinguishably different types of water [147]: (1) tightly bound (type B) at specific polymer sites, such as carbonyl groups; (2) more loosely bound (type A) that is more moderately influenced by the polymer matrix, for example, multilayer water and water in interstices; and, in samples with water content in excess of about 76 wt%, (3) bulk-like water that freezes at the vicinity of 273 K. Both type A and type B, which have nearly the same energy, are nonfreezable in the accepted sense of the term but undergo glasslike transitions at 170–200 K. NMR is sensitive to both type A and type B, whereas DSC is sensitive only to type A and correspondingly predicts a lower estimate for the amount of nonfreezable water [147]. The amount of nonfreezable water (defined relative to a very low temperature, e.g., ⫺100°C) may be determined by plotting the total melting enthalpy of water per unit weight of sample versus the sample composition and extrapolating to zero enthalpy [8], i.e., the nonfreezable water content is equated with the maximum amount of water for which no enthalpic peak has been detected [147]. We used a material balance method for this determination. During the investigation

Subzero Behavior of Water in Microemulsions

91

of systems A and B by SZT-DSC [10,45], we determined, among other things, the amounts of bound (‘‘interphasal’’) and free water for all the compositions studied. Using the equation W NF ⫽ W T ⫺ (W B ⫹ W F)

(5)

where W NF, W T, W B , and W F are the weights of nonfreezable, total, bound, and free water, respectively, per sample, the amount of nonfreezable water is readily calculated. In the case of water–polymer systems, W T was determined gravimetrically, and the amount of freezable water was computed from the peak area by using the heat of fusion for bulk water, ∆H°F ⫽ 333.2 J/g. This method was considered to be ‘‘clearly incorrect’’ [147]. In our opinion, even if this high value of ∆H°F were used, an indication for the absence of nonfreezable water might be achieved when W T ⬃ W B ⫹ W F. More accurate estimations of W NF can be obtained by using our Eqs. (1) and (2). Another indication of the presence of nonfreezable water is the appearance of bound water fusion peaks only after the total water content has reached a threshold value. This phenomenon was observed for several aqueous polymer solutions [40,85,148–150]. It should, however, be noted that for high water content microemulsions, as the surfactant is already saturated, all added water, either before the inversion to O/W microemulsions or after it, is free. The bound water fraction α ⫽ W B /W T then becomes smaller and smaller, and the error in determining W B from the area under its corresponding DSC peak is rather high. The difference W T ⫺ (W F ⫹ W B), which according to Eq. (5) would be equal to W NF, may in such cases just reflect a higher experimental error. Thus, the existence of nonfreezable water cannot be inferred from Eq. (5). Yet for water-rich microemulsions (especially after inversion), the formation of nonfreezable water is hardly conceivable. Schulz [8] suggests two mechanisms for the formation of nonfreezable water: 1. Water may exist in very small clusters centered on hydrophilic groups or ions. These clusters may be too small to form nuclei for ice formation. In some cases, water may be too viscous and vitrification occurs instead of crystallization, since diffusion becomes rate-limiting rather than nucleation [8]. 2. The hydrogen bond network typical of structured water is disrupted by energetically favored ion–water interactions. The presence of nonfreezable water was demonstrated, e.g., in binary ionic surfactant–water systems with surfactants such as AOT [151], sodium dioctylphosphinate [152], didodecyldimethylammonium bromide [44,45], and dioctadecyldimethylammonium bromide [44]. In the binary water–PC system the values for tightly bound water and the ‘‘inner hydration shells’’ show a much larger spreading (relative to those for

92

Ezrahi et al.

ordinary and loosely bound water; see above) depending on the physical techniques used. The values vary between 1 and 6 mol water/mol lipid [133]. However, there is no sharp border between nonfreezable and bound water. Bronshteyn and Steponkus [30] argue that overestimates of the unfrozen water content of DPPC liposomes are obtained owing to an erroneous determination of the baseline of DSC thermograms and to the dependence of the amount of water that freezes during cooling on the thermal history of the sample. Using an iterative procedure for a correct estimation of the baseline in the DSC thermograms and a three-step protocol of temperature change, they obtained hydration numbers of 4.7 and 5.6 mol water/mol DPPC for suspensions containing 30–70 and 16.2 ⫾ 0.2 wt% water, respectively. Gru¨nert et al. [153] used dielectric spectroscopy, X-ray diffraction methods, and DSC runs to show that DPPC–water mixtures with more than seven H 2 O molecules per molecule of lipid undergo a phase transition at subzero temperatures. Below the transition temperature, only seven H 2 O molecules per lipid remain between the bilayers and seem to be nonfreezable, at least down to ⫺40°C. The amount of bound water that exceeds these seven H 2 O molecules per lipid is thought to be squeezed out of the interbilayer regions together with the free water, which exists in samples with concentrations ⱖ15 H 2 O molecules/lipid [153]. However, the number of nonfreezable water molecules was only inferred from ˚ (typical of water– the jump of the interlamellar repeat distance from about 75 A DPPC mixtures with ⱖ15 mol water/mol lipid and of temperatures ⱖ0°C) to ˚ (typical of DPPC–water mixtures with fewer than seven H 2O moleabout 58 A cules per molecule of lipid and of temperatures lower than 0°C). On the other hand, the enlarged inset of thermogram 1a in Ref. 153 clearly shows an endothermic peak below 0°C of bound water superimposed almost completely on the free water melting peak at about 0°C. Due to the supercooling effect (which is not mentioned explicitly in Ref. 153), this bound water peak may be identical with the unexplained peak IV that appeared at about ⫺40°C during the cooling DSC run of the same sample (Fig. 1b in Ref. 153). If all bound water (except for seven H 2 O molecules per lipid molecule) were squeezed out of the interbilayer regions (as was assumed by Gru¨nert et al.), then no bound water peak could be detected by DSC measurements. It is more plausible that the seven H 2 O molecules per lipid constitute ‘‘real’’ nonfreezable water (which is not detected by DSC) and freezable interlamellar water (to which the above-mentioned melting peak below 0°C may be ascribed). This number is to be compared with the five nonfreezable water molecules per molecule of lipid plus five freezable interlamellar water molecules per molecule of lipid that were evaluated by Kodama and Aoki [134] for the gel phase of the ˚ (⫽ 65 ⫺ 58) DPPC–water system, using a deconvolution analysis. The ⬃7 A decrease in the interbilayer distance is then due to the loss of five molecules of

Subzero Behavior of Water in Microemulsions

93

free water per molecule of lipid that are present in the preregion 8 ⬍ N W ⬍ 15 [134] (see above). The behavior of ethoxylated alcohols depends on the length of their hydrophilic headgroup. Although there is no clear evidence for nonfreezable water in systems A [10,45] and B [45], nonfreezable water has unequivocally been observed in related systems such as the binary systems C 12 (EO) 23 (Brij 35)–water [44,45] and C 16 (EO) 20 (Brij 58)–water [44]. It is assumed [154] that some water is trapped in the helicoidal structure adopted by long polyoxyethylene hydrophilic chains. The space available for the trapped water is very restricted. Thus, the water–surfactant interaction may be strong enough to prevent the water from freezing. The short headgroups of C 12 (EO) 8 (system A) and C 18: 1 (EO) 10 (system B) do not form such coils [155] (system B can form only one coil at most; see below), and thus no nonfreezable water is expected [10]. The same considerations apply to model systems D and E [42].

E. Evaluation of the Thickness of the Bound Water Layer The thickness of the bound water layer in surfactant-based systems may be evaluated by several methods. In this review we focus on one that was originally derived from the interaction of interfacial water with solid surfaces. Gilpin [156] suggested the power law δµ w ⫽ al 0⫺α

(6)

where δµ w is the chemical potential of interfacial water; l 0 is the distance from the water/substrate interface (i.e., the thickness of the water layer adhered to the substrate); and a and α are adjustable parameters (α is usually taken as 2). Thus, δµ w and the freezing point depression ∆T of interfacial water decrease with l 0 [156]. On the basis of this power law and thermodynamic considerations the following equation was derived for planar bilayers [121]:

冢冣

∆T min l ⫽ 2 α⫹1 0 ∆T max L

α

(7)

where ∆T min is the highest melting point of ice (the position of the endothermic peak of free water), ∆T max is the maximum depression of the freezing point of water in the presence of the bilayers (the position of the endothermic peak of interphasal water), and L is (for microemulsion systems, which have such a bilayered microstructure) the thickness of the (total) water layers, alternating with surfactant (together with oil and alcohol) layers [10,45]. For system A, a local lamellar structure was directly imaged for the first time by cryo-transmission

94

Ezrahi et al.

electron microscopy (cryo-TEM) [138] along the water dilution line W5 (between about 20 and 60 wt% water). The existence of this structure was corroborated by data obtained from several techniques, including small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS), NMR, and electrical conductiv˚ ity [45,138,140,141]. L was evaluated from SAXS data, leading to l 0 ⬃3–6 A for 30–50 wt% of (total) water [10]. Other methods gave (for system A) about ˚ ; i.e., two monolayers of interphasal water are closely associated with the 5A surfactant. For the reversed micellar system of AOT–isooctane or cyclohexane– ˚ [157]. water, the bound water layer thickness lies between 3 and 5 A ˚ A thickness of about 5 A was evaluated for water freezing at ⫺10°C in cells of organic tissues [158]. The thickness of water layers freezing at temperatures ˚ [159]. between ⫺6°C and ⫺10°C on mineral surfaces lies in the range of 5–8 A ˚ A thickness of 4.5–6 A per two layers of bound water was determined for proteins [48] and clays [160]. Similarly, the thickness of the interfacial water layer in cylindrical pores was estimated to be 0.54 ⫾ 0.10 nm [161,162]. This determined thickness of the bound water layer is specifically related to the freezing of water. Thicker layers have been evaluated by defining other characteristic properties of bound water and using various experimental techniques. For example, a thickness close to 10 nm (36 water molecules) has been suggested as the distance over which the cooperativity of hydrogen bonding extends [163].

F.

