Introduction to Polarography and Allied Techniques

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Dedicated to fond memory of brother Sh. P.K. Zutshi who passed away on 3rd August 2001

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PREFACE TO THE SECOND EDITION The foundation of Polarography was laid by Late Professor Jaroslov Heyrovsky in 1922. The theory and practical implications were further extended by Professors : Jaroslov Kuta, B. Kucera, VI•cek, Kalousek Switch, R. Bridicka, I.M. Kolthoff, P. Zuman, L. Meites, J. O’M Bockris and other distinguished electrochemists. Significant progress has been made in this field, since then and I have been motivated to bring out this book which covers both the fundamentals as well as the recent developments. This volume is intended as a text book and includes questions and chemical examples. The book can be used in formal courses at the senior under graduate levels. The problems following each chapter have also been included along with some general questions. Some more topics have been added in this second edition. This has helped to cover the courses prescribed in other north Indian universities of the country. The chapter on corrosion has been given special attention and as such the chapter has been divided in two A and B. The details of laboratory procedure, such as the design of cells and the construction of electrodes has also been attended. The main feature lies in the important developments resulting from polarographic analysis in the study of organic systems by electrochemical method. The level at which the fundamental principles pertaining to the methods described in this text are presented and would help in understanding the essential principles underlying the applications of the methods described in the text. In addition to the treatment of the fundamental principles, some chapters do certain examples describing the applications of the methods described in the text. Apart from the general coverage, importance is given to the study of organic systems by electrochemical methods. The electro-organic synthesis involving direct and indirect electrode reactions has also been described in this text. The matter provided in this area of electrochemistry has been described mainly under categories like : Theory, Methods and Instrumentation. The incentive to prepare this work for publication has been provided by the members of my family. I wish to express my sincere thanks to my brothers and my niece for their interest and constant encouragement to complete this work. For bringing out the second edition as well as to include few more chapters has been given by one of my students : Prof. P.S. Verma of the Dept., University of Rajasthan, Jaipur. Kamala Zutshi

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PREFACE TO THE FIRST EDITION The foundation of Polarography was laid by Late Professor Jaroslov Heyrovsky in 1922. The theory was further extended by Professors : Jaroslov Kuta, B. Kucera, Vl•cek, Kalousek Switch, R. Bridicka, I.M. Kolthoff P. Zuman, J.O.M Bockris, L. Mcites and other distinguished scientists. Significant progress has been made in this field in recent times and this has motivated me to bring out this book which covers both the fundamentals as well as the recent developments. The book has been written to serve mainly the postgraduate students of the various Indian universities. The contents of the current research and modern textbooks in this area of Electrochemistry indicate beyond doubt that students of electrochemistry must have a working knowledge of various methods in this field. It is also necessary to understand the basic principles and limitations of these experimental methods in order to proceed for good research, unless the students have already had an introductory electrochemistry course. The level at which the fundamental principles pertaining to the methods described in this text are presented, shall help in understanding the essential principles underlying the applications of the methods described in the text. In addition to the treatment of the fundamental principles, some chapters do contain examples describing the applications of these methods, though the coverage may not be very detailed. The main feature lies in the important developments resulting from polarographic analysis in the study of organic systems by electrochemical methods. As a whole the text has been detailed as: The methods and instrumentation, Various types of electrodes and their working. Non aqueous systems, Inorganic systems as well as the Electrode processes. Apart from the general coverage, importance is given to the study of organic systems by electrochemical methods. The electro organic synthesis involving direct and indirect electrode reactions has also been described in this text. The matter provided in this area of electrochemistry has been described mainly under categories like: Theory, Methods and Instrumentation. The incentive to prepare this work for publication has been provided by the members of my family. I wish to express my sincere thanks to my brothers and my niece for their interest and constant encouragement to complete this work. Kamala Zutshi Jaipur, India

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CONTENTS PART–I : POLAROGRAPHY 1.

POLAROGRAPHY 1.1 Introduction and Basic Principles 1.2 Polarographs and their Applications 1.3 The Polarographic Cells and the Experimental Set Up 1.4 The Half-wave Potential and its Significance 1.4.1 Significance of Half-wave Potentials 1.4.2 Influence of Ionic Strength on Half-wave Potentials 1.4.3 Factors which Affect the Half-wave Potentials References

3 3 5 5 6 7 7 8 10

2.

THE ELECTRODES 2.1 Mercury Electrodes 2.1.1 Dropping Mercury Electrode 2.1.2 Flow of Mercury from Capillaries 2.1.3 Advantages of DME 2.1.4 Hanging Mercury Drop Electrode 2.2 Carbon Electrodes 2.2.1 Carbon Paste Electrodes 2.2.2 Glassy Carbon Electrode 2.3 Polarographic Cells and Saturated Calomel Electrode 2.4 Mercury Pool Electrode References

11 11 12 12 14 15 17 17 19 19 22 22

3.

THE TECHNIQUE 3.1 Polarographic Circuit 3.2 The Significance of Diffusion in Classical Polarography 3.3 Solvents and Supporting Electrolytes 3.3.1 Recommended Solvents and Electrolytes 3.4 Polarographic Maxima 3.4.1 Maxima of the First Kind 3.4.2 Suppression of Maxima of the First Kind 3.4.3 Polarity of Maxima of the First Kind

23 23 23 28 30 31 31 32 32

(xii)

3.4.4 Streaming of Electrolyte and Maxima of the First Kind 3.4.5 Maxima of the Second Kind 3.4.6 Suppression of Maxima of the Second Kind 3.4.7 Streaming of Electrolyte with Maxima of the Second Kind 3.4.8 Interpretation of Maxima of the Second Kind 3.4.9 Practical Applications of Polarographic Maxima 3.5 Polarography in Non-aqueous Solvents 3.5.1 Solvents that are Frequently Used References

34 35 35 36 36 37 37 38 40

4.

THEORY OF CURRENT POTENTIAL CURVES 4.1 The Ilkovi•c Equation 4.1.1 Consequences of Ilkovi•c Equation 4.2 Reversible and Irreversible Electrode Processes 4.3 Reversible Polarographic Wave 4.3.1 Cathodic Wave 4.3.2 Anodic Wave 4.3.3 Cathodic-Anodic Waves 4.4 Coupled Chemical Reaction and Chemical Reversibility References

42 42 44 46 48 49 52 53 55 57

5.

TYPES OF CURRENTS 5.1 Mass Transfer and Electrochemical Processes 5.2 Diffusion Current 5.2.1 Diffusion to Stationary Electrodes 5.2.2 Diffusion-Controlled Current 5.2.3 Linear Diffusion to a Growing Dropping Electrode 5.2.4 Diffusion Coefficient 5.2.5 Spherical Diffusion 5.3 Influence of Viscosity and of Complex Formation on Diffusion Current 5.4 Factors Affecting the Diffusion Current 5.4.1 The Limiting Current 5.4.2 The Residual Current 5.4.3 Migration Current 5.4.4 Kinetic Currents 5.4.5 Catalytic Currents 5.5 Adsorption Waves References

58 58 58 59 60 61 61 63

POLARIZATION 6.1 Polarization of the Dropping Mercury Electrode and Depolarization Processes 6.2 Reduction of Hydrogen Ions and Hydrogen Over Voltage

77

6.

64 64 67 67 68 71 73 74 76

77 78

(xiii)

6.3 Double Layer 6.4 Reduction of Cations References

80 81 82

7.

AMPEROMETRIC TITRATIONS 7.1 Types of Amperometric Titrations 7.1.1 Theory of Amperometric Titration Curves 7.2 Kinds of Amperometric Titrations 7.2.1 Redox Titrations 7.2.2 Complexometric and Chelometric Titrations 7.2.3 Compensation and Diffusion-Layer Titrations 7.3 Amperometric Titrations with Two Polarized Electrodes 7.4 Apparatus and Techniques 7.4.1 The Working Electrode : Reference Electrode 7.5 Two Working Electrodes 7.6 Chronoamperometry References

83 83 83 84 85 85 86 86 87 88 88 89 91

8.

POLAROGRAPHY OF METAL COMPLEXES 8.1 Reversible, Diffusion-controlled Systems Determination of Formulae and Stability Constants of Complexed Metal Ions 8.2 Determination of Stability Constants and Coordination Numbers of Metal Complexes 8.2.1 Calculation of Individual Complex Stability Constants 8.3 Mixed Ligand Systems–the Method of Schaap and McMasters References

92

9.

POLAROGRAPHY OF ORGANIC COMPOUNDS 9.1 Structural Effects 9.2 Nature of Electroactive Group 9.3 Steric Effects 9.4 Substituent Effects References

92 93 96 96 97 98 99 100 101 102 104

PART–II : ALLIED TECHNIQUES 10.

MISCELLANEOUS POLAROGRAPHIC METHODS : PRINCIPLES, THEORY TECHNIQUES AND ANALYTICAL APPLICATIONS 10.1 Square Wave Polarography 10.2 Alternating Current Polarography 10.2.1 The Technique and Instrumentation

107 107 114 117

(xiv)

10.3 Coulometry 10.3.1 Coulometry with Large Area Mercury Electrodes 10.3.2 Coulometry with a Dropping Mercury Electrode 10.3.3 Determination of n by Analysis of the Decrease in Limiting Current 10.3.4 Determination of n by Electrolysis at Constant-Current 10.4 Coulometry in Polarographic Analysis 10.5 Controlled-potential Electrolysis 10.6 Chronopotentiometry 10.7 Theory of Reversible Processes 10.7.1 Irreversible Processes 10.8 Experimental Methods 10.8.1 Apparatus 10.8.2 Cells and Electrodes 10.9 The Techniques 10.9.1 Measurement of Transition Times 10.10 Applications 10.10.1 Concentration Measurements 10.10.2 Electrode Kinetics 10.10.3 Electrode Pretreatment 10.10.4 Differential and A.C. Chronopotentiometry 10.10.5 Thin-Layer Chronopotentiometry 10.10.6 Chemical Kinetics 10.11 Adsorption 10.12 Applications References 11.

ADVANCES IN D.C. POLAROGRAPHY 11.1 Developments in D.C. Polarography 11.1.1 Principle of Potentiostatic (Controlled-Potential) Electrolysis 11.2 Time-derivative D.C. Polarography 11.2.1 Direct Proportionality of First Derivative Peak Heights to id 11.2.2 Relative Signal Levels in Regular and in First, Second, and Third Derivative D.C. Polarography 11.2.3 Criterion for Relative Resolving Power of Various Methods of Polarography 11.2.4 Geometrical Overlapping for Successive Waves 11.2.5 Mathematical Resolution of Overlapped First Derivative d.c. Polarograms 11.2.6 Mathematical Resolution of Regular Polarography Compared to First Derivative d.c. Polarography 11.2.7 D.C. Polarography in Non-aqueous Solvents and Particularly in Solvent Extracts

119 120 120 121 122 123 123 126 127 128 129 130 130 130 131 131 131 131 131 131 132 132 132 132 133 135 135 135 136 139 139 139 140 141 142 143

(xv)

11.3 Theory, Principles and Applications 11.3.1 Single Sweep Methods 11.3.2 Electrolytic Current 11.3.3 Kinetic Currents 11.3.4 Types and Forms of Voltage Sweeps 11.4 Multi-sweep Methods 11.5 Apparatus for Applied Voltage Oscillographic Polarography 11.6 Controlled Current Oscillographic Polarography 11.7 Pulse Polarography 11.8 Stripping Analysis References

143 144 146 149 149 149 150 150 152 153 160

12.

VOLTAMMETRIC METHODS 12.1 Voltammetry 12.1.1 Coulometric Methods 12.1.2 Voltammetric Methods 12.2 Large-amplitude Pulse Voltammetry (LAPV) 12.3 Differential and Derivative Voltammetry References

162 162 163 164 167 170 172

13.

CONTROLLED POTENTIAL ELECTROLYSIS

173

13.1 Electro-organic Synthesis and the Technique 13.1.1 Pure Electron Transfer 13.1.2 Conversion of Functional Groups 13.1.3 Substitution Reactions 13.1.4 Addition Reactions 13.1.5 Elimination Reactions 13.1.6 Coupling Reactions 13.1.7 Cyclization (Intramolecular and Intermolecular) 13.2 Electrochemical Activity in Heterocyclic Systems 13.2.1 Ring Closure Reactions 13.3 Experimental Technique 13.4 Circuit for Potentiostatic Method 13.4.1 Polarization Study 13.5 Current Efficiency References

173 173 174 174 174 175 175 175 176 176 177 178 179 184 185

CORROSION

186

14.

Part A : Principles and Control 14.1 Corrosion and Control 14.1.1 Ion Selective Electrodes 14.1.2 Operational Amplifiers 14.1.3 Potentiostat 14.1.4 Galvanostat

186 187 189 189 190

(xvi)

14.1.5 Polarography 14.1.6 Pulse Plating Sources 14.1.7 Micro Processor Based Instrumentation 14.1.8 Damage and Control 14.1.9 Sources of Hydrogen and Modes of Entry 14.1.10 Mechanism of Corrosion of H2S CO2 14.2 Mechanism of Carbon Dioxide Corrosion References

190 190 191 191 191 192 193 194

Part B : Stability of Metals 14.3 14.4 14.5 14.6 14.7 14.8 14.9 14.10 14.11

Thermodynamics and the Stability of Metals Potential–pH (or Pourbaix) Diaphragms: Uses and Abuses Electronation Reaction in Corrosion The Corrosion Current and Corrosion Potentials The Basic Electrodics of Corrosion in the Absence of Ozide Films Factors Affecting the Rate of Corrosion and Evans Diagrams Some Common Examples of Corrosion Control of Corrosion Current in the Corrosion Process Various Factors in Determining Corrosion

195 198 200 201 203 204 208 209 209

Part C : Passivation 14.12 Passivation : Transformation from a Corroding and Unstable Surface to a Passive and Stable Surface 212 14.13 The Mechanism of Passivation 213 14.14 The Thermodynamics of Passivation 213 14.15 Role of Hydrogen in Corrosion 214 15.

CONVERSION AND STORAGE OF ELECTROCHEMICAL ENERGY

216

Section A 15.1 15.2 15.3 15.4 15.5 15.6 15.7

Present Status of Energy Consumption Status of Energy Consumption Direct Energy Conversion by Electrochemical Means Direct Energy Conversion by Electrochemical Means The Maximum Intrinsic Efficiency of an Electrochemical Converter The Actual Efficiency of an Electrochemical Energy Converter Physical Interpretation of the Absence of the Carnot Efficiency Factor in Electrochemically Energy Converters 15.8 The Power Output of an Electrochemical Energy Converters

216 217 218 218 219 220 220 222

Section B Electrochemical Generators (Fuel Cells) Cells Using Fuels other than Hydrogen The Hydrogen-Oxygen Cell Hydrogen Air Cells

222 223 224 225

(xvii)

16.

17.

18.

ELECTROCHEMICAL ENERGY STORAGE : THE IMPORTANT QUANTITIES IN ELECTRICITY STORAGE

226

16.1 Electricity Storage Density 16.2 Energy Density Power Electricity Storage Classical Batteries Zinc Manganese Dioxide Relatively New Electricity Stores Silver Zinc Cell Storers with Zinc in Combination with an Air Electrode Future Electricity Storers Storage by Using Alkali Metals Storers involving Non-aqueous Solutions

226 226 229 230 233 234 235 236 237 238 239

KINETICS OF ELECTRODE PROCESS Introduction 17.1 Essentials of Electrode reaction 17.2 Butler – Volmer Model of Electrode Kinetics R Effects of Potential on Energy Barriers One Step, One-Electron Process 17.3 Implications of the Butler-Volmer Model for the One Step, One Electron Process 17.4 The Current Overpotential Equation 17.5 The Standard Rate Constant 17.6 The Transfer Coefficient 17.7 Approximate Forms of the i- n Equation (a) No Mass-Transfer effects (b) Linear Characteristic at Small η (c) Tafel Behaviour at Large η (d) Tafel Plots Exchange Current plots (Tafel Plots) 17.8 Effects of Mass Transfer References

241 241 243 244 244 246

BIOELECTRODICS Introduction Useful Preliminaries Membrane Potentials Simplistic Theory Modern Approaches to the Theory of Membrane Potentials Electrical Conduction in Biological Organisms Electrical Conduction in Biological Organisms Protonic

257 257 257 259 261 262 264 265

248 249 249 250 252 252 252 253 254 254 255 256

(xviii)

The Electrochemical Mechanisms of the Nervous System an Unfinished Section Enzymes as Electrodes Enzymes Electrodes Carrying Enzymes The electrochemical Enzyme-Catalyzed Oxidation of Styrene

266 267 267 267 269

APPENDIX Questions

270 279

PART-I

POLAROGRAPHY

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CHAPTER 1

POLAROGRAPHY 1.1 INTRODUCTION AND BASIC PRINCIPLES Polarography is the branch of voltammetry in which a dropping mercury electrode is used as the indicator electrode. It is the electroanalytical technique that deals with the effect of the potential of an electrode in an electrolysis cell on the current that flows through it. The electrode whose potential is varied is called the indicator electrode voltammetric indicator electrodes may be made from quite a large number of materials say for instance mercury, platinum, gold and graphite, having varying shapes and construction. They may be stationary or is motion and the solutions in which these are used may be stationary or quiet. Polarography was the first of the voltammetric techniques to gain prominence. Certainly the most popular constant potential method is d.c. polarography at a dropping mercury electrode (DME). The reason being that there are several advantages peculiar to the DME, these are described further. The essential features of current potential curves obtained with DME are shown in Fig. 1.1. Curve b is the polarogram of a dilute solution of hydrochloric acid and the curve a being obtained under exactly the same conditions after addition of a small concentration of cadmium ion. Here, each oscillation represents the life cycle of one drop. It is the difference between the currents on the two curves which is of interest. No detectable change of current results at potentials less negative than about – 0.5 V from the addition of cadmium ion. The reason being that these potentials are insufficiently negative to bring about the reduction of any appreciable fraction of the cadmium ion at the surface of the drop. At potentials more negative than this, however, a wave appears, i.e., the reduction of cadmium ion proceeds more and more rapidly as the potential becomes more negative until eventually, at potentials more negative than about – 0.7 V is attained. It is so fast that cadmium ions are reduced as rapidly as they get diffused from the bulk of the solution upto the surface of the electrode. The rate of this diffusion depends on a number of factors. Out of these the concentration of cadmium ion in the bulk of the solution is of special importance. More concentrated the solution, the greater the rate at which cadmium ions reach, the electrode surface, and the greater the diffusion current that results from their reduction. The proportionality between the diffusion current and the concentration of the substance responsible for the wave is the basis for nearly all quantitative polarographic analysis. The ease of reduction or oxidation differs for different substances, and is reflected by the position of the wave with respect to the potential

4

Introduction to Polarography and Allied Techniques

axis. This is termed by a parameter called the half wave potential (– E ½). This is defined as the potential at which the current due to the reduction or oxidation of the substance responsible for the wave, is half as large as on the plateau. The half wave potential of cadmium ion can be seen in Fig. 1.1 (a). Under a set of defined experimental condition, each ion has its own characteristic half wave potential which is the basis of qualitative polarographic analysis. In cases, the electrode reaction may be so rapid that equilibrium is closely approached at every potential in a time much shorter than the drop life. This indicates the wave to be reversible. Studying the effects of potential and solution composition on the currents along the rising part of the wave provides information on the thermodynamics of the half reaction.

C ur rent in micr o a mp e res

20

15

(a) 10 Diffusion Current E½

5

(b) 0 0

–0.3

–0.6 –0.9 E d.c Volts in S.C.E.

(a) 1 F hydrochloric acid with 0.5 mM Cadmium ion

–1.2

(b) 1 F hydrochloric acid alone

Fig. 1.1 : Polarogram

In some cases the electrode reaction may involve a step having a large activation over potential than the variation of the current potential and solution composition are due to kinetic rather than thermodynamic effects. In such cases information on the mechanism of the rate determining step can be secured. Polarographic analysis can be used directly for the determination of any substance solid, liquid or gaseous, organic compounds containing conjugated double or triple bonds including polynuclear aromatic ring systems, as well as compounds like oximes, imines, ketones, aldehydes nitro diazo compounds and halo substituted compounds.

Polarography

5

One of the most important advantage of polarography and other voltammetric techniques is that two or even more substances can be determined by a single current potential curve. Another important analytical technique closely related to polarography is that of amperometric titration. Polarography is getting more widely used in fields as biochemistry and pharmaceutical chemistry. Even it has been used to study such diverse topics like hydrolysis, solubility, complex formation, absorption, kinetics of chemical reaction and mechanism of electrode reactions.

1.2 POLAROGRAPHS AND THEIR APPLICATIONS There are two kinds of polarographs: manual and recording. With a manual instrument, the potential applied to the cell is adjusted to some desired value and the current is measured. A single point on the polarogram is thus obtained. If the whole curve is wanted, the procedure must be repeated many times. This is tedious, specially when several waves or a complex polarogram is to be observed as such, the manual polarograph is not very convenient. For such observations a recording instrument is most suitable. The manual polarographs are not a disadvantage either. The diffusion-current measurements can be made more precisely and more quickly with manual than with recording polarograph. In a recording polarograph, the potential applied to the cell is obtained from a motor-driven voltage divider. Two procedures have been most frequently employed for recording the current. In one, the current is passed through a galvanometer, and the deflections of the galvanometer are recorded photographically or a piece of photographic paper moving at a known rate past a slit. In the other, which is now by for the more common, the current is passed through a standard resistor in series with the cell, and the resulting iR drop is presented to a strip-chart recording potentiometer, which plots the iR drop against time. Correlating the rates of motion of the chart and the voltage divider makes it possible to interpret the curve as a plot of current against applied potential. Usually, a recording polarograph employs a rate of change of potential of about 0.2 volt per minute and furnishes a complete polarogram in about 10 minutes.

1.3 THE POLAROGRAPHIC CELLS AND THE EXPERIMENTAL SET UP The cell is that portion of the apparatus that contains the solution which being studied. It also includes a non-polarizable electrode to which the potential of the dropping electrode is referred. The most important part of a cell is its reference electrode. Two kinds of reference electrodes, “internal” and “external” are in general use. An internal electrode is in direct contact with the solution being studied, while an external electrode is separated from it by a salt bridge or a porous membrane. Internal electrodes are chiefly valuable in routine analyses in which a limited constancy of potential is unimportant. They are also often used in work (when very high negative potentials) where contamination by alkali metal ions or other constituents of a salt bridge would be harmful; in cells containing

6

Introduction to Polarography and Allied Techniques

only one or two drops of solution are used. Here the difficulty arises by bringing an external electrode into contact with so small a volume of the sample. In continuous polarographic analysis, where the slow contamination of an external electrode would eventually render its potential as uncertain as that of an internal one. Internal reference electrode is made by coiling about 15–20 cm of 14 gauge silver wire into a helix. It is often Galvanometer convenient to coil it around – + the dropping electrode. In a G solution containing an ion X– that forms an insoluble silver salt, the potential of – this electrode depends only – on the activity of X in the Mercury reservoir solution, provided of course, that the solution in saturated with Ag X. If its oxygen free nitrogen solubility is very small, enough Ag X to satisfy this requirement will be formed by reaction with dissolved oxygen, an air saturated solution of unknown subs. with excess inert salt solution is placed in contact with the electrode before + deaeration. If the solution is neutral and unbuffered, it may involve partial Fig. 1.2 : Experimental set up in Polarographic Experiment hydrolytic precipitation of heavy metal ions. The electrode should not be used unless a precipitate results when a drop of solution containing 0.01 M silver ion is added to 10 ml of the sample solution. Otherwise the concentration of dissolved silver ion, and hence the potential of the silver electrode, may change considerably during the recording of the polarogram. In addition the concentration of silver ion may become high enough to give rise to substantial current at the dropping electrode. The silver electrode is not workable in solutions containing ammonia, cyanide, thiosulphates and high concentrations of halides as well as in solutions containing only nitrate, acetate perchlorate and other ions whose silver salts are appreciably soluble. The coating of insoluble salts that terms on the electrode when it is used as the anode cell should be removed by treatment with ammonia, thiosulphate, or cyanide, followed by rinsing with distilled water.

1.4 THE HALF-WAVE POTENTIAL AND ITS SIGNIFICANCE The most important constant in polarography is the half-wave potential. Chemical, thermodynamic and structural information may be obtained from the measurements of the half-wave potentials of reversible and irreversible waves under varying experimental conditions.

Polarography

7

The manner in which the current is affected by electrode potential on the rising part of the wave is to be noted. On the plateau, electron transfer is so fast that the ions or molecules of the electroactive substances are reduced or oxidized as rapidly as they arrive or are formed at the electrode surface. As the potential moves from the plateau of the wave towards its foot, the rate of the electron-transfer process decreases and the reduction or oxidation becomes less and less complete. It is convenient to divide electrode reactions into two extreme classes : (i) Reversible reactions, and (ii) irreversible reactions. (i) The reversible reactions are so rapid that thermodynamic equilibrium is very nearly attained at every instant during the life of a drop at any potential. For such reactions the variation of current with potential reflects the changing position of the equilibrium and is described by Nernst equation. The other extreme is that of totally irreversible reactions, which are so slow that they proceed only by a fraction of the way towards equilibrium during the life of each drop. For these reactions it is the rate of the electron-transfer process and the manner in which this is influenced by the electrode potential that governs the relationship between current and potential. The polarographic data serve to elucidate the kinetics of the rate determining step in totally irreversible processes.

1.4.1 Significance of Half-wave Potentials It follows from the equation derived on current potential curves that the half-wave potentials given by the term, RT/nF. In D /v′, equals the standard oxidation-reduction potential found with other indicator electrodes such as platinum electrodes. This property holds only for an oxidation-reduction system, whose oxidized and reduced terms are both present in the solution, e.g., Fe2+/Fe3+. This was confirmed by many previous workers. If one of the two terms (may be the reduced one) reacts with the material of the electrode (metals with information of an amalgam), then the half-wave potential differs from the standard oxidation-reduction potential for the metal/ion system. It can be readily shown that the difference between the half-wave and the standard potential is given by the free energy of amalgamation.

1.4.2 Influence of Ionic Strength on Half-wave Potentials Very accurate measurements point to the fact that the half-wave potentials of cations depend on the ionic strength. Get shifted to more negative potentials with increasing ionic strength. This is caused by the dependence of E ½ on the activity coefficients of both the oxidized form f and the reduced form f ′. This is when the activities are considered instead of concentration. The potential of an oxidation-reduction system is given by the formula: E = E0 –

RT ( Red) ln nF (ox ) 0

...(1)

where ( ) denote the activities. On expressing the above equation in terms of concentrations the following equation results:

8

Introduction to Polarography and Allied Techniques

RT f ′ RT [Red]0 E = E 0 – nF ln f – nF [OX ] 0

...(2)

The half-wave potential is defined by the relationship

[Red]0 [ox ]0

=

D D′

...(3)

On obtaining this condition, we obtain E ½ = E0 –

RT f ′ RT D ln − ln nF f nF D′

...(4)

For the half-wave potential. In this equation the last two terms depend on the ionic strength. If cations are deposited a very dilute amalgam is formed and f ′ is virtually one. The activity coefficient f of the cation in the supporting electrolyte is, however, less than one and since f decreases with increasing ionic strength, E ½ is shifted to more negative potentials. Lingane studied it first [2]. Vlcek [1] mode more accurate thermodynamic calculations and recommended that E ½ be extrapolated to μ = 0 : (E ½)μ = 0 = E 0 –

RT D0 ln nF D′0

...(5)

[D0 and D0′ are the corresponding diffusion coefficient for μ = 0]. The half-wave potentials calculated from the thermodynamic standard potentials for μ = 0 agreed with the extrapolated half-wave potentials as was shown by Vl•cek [1] in cases of Tl+, Pb2+ and alkali metals.

1.4.3 Factors which Affect the Half-wave Potentials 1. The temperature coefficient of the half-wave potential is mostly between –2 and +2 mv/degree. For a reversible wave it may be either positive or negative. For an irreversible wave it is usually positive and may exceed several millivolts per degree. 2. The half wave potential is almost always independent of the concentration of the electroactive species (i.e., of the diffusion current) after proper correction is applied for the iR drop. However, the half-wave potential of a reversible wave does not vary with concentration if a solid product is termed, or more generally, whenever the number of the ions or molecules of the product of variable activity differ from the number of ions or molecules of reactant of variable activity in the equation for the half-reaction. Such variations can be described only by thermodynamic equations. The half-wave potential of an irreversible wave may also vary with concentration of the reaction mechanism involving some rate governing step that is not the first- or pseudo-first order. When it does vary, it most often becomes more negative as the concentration increases.

Polarography

9

3. The half-wave potential of a reversible wave is nearly independent of the capillary characteristics, i.e., m and t. When the diffusion current obeys the Koutocky equation and when the diffusion coefficient of the oxidized and reduced species differ a small dependence of the half-wave potential on t1/6 and m1/3 can be predicted. Changes in m, t and the concentration of the electroactive species may, however, produce apparent variations of the half-wave potential unless both are corrected. The iR drop always produces an apparent shift of the half-wave potential toward more negative values for the cathodic waves and toward more positive values for anodic waves and the shift is proportional to the limiting current. 4. The half-wave potential of a totally irreversible wave, however, varies significantly with t, becoming more positive for a cathodic wave as t increases. The magnitude of the variation depends on αn a and may be used for its evaluation. Typically, if αn a = 0.5, the half-wave potential becomes about 20 mV more positive if t is doubled. 5. Changes in the nature and concentration of supporting electrolyte may effect the half-wave potential in many ways. For reversible waves the effect is due to complex formation. Quite some information about the identities and dissociation constants of reversibly reduced metal complexes can be obtained from polarographic measurements. In the reversible reduction or oxidation of an organic compound it is the pH of the supporting electrolyte that is most important. For such processes it is possible to obtain information concerning the occurrence and equilibrium constants of acid-base reactions involving the oxidized and reduced forms of the couple. 6. When a complex metal ion is reversibly reduced to a metal soluble in mercury, its half-wave potential is always more negative than that for the reversible reduction of the corresponding simple or aquo-complex ion. The difference being related to the free energy of dissociation of the complex. When complex formation takes place the half-wave potential is usually more negative when a metal ion is reduced to a lower oxidation state and when the product remains dissolved in the solution phase. The opposite effect is only occasional and when it takes place it signifies that the reduced complex is more stable than the oxidized one. Hydrogen ion is nearly always consumed in the reversible reduction of an organic compound, and as such the half-wave potential for such a process always becomes more negative as the pH is increased. It may remain constant over a certain range of pH values because of the influence of prior or subsequent proton transfer reactions. 7. Complex formation may cause the half-wave potential in the irreversible reduction of a metal ion to become either more negative or more positive. This depends on the nature of the ligand used. Example could be of nickel ion. The half-wave potential is –1.01 V vs. SCE in 0.1 F sodium per chlorate but no wave in ethylene diamine tetra acetate solutions. Where as in media containing thiocyanate or high concentration of halide, the half-wave potentials of nickel (II) are considerably more positive than –1.0 V. The reason being that these

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Introduction to Polarography and Allied Techniques

ligands facilitate electron transfer and decrease activation energy involved in the reduction. The half-wave potentials for the irreversible reduction of an organic compound may also get affected by a chemical reaction with the supporting electrolyte. The example could be of carbonyl compounds. The halfwave potentials are altered by addition of ammonia or hydroxylamine, which converts them into imines or oximes. In the absence of any reaction with the supporting electrolyte the double layer effects and the liquid-junction potential can also produce changes in the half-wave potentials. 8. When there a change made in the supporting electrolyte concentration, the half-wave potential may be affected in irreversible waves. Where upon the rate of electron-transfer steps on equilibrium position of some fast chemical reaction that precedes it, could be the reason and also the potential difference between the electrode and that surface and thus the rate of electron transfer. The direction and magnitudes of these double-layer effects depend on the potential at which the wave occurs, on the nature of ionic medium, on the charge on the species actually reduced and on the mechanism by which the reduction occurs. In some cases the half-wave potential become more negative on increasing the salt concentration while in others it becomes more positive. Large shifts have been observed. It is therefore desirable to keep the nature and concentration of the supporting electrolyte nearly constant specially while studying irreversible processes. In studying the behaviour of an organic compound, the results can be obtained consistent by using buffers of identical ionic strengths [3]. 9. In reversible waves, the effects of salt concentration on the half-wave potentials are due to mass-action effects on complex equilibria, changes of activity coefficients of the species involved in the half reaction and variations of liquidjunction potential [4]. All these can be referred to the data (5) on the half-wave potential of cadmium ion in nitrate solutions at ionic strengths up to 12 M. 10. In non-aqueous solutions having low dielectric constants, electroactive ions will be largely converted with ion pairs or higher ionic aggregates. In this, it may be pointed out that one consequence of the Stern double-layer theory is that the dielectric constant decreases rapidly as the electrode surface is approached, becoming as small as 2 or 3 or the electrode-solution interface even in an aqueous solution. The transient formation of an ion-aggregate under these condition has no effect on the half-wave potential of a reversible wave, but because it may alter the charge borne by the electroactive species it may affect that of an irreversible one.

References 1. Vl•cek A.A., Chem. List Y. 48, 1474 (1954); Collection Czechoslov, Chem. Communs. 19, 862 (1954). 2. Lingane J.J.: J. Am. Chem. Soc. 61, 2099 (1939). 3. Meites L.J. Electroanal. Chem. 5, 270, (1963). 4. Moros, S.A. and Meites, L.J. Electrochem. 5, 103, (1963). 5. Lingane J.J., Electroanalytical Chemistry, Ins., N.Y., 2nd ed. 1958, pp. 351–415.

CHAPTER 2

THE ELECTRODES 2.1 MERCURY ELECTRODES Mercury is widely used in the practice of electroanalytical chemistry both for working electrodes and for reference electrodes, in the latter case usually as an electrode of the second kind. The use of mercury is nearly an ideal choice for the construction of working electrodes for several reasons. Mercury has a large liquid range (–38.9 to 356.9°C at normal pressure) and therefore electrodes of various shapes can easily be prepared. The surface of such electrodes is highly uniform and reproducible, if the mercury is clean. The preparation of pure mercury is not very difficult. All metals with a standard potential more negative than that of mercury may be oxidized easily (exception being Nickel, which forms an inter metallic compound) by dispersing mercury into a solution of its salts acidified with nitric acid and saturated with oxygen. The elimination from mercury of metals more noble than itself to accompanied by repeated distillation under reduced pressure. One of the most important reasons for the application of mercury to the construction of working electrode is the very high over voltage for hydrogen evolution on such electrodes. Relative to a platinum electrode, the over voltage of hydrogen evolution under comparable conditions on mercury will be –0.8 to –1.0 V. It is, therefore, possible in neutral or (better) alkaline aqueous solutions to reduce alkali metal cations at mercury electrodes giving relatively well-defined polarographic waves at potentials more negative than –2.0 V vs SCE. Using supporting electrolytes such as tetra alkyl-ammonium salts, potentials as high as –2.6 V vs SCE in aqueous solutions, while in some non-aqueous systems even –3.0 V vs SCE (aqueous) is possible. Mercury electrodes do have serious limitations in applications at positive potentials. Solid metal and carbon electrodes are useful in such cases. Oxidation of mercury occurs at approximately +0.4 V vs SCE in solutions of perchlorates or nitrates since these anions do not form insoluble salts or stable complexes with mercury cations. In all solutions containing anions which form such compounds, oxidation of the mercury proceeds at potentials less than +0.4 V vs SCE. For example, in 0.1 M KCl this occurs at +0.1 V, in 1.0 M KI at –0.3 V, and so on. A number of mercury electrodes have been widely used for voltammetry. Of these, the dropping mercury electrode (DME) has been extensively used both for analytical and fundamental studies. Others are hanging mercury drop electrode (HDME), streaming mercury electrode (SME), and mercury film electrode (MFE) so also the static mercury drop electrode (IMDE) which is recently developed.

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Introduction to Polarography and Allied Techniques

2.1.1 Dropping Mercury Electrode The DME is the essential component of all polarographic experiments. It was introduced by Kucera in 1903 [1]. Later in 1921, Heyrovsky applied this electrode in the original polarographic apparatus [2]. Usually, the DME is formed of glass capillary tubing connected to a stand pipe of plastic or glass attached to a mercury reservoir. When the level of the mercury in the standpipe is sufficiently high with respect to the tip of the capillary, mercury flows from the capillary at a steady rate and small drops from at the end and fall at a regular interval. These drops have nearly spherical shape if their mass is not greater than about 15 mg and the radius of the capillary is of the order of 0.05 mm. Electrolysis is carried out on the surface of the mercury drops. One of the most important advantages of (DME), as given further, is the continuous renewal of the electrode surface. The periodicity of this renewal is governed by the life of an individual drop. The basic concept involved in the formation of mercury drops are used to define the capillary characteristics required for satisfactory electrodes. This is partially discussed by Kolthoff and Lingane [3].

2.1.2 Flow of Mercury from Capillaries The rate of flow of a liquid through a capillary can be defined by the Poiseuille equation. The volume V of liquid that flows in time t is given by V =

π rc4 Pt 8ln

...(i)

where rc and l are the internal radius of a capillary and its length, n is the viscosity of the flowing liquid, and P is the effective hydrostatic pressure (i.e., P is not exactly equal to the pressure created by the difference between the level of liquid in the reservoir and the lower end of the capillary). The above equation can be rearranged to from m=

Vd π rc4 Pd = t 8ln

...(ii)

where d is the density of the liquid. The effective pressure that acts on the mercury is not exactly equal to the total pressure, Pt, which is given by the equation Pt = h t gd

...(iii)

where h t is the vertical distance between the end of the capillary and the level of the mercury in the reservoir and g is gravitational constant. Mercury flows from the capillary in small drops. The size of these drops is determined by the interfacial tension at the mercury solution interface. The internal pressure in the drop acting against Pt is, according to Ku•cera [1], given by the relation

The Electrodes

13

Pb =

2r r

...(iv)

This internal pressure Pb, often called back pressure is proportional to the interfacial tension r at the mercury solution interface and is inversely proportional to the radius of the drop. Equation (iv) shows that the back pressure in a given solution changes with the growth of a drop and reaches the smallest value at the moment of detachment of a drop from the capillary. Taking an example, a capillary with an internal diameter of 0.06 mm placed into 3 M KCl at a potential –0.6 V, the back pressure changes from 10.44 to 0.97 cm of mercury during the life of the drop. If the mercury column is lower than the first value, obviously the outflow of mercury will not be observed. For construction of the electrode (DME) capillaries are commercially available. In case it is to be prepared from capillary tubing manually, the uniformity is the prime consideration. The length of the capillary used depends on its internal diameter and on the experimental objectives. Usually, the largest drop times should Mercury not exceed 7–8 sec. In general, the capillary Reservoir should be such as to give a drop time of the order of 3–4δ with h t equal to ca. 40 cm when the capillary is dipped into solution. If drop times are too long, it should be cut because a linear dependence exists between length of the capillary and td. The mercury reservoir usually has a volume varying between 100 and 200 cm3. The platinum wire used to make contact to the DME may be dipped in mercury reservoir or sealed in the stand tube. The common assembly used is shown in Fig. 2.1. The connection to the mercury Drop knocking reservoir in normally made using a soft plastic device tubing such as Tygon. The inside diameter of this tubing should be of the order of 5–7 mm Capillary and the connection to the capillary should be reinforced with wire. Once the capillary has been connected, the mercury reservoir should be filled with pure mercury (triply distilled mercury). While filling entrapping of air bubbles should be minimised. The DME requires a stand that facilitates changing position of the mercury reservoir. The mercury reservoir should always be elevated and Fig. 2.1 : Mercury reservoir assembly the flow of mercury observed, before the capillary for use in dropping mercury electrodes

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Introduction to Polarography and Allied Techniques

is placed in an experimental solution. When the experiment is over, the capillary be placed in distilled water, washed well with it (if required non-aqueous solvent). Mercury should drop there before washing. For parameters characterizing the DME could be determined in the following way. The capillary is placed in a solution of the supporting electrolyte. The mercury reservoir is adjusted to a given h t and a potential is applied, either a value related to experimental measurements or in the range –0.5 to –0.6 V vs S.C.E. A stop watch is used to measure the time for 10–20 drops to form and the drop time, td, is obtained by dividing the elapsed time by the number of drops collected. Mass flow rate of mercury, m, can be measured by collecting drops for a measured time and then weighing the washed and dried mercury. Usual units are milligrams per second.

2.1.3 Advantages of DME The dropping mercury electrode has several advantages over solid electrodes, these are summarized as follows : 1. The drops are very easily reproduced and thus give reproducible results. The regular dropping of pure mercury ensures that the electrochemical process always occurs at a fresh surface, virtually independent of the preceding polarization. As already indicated the results obtained in this manner are reproducible regardless of the irregular dropping in case precipitates are formed. The regular renewal of the surface ensures that the current is independent of the time of electrolysis and that the current voltage curve is the same whether recorded with increasing or decreasing voltages or even rapidly or slowly. 2. Owing to the very high over voltage of hydrogen towards mercury, the DME can be used over a considerable cathodic range of potentials without interference from hydrogen evolution. Polarographic curves for alkali metal ions may be recorded before hydrogen evolution takes place. Instead of mercury dilute amalgams may drop from the dropping electrode and anodic processes in the dissolution of the less noble metals may be studied. With commonly used supporting electrolytes, such as potassium chloride and potassium nitrate, the range extends to about 1.8 V (vs SCE). 3. In view of the behaviour of mercury as a noble metal, relatively positive potentials, but not of course exceeding that for the dissolution of mercury (about +0.4 V vs NCE) may be applied to the DME and the electrode may serve as an indifferent redox electrode for the study of oxidation reduction systems. Moreover, it is not subject to passivation or poisoning owing to constant renewal of mercury surface. This is in contrast to other electrodes. 4. Only small quantities of substances are deposited in the vicinity of the dropping electrode during electrolysis. For the reason there is no depletion of the depolarizer in the solution provided the volume of the electrolyzed solution is not too small. The curves obtained are identical even after several runs. 5. There is also an important factor for the application of polarogaphy is microanalysis because with a thin drawnout capillary the electrolysis of very small volumes (0.01 – 0.005 ml) may be studied.

The Electrodes

15

6. Processes may be studied that take place in aqueous solution in the potential range +0.4 to –2.6 V; and in non-aqueous solution upto –3.0 V (mix of dioxan and water) against the (NCE) normal calomel electrode. At potentials more positive than +0.4 V anodic dissolution of mercury and at potentials more negative than –2.6 V (or –3.0 V) decomposition of water or of the given solvent takes place. Besides, the advantages the use of DME is somewhat restricted. At positive potentials mercury undergoes oxidation and therefore other type of electrodes (standing mercury electrode or solid electrodes) must therefore be used. The volatility of mercury prevents the use of the DME in melts at higher temperatures. Good results are obtained at temperatures upto 100°C.

2.1.4 Hanging Mercury Drop Electrode (a) HMDE Suspended on a Metallic Contact : A simple HMDE was developed by Gerischer [4]. Using this approach 1 or 2 mercury drops falling from the classical DME are collected on a miniature spoon and transferred to a small metal contact scaled is glass or plastic material (Fig. 2.2). The length of the exposed contact wire is usually on the order 0.1–0.5 mm and its diameter is about 0.5 mm. Electrodes of this sort have many different Threaded plunger chemical properties from pure mercury electrodes, because of the formation of a gold or platinum amalgam [5]. Normally, a drop is suspended just prior to an experiment and this problem will, therefore, be of no consequence. Nevertheless, Plastic collar since the solubility of these noble metals in mercury is of the order of 0.05 M, the concentration of gold or platinum in mercury may be quite significant on a longer time scale. In such Reservoir and cases gold or platinum may form intermetallic Capillary (glass) compounds with several metals which are electrodeposited into the mercury [5]. (b) Capillary HMDE : This type of the HMDE consists of a small mercury drop with radius usually not exceeding 1 mm which hangs on a thin mercury thread in a glass capillary. The inner diameter of this capillary is about 0.15–0.21 mm, considerably Fig. 2.2 : Assembled unit, larger than for the DME. An electrode of this Hanging Mercury Drop type was used for the first time by Antweiler [6]. Electrode Preparation of reproducible HMDE as per this original model was very difficult. Kemula and Kublik [7] pointed out that suspended HMDE is more reproducible in comparison to the early design capillary HMDEs.

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Introduction to Polarography and Allied Techniques

In the most successful designs, the mercury is pushed out mechanically. Randles and White [8] used this type of electrode, where mercury was pushed from the capillary by turning micrometer screw. The most popular electrode used these days was developed by Kemula and Kublik [7]. A detailed assembly of this electrode is shown in Fig. 2.2. It is composed of a thick walled glass tubing with an internal diameter of 4 mm, approximately 5 cm long. This forms a mercury reservoir which is sealed to a thick wall capillary. The internal diameter of this capillary is commonly 0.18 mm, but may vary somewhat around this value. The length of the capillary will depend on the size of the electrolytic cell. A groundglass joint on the mercury reservoir can provide a convenient means of supporting electrode in a cell. A Teflon thermometer adapter also works well. The top of the reservoir resembles a glass ring which is flat and very smoothly polished. This part of the electrode is connected to the plastic head, which is composed of two parts. These parts are shown in Fig. 2.2. After the capillary is inserted through part b, part c is screwed rather tightly into part b. The end of the mercury reservoir should then be tightly sealed by the bottom part c. To provide a tight seal a small plastic cylinder is extended from part c, being bit thicker than the internal diameter of the glass tubing. This small cylinder, schematically shown in Fig. 2.2, should enter into the reservoir tubing with a pressed fit when all parts of the HMDE are put together. A threaded steel piston of 2 mm in diameter moves in part c. By turning this screw by a fixed angle, for instance 90° or 180° mercury will be pushed out from the capillary and will hand as a drop from its end. It is important that the piston screw be set tight in the polyethylene part as shown in Fig. 2.2. In Fig. 2.2 the HMDE is shown ready for use. To ensure that the electrode works properly, special care should be taken to coat the internal part of the capillary with a hydropholic silicone film. The capillary should be thoroughly cleaned before a new coating is applied. Sodium hydroxide (2 M) should be used to remove any residual silicone. The capillary should them be washed with 3 M nitric acid, rinsed with distilled water, and dried thoroughly. Then a 5% solution of dichlorodimethylsilane in CCl4 is pulled through the capillary, followed by air. After several hours at room temperature or about 15 min. at 110°C, the capillary is ready for use. The silicone coating should be renewed from time to time. Specially when ranging drop tends to fall during an experiment. This happens when the silicone coating and the capillary wall is partly destroyed and solution enters between the glass and the mercury thread. The mercury reservoir and the capillary should be completely filled with mercury. There must be no entrapped air. The vessel should be filled with mercury such that the end of the capillary is covered when the vessel is placed in a horizontal position. With all of the mercury in part b, the vessel in connected to a vacuum pump, with a three way stop cock to decrease the pressure in the vessel and in the electrode down to 0.01 mm. After evacuation, the vessel is tilted into the horizontal position as shown in the Fig. 2.3 and the stop cock is turned to disconnect the pump and then turned further to admit air into the vessel. The pressure of air acting on the mercury in the vessel

The Electrodes

17

pushes it into the reservoir and the capillary of the HMDE. If the pressure had been decreased to 0.01 mm, mercury fills in the reservoir and capillary completely. The HMDE is now ready for use. By turning the screw to a fixed angle, a known amount of mercury is pushed out, forming a drop. Such an electrode can be prepared in the laboratory. These electrodes are equipped with a micrometer type of screw of pressing out a well-defined amount of mercury.

2.2 CARBON ELECTRODES Many interesting reactions can be studied which are not accessible at a mercury surface. A wide range of materials have been employed as solid electrodes, but the noble metals particularly platinum and gold, and carbon have emerged as the most popular ones. The ideal properties of a material for use as solid electrode are that: (i) it should be easy to incorporate into an electrode, (ii) it should have a large potential range, a low electrical resistance, and (iii) an easily reproducible surface. These criteria are met only to some degree by many materials. The properties of various types of carbon make it the material of choice for many applications.

2.2.1 Carbon Paste Electrodes The carbon paste electrodes (CPE) was introduced by Adams [8] and generally consists of a Teflon well into which is inserted a platinum, copper, steel or graphite 3 mm spectroscopic contact. The Teflon well may be mounted graphite in the end of a suitable glass tube or consists simply of a piece of Teflon tube as illustrated in the Fig. 2.3. 7 mm O.D. Pyrex The well is filled with a paste, made tubing by mixing powdered graphite with a suitable mulling liquid. Practical consideration require that the mulling liquid should have a low volatility, purity with respect to electroactive impurities, and very low solubility in the medium to be employed. These consideration generally limit the choice of mulling liquid to bromoform, bromonaphthalene, or mineral oil (Nujol). Preparation : A typical paste for CPE may be prepared by mixing Nujol 10 mm Teflon insert machined and graphite powder thoroughly (could for press fit be UCP 1 M from ultra carbon corporation) until the mixture is Polished flat uniformly wetted. The resultant paste should have a consistency similar to that Fig. 2.3 : Conventional Carbon Paste Electrode

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Introduction to Polarography and Allied Techniques

of peanut butter. The best would be to take 3 gm of carbon to 2 ml of oil. Carbon rough surface should not be used since they give poorer peak current reproducibility. Pastes that appear satisfactory for conventional experiments at millimolar concentration may give rise to many disconcerting background peaks when pulse voltammetry at the micromolar level is tried. High purity graphite is important and the graphite (and paste) should not be unnecessarily exposed to the laboratory atmosphere. It is advisable to divide freshly prepared paste into lots of about 1 gm and to store these in small wide mouth vials. In practice a small amount of paste is placed on a clean card (could be an unused IBM computer card); the electrode is gently pressed into this pile and then rubbed on the card to remove excess paste and to attain a flat surface. The well is filled completely, leaving no holes or channels. Any paste remaining on the mantle is carefully wiped away with a paper tissue. Electrodes may be assembled and packed in quantity and stored in covered box. Electrodes may be renewed by removing a small amount of paste from the surface with a paper tissue and repacking with fresh paste. It is important to note that when packing the well, avoid applying too much pressure. This may result is separation of the carbon and oil. This would result in high resistance contact between the paste and the metal. Other methods of pastes and electrode preparation are being described by many workers. The formulations and methods of preparation of the CPE as described above are quite satisfactory for use in aqueous solutions containing perhaps as much as 25% alcohol or other solvents. However, when carbon paste electrodes of this type are used in non-aqueous media (e.g., acetonitrile, nitromethane, propylene carbonate), the pool of carbon paste tends to disintegrate. The cause of this disintegration appears to be dissolution of the mulling liquid or the preferential wetting of the graphite by the solvent. This difficulty can be overcome by addition of a surface active agent, such as sodium lauryl sulphate, to the paste [15]. The advantage is that the latter compound causes the graphite to be wetted equally well by both, mulling liquid and the nonaqueous solvent. It is a normal practice to prepare a new electrode surface before running each voltammogram. This is done by removing the surface layer of paste and refilling the Teflon holder. This is quickly reproducible manually as recommended by many workers. The preparation of a CPE with an increased positive potential range (+ 1.7 V vs SCE is 0.1 M H2SO4) has also been described [17]. It has been reported by several authors that adsorption of electroactive species at the electrode surface takes place while using CPE. This may be due primarily to the dissolution of the electroactive species in the organic phase of the CPE, although the effect is not of a major importance. All carbon paste electrodes described in the literature have been designed for voltammetric studies. The range of potentials over which the CPE can be used in quite large (large literature values are available).

The Electrodes

19

2.2.2 Glassy Carbon Electrode Glassy carbon was first used as an electrode material by Zittel and Miller [34], although it is commercially available. For this electrode a length of 3 mm diameter glassy carbon rod is scaled into a length of 5-mm tubing with epoxy cement. A few millimeters of carbon are then exposed then from the end of the glass tube using a glass cutting wheel. The end of glass tubecarbon rod assembly is then polished with emery paper, followed by polishing alumina until a mirror finish is obtained. Before each voltammogram is run the electrode is buffed for about 5 sec. with 1μ m alumina, rinsed and placed in the electrochemical cell. Some authors also used the electrode for stripping analysis and others have used it in molten salts as well. Typical data on positive and negative potential limits at GCE are given in the literature. Methods to modify the electrode are already in progress.

2.3 POLAROGRAPHIC CELLS AND SATURATED CALOMEL ELECTRODE

5 mm O.D. Pyrex tubing

Mercury

3 mm Glassy Carbon sealed with epoxy resin

Fig. 2.4 : Typical Glassy Carbon electrode for Voltammetric Studies

It is a long-standing custom of referring all polarographic potentials to the saturated calomel electrode. This is done to permit comparison of half-wave potentials measured in different media. Since the potential of an internal reference electrode varies from one medium to another such comparisons can be made only if the potential of the internal electrode is measured against an external saturated calomel electrode. The cell is that portion of the apparatus which contains the solution being studied. It also includes a non-polarizable electrode to which the potential of the dropping electrode is referred. Oxygen must usually be removed by bubbling an inert gas through the solution before measurement, because oxygen is reducible at the dropping electrode over most of the range of potentials which are important in polarography. It may also have other undesirable effects. The most important part of a cell is its reference electrode. The polarograph applies a voltage across the cell; even neglecting for the moment the iR drop. Any variation or error in the potential of the reference electrode leads to a corresponding uncertainty in the potential of the dropping electrode. It is also important that the potential of the reference electrode be not only known but also essentially independent of the current flowing through it. Two kinds of reference electrodes are in general use. These are “internal” and “external” electrodes, which are generally used. An internal electrode is in direct contact with the solution being studied, while the external electrode is separated

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Introduction to Polarography and Allied Techniques

from it by a salt bridge or a porous membrane. Internal reference electrodes cannot be used in solutions containing oxidizing agents which have powerful energy to oxidize the electrode metal, or reducing agents are powerful enough to reduce the poising salt (Ag X, Hz 2 X2). Not are they as useful when the dropping electrode is the anode or when it is the cathode. In the former case the solution is usually capable of reducing the poisoning salt chemically, and even of this reaction were slow the poisoning salt would be reduced at the reference electrode as the polarogram was recorded. External reference electrodes, on the other hand have potentials that are either accurately known or can be measured once and for all (usually the SCE is used) and that are independent of the composition of the sample solution. With this only very frequent checking is needed to ensure that no contamination has occurred. When carefully used they rarely need renewing. They may be used with solution containing strong oxidizing or reducing agents. They also render the presence of a depolarizing anion in the sample unnecessary, thereby permitting the range of the dropping electrode to be extended to somewhat more positive potentials. The most widely used cell with an external reference is the H-cell. For Contact to A sample is shown in Fig. 2.5. It consists Mercury Column of two compartments. One containing the solution being studied and the other containing the reference electrode. To avoid ConstantHead polarization of the reference electrode, the Mercury Reservoir compartment containing it should be made from tubing of at least 20 mm i.d. The dimension of the solution compartment can 75 cm be varied widely to accommodate any desired volume of solution. As per the LinganeLaitinen cell as shown in the Fig. 2.5, these compartments are separated by a crossCapillary Tube member filled with a 4% agar-saturated potassium chloride gel, which is held in place Annular For Contact by a medium-parosity sintered-Pyrex disc. Space for To Reference Escape of Nitrogen Electrode In order to facilitate rapid and complete Nitrogen Inlet Tubes deaeration of the solution, the disc should be placed as near to the solution Agar compartment as possible. At the same time Plug Reference the side tube through which the inert gas is 10 cm. Cell passed through the solution should be as near to the bottom of the cell as possible. Sintered Solution The agar gel is prepared by warming 4 Glass Disc of Sample gm of agar and 90 ml of water in a small flask which is put in large beaker filled with boiling water or on a steam bath until Fig. 2.5 : H-cell and stand tube according to Lingane and Laitinen solution is complete. After this 30 gm of

The Electrodes

21

potassium chloride are added and the whole thing is stirred thoroughly. After this the gel is allowed to solidify which must be white to avoid contamination of the solution coming in contact with it. When the salt is dissolved, the clean dry cell is clamped with the cross-member vertical and the solution compartment down. The gel is pipetted into the cross-member until it is almost completely filled. The cell is then allowed to stand undisturbed until the gel is solidified. The unused gel may be stored in a lightly stoppered flask which could be used again after reliquing it. After the gel is solidified, the cell is turned upright the enough pure mercury is added to the reference-electrode compartment to give a layer 1 to 2 cm deep. This is then covered with an equally thick layer of a paste made by stirring equal weights of mercurous and potassium chlorides with a little saturated potassium chloride. The compartment is then filled with saturated potassium chloride solution containing a large excess of solid salt. Electrical connection to the mercury is made by means of a glass tube through which a small platinum wire is sealed so as to project into the mercury for a few millimeters. This tube is filled with mercury and inserted into a rubber stopper which serves to seal the reference-electrode compartment lightly. The wire leading to the reference-electrode terminal of the polarograph is simply dipped into the mercury in this tube. The solution compartment of the cell should finally be filled with saturated potassium chloride solution and a day or two should be allowed for the SCE to attain equilibrium. While in use, the solution compartment is emptied, washed with water and either dried or rinsed with several portion of the sample. Then enough solution is added to cover the entire fritted disc. Dissolved air is removed by passing nitrogen into the side tube so that it bubbles through the solution. Measurements should not be attempted while the gas is bubbling through the solution. Stirring may cause high erratic currents. Finally the dropping electrode is inserted through another hole in the stopper and the measurements be carried out. It is advisable to keep two cells available in routine work so that the solution can be deaerated in one while the other solution is being examined in the other cell. Insertion of dropping electrode should be deferred to avoid prolonged contact between mercury and the solution. If it is inserted before deaeration is complete, mercurous or mercuric ion may be formed according to the reaction: 4 Hg + O2 + 4H+ = 2Hg2++ + 2H2O In case, the solution in acidic and contains no ion yielding in soluble mercury salt, or an appreciable fraction of a heavy metal ion may be lost by a reaction like Pb++ + 2Hg + 2Cl– +

1 O + H2O = Hg2Cl2 + Pb(OH)2 2 2

if the solution is neutral and unbuffered. The solution compartment of an H-cell should never be allowed to stand empty for more than a few minutes at a time. The agar bridge will dry out and shrink, allowing bulk flow of the liquid between the two compartments of the cell. It should always be

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Introduction to Polarography and Allied Techniques

kept filled with either water or, for overnight or longer period with saturated potassium chloride. Mercury must also be removed before the cell is allowed to stand even overnight to avoid air oxidation of mercurous salts. Contamination of H-cell must be avoided using various samples.

2.4 MERCURY POOL ELECTRODE Mercury pool reference electrode has been widely used since the beginning of polarography. It is simply a pool of pure mercury on the bottom of the cell, connected to the polarograph via a platinum wire sealed through the wall of the cell. The area of the mercury pool electrode should not be too small but need not exceed several square centimeters. Micro cells of various sizes can also be used which may contain small volumes of solution. Mercury pool electrodes should be used only in solutions that contain ions giving insoluble mercurous or mercuric ions.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

Ku•cera, B. Ann. Phys. 11:529 (1903). Heyrovspy, J., Chem. Listy 16:256 (1992) Philos. Mag. J. Sci. 45:303 (1923). Kolthoff, I.M., and Lingane J.J., Polarography, Vol. I, Inter Science, N.Y. 1952. Gerischer, M., Z. Phys. Chem. 202:302 (1953). Kemula M. and Coworbers, Bull. Acad., Pol. Sci. Cl. 111 7:73 (1959). Ant Weiler, H.J., Z. Electrochem. 44:831 (1938). Kemula W., and Kublik Z., Advances in analytical Chemistry and Instrumentation, Vol. 2, Wiley Int. N.Y. (1963) p. 123. Randles, J.E.B. and White. W., Z. Electrochem. 59:666 (1955). Adams R.N., Anal. Chem. 30:1576 (1958). Marcoux, L.S. and Coworbers, Abel. Chem. 37:1446 (1965). Lind quist, J. Anal. Chem. 45:1006 (1973). Zittel, H.E. and Miller, F.J., Anal. Chem. 37:200 (1965).

CHAPTER 3

THE TECHNIQUE 3.1 POLAROGRAPHIC CIRCUIT Polarography constitutes a unique type of electrolysis in that it involves the study of current voltage relationships at a dropping mercury electrode under certain controlled conditions. A current-voltage (or current-potential) curve can be obtained by gradually increasing the applied voltage and measuring the corresponding mean currents; plotting the currents against voltage. In order to avoid time consuming measurements and curveplotting, automatic recording polarographs are available. These instruments serve for recording based on electrochemical polarization. Any electrolysis involves two main types of processes, e.g., transference of matter through a solution towards and away from electrodes and electrochemical processes involving as an essential part the exchange of electrons at the electrode surfaces. During an electrolysis, three mass transfer processes are of importance, namely, migration, diffusion and convection. The first of these is an electrical effect depending upon the charge carried by an electroactive species and upon its transference number. Thus, the effect is encountered only with charged species. Since processes of diffusion are non electrical in origin, these are for all species in solution whether they are charged or not. Convection effects include motion of small particles under the influence of stirring, mechanical agitation, and temperature gradients.

3.2 THE SIGNIFICANCE OF DIFFUSION IN CLASSICAL POLAROGRAPHY While studying the polarographic work, the migration effect is usually eliminated and it is usual to study the oxidation or reduction of electroactive species in solution under conditions such that the latter arrives at the indicator electrode by natural diffusion only. Suppression of migration effect is achieved by mixing together with the species under study, an excess of supporting “electrolyte” or “indifferent” electrolyte normally 50–100 fold is excess of the electroactive component of the solution. This added electrolyte is so chosen that no electrode reactions characteristic of it interferes with those of the species under investigation. Supporting electrolytes serve as current carriers and, by virtue of being in excess effectively reduce their transference numbers to zero. Convection effects are eliminated by carrying out the electrolysis in adequately controlled thermostats so as to protect the apparatus from all forms of shocks and vibrations.

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Introduction to Polarography and Allied Techniques

Current i

Basically, polarography consists of electrolysing a solution containing several cations between a dropping mercury electrode and some reference electrode. The –ve dropping mercury electrode (DME) usually functioning as cathode. A potential is applied between these electrodes and increased in a step-wise manner. During this process, corresponding current changes being observed at each applied potential. Essentials of the electrical circuit required +ve are shown in the Fig. 3.1. The applied potential is varied by means of a potential divider circuit while the current flowing is indicated on a sensitive galvanometer. Diffusion-controlled currents observed in Fig. 3.1 : Essential Polarographic Circuit polarography are usually of the order of a few micro-amperes since the electroactive material used is of the order of 10–3 molar. As already given in Chapter 2, a dropping mercury electrode consists of a series of small mercury droplets which emerge, at a constant rate, from the tip of a capillary attached to a constant head device. The life-duration of each drop normally lies between 3–7s. Considering the reference electrode and anode a large area mercury pool on the bottom of the electrolysis cell is shown to be used. This is just for the sake of simplicity. Due to its large area and the small magnitude of the currents normally encountered, the potential of such a electrode remains fairly constant with varying applied potential. For most practical measurements, it is normal to replace this by a saturated calomel electrode (SCE) [see Chapter 2] or some other reliable reference electrode whose potential is independent of the imposed Diffusion current id potential. To examine the nature of the current voltage relationships Residual current observed on reduction of a metal ion in solution, it is necessary to flush the working solution with some inert gas, such as nitrogen or hydrogen, so as to remove dissolved oxygen which may cause Half wave applied e.m.f. potential E½ interference by itself undergoing reduction, in two stages, within the Fig. 3.2 : Essential features of a polarographic currents normal potential working range. voltage curve/polarogram or polarographic wave When this interference is removed

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the current-voltage curve for the reduction of the metal ion will have the appearance of that shown in Fig. 3.2. At first, as the potential is increased cathodically from zero, only a very small currents flows. This is called the residual current. This is essentially a charging current arising from the charging of the double layer at each drop and is non-faradaic. The residual current may also contain small (faradaic) components due to the presence of reducible impurities in the solution. These may be introduced through the high concentration of the supporting electrolytes used. Only the residual current flows until the decomposition potential of the reducible ionic species is reached. At this point the ions, designated mn+, begin to be discharged owing to their reduction by the process: Mn+ + ne

M (Hg)

...[1]

↓ (Product of electrode reaction) Very often the metal atoms produced are absorbed into the mercury drop in the form of amalgam. A steep rise in current is now observed and, with a further small increase in applied, potential, the rise will continue. However, the Mn+ ions Depolarizer Concentration arrive at the DME by the relatively slow process of natural diffusion. Since C0 = Bulk concentration the rate of reduction increases with the applied potential, a point is eventually reached at which the ions Electrode are reduced as fast as they diffuse Surface C = Surface concentration solution across the concentration gradient set up at the electrode surface. The Fig. S = Diffusion layer thickness 3.3, represents the concentration gradient in the immediate vicinity of planar section of the electrode surface. Distance from electrode surface→ When the concentration of ions at the electrode surface approaches zero, the Fig. 3.3 : Concentration gradient at coplanar section of electrode surface induced by the current no further increases in the occurrence of an electrode process. overall electrode reaction rate which is now the decomposition potential of some other reducible species present in solution is reached. This could be regarded as the discharge of supporting electrolyte cation, though not hydrogen due to the exceptionally large hydrogen overvoltage on mercury. Particles reduced at the mercury surface subsequently diffuse away from the surface and this may occur in one of the two ways: (i) If an amalgam is formed, e.g., with thallium, lead, cadmium, zinc and alkali metals. In this case, the reduced particles diffuse from the drop surface into the bulk of mercury forming the drop which subsequently detaches from the capillary tip;

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Introduction to Polarography and Allied Techniques

(ii) If amalgam formation does not occur, e.g., for the reduction processes Fe3+ Fe2+ and Sn4+ Sn2+. The reduced species simply diffuse back into the bulk of the solution. The importance of polarography for quantitative analysis lies in the direct proportionality which exists between the limiting diffusion current and the concentration of the reducible species or “depolarize”. It is to be noted that at the foot of the currentvoltage curve, or polarographic “wave”, and at the limiting current plateau, the dropping electrode behaves is accordance with the definition of a “polarized” electrode. That is to say, the potential applied to it may be altered at will within these regions without sifnificantly altering the current flow. On the rising part of the wave, the current changes considerably for only a small variation in applied potential and the DME is said to be “depolarized”. In the region of the plateau current, id, the dropping electrode is completely “concentration polarized”, since the electrode reaction rate is controlled by the diffusion rate and hence by the concentration gradient at the electrode surface. The potential corresponding to the mid-point of the wave, where the current is exactly one-half of the maximum value id/2, is known as the “half-wave potential”, E ½. This is depolarized under fixed solution condition. Measurement of half-wave potentials therefore serves as a means of identification of different reducible species. (ii) Experimental Technique : For experimental purpose let us consider the electrolysis of a solution containing a cation or a solution containing several different cations, e.g., Cu+2, Tl+, Zn+2, etc. There is a certain reversible potential at which each ion is discharged at the cathode. The potential depends on the standard E 0 of the electrode M/M+2 and on the concentration of M+2 in the solution. At 25°C, E = E0 +

00592 . +2 log aM [z ]

...[2]

Thus a tenfold change in the ionic activity changes the discharge potential of the ions by 0.0592/(z) volts. A factor of 102 in activity corresponds to 0.1184/(z) volts. On gradually increasing the potential applied to the cell, the cation with the highest value of E deposits first. On continuing to increase the applied potential, the current density also increase. As the current density rises, the concentration of the ion being discharged becomes more and more depleted in the neighbourhood of the cathode, particularly if the solution is not stirred. This is the phenomenon of concentration polarization. Eventually the limiting value of Id′ is reached for the care of stationary electrodes. The Id vs voltage curve becomes flat and the potential rises to a value determined by the reversible discharge potential of the cation with next higher E. When this happens the second ion begins to be discharged, even though there may still be an appreciable concentration of the first ion in the bulk of the solution. With increasing E, this process may be repeated with a third kind of ion, and so on. If concentration polarization is used to differentiate reducible substances in a solution, it is necessary to have a cathode of tiny area, since otherwise the current

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27

through the cell would become very high. Transference must also be eliminated on the part of the electroactive ion so that the current is not strongly dependent upon the mobility of the anion present. Also the cathode surface should be clean, reproducible and, readily renewable. These conditions are met by the DME, which provides a continuous flow of droplets of mercury, about 0.5 mm in diameter. The anode should be practically non-polarizable. A pool of mercury located at the bottom of the cell can serve as a reference electrode and anode. It is negligibly polarized because of its large area. Alternatively, standard reference electrodes of large area can be used as reference anodes. These specifications are already given in previous chapters. A typical current density vs voltage curve in shown in Fig. 3.4.