Alcohol Interaction with Other Constituents

It was demonstrated for system A that although pentanol enhances water solubilization and is present at the interface, its interaction with water or surfactant is not revealed by SZT-DSC. This point has been investigated in the same way as the water–surfactant interaction [10]. We determined the concentrations of pentanol from the measured enthalpy change associated with the pentanol peak and the enthalpy change associated with pure pentanol. The derived concentrations were compared with the actual concentrations determined gravimetrically (see Table 2) [45]. These results suggest that no evidence for interaction of pentanol with water or surfactant can be found in SZT-DSC measurements [10]. Two arguments may be suggested to explain this behavior [45]: 1.

The amount of alcohol that is present at the interface is rather small. Thus, for system A, the interfacial molar ratio of pentanol to C 12 (EO) 8 is 2 at most [140]. Pentanol has only one hydroxyl group (residing, in contrast to the hydrophobic alkyl chain of the alcohol, at the hydrophilic side of the inter˚ 3 [164], while the much bulkier (moface), whose molecular volume is 17 A ˚ 3 [165]) headgroup has eight or nine binding sites. lecular volume ⬃508 A The surfactant has then a higher probability of interacting with water.

Subzero Behavior of Water in Microemulsions

95

TABLE 2 Pentanol Concentration in Microemulsions of System A Along the Dilution Line W5 Total water concentration (wt%) 2.9 10.0 20.1 22.9 25.0 35.3 45.0 47.9 51.9 58.0 79.9

Pentanol concentration (wt%) Determined gravimetrically

Evaluated from SZT-DSC data

24.2 22.5 20.2 19.4 18.7 16.0 13.7 13.1 12.0 10.5 5.1

22.8 23.8 19.1 20.9 18.4 14.8 13.6 12.8 11.9 10.3 4.5

2. When water competes with alcohol for the binding sites of the surfactant, the alcohol is rejected from the solvation shell. This type of behavior was demonstrated for several systems [135,166]. TDS measurements indicate a possible migration of alcohol from the interface to the oil phase as a preliminary step before the inversion (to O/W microemulsions) in systems A and B [136]. It can then be suggested that alcohol affects water solubilization via indirect mechanisms. Alcohol adsorbs at the interface and makes it more flexible. In addition, alcohol molecules may function as spacers for the surfactant molecules, thus making more room for the formation of the water core typical of swollen micelles and microemulsions. Alcohol may also affect the distribution of (total) water between the free and bound states. It was shown [45], for example, that the swelling of a fixed amount of 1: 1 (by weight) water–C 12(EO) 8 mixture with increasing amounts of 1:1 (w/w) solution of pentanol ⫹ dodecane led to the formation of free water above a threshold concentration of the alcohol (Fig. 18). It should be stressed that in this case the relative amount of (total) water was constantly decreased upon the addition of pentanol (and dodecane). Nevertheless, when the pentanol concentration reached a certain value, some of the (bound) water became free. This phenomenon may be interpreted by assuming that the pentanol molecules residing at the interface distort the three-dimensional tetrahe-

96

Ezrahi et al.

FIG. 18 Variation of interphasal and free water content as a function of pentanol content along a swelling line on which pentanol ⫹ dodecane 1: 1 (w/w) solution is added in increasing amounts to a fixed amount of 1: 1 (w/w) water–C 12(EO) 8 mixture. (䊊) Free water; (䊉) interphasal water. (From Ref. 45.)

dral network of water about the surfactant headgroups, thereby tearing the outer water layers [45]. The same phenomenon was observed in system G. The alcohols used were ethanol, butanol, and hexanol, and free water content increased in that order [82]. In contrast, it was found, for sucrose ester–based microemulsions, that at the same total water content the formation of free water will be inhibited as a function of alcohol hydrophilicity (i.e., the effect will be inversely proportional to the alcohol chain length) and concentration [79]. This is understandable in view of the increased solubility of shorter alcohols in water. Alcohol also strengthens the interaction of the surfactant with water molecules adjacent to it. This is revealed by the shift of the endothermic peak (ascribed to interphasal water) toward more negative temperatures upon the addition of alcohol. We showed this behavior for system A (peak at about ⫺10°C) compared with that of the binary system water–C 12 (EO) 8, which has an endothermic peak at ⫺3 to ⫺4°C (see above). It was found that the effect of alcohol becomes more pronounced as the alcohol chain shortens. This phenomenon was observed for bound (and interphasal) water endothermic peaks in systems A and B [45] and in systems D and E [42]. However, the melting temperature of bound water in these systems levels off at a

Subzero Behavior of Water in Microemulsions

97

certain alcohol chain length. In system A, for example, this plateau is formed at ⫺10°C, beginning with butanol [45]. We assume that melting temperatures on the plateau characterize systems in which the alcohol operates via its adsorption at the interface. On the other hand, the variation of the melting points (before the plateau) as a function of alcohol chain length is typical of water-soluble alcohols. These alcohols may affect water binding via cyclic intermediates like that suggested by Bastogne et al. [135]. The variation of the melting temperature of bound water depends on the relative roles of both surfactant and alcohol in determining water binding. For example, C 18: 1 (EO) 10 (Brij 97) is a commercial product that has headgroups of varying lengths. Water may then be trapped in the voids formed between these nonuniform headgroups. Using NMR [167], the same effect was shown for commercial Triton X-100. In addition, the 10 EO groups may form one coil [155], within which water may be caged. It was argued that a stable trihydrate (melting at ⫺10°C) is formed in a water–polyethylene oxide system, where the molecular weight of the polymer is ⱖ440 [i.e., at least 10 monomers, having the same length as the headgroup of C 18 :1 (EO) 10] [168]. Even if we assume that Brij 97 is not able to form such a definite structure in the four-component system B, the surfactant still has one more way of stabilizing the system that is not applicable to polyethylene oxide. C 18: 1 (EO) 10 has a long hydrophobic chain [relative to C 12 (EO) 8, for example], which is better dissolved in oil and thus helps to stabilize the quaternary system. It may also be suggested that the unsaturated alkyl chain of Brij 97 can induce a more favorable arrangement of its headgroup, leading to more hydration of the surfactant. A similar phenomenon was observed in a system based on polyoxyethylene (20) sorbitan. The measured molar ratio of bound water to EO group, N W/EO, was 4.42 when the hydrophobic residue was monolaurate, increasing to N W/EO ⫽ 6.07 for monostearate and to N W/EO ⫽ 8.84 for monooleate [169]. That is for surfactants having the same headgroup, the degree of hydration is determined by the hydrophobic residue, being higher for the unsaturated alkyl chain of oleyl alcohol as in Brij 97 [45]. Indeed, the variations of the melting temperature of bound water as a function of alcohol chain length is much less prominent in system B (based on Brij 97) than in system A, where C 12 (EO) 8 plays only a minor role in determining water binding [45]. In contrast to water-insoluble alcohols (like pentanol in system A), the melting peaks of water-soluble alcohols in quaternary systems (like butanol in system B) do not coincide with those of the corresponding pure alcohols. The same behavior was observed in system F [82]. Even in a 2.5 wt% water–butanol solution, the melting peak of butanol disappears, presumably because water molecules break the alcohol chain–like structure [82]. Increasing the TC/butanol weight ratio in system F leads to the formation of more free water at the same fixed (total) water content [82]. This phenomenon, which deserves further study, may be assigned to factors such as diminished water solubilization in the continuous phase or a

98

Ezrahi et al.

migration of butanol from the interface. Such a migration may weaken water– surfactant interactions that are mediated by water-soluble alcohols (see above). Comparing the systems 30 wt% PC/(TC ⫹ butanol) ⫽ 1:9 (w/w)–water and 20 wt% PC/(TC ⫹ butanol) ⫽ 3:1 (w/w)–water, we found that in both systems the free water content increased as a function of (total) water added but was higher by 3–5 wt% in the alcohol (and surfactant)-poor system [82]. These results are readily explained just by the higher proportion of bound water (i.e., leaving less free water) in the surfactant-rich system. Simple calculations have shown that the alcohol contribution in this case was rather small, even though the difference in butanol content between the two systems is 2700% [82]. We have shown (Fig. 18) that adding pentanol (and dodecane) to fixed amounts of 1:1 (w/w) water–C 12 (EO) 8 mixtures leads to the formation of free water above a threshold concentration of pentanol. In these PC-based systems, the amount of water is constantly increased and, moreover, butanol is considerably dissolved in TC. Thus, the alcohol can hardly reach the threshold concentration presumably needed for the tearing off of outer water layers and for the formation of free water. Surfactants behave virtually the same as water-soluble alcohols. Thus, pure C 12 (EO) 8 melts at ⫹29.5°C, but its melting point shifts to 18°C or 13°C [45], and this melting peak is reduced or even disappears when the system contains water, as a result of their interaction [10]. The effect of water is also manifested at ambient temperatures. For example, the melting temperatures of both the alkyl chains and the polar headgroups of monosodium n-decanephosphonate and disodium n-decanephosphonate decrease in the presence of water, the effect being inversely proportional to water content [170]. Similar behavior is observed for transitions such as solid to liquid crystal or gel to liquid crystal occurring in binary systems of water and surfactants such as dioctadecyldimethylammonium bromide [171] and didodecyldimethylammonium bromide [16,44]. It is thought that the introduction of water weakens the ionic layer and disrupts the crystalline structure of the surfactant, thereby leading to reduced melting points [170,171].