Current , microamperes

2

a

b

c

1

0 –1.2

–1.2

–1.2 Ed.e. , volts vs. S.C.E

–1.6

Fig. 3.4 : Polarograms of 0.5 mM zinc (II) in 2F sodium hydroxide. The drop time at – 1.6 V. vs. S.C.E. was (a) 12, (b) 4, and (c) 1.4 sec.

The high over voltage for hydrogen discharge on mercury is a great advantage in the polarographic study since, it allows many ions to be studied which have reversible electrode potentials below H2 / H+. Even Na+ and K+ may be discharged before H+ at the dropping mercury electrode. During the process of experiment, the current oscillates between a maximum and a minimum as each mercury drop grows and falls. The overall rise from one flat portion

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Introduction to Polarography and Allied Techniques

of the curve to the next is called the polarographic wave (as already described). The half-wave potential (already shown in figures) serves to identify the reducible ion. The value of the diffusion limited current for each ion is proportional to the concentration of the ion. The theoretical calculation of diffusion current is a solution of the diffusion equation given by Ilkovi•c, [2] I = 0.732F |z| D1/2 cm2 t1/6

...[3] where m is the mass of mercury flowing per second, D is the diffusion coefficient of the ion, t the drop time and c the molar concentration. This proportionality is the basis of quantitative application of polarography. It is to be noted that the current is proportional to the concentration for a given capillary and for a given ion. The Ilkovi•c equation can also be used to estimate [z] or D under the conditions of the experiment. Stationary micro electrodes are seldom used in practical polarography because the diffusion current decreases markedly with time as the thickness of the diffusion layer, δ, increases. In such experiments rotating platinum electrodes are used. From the equation [3] it is predicted that the plot of Ed.m.e. vs log [I / I ′ –I ] should be linear for a reaction that behaves reversibly under diffusion controlled conditions and the slope of this linear plot should be RT/2.303/z/F and that the intercept denotes the E ½. Polarography is useful in research because it is a convenient method for measuring electrode potentials and for studying electrode reaction.

3.3 SOLVENTS AND SUPPORTING ELECTROLYTES All electrochemical phenomena occur in a medium, which generally consists of a solvent containing a supporting electrolyte. The “solvent system” is a term to describe the medium consisting of both the solvent and the supporting electrolyte. As a matter of fact there is no universal solvent, and generally a system is used whose merits outweighs its disadvantages for a particular application. It may happen that a good solvent system for one type of experiment or compound may be totally unacceptable for other application. It is therefore one’s choice as to how the chemical and electrochemical properties of the electrode reaction in which one is interested may be affected by a particular solvent system. For all practical purposes, the solvent system should not undergo any electrochemical reaction over a range of potentials on which the reaction is to be carried out. A solution of tetrabutyl ammonium hexafluorophosphate in acetonimile exhibits positive and negative decomposition potentials of +3.4 and –2.9 V (SCE) respectively. In practice one rarely needs both positive and negative ranges in a single set of experiments. Solvents are often used which exhibit either a very negative or very positive decomposition potential, but not both. For example both nitrobenzene [3] and methylene chloride [3] have been used for studies of oxidation processes because they are oxidized with difficulty, not withstanding with the fact that they are actually quite easily reduced. On the contrary, liquid ammonia and methlamine are good solvents for electrochemical reduction, although poor for oxidation.

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As a matter of fact the potential limit in a given solvent system is set not by the solvent itself but by the electrochemical behaviour of the supporting electrolyte. It has been known for years that the reduction of alkali metal ions to the corresponding metals (–2 V vs SCE) is generally the potential limiting process in aprotic solvents and that by use of tetra alkyl ammonium salts one can reach considerably more negative potentials. The decomposition potentials of tetra alkys ammonium ions of mercury become more negative as the alkyl groups become larger, e.g., Me4 N+ : 2.65 V; Bu4 N+ : – 2.88 V. In order to support passage of an electrical current, the solvent system should have low electrical resistance and a moderately high dielectric constant (≥ 10). A number of most commonly used solvents used in organic electro chemistry have satisfactory dielectric constants, e.g., dimethyl formanide (3.6), acetonitrile (37.5) and dimethyl sulphoxide (46.7). So also their electrolytic solutions have acceptably high conductances. Considering the solvent power, an electrochemical solvent must be able to dissolve a wide range of substances at acceptable concentrations. This generally means that electrolytes must be soluble at least to the extent of 0.1 M, while the electroactive material must form approximately millimolar solution for application of the various electroanalytical techniques or greater for preparative electrolyses. Tetra alkyl ammonium perchlorates, hexafluoro phosphates and tetra fluoroborates generally exhibit the most satisfactory solubility as electrolytes in organic solvents. As a matter of fact chemical inertness of the solvent is an important aspect to be considered. The solvent, as such should not react with the electroactive material, nor with intermediates or products of the electrode reaction under investigation. No one solvent could reasonably be expected to be unreactive toward all of the many kinds of reactive species which can be generated electrochemically. It is known that many anodic organic reactions generate cationic species [1] and hence to use a nucleophilic solvent is not desirable. Acetonitrile is commonly used in anodic studies but it is moderately nucleophilic. Therefore attempts to characterize electrochemically generated cations may require a less reactive solvent, e.g., methylene chloride or one of the “super acid” solvents. On the other hand, reductions of organic species generally form anions, and use of protic solvents to avoid acid-base reactions between the solvent and cathodically generated intermediates. On the whole solvent should reasonably be stable so that purification, preparation, and storage of standard solution does not create major problems. Also the solvent should have a convenient liquid range. No doubt this depends on the experiment involved. Much depends whether the experiment is to be carried out at room temperature or otherwise. Moreover the solvents and electrolytes should be inexpensive, nontoxic, and non-flammmable. The latter two characteristics are not well satisfied by most organic solvents. They can be used with in acetonitrile and are stable to very positive and negative potentials salts like hexa fluorophosphate are rather insoluble in water, which means that they are non-hydroscopic and can often be separated from reaction products by evaporation of the acetonitrile followed by appropriate treatment (e.g., extraction with a non-polar solvent). Inorganic electrolytes like NaBF4 or NaClO4 may be useful in such cases. Methylene chloride is useful in organometallic

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Introduction to Polarography and Allied Techniques

electrochemistry in situations where acetonitrile is found to displace ligands coordinated to a metal center. Dimethyl formamide, acetonitrile, and dimethyl sulphoxide are all excellent solvents for reductive electrochemistry of organic compounds. Water and alcohols are useful for inorganic electrochemistry. Dimethyl sulfoxide is particularly useful solvent for cathodic electrochemistry, although with inconvenient liquid range (18–189°C). TBAHFP and TBATFB are good electrolytes for use in organic solvents. Dimethyl sulphoxide is an excellent solvent for both organic and inorganic compounds. Water which is always present in dipolar aprotic solvents is a poor proton donor in DMSO. TBAHFP and TBATFB are two of many electrolytes for use in DMSO. Irregular drop time behaviour is observed in polarography in DMSO, possibly due to strong proper ventilation and safety precautions. Nevertheless, the property, viscosity may be of importance. When time interval is wished to be extended, i.e., the time interval over which mass transfer is occurring solely by diffusion (e.g., potential-step experiments) but would be a disadvantage where efficient mass transfer is required, as in preparative-scale electrolyses.

3.3.1 Recommended Solvents and Electrolytes Much inorganic oxidative and reductive electrochemistry has been carried out in water with little difficulty. Organic and organometallic compounds generally either are not very soluble in water or are reactive towards it. This has created interest in the use of non-aqueous solvents in electrochemistry. Ethanol and methanol are good organic solvents, inexpensive, readily available in high purity and dissolve salts readily. Alcohols, like water are rather easily oxidized and are highly nucleophilic. Hence it has been more common to use aprotic organic solvents for electrochemical oxidations. At the present time acetonitrile is the most commonly used organic solvent for anodic electrochemistry. It is preferred solvent for most purposes having a convenient liquid range (–45.7– 81.6°C). Tetrabutyl ammonium hexafluorophosphate or tetrafluoroborate salts are highly soluble adsorption of DMSO or dimethyl sulphide on the mercury surface. Most widely used organic solvent for cathodic chemistry has been DMF. It has a number of desirable properties at the same time it is quite toxic and undergoes undesirable reactions on storage. It is felt that acetonitrile and dimethyl sulphoxide are preferable to DMF as solvents for most applications. Hexamethyl phosphoramide (HMPA), ammonia and methylamine are excellent solvents for electrochemical generation of solvated electrons. Lithium chloride is recommended as the supporting electrolyte for this application. The properties of HMPA are otherwise generally similar to those of DMF and DMSO. Tetrahydrofuran (THF) and other ether solvents are useful aprotic solvents for cathodic electrochemistry inspite of their low dielectric constants, because they can be dried more efficiently than the other polar solvents. Note : More details are given in the chapter describing non-aqueous solvents.

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3.4 POLAROGRAPHIC MAXIMA It is often observed on polarographic curves that an increase of current above the limiting value takes place in the form of various shapes. In some cases the origin of the current maximum is connected with the mechanism of the electrode process, as happens during the catalytic discharge of hydrogen ions. More frequently, the polarographic maxima are caused by increased transport of the depolarizer towards the electrode by a streaming motion of the solution. Such maxima are reproducible and are called streaming maxima. These are divided into maxima of the first and of the second kind. Maxima of the first kind appears on the rising portion of the polarographic curve and usually occur in dilute solutions. The maxima of the second kind are observed in more concentrated solutions and at high mercury flow rates. They appear only over the range of the limiting current. These are usually rounded and do not fall discontinuously to the limiting current like the maxima of the first kind.

3.4.1 Maxima of the First Kind Kucera [3] put forth that streaming maxima of the first kind are connected with the anomalies observed on electrocapillary curves. Maxima of this kind appears on polarographic curves for currents governed by diffusion, usually in dilute solution of the supporting electrolyte used (below 1 N), the ratio of the concentration of depolarizer to that of the supporting electrolyte being from 1 : 1 to 1 : 100. Maxima have been observed during the polarographic reduction and oxidation [4] of cations, anions and neutral molecules and with anodic waves for the dissolution of amalgam [5], in both aqueous and non-aqueous [6] solutions and in melts [7]. Their shape is characteristic. The increase in current starts on the rising portion of the polarographic wave. The current rises rapidly with increasing voltage until it is several times greater than the limiting current. The maximum for the reduction of mercurous ions can be as much as 40-times higher than the limiting current [8] and then falls discontinuously to the normal current. Thus, a more or less sharp current peak which is typical of this kind of maxima is formed on the curve. The height of the maximum varies with different depolarizers. With the same substance it depends on the supporting electrolyte, on its concentration and on the presence of other substances present in the solution. At constant depolarizer concentration, the maximum increases with increasing concentration of supporting electrolyte upto a certain limit and then decreases again. The dependence of the maximum on temperature, drop-time and mercury flow-rate cannot be expressed by simple a relationship [9]. The height of the maximum is virtually independent of the height of the mercury head. In addition to other factors (depolarizer concentration, conductivity of the solution and drop-time), the voltage at which the decrease in maximum current starts depends on the direction in which the applied electromotive force is varied. The peak of the maximum on a reduction wave is upto 100 mV more negative with an increasing applied electromotive force than with a decreasing one. This phenomenon, called “hysteresis of the maximum” [10] is specially evident with longer drop-times and solutions of low conductivity.

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Introduction to Polarography and Allied Techniques

Streaming mercury electrodes do not give maxima. Particularly high maxima are termed during reduction of silver, mercury, copper, indium and alkali metals, persulphates and molecular oxygen. The cations of alkali metals, on the other hand, give small maxima. Cadmium which is reduced at the same potential as indium forms no maxima. As a rule, no maxima are observed with aldehydes and most nitro compounds. Maxima on the anodic waves for dissolution of amalgams exhibit the same features as those on the polarographic curves for depolarizers present in solution. The highest maxima about twice as high as the limiting current are given by amalgam of thallium, cadmium, and zinc. Smaller maxima were observed with tin and lead [11].

3.4.2 Suppression of Maxima of the First Kind The height of a maximum of the first kind is very sensitive to the presence of surface active substances in solution. Due to maxima it is impossible to evaluate precisely the polarographic curves. Hence, it is necessary to remove maxima by adding surface active agents. In practice, gelatin is usually employed but also, similar effect is found with other higher-molecular organic substances such as various acids and alcohols, dyes, terpenes and neutral detergents like Triton X and some others. These substances suppress maxima over potential range within which they are adsorbed on the mercury surface, hence the influence of the same surface agent on the maxima of different depolarizers is different. In cases where individual substances do not suppress maxima sufficiently, their mixtures are often used [6]. It is important not to add more surface active agent than is necessary. Even a slight excess may affect the electrode process which would not allow correct evaluation of the polarographic curve. Substances with a higher molecular weight or a low solubility suppress the maxima more efficiently than low molecular and easily soluble substances.

3.4.3 Polarity of Maxima of the First Kind In cases where the mercury surface bears a positive charge, the maximum is described as a positive maximum. This takes place if the half-wave potential of the depolarizer, the maximum for which is being investigated, lies on the positive side of the electrocapillary curve. If on the other hand, during the formation of the maximum, the electrode is negatively charged with respect to the solution, it is reported as negative maximum [Fig. 3.5]. No maxima of the first kind are formed at the potential of electrocapillary zero. The reduction of cadmium ions [12] can be taken as an example. At about –0.60 V (vs NCE) is the half-wave potential of free cadmium ions and no maximum is formed on the wave. On adding a trace of iodide the maximum on the electrocapillary parabola shifts to a more negative potential and a positive maximum appears on the cadmium wave. In the presence of ammonia or cyanides, both of which form stable complexes with cadmium ions, the reduction potential of cadmium shifts to negative potentials and a negative maximum occurs on the reduction wave.

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The polar character of maxima becomes evident from the way in – which they are suppressed [Fig. 3.6]. The negative maxima are – suppressed by polyvalent cations at sufficiently lower concentration + by di- or monovalent cations. The Mn suppression occurs in this case regardless of the anion of the –1.6V added salt. On the other hand the Ni positive maxima are not sensitive Tl to the valency of the cations. They –1.0V are more easily suppressed by S = 3:1000 –0.3V electrolytes with divalent than with monovalent anions. Other properties of ions are effective Fig. 3.5 : Positive maximum on the reduction wave for besides the charge. Thus heavy thallus ions and negative maxima for nickel (II) and cations suppress maxima more manganese (II) ions readily than those of the light elements. The polarity of positive and negative maxima also appears when dyes and colloids are added. Positive maxima are suppressed by anionic dyes, but negative maxima by cationic dyes or alkaloids. Similarly positive colloids easily suppress negative maxima and negative colloids are more powerful in suppressing positive maxima. Apart from the different behaviour of suppression, the positive and negative maxima differ somewhat in their shapes. The positive maxima exhibits a relatively broad rising portion, rounded peaks too and fall directly to the limiting current. The 1 negative maxima on the other hand 2 are on the lower side, more acute 3 and often decrease below the 4 5 limiting current. Fig. 3.6 : Influence of Ba2+ on positive and negative maxima. To 25 ml of 5.10–3 N TlCl and NiCl2 the following volumes were added: 1 0; 2 0.05 ml; 3 0.1 ml; 4 0.2 ml; 5 0.4 ml of 1 N BaCl2.

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Introduction to Polarography and Allied Techniques

3.4.4 Streaming of Electrolyte and Maxima of the First Kind Bruns and his co-workers [13] observed a streaming accompanying the maxima at a mercury cathode of 5 m diameter during the reduction of mercurous nitrate (in nitric acid with 70% ethanol) at low temperatures. The streaming occurs both at room temperature and at –37°C. At –38°C, when mercury solidifies, the streaming and the maximum disappears. Examples of streaming and maxima do not appear with solid electrodes except during the reduction of mercurous ions at a platinum electrode when a film of metallic mercury [14] forms on the platinum surface. Popova and Kryukova [15] demonstrated that the stirring at the surface of a dropping mercury electrode and the corresponding polarographic maximum can be evoked by placing the dropping electrode in an electric field between two platinum electrodes. In cases where, the surface active agents are added to the solution they are adsorbed on the electrode surface and are carried away by the motion of the mercury and of the electrolyte to the place of greatest surface tension. They accumulate there and decrease the surface tension and thus a force against the streaming arises. The iR drop increase with the growth of the mercury drop provided the resistance of the circuit is sufficiently large and the potential of the drop becomes more positive. Thus streaming may start suddenly on a drop through which a diffusion current passed at the beginning and on the current-time curve a jump up to the maximum current appears. This mechanism may explain the current-time curves observed by Bridi•cka [16] and the hysteresis of the polarographic maxima. If a polarographic cathodic curve is recorded with decreasing voltage then the iR drop in the diffusion current is smaller than that at the maximum and the zero potential is reached, i.e., the maximum appears at the lower applied voltage than with polarization in the reverse direction. Maxima of the second kind may be suppressed by reducing the flow rate, e.g., by lowering the height of the mercury head. In accordance with this dependence on the flow rate, no maximum of this kind has been observed with stationary mercury or other electrodes. It occurs with a rotating mercury electrode, but not with a streaming mercury electrode because of its specific hydrodynamic properties. At constant flow-rate and constant drop-time, a maximum of the second kind increases as a linear function of the depolarizer concentration. With increasing concentration of the supporting electrolyte, the decrease in current in the direction from the potential of electrocapillary zero becomes less steep. An external resistance in the polarizing circuit does not affect the height of a maximum of the second kind. No hysteresis has been observed with maxima of this kind. The temperature coefficient is greater than with diffusion currents.

3.4.5 Maxima of the Second Kind Maxima of the second kind occurs on both cathodic and anodic polarographic diffusion currents [17]. These occur usually in concentrated solutions of supporting electrolyte, above 0.1 N. They appear on the limiting current and may, depend on the purity of the

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35

solution, exceed it five times. In contrast to the maxima of the first kind, the current for these maxima does not fall back abruptly to the limiting current. It only decrease slowly and the greater the distance from the electrocapillary zero the slower the decrease. Exceptionally, a maximum of the second kind may occur with an extremely pure solution of 0.01 N –0.1 N supporting electrolyte at the potential of the electrocapillary zero. Its form then resemble a maximum of the first kind [Fig. 3.7]. The flow rate of the mercury is a decisive factor for the occurrence of maxima of the second kind. They appear as curves as soon as the linear speed of flow exceeds 2 cm / sec, this corresponds to m = 2.14 mg sec for a capillary with a diameter of 0.1 mm. The maximum grows approximately linearly with increasing flow-rate. Above the rate 8 cm/sec further growth of the maximum is retarded.

3.4.6 Suppression of Maxima of the Second Kind

μA

Maxima of the second kind are also sensitive to the presence of surface active agents like those of the first kind. They reflect better the adsorption of substance of widely differing character, since they are drawn out over a broader range of potentials than those of the first kind. A decrease in the maximum on a polarographic curve occurs in the presence of a surface active substance at the potential, at which the 40 substance is adsorbed. At the adsorption potential, the current attains the original value associated with the absence of 30 adsorption. The sensitivity of a maximum of the second kind to adsorption is some one hundred times greater than the 20 sensitivity of the shape of electrocapillary curves to adsorption, with increasing id concentration of adsorptive substance, the 10 decrease on the curve becomes more pronounced until the current falls finally to the normal limiting values and the 0 –0.5 –1.0 –1.5 V maximum of the second kind remains suppressed until the desorption potential Fig. 3.7 : A maxima of the second kind is reached. The plot of the maximum current against the logarithm of the concentration of the surface active substance is S-shaped curve, i.e., the maximum is most sensitive to the addition of a surface-active substance when the maximum has been suppressed to one-half of its original height. The maximum to the suppressive action of surface-active substance rises with increasing drop-time. The adsorption of a number of normal aliphatic alcohols were investigated by Kryukova and Frumkin [18] who suppressed the maxima on the Hg 2Cl2 wave in 3 N

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Introduction to Polarography and Allied Techniques

KCl. The adsorption of the alcohol on the electrode rises with increasing chain length. With easily soluble alcohols like ethanol, propanol or butanol, they observed increasing suppressive activity upto a certain concentration. On further addition, the maximum increased again. While preparing solution for studying adsorption by means of a maxima of the second kind, the utmost purity must be secured. Micka [19] recommended the purification of solutions by means of active carbon. The shape of a polarographic wave with a maximum of the second kind depends on the purity of the solution as regards surface-active agents.

3.4.7 Streaming of Electrolyte with Maxima of the Second Kind The increase of current above the limiting value due to a maximum of second kind is accompanied by streaming of the solution around the dropping electrode [20]. The direction of this streaming is always the same from the bulk of the solution to the bottom of the drop, over the mercury surface to the neck of the drop and there horizontally along the tip of capillary into the solution (Fig. 3.8). The intensity of this motion attains its maximum at the potential of the electrocapillary zero and slowly decreases with the distance from this potential. The velocity of this streaming exceeds for that for maxima of the first kind by about one order. There is a linear dependence between the flow rate of the mercury and the speed of motion of the solution.

Fig. 3.8 : Direction of stirring action in mercury and in a solution with a maximum of the second kind

3.4.8 Interpretation of Maxima of the Second Kind As maxima of the second kind have a purely hydrodynamic origin, as compared with the maxima of the first kind, and are not caused by any process at the electrode. As with the maxima of the first kind, the relative motion of the mercury and of the solution or maxima of the second kind is analogous to the fall of a mercury drop in the solution. The fall in the maximum with potential on either side of the electrocapillary zero is caused by increasing inhibition of the motion of the surface due to electric charge of the double layer, which because of streaming accumulates at the neck of the drop. Thus, an electric field is formed which decreases the surface tension and counteracts the motion of the mercury. If a surface-active substance is present in solution it is adsorbed at the electrode surface and the motion of mercury carries it to the neck of the drop where it accumulates. The mechanism of suppression is the same as that for maxima of the first kind, because of increased adsorption the surface tension at the neck decreases as compared with that at the bottom. The difference in surface tension gives rise to force opposing the direction of the motion. When the drop-time is lowered, there is not enough time for

The Technique

37

the accumulation of a sufficient amount of suppressing agent. At this stage, the “false waves” disappear and pure maxima occur. A sufficient decrease in the flow-rate removes the “false waves” by stopping the motion of the mercury surface. It often happens in practical polarography that the experimental conditions favour the formation of maxima of both the first and second kind as a single curve. The fundamental requirement is a sufficiently high flow rate of mercury. Also curves with different shapes are encountered that at first sight could be ascribed to maxima of either the first or the second kind, but are due to catalytic origin only.

3.4.9

Practical Applications of Polarographic Maxima

Since the maxima are sensitive to the presence of surface-active agents, maxima that interfere with the accurate evolution of polarographic curves in normal polarographic measurements sometimes permit the detection and the determination of substances that are neither oxidizable nor reducible, but are only absorbed on the electrode surface. Thus, the so called polarographic adsorption analysis is not specific, but it proved to be useful in determining the purity of various substances which contain impurities of colloidal character mostly of organic. The methods making use of a maximum of the first kind are on an average sensitive to 0.0001% of impurities. Those based on suppression of a maximum of the second kind are more exacting as regards the purity of the solutions and chemicals used, but they are by about two orders more sensitive. Polarographic adsorption analysis is used extensively: (i) In the control water purity, (ii) In sugar industry for refining sugars, (iii) The chemistry of polymers, oils and photographic gelatins, (iv) In food analysis, analysis of industrial products, (v) Soil analysis and plant physiology.

3.5

POLAROGRAPHY IN NON-AQUEOUS SOLVENTS

The polarographic investigations of chemical substances to measurements in aqueous solutions only. The search for suitable solvents was initiated to investigate great number of water-insoluble organic compounds. Not only the pure solvents but also the mixture of solvents was found to be suitable for quantitative analysis. The magnitude of diffusion current and, sometimes, the shape of the wave so also the half-wave potential are influenced by using non-aqueous solvents. These effects are chiefly due to change in solvation and in the diffusion coefficients. Well defined waves can be obtained in non-aqueous solvents for substances that give curves with ill-defined limiting currents in water. We can take for example, Ca2+ and Mg2+ give easily measurable waves in acetonitrile in contrast to their behaviour in water. The theoretical investigation of substances in non-aqueous/solvents e.g., in the determination of diffusion coefficients and standard potentials, to the reversibility of the electrode process and complex equilibria has been drawn in the polarographic studies. Thus for solvents with a low dielectric constant, Schaap [21] derived an equation for the reversible wave of a cation, the reduced form of which yields an amalgam with

38

Introduction to Polarography and Allied Techniques

mercury. The formation of ionic pairs is operative in this case and the derivation is similar to that for consecutive complex formation.

3.5.1

Solvents that are Frequently Used

(i) Acetic Acid : The possibility of polarographic analysis in acetic acid was first mentioned by MacGillavry [22]. More detailed investigation since then were given by many workers. The diffusion currents for cations, e.g., Cd2+, Pb2+ and Zn2+ are about two-thirds of those is water. This is due to the greater viscosity of glacial acetic acid. Ions, such as Cu2+, which are reduced at very positive potential form acute maxima. This could be suppressed by Puchsin as shown by previous workers. Not only this there were several other substances found suitable for suppressing maxima in glacial acetic acid. (ii) Acetonitrile : Among other solvent acetonitrile proved very convenient and useful. Previous workers, e.g., Kolthoff and Coetzee [23] and many others have given quite useful information on such investigations. The energies of solvation of the cations and the anions are smaller than in water and most cations are reduced at more positive potentials than in water. In addition to this, more negative potentials can be attained than in water, and well-defined waves for ions like calcium and magnesium can be obtained using tetraethyl ammonium perchlorate or tetra butyl-ammonium iodide as supporting electrolyte. Normally an aqueous saturated calomel electrode is employed as reference electrode with an Ag/Ag+ or Ag/AgCl electrode as already pointed out by previous workers. The potentials, referred to an aqueous SSE for the Ag/Ag+ couple in acetonitrile in the presence of different supporting electrolytes have also been compared. Inorganic ions have been divided into two groups by Kolthoff and Coetzee [24]. The first group includes cations with similar behaviour in acetonitrile and in water. The half-wave potentials become more positive in sequence Li+, Rb+, K+, Na+, NH4+, Ca+, Sr2+, Ba2+, Zn2+, Cd2+, whereas in water the following sequence holds: Li+, Ca2+, K+, Na+, Sr2+, Rb+, Ba2+, Zn2+, Cd2+. The reduction of nNa+, K+, Rb+ and Zn2+ proceeds reversibly, and that of other ions irreversibly. The influence of anions on the electrode process is peculiar. Zinc nitrate in tetraethyl ammonium perchlorate gives a reversible wave at –0.70 V vs. NCE, while zinc chloride in tetraammonium bromide gives an irreversible wave at almost –2.0 V. The horizontal portion of the diffusion current cannot be obtained in the presence of tetraethyl ammonium iodide. According to Kolthoff and Coetzee [24] the second group involves cations whose polarographic behaviour in acetonitrile differs considerably from that in water. In contrast to their behaviour in water, these cations are mostly reversibly reduced or at least approach a reversible behaviour in acetonitrile. The following reductions take place reversibly : AgI/Ag0, CuI/Cu0, MNII/Mn0...well defined waves, although not fully reversible, are obtained with FeII, CrII, BeII...Eu0 and YbII → Yb0.

The Technique

39

When small amounts of water is added to acetonitrile formation of hydrated cations take place. The waves which in acetonitrile were reversible and appeared at positive potential, become irreversible and are shifted to more negative potentials. Changes in diffusion coefficients of Ag+, Tl+ and Cu2+ were investigated by Tachi and Takahashi [25] in mixtures of acetonitrile and water. The hydrogen overvoltage in anhydrous acetonitrile is considerably lowered. Vl•cek [26] found E ½ = –0.60 V (vs NCE) for the half-wave potential of hydrogen reduced from perchloric acid in Acetonitrile saturated with tetra methyl ammonium iodide and the over voltage η1/2 = –0.56 V as compared with η1/2= –1.34 V in water. Coetzee and Kolthoff investigated a large number of acids in acetonitrile and found a far greates dispersion of half-wave potentials than in water. But due to the irreversibility of the process, the strength of acids in acetonitrile cannot be compared on the basis of their half-wave potentials. (iii) Alcohols : Alcohols, e.g., ethanol, methanol and their mixtures with water are most frequently used as solvents. The diffusion currents are usually smaller than those in water. According to Vl•cek[27] anodic waves for alkali metals are obtained in absolute ethanol. Also, the amalgam of alkali metals are relatively stable so that oxidation reduction waves for the system ion amalgam of the alkali metals can be obtained. As such these waves provide a proof of the reversibility of alkali metals at the DME. Properties of complexes also change considerably in alcoholic solution as shown by previous workers. Also the formation of cadmium complexes with chlorides, bromides and thiocyanates take place at much lower concentration than in water. Most organic substance are readily soluble in mixtures of ethanol or methanol with benzene in water permiting polarographic estimations. The reversible organic substances which consume protons during the electrode process, the addition of organic solvents only produces a change in half-wave potential. This was described as a change in the activity of the hydrogenious, Schwabe [28] also determined pH value from change in half-wave potential while with irreversible processes the influence of solvent on E ½ is more complicated. It was also evident that the rate constant for the electrode process measured at constant potential decreases exponentially with increasing concentration of ethanol. (iv) Ethylenediamine : Ethylenediamine is also suitable for polarographic analysis since a number of salts dissolve in it. In reversible electrode process, an estimate of the magnitude of stability constant [29] for the corresponding ethylenediamine complex in water can be determined from the difference between the half-wave potentials of the cations in water and in ethylenediamine. The potential of the anode could be determined from the activity of mercuric ions in liquid ammonia while working with a mercury pool anode. (v) Sulphuric Acid : For studying the property like dehydration of the depolarizer, the acid is useful. Concentration up to a 92 vol. % or 17 M has been used which

40

Introduction to Polarography and Allied Techniques

displays minimum viscosity and maximum conductivity which is quite comparable to that of 1 N KCl. In sulphuric acid Tl+ [30] form a complex which is reduced reversibly and has a half wave potential 0.5 V. This is more negative than that in water (–1.01 V vs NCE). The behaviour of Tl+ is worth mentioning because it rarely forms complexes in aqueous solution (e.g., with EDTA) and has a half-wave potential that is taken as reference in aqueous solutions. (vi) Formic Acid : In formic acid solution [31] the half-wave potentials of cations are more positive than those in water. The maxima of the first kind are also suppressed to a large extent by the surface-active molecules of formic acid. (vii) Liquid Ammonia : Alkali metals are reduced reversibly giving valuable results. The limiting currents follow Ilkovi•c equation. The temperature was kept constant at –36°C ± 0.2°C. The diffusion currents for alkali metals in the solvent at this temperature are 2–3 times higher than those in water at 25°C. The migration, is not fully suppressed, because tetrabutyl ammonium iodide, used as supporting electrolyte, is only soluble up to 5.7, 10–3 M. The sequence of ions of the alkaline earths is the same as in water. Thallium [32] is reduced almost reversibly. Cu2+ give two waves of equal height. The first one is reversible. The diffusion coefficients for thallium and copper agree with those determined from the conductivity data obtained at infinite dilution. Aluminium also gives a measurable wave in liquid ammonia. Mercurous ions, Hg 22+ are unstable in liquid ammonia. Mercuric ion, Hg2+, are reversibly reduced to Hg. As a consequence, the Hg2+/Hg electrode functions reversibly. The potential of a mercury pool anode does not depend on the concentration of nitrate, chloride, iodide or ammonium ions, but only on the concentration of mercuric ions. The half-wave potential of Thallium was taken as reference for determining the half-wave potentials. Polarization is repeated two or three times in usual practice. This results in anodic dissolution of small quantity of mercuric ions, which control the electrode potential. (viii) Other Solvents : The polarographic behaviour of several cations and also oxygen in anhydrous ethylene glycol has also been studied [33]. Well defined waves with half-wave potentials almost the same as those in water were obtained. Other solvents like acetone [34], acetic anhydride [35], aniline [36], benzoyl chloride [37], butanol, dimethyl formamide [38], dimethyl sulphoxide [39], and dioxan [40]–[50] also the mixtures with water have also been used. Research in this area also continues.

References 1. 2. 3. 4.

Graham, D.C.J. Am. Chem. Soc. 68:301 (1946). Ilkovi•c D. : J. Chem. Phys. 35, 129 (1938). Ku•cera G. : Ann. Physik IV. Folge 11, 529, 698 (1903). Kalousek M. : Collection Czechoslov. Chem. Communs. 11, 592 (1939).