G. Exothermic Peaks The a priori surprising appearance of exothermic peaks during the heating of previously ‘‘frozen’’ samples was first reported by Luyet et al. [172] for aqueous solutions of glycerol, ethylene glycol, and polyvinylpyrrolidone (PVP). Similar peaks were observed in the ternary systems H 2O–NaCl–glycerol and H 2O– NaCl–dimethyl sulfoxide (DMSO) [173]. This phenomenon was also reported in binary systems of water and synthetic polymers such as polyethylene oxide [33,34,96,174,175], PVP [174,175], and poly(vinyl methyl ether) [174,175]. Such exothermic peaks also occurred in cross-linked hydrogels of dextran [176], hydrogels of poly (2-hydroxyethyl methacrylate) [147,177,178], concentrated aga-

Subzero Behavior of Water in Microemulsions

99

rose gels [179], hydrogels of xanthan [85], hydrogels of guar and of polyacrylamide ⫹ a cross-linker (e.g., chromic nitrate) [180], gelatin, and urea-(but not SDS-) denatured globular proteins in water [174,175], The position and size of the exothermic peaks depend on structural and chemical factors such as the nature of the polymer, its structure and degree of cross-linking, the size of pores available for water within the cross-linked network of the polymers, water content, and the presence of additives (such as silver iodide crystals, which inhibit supercooling) [174,175]. The exothermic peaks are also affected by thermal factors such as the cooling and subsequent heating rates and the number of freeze–thaw cycles. We observed such exothermic peaks in some microemulsion systems based on ethoxylated polymethylsiloxanes (Silwets) [46,47], ethoxylated alcohols [e.g., C 18: 1(EO) 10 (Brij 97), but not C 12(EO) 8!] [45], and sucrose esters [42]. For example, exothermic peaks were observed in system C (surfactant/oil ⫽ 3:7, by weight) with 10–20 wt% water (Fig. 19).

FIG. 19 Thermal behavior of microemulsions prepared with dodecanol and Silwet L7607 at surfactant/oil weight ratio of 3:7 and in the presence of 10, 20, and 30 wt% solubilized water (heating rate 3°C/min). (From Refs. 46 and 47.)

100

Ezrahi et al.

Comparing sucrose esters with the same headgroup but different hydrophobic tails has led us to the notable observation that in the system dodecane ⫹ butanol ⫹ sucrose ester (1: 1:1.5, w/w)–water, only with the most hydrophilic surfactant, sucrose laurate (L-1695), is an exothermic peak observed (Fig. 20). In the sucrose laurate–based system, the exothermic peak disappears as water content approaches 30 wt% (Fig. 21). When an exothermic peak appears, heat is given off during the warming period, in apparent contradiction to the Le Chatelier principle [175]. Luyet et al. [172] explained this phenomenon on the basis of a devitrification process, contending that a prior rapid cooling converts normal liquid water to amorphous ice and that it is the transformation of this vitreous ice into normal ice I during rewarming that gives rise to the heat-releasing exothermic peaks [172,175]. This explanation was refuted by Zhang and Ling [174,175], who stressed (along with other evidence) the fact that polymer–water systems cooled to ⫺70°C remain viscous liquids and not solid vitreous ice. They offered the explanation that in the presence of certain polymers of suitable concentration, the bulk of water does not exist as normal liquid water but rather in the state of polarized multilayers (which, in fact, we may envisage as ‘‘bound’’ or ‘‘interfacial’’ water).

FIG. 20 Thermal behavior of microemulsions prepared with sucrose ester ⫹ dodecane ⫹ butanol (1.5: 1: 1, by weight) in the presence of 16 wt% solubilized water (heating rate 5°C/min). L-1695 ⫽ sucrose laurate; M-1695 ⫽ sucrose myristate; P-1670 ⫽ sucrose palmitate; S-1570 ⫽ sucrose stearate. (From Ref. 42.)

Subzero Behavior of Water in Microemulsions

101

FIG. 21 Thermal behavior of microemulsions prepared with L-1695 ⫹ dodecane ⫹ butanol (1.5 : 1:1, by weight) in the presence of various amounts of added water (heating rate 5°C/min). The thermogram for 16 wt% water is identical to that of L-1695 in Fig. 18. (From Ref. 42.)

The restricted motion of water molecules in this state forms a substantial energy barrier that impedes the transformation of this water into ice I. Two ways may be suggested to overcome this energy barrier: increasing temperature and lengthening the time of exposure to the low temperatures of the cooling stage in the endothermic mode of SZT-DSC. This interpretation may help us to understand the thermal behavior of system B along the dilution line XB4 (Figs. 22a and 22b). The crystallization of a commercial surfactant like Brij 97 on cooling is hindered by the presence of entrapped water (and, in quaternary system B, of dissolved butanol too) within the voids formed between the unequal headgroups and by the nonuniformity of the chains of the surfactant itself. Heating the system leads to the release of surfactant molecules. The subsequent glass transition is sometimes reflected as a broad step in the thermogram (not seen in Fig. 22). Such a step was observed between ⫺80°C and ⫺70°C in the polyethylene oxide–water system [96]. Additional heating accelerates the rearrangement of surfactant molecules into a regular crystalline structure, thereby giving rise to the heat-releasing exothermic peak at ⫺75°C in system B (Fig. 22a) and at about 60°C in the binary Brij 97–

102

Ezrahi et al.

(a)

(b) FIG. 22 Thermograms for a system B microemulsion sample lying on the dilution line XB4. (a) Composition (in wt%): dodecane, 22.4; butanol, 22.4; Brij 97, 30.0; water, 25.2. Heating rate 3°C/min. (b) Composition (in wt%): dodecane, 18.0; butanol, 18.0; Brij 97, 24.0; water, 40.0. Heating rate 3°C/min. (From Ref. 45.)

Subzero Behavior of Water in Microemulsions

103

water system. The water concentration in both systems is about the same, but the surfactant concentration in the binary system is nearly 2.5 times as high as in the quaternary system. These exothermic peaks did not shift to lower temperatures when the water was replaced by D 2O [45]. For comparison, an exothermic peak at ⫺53°C in the polyethylene oxide–water system was ascribed to eutectic polyethylene oxide [181]. It may be assumed that the exothermic peak in system B and in its binary counterpart is due rather to the crystallization of the surfactant headgroups. A difference between the melting points of the polar headgroups and alkyl chains of the same surfactant was observed at ambient temperature in a hydrous surfactant such as C 18(EO) 7 [182] and sodium dioctylphosphinate [152] and in hydrated surfactants such as monosodium n-decanephosphonate and disodium n-decanephosphonate [170]. The difference between our quaternary and binary systems is attributed to the presence of butanol in system B. Alcohol molecules participate in retarding the crystallization of, presumably, surfactant headgroups, thus leading to a lower temperature exothermic peak in the quaternary system. Further heating induces more motional freedom (both translational and rotational) for the surfactant and water molecules. These molecules reorient themselves in unison, leading to the crystallization of a hydrate that may have a definite structure. In system B and in the Brij 97–water system, the corresponding exothermic peaks were observed at about ⫺46°C, and in both cases the peaks were shifted to less negative temperatures when D 2O was substituted for the water [45]. Such a water-related exothermic peak was observed between ⫺50°C and ⫺40°C in many systems. For example, in system C microemulsions (based on polymethylsiloxanes), this exothermic peak was observed at ⫺45°C (Fig. 19). In sucrose ester–based microemulsion systems, it was observed only for sucrose laurate (the most hydrophilic surfactant investigated in this study [42]), and it shifted from ⫺35°C to ⫺42°C as water content increased from 10 wt% to 22 wt% (Figs. 20 and 21). In a polyethylene oxide–water system (where the polymer crystallizes at ⫺53°C), the water-related exothermic peak was observed at ⫺44°C [181]. In other reports it was observed between ⫺44°C and ⫺38°C [174], at ⫺50°C [33], at ⫺41°C [183], and between ⫺40°C and ⫺50°C [34]. In a xanthan–water system, this exothermic peak was observed between ⫺40°C and ⫺50°C [85]; in water–chromium nitrate (cross-linker)–guar systems, it was observed at ⫺35 ⫾ 5°C [180]; in hydrogels of poly(2-hydroxyethyl methacrylate) [177] at ⫺40°C; and in water–sodium cellulose sulfate systems at ⫺43°C [150]. Obviously, the peak temperature and size depend on many experimental variables, and crystallization temperatures were also observed outside the range of ⫺50°C to ⫺40°C. Further heating should melt the hydrate. The endothermic peak at ⫺25°C in system B (Fig. 22a), which is the direct continuation of the exothermic peak at ⫺46°C, may be interpreted in this manner. The temperature range

104

Ezrahi et al.

between ⫺46°C and ⫺25°C indicates the strength of surfactant–water interaction in the system, because if ordinary ice were formed at ⫺46°C, just a slight warming would suffice to melt it. A significant temperature difference between related exothermic and endothermic peaks was also observed in a 55 wt% C 12 (EO) 23 (Brij 35)–water binary system sample (Fig. 23). There is a 50° difference between the water-related exothermic peak at ⫺59.4°C and the endothermic peak at ⫺9.5°C. It seems that the relatively long headgroups of Brij 35 inhibit water crystallization more than the shorter headgroups of Brij 97 [45]. This suggestion may be further supported by the observation of some nonfreezable water in Brij 35–water systems [16,44,45]. The same phenomenon also occurs in polymer–water systems. For example, in a polyethylene oxide–water system, crystallization was observed at ⫺44°C, with melting occurring between ⫺30°C and ⫺22°C [181], or crystallization at ⫺41°C, with melting at ⫺8°C [183]. A more complicated behavior is exhibited in Fig. 24. In Fig. 24 it may be seen that one water-related exothermic peak is split into two peaks at ⫺72°C and ⫺68.2°C. Splitting of exothermic peaks was also observed in some compositions of water–nonionic polyacrylamide–ammonium nitrate (cross-linker) [180] and in the recrystallization of amorphous cellulose at

FIG. 23 Thermogram for a 55 wt% C 12 (EO) 23 (Brij 35)–45 wt% water system sample. Heating rate 3°C/min. Note the broad step (ascribed to the glass transition of the surfactant) near the exothermic peak. (From Ref. 45.)