The Technique

41

5. Vl•cek A.A. : Chem. Listy 48, 1485 (1954); Collection Czechoslov, Chem. Communs. 20 413 (1955). 6. Hans W., Sturm V.F. : Angew Chem. 65, 393 (1953). 7. Christie J.H., Oster Young R.A. : J. Ann. Chem. Soc. 82, 1841 (1960). 8. Stackelberg V.M., Doppelfeld; Advances in Polarography, p. 68 I.S. Longmuir, Ed. Pergmon Press, London 1960. 9. Hassel bach H., Jahn D., Schwabe K. : Z. Physik, Chem. (Leipzig), Sonderheft (1958), 17. 10. Heyrovsk•y J., Simunek R. : Philos, Mag. 7,951 (1929). 11. Heyrovsk•y J. : Chim Listy 36, 267 (1942). 12. Heyrovsk•y J. Vascautzanu E. : Collection Czechoslov. Chem. Communs. 3, 418 (1931). 13. Bruns B., Frumkin A., Iofas, Vanyukova L., Zolot arev Skaya S. : Acta Physicochem. URSS 9, 359 (1938): Zh. Fig. 13, 786 (1939). 14. Rodeburg : Thesis, Bonn (1942). 15. Popova T.I., Kryukova T.A. : Zh. Fig. Khim 25, 283 (1951). 16. Bridi•cka R. : Collection Czechoslov. Chem. Communs. 8, 419 (1936). 17. Dvo•ra•k J. : Chem. Listy 47, 969 (1953): Collection Czechoslov. Chem. Communs. 19, 39 (1954). 18. Kryukova T.A., : Frumkin A.N.: Zh. Fig. Khim. 23, 819 (1949). 19. Micka K. : Chem. Listy 49, 1148 (1955). 20. Kryukova T.A. Zavodskaya Lab. 9, 691, 699 (1940). 21. Schapp W.B. : J. Am. Chem. Soc. 82, 1837 (1960). 22. Mac Gillavry D. : Trans. Faraday Soc. 32, 1447 (1936). 23. Kolthoff I.M., Coetzee J.F. : J. Am. Chem. Soc. 79, 870 (1957). 24. Kolthoff I.M., Coetzee J.F. : J. Am. Chem. Soc. 79, 1852 (1957). 25. Tachi I., Takahashi R. : Collection Czechoslov. Chem. Communs. 25, 3111 (1960). 26. Vl•cek A.A. : Chem. Listy 48, 1741 (1954); Collection Czechoslov. Chem. Communs. 20, 636, (1955). 27. Vl•cek A.A. Chem. Listy 48, 1485 (1954); Collection Czechoslov. Chem. Communs. 20, 413 (1955). 28. Schwabe K. C : Z. Elektrochem. 61, 484 (1957), z. Physik. Chem. (Leipzig); Sonderheft 1958, 289. 29. Shaap W.B., Messner A.E., Schmidt F.C.: J. Am. Chem. Soc. 77, 2683 (1955). 30. Vl•cek A.A. : Chem. Listy 45, 297, 377 (1951); 46, 258 (1952); Collection Czechoslov. Chem. Communs. 16, 230, 465 (1951). 31. Pinfold T.A. Seba F.: J. Am. Chem. Soc., 78, 2095, 5193 (1956). 32. Mc Elroy A.D.; Lattinen H.A. : J. Am. Chem. Soc. 57, 564 (1953). 33. Gentry C. H.R. : Nature 157, 479 (1946). 34. Arther P., Lyons H.: Anal. Chem. 24, 1422 (1952). 35. Gutmann W., Nedbalek E. : Monatsch, 89, 203 (1958). 36. Novak J.V.A. : Collection Czechoslov. Chem. Communs. 11, 573 (1939). 37. Gutmann W., Sch•ober G.: Monatsh. 88, 404 (1957). 38. Given P.H., Poever M.E.: J. Chem. Soc. 1960, 385, 465. 39. Sch•ober G.; Gutmann W.: Advances in Polarography I.S. Longmair, Ed. p. 940. Pergmon Press, London 1960. 40. Stackelberg M.V., Stracke W. : Z. Elektrochem. 53, 118 (1949).

CHAPTER 4

THEORY OF CURRENT POTENTIAL CURVES 4.1 THE ILKOVI•C EQUATION The direct proportionality between the limiting diffusion current and depolarizer concentration is expressed in an equation derived by Ilkovi•c. Due to the growth of each drop of mercury, the observed diffusion current varies with the variation of the surface area of each drop. Thus, at a particular applied potential the current will be observed to oscillate between well-defined upper and lower limits. For an instantaneous current at any time during the drop-life, the Ilkovi•c equation may be expressed in the form: id = 706n D1/2 m2/3 t11 6 C

...(1)

Here, n is the number of electrons transferred in the reduction process [the ions designated as Mn+ which begin to be discharged owing to their reduction by the process: Mn+ + ne M (Hg)(1´) and the ions Mn+ arrive at DME by the relatively slow process of natural diffusion m is the rate of mercury flow expressed in mgs–1, D is the diffusion coefficient of the depolarizer in cm2.5–1, t1 is the drop-time expressed in seconds and C is the depolarizer concentration given in m moles per liter. With these units and the numerical constant 706, the observed current is given in microamperes. It is more usual to consider mean currents. It is observed that the instantaneous current at the end of the drop-life, imax, is related to the mean current during the drop-life, i, by the 6 i . Thus, the form of the Ilkovi•c equation for the mean diffusion 7 max current is expressed as:

relation, τ =

id = 607n D1/2 m2/3 t1/6 C

...(2)

The Ilkovi•c equation is alternatively used in the following form, for the mean diffusion current id = 0.627n D1/2 m2/3 t11 6 C

...(3)

which, for D in cm2s–1, m in gs–1, t1 in seconds and C in mole cm–3, gives the current in amperes. For most work the Ilkovi•c equation in the above forms has proved to be satisfactory, the linear relation between id and C being maintained to within ± 1%. However, the diffusion current constant I, defined by

Theory of Current Potential Curves

43

I = 0.627n FD1/2 =

id 23 16 cm t1

...(4)

only maintains constancy within ± 5%. A typical calibration curve is shown in Fig. 4.1. 5

(μ A )

4 3 2 1 0

0.3

0.4

0.5

0.6

0.7

0.8

Fig. 4.1 : Polarogram showing current oscillations. Working composition : 5 × 10–4 M Cd4, 0.1 M KNO3, 0.001% gelatin

Many corrected forms of the equation have been derived by several workers. The final forms of which essentially identify with the equation and differ only in the value given to numerical constant, A. Equation (2) may be written in the form id = 0.627n FD1/2 C : m2/3 t11 6

...(5)

id μA

15.0

10.0

5.0

0.0 0.5

1.0 .5 C(mM/L)

Fig. 4.2 : Mean diffusion current versus millimolar concentration for Cd2+ in the range 0.163 mM to 1.22 mM, 0.1 M KNO3 as supporting electrolyte with 0.001% gelatin

44

Introduction to Polarography and Allied Techniques

Solution factors : electrode factors If the solution factors are maintained constant, then id = const. m2/3 t11 6

...(6)

By Poiseuille’s equation the rate of flow of liquid through a capillary under a head of the liquid is directly proportioned to the height of the column, h. Thus the rate of flow, v is the proportional to m which is porportional to h. Also v is proportional to 1/t1. ...(7) Therefore, id = const. h 2/3 . h –1/6 = const. h 1/2 The proportionality which is being observed between id and h 1/2 is an acceptable criterion of a diffusion controlled process. See for example the Fig. 4.2.

4.1.1 Consequences of Ilkovi•c Equation The following consequences can be drawn from the Ilkovi•c equation. 1. The diffusion current is directly proportional to the analytical concentration of depolarizer in the solution, e.g., id = •kc ...(8) This is followed from the Ilkovi•c equation and the conditions being that for a given value of m and t1, i.e., when the same capillary is used with a constant height, where k is the Ilkovi•c constant, e.g., • = 0.627 FD1/2 m2/3 t1/6 ...(9) k n

This equation forms the basis of quantitative determination in polarographic analysis. If the limiting diffusion current values or wave heights is mm are plotted against the concentration of a given compound, a straight line passing through the origin is obtained. See Fig. 4.3. This may be used as a calibration curve for determining the concentration of the compound in unknown samples. 40

Zn2+

id (arb.)

30

Cd2+

20

10

0

1

2

3

4

5

6

7

8

9

h(cm½)

Fig. 4.3 : id versus

–4 2+ h plots for a solution containing 5 × 10 M Cd and

9.8 × 10–4 M Zn2+; 0.1 M KNO3 as supporting electrolyte with 0.001% gelatin.

Theory of Current Potential Curves

45

The linear dependence of diffusion current on cencentration does not bold exactly with short drop-times as was first shown by Mass [2] and other workers too. As a result the drop-time should not be less than two sec. The reason being that under these conditions whirling occurs and destroys the diffusion layer and the currents gets increased. The most suitable drop-time is from 3 to 5 sec. It further follows from equation (8) that equivalent concentrations of substances with equal diffusion coefficients give equal currents, since a large number of cations have similar diffusion coefficients and since small differences have only a small effect. The reason being that square root of D is used in the calculation, diffusion currents for the same equivalent concentrations are roughly equal (Table 4.1). TABLE 4.1 Comparison of percentage differences between observed and calculated mean diffusion currents Ion

Δid Ilkovi•c equation %

Δid correct equation %

Tl+ Pb2+ Cd2+ Zn2+ Cu2+

–0.8 +1.0 +7.8 +4.9 –1.3

–13.7 –8.7 0 –3.7 –10.7

IO − 3

+0.4

–9.3

3– Fe ( CN )6

+8.1

–16.9

2– CrO4

–3.6

–15.2

If the diffusion coefficient is known the number of electrons ‘n’ participating in the electrode process may be calculated from the Ilkovi•c equation. Actually comparison can be made under the same condition the diffusion current of substances to be investigated with the diffusion current of a substance taking up a known number of electrons, i.e., with the same capillary, concentration, height of mercury head and temperature. From the ratio of the diffusion currents, the value of n can be determined. 2. Dependence on the Height of Mercury Head, Capillary Characteristics and Potential : If the height of the mercury head is changed at constant concentration of the substance, the flow-rate m and drop-time t charge simultaneously. According to the following equations: m = k' h = k' (h a – h b) t1 = k n

1 h

...(10) ...(11)

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Introduction to Polarography and Allied Techniques

m is directly proportional and t1 inversely proportional to the corrected height of h of the mercury head: 1 m = k' h; t1 = k" ...(12) h Substituting in the Ilkovi•c equation it takes the form:

⎛ k" ⎞ id = Km2/3 t11 6 = K (k' h)2/3 ⎜⎝ ⎟⎠ h

16

...(13)

and on combining all constants ...(14) id = k h i.e., the diffusion current is directly proportional to the square-root of the corrected height of the mercury head (reservoir). This linear dependence provides an easily accessible experimental test for diffusion controlled currents. The corrected height of the mercury head may be calculated from the above equation (10). In quite some investigations into the character of limiting currents it is sufficient to plot the limiting current against the square-root of the actual height of the mercury head. In case of diffusion controlled current the plot gives a straight line, but this line does not pass through the origin, it only cuts a small intercept on the current axis.

4.2 REVERSIBLE AND IRREVERSIBLE ELECTRODE PROCESSES It is quite possible to control the rates of most electrode processes with some precision, which is quite unlike the case for normal chemical reactions. Control of the applied potential controls the current flow by controlling the height of the activation energy barrier for the process. A simple electrochemical reduction process is considered here, e.g., A + ne

B

...(15)

which is occurring at an inert electrode and also that both oxidant and reductant are soluble in the solvent medium used. A simple view of the effect of an applied potential, E, assumes it to cause a decrease in the reaction energy barrier in one direction and an increase in the reverse direction. An increase of negative potential increases the forward rate of reaction Eq. (15), the energy barrier to its progress being reduced by an amount α (E – E 0) nF. The energy barrier of the reverse reaction is correspondingly increased by an amount β (E – E0) nF. Here the expressions E and E 0 are the applied and standard potentials respectively, while α and β are termed the “transfer coefficients” related through the expression α + β = 1. A transfer coefficient may thus be regarded as the fraction of the applied potential which either assists or hinders the process under consideration. Observing the diagram below, the significance of α and β can be seen in Fig. 4.4.

Theory of Current Potential Curves

47

Forward (reduction) process

α (E–E 0)nF

β (E–E 0)nF

Backward (oxidation) process

Fig. 4.4 : Diagram showing effect on forward and backward reaction activation energy barriers of an applied potential in excess of E 0.

In terms of current densities, the rates of forward (reduction) and backward (oxidation) processes for the reaction* (15) may be expressed as follows: r1 =

and

r2 =

Icath = kcath [A]e nF

...(16)

I an = kan [B]e nF

...(17)

In these equations r1 and r2 represent the two rates, Icath and Ian, i.e., the cathodic and anodic current densities respectively. The terms kcath and kan and the appropriate rate constants. [A]e and [B]e refer to concentrations of oxidized and reduced forms of the depolarizer at the electrode surface. If the applied potential is E 0, with forward and backward rates being equal, the every barrier to either process is the activation energy, Q. That is to say, Q is the activation energy of the electron transfer from electrode to depolarizer particle A, at the surface, at zero applied potential between the electrode and the solution. At an applied potential difference, E, this energy is reduced by an amount α ne E, e being the unit electronic charge. Thus, for the rate of electro-reduction we have

⎡ Q + αne E ⎤ r 1 = k′ [A]e exp ⎢ − ⎥ kT ⎣ ⎦

...(18)

⎡ αn FE ⎤ = k′′ [A]e exp ⎢ − ⎣ RT ⎥⎦ where k′ and k′′ are constants for the particular process and k is the Boltzmann constant. k′′ includes the term e–Q. A analogous expression may be had for the rate of electro-oxidation.

48

Introduction to Polarography and Allied Techniques

Cathodic and anodic rate constants may be expressed as:

(

)

⎡ α nF ⎤ E − E0 ⎥ kcath = k0 exp ⎢ − RT ⎣ ⎦

...(19)

⎡ (1 − α ) n F ⎤ E − E0 ⎥ kan = k0 exp ⎢ RT ...(20) ⎥⎦ ⎣⎢ In the above equations, k0 represents the heterogeneous rate constant of the electrode process at the standard potential, E 0, and includes the term e–Q. These expressions may be inserted in the equations (15) and (17) to give:

(

and

)

(

)

⎡ α nF ⎤ E − E0 ⎥ Icath = nFk0 [A]e exp ⎢ − ⎣ RT ⎦ and

(

...(21)

)

⎡ βnF ⎤ E − E0 ⎥ Ian = – nF k0 [B]e exp ⎢ ⎣ RT ⎦

...(22)

In these latter two equations, the convention that has been adopted as regard to a cathodic current as positive and an anodic current as negative. The algebraic sum of the cathodic and anodic contribution, as observed by the current density I, are represented as:

(

)

(

)

⎧ ⎡ α nF ⎤ ⎡β F ⎤⎫ E − E 0 ⎥ − [ B ]e exp ⎢ n E − E0 ⎥ ⎬ I = nF k0 ⎨[ A ]e exp ⎢ − ⎣ RT ⎦ ⎣ RT ⎦⎭ ⎩ or

(

)

(

⎧ ⎡ α F ⎤ ⎡β F I = I 0 ⎨[ A ]e exp ⎢ − n E − E 0 ⎥ − [ B ]e exp ⎢ n E − E0 RT ⎣ ⎦ ⎣ RT ⎩

) ⎤⎥⎦⎫⎬⎭

...(23)

...(24)

where I0 = nF k0 and is termed the “exchange current density” i.e., the condition when E = E 0 at which no net current is observed, the cathodic and anodic components being of equal magnitude but flowing in opposite directions. For small values of Q, k0 is very large; such a condition is found in “reversible” systems where the electrochemical processes are considered to be very rapid. For considering the essential differences between reversible and irreversible electrode processes, the form taken in the above equation I and E under such conditions that k0 is very large or very small.

4.3 REVERSIBLE POLAROGRAPHIC WAVE A system consisting of a perfectly polarizable dropping mercury electrode and a nonpolarizable stationary electrode. If an external voltage is applied to such a system, the entire potential drop is concentrated at the interface between the dropping electrode and the solution under investigation. Due to this reason the polarographic curves are determined solely by the processes occurring at the DME. The dependence of the current on the potential of the mercury electrode, the polarographic curve gives a particular shape. This concludes the character of the electrode process arising out of the current voltage curves.

Theory of Current Potential Curves

49

The particles of depolarizer subject to electrochemical change i.e., reduction or oxidation at the electrode reach the electrode by diffusion only. The equation derived for this kind of current, the diffusion current, requires a constant concentration of depolarizer at the surface of the electrode for a given potential. If the shape of the current potential curve is to be derived, the relationship between the concentration at the electrode surface and the potential must be taken into account. For reversible processes, this relationship is obtained from the Nernst equation. By a reversible process is meant one in which the ratio of the concentrations of oxidized reduced form at the electrode surface is given by the Nernst equation: E = E0–

RT [Red]0 ln nF [OX ]0

...(25)

In this equation [Red]0 and [OX]0 denote the concentrations of the reduced and oxidized form of the depolarizer at the electrode surface respectively. E 0, the standard oxidation reduction potential of the system and E the potential of the dropping mercury electrode as determined by the applied e.m.f. It is convenient to refer both potentials to the potential of the non-polarizable electrode rather than to the standard hydrogen electrode, E is then numerically equal to the applied e.m.f. Emphasis is laid on the fact that Nernst equation which holds for reversible thermodynamic equilibria, i.e., under conditions when no current is flowing. The use of the Nernst equation is justified if the equilibrium rate of electron exchange between electrode and reactants is so great that it can easily accommodate the small net current flow without a significant departure from the equilibrium concentration.

4.3.1 Cathodic Wave On considering a cathodic reduction the oxidized form of the depolarizer (e.g., Tl+, Cd2+ or reducible molecules) alone is present in the solution. It accepts electrons from the dropping electrode and so electrons flow from the non-polarizable electrode i.e., anode to the DME via the external circuit. This is the so called cathodic current. The polarograph is conventionally connected in such a way that on polarograms this current appears above the galvanometer zero-line. According to the Ilkovi•c equation, the mean current supplied by diffusion of a depolarizer to the electrode surface is given by:

in which

i = k [OX] – [OX]0

...(26)

k = 0.627nF D1/2 m2/3 t11 6

...(27)

is the Ilkovi•c constant. The particles reduced at the surface thereupon diffuse away. In cases where amalgam formation takes place, e.g., in metals like Tl, Pb, Cd, Zn and alkali metals, these are transported by diffusion into the mercury drop. If no amalgam is formed, e.g., in reductions of Fe3+ → Fe2+, Sn4+ → Sn2+ and in some organic systems like quinone → quinol, the reduced particles diffuse back into the bulk of the solution. The equation governing this diffusion away from the surface in either direction is:

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Introduction to Polarography and Allied Techniques

i = k' [Red]0 – [Red]

...(27a)

in which •k' = 0.627nF D1/2 m2/3 t11 6 differs form k only in the value of diffusion coefficient for the reduced particle D′ . As already stated above, it is assumed that only the oxidized form is present in the bulk of the solution, i.e., [Red] = 0, and so the preceding equation now takes the form: i = •k' [Red]0

...(27b)

If the concentrations of the reduced and oxidized forms at the surface of the electrode are eliminated from equations (27, 27a, 27b). The following equation is obtained: E = E0 –

RT i k ln · nF k '[OX ] − i k '

...(28)

Heyrovsky and Ilkovi•c first derived this equation for a cathodic wave [4].

Fig. 4.5 : Reversible cathodic wave. 5. 10–3 M Tl2SO4, 1 M Li2SO4, 0.04% gelatin; sens. 1 : 150, 208 mV/scale unit

Since

k [OX ] = id ,

...(29)

where id is the mean limiting cathodic diffusion current, equation (28) is readily transformed into the Tomes form [5]

Theory of Current Potential Curves

51

0

E =E −

RT i ln nT id − i

D ; D′

...(30)

D D′ Since for many depolarisers the diffusion

the ratio of the Ilkovi•c constant •k/•k' is

coefficient of the oxidized and the reduced forms are nearly equal and, in their square root form, the expression

D D′ may be set equal to unity. The forgoing equation then

finally takes the form: 0

E=E −

RT i ln nF id − i

...(31)

This equation is the simplest mathematical expression for the shape of a reversible cathodic wave. Experimental reversible cathodic waves accord perfectly with the derived equations. The point on the polarographic curve corresponding to one-half of the limiting diffusion current represent the inflexion point of the curve. It is termed the half-wave point or correspondingly the half-wave potential, E ½. The expression for the half-wave potential may readily be derived from the equation for the polarographic wave introducing i = id /2. Thus is obtained: E ½ = E0 –

RT D ln nF D′

...(32)

from the equation (22) or E ½ = E 0 from equation (23) The half-wave potential is a constant that is independent of the concentration of the depolarizer, of the capillary characteristics and of the galvanometer sensitivity and has a value characteristic of the given depolarizer. If the reduction product does not form an amalgam with mercury, the half-wave potential is virtually identical with the standard oxidation-reduction potential (Eq. 23). If an amalgam is formed, the halfwave potential corresponds to the standard potential of the amalgam electrode (see half-wave potential and its significance). When the depolarizer concentration is varied, the height and the target-potential of the wave change, the half-wave potential for a reversible wave remains constant. Not only this but the relative height i/id of the wave at a given potential is independent of depolarizer concentration. An important property of a reversible polarographic curves is its symmetry with respect to E ½. Thus the distance between E ¼ and E ½ is the same as that between E ½ and E ¾. If an amalgam is formed the half-wave potential corresponds to the standard potential of the amalgam electrode as given in Chapter 1. When the depolarizer concentration is varied, the height and the tangent potential of the wave change, but the half-wave potential for a reversible wave remains constant (see Fig. 4.6). Furthermore, the relative height i/id, of the wave at a given potential is independent of depolarizer concentration. From the equations derived for the polarographic wave, the final equation is:

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Introduction to Polarography and Allied Techniques

E =E ½ –

4.3.2

RT i ln nF id − i

...(33)

Anodic Wave

Anodic oxidations are of two kinds: (i) The reduced form is in mercury drop so that instead of pure mercury an amalgam flows out of the capillary [3– 6]. This reduced form in which the metal is oxidized at the surface of the DME and the cations thus formed are transported by diffusion into the bulk of the solution, and (ii) The reduced form of the depolarizer is present in the solution and is transported by diffusion to the DME, where it is oxidized and then returned to the bulk of the solution. Here the example of Fe2+ and quinol is workable. In both oxidations, the direction of diffusion of the oxidized and reduced forms is the reverse of that in a cathodic reduction. The electrons flow from the DME through the external circuit to the non-polarizable +∞ –∞ E electrode. The resulting anodic current (negative sign) is recorded beneath the galvanometer zone-line (exceptions are Fig. 4.6 : Independence of half-wave potential from concentration. The concentration of Cd2+ of mixed currents). –3 Considering the diffusion of the increases up to 10 N reduced form the following relationship must hold: –i = •k ([Red] – [Red]0)

...(1)

The oxidized form diffuses from the surface of the electrode back into the bulk of the solution, where its concentration is zero. The current can, therefore, be rewritten as –i = •k [OX]

...(2)

On substituting these diffusion relationships (foregoing equations) in the equation: E = E0 –

RT ln nF

[ Red] 0

[OX 0 ]

...(3)

Theory of Current Potential Curves

53

the equation of the current-potential curve for anodic oxidations at DME is obtained as follows: RT k'Red k ln +i· ...(4) nF k' −i The anodic diffusion current [Red]0 = 0, is attained when [Red]0 = 0, hence on substituting this relationship in the foregoing equation we obtain: E = E 0–

RT i −i D ln d ...(5) nF i D′ The whole anodic curve appears beneath the galvanometer zero line as is shown in the Fig. 4.7. If, as in the cathodic reduction, i is made equal to id /2, and expression identical with equation is obtained e.g., E = E0 –

RT D ln = E0 ...(6) nF D′ when i can be neglected compared with id = k′ [Red] in equation (7) we obtain the exponential form of the anodic curve without concentration polarization i.e., the +i concentration of the depolarizer at the electrode surface was the same as that in the –E +E body of the solution, even with a current passing through the system: E ½ = E0–

E = E0–

RT k' Red + i k ln · nF k' −i

–id

...(7) –i

4.3.3

Cathodic-Anodic Waves

While considering an oxidation-reduction Fig. 4.7 : A Typical Anodic wave system, where both forms are available for electrolysis, it is observed that two diffusion currents are resulting. With increasing negative potentials, the dropping mercury electrode becomes depleted of the oxidized form and the cathodic diffusion current id appears. And an depletion of the reduced form with increasing positive potentials the anodic diffusion current (see Fig. 4.8) appears. Two situations are observed: (a) The oxidized form is in solution (e.g., cations of metals such as Tl+ and Cd2+) and the reduced form in the mercury (i.e., the metals that form amalgam). (b) Both the oxidized and reduced form are in the solution Fe2+ and Fe3+ in oxalate. In both the situations the current is given by the equations: ...(8) i = •k [OX] – [OX ] 0

i.e., diffusion of the oxidized form to the electrode surface.

CHAPTER 5

TYPES OF CURRENTS 5.1 MASS TRANSFER AND ELECTROCHEMICAL PROCESSES Two main types of processes are involved in any electrolysis. These are : transference of matter through a solution towards and away from the electrodes, and the other is in which the electrochemical process involves the exchange of electrons at the electrode surface as an essential part. During an electrolysis three mass transfer processes are of importance, e.g., migration, diffusion and convection. The first of these i.e., migration is an essential effect depending upon the charge carried by an electroactive species and upon its transference number. Thus, the effect is encountered only with charged species. Since the processes of natural diffusion are non-electrical in origin, these are observed for all species in solution whether they are charged or not. Convection effects include the motion of small particles under the influence of stirring, mechanical agitation, and temperature gradients. In polarographic work the migration effect is usually eliminated. The convection effects are eliminated by carrying out any electrolysis in an controlled thermostat and also by protecting the apparatus from all forms of vibrations and shocks.

5.2 DIFFUSION CURRENT The most important component of the wave height is the diffusion current, which reflects the rate at which the ions or molecules of the substance responsible for the wave reach the electrode surface under the sole influence of a diffusive force. On the plateau of the wave these ions or molecules get reduced of oxidized as rapidly as they reach the electrode surface, and their concentration in the layer of solution immediately adjacent to the electrode surface in therefore virtually zero. Hence there is a concentration gradient between the bulk of the solution and the layer at the electrode surface, and it is this concentration gradient which is responsible for the existence of the diffusive force. The diffusion current is very important in polarographic analysis because most practical methods are based on its measurements. The rate at which the electroactive material can reach the electrode surface may however be affected by many other phenomena. The original species or another electroactive one, may be regenerated by a reaction between the product of the electrode reaction and some other constituent of the solution, and in such a case, the current due to the reduction of the regenerated substance will then also be included in the wave height.

Types of Currents

59

If the solution contains a species that is not electroactive is in slow equilibrium with one that is, the wave height will include not only the diffusion current of the electroactive species but also a current due to the reduction of additional electroactive materials formed from the non-electroactive species as equilibrium between them is displaced at the drop surface. In some cases excess of the electroactive substance to the electrode surface may be barred by a film of adsorbed material, or the electroactive substance or its reduction (or oxidation) product may undergo adsorption on the drop surface and the current may then be limited by the number of ions or molecules which can be adsorbed on each drop. As already described a current whose magnitude is controlled by the rate of diffusion is called a diffusion current. In polarographic measurements an excess of supporting electrolyte is used for several reasons. It not only eliminates the effects of migration, instead it also greatly diminishes the potential drop iR, thus transforming the current voltage curves at DME into current potential curves. The supporting electrolyte also signifies great practical influence in analytical polarography. A general relationship may be written for the electrolytic current at DME, according to Faraday’s law: i = nF

dN dt

...(1)

where dN/dt denote the number of mole of the depolarizer that reaches the electrode in unit time and is subject to electrochemical change. [F is the Faraday (96500 cont.) and n is the number of electrons taken up or derived by a single molecule of depolarizer during the electrode process]. If the depolarizer is transported to the electrode by diffusion alone, the value dN/dt can be calculated from Fick’s Second Law. In this way, the equation for the diffusion current can be derived.

5.2.1 Diffusion to Stationary Electrodes Linear Diffusion : Diffusion may be described as a spontaneous process leading to equilibration of concentration differences in concentration gradients. If a concentration gradient arises in solution, the solute starts to move from areas of high to those of lower concentration. The rate of diffusion is proportional to the concentration gradient, but also depends on the properties of the diffusing particles. If diffusion occurs in one direction only, the process is termed linear diffusion. Considering linear diffusion to a plane electrode (cross section q), the concentration of depolarizer decreases in the direction perpendicular to the electrode E owing to an electrochemical change at the electrode (Eq. 2). The number of moles dN of the substance that diffuses across the area q at a distance x is proportional to the area q, to the concentration gradient de/dx and to the time interval [Fick’s first law]. dN = Dq

dc dt dx

...(2)

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Introduction to Polarography and Allied Techniques

In this expression the proportionality constant is the diffusion coefficient D, indicating the number of moles of the substance that passes by diffusion through unit area at a concentration gradient of one in unit time.

5.2.2 Diffusion-Controlled Current Fick’s Law : Diffusion may be described as a spontaneous process leading to equilibration of concentration differences in concentration gradient. If a concentration gradient arises in solution, the solute starts to move from areas to high to those of lower concentration. The rate of diffusion is proportional to the concentration gradient, but also depends on the properties of the diffusing particles. If diffusion occurs in one direction only the process is termed linear diffusion. Consider a cylinder with a cross section q. Fig. 5.1. The concentration of depolarizer decreases in the direction perpendicular to the electrode E owing to an electrochemical change at the electrode. The number of moles dN of the substance that diffuses across the area q at distance x is proportional to the area q, to the concentration gradient dc/dx to the time interval dt dN = Dq

dc dt dx

...(3)

(Fick’s First Law derived in 1855). In this expression the proportionality constant is the diffusion coefficient D, indicating the number of moles of the substance that passes by diffusion through unit area at concentration gradient of one in unit time. Diffusion coefficients are normally of the order, 10–6 – 10–5 cm2. sec–1. The diffusion current is determined by the concentration gradient at the surface of the electrode, i.e., ( ∂c/∂ x) x=0, which is time-dependent (as are the concentration gradients at all other distances). Thus i = nF

dN ⎛ dc ⎞ = nFq D ⎜ ⎟ ⎝ dx ⎠ x = 0 dt

...(4)

E x=0

X X

x + dx

c c + dc

qx qx + dx

Fig. 5.1 : Linear diffusion to Plane Electrode

This concentration gradient may be calculated from Fick’s Second Law: 2

∂c ∂ c =D ∂t ∂x 2

...(5)

Spherical diffusion : When determining the concentration gradient towards a stationary spherical electrode the derivation must be based an Fick’s Second Law, which in spherical co-ordinates has the form;

⎡ ∂2 2 2 ∂c ⎤ ∂c =D⎢ + ⎥ 2 ∂t r ∂r ⎦⎥ ⎣⎢ ∂r Note : For details more books be consulted.

...(6)

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61

If the depolarizer is transported to the electrode by diffusion alone, the value dN/dt can be calculated from Fick’s Second Law and the equation for diffusion current can be derived.

5.2.3 Linear Diffusion to a Growing Dropping Electrode The Ilkovi•c Equation : Calculation of the concentration gradient towards a growing dropping electrode is quite complicated. In 1934, Ilkovi•c [1] solved this problem. He assumed that the dropping electrode behaves as a plane electrode with an area equal to that of the surface of the drop, i.e., area increasing with time. Considering the growth of the drop by the decrease in thickness of the diffusion layer as it spreads out over the growing surface of the drop. Experimental findings of Kemula [2] helped Ilkovi•c in deriving the diffusion current equation that capillaries with equal flow-rates give approximately equal limiting currents and that the dependence of the diffusion current on the height of the mercury column is parabolic.

5.2.4 Diffusion Coefficient The values of the diffusion coefficients for the depolarizers must be known in order to calculate the magnitude of diffusion currents: Nernst [3] Nernst W.; Z. Physik, Chem., 2, 613 (1988) derived the formula: D∞ =

RT

A ...(7) 2 ∞ nF Substituting R = 8.317 V, Coul., deg.–1 and F = 96500 coul., then at 25°C : −7

2.6 7 .1 0 Λ∞ ...(8) n The following Table 5.1 as taken from the following books give some values of diffusion coefficients: [Table 5.1 from Principles of Polarography by Heyrovsky & K•uta, p. 105] D∞ =

TABLE 5.1 Diffusion Coefficients for Ions at Infinite Dilution at 25°C Ion

Λ∞ Ω–1 . cm2

H+ Li+

350 39

9.34 1.04

OH– Cl–

196 76

5.23 2.03

K+

74

1.98

NO3−

72

1.92

Na+

50.5

1.35

IO3−

41

1.09

+ NH 4

73.4

1.96

IO4−

54.4

1.45

D∞ . 105 cm2 . sec–1

Ion

Λ∞ Ω–1 . cm2

D∞ . 105 cm2 . sec–1

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Introduction to Polarography and Allied Techniques Cs+

79

2.11

BrO3−

54

1.44

Ag+

61.9

1.65

2− SO4

81

1.08

75

2.00

2− CrO4

80

1.07

Mg2+

53.06

0.71

− CH3CO2

41

1.09

Ca2+

59.5

0.79

C6H5CO− 2

32.3

0.86

Sr2+

59.46

0.79

HC 2O−4

40.2

1.07

Ba2+

63.64

0.85

2− C2O4

74.1

0.99

Cd2+

54

0.72

− Fe (CN )3 6

100

0.89

Zn2+

54

0.72

Fe( CN)64 −

110.5

0.74

2+

54 52 73

0.72 0.69 0.95

Tl+

Cu Ni2+ Pb2+

As a matter of fact diffusion coefficients are normally of the order, 10–6–10–5 cm2 . sec . The diffusion current is determined by the concentration gradient at the surface of the electrode, i.e., (∂c/∂x)x=0, which is time dependent (as are the concentration gradients at all other distances). Thus –1

i =nF

dN ⎛ ∂c ⎞ = nFqD ⎜ ⎟ ⎝ ∂x ⎠ x = 0 dt

...(9)

This concentration gradient may be calculated from Fick’s Second Law; (already given) ∂c ∂ 2c =D 2 ∂t ∂x

...(10)

From equation (9) current is obtained towards a planar stationary electrode: i = nFq D

C* −C 0

...(11)

( πDt )

For the limiting diffusion current C*

(C0 = 0); i1 = nFq D

( πDt )

...(12)

According to this equation the current decreases with time as required by the relationship i = kt–1/2. The expression

( πDt ) is the so called differential thickness of

the diffusion layer and is a function of time.