Subzero Behavior of Water in Microemulsions

105

FIG. 24 Thermogram for a Brij 35-based quaternary system sample. Composition (in wt%): Brij 35, 34.9; water, 35.1; dodecane, 15.2; pentanol, 15.0. Heating rate 3°C/min. (From Ref. 45.)

elevated temperatures [184]. These two peaks may be ascribed to the interaction of water with different headgroups of the commercial surfactant Brij 35. The temperatures of both exothermic peaks are lower (more negative) than that observed in the absence of pentanol (Fig. 23). It seems that pentanol molecules adsorbed at the interface retard the reorganization of both Brij 35 and water. In Fig. 24 small water-related exothermic peak is observed at ⫺28.7°C. This peak may represent the crystallization of an additional amount of freezable water that melts at ⫺13.8°C just after it has crystallized [45]. Another distinction between the exothermic peaks at ⫺75°C and ⫺46°C in system B is revealed upon the addition of water. The temperature of the surfactant-related peak increases (i.e., it becomes less negative) while the temperature of the water-related peak decreases (i.e., it shifts to more negative values). A possible interpretation is that as more water interacts with the surfactant, the reorientation of surfactant molecules (as a preliminary stage before crystallization) will be more restricted so that higher temperatures will be needed. On the other hand, at higher water content, more water molecules will be available for the formation of a hydrate by interacting with surfactant molecules. Less energy will then be required, and accordingly the hydrate will crystallize at a lower temperature [45].

106

Ezrahi et al.

The exothermic peaks vanish upon the formation of free water (compare Figs. 22a and 22b). The same phenomenon was observed for Brij 35-based systems (Fig. 25). At such a relatively high water content, there are no exothermic peaks. The endothermic peaks at ⫺10.4°C and ⫺3.0°C were ascribed to interphasal and free water, respectively [45]. It is easily understood that at high water content some water molecules have such freedom of motion that they are more eligible for freezing (crystallization) in the initial cooling run of the SZT-DSC cycle, giving rise, therefore, to melting peaks of free and interphasal water in the subsequent heating stage [45]. In a similar way, the exothermic peak in hydrogels of dextran disappears (or becomes very small) when the pores of the cross-linking network are large [176]. In system C [Silwet L-7607/dodecanol ⫽ 3:7 (w/w)], the exothermic peaks observed at 10 and 20 wt% water disappear at 30 wt% (Fig. 19). These exothermic peaks are also absent from the 50% water–Silwet L-7607 binary system [47]. Another way to dispose of (or diminish) exothermic peaks is to cool the system slowly in the initial state of the SZT-DSC cycle. For example, a system B microemulsion sample containing (in wt%) 30.8 Brij 97, 23.2 butanol, 23.1 dodecane, and 22.9 water was cooled to ⫺120°C at a rate of 100°C/min and then heated back to ambient temperature at a rate of 3°C/min. Two exothermic peaks were observed, at ⫺73°C and at ⫺40°C, in addition to the usual endothermic peaks at ⫺25°C and ⫺11°C. Another sample of the same composition was cooled to

FIG. 25 Thermogram for a Brij 35-based binary system sample. Composition (in wt%): Brij 35, 35.0; water, 65.0. Heating rate 3°C/min. (From Ref. 45.)

Subzero Behavior of Water in Microemulsions

107

⫺120°C but this time at a rate of 5°C/min. As the sample was heated back to ambient temperature at the rate of 3°C/min, the exothermic peaks disappeared altogether [45]. However, in some polymer–water systems, the appearance of exothermic peaks does not depend on rapid cooling. For instance, a 250-fold slowdown of the cooling rate did not alter the exothermic peaks of a 50% poly(vinyl methyl ether) aqueous solution [175]. In such a case, the favored way (besides heating) to achieve the transformation from the ‘‘chilled multilayer state’’ [175] to the (ordinary) ice I state is to lengthen the time of exposure to the minimal (most negative) temperature of the SZT-DSC cycle. This prolonged exposure enables all the water molecules to cross the energy barrier and to gear themselves (albeit slowly) toward the more stable state of ice I [175] and, in many systems, toward various types of ‘‘bound’’ water, which have definite freezing (and melting) temperatures.

H. The Problem of Phase Separation The usefulness of SZT-DSC hinges on the solution of the problem of extrapolating low-temperature data to ambient temperature. It is surprising, therefore, that this question rarely merits a short discussion, let alone a detailed analysis, in relevant papers and reviews. The main argument against the use of SZT-DSC in the investigation of microemulsions is that the cooling and freezing of an equilibrated microemulsion system might lead to phase separation as has been observed in numerous cases [185– 187]. Obviously, such a frozen phase-separated mixture of water, surfactant, and oil (and, in many cases, cosurfactant) cannot be defined as a microemulsion even though the same composition would unequivocally be regarded as a microemulsion at room temperature. Yet this is not always the case. The degree and rate of phase separation is a function of several factors such as the microemulsion stability, the water-to-surfactant ratio, and the cooling temperature. Thus, depending on the kinetics (which are expected to vary from system to system), the DSC experiment may be probing—at one extreme—a frozen high temperature structure or—at the other extreme—an intensive phase separation, or perhaps some intermediate situation. Cooling a microemulsion may also cause a phase transformation. Thus, the reversed micelles in the AOT–isooctane–water system are spherical at 20°C but become rodlike at ⫺15°C and below [187]. Another instance is related to system A microemulsions, which, upon cooling, have been transformed to lamellar (L α) and hexagonal (H I ) liquid crystalline phases as was confirmed by using smallangle X-ray scattering (SAXS) data (Figs. 26a, 26b). It is seen that whereas at room temperature only a single scattering peak is observed, cooling the sample to 4.5°C leads to the appearance of two scattering peaks separated by a distance typical of lamellar phases [45,140]. In a similar

108

Ezrahi et al.

FIG. 26 Variation of scattering intensity I(q) as a function of the scattering vector q for a system A microemulsion sample having the composition (in wt%) C 12 (EO) 8, 45; pentanol, 15; dodecane, 15; water, 25. (a) 23°C; (b) 4.5°C. (From Ref. 45.)

Subzero Behavior of Water in Microemulsions

109

case, a microemulsion sample containing 48 wt% C 12(EO) 8, 10 wt% pentanol, 10 wt% dodecane, and 32 wt% water was cooled to ⫺14°C and transformed to a hexagonal (H I ) liquid crystalline phase. The surfactant surface areas thereby calculated fit well into the pattern set by the other samples (of the same quaternary system), which are liquid crystals at room temperature [45,140]. Our efforts are therefore aimed at demonstrating that though phase separations and transformations are frequently observed upon cooling of microemulsion systems, as far as surfactant–water interactions are concerned SZT-DSC measurements give reliable results. Our arguments are based on three proofs: 1. Analysis of DSC endotherms utilizing the ability of the DSC instrument to distinguish between free and bound water 2. Similarity in the thermal behavior of binary and multicomponent systems 3. The effect of different oils on the thermal behavior of otherwise identical systems The first proof is the most conclusive. When the water content of a microemulsion system is gradually increased, it is usually observed that the surfactant interacts with the added water, and only after it becomes fully (or almost fully) hydrated is free water formed and detected as a melting peak (providing the endothermic mode is used) at about 0°C (see above). It is not possible that free water is formed but not revealed by this peak. In most cases, no peak of free water is seen before the saturation of the surfactant. If the phase separation that evidently occurs during cooling can lead to the detachment of water molecules that are already bound to the surfactant headgroups, and thereby to the inevitable formation of free water, then this specific water should be detected by SZT-DSC in two ways: (1) the appearance of a freezing (melting) peak of free water, as we have shown, and (2) the vanishing of (or significant decrease in) the bound (or interfacial) water peak. Moreover, we may also safely rule out the opposite possibility—that free water that has been formed during the equilibration of the microemulsion sample at room temperature would rather interact with surfactant molecules at subzero temperature during the cooling stage of a DSC experiment and become bound water. The very fact that before the saturation of the surfactant no peak of free water is seen while the peak of bound water steadily increases clearly shows that free water is not formed by breaking off the surfactant–(bound) water interaction but rather by the addition of water to a fully (or almost fully) hydrated surfactant. This free water is inevitably formed at room temperature (during the preparation and equilibration of the microemulsion samples) before the beginning of SZTDSC measurements. The phase separation should then be conceived, in our opinion, as a segregation of some (or all) of the pure (free) components (water, oil, or alcohol) of the microemulsion. Our argument implies that the distribution of bound and free water in a microemulsion system does not depend on the degree

110

Ezrahi et al.

of phase separation [10,45]. More light may be shed on this understanding of SZT-DSC data by examining the interaction of water with individual surfactants (and, for that matter, with other organic compounds having hydrophilic groups— polymers, proteins, etc.). We first exemplify our ideas using system A. In this system, the DSC results demonstrate that no free water is detected below about 30 wt% of the total water [10], whereas in the binary counterpart [water–C 12 (EO) 8 mixtures] no free water is detected below about 60 wt% of the total water (!) [44]. The same water content at surfactant saturation was observed in the water–C 16 (EO) 20 system [44]. In the binary system water–C 12 (EO) 8, interphasal water indeed melts at about ⫺3°C, but when free water forms it melts at about ⫺1°C [45]. It may then be concluded that the freeze–thaw process imposed on the interphasal water clearly does not cause water segregation. At higher water concentrations, free water begins to appear. The interphasal water concentration (relative to the constant total weight of the microemulsion) is not altered. Yet its fraction in total water content constantly decreases as more and more free water is formed. Thus, a gradual decrease of its peak (at ⫺10°C) is expected and observed [10,45]. The amount of total water (revealed as free water) equals, more or less, that of added water plus the fixed amount of interphasal water at saturation, for each microemulsion sample. It is most probable that free water at subzero temperature maintains the form of ice lumps within what is called (when the sample is kept at room temperature) a ‘‘microemulsion core,’’ or as an outer ice shell after the inversion to an O/W microemulsion. The thermal behavior of system A is then quite clear: Free water is not formed by breaking off the surfactant–(bound) water interaction but rather by the addition of water to a fully hydrated surfactant. The problem of phase transformation is more complex. We have already shown that system A microemulsions transform to liquid crystalline phases upon cooling. Such a transformation could, in principle, lead to a change in the bound and free water distribution in the system. In our opinion, the onus of proof that, in such a case, bound water is torn away from the surfactant and transforms into free water rests with the claimant. Indeed, in the case of the DPPC–water system, Gru¨nert et al. [153] argued— relying on X-ray diffraction data—that bound water is squeezed out of the interbilayer regions. We, on the other hand, have tried to show that the expulsion of only free water is sufficient to interpret their data (see above). In the case of system A, no such attempt was made. Since no free water melting peak is detected below 30 wt% of total water, the only discussible argument might be that water, which is presumably free in the microemulsion at ambient temperature (before the surfactant has become saturated), interacts with the hydrophilic headgroups during the phase transformation. This argument is refuted by using room temperature electrical conductivity data, which show a sharp increase beginning at about 30 wt% water [45,140]. Moreover, at about 55–60