Types of Currents

63

5.2.5 Spherical Diffusion When determining the concentration gradient towards a stationary spherical electrode the derivation must be based on Fick’s Second Law, which in spherical coordinates has the form ⎡∂ 2c 2∂ ⎤ ∂c =D ⎢ 2 + c ⎥ ∂t ⎣⎢ ∂r r ∂r ⎦⎥

...(13)

The solution of this equation is carried out for the appropriate initial and boundry conditions: for t = 0, c = c*, i.e., at the beginning of the electrolysis the same initial concentration of depolarizer is present both is the bulk of the solution and at the electrode. During electrolysis (for limiting diffusion current, i.e., for t = 0 and for r = r0, where r0 is the radius of the spherical electrode). The concentration in zero, c = 0. The differential equations when simplified, the solution leads to the relation for the original variable: c = f (r, t) = c* .

1

2

3

r02 ⎛ r −r0 erf ⎜ ⎝ 2 Df r π

⎛ r0 ⎞ ⎞ ⎟⎠ +c* ⎜1− r ⎟ ⎝ ⎠

...(14)

4

Fig. 5.2 : Polarogram illustrating the dependence of the diffusion current on the mercury head. Zn2+ in 1 M NH3, 1 M NH4Cl (gelatin + Sulphite). Mercury head : 1h = 90, 2 58, 3 40, 4 27 cm

It follows from this equation that when r approaches r0, the solution of the equation resembles that for diffusion towards a plane electrode. Thus diffusion within a short distance from the surface of a spherical electrode may be regarded as linear.

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Introduction to Polarography and Allied Techniques

5.3 INFLUENCE OF VISCOSITY AND OF COMPLEX FORMATION ON DIFFUSION CURRENT Referring to the quantities in Ilkovi•c equation it is to be noted that the drop-time, the diffusion coefficient and to a large extent the rate of mercury flow (through the change is back-pressure) may be affected by a change in composition of the solution. Moreover, the drop-time may vary considerably is different media, but since only 6th root appears in the equation its influence on the observed phenomena is negligible. Further, the drops-time is easily measured. However, the charge in diffusion coefficient is given by Stokes-Einstein law, which states that the diffusion coefficient is inversely proportional to the viscosity of the solution: D =

k η

...(15)

The relation for dependence of diffusion current on viscosity id η = const.

...(16)

The validity of this relation is limited by that of Stokes-Einstein law, which assumes a satisfactory state that the diffusing particles are spherical and are considerably larger than the solvent particles.

5.4 FACTORS AFFECTING THE DIFFUSION CURRENT The Concentration of the Electroactive Substance : The rate at which the electroactive substance reaches the electrode surface, and consequently the current resulting from its reduction or oxidation as rapidly as it arrives there is proportional to its concentration in the bulk of the solution. The shape of the electrode does not matter. It may be plane, spherical, cylindrical or some other. It may be stationary or moving. Its area may be or may not be constant, or, the mass transfer of the electroactive substance occurs by diffusion, Laminar flow or convection. Two things are generally required: (i) the supply of electroactive substance at the electrode surface must not be affected by any chemical or physical process. This includes kinds of slow chemical reactions, or adsorption on the electrode surface, and (ii) is that the thermodynamics and mechanism of the mass-transfer process must be independent of the concentration of electroactive substance. In all voltammetric techniques, this proportionality between the mass-transfer controlled current and concentration is observed and is the basis of the vast majority of the practical analytical methods and physico chemical application which are based on these techniques. From the Ilkovi•c equation, it follows that for given values of m and t1 i.e., if the some capillary is used with a constant height of the mercury head, the diffusion current is directly proportional to the analytical concentration of depolarizer in the solution : id = k c

...(17)

12 16 k = 0.627 nFD m 2 3t 1

...(18)

where k is the Ilkovi•c constant;

Types of Currents

65

This equation forms the basis of quantitative determinations in polarographic analysis. If the limiting diffusion current values or wave heights in mm are plotted against concentration of a given compound, a straight line passing through the origin is obtained. This could be used as a calibration curve for determining the concentration of the compound in unknown samples. It has been repeatedly verified that the diffusion current is proportional to the concentration of electroactive substance. The linear dependence of diffusion current on concentration does not hold exactly when the drop-time is short. The most suitable drop-time is from 3 to 5 sec (as already stated). Dependence on the Height of the Mercury Head, Capillary Characteristics and Potential: The diffusion current depends on the capillary characteristics m and t, and is therefore affected by varying them and thus how the numerous factors influence them [m is the average rate of flow of mercury in milligrams per second and t is the droptime in seconds]. If the height of mercury head is changed at constant concentration of the substance, the flow rate m and drop-time t changes simultaneously. According to the equation m is directly proportional and t1 inversely proportional to the corrected height h of the mercury head: 1 m = k' h; t1 = k" ...(19) h substituting in Ilkovi•c equation 2/3

id = K m

16

t1

= K (k ' h )

2 3 ⎛ k" ⎞

⎜⎝ h ⎟⎠

16

...(20)

and combining all constants: ...(21) id = k h I i.e., the diffusion current is directly d proportional to the square root of the corrected height of the mercury head (reservoir) Fig. 5.2 and 5.3. The linear dependence as shown in the figures not only represents a further verification of the validity of the Ilkovi•c equation but it also provides an easy test for veryfying diffusion controlled currents. For majority of investigations into the character of limiting currents it is sufficient to plot the limiting current against the square root of the actual height h of mercury head, i.e., the distance from Fig. 5.3 : Dependence of diffusion current the capillary orifice to the mercury level on the square-root of the mercury head.

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Introduction to Polarography and Allied Techniques

in the reservoir. When the current is diffusion controlled, the plot gives a straight line (Fig. 5.3) but this line will not pass through the origin. It cuts a small intercept on the current axis. Since diffusion currents depend on m2/3 t1/6, further caution is necessary in practical quantitative determinations. When the diffusion currents for the same substance are recorded with two different capillaries the diffusion currents are in the ratio:

( m1 )2 3 (t1 )11 6 ( m2 ) 2 3 (t1 ) 21 6

...(22)

Thus, when concentrations obtained with different capillaries are to be compared the flow rates and drop-times for the capillaries must be known. Consequently, it is desirable for the comparison of results to include m and t1 values characterising the capillary in an account of the experimental data. As already given earlier, flow rate is independent of potential except in the correction term for back pressure, where its influence is negligible, but drop-time depends on potential in the same way as does surface tension. For this reason it is expected that at potentials more negative than the maximum of the electrocapillary parabola–0.56 V vs NCE in chlorides a decrease in the diffusion current with increasing negative potential will occur since the surface tension and also the drop-time decrease. The maximum value of the diffusion current is attained at the potential of the electrocapillary zero then it decreases at more positive potentials. Except at rather negative potentials a change of drop-time with potential, exerts but a small influence on the diffusion current

(

16

(since the diffusion current is a function of the sixth root of drop-time id = kt1

) . If the

diffusion current is recorded in the potential region from –0.56 to –2.0 V (vs NCE) and the drop-time decreases to one half, the diffusion current will fall to (1/2)1/6 i.e., by about 11%. The decrease in the diffusion current with increasing negative potentials must be taken into account specially when comparing the diffusion currents of two different substances of equal concentrations but having different half-wave potentials. Influence of Temperature on the Diffusion Current : An increase in temperature causes an increase in the diffusion coefficient. The effect of temperature on the diffusion current may be derived theoretically as shown by Ilkovi•c [4]. Among the quantities in the Ilkovi•c equation: id = 0.627n Fc D1/2 m2/3 m 2 3t 11 6

...(23)

only D, m and t1 depend on temperature. Further details can be obtained by differentiating Ilkovi•c equation and the above factors into account. On varying various factors it is concluded that the temperature must be kept constant within at least ± 0.5°C in order to keep the error in the determination of diffusion current below 1%. If the temperature coefficient is much larger than about 2% deg., the current is probably at least partly kinetic or catalytic, for the rates of most chemical reaction increase much more rapidly with temperature than rates of diffusion do. This may or may not be always true.

Types of Currents

67

5.4.1 The Limiting Current The total or limiting current that flows on the plateau of a wave includes contributions from several different process. It includes the current that would flow under the same conditions but in the absence of the substance responsible for the wave is called the residual current. The wave height is defined as the difference between the current and the residual current, and is the current due to the presence of the substance of interest. If the substance is ionic, there will be an electrostatic force between its ions and the electrode. The force may be either attraction or repulsion and in either case it affects the rate at which the ion, reaches the electrode surface and undergoes reduction or oxidation. The difference between the limiting current actually obtained and the limiting current that would be obtained in the absence of any electrostatic force is called the migration current. For all polarographic experiments the migration current is rendered negligible by the presence of a relatively large concentration of an indifferent electrolyte, supporting electrolyte, whose ions serve to conduct current through the solution and thus dissipate the electrostatic force but are not reduced or oxidized over the range of potentials that is being studied. Galvanometer G

–

+

– Mercury reservoir oxygen free nitrogen

solution of unknown subs. with excess inert salt +

Fig. 5.4 : The Polarographic set up.

5.4.2 The Residual Current The nature of the layer of an electrolyte solution immediately adjacent to the surface of a mercury drop depends on the potential applied to the drop. If a dropping mercury electrode disconnected from the external circuit is immersed in a pure solution of say potassium chloride, the chloride ions will be preferentially adsorbed on the surface of

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the drop, and as a result the mercury in the reservoir will acquire a negative charge. This, in turn, will be imparted to the succeeding drops, which will, therefore, adsorb fewer and fewer chloride ions until equilibrium is attained. The negative charge accumulated by the mercury will then be just great enough to counter-balance the tendency for adsorption of excess chloride ions to occur on the surface of the drop. Considering the equation ic = 0.008532 (Emax – E) m2/3 t1/3 ...it is given that the equation describes several important properties of the charging current. It is approximately linearly depended on potential, both at potentials more positive than Emax and at potentials more negative than Emax. With a typical capillary, which has the characteristics m and t 2 mg/sec and 4 sec, respectively, the charging current curve would have a slope of about 0.35μ amp./V in the first of these region and a slope of about 0.15μ amp./V in the second. These values are different because the values of x are different. The majority of practical polarographic analyses are performed by recording a polarogram of the solution being analysed, and extrapolating the portion of the residual current curve that precedes the wave of interest, thus measuring the vertical distance from the plateau to the extrapolated line. The plateau could be extrapolated backwards and the height measured at the half-wave potential. It is to be noted that neither m2/ 3 1/3 t nor x is quite independent of potential, the linear extrapolation is not perfectly accurate, even though the error is negligibly small unless the solution being investigated in extremely dilute or unless the extrapolation crosses Emax. The above equation as well be written as: ic = (kt1/2) m2/3 t1/6 for a particular solution and a particular applied potential. It will be shown in the section of diffusion current that the average diffusion current during the life of a drop, id, is proportional to m2/3 t1/6. Hence the ratio i d /ic is proportional to t1/2. Decreasing the drop-time by increasing the height of the column of mercury above the capillary, therefore decreases this ratio because it causes the charging current to increase more rapidly than the diffusion current, and so attainable sensitivity becomes poorer even though the diffusion current increases.

5.4.3 Migration Current If a dropping electrode is immersed in pure dilute solution of a salt like lead perchlorate, and if a potential on the plateau of the lead wave is applied to it, lead ions will be reduced as fast as they reach the surface of the drop. A current will therefore flow through the cell. Some anodic reaction will occur at which ever reference electrode is being used, and the ions will move through the solution to conduct the current from one electrode through the other. Lead ions will move toward the dropping electrode and the perchlorate ions will move towards the reference electrode. This motion of lead ions causes them to arrive at the drop surface more rapidly than they would if electrical migration did not occur, and this is the cause of the migration current. The value of migration current depends on the transference number of the ions being reduced or oxidised at the drop surface. The larger this transference number, the greater the fraction of the current carried by the motion of that ion. The addition of

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supporting electrolyte, whose ions contribute to the conductance but do not contribute to the current because they cannot be oxidized or reduced to any significant extent when they arrive at the drop surface, causes the transference number of the electroactive ion to decrease. If the concentration of the supporting electrolyte is very high, the transference number of the electroactive ion becomes practically zero. Current is then carried across the drop solution interface by the reduction or oxidation of the electroactive ion. It is thus carried through the solution by the motion of the ions of the supporting electrolyte. In such a solution when the transference number is small, the electroactive ion plays only a negligible part in electrolytic conduction through the solution and its motion is affected by the diffusive force alone. The sign of the migration current depends on the sign of the charge on the electroactive ion. Cations are attracted to a cathode, and therefore the migration current increases the wave height when a cation is reduced at the dropping mercury electrode. Anions migrate away from the cathode and therefore the migration current decreases the wave height when anion like iodate or chromate is reduced at the dropping electrode. On examining the figures from literature it can be observed that the addition of supporting electrolyte decreases the wave height of cadmium ion while it increases that of iodate ion. It is assumed that the mechanism of diffusion is the same in a pure salt solution as in the presence of excess of supporting electrolyte, so that the diffusion current is the same in the two cases and that the migration current is given by the product of the total limiting current by the transference number of the electroactive ion [5, 2] il = id + im = id + il t+ = id/(1 – t+) ...(1) for the reduction of a cation, and for the reduction il = id – im = id – il t– = id /(1 + t–)

...(2)

of an anion. Equivalent expression are easily written for the oxidation of cations and anions, for which the migration currents are opposite in sign to those for cathodic waves. Thus, for example, the height of the anodic wave of a cation would increase as supporting electrolyte was added. All practical polarographic work is done under conditions that serve to render the migration current negligible. There are several reasons for this. One of the most important one is that it would be quite undesirable to calculate the concentration of the substance (one which is of interest) a wave height that depended not only on that concentration but also on the concentration and nature of every one of the other ions present. It is plain that the wave heights of lead ions would be quite different in solutions of lead chloride and had perchlorate even though the concentration of the two salts were the same, for the equivalent conductances of the chloride and perchlorate ions are sufficiently different to change the transference number of lead ion by about 3% even if complextion with chloride ion is neglected. It is observed that traces of sodium nitrate or potassium nitrate would affect the limiting current obtained with any given concentration of lead ion, and would do so to different extents because the equivalent conductance of these salts are not at all the same.

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Another reason for using a considerable excess of supporting electrolyte in practical polarographic work is directly related to these considerations. It is to be noted that the addition of supporting electrolyte produces smaller variations of the limiting currents than it should according to the above equations. This is because a few tenths of a millimole per liter of electrolyte entered the solution from the salt bridge during the preparation and deaeration of the solutions. This would be immaterial if a large excess of electrolyte were already present. Also, the slopes of the waves increase and that the half-wave potentials becomes less negative as the electrolyte concentration rises. This is because the resistance of the solution is fairly high in the absence of added electrolyte and so an appreciable fraction of the voltage applied by the polarograph is dissipated as iR drop through the cell. It is certainly easy to decrease the resistance by adding electrolyte whenever it is possible. A useful rule in order to suppress the migration current to nearly completely, that further variations of the electrolyte concentration will have no effect, the concentration of the supporting electrolyte should be at least 50 times that of the electroactive ion. This is based on the conductance equation. The transference number: t j = c j λ j / ∑ c i λi i

of the jth ion in a solution is also given by the equation. Where in conductance equation, the c’s are the concentrations in equivalents per liter and the λ’s are the equivalent ionic conductances. The concentrations must be expressed in equivalents per liter. This will decrease the transference number of the electroactive ion to about 0.01. A higher concentration of supporting electrolyte is needed if the electroactive ion has an unusually high equivalent conductance (as does hydrogen ion). A lower one will suffice if it has an unusually lower one will suffice if it has an unusually low equivalent conductance (as in large organic ions). Most polarographic work can be carried out with the concentration of supporting electrolyte between 0.1 M and 1 M. In some cases of inorganic polarography even much higher concentrations are often useful. These are other cases where the use of a very concentrated medium may serve to mask an interfering ion. Take for example, thallus ion which yields a wave in almost every known supporing electrolyte but is masked in concentrated hydrochloric acid because of the formation of a chloro complex. Non-ionic substances should not give migration currents. Supporting electrolytes are still used for two reasons. One is to decrease the iR drop through the cell; and the other is to buffer the solution. The resistance of the solution is fairly in the absence of added electrolyte and so an appreciable fraction of the voltage applied by the polarograph is dissipated as iR drop through the cell. It is certainly easy to decrease the resistance by adding electrolyte whenever it is possible. The sign of the migration current depends on the sign of the charge on the electroactive ion. Cations are attracted to a cathode, and therefore the migration current increases the wave height when a cation is reduced at the dropping mercury electrode.

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Y is CY0 , this rate is equal to kf CY0 . Very little Y will be consumed since the reaction is very slow. So CY0 will be virtually identical with CY, the concentration of Y in the bulk of the solution. Additionally, the current at any instant will be proportional to the area of the electrode at that instant. It will also be affected by the rate of the backward reaction because this competes with reduction of O. Considering the derivation

(

12

ik = 493n D1/2 CY m2/3 t2/3 k f /k b

)

(3)

where ik is the average kinetic current during the life of the drop and D is the diffusion coefficient of Y or O. It is reasonably assumed that these are equal because molecules of these substances will probably have nearly equal sizes. The value of ik will be given in microampere of CY is expressed in millimoles per liter. It is easy to recognize a kinetic current with the help of the Eq. (3) since m2/3 t2/3 does not vary with the height of the column of mercury above the capillary. If all other condition are kept constant, the height of kinetic wave is independent of h corr. This

(

12

)

behaviour is quite different from the behaviour of a diffusion current id /hcorr = k1 . It constitutes the fundamental test for kinetic control of the wave height. There are a number of differences between the kinetic and diffusion-controlled waves giving supporting evidence. However, no conclusive evidence is obtained about the nature of the unknown wave which is suspected to be kinetic. The height of the kinetic wave is larger than the diffusion current that would correspond to the equilibrium concentration of O in the solution. But is smaller than the diffusion current that would correspond to the reduction of the O and Y together. In case n is known, Y can be approximated by applying Ilkovi•c equation. It is not safe to conclude that a wave is kinetic due to its unexpectedly small height, because it also happens with those of adsorption waves. The height of a kinetic wave is influenced by the experimental condition that affect the reaction rates. These include pH, temperature, and ionic strength. The effect of ionic strength depends on the charges borne by the species involved. By changing the composition of the supporting electrolyte in order to displace the equilibrium in favour of O a solution can be obtained in which the concentration of Y is negligible and in which O gives a diffusion controlled wave. When Y is reducible at a more negative potential than O, the total current on the plateau of the wave of Y can be measured. When the equation (3) applicable, the variation of kinetic current with the composition of the solution can be used to elucidate the stoichiometry of the ratedetermining chemical step. Various other kinds of behaviours are possible which have also been observed by many workers. If the pseudo-first order rate constant kf is extremely small, then only little Y will be transformed into O during the life of the drop and as such the kinetic current will be too small to detect. In such a case the wave height of O will be diffusion

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controlled and proportional to the concentration of O in the bulk of the solution. On the other hand, if kf is extremely large the wave height will again be diffusion-controlled but will be proportional to the sum of the concentrations of O and Y because actually all of the Y reaching the drop surface will be transformed into O and reduced. In case, where bulk of the solution contains appreciable concentration of both O and Y and where the transformation of Y into O is neither + instantaneous nor slow, the wave height will be the sum of the diffusion current of the O already present. A kinetic current reflecting the formation of additional O at the expense of part of the Y at the drop surface as the equilibrium between them is displaced by reduction. The diffusion current will be proportional to m2/3 t1/6 within the limits of error. The wave height may slow any behaviour intermediate between that of a pure diffusion current at one extreme and that of a pure kinetic current at the other. This depends on the position of the equilibrium between Y and O in any particular solution and on the rate at which it is attained. It is not advisable to use kinetic waves in practical analysis for two reasons: (i) They afford poorer sensitivities than diffusion-controlled waves, and (ii) an impurity may alter the height of the kinetic wave by catalysing the rate-determining step. It is better to explore conditions to obtain diffusion-controlled wave. These can be obtained by investigating the effects of variables such as pH and temperature.

5.4.5 Catalytic Currents Catalytic waves arise from mechanisms like O + ne ⎯⎯→ R

...(1)

kt R + Z ⎯⎯⎯ ...(2) → O in which a substance Z, which would not be reducible at a certain potential if it were present alone, causes the current obtained from the reduction of an electroactive substance O at that potential to increase by reacting with the product R to regenerate O or to form some other substance that is reducible. Catalytic waves are obtained in many mixtures of transition metal ions, such as tangstates, vanadate, molybdate and titanium (v), with oxidizing agents like nitrate, hydrogen peroxide, chlorate. The behaviour of the limiting current in any particular case depends on the relative magnitudes of the diffusion and catalytic currents. The heights of catalytic waves are as sensitive to variations of pH, temperature, and other experimental conditions as those of kinetic ones. The use of a catalytic wave for analytical purposes may often be advantageous because of high sensitivity that may be attained. For examining the catalytic current of nitrate take for example nitrate ion (= Z) does not give a wave in a supporting electrolyte contain 0.1 F sulphuric acid and 0.2 F sodium sulphate. Molybdenum (vi) gives a double wave. The first wave representing reduction to molybdenum (v), and the second represents reduction to molybdenum (iii). Molybdenum (iii) reacts fairly rapidly with nitrate in an acidic solution. At a potential on the plateau of the second wave of molybdenum (vi) in a solution containing nitrate, the molybdenum (iii) formed by the electrode reaction is particularly reoxidized by nitrate and the oxidized molybdenum species is then reduced with more nitrate and so on. The increase of current resulting from the presence of the nitrate that is the

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difference between the total height of the wave and the diffusion current obtained in the absence of nitrate is the catalytic current of nitrate. In cases where the diffusion current of O is appreciable it may be measured separately in the absence of Z and the catalytic current can then be obtained by difference. Like kinetic currents, catalytic currents can be identified by the fact that they do not vary with h corr. In general these two kinds of currents behave very similarly, but they are easily distinguished because of the peculiar chemical circumstances in which catalytic waves appear. Another important type of catalytic current is observed in solutions containing a base B that is not reducible but that can catalyze the reduction of protons by the following mechanism: B + HA HB+ + C 2HB

HB+ + A–

...(3)

HB

...(4)

H2 + 2B

...(5)

where HA may be hydronium ion or another proton doner. Such catalytic waves are obtained with many organic compounds, including amines, amino acids, proteins, alkaloids. These display complex behaviour. At very low concentrations of catalyst B, the bi-molecular reaction represented by Eq. (5) may be rate determining on the plateau of the wave, where the electron transfer reaction (4) is very fast and then the wave height will increase very rapidly than CB, the bulk concentration of B. But as CB is increased the proton transfer reaction (3) tends to become rate determining. Thus the observed behaviour depends on whether this reaction occurs at the surface of the drop or is the bulk of the solution and this in turn depends largely on the extent to which B can be adsorbed on the drop surface. Most often the ratio of wave height to the concentration of B decreases in the manner of an adsorption isotherm. The dependence on acidity is quite complex. At moderate acidities the wave height may be proportional to the concentration of acid because the proton-transfer reaction is rate-determining, but at high acidities the regeneration of the catalyst, e.g., 2HB

H2 + 2B

may become rate determining step. Then the wave height increases less rapidly than the concentration of acid. Catalytic hydrogen waves are also observed with some inorganic substances. In cases as with the ions of several of the platinum metals they are probably due to the effects of the deposited metals on the over potential for hydrogen evolution.

5.5 ADSORPTION WAVES An adsorption wave may be observed in case either the electroactive species or the product of the electrode reaction is adsorbed onto the surface of the drop. Suppose that the product R of the electrode reaction O + ne → R is adsorbed, its activity is lower in the adsorbed state than in solution which facilitates the reduction of O. There is only a single wave at a very low concentratic of O representing the reduction of O to adsorbed

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R. The height of this will be diffusion-controlled, which will be proportional to the 1 2 . In case as the concentration of O is increased, a concentration of O and also to hcorr point is reached at which sufficient R is formed during the life of the drop cover the entire surface. More than this amount of R can be formed only if excess remains in solution. The reduction of the excess O will produce a second wave at a more negative potential because it is more difficult to reduce O to dissolved R than to reduce it to adsorbed R. The original wave is the adsorption wave, whose height will be constant and independent of any further increase in the concentration of O. The second wave which represents the reduction of O to dissolved R is the “normal” wave. The total height of the double wave corresponds to the reduction of all of the O diffusing to the surface of the drop, and is therefore diffusion-controlled and proportional to both the concentration 1 2 . Individually these waves do not follow exactly. of O and hcorr A single wave is obtained at very low concentrations of O represents the reduction of adsorbed O. This is the case when O is adsorbed and R is not. This will reach a limiting height when the amount of O diffusing up to the surface of each drop is just sufficient to cover the drop surface. This happens on increasing the concentration of O. At a still higher concentration, the excess of O remaining dissolved at the drop surface produce a “normal” wave at a less positive potential. The adsorption is due to surface forces. The range of which usually does not exceed molecular dimensions, so that as a rule the adsorbed particles form a monomolecular layer. The particles of the dissolved substances may be bound to the surface by physical, chemical or electrical for a capillary forces causing adsorption in solutions are regarded as physical forces. Adsorption at a DME causes charges in the capacity current and may also influence the faradaic currents. The polarographic currents may be influenced by adsorption by two mechanisms: (i) The depolarizer or its electrode reaction product is adsorbed. In such a case, a separate wave, the so-called adsorption wave is formed. (ii) When some other component of the solution is adsorbed and by its presence at the electrode surface influence the depolarization process splitting the wave for the depolarizer. (iii) Polarographic Currents Influenced by Adsorption of Electroactive Substances. (a) Reversible Processes : Adsorption currents of this type were first observed by Brdi•cka and Knobloch [6] in the reduction of riboflavin and methylene blue respectively. Both compounds formed reversible oxidationreduction systems. At very low concentration of methylene blue (less than 6.10–6 M) only a single reduction wave is observed. At higher concentrations a more negative wave appears which increases linearly with concentration. Whereas the height of the original positive wave remains constant after attaining a certain limiting value. [7] Considering the adsorption of depolarizer, it is assumed that the oxidized form which is subject to a reversible reduction is adsorbed at the dropping mercury electrode whereas the reduced form is not. The reduction of

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adsorbed molecules requires more energy than that of free molecules because the energy of adsorption has to be overcome. The result is that the reduction of adsorbed molecules must take place at a more negative potentials. (b) Irreversible Processes : In some irreversible reduction two waves are observed. The first one is which is concentration independent above a certain limiting concentration. The shape of the current-time curve may resemble the adsorption pre-wave for the adsorption of the reduction product in reversible systems. In an irreversible reduction, however, it is not expected that the adsorption of the reduction product will facilitate the reduction process. The double-wave may be due to the inhibition of the electrode process by a film of the reduction product and the second which is more negative may correspond to reduction with a higher overvoltage at the covered electrode surface. Such process resembles the inhibition by adsorption of electro-inactive substances. The effect of surface-active substances on the electrode processes also plays a sufficient role. The surface active substances that effect the electrode process are classified according to their charge. Non-ionic more commonly in these are camphor, thymol, gelatine charge depending on the pH values of the solution. Among cationic compounds are the tetra-alkyl ammonium, and tribenzyl ammonium cations which have been specially investigated. A current which at a free surface is controlled by diffusion, may be retarded by a surface-active substance to such an extent that the electrode process becomes ratecontrolling. Sometimes, the electrode process is only accelerated sufficiently at much more negative potentials (considering reduction case) for diffusion to become again, the controlling process. In this way, the increased “irreversibility” in the presence of a film is explainable as evidenced by the decrease in limiting current. The shift of the wave, or the formation of a new diffusion-controlled wave at a more negative potential, though before the desorption potential of the surface-active substance takes place. On the other hand, it also sometime happens that the electrode process takes place at a greater rate when a film is present than when the surface is free. The absorbed substances facilitate the electron transfer, specially with surface active substances of the ionic types.

References 1. 2. 3. 4. 5. 6.

Ilkovi•c, D. : Collection Czechoslov. Chem. Communs. 6, 498 (1934). Kemula W. : Trabojos IX Congr. inter. quim. puray aplicada; Tomo II 297 Madrid (1934). Nernst, W. : Z Physik Chem. 2, 613 (1888). Ilkovi•c D. : Collection Czechoslov. Chem. Communs. 10, 249 (1938). Heyrovsky J. : Arhiv. Hemi Farm, 8, 11 (1934). Bridi•cka R., Knobloch E. Z. Electrochem. 47, 721 (1941).

CHAPTER 6

POLARIZATION 6.1 POLARIZATION OF THE DROPPING MERCURY ELECTRODE AND DEPOLARIZATION PROCESSES When a current passes through an electrode system immersed in a solution containing a common electrolyte, the following relation holds : Eυ − P ...(1) R where Eυ denotes the applied voltage, R the resistance of the polarographic cell and P the polarization, i.e., the electroactive force acting against the electromotive force of the source. Polarization is caused by chemical or physical changes at the electrodes due to the passage of current. In the example given above, it is defined as the difference between the potentials of the two electrodes : P = Ea – Ek ...(2) i=

where ka is the potential of the stationary mercury electrode (mercury pool on the bottom of the cell) and Ek the potential of the dropping mercury electrode regardless of whether it functions as a cathode or as an anode. The relation (3) given in the equation ahead is not as the simple Ohm’s law i.e., Eυ ...(3) R Polarization refers only to the dropping mercury electrode, since the potential of the stationary mercury electrode (i.e., the non-polarizable reference electrode) is constant. This means that the total polarization of the cell can be observed only with a dropping mercury electrode, which is regarded as perfectly polarizable. From the above equation (2) it follows that : i=

P = Eυ – iR

...(4)

This formula shows that the polarization ‘P ’ is smaller than the applied voltage by a value that is given by the potential drop, i.e., iR. While working with more concentrated electrolytes (so called indifferent or supporting electrolytes) the resistance of the electrolyte may be as low as 100Ω . Unless the current exceeds 10–5 A, the product iR is about 1 mV and may be neglected. P

Eυ

On combining this relation with equation (6) we obtain

...(5)

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Ek = –Eυ + Ea

...(6)

which shows that an external voltage when applied to both electrodes operates only at the dropping mercury electrode. To which it imparts a potential that equals the difference between the potential of the reference electrode and that of the applied voltage. In cases where the current voltage curves are referred to the same reference electrode, the constant Ea may be by convention made equal to zero and hence we get Ek = –Eυ ...(7) i.e., except for its sign, the potential of a completely polarized dropping mercury electrode equals the external applied voltage. A separate reference electrode is usually taken. This is for more accurate determination of potentials on current-potential curves. Secondary electrodes, e.g., calomel, silver chloride are the ones normally used as non-polarizable reference electrodes. Other successful electrodes which have been used at higher current densities are amalgam electrodes, e.g., 1% cadmium amalgam in a cadmium sulphate solution, or oxidation-reduction electrodes like platinum electrode in a mixture of ferric and ferrous ions in 1 : 1 ratio have also been used. The surface area of mercury pool must be sufficiently large to the extent of several square cms in order that it remains non-polarized. Its potential depends on the kind and the concentration of anions in the solution to be electrolized. In such cases, the potential of the mercury pool can be estimated from the composition of the solution.

6.2 REDUCTION OF HYDROGEN IONS AND HYDROGEN OVER VOLTAGE Among the most typical and most frequently studied examples of an irreversible process is the reduction of hydrogen ions. The over voltage of this process varies greatly with the nature of the electrode. The difference between the half-wave potential of the irreversible wave and the standard potential E 0 (virtually equal to the half-wave potential of a reversible wave) is the polarographic over potential (over voltage) η1/2 i.e., η1/2 = (E1/2)irrev – E 0

...(8)

Hydrogen over voltage is usually investigated at constant current density j and is defined as the difference between the electrode potential E, at which hydrogen is reduced at this current density, and the potential Er of a reversible hydrogen electrode in the same solution, i.e.,

η = E – Er

...(9)

Heyrovsky [3] suggested the following reaction mechanism : ...(10) H+ + e → H + + where H is written instead of H3O , for the sake of simplicity. It is supposed that the uptake of a single electron by a hydrogen ion occurs very rapidly and that the rate determining step is the reaction : H+2 + e → H2

...(11)

This mechanism is in accordance with the discharge of hydrogen on some electrodes. In order to explain the shape of the current voltage curve at a dropping mercury

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79

electrode, Heyrovsky assumed (Ref. as above) that the surface of the electrode is occupied by the evolved molecules of hydrogen, which reduce at the free surface on which the following reaction takes place : ...(12) H + H+ → H+2 K•u ta [4], derived an equation for the polarographic wave of hydrogen ions based on this assumption. K•u ta’s experiments with a streaming mercury electrode [K•uta] [4] collection Czechoslov. Chem. Communs 23, 383 (1958) showed that the concept of surface coverage by hydrogen molecules was not justified. The best agreement with polarographic results is obtained by assuming the reaction: H+ + e → H ...(13) This is supposed to be the slowest step in the proposed mechanism. In fact the influence of the electrode double layer on the discharge of hydrogen ions must also be taken into account. A brief survey of the experiments on the discharge of hydrogen ions at the dropping mercury and the streaming mercury electrode is described below : (i) Current-voltage curves for hydrogen ions without concentration polarization. Workers at about the same period found that in more concentrated solutions of strong acids (e.g., 0.01–0.1 N HCl) and in the absence of neutral salts the above defined reduction potential of hydrogen shifts in accord with the relationship : RT ln ⎡ H+ ⎤ ...(14) ⎣ ⎦ F whereas, with an excess of an indifferent electrolyte the dependence is given by E = const +

2RT ln [H+] ...(15) F In buffer solutions, with one unit increase in the buffer pH shifts the reduction potential of hydrogen by 116 mV to more negative potential. On adding small amounts of neutral salts, the over-voltage is markedly increased. In other words the reduction potential is displaced to more negative potentials, whereas, with increasing concentration of the neutral salt, the reduction potential approaches a constant value that depends on the hydrogen ion concentration. The valency of the neutral salt is also to be taken into account. (ii) Polarographic Waves for Hydrogen Ions Given by Strong Acids : Examining the shape the current-voltage curve and its dependence on the hydrogen ion concentration, it had been inferred that these are the two fundamental quantities in the theory of hydrogen over voltage. It has been stated that the hydrogen wave is asymmetric (Tomes [6],) and that its half-wave potential depends on the hydrogen ion concentration (Tamamushi [5]). (iii) The behaviour of weak non-reducible acids which give reduction waves for hydrogen ions is quite complicated. The limiting current is diffusion controlled for acids with pKa 2–5. The half-wave potential is displaced to more negative E = const +

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values with increasing concentration of the acid and, particularly of its anions. At the same time, the slope of the wave decreases. Only with very weak boric acid a kinetic limiting current controlled by dissociation rate was observed by past workers.

6.3 DOUBLE LAYER The layer of negative charge at the surface of the electrode and the layer of positively charged solution adjacent to it constitute the so-called double layer. To charge the double layer upto any potential E, a certain quantity of electricity is required. For an electrode of constant area A (in cm2) this is given by q = xA (Emax – E)

...(16)

where q is the quantity of electricity in microcoulombs, x is the differential capacity of the double layer in microfarads/square centimeter, and Emax is the potential of the electrocapillary maximum. The value of x is not independent of potential. In dilute solutions of hydrochloric acid or alkali metal halides it is approximately 40µf/cm2 at potentials more positive than Emax but only about 18 µf/cm2 at potentials more negative than Emax and in each of these regions there are definite further variations with potential [1]. It is evident that the quantity of electricity described by the above equation is positive when E is more negative than Emax, zero when E and Emax are equal, and negative when E is more positive than Emax. The reversal of sign occurs because of the polarity of the double layer is reversed in going from one side of the electrocapillary maximum to the other, and the signs are so chosen as to accord with the customary polarographic convention, in which the flow of electrons into the dropping electrode is taken to constitute a positive current. It can as well be said that the curent is taken to be positive when the dropping electrode is the cathode, and negative when it is the anode. When a reaction is said to take place at the surface of an electrode, it is not implied that the electroactive species must come into actual physical contact with the electrode. There is a potential gradient around an electrode immersed in an electrolyte solution. The potential difference between the electrode and the bulk of the solution may be represented by (E – Emax) where E is the potential of the electrode and Emax is the electrocapillary maximum potential or potential of zero charge. If this is negative, then any surface near the electrode will be at a more negative potential than the bulk of the solution and the potential will become more and more negative as the electrode surface more closely approached. An ion a molecule diffusing toward the electrode will reach a point (whose distance from the electrode surface is always negligible compared with the thickness of the diffusion layer under polarographic condition) at which the potential is sufficiently negative to bring about its reduction. All these points will lie on a spherical surface with a dropping electrode at any instant. There is a simple case in which there is no specific adsorption at the electrode surface and in which the potential varies montonically with distance from the electrode. In more complicated cases specific adsorption does occur and in which the dependence of potential on distance from the

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81

– + + – – – – + electrode is no monotonic. + – – – – – – + These are depicted schemati– – – – – – + – + + cally in the Figure 6.1. Electrode – + – + + Electrode – – – + + Fig. 6.1 schematic diagrams + + – + + – – – + of the electrical double layer at – – – – – – – – + an electrode whose potential is – – + – – + – – + + – + more negative than the – – + – – – + – potential of the electrocapillary – – ++ – – – + + maximum. (a) No specific – – + – – – + – adsorption, and (b) when the – – – – – – – – + specifically adsorbed cations Helmholtz Diffuse Helmholtz Diffuse are present in the inner layer layer double double Helmholtz plane. layer layer (a) (b) On the basis of the polarographic observations it Fig. 6.1 can be qualitatively described that the surface at which the reaction occurs coincides with the boundary between the Helmholtz layer and the diffuse double layer. Influence of structure of the electrode double layer on the rate of on irreversible process. The double layer affects the rates of electrode processes by its influences on the surface concentration of the depolarizer and on the kinetics of the electrode reaction. This effect was first considered by Frumkin [1] in the case of hydrogen ions. According to Frumkin [1], the electrode process involves only ions in direct contact with the electrode and that electron transfer to more distant ions is not likely. Thus, the electrochemical reaction occurs only in that part of the double layer, which does not exceed the effective ionic radius. Several examples of irreversible processes in which the double layer plays an important role are being described on time to time.

6.4 REDUCTION OF CATIONS (a) Reduction of Hydrogen Ions and Hydrogen Over Voltage : Among the most typical and most frequently studied examples of an irreversible process is the reduction of hydrogen ions [4]. The over voltage of this process varies greatly with the nature of the electrode. The difference between tha half-wave potential of the irreversible wave and the standard potenital E 0 (which is virtually equal to the half-wave potential of a reversible wave) is the polarographic over potential (over voltage) η1/2, η1/2 = (E1/2)irrev – E 0 ...(17) i.e., Hydrogen overvoltage is usually investigated at constant current density j and is defined as the difference between the electrode potential E, at which hydrogen is reduced at this current density, and the potential Er of a reversible hydrogen electrode in the same solution, i.e., η = E – Er .

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The sequence of reaction could be 2H+ + 2e → 2H

...(i)

2H → H2

...(ii)

Heyrovsky [3] suggested the following reaction mechanism. For the sake of simplicity, H+ is written instead of H3O+. H+ e → H

...(18)

H + H+ → H+2

...(19)

H+2 + e → H2

...(20)

It is supposed that the update of a single electron by a hydrogen ion occurs very rapidly and that the rate determining step is reaction (19). This mechanism is in accordance with the discharge of hydrogen on some electrodes. (b) Polarographic Waves for Hydrogen Ions as given by Strong Acids : As regards the shape of the current-voltage curve and its dependence on the hydrogen ion concentration. These two are very important and fundamental quantities in the theory of hydrogen over voltage. It has been stated, for example, that the hydrogen wave is asymmetric [1] and its half-wave potential depends on the hydrogen ion concentration [6]. (c) Polarographic Waves for Hydrogen Ions Given by Weak Non-Reducible Acids: The behaviour of weak non-reducible acids that give reduction waves for hydrogen ions is quite complicated. For acids which have ka between 2–5, the resulting limiting current is diffusion controlled. The half-wave potential is displaced to more negative values with increasing concentration of the acid and particularly of its anions and at the same time, the slope of the wave decreases. A further example characterized by the strong influence of the double layer on polarographic behaviour could be represented by the system Eu 3++e

Eu2 +

...(21)

The standard oxidation reduction potential for this system is –0.601 V (in 1 M NaClO4) so that the influence of the double layer may be studied on either side of the electro-capillary zero.

References 1. Frumkin A. N. : 2, Physik. Chem. 164 A, 121 (1933). 2. Graham, D.C., J. Electrochem. Soc., 98, 343 (1951) and J. Am. Chem. Soc., 71, 2975 (1949). 3. Heyrovsky, J., Chem. Listy 31, 440 (1937). 4. K•uta J., Chem. Listy 50, 991 (1956). 5. Tamamushi R. : Bull Chem. Soc., Japan 25, 287, 293 (1952) : 26, 56 (1953). 6. Tomes J., Collection Czechoslov. Chem. Communs. 9, 1950 (1937).

CHAPTER 7

AMPEROMETRIC TITRATIONS A conventional amperometric titration is one whose course is followed by measuring a current—almost always a limiting current at a voltammetric indicator electrode. Depending on the potential of the electrode and the voltammetric characteristics of the chemical substances involved, the current may be proportional to the concentration of the substances being titrated, to the concentration of the excess of reagent, or to the concentration of one of the products of the reaction, or it may depend on two of these concentrations. The titration curve is a plot of the limiting current against the volume of the reagent added. If necessary it may be corrected for the residual current and for dilution by the reagent. Ideally it consists of two straight lines intersecting at the equivalence point. Amperometric titrations can be used to determine many substances, such as phosphate and sulphate that are not electroactive besides amperometric titrations are usually less tedious and more precise.

7.1 TYPES OF AMPEROMETRIC TITRATIONS 7.1.1 Theory of Amperometric Titration Curves The shape of an amperometric titration curve depends on the substance being titrated, the reagent used, and the potential applied to the indicator electrode. Many different combinations are possible but the features common to most titrations curves can be explained by taking the titration of lead ion in weakly acidic supporting electrolyte with standard potassium chromate, using dropping electrode at a potential where both lead ion and chromium (vi) yield their diffusion currents. For the sake of simplicity it is assumed that the solubility of lead chromate is negligibly small in the medium employed and that the concentration of supporting electrolyte is so high that the migration current can be ignored. The chemical equilibrium is attained between the addition of each aliquot of reagent and the measurement of the current, and that the diffusion current of each ion is proportional to its concentration. An amperometric titration curve is a plot (i – ir) [V 0 + v] against v, where V 0 is the volume of solution titrated and υ the volume of reagent added. The factor (V 0 + v)/V 0 serves as a correction for dilution by the reagent. In case the reaction proceeds virtually to completion at every point during titration, the plot consists of two straight lines which intersect the equivalence point. The slope of the line preceding the equivalence point depends on the value of k′ i.e., the ratio of diffusion current to concentration for the substance being titrated; that of the line following the equivalence point depends on the value of k for the reagent.

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The example of lead being titrated with chromate (that has been taken) (i) both k’s are positive at potentials where both ions can be reduced and in this case the plot is V shaped. (ii) In the same titration when it is performed at a potential where chromate ion is reduced but lead ion is not. In this case kcr would be positive while kpb would be zero. Then the current would remain equal to residual current until the equivalence point is reached, the titration curve would be _/-shaped. (iii) If the chromate ion would be titrated with lead ion at the latter potential, the current would decrease until equivalence point is reached and remain zero after it had been passed. The curve would be\_-shaped. On titrating lead ion with sulphide at a potential where lead ion gives a cathodic current while sulphide gives anodic one so that kPb would be positive while ks negative. The cathodic current would decrease to zero at the equivalence point, and the anodic current would increase thereafter if the two ks ′ were numerically equal. A single straight line intersecting the zero current axis at the equivalence point would be obtained. There is a probability that their values would differ slightly. In such a case the curve would consist of two straight lines intersecting each other (at a very obtuse angle) and the zero current line at the equivalence point. For the titration of lead ion with chromate, the point of intersection of the two line segments is described by the rearranged equation: v cr =

0 0 V ib CPb C cr

...(1)

which is exactly the volume of the reagent required to reach the equivalence point. This is true of all amperometric titrations. No matter what kind of chemical reaction may be involved, or what shape of the titration curve is attained and no matter what values of ks ′ may be there. The line segment should always intersect at the equivalence point. Sources of error do remain in amperometric titration as well. Amperometric titrations are useful in cases where potentiometric titrations fail. There are two kinds of interferences in amperometric titration. (i) substances that consume the reagent, that co-precipitates, (ii) that take part in induced reactions with the substance being determined. Interference in amperometric titrations takes place as is there in any other technique. Amperometric titrations have often been employed to evaluate solubility products and other equilibrium constants. For example, if a reducible ion Mn+ is titrated with an inert one Xn– to give the precipitate Mx, and if the concentration of both solutions are known the value of kt under conditions of the titration is easily obtained by appropriate use of the equations. The equilibrium-constant expression would be : ...(2) [Mn+] [Xn–] = 1/kt The apparatus and technique are described ahead.

7.2 KINDS OF AMPEROMETRIC TITRATIONS (i) (a) Redox Titrations, (b) Complexometric and Chelometric Titrations, (c) Compensation and Diffusion-Layer Titrations. (ii) Amperometric Titrations with Two Polarized Electrodes.

Amperometric Titrations

85

7.2.1 Redox Titrations The titration curve obtained in an amperometric redox titration may have any of a fairly large number of shapes. The possibilities are more numerous than in a precipitation titration because there are four substances—the oxidized and reduced forms of each of the two couples involved which may contribute to the current. Each of the four may give a cathodic current (k > 0) or an anodic one (k < 0), or may be electrolytically inert (k = 0), at the potential selected. (k denotes the ratio of diffusion current to concentration). However, two cases are more common than others. In one of them, only one of these four substances yields a current, which may be either cathodic or anodic. In the other, the oxidized form of one couple yields a cathodic current while the reduced form of the yields an anodic one. For the first case example which can be furnished is the titration of vanadium (iv) with vanadium (ii) in 1 F sulphuric acid, using the dropping mercury electrode as the indicator electrode. The following equation describes the reaction : VO++ + V++ + 2H+ = 2V+++ + H2O

...(3)

The second kind of redox titration curve could be exemplified in a titration of iron (111) with vanadium (11) in a neutral citrate medium. At – 0.8V vs SCE iron (111) is reduced to iron (11) giving a cathodic current while vanadium (11) is oxidized to vanadium (111) giving an anodic current. Mercury electrodes are specially advantages in titrations with strong reducing agents because very negative potentials can be attained and because the electrode surface does not catalyze the oxidation of the reagent by water or hydrogen ion. The rotating platinum wire electrode in particular has been very widely used in amperometric titrations.

7.2.2 Complexometric and Chelometric Titrations Amperometric techniques cna be used to find the end point of a complexometric or chelometric titration in several ways. If the metal ion is electroactive and the complex or chelonate is fairly stable, it may be possible to find a potential at which the unreacted metal ion yields its limiting current while the reaction product is inert [6]. The titration of cupric ion with ethylene diamine tetra acetate may be performed with a dropping electrode at a potential where cupric ion is reduced but the chelonate is not can be taken as an example. The current due to the reduction of unreacted cupric ion decreases as the equivalence point is approached and becomes very small after it has been passed. In a redox titration, e.g., O x1 + Red2 = Red1 + O x 2 ; the measurement of the diffusion current of O x1 appreciable kinetic currents will be obtained near the equivalence point unless the reverse reaction is quite slow, although such a situation is quite rare. One can titrate an ion giving a chelonate more stable than that of the indicator in the presence of other giving less stable ones by appropriate selection of the indicator.

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7.2.3 Compensation and Diffusion-Layer Titrations Compensation titrations are those titrations in which the “reagent” and the “substance being titrated” give currents of opposite signs at some potential, but ideally do not react with each other at all. The end point of such a titration is the point where the cathodic current due to the reduction of one of them is just equal to the anodic current due to the oxidation of the other. In such a case the measured current is just equal to the residual current. This occurs when the electrode itself is oxidized in the anodic half-reaction. This is quite likely to be possible if the electrode is made of mercury, aluminium, silver, or some other relatively base metal [4] the titration of oxygen with sulphide at a mercury electrode [3] is a typical example. In principle, a compensation titration could be performed even if no net chemical reaction could occur at all. Example could be iron (iii)–iron (ii). The couple behaves reversibly at a dropping mercury electrode in a weakly acidic solution containing citrate, ethylene diamine tetra acetate, oxalate or tartrate. In any of these media ferric iron could be titrated with ferrous iron at any potential on the rising part of their waves, where ferric iron would give a cathodic current and ferrous iron an anodic one. Diffusion-layer titrations can be exemplified by the titration of oxygen with a strong acid [2]. The titration can be performed with a dropping mercury electrode at a potential (– 1.8 V vs SCE) where both oxygen and hydrogen are reducible. A neutral but unbuffered supporting electrolyte should be used to suppress the migration current of hydrogen ion. When oxygen is reduced, hydroxyl ions are formed at the electrode surface by the half reaction O2 + 2H2O + 4e = 4OH– As these diffuse away from the electrode surface they react with hydrogen ions diffusing towards it. Hydrogen ions are thus prevented from reacting the electrode surface until their flux equals that of hydroxyl ion, when D1/2 H + C+H = 4D1 2O2 CO2 . Upto this point the value (i – ir ) remains constant after correction is made for dilution. After this it increases linearly with the volume of the acid added in excess.

7.3 AMPEROMETRIC TITRATIONS WITH TWO POLARIZED ELECTRODES In such a case qualitatively different curves are obtained with two polarized electrodes, also known as dual-electrode amperometric titrations. These are titrations in which the current-potential curve for each of the two electrodes changes as the composition of the titration mixture changes. Case is easy to discuss in which two electrodes are identical, because then the behaviour of both can be explained with the aid of a single currentpotential curve. It is not necessary for these to be identical, they may have different areas, the efficiencies of stirring at their surfaces may differ, and they may even be made from different materials. In such an arrangement the difference between the potentials of the two indicator electrodes must be equal to the applied potential (neglecting iR drop through the cell), and the current flowing through the indicator cathode must be equal to (but have the opposite sign from) that flowing through the indicator anode.

Amperometric Titrations

87

The current varies as the titration proceeds and the shape of the titration curve depends on the reversibilities of the couples involved and on the magnitude of the potential difference applied. In principle these titrations can be made with electrodes of any kind, but stationary platinum wire electrode in stirred solutions are much the most commonly used. Amperometric titration with two polarized electrodes have sometimes been claimed to be more sensitive than those employing one polarized electrode. For this reason they have been widely used in coulometric and other titrations in which high sensitivity is needed. The principles and applications of these titrations have been reviewed by Stock [7], Delahay [10] and Lingane [5].

7.4 APPARATUS AND TECHNIQUES Experimentally, amperometric titrations are much simpler than other polarographic or voltammetric techniques. Since the current has to be measured at only a single potential, simple apparatus is needed. Fewer variables need to be controlled because the exact value of the current at any point is not important : all that matters is, how it varies as the reagent is added. The temperature, the composition of the supporting electrolyte, the height of the mercury column above a dropping mercury electrode or the rate of rotation or stirring of another electrode is used. Other factors which are very important in other voltammetric technique are, therefore, of little concern in amperometric titrations, what is necessary to avoid significant variations during the course of any one titration. All amperometic titrations are performed by measuring the current after the addition of each of a fairly small number of aliquots of the reagent. In order to avoid reduction wave of dissolved oxygen, inert gas is bubbled for sufficient time after each addition. More useful would be to use a microburette equipped with a three-ways stopcock. If the solution is sensitive to air precautions must be taken. Mixing after each addition is necessary even when deaeration is not. A stream of inert gas can be used for stirring even if it is not required for deaeration. Stirring must be stopped before the current is measured except in the case of rotating wire and stirred pool electrodes. Amperometric titration can be performed with any voltammetric indicator electrode. Widely used are rotating platinum wire electrodes. In amperometric titrations concentrated reagents are to be employed. There are two reasons for it. One, as is already indicated is to minimize the importance of the theoretically necessary correction for dilution. The other is to minimize variations in the concentrations of the supporting electrolyte, which would affect the diffusion current constants of the substances that contribute to the measured current. Regardless of the shape of the titration curve, failure to correct for dilution always causes the end point found by the usual extrapolative procedure to occur a little earlier than it should changes in the concentration of the supporting electrolyte may displace the end point in either direction. The simplest example could be of a solution containing high concentration of sodium perchlorate as supporting electrolyte which is being titrated with a very dilute reagent.

Introduction to Polarography and Allied Techniques

Most amperometric titrations are performed with reagents having normalities at least 10 or 20 times as large as those of the solutions titrated. Comprehensive reviews of the applications of amperometric titrations in practical analysis have been given in the literature cited. As already stated that an amperometric titration is one in which the end point is determined by the current resulting from a potential applied across the two electrodes.

ic

current

88

0

100

200

%c.p.

ia

7.4.1 The Working Electrode : Reference Electrode

Fig. 7.1 : Amperometric titration curve for applied potential at E1 and E2

In the case in which the potential of a working electrode is controlled relative to a reference electrode, the potential is applied so that a limiting current which is proportional to the concentration of one or more of the reactants or products of the titration is measured. As a result a titration curve is obtained by plotting the limiting current as a function of volume of titrant added. The shape of the titration curve can be predicted from hydrodynamic voltammograms of the solution obtained at various M stages of the titration. The Fig. 7.1, shows resulting amperometric titration curves for two values of applied potential. Their shapes are determined by the behaviour of the limiting current of the voltammogram at the – particular potential during the titration. Fig. 7.2, described the experimental set up of titration assembly.

7.5 TWO WORKING ELECTRODES +

In brief, a useful variation of the amperometric Fig. 7.2 : Wiring diagram for a titration involves meaning the current resulting titration assembly without an from a small fixed potential applied across two external applied voltage (with a working electrodes. One of these electrodes rotating electrode) functions as an anode and the other as a cathode. The expected current behaviour during a titration can be explained by means of hydrodynamic voltammograms. The advantage of the two working electrode variation is the elimination of a reference electrode, which can be troublesome in non-aqueous solvents. One advantage of amperometric titration is it ease of automation. A titrator can be signaled to shut off when a specified current level is reached.

Amperometric Titrations

89

7.6 CHRONOAMPEROMETRY

P o tential

C urr ent

The excitation signal in chronoamperometry is a square-wave voltage signal. This is shown in Fig. 7.3 (a) which steps the potential of the working electrode from a value at which no faradaic current occurs, Ei, to a potential, Es , at which the surface concentration of the electroactive τ Es species is effectively zero. The 0 potential can either be maintained τ at Es until the end of the experiment or be stepped to a final Ei potential Ef after some interest of Ef time T has passed. The latter experiment is termed doubleTime Time potential-step chronoamperometry. Current as a function of time (a) Potential excitation (b) Current-time response signal for double signal (chronoamperois the system response as well as potential step gram) the monitored response in chronoampe-rometry. A typical Fig. 7.3 : Chronoamperometry. double potential-step chronoamperogram is shown by the solid line in Fig. 7.3 (b) (the dashed line shows the background response to the excitation signal for a solution containing supporting electrolyte only. This current decays rapidly when the electrode has been charged to the applied potential). The potential step initiates an instantaneous current as a result of the reduction of O to R. The current then drops as the electrolysis proceeds. It is important to note that the charge Q passed across the interface is related to the amount of material that has been converted, and the current i is related to the instantaneous rate at which this conversion occurs. Current is physically defined as the rate of charge flow. Therefore, Q = nFN

...(1)

where N is the number of moles converted, and the instantaneous current at time t is

⎛ dQ ⎞ ⎛ dN ⎞ = nF ⎜ it = ⎜ ⎟ ⎝ dt ⎠ t ⎝ dt ⎟⎠ t

...(2)

The rate of conversion, dN/dt, is directly proportional to the electrode area and to the flux of material to the electrode as described by the following equation (which is derived from Fick’s first law) :

⎛ ∂C 0 ⎞ it = nF AD0 ⎜⎝ ∂X ⎟⎠ X =0, t

...(3)

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Introduction to Polarography and Allied Techniques

where

it = current at time t, A n = number of electrons, eq/mol F = Faraday’s constant, 96,485 C/eq A = electrode area, cm2 C = concentration of O, mol/cm3 (mol/L!) D = Diffusion coefficient of O, cm2/s t = time’ s X = distance from the electrode, cm Chronoamperometry has proven useful for the measurement of diffusion coefficient of electroactive species. An average value of it1 2 over a range of time is determined at an electrode the area of which is accurately known and with a solution of known concentration. The diffusion coefficient can then be calculated from it1 2 via the Cattrell equation [8]. The electrode area can be physically measured, but the common practice is to measure it electrochemically by performing the chronoamperometric experiment as a redox species whose diffusion coefficient is known [1]. The value of A is then calculated from it1 2 . If the heterogeneous electron transfer of the redox species with the electrode itself is slow, the current after the potential step in necessarily less than in a system in which the electron transfer is rapid. This aspect of chronoamperometry has been used for the measurement of heterogeneous rate constants [9] [7]. The behaviour of it1 2 as a function of time can be influenced substantially by the presence of chemical reactions that are coupled to the electrode process. Consequently, characteristic variations of it1 2 vs t have been effectively utilized for the quantitative study of such homogeneous chemical reactions. The ECE reaction in which a chemical step exists between two electron transfer steps is one mechanism that has been investigated by means of chronoamperometry : E : O + e ⎯⎯→ R k

C : R ⎯⎯→ X E : X + e ⎯⎯→ P. As shown in the reaction sequence above, a rate determining chemical step in interposed between the two electrode reactions. The two dashed lines in Fig. 7.3 (a) show hypothetical chronoamperograms for the 1e reduction of O to R and for direct 2e reduction of O to P with no kinetic complications. The solid line shows a typical chronoamperogram for an ECE mechanism. The current is intermediate between the 1e and 2e reductions, since the reduction of X to P is controlled by the rate of the chemical reaction of R to generate X. The exact position of the solid line is determined by the value of the rate constant k. Chronoamperometry has been applied to the study of several electrode mechanisms [12,13]. In such studies different mechanisms may exhibit similar responses [1, 6]. Double-potential step chronoamperometry is particularly suited for studying systems that follow EC [12] or dimerization [16] mechanism.

Amperometric Titrations

91

References 1. Delahay, P., New Instrumental Methods in Electrochemistry, Interscience, N7. 1954. pp. 258–264. 2. Kemula, W., and Siekierski, S., Collection Czechoslov. Chem. Communs. 15, 1069 (1950). 3. Kolthoff, I.M., and Miller, C.S., J. Am. Chem. Soc. 62, 2171 (1940). 4. Kolthoff, I.M., and Sambyctti, C.J., Anal Chem. Acta, 21 71 (1959); 22, 253, 351 (1960). 5. Lingane, J.J., Electroanalytical Chemistry, Interscience., N.Y., 2nd ed., 1958, pp. 280– 295. 6. Pribil, R., and Matyska, B., Collection Czechoslov. Chem. Communs., 16, 139 (1951). 7. Stock, J.T., Anal. Chem., 36, 355 R (1964). 8. Cottrell eq. p. 58 Kissinger Peter T., Heinman W.R., Laboratory Technique Marcel Dekker Inc. N.Y. 9. William R. Heinman, Dept. of Chemistry University of Cincinnati, Ohio Kissinger Peter T., Dept. of Chem. Purdue University, Inc., West Lafayette, Indiana. 10. Adams, R.N., Electrochemistry at Solid Electrodes, Marcel Dekker, New York, 1969. 11. Bard, A.J, and Faulkner, L.R., Electrochemical Methods : Fundamentals and Applications, Wiley, New York, 1980. 12. Albert, G.S., and Shain I., Anal. Chem. 35 : 1859 (1963). 13. Hawley, M.D., and Feldberg, S.W., J. Phys. Chem. 70 : 3459 (1966). 14. Feldberg, S.J., Phys. Chem., 73 : 1238 (1969). 15. Schwaz, W.M., and Shain I., J. Phys. Chem. 69 : 30 (1965). 16. Olmstead, M.L., and Nicholson, R.S., Anal. Chem. 41 : 851 (1969).

CHAPTER 8

POLAROGRAPHY OF METAL COMPLEXES 8.1 REVERSIBLE, DIFFUSION-CONTROLLED SYSTEMS DETERMINATION OF FORMULAE AND STABILITY CONSTANTS OF COMPLEXED METAL IONS

id(μ A)

Effects of Ligands on Polarographic Waves : When metal ions in solution undergo complexation with ligands other than water molecules, their polarographic reduction waves appear in two quite distinct ways. Firstly, the half-wave potential is shifted to more negative potential. This happens almost invariably. Secondly, the diffusion current charges and usually becomes 6 smaller (Fig. 8.1). 5 Studies of the stabilities of metal 4 complexes polarographically, involve the 3 determination of shifts in half-wave 2 potentials or limiting currents of metal ions 1 in the presence of increasing amounts of 0.3 0.4 0.5 0.6 0.7 0.8 complexing ligands. The shift of half wave potential of the reduction of a metal ion Fig 8.1 : Effect of complexation on taking place reversibly, both in the absence reduction wave of a metallic ion and presence of complexing agents, shifts towards cathodic direction. The shift increases with increasing ligand concentration. The rate of the electron exchange process remains relatively fast with respect to that of diffusion so that the latter is still rate determining. It is also to be noted that in the presence of the ligands, the reduction wave has a shape indicative of a greater degree of reversibility than that observed for the reduction of the aquo ion, which is attenuated and of lower slope than expected for a 2-electron reversible reduction. The decrease of diffusion current with increasing ligand concentration is to be expected owing to the increased bulk of the complexed ions relative to that of aquo ions. Such variations of diffusion coefficient have been used as the basis of methods of determining stability constants of complexes in solution. Methods for determining stability constants of metal complexes by polarographic method are being divided into three categories : (i) Methods which are applicable to reversible reductions only.

Polarography of Metal Complexes

93

(ii) Methods applicable to irreversible reductions. (iii) Methods which may be applicable to both reversible and irreversible systems. The polarographic technique, involving the direct measurement of half-wave potentials of aquo and complexed metal ions may be used to determine the stability constants of metal-ligand systems of a variety of types. Cases where reversible reductions take place, three main types of metal-ligand systems are applicable. (i) Those in which a single complex species is formed to the virtual exclusion of all others over the entire ligand concentration working range. (ii) Those in which several complexes are formed in stepwise manner, but whose stabilities differ sharply from one another between the limits of ligand concentration. (iii) Cases in which a set of mobile equilibria exists between the various complexes and the aquo ion. This is being represented by the following equation : M(H2O)n

MX(H2O)n–1

MX2(H2O)n–2

::: MX4

...(1)

In such systems, several types of complexes are present at every ligand concentration. The proportion of higher species increases with increasing concentration of ligand. Finally, the predominent species is that with the highest possible coordination number. Large number of systems have been studied polarographically in this category by previous authors.

8.2 DETERMINATION OF STABILITY CONSTANTS AND COORDINATION NUMBERS OF METAL COMPLEXES (i) The method of Lingane [3]. (ii) The method of DeFord and Hume [1] for determining consecutive overall stability constants. (iii) The method of Schaap and McMasters [5] Mixed ligand systems. (i) The Method of Lingane : The reduction of a complexed ion to the metallic state (as an amalgam) is being considered at the dropping mercury electrode. The electrode reaction may be expressed as :

( n− jm) + + ne = Hg

MX f

M(Hg) + j (Xm–)

...(2)

where MXf is the complex of metal ion M with ligand X carrying a charge (n – j m). The charge on the metal being n + and on the ligand species as m–. This overall process is represented as being made up of two reactions. The first one involving prior dissociation of the complex ion into aquo ions and ligand. The second one is the electrochemical reaction of the aquo ion itself, thus : MXf (n – j m)+

M n + j X m− 0

...(3)

| ne, E M If these processes take place reversibly and much more rapidly than the rate of natural diffusion of ions to the electrode surface, then the potential of the DME at all points on the polarographic wave may be given by :

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Introduction to Polarography and Allied Techniques

E = E0A −

0

RT C γ ln 0A A nF C M γM

...(4)

where CA0 is the concentration of amalgam formed on the surface of the DME and γA 0 is the concentration of the metal ion M in the solution at the its activity coefficient C M

drop surface and

0 M its activity coefficient. E A is the standard potential of the amalgam.

The overall thermodynamic stability constant, βM X + , of the complex MXf (omitting the charges) is given by the expression.

βMXf =

[ MX f ] [ M ][ X ]f

...(5)

here the bracketed terms represent activities. The concentration of the complex in the bulk of the solution, for a given concentration of metal ion and ligand may be written as : C MXf =

βMXf CM γ M [ X ]

f

...(6)

γ MX f

At the electrode surface the metal ion will have a concentration given by the expression : 0 C MX f

=

0 βMX f Cm γ M [X ]

f

....(7)

γ MXf

where, as before, the superscript° refers to the values at the surface. This equation is valid if it be assumed that the concentration of the ligand is large and constant throughout the solution with the same value of activity coefficient both in the bulk and at the electrode surface. The shift in the half-wave potential, produced by the presence of an excess of ligand X, is given by :

γ MI MXf βMXf [ X ] . RT . (E1/2)S – (E1/2)C = Δ E1/2 = 2303 log nF IM γ MX f

f

...(8)

If it is assumed that the diffusion current constants IM , IMX are approximately equal. Thus, the equation in its simplified form as was originally used by Lingane [3] is given as :

Δ E1/2 =

2.3 0 3RT 00591 . 00591 . log βMXf C X' = log βMXf + j log c x ( at 25°C) nF n n

The equation :

...(9)

Polarography of Metal Complexes

95

E = (E1/2)c –

00591 . i log at 25°C n id − i

...(10)

is seen to be identical with the Heyrovsky- Ilkovi•c equation for the reduction of an aquo ion. The equation thus holds both for simple and complexed ions provided that the reduction of both proceeds reversibly. A more simplified equation based on the assumption that the half-wave potential is independent of the concentration of the complex species is given below : 00591 . 00591 . log βMXf − j log C X ...(11) n n It is evident that the rate of charge of half-wave potential with ligand concentration may be expressed as, 0 (E1/2)c = E A −

(

d E1 2

)c

d log C X

= −j

. 00591 at 25° C n

...(12)

Thus, a plot of (E1/2)c versus log CX should be linear of slope – j (0.0591/n) from which the coordination number, j, of the complex, M X f , may be found. Once j is found, it is simple to calculate βMx from the equation given below : f

00591 . 00591 . log βMX j − j logCX at 25° C n n This equation was originally used by Lingane.

Δ E1/2 =

...(13)

(ii) The method of DeFord and Hume [1] for determining consecutive overall stability constants DeFord and Hume made the first attempt in polarography, regarding the stepequilibria between successfully formed complexes in solution. The concentration of each complex species, for a given free ligand concentration, is given by the expression of the form of equations (6 and 7) which are already given. The equation 7 on summing up over all possible (mononuclear) species, now takes the form: N

N

0

0

0 0 M∑ = CM ∑ C MX

βMXf [ X ]

f

M Xf

...(14)

where j = 1, 2, 3, ..., N. The shift in half-wave potential is now finally expressed by :

Δ E1/2

⎛ I 2.3 0 3RT log ⎜ γ M C = nF IM ⎜⎝

f βMXf [ X ] ⎞ ⎟ ∑ γ ⎟⎠ MXf 0 N

...(15)

In order to calculate the individual overall constants, it is convenient to rearrange the above equation and finally express in the form :

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γ (γ ) γ (γ ) γM γ X + β2 [ X ]2 M X + ... + βN [ X ]N M X γ MX γ MX 2 γ MX 2

F0 [X] = β0 + β1 [X]

N

...(16)

N

In the equation (16) the left hand side has been written as F0 [X] which denotes that it is a function of the free ligand concentration. The summation, on the right hand side has been given in the expanded form. The initial term β0, is the stability constant of the “zero complex” which by definition, has the value unity. It is, therefore, possible in principle to calculate the N stability constants form N values of the function F0[X] corresponding to the range of [X] values. In actual practice, it is necessary to use many more values of [X] than the normal value of N.