Subzero Behavior of Water in Microemulsions

111

wt% water, system A is inverted from a W/O to an O/W microemulsion, as has been confirmed with room temperature NMR [14] and electrical conductivity [140] data as well as SZT-DSC measurements [10]. The same agreement between ambient temperature methods such as electrical conductivity and viscosity [67] and SZT-DSC [45,67] was also observed for system B (see above). We may then safely conclude that although system A undergoes a phase transformation at low temperatures, its free and bound water distribution is not changed. It is thus obvious that ‘‘suspected’’ systems should be individually analyzed according to these principles in order to interpret their SZT-DSC data. Another piece of evidence showing that bound water is not separated by cooling is based on the similarity between binary (water ⫹ surfactant) and multicomponent (surfactant ⫹ water ⫹ oil, with the possible presence of a cosurfactant) systems in thermal behavior. For example, the data derived from an isotropic three-component micellar dispersion of the AOT–isooctane–water system [12] (which was cooled to ⫺40°C and thus phase separated) were in good agreement with the DSC results obtained from aqueous AOT dispersions containing no organic solvents and forming lamellar (smectic) phases. Both kinds of dispersions gave a consistent set of data from which it can be concluded that about six water molecules are bound per AOT molecule. This water was unfreezable in AOT reversed micelles (presumably due to supercooling that took place in the submicroscopic droplets of AOT reversed micelles) but froze in the lamellar phase (with peaks at ⫺7°C and ⫺11°C) [12]. This behavior may alternatively reflect the weakness of surfactant–water interactions in binary systems relative to the same interactions in multicomponent systems, as we have shown for system A (see above). Similar behavior of related binary and quaternary systems was shown for phosphatidylcholine (PC). In contrast to the AOT-based system, where NMR data indicated 13 bound water molecules per AOT molecule, compared with only six as revealed by DSC measurements [12], several experimental techniques (including 2 H NMR and DSC; see above) show that, on average, about 12 molecules of water per PC molecule are bound in binary PC–water systems [133]. The same ratio was determined for the quaternary model system F [82] (see above). It should be noted that the evidence based on the similar behavior of binary and multicomponent systems is only significant after the fact. This is because, as we have seen, there need not, a priori, be any relationship between the hydration properties of the compared systems. For instance, N W/EO for the binary C 12 (EO) 8 –water system is almost twice that of the quaternary model system A [45]. We explained this behavior on the basis of the different structures of the systems, which were fixed during the preparation and equilibration of the samples at room temperature. The third proof is related to the effect of different oils on the thermal behavior of a microemulsion system as revealed by SZT-DSC. Oil may be indirectly involved in surfactant–water interactions. Thus, in the system AOT–dodecane–

112

Ezrahi et al.

water, all the water, except for the last 6.5 water molecules, freezes when the AOT reversed micelles are cooled to ⫺50°C. The same applies to the AOT– isooctane–water system, where all the water, except for the last 4.5 water molecules, freezes when the AOT reversed micelles are cooled to ⫺50°C. It was suggested that this effect is due to the diminished penetration of the longer dodecane within the hydrophobic chains of AOT molecules [27]. Obviously, the degree of penetration is determined at room temperature, when the oil molecules have great freedom of motion and are not in their frozen state. This phenomenon may be interpreted in terms of the Hou and Shah mechanism [86–88] (see Section VII.A). This behavior was confirmed at room temperature, e.g., for the system C 18 :1 (EO) 10 (Brij 97) or C 18(EO) 10 (Brij 76)–butanol ⫹ oil 1: 1 (by weight)–water [89]. Water solubilization goes through a maximum in such cases because of the opposite effect of the critical radius R c , which limits the increase of the droplet size due to interdroplet attractive interactions. As shorter chain oils penetrate more easily, water solubilization controlled by R c will increase with the decreasing length of the oil molecule. The reasoning underlying this proof is eventually based, as a little reflection will show, on our argument that the interaction between the microemulsion components will preferentially occur at ambient temperature. An interaction that is not possible at room temperature will not occur at subzero temperature either. As for oil, prima facie objection to what we argued may be made. In the case of a significant difference between the melting points of the alcohol and the oil, it may happen that at some temperature during the heating stage of the SZT-DSC cycle, the water, alcohol, and surfactant (or at least its polar headgroups) will be in a liquid state encapsulated within a core crusted over with solid oil. Such an aggregate is obviously different from an ordinary microemulsion, so a totally different distribution of water states might be expected for the capsule and the microemulsion. Nevertheless, we again contend that the distribution of the water states, even in such an encapsulated system, was determined at room temperature before the DSC experiments were conducted. Let us first take a hypothetical case, where excess liquid alcohol is contained in the capsule together with water and surfactant. If the alcohol could interact in any way with water or surfactant at subzero temperature, it would have undergone the same interaction, faster, at room temperature. The reason for this is that usually the oil is not directly involved in interactions with the polar headgroups of the surfactant, and even less with water. (The relatively rare case of system C, in which the oil itself interacts with surfactant or water, is analyzed in the following.) Obviously, the alcohol cannot cause a saturated surfactant to bind more water, nor can it detach (free) water from a partially hydrated surfactant. Thus, in a microemulsion sample containing 18.6 wt% hexadecane, 18.6 wt% pentanol, 37.2 wt% C 12(EO) 8, and 25.6 wt% water, only two melting peaks were observed: one at ⫺10.4°C for interphasal water and one at ⫹15.3°C for hexadecane. This

Subzero Behavior of Water in Microemulsions

113

oil is, of course, still frozen at 0°C. C 12(EO) 8 is almost fully hydrated at this (total) water concentration; nonetheless, free water is not detected yet [10,45]. The case of system F also supports our argument. The oil (TC) is still frozen at 0°C, but the distribution of bound (to surfactant and alcohol) and free water is such that the amount of water bound to PC agrees with that determined for the corresponding water–PC binary system by both 2 H NMR and DSC. As was evidenced by the shift in its melting point and by the decrease in its enthalpy of fusion, the oil (dodecanol) in system C participates, to some extent, in the structure of the aggregated system and, unlike many other oils in W/O microemulsions, does not behave as a free, continuous-phase oil. The penetration of the OH groups of the oil into the water phase facilitates the formation of structures capable of solubilizing significantly more water [46,47]. One may ask how this behavior is to be reconciled with the fact that dodecanol melts at ⫹24°C so that it is still frozen in the temperature range within which bound water melts. If water and oil molecules compete for available binding sites on the surfactant, then the immobilization of dodecanol might lead to enhanced water–surfactant interactions that should be reflected in higher N W/EO values. Since such arguments have been raised in relation to system C, we shall treat them in more detail. First, it should be emphasized that there can be no free water at ambient temperature available for additional binding to the surfactant after the thawing of all components, except for the oil. If the dodecanol–Silwet L-7607 interaction is the favored one at room temperature and it prevents the water from replacing the alcohol, then why does the same water at subzero temperatures ‘‘prefer’’ to reject the dodecanol (and ‘‘succeed’’) instead of crystallizing as stable ordinary ice? The observation of the reduced enthalpy of fusion of dodecanol and the shift of its melting point to lower temperature implies that this oil (alcohol) participates in some kind of interaction with the surfactant, or rather with water. Should such an interaction occur, the bound water would not be torn off from the surfactant, as no free water melting peak is observed. The same consideration applies to the oil. If all dodecanol is free of any interaction, then it should melt only at its usual melting temperature, with unreduced enthalpy of fusion. So, the frozen dodecanol (which melts only at ⫹24°C) is that part of the oil which is not involved in any interaction.

VIII.

CONCLUSION

In this chapter we surveyed the use of SZT-DSC in recent investigations of microemulsions. Two factors combine to militate against the more frequent use of this technique in microemulsion research. First, a great deal of careful work is required to obtain insight into the nature of interactions between microemulsion components and, especially, into the role of water in such interactions. Second,

114

Ezrahi et al.

subzero data must be extrapolated in order to predict microemulsion behavior at ambient temperature. This problem takes on added poignancy with the welldocumented observation that microemulsions can phase separate at low temperatures. Before recalling the ways that have allowed us to validate the conclusions reached by way of the SZT-DSC data, it is worthwhile to stress that the data derived from SZT-DSC refer to concept such as bound and free water that have operational definitions based on the low temperature behavior of water. For example, water in which the thermodynamic properties have been sufficiently modified that it remains unfrozen at subzero temperature may be called bound water [10]. Sometimes it is difficult to confirm data, such as the amount of bound water in a microemulsion sample, by using independent techniques that operate at ambient temperature. However, as was shown in this review, a close agreement of such techniques and SZT-DSC was obtained, for instance, regarding the evaluation of the water concentration range within which an inversion (from W/O to O/W microemulsions) occurs. We maintain that a central key to justifying the use of SZT-DSC data lies in recognizing that the interactions between the components of microemulsion samples are fixed during the preparation and equilibration of the microemulsions before application of the freeze–thaw cycle. The distribution of the various water states is not altered, and thus useful information about the microemulsion system can be safely obtained. Moreover, this conclusion is, in our opinion, virtually inevitable in light of the operational definitions of bound and free water. The surfactant–water interaction is manifested by the interference with the melting of frozen water at 0°C. SZT-DSC shows only the degree of this interference. Thus, the freedom of ‘‘free’’ water molecules assumed to form at room temperature is revealed only at subzero temperatures. When we say that a certain amount of water is free at room temperature, we only mean that after being frozen this water will melt at about 0°C. Had we used another experimental technique to determine the distribution of the various water states, the same water might be considered as bound.