8.2.1 Calculation of Individual Complex Stability Constants In the equation (16) the function F0[X] expresses in terms of the concentration of free uncomplexed ligand and also a set of activity coefficients. Working in solutions of constant ionic strength, the values of activity coefficients can be maintained constant. Not only so, in condition of constant ionic strength, it is assumed that the activity coefficient in the equation (16) may be dropped and finally the latter takes the form : F0[X] = 1 + β1[X] + β2[X]2 + ... + βN [X]N

...(17)

In normal practice it is desirable to determine the shift in half-wave potential of a given metal ion for about twelve values of ligand concentration in the range of 0.1 to 2.0 M depending upon the ligand’s solubility. The metal ion concentration which is normally to be used is 5 × 10–4M to 10–3M. The choice has a latitude as the half-wave potential shifts are independent of it. It should, however, normally be maintained strictly constant over any particular run of ligand concentration in order to correctly and easily allow for the variation of the limiting current. After making suitable corrections to the observed E1/2 values, the various F0[X] functions are calculated for each value of [X]. To determine β1, ..., βN , the graphical extrapolation method devised by Leden [2] is applied. On plotting the derived F1[X] values against corresponding values of X, a limiting slope is obtained, as [X] tends of zero, of β2 and an intercept, on the F1[X] axis of β1. Thus a confirmative estimation of β1 is possible and in addition, a preliminary value of β2 is obtained. A function F2[X] can thus be defined similarly. In order to account for N complexes, this procedure is continued. As such the FN–1[X] versus [X] plot gives is a straight line and indicating directly, that the penultimate function has been reached. It is a usual practice to attempt measurement of half-wave potentials to the nearest 0.1 mV.

8.3 MIXED LIGAND SYSTEMS–THE METHOD OF SCHAAP AND MCMASTERS The method signifies the logical extension of the DeFord and Hume method. The method was applied in cases where the metal ions complex with two ligand species are simultaneously present in the solution.

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97

Considering a complexing reaction of the type : M + i X + jY

M Xi Y f

...(18)

in which, i, j are stoichiometry numbers and X, Y are two different ligands species. In this method [Y] is regarded as maintained constant while [X] is varied. A relation of identical form holds under such conditions that [X] is constant and [Y] varied. This principle was applied by Schaap and McMasters to the copper and cadmiumethylene diamine-oxalate systems. The oxalate concentration being held constant while that of ethylene diamine was varied. For this system, three mixed complexes are possible, e.g., Cd (en) (OX), Cd (en)2 (OX) and Cd (en) (OX )2− . By using the conventional DeFord2 Hume method values of the two constants could be determined from studies on the simple cadmium-ethylene diamine and cadmium oxalate systems. The other constant could be found from F10 function by obtaining the intercept from a plot of F10 (en, OX) versus [en]. For more details the readers are advised to consult valid literature on the subject. The polarographic technique, involving the direct measurement of half-wave potentials of aquo and complexed metal ions, may be used to determine the stability constants of metal-ligand systems of a variety of types. All these methods are applicable when the electrode process of both simple and complexed species occur reversible. Irreversible reductions have been taken up later on. The method of Schwarzenbach [6] and Ringhbom and Eriksson [4] have been quite popular and useful.

References 1. 2. 3. 4. 5. 6.

Deferd, D.D., Hume, D.N., J. Am. Soc. 73, 5321 (1951). Leden, I., Z. Phys. Chem. 188, 160 (1941). Lingane, J.J., Chem. Rev. 29, 1 (1941). Ringbom, A., and Eriksson, L., Acta. Chem. Scand. 7, 1105 (1953). Schaap, W.B., and McMasters, D.L., J. Am. Soc. 83, 4699 (1961). Schwarzenbech, G., and Akermann, H., Helv. Chim. Acta. 35, 485 (1952).

CHAPTER 9

POLAROGRAPHY OF ORGANIC COMPOUNDS The polarographic activity of organic compounds is due to the presence of one or more functional groups in the molecule. Out of the more important compounds are aldehydes, α−β unsaturated ketones, nitro and nitroso-compounds, disulphides, polymer hydrocarbons, halides, and peroxides. As a rule, the reduction waves of organic substances are governed by the rate of the electrode process and by diffusion. In the reduction of organic substances, the hydrogen ion concentration has a similar significance as the concentration of the complex forming agent in the reduction of complexes. For this reason, the half-wave potential is usually a function of pH, e.g., OX + pH+

HP O P X + ne → H 1 Red.

...(1)

As already described applications of polarography are based on the measurement and interpretation of current voltage curves. In 1922, however. Dr. Jaroslov Heyrovsky of Charles University, Prague, introduced the dropping mercury electrode. This electrode consists of mercury drop, hanging for a few seconds at the orifice of a glass capillary from which the mercury regularly drops out. The electrode and a reference electrode are immersed into the solution to be electrolysed. When an external voltage is applied across these two electrodes controlled potential electrolysis can be carried out (Fig. 9.1). The variation of current with a continuously increasing voltage can be measured by an instrument in the circuit. This measurement gives courrent-voltage curves i.e., i vs E. These curves, obtained with a dropping mercury electrode or even with any other electrode with a periodically renewed surface are completely reproducible and are called polarographic curves. These curves depend only on the composition of the electrolysed solution, with experimental conditions kept constant. In the presence of substances which undergo reduction or oxidation at the surface of the dropping electrode, or substances that catalytically effect the electrode process, or those that form stable compounds with mercury, an increase in cathodic or anodic current on the currentvoltage curve is observed. The current rises in a given potential range and this increase is followed by a region of potential in which the current has reached a limiting value. The S-shaped portion of the current-voltage curve is called a polarographic wave. The shape and position of polarographic waves provides us with information on both the quantitative and qualitative composition of the electrolysed solution. The difference

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between the limiting currrent and the current before the waves rise, is called the wave height. This usually depends in the concentration of the electroactive substance in solution. Most analytical applications of both organic and inorganic polarography are based on the increase in wave height with concentration. Another important quantity is known as half-wave potential. This is the point on a polarographic curve at which the current reaches half of its limiting value. The wave height, although, it depends on concentration, the half-wave potential is practically independent of the concentration of the electroactive species. But its value does depends on the kind of organic compound involved. The half-wave potential is a quantity that can be used for qualitative characterization of organic substances because, the half-wave potential depends on the nature of electrolysed solution and also on the composition of the solution. Measurements of both wave heights and half-wave potentials are important in solving problems in fundamental organic chemistry. The measurements of wave heights can be applied to the study of some slowly established equilibria, of reaction kinetics and hence of optimum conditions for any desired syntheses. The half-wave potentials offer information about rapidly established equilibria, reactivity towards nucleophilic attack and similar reactions, and the presence of certain structural groups in the molecule. Commonly used in chemical analysis, the polarographic technique can solve some problems of structure, reactivity, mechanism and synthesis in organic chemistry.

9.1 STRUCTURAL EFFECTS As already indicated in Chapter 1 that for systems in which the equilibrium between the oxidised and reduced forms is rapidly established at the surface of the electrode. These are called reversible systems and the half-wave potentials measured polarographically are practically equal to standard oxidation-reduction potentials measured potentiometrically. In these cases the half-wave potentials are a function of the equilibrium constants of the oxidation-reduction equilibrium. The possibility of characterising oxidation reduction properties of numerous systems is offered by polarography whereas application of potentiometry is not possible. Systems which involve a step with a high activation energy, are called irreversible systems. The half-wave potential is a function of the rate constant of the electrode process involved. It is not surprising to find correlations between the values of half-wave potentials and the structure of organic compounds. This is because of the relationship of half-wave potentials to equilibrium or rate constants. Among structural factors that effect halfwave potentials are : (i) the nature of the electroactive group, i.e., the group where cleavage or formation of bond occurs during electrolysis, (ii) stereochemistry, and (iii) the nature of substituents. In general, the shift towards more positive potentials of a cathodic wave, corresponding to a reduction process, indicates that the reduction is proceedings more readily. A shift toward more negative potential indicates that the reduction is proceeding with greater difficulty. Similarly, for anodic waves, corresponding to an oxidation process, the shift towards more negative values indicate that the oxidation proceeds more readily.

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9.2 NATURE OF ELECTROACTIVE GROUP The decisive factors for determining the polarographic behaviour of the organic molecule are : the nature of atoms in the electroactive group, their arrangement in space, and the type of bond cleaved or formed. The polarographic behaviour also depends on the molecular frame to which the electroactive group is bound, the substituents present, and in particular on the groups present in the immediate vicinity of the electroactive group. Some such groups are more susceptible to the effects of the molecular framework. Valid quantitative comparison of half-wave potential is possible when the electrode processes follow the same mechanism for all the systems to be composed. It is generally true that reduction proceeds more easily when conjugation of double or triple bonds of the electroactive group with a multiple bond or with an aromatic ring occurs. Taking the example of the reduction observed in Δ 4 – 3 ketosteroids is shifted to more positive potential for Δ 1.4 – 3 ketosteroids by 0.15 to 0.22 volts. But for Δ 4.6 – 3 ketosteroids by 0.29 to 0.45 volt. Similarly as the number of condensed aromatic rings increases, the reduction is made easier. Single C – X bonds are usually reduced at more negative potentials than C = C – CX, but at more positive potentials than C – C = C – X (X is halogen). A rigorous comparison of electroactive groups is restricted to a sequence of closely related groups such as C – F < C – Cl < C – Br < C – I in which the ease of reduction of the C – X bond increases with the increasing polarizability of the halogen X. There are some other examples also. Examples of simplified reduction processes are given in the Table 9.1 and 9.2. TABLE 9.1 These bond types can be reduced at a dropping mercury electrode

C – C C = C C≡ C

C – N C = N C≡ N N – N N = N

Condensed benzenoid rings Carbonium ions Some heterocyclic rings

C–O C = O

C–S C = S

N – O N = O O – O

N – S O – S S – S

C–X

O – X S – X X = Halogen

Polarography of Organic Compounds

101 TABLE 9.2

A system of conjugate multiple bonds represents a single electroactive group

C=C–C ≡C–C=O Electroactive Group

<

<

C=C–C–X +δ –δ Increased reactivity

C–C=C–X –δ +δ Decreased reactivity

Increasing the number of condensed aromatic rings increases reactivity. For compounds with a carbon-halogen bond, an allylic group increases reactivity and a vinyl group decreases reactivity.

9.3 STERIC EFFECTS Steric effects on half-wave potentials are those in which there is a steric hindrance of coplanarity. In these cases the shifts of half-wave potentials toward more negative values are in agreement with values obtained by independent methods. Hence the shift of –0.085 volt observed for 3 – 0-tolylsydnone is in good agreement with the value of 0.10 volt for the resonance contribution of the 3-phenyl group. This is deduced from the deviation of half-wave potential of 3-phenyl sydnone from the modified Taft [3] equation for 3-substituted sydnones. The smaller value obtained from steric hindrance of coplanarity indicates that the methyl group is the ortho position does not present all resonance interaction between the phenyl and the sydnone rings. Cis and trans isomers in some cases differ in their half-wave potentials. This difference provides a means of distinguishing the isomers and analysing a mixture of these. The presence of bulky alkyl groups also sometimes shift the half-wave potentials towards more negative values. TABLE 9.3 The molecular frame can determine the polarographic behaviour of a group Independent of molecular frame

Limited dependence on molecular frame

Strongly dependent on molecular frame

C = NNHCONH2

C – NO2

C – CN

C – SH

C – CHO C – COCH3

The presence of bulky groups also shifts the half-wave potentials toward more positive values. This is explained by changes in the mechanism of electrode process and also by relief of steric strain. An example cited in this regard is the reduction of alkyl and cyclo alkyl bromides.

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9.4 SUBSTITUENT EFFECTS Hammett [1] was the first to derive an equation for the linear dependence of two series of rate and equilibrium constants for aromatic substances substituted in the para-and meta-positions with respect to the reacting group. The validity of the following relationship has been confirmed for a number of measured reaction rates and equilibrium constants log k – log k 0 = ρ (log k – log k 0)

...(2)

log k – log k = ρσ

...(3)

log k – log k = ρσ

...(4)

0

or

0

where k are the rate constants for a homogeneous chemical reaction, K are the equilibrium constant, ° denotes the constants for the non-substituted substance, σ is a constant characterising the substituent and ρ is the reaction coefficient, which is constant for a given reaction and does not change with individual derivatives. A similar equation for substitution in the aliphatic series has been derived by Taft [3]. The values of ρ and σ have been tabulated for certain reactions. Applying the following equation : E1/2 = E10 2 = ρσ ; [5] in polarography it can be written in view of the equation. The above equation requires D = D 0 and α n = (α n)0. A number of measurements have confirmed the validity of this equation for half-wave potentials so that it can be assumed that the heterogeneous rate constant for an electrode process varies with the nature of the substituent in the same manner as the constants for homogeneous chemical reactions [6]. The effects of substituents on half-wave potentials are usually treated quantitatively using relations analogous to the Hammett and Taft equations and correlating half-wave potentials (E1/2) with the substituent constants (σ, σ0, and the like). Such treatment of half-wave potentials is better sustained than that of most other physico-chemical data. This is because the half-wave potentials are a single function of the logarithms of the rate constants of the electrode processes (k0) or of the equilibrium constant k for reversible processes. Hence by plotting E1/2 against σ we actually plot log k0 (or log k), just as in homogeneous kinetics we plot log k0 (or log k). There are a number of advantages of the application of polarographic data. These are : (i) The measurement of half-wave potentials is less tedious than the separation of the simple rate constants suitable for structural correlations. (ii) The values can be measured with good reproducibility. (iii) The reaction conditions do not vary substantially. (iv) One reaction partner, i.e., the electrode, remains the same for all the reactions that are compared. This above advantage enables us to compare quantitatively the susceptibility of various reaction centres (as expressed by the reaction constant ρ) towards substituent effects. Deviations from linear E1/2 vs σ plots may allow the detection of variations in the mechanisms of the electrode process and changes in the adsorbability in the studied reaction series. Polarography can also be used to detect and follow intermediates in some reactions. The reactive intermediates are often polarographically active and give separate waves.

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103

Classical polarography permits intermediates with life times larger than about 15 seconds to be followed and special oscilloscopic techniques will follow even these with life times two orders of magnitude less. See Table 9.4. It can, therefore, be concluded that polarography certainly deserves more interest for organic chemists and they can easily consider adopting this method as an effective working tool. TABLE 9.4 Intermediates can be detected and followed by polarography

RCOCH = CHR′ + OH –

1

=1

(–) RCOCHCHR OH

(–) RCOCHCHR′ + HO 2

1

RCOCH 2CHR′ + OH –

fast OH

OH

RCOCH2 CHR′ + OH

2

RCOCH 2C H R′ + H2O

fast OH

O (–)

RCOCH 2CHR ′

2

RCOCH 2(–) + RCHO ′

–2 O(–) RCOCH2 (–) + H2 O

RCOCH 3 + OH–

For the reaction of chalcone in alkaline solution, the determination of the ketol, RCOCH2CH(OH)R′ , and measurement of its changes with time enable one to separate the rate constants k1, k–1, k2, k–2.

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Introduction to Polarography and Allied Techniques TABLE 9.5 Polarographically Reducible Functional Groups

ΦC = O

CHO

ΦC = O

C=N–

ΦC = O –

–C ≡ N

C=C–C=C–

–N = N–

C=C–C=O

–O – O–

O=C–C=O Heterocyclic double bond

–S – S–

CXn

– NO2

Φ X*

– NO

Φ CX*

– NHOH – ONO

O = C – CX

– ONO2 – NO = N –

Polynuclear aromatic ring system

*X is a halogen atom.

References 1. Hamett, L.P., Physical Organic Chemistry, McGraw-Hill, N.Y. (1940). 2. Heyrovsky, J. and K•uta, J., Principles of Polarography, Aca. Press, N.Y. (1966) p. 256. 3. Taft, R.W., Jr., Steric Effects in Org. Chemistry, M.S. Newman Ed., J.W., N.Y. (1956).

PART-II

ALLIED TECHNIQUES

7+,6 3$*( ,6 %/$1.

CHAPTER 10

MISCELLANEOUS POLAROGRAPHIC METHODS : PRINCIPLES, THEORY TECHNIQUES AND ANALYTICAL APPLICATIONS 10.1 SQUARE WAVE POLAROGARPHY In an attempt to overcome the interference from the capacity current encountered in Brayer’s A.C. method, this particular technique was developed. A small 225 c/s square wave voltage of not more than 30 mV was superimposed on a slowly changing applied D.C. voltage by Barker and Jenkins [20]. Just before each change in sign of the alternating voltage, the measurement of A.C. component of the cell current was made. At the end of each half cycle, there is a superior faradaic to non-faradaic current ratio. This fact remain the basis of the method. This particular situation arises because the component due to the capacity current decays exponentially with time and may become negligibly small just prior to the change in the sign of the voltage. Kalousek [23] comprised a mechanical commutator which alternatively polarised the dropping mercury electrode to a potential at which the reduction occured and to a more positive potential at which oxidation of the reduction product formed at the electrode was expected. The corresponding anodic current can be observed with the Kalousek circuit, in case the product is electro-oxidizable. Fig. 10.1 denotes the period of switching (the frequency f = 1/(T), t′ , t′′ , t′′′, the times of switching and Δ E the amplitude of the squareΔE wave voltage. The original commutator was so designed that it gave square-wave voltage with a constant frequency of 5 c/sec. Thus during the drop-life of a normal drop (2 to 4 sec), 10 to 20 t′ t′′′ t′′ cycles of the square-wave voltage occured. As in normal polarography a damped galvanometer is Fig. 10.1 : Time-dependence of a used for registering the current which records square-wave voltage applied to an the mean current during the drop-life of the electrode. t′ , t′′ , t′′′ , times of switching, individual drops. The curve is recorded on T period of square-wave voltage, ΔE applying the voltage because of the continuous amplitude of square-wave voltage

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increase of voltage from the polarograph, the actual voltage obtained by this method is trapezoidal. However, the change in voltage during one cycle is so small that both voltage may be considered constant. –E

a

b

t

Fig. 10.2 : Time-dependence of the polarizing voltage at the electrode, a circuit as in schemes I and II, b as in scheme III

1. Selection of the commutated voltage and the character of the recorded current voltage curves. The shape of the current voltage curve depends on the choice of the commutated voltage with respect to the half-wave potential of the depolarizer. This is true when only the oxidized form of the depolarizer is present in the solution. (a) If the constant auxiliary voltage applied to the dropping mercury electrode during the producing half-cycle is more negative than E1/2 for the depolarizer. (i.e., at the potential of the limiting cathodic current) and if during the recording half-cycle the voltage applied from the potentiometric bridge of the polarograph changes from values considerably more positive than E1/2 (i.e., from the potential of the limiting anodic current to more negative values (Fig. 10.2), the shape of the waves corresponds to the curve in Fig. 10.3. While producing the half cycles reduction of the substance studied occurs at the D.M.E. The reduced form of the substance as a product of the electrode process accumulates close to the electrode surface. If this form can be reoxidized at the electrode, an anodic current curve 1 and 2 below the zero line (Fig. 10.4) flows the galvanometer in the recording cycles at more positive potentials than the half-wave potential. The height of this anodic wave exceeds that of the normal polarographic wave at the same concentration. This is due to the formation of depolarizer i.e., the reduced form at the electrode surface while producing the half-cycle.

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109

3

1

2

Fig. 10.3 : Wave-shapes for different degrees of irreversibility recorded with the Kalousek commutator scheme I. 1. Reversible electrode process. 10–3 M Cd2+, 1 M NH3, 1 M NH4Cl, 0.01% gelatin. Auxiliary potential E2 = –1.1 V (vs SCE), from –0.3 to –1.3 V (vs SCE). 2. Partly irreversible electrode process. 10–3 M Zn2+, 1 M NH3, 1 M NH4Cl, 0.01% gelatin. Auxiliary potential E2 = –1.6 V (vs SCE), from – 0.7 to – 1.7 V (vs SCE) 3. Totally irreversible electrode process. 10–3 M Co2+, 0.1 m KCl, 0.01% gelatin. Auxiliary potential E2 = –1.5V (vs SCE), from – 0.7 to – 1.6 V (vs SCE). 200 mV/scale unit, sens 1 : 150, t 1 = 2.6 sec, f = 12.5 c/sec

3

E

1 2

Fig. 10.4 : Dependence of the shapes of Kalousek polarograms upon the degree of reversibility of the electrode process. 1. Completely reversible electrode process, 2. Partially irreversible process. 3. Completely irreversible process

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No current flows, of course, in this potential range of the reduced form and cannot be re-oxidized at the electrode (a totally irreversible electrode process, see curve 3 (Fig. 10.3). If the reduced form is capable of oxidation at the electrode, but the oxidation potential of the reduction product does not agree with the reduction potential, then during the recording halfcycle, the anodic current falls to zero when the potential is too negative to facilitate oxidation but too positive for reduction, curve 2 (Fig. 10.3). The limiting value of the cathodic current is one half of that for the normal polarographic wave for both reversible and irreversible processes. This is due to the fact that reduction proceeds over the whole drop-life, but the current passes through the galvanometer only during one-half of this time. In the case of a reversible electrode process and anodic wave is formed at the same potential as the reduction wave in normal polarography, see curve 2 in Fig. 10.5.

1

2

Fig. 10.5 : Wave-shapes for reversible and irreversible electrode processes recorded with the Kalousek’s commutator circuit as in scheme II. 10–3 M Cd2+, 10–3 M Co2+ in 0.1 M KCl. Curve 1 conventional polarographic curve; 2. commutated curve, constant auxiliary potential =–0.2 V (vs SCE), f = 12.5 c/sec, from –0.2 to –1.6 V (vs SCE), 200 mV/scale unit, sens. 1:150.

Fig. 10.6 shows schematic square wave polarograms Kalousek’s [5] commutator method was originally devised as a means of assessing the reversibility of polarographic electrode processes. However, it also forms the basis of the square-wave and pulse-polarographic techniques. In conventional polarography, coincidence of the half-wave potentials of cathodic and anodic waves was regarded as the accepted criterion of reversibility. With the aid of Kalousek circuit, it is possible to test the reversibility with only one form of the redox system.

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product of the electrode process is reconverted, by a first order chemical reaction, to the original depolarizer. The 0.5 calculation of the mean current for the 7 5 6 complete cycle leads to a simpler and final expressions for the current than the calculation of the current in the recording of t– 0 half-cycle followed by the calculation of the 4 average value over the complete cycle of the square-wave voltage. –0.5 3 (c) Mean Currents in Irreversible Electrode Processes : The calculation of the mean currents has been carried out for the 2 –40 case when the mean value over a complete cycle of the square-wave voltage is taken for 1 the current flowing in the recording of half100 0 –100 –200 – 3 0 0 m V cycle, and for the case of the so-called quasistationary state, i.e., for the state after the E – E° passage of a number of cycles at the dropping Fig. 10.8: Shapes of commutated waves for mercury electrode. Matsuda’s treatment for different constants of the electrode process. the dependence of the shape of the currentValues of rate constants 0 = → ∝, 2. 0 = voltage curve on the magnitude of the rate 10–1 cm. sec–1, 3. 0 = 3. 10–2 cm. sec–1, 4. 0 e –2 –1 –3 –1 = 10 cm. sec , 5. 0 = 10 cm. sec , 6. 0 constant k 0 for the electrode process (at = 10–4 cm. sec–1, 7. 0 = 10–5 cm. sec–1. Scheme standard potential also presents the III, computed for α = β = 0.5, n = 2, surface- possibility of a useful quantitative estimation area of the drop at the end of drop-life q1 = of the value of this constant, nicely demon10–2 cm2/sec–1, = 10–5 cm2sec–1, c = 5.10–4 M, strated in Fig. 10.8. t 1 = 4 sec, f = 50 c/sec, E2 – E1 = 10 mV, t = It can be observed in the figure that at 25ºC. The mean current (µA) is plotted on high value of k e , the anodic current 0 the ordinate, and the difference E – E 0 [E = increases in the vicinity of the reversible half1/2 (E1 + E2) and E 0 is the standard potential] wave potential and the shape of the curve on the abscissa. approaches the reversible process. With decreasing values of k e0 , the anodic current rapidly falls and practically vanishes at k e0 < 10–3 cm sec–1. It is evident that for given experimental conditions, an estimate of the magnitude of k e0 can be made up to values approaching unity. For this reason, the relatively simple methods of a periodically changing square-wave voltage provides us with the same opportunties for estimating k e0 as the other experimentally more complicated methods. (d) Charging Currents : The current measured by the periodically changing square-wave voltage method consists of two components : (i) The electrolytic and the (ii) charging current. At the abrupt change in potential at the beginning of each half-cycle, at the instant, the electrode behaves approximately as a condenser of capacity μA

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113

C in series with resistance R. The charging current in one half-cycle follows the equation: i =

ΔE ⎛ T ⎞ exp ⎜ − ⎝ RC ⎟⎠ R

...(2)

where Δ E is the amplitude of the square-wave voltage and t is the time, measured from the beginning of the half-cycle. The capacity C is also a function of time since it changes with the surface area of the electrode. The mean value of the charging current ic over the recording half-cycle is given by the equation : 1

2 ic = T

2

∫

i dT ;

...(3)

0

it increases with increasing frequency of the square-wave voltage more rapidly than the electrolytic current and it may exceed it at higher frequencies. At this stage T is decreasing. By decreasing the amplitude of the square-wave voltage Δ E and the total resistance, in the electrode circuit R this charging current can be suppressed, which makes evaluation of the electrolytic current difficult. Also, we can restrict our current measurements to the region towards the end of the half-cycle. This last P b 2+ possibility follows from the fact that the 2+ instantaneous charging current decreases more In 3+ C d rapidly than the electrolytic one in the half-cycle TI + C u 2+ after the potential jump. The dropping mercury electrode is polarized Zn 2+ by a square-wave voltage applied over the whole period of the drop-life, but the electrolytic currents are only recorded within a very short period of time, i.e., 30 m sec during a certain –0.2 –0.4 –0.6 –0.8 –1.0 phase of the growth of the drop which is usually 2 sec, after the beginning of the drop-life. Over Fig. 10.9 : 1. Square-wave polarogram this short interval the growing mercury drop of a solution containig, 2. 10–5 M Cu2+, 2+ 2+ 2+ –6 3+ behaves in a very good approximation as a Pb , Tl , Zn and 4. 10 M ln . stationary mercury electrode with a constant surface area. The capacity currents are suppressed by recording the electrolytic currents only during 100–200 µsec at the end of each half-cycle of square-wave voltage. The recording apparatus measures the amplitude of the alternating component of the cellcurrent as a function of the linearly increasing voltage E. The square-wave polarogram has the shape of a derivative polarogram. The reduction of an irreversible depolarizer is much more complicated [2]. It demonstrates that the current given by an irreversibly reduced depolarizer is much

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As already indicated, a small amplitude alternating potential is superimposed on the D.C. potential which is varied linearly with time. The resulting fundamental harmonic alternating current is recorded as a function of direct potential. This approach was entitled A.C. polarography. The form of the fundamental harmonic A.C. polarographic wave obtained upon recording the alternating current as a function of direct potential is shown in Fig. 10.10. Faradaic alternating current flows only when both oxidized and reduced forms are present simultaneously at the interface, that is, on the rising portion of the D.C. polarographic wave. Thus a polarogram is obtained with a maximum corresponding roughly to the shape of the derivative of the D.C. wave. The details regarding shape and magnitude of the A.C. polarographic wave are influenced markedly by kinetics of the various rate processes associated with the electrode reaction. Herein lies the basis for the application of A.C. polarography in kinetic studies. For kinetic investigations, the study of the quasi-reversible fundamental harmonic as process has received considerably greater interest than any other type of kinetic scheme. Much of this work was carried out by employing the classical faradaic-impedance measurement at the equilibrium potential (i = 0) considerable kinetic data for the charge transfer porcess has been the reward of such efforts (Breyer and Bauer). Electrode processes in which currents are influenced by kinetics of coupled homogeneous chemical reaction are well known from studies of the D.C. polarographic wave. Quantitative theory for A.C. polarographic influenced in any way be adsorption process is not in existence. This is because when heterogeneous charge transfer and adsorption occur simultaneously Few theories characterizing adsorption process at the electrodes in the absence of alternating currents have been widely accepted and extending these ideas to A.C. methods is teaching. Adsorption process may influence A.C. polarographic data in the following ways : (1) Adsorption of electroactive surfactants has a profound effect on the double layer capacity leading to considerable depressions of the double layer charging current in the region of the electrocapillary maximum and often a sharp peak at potentials (both positive and negative) well removed from the electrocapillary maximum, where the coulombic forces between the electrode and ions of the electrolyte lead to desorption [33]. (2) Adsorbed electroactive surfactants can have a profound influence on kinetics or charge transfer and other steps associated with the electrode process [34]. (3) Adsorption of electroactive species may markedly influence the characteristics of faradaic alternating current through alteratins of the mass transfer process by chemical reactions occuring only on the electrode surface. The example could be hydrogen atom combination on platinum [35] and, as with electro inactive surfactants, the double layer capacity can be altered. And accurate model for adsorption kinetics and the isotherm, together with proper treatment of the mass transfer process, is sufficient of develop a theory for the tensammetric process in A.C. polarography that is, the influence of adsorbed species on differential capacity of the electrical double layer :

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Adsorption of the electroactive species probably represent the most important adsorption scheme in A.C. polarography. Application of simple qualitative concepts to develop same idea regarding how such phenomena might influence the faradaic impedance. The most convincing argument in this regard that could be applied is the phase angle. A well known relation in A.C. circuit theory is for example, [40] = EI cos ϕ ...(2) where P is the average power dissipation in the A.C. process, E is the amplitude of alternating voltage, I is the amplitude of alternating current, and ϕ is the phase angle. A phase angle of 0° represents the maximum power dissipation. The more conservative of energy the A.C. process, the closer the phase angle approaches 90°. In the theory developed shown that a diffusion controlled process yields a predicted phase angle of 45°. This implies that the mass-transfer process leads to some but not total, energy dissipation. This is expected result qualitatively. Because, although some oxidized or reduced species generated on one half-cycle can be dissipated through the diffusion process which means that diffusion into the solution to be lost to the electrode process, same can also be made available through diffusion for the reverse electrode reaction on the following cycle. These ideas are in agreement with the concept that additional slow steps lead to a faradaic process which is less efficient in the passage of alternating current, that is, less conservative of energy. Applying these ideas to the processes involving adsorption of the electroactive form, the conclusion that could be drawn is that the overall mass-transfer process in the presence of adsorption will be more conservative of electrical energy, because the adsorption leads to excess surface concentrations and less freedom for these surface concentrations to be dissipated by the diffusion process. For very rapid electrode process and or low frequencies, the possibility suggested is that the phase angle may exceed 45°, a phenomena not predicted by any of the mechanism considered earlier. Although a quantitative theory for A.C. polarography (A.C. and D.C. flow) has not been forthcoming, several workers have presented theoretical equations for the faradaic impedance at the equilibrium potential. It should be noted that adsorption and double-layer effects cannot be considered on a separate basis. Characteristics of adsorption processes on metals in electrolyte solution are influenced intimatelay by the electrical double layer and vice-versa. However, in the absence of strong interaction between the electrode material and species in solution i.e., specific adsorption, electrode processes may still be perturbed significantly by forces operative within diffuse double-layer. Frumkin 1933 [37] made the earliest attempt to interpret the influence of doublelayer structure by pointing out that the concentration of reacting particles in the doublelayer is different from the bulk of the solution, and the electrical energy available for assisting or retarding the electrode reaction is less than the potential difference between electrode and solution. It has also been pointed out that correction for the double-layer by the Frumkin theory is valid only when the thickness of the diffuse double-layer is negligible in comparison with the diffuse layer. Also it was shown that the double-layer effects would be negligible if the reaction-layer thickness is much larger than the diffuselayer thickness.

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Because Koutecky’s treatment is applicable only to reversible processes, there is no disparity between the work of Koutecky and Matsuda. The drop growth contribution predicted by Matsuda appears to arise because the faradaic impedance is markedly dependent on the magnitudes of the D.C. concentration of oxidized and reduced forms at the interface. When the D.C. process is controlled solely by diffusion, the Nernst equation is obeyed and the interface concentration are independent of electrode growth. However, if non-nernstian conditions exist, derivations of D.C. concentrations from equilibrium are influenced by the motion of the electrode surface into the solution which aids mass transfer. It is therefore suggested that, if the D.C. interface-concentration components are in a non-equilibrium state, any factor, influencing the D.C. mass transfer process, can, in turn, affect the magnitude of the A.C. wave. Electrode geometry would fall in this category. In addition one is led to conclude that the non-equilibrium state need not be concerned only with the charge transfer step. Non-equilibrium conditions related to coupled homogeneous chemical reactions and adsorption may introduce electrode geometry and growth contributions. The hypothesis that electrode geometry can be important is readily subjected to theoretical examination by examining equations for the A.C. polarographic wave with a quasi-reversible process for diffusion to a stationary sphere. As a result of the facts stated above, it can be concluded that accurate A.C. polarographic work the DME will require incorporation of contributions of drop growth and geometry into theoretical expressions whenever investigations are concerned with systems exhibiting amalgam formation and/or non-equilibrium conditions in the D.C. process with respect to either the electrochemical charge-transfer step or coupled chemical reactions. Apparently the only type of system immune to these effects is one in which both forms of the redox couple are soluble in the solution phase and the D.C. process is controlled solely by diffusion, provided diffusion coefficients of the two redox form do not differ markedly. These conclusions represent a considerable departure from the original concept that the A.C. polarographic wave would not be significantly influenced by electrode growth and geometry. However, the latter thinking neglects subtle aspects of the “coupling” between the D.C. and A.C. processes in the A.C. polarographic experiment.