ACKNOWLEDGMENTS We thank Dr. I. Tiunova for her careful experimental work pertinent to many microemulsion systems described in this review and Dr. G. Berkovic for critical reading of the manuscript and helpful discussions.

REFERENCES 1. ID Kuntz Jr, W Kauzmann. Adv Protein Chem 28:239 (1974). 2. D Senatra, L Lendinara, MG Giri. Can J Phys 68:1041 (1990).

Subzero Behavior of Water in Microemulsions

115

3. W Derbyshire. In: Water: A Comprehensive Treatise, Vol 7 (F Franks, ed.) Plenum Press, New York, 1982, pp. 339–469. 4. JL Finney, HFJ Savage. In: The Chemical Physics of Solvation, Part C: Solvation Phenomena in Specific Physical, Chemical and Biological Systems (RR Dogoonadza, E Kalman, AA Kornyshev, J Ulstrup, eds.), Elsevier Scientific, Amsterdam, 1988, p. 603. 5. D Vasilescu, J Jaz, L Parker, B Pullman (eds.). Water and Ions in Biomolecular Systems, Birkhauser Verlag, Basel, 1990. 6. DJ Lee, SF Lee. J Chem Tech Biotechnol 62:359 (1995). 7. JT Edsall, HA McKenzie. Adv Biophys 16:53 (1983). 8. PC Schulz. J Thermal Anal 51:135 (1998). 9. D Senatra, G Gabrielli, G Caminati, Z Zhou. IEEE Trans Electr Insul 23:579 (1988). 10. N Garti, A Aserin, S Ezrahi, I Tiunova, G Berkovic. J Colloid Interface Sci 178: 60 (1996). 11. D Senatra, GGT Guarini, G Gabrielli. In: Physics of Amphiphiles: Micelles, Vesicles and Microemulsions (V Degiorgio, M Corti, eds.), Proc SIF, Course XC, North-Holland, Amsterdam, 1985, pp. 802–829. 12. H Hauser, G Haering, A Pande, PL Luisi. J Phys Chem 93:7869 (1989). 13. D Senatra, L Lendinara, MG Giri. Prog Colloid Polym Sci 83:122 (1991). 14. D Waysbort, S Ezrahi, A Aserin, R Givati, N Garti. J Colloid Interface Sci 188: 282 (1997). 15. G Giammona, F Goffredi, V Turco Liveri, G Vassalo. J Colloid Interface Sci 154: 411 (1992). 16. JE Puig, JFA Soltero, EI Franses, LA Torres, PC Schulz. In: Surfactants in Solution (AK Chattopadhyay, KL Mittal, eds.), Surfact Sci Ser Vol. 64, Marcel Dekker, New York, 1996, pp. 147–167. 17. TK Jain, M Varshney, A Maitra. J Phys Chem 93:7409 (1989). 18. G Onori, A Santucci. J Phys Chem 97:5430 (1993). 19. TL Tso, EKC Lee. J Phys Chem 89:1612 (1985). 20. GE Walrafen. In: Hydrogen Bonded Solvent Systems (AK Covington, P Jones, eds.), Taylor & Francis, London, 1968, pp. 9–29. 21. H-X Zeng, Z-P Li, H-Q Wang. J Dispersion Sci Technol 20:1595 (1999). 22. A Goto, H Yoshioka, H Kishimoto, T Fujita. Thermochim Acta 63:139 (1990). 23. A Goto, H Yoshioka, H Kishimoto, T Fujita. Langmuir 8:441 (1992). 24. A Goto, S Harada, T Fujita, Y Miwa, H Yoshioka, H Kishimoto. Langmuir 9:86 (1993). 25. S Lagerge, E Grimberg-Michaud, K Guerfi, S Partyka. J Colloid Interface Sci 209: 271 (1999). 26. D Senatra, G Gabrielli, GGT Guarini. Europhys Lett 2:455 (1986). 27. C Boned, J Peyrelasse, M Moha-Ouchane. J Phys Chem 90:634 (1986). 28. F Franks. In: Protein Biotechnology (F Franks, ed.), Humana, Totowa, NJ, 1993, pp. 437–465. 29. ID Kuntz. J Am Chem Soc 93:516 (1971). 30. VL Bronshteyn, PL Steponkus. Biophys J 65:1853 (1993). 31. F Franks. In: Protein Biotechnology (F Franks, ed.), Humana, Totoma, NJ, 1993, pp. 489–531.

116

Ezrahi et al.

32. L Ter-Minassian-Saraga. Pure Appl Chem 53:2149 (1981). 33. KP Antonsen, AS Hoffmann. In: Poly(Ethylene Glycol) Chemistry: Biotechnical and Biomedical Applications (JM Harris, ed.), Plenum Press, New York, 1992, pp. 15–28. 34. T de Vringer, JGH Joosten, HE Junginger. Colloid Polym Sci 264:623 (1986). 35. D Senatra, Z Zhou, L Pieraccini. Prog Colloid Polym Sci 73:66 (1987). 36. D Senatra, GGT Guarini, G Gabrielli, M Zoppi. J Phys 45:1159 (1984). 37. D Senatra, G Gabrielli, GGT Guarini. In: Progress in Microemulsions (S Martellucci, AN Chester, eds.), Ettore Majorana Int Sci Ser Phys Sci Vol. 41, Plenum Press, New York, 1989, pp. 207–215. 38. D Senatra, G Gabrielli, G Caminati, GGT Guarini. In: Surfactants in Solution Vol. 10 (KL Mittal, ed.), Plenum Press, New York, 1989, pp. 147–158. 39. D Senatra, G Gabrielli, GGT Guarini, M Zoppi. In: Macro- and Microemulsions: Theory and Applications (DO Shah, ed.), ACS Symp Ser Vol. 272, American Chemical Society, Washington, DC, 1985, pp. 133–148. 40. K Nakamura, T Hatakeyama, H Hatakeyama. Polymer 24:871 (1983). 41. D Senatra, R Pratesi, L Pieraccini. J Thermal Anal 51:79 (1998). 42. N Garti, A Aserin, I Tiunova, M Fanun. Colloids Surfact A, 170:1 (2000). 43. FD Blum, WG Miller. J Phys Chem 86:1729 (1982). 44. PC Schulz, JE Puig. Colloids Surf A 71:83 (1993). 45. S Ezrahi. Microemulsion systems as a basis for fire resistant hydraulic fluids. PhD Thesis, Jerusalem, 1997. 46. N Garti, A Aserin, I Tiunova, S Ezrahi. J Thermal Anal 51:63 (1998). 47. N Garti, A Aserin, E Wachtel, O Gans, I Shaul. J Colloid Interface Sci, submitted. 48. JA Rupley, G Careri. Adv Protein Chem 41:37 (1991). 49. GN Malcolm, JS Rowlinson. Trans Faraday Soc 53:921 (1957). 50. K Fontell. J Colloid Interface Sci 44:318 (1973). 51. SL Hager, TB Macrury. J Appl Polym Sci 25:1559 (1980). 52. M Clausse. In: Encyclopedia of Emulsion Technology, Vol 1 (P Becher, ed.), Marcel Dekker, New York, 1983, pp. 481–715. 53. I Mukhopadhyay, PK Battacharya, SP Moulik. Colloids Surf 50:295 (1990). 54. S Ray, SR Bisal, SP Moulik. J Chem Soc Faraday Trans 89:3277 (1993). 55. S Ray, S Paul, SP Moulik. J Colloid Interface Sci 183:6 (1996). 56. P Alexandridis, JF Holzwarth, TA Hatton. J Phys Chem 99:8222 (1995). 57. LMM Naza´rio, TA Hatton, JPSG Crespo. Langmuir 12:6326 (1996). 58. D Liu, J Ma, H Cheng, Z Zhao. J Dispersion Sci Technol 20:513 (1999). 59. D Vollmer, J Vollmer, H-F Eicke. Europhys Lett 26:389 (1994). 60. B Antalek, AJ Williams, J Texter, Y Feldman, N Garti. Colloids Surf: A 128:1 (1997). 61. Y Feldman, N Kozlovich, I Nir, N Garti, V Archipov, Z Idiyatullin, Y Zuev, V Fedotov. J Phys Chem 100:3745 (1996). 62. H Mays. J Phys Chem B 101:10271 (1997). 63. Yu Feldman, N Kozlovich, I Nir. Phys Rev E 51:478 (1995). 64. B Lindman, U Olsson. Ber Bunsenges Phys Chem 100:344 (1996). 65. F Franks, MH Asquith, CC Hammond, H le B Skaer, P Echlin. J Microsc 110:223 (1977).

Subzero Behavior of Water in Microemulsions 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102.

117

Ch Ko¨rber, MW Scheiwe, P Boutron, G Rau. Cryobiology 19:478 (1982). S Ezrahi, A Aserin, N Garti. J Colloid Interface Sci 202:222 (1998). S Keipert, G Schulz. Pharmazie 49:194 (1994). MA Thevenin, JL Grossiord, MC Poelman. Int J Pharm 137:177 (1996). MA Pes, K Aramaki, N Nakamura, H Kunieda. J Colloid Interface Sci 178:666 (1996). J Schreiber, M Klier, F Wolf, A Eitrich, S Gohla. Patent Germany 19 509 079 A1 (1996). N Nakamura, T Tagawa, K Kihara, I Tobita, H Kunieda. Langmuir 13:2001 (1997). K Aramaki, H Kunieda, M Ishitobi, T Tagawa. Langmuir 13:2266 (1997). MA Bolzinger-Thevenin, TC Garduner, MC Poelman. Int J Pharm 176:39 (1998). MA Bolzinger-Thevenin, JL Grossiord, MC Poelman. Langmuir 15:2307 (1999). N Garti, V Clement, M Leser, A Aserin, M Fanun. J Mol Liquids 80:253 (1999). N Nakamura, Y Yamaguchi, B Ha¨kansson, U Olsson, T Tagawa, H Kunieda. J Dispersion Sci Technol 20:535 (1999). N Garti, A Aserin, M Fanun. Colloids Surf A, 164:27 (2000). N Garti, V Clement, M Fanun, ME Leser, J Agri Food Chem, accepted for publication. N Garti, D Lichtenberg, T Silberstein. Colloids Surf A 128:17 (1997). N Garti, D Lichtenberg, T Silberstein. J Dispersion Sci Technol 20:357 (1999). T Silberstein. Microemulsion systems as a basis for phosphatidyl choline hydrolysis. PhD Thesis, Jerusalem, 1999. Y Ikeda, M Suzuki, H Iwata. In: Water in Polymers (SP Rowland, ed.), American Chemical Society, Washington, DC, 1980, pp. 287–305. BA Andersson, G Olofsson. Colloid Polym Sci 265:318 (1987). H Yoshida, T Hatakeyama, H Hatakeyama. Polymer 31:693 (1990). R Leung, DO Shah. J Colloid Interface Sci 120:320 (1987). R Leung, DO Shah. J Colloid Interface Sci 120:330 (1987). MJ Hou, DO Shah. Langmuir 3:1986 (1987). N Garti, A Aserin, S Ezrahi, E Wachtel. J Colloid Interface Sci 169:428 (1995). H Kunieda, A Nakano, M Angeles Pes. Langmuir 11:3302 (1995). P-G Nilsson, B Lindman. J Phys Chem 87:4756 (1983). G Carlstro¨m, B Halle. J Chem Soc Faraday Trans I 85:1049 (1989). C Tanford, Y Nozaki, MF Rohde. J Phys Chem 81:1555 (1977). M Jonstro¨mer, B Jo¨nsson, B Lindman. J Phys Chem 95:3293 (1991). NB Graham, NE Nwachuku, DJ Welsh. Polymer 23:1345 (1982). B Bogdanov, M Mihailov. J Polym Sci Polym Phys Ed 23:2149 (1985). TWN Bieze, AC Barnes, CJM Huige, JE Enderby, JC Leyte. J Phys Chem 98:6568 (1994). KJ Liu, JL Parsons. Polymer 2:529 (1969). J Breen, D Huis, J de Bleijser, JC Leyte. J Chem Soc Faraday Trans I 84:293 (1988). N Kimura, J Umemura, S Hayashi. J Colloid Interface Sci 182:356 (1996). G Close, F Stelzner. Biochim Biophys Acta 363:1 (1974). D Chapman, RM Williams, BD Ladbrooke. Chem Phys Lipids 1:445 (1967).

118

Ezrahi et al.

103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133.

MJ Ruocco, GG Shipley. Biochim Biophys Acta 684:59 (1982). N Albon. J Cryst Growth 35:105 (1976). N Albon, J Sturtevant. Proc Natl Acad Sci USA 75:2258 (1978). PH Elworthy. J Chem Soc 5385 (1961). PH Elworthy. J Chem Soc 4897 (1962). GL Jendrasiak, JH Hasty. Biochim Biophys Acta 337:79 (1974). DA Wilkinson, HJ Morowitz, JH Prestegard. Biophys J 20:169 (1977). PH Elworthy, DS McIntosh. J Phys Chem 68:3448 (1964). RL Misiorowski, MA Wells. Biochemistry 12:967 (1973). C Huang. Biochemistry 8:344 (1969). L Saunders, J Perrin, D Gammack. J Pharm Pharmacol 14:567 (1962). C Huang, JP Charlton. J Biol Chem 246:2555 (1971). DM Small. J Lipid Res 8:551 (1967). A Tardieu, V Luzzati, FC Reeman. J Mol Biol 75:711 (1973). MJ Ruocco, GG Shipley. Biochim Biophys Acta 691:309 (1982). JF Nagle, MC Wiener. Biochim Biophys Acta 942:1 (1988). C Grabielle-Madelmont, R Perron. J Colloid Interface Sci 95:483 (1983). BD Ladbrooke, D Chapman. Chem Phys Lipids 3:304 (1969). L Ter-Minassian-Saraga, G Madelmont. J Colloid Interface Sci 81:369 (1981). Z Veskli, NJ Salsbury, D Chapman. Biochim Biophys Acta 183:434 (1969). KP Henrikson. Biochim Biophys Acta 203:228 (1970). WV Walter, RG Hayes. Biochim Biophys Acta 249:528 (1971). NJ Salsbury, A Darke, D Chapman. Chem Phys Lipids 8:142 (1972). BA Cornell, JM Pope, GJ Troup. Chem Phys Lipids 13:142 (1972). K Gawrisch, K Arnold, T Gottwald, G Klose, F Volke. Stud Biophys 74:13 (1978). Y Tricot, W Niederberger. Biophys Chem 9:195 (1979). EG Finer. J Chem Soc Faraday Trans II 69:1590 (1973). EG Finer, A Darke. Chem Phys Lipids 12:1 (1974). JL Rigaud, CM Gary-Bobo, Y Lange. Biochim Biophys Acta 266:72 (1972). C-H Hsieh, W Wu. Biophys J 71:3278 (1996). H Hauser. In: Water: A Comprehensive Treatise, Vol. 4 (F Franks, ed.), Plenum Press, New York, 1974, pp. 209–303. M Kodama, H Aoki. This volume, Chap. 7. F Bastogne, BJ Nagy, C David. Colloids Surf A 148:245 (1999). I Nir. Investigation of microemulsions by the TDS method. PhD Thesis, Jerusalem, 1997. H Caldararu, A Caragheorgheopol, M Vasilescu, I Dragutan, H Lemmetynen. J Phys Chem 98:5320 (1994). O Regev, S Ezrahi, A Aserin, N Garti, E Wachtel, EW Kaler, A Khan, Y Talmon. Langmuir 12:668 (1996). Y Feldman, N Kozlovich, I Nir, A Aserin, S Ezrahi, N Garti. J Non-Cryst Solids 172–174:1109 (1994). S Ezrahi, E Wachtel, A Aserin, N Garti. J Colloid Interface Sci 191:277 (1997). S Ezrahi, A Aserin, N Garti. In: Handbook of Microemulsion Science and Technology (P Kumar, KL Mittal, eds.), Marcel Dekker, New York, 1999, pp. 185–246. TM Usacheva, NV Lifanova, VI Zhuravlev. Colloid J 59:73 (1997).

134. 135. 136. 137. 138. 139. 140. 141. 142.

Subzero Behavior of Water in Microemulsions

119

143. O Gans. Water solubilization within hydrophobic polymeric self assemblies. MSc Thesis, Jerusalem, 1999. 144. DC Steytler, DL Sargeant, BH Robinson, J Eastoe, RK Heenan. Langmuir 10:2213 (1994). 145. JC Ravey, M Bouzier, C Picot. J Colloid Interface Sci 97:9 (1984). 146. JC Ravey, M Bouzier. J Colloid Interface Sci 116:30 (1987). 147. FX Quinn, E Kampf, G Smyth, VJ McBrierty. Macromolecules 21:3191 (1988). 148. K Nakamura, T Hatakeyama, H Hatakeyama. Polym J 15:361 (1983). 149. T Hatakeyama, K Nakamura, H Yoshida, H Hatakeyama. Thermochim Acta 88: 223 (1985). 150. T Hatakeyama, H Yoshida, H Hatakeyama. Polymer 28:1282 (1987). 151. PC Schulz. Thermochim Acta 231:239 (1994). 152. PC Schulz, JE Puig. Langmuir 8:2623 (1992). 153. M Gru¨nert, L Bo¨rngen, G Nimtz. Ber Bunsenges Phys Chem 88:608 (1984). 154. EG Elias. Macromol Sci Chem 47:601 (1973). 155. M Ro¨sch. In: Non-Ionic Surfactants (MJ Schick, ed.), Surfact Sci Ser Vol. 1, Marcel Dekker, New York, 1966, p. 753. 156. RR Gilpin. J Colloid Interface Sci 68:235 (1979). 157. M Kotlarchyk, JS Huang, S-H Chen. J Phys Chem 89:4382 (1985). 158. P Mazur. Ann NY Acad Sci 125:658 (1965). 159. A Banin, DM Anderson. Nature 255:261 (1975). 160. S Yariv. In: Modern Approaches to Wettability—Theory and Applications (ME Schrader, GI Loeb, eds.), Plenum Press, New York, 1992, p. 279. 161. EW Hansen, M Sto¨cker, R Schmidt. J Phys Chem 100:2195 (1996). 162. R Schmidt, EW Hansen, M Sto¨cker, D Akporiaye, OH Ellestad. J Am Chem Soc 117:4049 (1995). 163. PM Wiggins. Curr Topics Electrochem 3:129 (1994). 164. E Caponetti, A Lizzio, R Triolo, WL Griffith, J Johnson. Langmuir 8:1554 (1992). 165. MJ Suarez, H Levi, J Lang. J Phys Chem 97:9808 (1993). 166. WO Parker Jr, C Genova, G Carignano. Colloids Surf A 72:275 (1993). 167. K Beyer. J Colloid Interface Sci 86:73 (1982). 168. NB Graham. In: Poly(Ethylene Glycol ) Chemistry: Biotechnical and Biomedical Applications (JM Harris, ed.), Plenum Press, New York, 1992, pp. 263–281. 169. SP Moulik, S Gupta, AR Das. Can J Chem 67:356 (1989). 170. JFA Soltero, JE Puig, PC Schulz. J Thermal Anal 51:105 (1998). 171. PC Schulz, JL Rodriguez, JFA Soltero-Martinez, JE Puig, ZE Proverbio. J Thermal Anal 51:49 (1998). 172. B Luyet, D Rasmussen, C Kroener. Biodynamica 10:53 (1966). 173. FH Cooks, WH Hildebrandt, ML Shepard. J Appl Phys 46:3444 (1975). 174. GN Ling, ZL Zhang. Physiol Chem Phys Med NMR 15:391 (1983). 175. ZL Zhang, GN Ling. Physiol Chem Phys Med NMR 15:407 (1983). 176. N Murase, K Gonda, T Watanabe. J Phys Chem 90:5420 (1986). 177. TW Wilson, DT Turner. Macromolecules 21:1184 (1988). 178. K Hofer, E Mayer, GP Johari. J Phys Chem 94:2689 (1990). 179. M Watase, K Nishinari, T Hatakeyama. Food Hydrocolloids 2:427 (1988). 180. E Ahad. J Appl Polym Sci 22:1665 (1978).

120

Ezrahi et al.

181. B Bogdanov, M Mihailov. J Macromol Sci Phys B 26:59 (1987). 182. JA Bouwstra, DA van Hal, HEJ Hofland, HE Junginger. Colloids Surf A 123–124: 71 (1997). 183. NB Graham, M Zulfiker, NE Nwachuku, A Rashid. Polymer 30:528 (1989). 184. M Kimura, T Hatakeyama, J Nakano. J Appl Polym Sci 18:3069 (1974). 185. PL Luisi, LJ Magid. CRC Crit Rev Biochem 20:409 (1986). 186. M Zulauf, H-F Eicke. J Phys Chem 83:480 (1979). 187. P-O Quist, B Halle. J Chem Soc Faraday Trans I 84:1033 (1988).

4 DSC Analysis of Surfactant-Based Microstructures PABLO C. SCHULZ Departamento de Quı´mica e Ingenieria Quı´mica, Universidad Nacional del Sur, Bahı´a Blanca, Argentina J. F. A. SOLTERO and JORGE E. PUIG Departamento de Ingenierı´a Quı´mica, Universidad de Guadalajara, Guadalajara, Mexico

I. Introduction II.

Experimental and Theoretical Remarks

122 123

III. Heat Capacity and Other Thermodynamic Properties

124

IV.

132

The Phase Diagram

V. Thermal Transitions Detected in Phase Studies A. Melting B. Liquid crystal transitions C. Vaporization D. Decomposition E. Vesicles and liposomes VI.

VII.

Micellization of Block Copolymer Surfactants A. Effect of other surfactants on block copolymer micellization

153

Emulsions

157

VIII. The State of Water in Surfactant-Based Systems IX.

132 132 141 142 143 143

156

159

Lowering of the Melting Point

166

References

172

121

122

Schulz et al.

I. INTRODUCTION Differential scanning calorimetry (DSC) is widely used for studying binary and multicomponent systems containing surfactants. Transition temperatures and enthalpies are often determined and used to draw the limits of existence of the different phases of surfactant-based systems [1–6]. The state of the surfactant molecules in these phases is studied by means of thermal analysis [7,8]. DSC is also a useful technique to obtain information about the phase diagrams of surfactant-based systems and the various microstructures formed in these systems. The properties that can be obtained from DSC for binary systems are the following [6]: 1. 2. 3. 4. 5. 6. 7. 8. 9.

Type of phase transition (isothermal or nonisothermal, transformation of one phase into another or a three-phase process) Temperatures of invariant transitions, initial and final temperatures for univariant phase transitions Phase boundaries, extent of heterogeneous regions, coordinates of invariant points for a complete phase diagram consistent with the phase rule Enthalpies of phase transitions; Tamman triangles and enthalpies of threephase processes Specific heats of systems in homogeneous states Heat capacity of systems in heterogeneous states Heat capacity jumps taking place when the number of phases present in the system changes Three-dimensional diagrams of the dependence of the system heat capacity on temperature and composition Differential entropy and enthalpy of dissolution of one phase in another

In particular, the enthalpies of invariant processes (melting of pure substances, eutectic and peritectic points, extreme phase transition temperature, etc.) can be measured with great precision. Calorimetric methods are isoplethal, that is, they follow a line on a phase diagram (binary or ternary) along which the composition remains constant as temperature is varied. Differential scanning calorimetry is widely used to obtain phase information. Many phase diagrams are inferred from calorimetric data jointly with some other techniques. Calorimetry has been used extensively for physical studies of polar lipids and provides invaluable information about the numerical values of the thermodynamic variables [9]. A sample cannot be viewed during calorimetric studies, but in combination with observations in hot stage microscopy (with common and/or polarized light) the nature of phase transitions and their temperature can be determined.

DSC Analysis of Microstructures

123

There are some limitations to the use of DSC in phase studies in addition of its inability to identify phases [5]. They are that (1) there are difficulties in locating very steep phase boundaries in heterogeneous systems from DSC data alone because heat capacity depends strongly on the slope of phase boundaries and so the heat capacity jumps are small [10] and (2) the determination of phase boundaries in systems with slow nucleation rate, interfacial transport problems, or inherently slow phase changes may not be possible [11]. This is why it is hard to discover a liquid miscibility gap by DSC measurements.

II.

EXPERIMENTAL AND THEORETICAL REMARKS

Pans for volatile samples must be used to run DSC thermograms of surfactant– water systems and of systems containing other volatile solvents. Samples must be weighed before and after DSC runs, and results of samples that lost weight must be discarded. To facilitate mixing and homogenization and to obtain reproducible thermograms, the samples are often heated and cooled before the actual measurements are taken [12]. However, if the temperature of a fluid liquid phase is reached during this procedure, it is not recommended that the equilibrium state be attained by this method because high-temperature phases at phase transitions are highentropy phases. The rate of phase equilibration is in general fast during the heating stage but comparatively slow during the cooling stage. Reheating a cooled sample (that may have partially reached equilibrium) will therefore rapidly destroy any low-entropy phase (such as crystals) that may have started to form. State equilibrium may exist at the end of the heating stage, but it may not at the end of the cooling stage. The attainment of equilibrium from the disordered state during cooling must therefore start anew during each cooling stage. For example, for the determination of the Krafft boundary, either a new sample must be used in each scan or conditions must be maintained such that equilibrium is attained after cooling below the phase boundary temperature [13]. Changing the temperature of a mixture often dictates that not only heat transport but also mass transport must occur to maintain the state equilibrium. Heat flow is relatively fast, but mass transport may be much slower. Whether or not sufficient time is allowed for the mass transport equilibration to occur is determined by the scanning rate, and during most calorimetric studies the scanning rates are too fast for reaching mass transport equilibrium. In the SDS–water system, even a scanning rate of 0.2°C/min was too fast to maintain equilibrium, and a qualitative distortion in the form of the thermograms occurred at this scanning rate. Only when the scanning rate was less than 0.08°C/min was the true phase boundary peak detected. With sufficiently low scanning rates (0.1°C/min), narrow, sharp well-defined peaks form in invariant phase processes, i.e., in isothermal transitions. In fact,

124

Schulz et al.

the peak width tends to zero as the scanning rate goes to zero. Wider peaks appear in univariant (nonisothermal) processes; nonzero values of the transition temperature intervals are observed as the scanning rate goes to zero [14]. The theoretical forms of thermograms for a variety of situations that take into account the dynamics of heat flow have been suggested by Kessis [15] and by Wunderlich [16] and have also been incorporated into the analysis of thermograms by Grabielle-Madelmont and Perron [17]. A particularly important aspect of these theories is that a phase transition that is strictly isothermal (that is, a transition that spans a zero temperature range) inevitably yields a peak that spans a finite temperature range. A theory of heat transfer inside water-in-oil (W/O) emulsions in DSC experiments and during crystallization of undercooled droplets developed by Dumas et al. [18] shows that, despite the small cell size, important temperature gradients appear that explain the shape of the thermograms upon cooling. Their model indicates that the undercooling is well characterized by the beginning of the peak and not by the peak minimum as suggested earlier [19]. A model of heat transfer inside emulsions near the melting temperature of the crystallized droplets demonstrated significant temperature gradients, in contrast to the classical assumption of uniform melting temperature. The melting kinetics of the droplets depends on their location [20]. The evaluation of thermodynamic properties (enthalpy, entropy, and free energy) by DSC was discussed by Richardson [21]. He found that isothermal enthalpy changes are readily obtained by simple extrapolation even though the apparent location of a thermal event is much influenced by rate effects. The corresponding entropies are always flawed by departures from reversibility, and data must be corrected by forcing them to obey the condition of ∆G ⫽ 0 at a first-order transition. Free energy curves may then be used to define the relative stabilities of the different structures. The DSC-measured phase transition enthalpies are often complex functions of the true phase transition enthalpy and the heat capacity difference between the coexisting phase [21]. Thermodynamic properties may also be obtained from conventional DSC heat capacity measurements [22,23] without the need of time-consuming extrapolations to zero heating rate [21].

III. HEAT CAPACITY AND OTHER THERMODYNAMIC PROPERTIES In general, the enthalpy and temperature of thermal transitions are directly determined from DSC thermograms. However, other thermodynamic properties, such as heat capacity, can also be obtained from these experiments.

DSC Analysis of Microstructures

125

Differential scanning calorimetry is a simple and rapid method for measuring heat capacities of small samples over a wide temperature range. It is applicable to any liquid and solid materials in a variety of forms (powders, films, granules, etc.) [24]. The raw data produced by DSC are the difference in the amount of heat transferred to a sample relative to a reference, q, as a function of temperature. The heat capacity is then equal to dq/dT. Differential scanning calorimetry studies of aqueous surfactant mixtures are typically measured in closed hollow containers or pans where the expansion of condensed phases causes only a minimal increase in pressure under these circumstances. Changes in pressure in surfactant–water systems resulting from the increase in water vapor pressure are typically small (a few atmospheres at most). In these cases, the measured heat capacities can be precisely defined as heat capacities at saturated vapor pressure [25], but usually they are numerically similar to those that would be obtained during constant pressure measurements [26] and so they are commonly taken as the latter. A DSC determination of heat capacity (c p) is based on the comparison of signals in the scanning mode from the sample (subscript s) and a calibrant (subscript c) of known heat capacity, c c . The calibrant must not be mistaken for the reference, which is usually an empty (inert) cell. Determinations of c p are based on changes of signal in sequential runs with empty (subscript e) and loaded cells. The sample heat capacity is given by [24] cs ⫽

冢 冣

SS s ⫺ SS e m c c c SS ⫺ SS e ⫽ s SS c ⫺ SS e m s Km s

(1)

where m x is the additional mass of sample (x ⫽ s) or calibrant (x ⫽