10.2.1 The Technique and Instrumentation Four experimental techniques are possible for combining control of direct current or potential with control of sinusoidal alternating current or potential to study the smallamplitude faradaic impedance. A.C. polarography represents one combination. A.C. chronopotentiometry employs control of the direct and alternating components of current while measuring the resulting alternating component of potential as a function of time. (or, alternatively, as a function of direct potential). These techniques are related closely, both in principle and theory. In other words, the impedance of a polarographic cell can be studied as a function of D.C. potential by controlling either the alternating current or potential and measuring the uncontrolled A.C. parameter. The D.C. potential can be

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scanned either by controlling this potential or controlling direct current, permitting the normal chronopotentiometric process to proceed. The theoretical equation for the measured alternating current or potential is then obtained for the technique of interest from the generalized form of Ohm’s law (E = i ) and by substituting the appropriate form of direct current for the ψ0 (t) term. It is seen that the status of the D.C. polarographic process is of major concern here, just as in the discussion of time dependance and contributions of electrode geometry and growth. This emphasizes the point that the A.C. polarography serves not only as an approach to examining the rapid electrode, but also as effective “probe” for investigating the D.C. process. The operational-amplifier method confines to a single instrumental concept. The A.C. polarograph constructed from operational amplifier provides a number of advantages. Foremost among it is drastic reduction of ohmic resistance. With a three electrode configuration, the operational amplifier potential control loop provides for automatic compensation of much of the series resistance normally associated with the electrolytic cell and experimental circuitry. This is particularly important in A.C. polarography, where the low impedance of electrode-solution interface enhances such problems. In brief, it can be said that with typical operational-amplifier circuitry, the only uncompensated resistance is the ohmic drop between the tip of the reference electrode probe and the summing point of the current measuring amplifier. An unfortunate disadvantage of operational amplifiers employed in most existing electroanalytical instrumentation is limited frequency response. This has restricted A.C. polarographic investigations with operational amplifier instrumentation to frequencies of ~ 1 kc or less. Highly 100 K selective tuned amplifiers Initial Voltage are useful in A.C. polaro100 K D.C. Ramp graphy. A conventional C (fundamental harmonic) 100 K Sinusoidal A.C. polarograph can be Oscillator 100 K constructed from the aux potential-control loop, ref CELL F potential sources, tuned ind Cm amplifier, and rectifier as shown the schematic Rm diagram with a suitable Tuned recorder. The schematic Rectifier I Amplifier To Recorder diagram is given below [3]. A.C. Polarograph : Three Fig. 10.11 : Schematic of fundamentaltypes of signal sources are harmonic A.C. polarograph required in A.C. polarography. (a) a D.C. potential source whose output can be varied conveniently to serve as source of the initial potential. (b) A source of a linear scanning D.C. potential–a ramp generator whose scan rate and direction can be altered conveniently, (c) a sinusoidal

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oscillator. High-quality signal source of these type can be constructed from operational amplifiers. The A.C. polarographic signal contains quite a number of information in the form of the D.C. polarographic current, the components of which manifest the impedance of the polarographic cell at D.C. and over a range of A.C. frequencies. Finally it is taken to be desirable for measuring many of the components (not mentioned here) simultaneously, although it may need some more complicated electrode processes.

10.3. COULOMETRY Investigating the mechanism of an electrode process, it is desirable to determine the number of electrons ‘n’ that are consumed by a single ion or a molecule of the depolarizer on reduction or oxidation. In the case of a reversible diffusion-controlled process, ‘n’ can easily be determined by poltting log i/(i – i) against E. Considering the equation (1)

(

)

n i E1 2 − E = log 0058 . i −i

...(1)

it is assumed that log i/(i – i) on the potential E, must be a straight line with a slope of n/0.058. The potential, at which the value of log i/(id – i) is zero, gives the half-wave potential Fig. 10.12 (a), (b) and, (c). In multi-electron process and, in particular in the case of complicated and bulky compounds, the number of electrons has to be determined by coulometry. If follows from Faraday’s laws that : n =

M G F

...(2)

where G is the quantity of substance with molecular weight, M transformed by the passage of an electric charge Q, F has the significance (96500 coul). Consequently n, G in or G in mole and Q in coul. must be measured. Besides several other methods

log

I

log

I dI

I I dI

log

P b 2+

C d2+

I I dI

In 3+

TI+

29 mV

58 mV 0.45

a

0.50

0.55V –E

0.45 0.50

29 mV

b

0.60

0.65 V –E

19 mV 0.60 0.65 c

Fig. 10.12 : Logarithmic analysis of polarographic curves. log i/(i – i) – E plots : (a) Tl+, (b) Pb2+ and Cd2+, (c) In3+

0.70 V –E

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in polarography, electolysis with a large area mercury electrode at a controlled potential and in series with a coulometer is employed. In addition, a number of methods have been worked out that make direct use of electrolysis with a dropping mercury electrode. Lingane [28] was the first to apply coulometry in polarography, number of authors also applied this method for determination of n for both organic and inorganic substances.

10.3.1 Coulometry with Large Area Mercury Electrodes A known volume of the same solution as that subjected to polarographic investigation can be electrolysed with a large area mercury electrode. This is done at a controlled-potential Fig. 10.13 : Apparatus corresponding to the limiting current of the substance to be for electrolysis with a studied. Control of the potential is effected by means of a large area mercury potentiostat and the potential is referred to a standard electrode [28] reference electrode with no current passing. The second working electrode is usually made of platinum (Fig. 10.13). Transport of the depolarizer towards the electrode is accelerated by stirring. The decrease in the concentration of the depolarizer due to electrolysis may be obtained by direct polarographic measurements in the electrolysis cell. If i10 is the limiting current before and i, that after electrolysis, v the volume of the solution in liters and c ′=0 the initial concentration of the substance in mole, liter–1, then the eqn. (1) may be written in the form : n =

i10

Q

( i10 − i1 ) c =0v F

...(3)

and the results of the polarographic investigations can be directly sunstituted in this formula. The condition is that electrolysis continues until the solution is virtually true from the depolarizer. The term G is given directly by the product c =0.v. To determine the charge Q passed through the solution, a coulometer is placed in the circuit in series with the electrolysis cell.

10.3.2 Coulometry with a Dropping Mercury Electrode Polarographic apparatus can be utilized in direct coulometry with a dropping mercury electrode, with all polarographic conditions. Such an arrangement is also named as milli-or microcoulometry. In normal polarographic analysis, the consumption of depolarizer is so significant that the concentration in the solution remains virtually uncharged after electrolysis. On decreasing the volume of the solution to a fraction of a ml. and carrying out the electrolysis with a D.M.E at constant potential for a sufficiently long period of time, for about ten to hundreds of mins. On this the decrease in depolarizer concentration becomes polarographically measurable, Fig. 10.14. The solution needs to be stirred before each measurement as the depolarizer is more readily exhausted in the vicinity of the

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i = nF

dN dt

...(4)

d ( cv )

...(5) dt where N, may be written as the product of concentration c and volume v. Hence for representing, the decrease in concentration the equation (5), could be written as or i = nF

dc i = dt nFv During electrolysis, concentration c decreases and so also i; i becoming the limiting current i1. It therefore holds that i i1 = 10 c ct =0

...(6)

where t = 0. The final equation now takes the form : i10 log i10 – log il = 2.3n F v t c t =0 Since all two other constants are known Fig. 10.15 the foregoing equation permit the graphical determination of the number of electrons n from the slope of the log il –t plot. This particular simple method was first employed by Gilbert and Rideal [26] and later used by many authors.

10.3.4 Determination of n by Electrolysis at Constant-Current Mark, Smith and Reilley [29] proposed a method for the dropping mercury electrode. The electrode is polarized by a constant current, which over the whole time of electrolysis is kept lower than the limiting diffusion current of the depolarizer under study. Extreme negative potential from reactions prevented the first instants by connecting a condenser (capacity 20µF) in parallel to the electrodes. This may happen at the first instants of the drop-life because of high current density, because at these

...(7)

log T1 1.25

1.20

1.15

1.10 2000

4000 6000 t(s)

8000

Fig. 10.15 : Plot of log id against the duration of electrolysis in the reduction of Pb2+ in 0.1 N KCl. From the slope of the straight line, n = 2.2 is obtained [33].

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123

potentials, the supporting electrolytes are likely to be decomposed. In such an arrangement, the change in electrode potential does not exceed 20 mV during the droplife and all current supplied is consumed in electrolyzing the depolarizer. The method thus allowed the authors to determine the number of electrons in the reduction of several organic as well as inorganic substance.

10.4 COULOMETRY IN POLAROGRAPHIC ANALYSIS Meites [30] proposed a combination of polarographic and coulometric measurements for analyzing a solution containing two substances giving polarographic waves at the same potential. The example of the combined waves of lead and thallium were taken in acid solution. The results showed accuracy upto a ratio of 1 : 50.

10.5 CONTROLLED-POTENTIAL ELECTROLYSIS

Potential, v. vs. S.C.E.

When, in an experiment, the indicator electrode in a voltammetric cell is maintained at a potential on the plateau of a wave, the electroactive substance responsible for the wave is reduced or oxidized as rapidly as it arrives at the electrode surface. Its concentration in the bulk of the solution decreases, and therefore the wave height also –1.0 decreases. With most voltammetric indicator electrodes the bulk concentration decreases so slowly that the wave height remains nearly –0.5 constant over long periods of time. For example, if 25 ml. of a solution of an electro active substance for which I = 4.0 and n = 2 is electrolyzed at a potential on the plateau of 0 its wave with a dropping electrode for which m2/3t1/6 = 2.5, the rate of decrease of bulk concentration will be only 0.8 % / hr. Polarograms of stable solutions can be 0 50 100 150 recorded over and over again without sensible change. Variations of wave height with time Fig. 10.16 : Chronopotentiogram obtained are easily corrected with the rates of chemical with a mercury electrode having an area reactions occurring in the bulk of the solution. of approximately 1 cm2 for a solution There are many reasons for which it is containing 10 mM copper (II) and 10 mM desirable to perform quantitative electrolyses cadmium (II) in 2F perchloric acid, using in reasonable lengths of time. For doing this a current of 0.50 m amp a large electrode like mercury pool or a cylinder of platinum gauze are useful in an efficiently stirred solution. This is because, the processes that occur at the electrode-solution interface under any given condition are mainly dependent on the potential of the electrode. Voltammetric data can easily be used to find the potential that is best suited to carrying out any desired electrode

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E. Volts vs. S.C.E.

reaction. The results of such analysis are very useful in 0.4 – interpreting the voltamme0.2 – tric observation. 15 Sec. The electrogravimetric 0– determination of metals [31] at solid eletrodes is the most –0.2 – frequent application of –0.4 – controlled-potential electrolysis. –0.6 – The familiar technique of separation in the electrolysis –0.8 – of stirred solution with large mercury cathodes employing Time nearly constant electrolysis current. This is because in Fig. 10.17 : Chronopotentiogram of 0.01 M analytical laboratories it is potassium ferric cyanide in 1 M potassium chloride often required to separate elements such as iron, chromium, cobalt, copper and nickel. These are deposited into the mercury from acidic solutions. Others like aluminium, titanium, tungsten and vanadium remain in solution. Such constant-current separations depends on the fact that, the potential of the mercury electrode must always assume a value determined by the composition of the solution at the instant under consideration. If the electroactive species is consumed in a controlled-potential electrolysis the current must decrease. In polarographic work it is usually possible to employ a two-electrode cell in which the electrolysis current flows through a reference electrode. This is because the iR drop through the cell is usually so small that the applied voltage is nearly identical with difference between the potentials of the electrodes, and also because the potential of a properly designed reference electrode is virtually unaffected the flow of a few microamperes of current through it. Hovever, the situations is quite different in controlled potential electrolysis. The iR drop may be as large as 100 V, or even larger while working in non-aqueous solutions, and several amperes may flow through the electrolysis circuit. A typical cell is shown in Fig. 10.18. Slight modification may be required in prolonged experiment with air sensitive solutions. The electrolysis current flows through the mercury-pool working electrode and an auxiliary electrode which may be either a helix of platinum wire as shown or in graphite rod. Unless the solution being electrolyzed is extremely dilute, which is unusual, it is therefore necessary to employ a three electrode cell. In order to avoid anodic attack on the platinum, it is advisable to add a little hydrazine or hydroxylamine to the auxiliary-electrode compartment. In some applications of controlled-potential electrolysis it is feasible to place the working and auxiliary electrodes in the same solution. As such, a beaker can be used as the electrolysis cell. Diaphragm cells like the one already shown are quite useful, in the sense that they

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125

prevent the products formed at the auxiliary electrode from Working A U X . R E F . Electrode reacting the working electrode. It is because that they might consume current or react with the desired product. Also to prevent the cyclic oxidation and reduction that might sometimes occur; if the latter comes in contact with the auxiliary electrode. The cell resistance depends on the supporting electrolyte used. The cell is allowed to stand for a while with the electrolyte solution (in the center compartment) because the resistance of a dry fitted disc is very high. It is desirable to exclude from the working electrode compartment Cell by continuously passing a rapid stream of nitrogen. The working electrode potential is monitored with the aid of a reference-electrode. Many important applications are available by use of Fig. 10.18 : Chronocontrolled potential electrolysis: potentiometric cell with A brief account of these are described below : 1. It is used in effecting separations prior to shielded platinum working polarographic analyses. Very complex solutions can electrode readily be analysed. A polarogram of the solution is recorded at a sensitivity so chosen as to give an easily measurable height for the first wave. The solution is electrolysed with a mercury cathode whose potential is maintained constant at a value on the plateau of this wave, if it is reversible or on its rising part of it is irreversible and poorly separated from the wave that follows. When the electrolysis is completed a second polarogram is recorded and the height of the second wave is measured and so on. It is also convenient to insert a dropping electrode directly into the working-electrode compartment of the electrolysis cell. The electrolyses can then be performed without any transfer of solution and the polarogram could be recorded. Like this the wave-order problem is practically over. 2. It is used in recovering electroactive impurities from supporting electrolytes by using electrodes such as hanging drop or the stirred mercury pool and applying techniques such as square-wave polarography and stripping analyses, it has been possible to analyse solution in the range of concentration down to about 10–10 or ever up 10–11 M. 3. Electroactive species that are very sensitive to air oxidation can be prepared and studied with great ease. The peculiar virtue of the technique is that it not only gives an essentially equantitative yields of the desired product, but does so without introducing foreign reducing or oxidizing agents. Above all the extreme selectivity that is achieved is of special importances. The most common applications of the techniques has been in elucidating the products and n values of the half-reactions that occur in voltammetry. An example could be of mercap to benzothiazole gives an anodic wave at D.M.E. For more details the original literature may be consulted.

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10.6 CHRONOPOTENTIOMETRY Chronopotentiometry is an electrochemical method characterized by the application of a constant current through a stationary indicator electrode in an unstirred solution and subsequent measurement of the working-electrode potential as a function of time. The resulting chronopotentiogram showing the variation of potential with time can be used for a variety of analytical purpose. It also includes the measurment of concentration of electroactive species, as well as electrode or solution kinetics. There have been some analytical applications of chronopotentiometry, but it can not be regarded as a very promising analytical technique, although it is capable of good precision under favourable conditions. Its limit of detection is even inferior to polarography due to the double layer charging and, at solid electrodes, oxide formation. A typical chronopotentiogram, taken as an example, is obtained with a small mercury pool in a perchloric acid solution containing copper (II) and cadmium (II). This is shown in Fig. 10.1 The zero current potential is shown by the short horizontal line at the left hand side of the figure. When the current how is stated, the potential shifts towards more negative values on the rising part of the copper wave. The shift is raped at first, then slows down as the concentration of copper (II) decreases while the concentration of copper (O) increase at the electrode surface until the point of maximum poisioning capacity is reached. These after again accelerates as the concentrate of copper (II) becomes still smaller. Eventually, the flux of copper (II) at the electrode surface becomes too small to consume all the current. The potential shifts rapidly to the value at which cadmium (II) is reduced. The time (in seconds) required to reach the point of maximum slope is the “transition time” T. Sand equation [19] iT1/2 = 1/2 (π1/2 nFD1/2 AC) ir 1 2 =

(

1 12 π nFD 1 2AC 2

...(1)

)

where i is the current in microamperes, A is the area of electrode in square centimeters, and C is the bulk concentration of the electroactive substance describes approximately for linear diffusion to plane electrode. Here the double-layer charging is ignored. A second transition time is observed, when cadmium ions are more and more removed completely from diffusion layer on prolonged electrolysis. The difference between the two transition times is longer than the single transition time if the cadmium ions had been present alone. This is because the reduction of copper (II) continue while that of cadmium (II) is taking place. In a mixture of two substances the first transition time r1 is given by the foregoing equation (1). The sum of the two transition times, (r1' + r2), is given in the following equation :

(

)

i ⎡⎢ (r1 + r2 ) − r11 2 ⎤⎥ = 1 /2 π 1 2n 2FD 21 2 AC 2 ...(2) ⎣ ⎦ Sand, as already reported, showed that in an unstirred solution and under conditions of linear diffusion, the transition time t (in secs) is related to the concentration 12

Miscellaneous Polarographic Methods : Principles...

127

π1 2nF AD 1 2C 0 ...(3) 2i where F is the number of faradays per molar unit of reaction, i is the constant current in amperes, A is the electrode area (in square centimeters), F is the faraday. (96, 493 coulombs), D is the diffusion coefficent (in square centimeters per second) and C 0 is the bulk concentration in moles per cubic centimeters. Butter and Armstrong [4], after the work of Sand coined the term “transition time”. Monograph of Delahay [7] expressed a number of developments for it. The most interesting feature of Sand equation, given above is that the square root of the transition time is proportional to the bulk concentration of the electroactive substance. This property has great utility is analytical investigations. Analysis involving oxidations can be carried out chronopoteniometrically with much better results the polarography with a rotating platinum electrode, specially in the milli molar concentrations range. Most recent application of chronopotentiometry is kinetic measurements involving both electrotransfer and “chemical” to studies of adsorption on the electrode surface. This can be regarded as a general electrochemical tool. i1 2 =

10.7 THEORY OF REVERSIBLE PROCESSES The chronopotentiogram as shown in the Fig. 10.1, may be considered to result from a single electrochemical reaction. This is without kinetic or catalytic complications. The experimental conditions so selected are such that the diffusion is the sole means of mass transfer. Also, the electrode may be considered a plane, with both oxidized and reduced species being soluble in the solution. The Sand equation applies to all such cases, whether reversible or irreversible. But the original potential time relation as given by Karaoglanoff [11] applies only to those cases for which the magnitude of the forward and reverse electrochemical rate constants is large enough so that Nernst equation i obeyed, i.e., the electrochemical process may be considered to be reversible. The usual symbolization of the process is given as : O + ne

R

The equation of Karaoglanoff (11) for both O and R soluble is : RT t1 2 ...(5) ln nF r 1 2 − t 1 2 where RT/nF has its usual significance, t is the time in seconds, and τ is the transition time. This is analogous to similar equation for polarographic waves. It may also be shown that E = Eτ/4 –

Et/4 = E1/2

...(6)

(the polarographic half-wave potential) provided the experiment is done with mercury electrode. Also Et/4 is related to the standard potential of the electroactive couple by

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Er/4 = E 0 –

RT f R D1 2 ln 12 nF f0 D R

...(7)

The equation (5) indicates that a plot of log [(t1/2 – t1/2)t1/2] versus E should yield a straight line whose reciprocal slope is 2.303 (RT/nF) or 0.0591/n at 25°C.

10.7.1 Irreversible Processes The irreversible electrode reaction is represented by O + ne → R

...(8)

The relationship given on eqn. (5) may be applied to relate transition time to concentration, just as the Ilkovi•c equation may be applied to both reversible and irreversible polarographic processes. The potential of the working electrode during a “totally” irreversible electrode reaction has been related to the current [13] thus

⎛ −αna FE ⎞ i = nAF Ck f0exp ⎜ ⎝ RT ⎟⎠

...(9)

where α is the transfer coefficient of the electrode processes, C is the concentration of the electroactive species at the electrode surface, n a is the number of electrons involved in the rate, determining step, and k f0 is the rate constant for the irreversible process in centimeters per second at E = 0 (versus the normal hydrogen electrode). The assumption using this equation is that the rate of the reverse process is negligible and that the kinetics of the electron transfer reaction is controlled by a single rate determining step. By introducing the transition time from the equation (3), the following potential time relationship is obtained [7]. From the proceeding equation (10), it is apparent that a plot of ln (τ1/2 – t1/2) versus E should give a straight line of slope RT/α n a F. In addition, the E τ4 for the irreversible E=

(

)

RT RT 2k 0 f ln τ1 2 − t 1 2 + ln αna F αna F ( πD )1 2

...(10)

case shifts linearly with ln C 0 and with the current density I. Values of α na and k f0 can be determined through the use of equation (10), which is convenient to work. Chronopotentiometry has certain advantages over polarography for this type of work. The reason being that the diffusion process involved is much simpler. Electrodes other than mercury can also be used and the reaction can be studied in both directions by reversing the current. It is also to be noted that when kinetic complication precede the charge transfer process, It1/2 is not directly proportional to concentration.

Miscellaneous Polarographic Methods : Principles...

Two component systems have also been studied by current-reversal chronopotentiometry and can be treated quantitatively under assumption that all species have equal diffusion coefficients. A variation of current reversal chronopotentiometry is cycle chronopotentiometry in which current is reversed repeatedly at potentials taken at the transition times of various waves. Several cases, including diffusion controlled single component system, electron transfer followed by a chemical reaction, and multi-component systems and stepwise reaction have been examined by various workers in the past.

10.8 EXPERIMENTAL METHODS 10.8.1 Apparatus

129 AUX.

REF.

Fig. 10.19 : Chronopotentiometric cell with mercury-pool working electrode

E . V olts v s . S .C .E .

1. Current supplies : In order to use high currents continuously, it is convenient to use a variable high-voltage power supply of good quality. Elese for constant current supply may easily be constructed from several 45-volt batteries and a series of resistors arranged in such a way that currents from a few milliamperes to a few microamperes may be obtained [10]. In order to minimize the heating effects if the resistors are of a fairly high voltage. The constant current can be measured by inserting Time a standard resistor (Rs ) as shown in the Fig. Fig. 10.20 : Methods of transition-time measurement; 10.20 in the circuit and irreversible or distorted curve measuring the voltage drop across this resistor with a potentiometer during electrolysis. Constant current sources of high quality can also be constructed from operational amplifiers [17] by placing the cell in the feedback loop of an amplifier, the

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output of which is a known potential through a known resistor. A constant current will pass through the cell, if the potential is constant. The main advantage of this type of circuit is for those methods which make use of variable currents such as, power of time chronopotentiometry [14]. A great variety of recorders (standard strip-chart) are usually adequate when the chart drive is constant with time and the pen speed is at least 1 sec. full scale. An oscilloscope of appropriate type can also be used for measurement of transition times.

10.8.2 Cells and Electrodes Ordinary cells with three electrodes are used for chronopotentiometry. The working electrode, the auxiliary electrode and the reference electrode [B] Fig. 10.19. Graphite electrodes are also useful. This is because their anodic range is greater than that for either platinum or gold. Three types of mercury electrode’s have found general use for chronoptentiometry. For example, Mercury pool, hanging drop, and the dropping mercury electrode. In order to obtain reproducible electrode area, the mercury pool should be of uniform cross section. The hanging mercury drop electrode has greater utility due to its convenience, reproducible area (about 0.2 per cent), and the saving that results in the quantity of mercury consumed. Hanging mercury drop electrode can also be formed by the expulsion of a small quantity of mercury from a micro-syringe fitted with a micrometer. These devices are also commercially available. In order to synchronize the measurement of drop formation, using some means, the dropping mercury electrode can also be used.

10.9 THE TECHNIQUES 10.9.1 Measurement of Transition Times The accuracy of chronopotentiometric methods depends on the exactness with which transition times can be measured. Fig. 10.8 shows a typical reversible chronopotentiogram without much distortion. To, measure transition time, the simplest method is to draw Fig. 10.9, the tangent lines CF and AD and locate the point Z. Here the potential time curve departs from a straight line. The transition time is then takes from Z to AD. In an accurate system the potential at which Z is located will be very close to constant. In such systems precise results can be obtained simply by measuring τ at some constant potential nearby but not necessarily at, Z. The method of finding Z, is to be preferred if n values and even more important, if diffusion coefficient are of interest. The method appears to be superior as regards simplicity and accuracy. If the potential-time curve is distorted or as the working electrode as well. Micro reference and auxiliary electrode are made to contact the drop above. A mercury electrode of special design can also be used. The standard chronopotentiometric relationship apply to this apparatus.

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Some interesting work can also be reported in which a thin layer of solution is f confined next to the working electrode surface [6]. Thin layer chronopotentiometry also has advantages like : 1. Chronopotentiograms are often less distorted than the corresponding semi infinite-diffusion case. 2. Kinetic studies, particularly of slower reactions, can be carried out. This is due since the product of electrode reaction are held near the electrode and are thus available for further study. 3. Studies of adsorbed reactants can be made since in many cases an appreciable fraction of a species in the cell may be removed by adsorption.

10.10 APPLICATIONS 10.10.1 Concentration Measurements Chronopotentiometry is not as large as compared to polarography, Chronopotentiometric under optimum conditions is capable of measuring concentrations with an accuracy of 0.5 to 1% [8]. Work with electrodes other than mercury can be carried out with superior results to polarography. Specially with rotating, electrode. It could be a matter of choice in chronopotentiometry for working at anodic potentials, although cyclic voltammetry and rotating disk electrode are extensively used.

10.10.2 Electrode Kinetics Various methods for measuring transition times of irreversible chronopotentiometric waves have been compared and comments reported [18] irreversible Fig. 10.20. Practically it is desirable to construct two tangent lines necessary to locate point A. The transition time is then taken from A to the tangent line for the beginning portion of the curve. The method of locating Z, as already given is preferable. Here τ being taken from Z to extension of the starting portion of the potential time curve. Too large values of τ are obtained when the chronopotentiogram is very distorted.

10.10.3 Electrode Pretreatment A fresh surface is easily obtainable while using DME or the hanging drop, and this the main advantage of these electrode rather than using solid electrodes like platinum. The noble metal surfaces are liable to be oxidized. In such cases pretreatment of electrodes is necessary [2].

10.10.4 Differential and A.C. Chronopotentiometry A method of determining transition times, differentiation of potential time curve has been suggested [9]. Differentiation is accomplished in reversible processes since the magnitude of the sinusoidal component of the potential is proportional to dE/dt. Curve, if they are of dE/dt type, show a maximum at the inflection of the potential time curve or change sign if of the d 2E/dt2 type.

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10.10.5 Thin-Layer Chronopotentiometry Chronopotentiograms can, however, be taken on single drops [10] with a value of only 0.05 ml. The cell used consists of a platinum plate with a small depression to hold the drop in place. This plate serves best results were obtained with an algebraic method of calculating the transition times. With the aid of a digital computer, a least square analysis of chronopotentiometric curve was also accomplished. However, chronopotentiometry is quite important for the study of irreversible reactions [13]. The fact remain that chronopotentiometry has not been extensively used to measure the kinetic parameters like k° and α for irreversible reaction may be due to better and more rapid techniques.

10.10.6 Chemical Kinetics One of the major applications of chronopotentiometry to date has been the study of chemical reactions either preceding or following electron transfer reactions. Chronopotentiometry can be applied to chemical kinetics in a way analogous to any other concentration measuring technique. The main advantages of chronopotentiometry involves investigation of chemical reactions closely coupled with electron transfer reactions. Reactions which precede the electrode transfer include both the addition or loss of hydrogen or hydroxide ion and the dissociation of metal complexes. Mark and Anson [12] made quite some investigation in the area. Reactions which follow electron transfer reaction can also be studied. Current reversal chonopotentiometry is quite helpful for such a work.

10.11 ADSORPTION Adsorbed molecules are in lower free-energy state than those in solution and thus more difficult to reduce or oxidize [5]. Another reasonable possibility is then to assume that the adsorbed layer undergoes electrolysis only after the usual transition time for the diffusing species. The fact is that, while the adsorbed layer is reacting toward the end of the electrolysis, more soluble species diffuse upto the electrode thus reducing the current efficiency. Recently, radiotracer methods and thin-layer chronopotentiometry have been used to investigate adsorption of various substances specially that of iodine [15].

10.12 APPLICATIONS One of the most interesting has been the work on fused salt, where several other standard method, such as polarography cannot be applied. Thickness of thin films on various metals has also been studied by chronopotentiometric methods [38], [39]. The method is similar to that used to study electrode oxidation. Calculation of thickness could be calculated by the formula T = 105 M iτ/An Fd

...(2)

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where, T is the thickness in angstroms, M is the gram formula weight of the compound, d is the density of the compound, and A is the specimen area. Other symbols have the standard meaning.

References 1. Bard, A.J. Anal Chem. 33, 11 (1961). 2. Bard, A.J. Electroanalytical Chemistry, Dept. of Chemistry, Univ. of Texas Austin, Texas.Vol I. p. 178 and 183. 3. Berzins T. and Delahay, P.J. Am. Chem. Soc., 75 4205 (1953). 4. Butter J.A. and Armstrong. Trams. Faraday Soc., 30 1173 (1943). and Anal. Proc. Royal Soc., London A 139, 406 (1933). 5. Brdi•cka R., Collection Czech. Commun. 12, 522 (1947). 6. Christen C.K. and Ason, F.C. Anal. Chem. 36, 723 (1964). 7. Delahay P. and Berzins T. J. Am. Chem. Soc., 75, 2486 (1953). 8. Davis, D.G. Anal. Chem. 33, 1839 (1961). 9. Iwamoto, R.T. Anal. Chem. 31, 1062 (1959). 10. Iwamoto, R.T. and Adams R.N. and H. Lott, Anal. Chem. Acta. 20, 84 (1959). 11. Karaoglan off. Z. Electrochem. 12.5 (1906). 12. Mark H.B. and Ason, F.C., Anal. Chem. 35, 722 (1963). 13. Moorhead E.D., and Furman N.H. Anal. Chem. 32, 1507 (1960). 14. Murray R.W. and Reilley C.N.J. Electroanal. Chem. 3, 64 (1962). 15. Oster Young R.A. and Anson F.C., Anal. Chem. 36, 975 (1964). 16. Reilley, C.N. Manotov G. Anal. Chem. 27, 4786 (1955). 17. Reilley, C.N.J. Chem. Edu. 39, A 853 (1962). 18. Russel R.C.D. and Peterson, J.N.J Electroanal. Chem. 5, 467 (1963). 19. Sand, M.J.S. Phil. Mag. 1, 45 (1901). 20. Barker G.C. Jenkins I.L. Analyst 77, 685 (1952). 21. Barker G.C. Progress in Polarography (P. Zuman and I.M. Kolthoff) Vol. 2. p. 411 interscience N. 7 (1962). 22. Kambara Bul. Chem. S.C., Japan 27, 523, 529 (1954). 23. Kalouscek, M. Chem. Listy 40, 149 (1946) Colln. Czech. Chem. Commun. 13, 105 (1948). 24. Koutecky J. Chem. Listy 49, 1454 (1955) Collection Czechoslov. Chem. Communs. 21, 433 (1956). 25. Werber J. Chem. Listy 52, 1888 (1958) Collection Czechoslov. Chem. Communs. 24, 1770 (1959). 26. Gilbert G.A., Ri DEAL E.K. : Tans. Faraday Soc., 47, 369, (1951) 27. Lingane, Electroanalytical Chemistry Interscience, N.Y. 2nd Ed. 1958 pp. 351–415. 28. Lingane J.J. : J. Am. Chem. Soc., 67 1916 (1945). 29. Mark H.B., Smith E.M., Reilley C.N. : J. Electroanal. Chem. 3, 98, (1962). 30. Meites L : Anal. Chem. 27, 1114 (1955). 31. Lingane. J.J. Electroanalytical Chemistry, Index Science, New York 2nd. ed. (1958), pp. 315–415. 32. Breyer, B. Gutman F. and Hacobian S., Aust. J. Scient. Res. A/3, 558 (1950). 33. Breyer, B. and Bauyer H.H., “Alternating Current Polarography and Tensammetry,” in Chemical Analysis (P.J. Elving and I.M. Kolthoff, eds.), Vol. 13, Wiley (Interscience), New York, (1963).

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34. Reilley C.N. and Stumm W.; in Progress in Polarography (P. Zuman, ed., with the collaboration of I. M. Kolthoff), Vol. I. Chap. 5, W. Int. Sci. N.Y. (1962). 35. Graham, D.C., J. Electrochem. Soc., 98, 370C (1952). 36. Kambara T., and Tachi, I. Bull. Chem. Soc., Japan 25, 135 (1952). 37. Frumkin, A.N., Z. Physik. Chem., 164, 121 (1933). 38. Evans U.R., and Bannister, L.C., Proc. Royal Soc. (London), A125, 370 (1929). 39. Campbell W.E., and Thomas U.B., Bell Telephone System, Tech. Publ. Monograph B. 1170 (1939). 40. Kambara T. and Tachi, I. Bull. Chem. Soc. Japan, 25, 135 (1952).

CHAPTER 11

ADVANCES IN D.C. POLAROGRAPHY 11.1 DEVELOPMENTS IN D.C. POLAROGRAPHY The d.c. polarography is defined to mean current-voltage relationships (voltammetry) at constant potential when a dropping electrode (D.M.E.) is used. This is the classical d.c. polarography, originated by Professor Jaroslav Heyrovsly in about 1922. In usual practice, the voltage of the D.M.E. with respect to a reference electrode, usually calomel, is scanned linearly and the resulting current is recorded as a function of voltage. The condition of constant potential is adequately satisfied if the rate of voltage scan is enough so that the change of voltage during the life of each D.M.E. drop is less than about 10 mV. D.C. polarography is particularly useful for inorganic and for organic chemical analysis of minor and of trace level constituents in aqueous and in non-aqueous solvents. It has also contributed to theoretical electrochemistry. In d.c. polarography with a potentiostat, i.e., at controlled potential there are certain advantages like : iR does not significantly affect the D.M.E. so that the regular polarograms are undistorted and the effective scan rate remains constant, a necessary condition for quantitative time-derivative polarography. Also convenient pH-type reference electrode may be used when E1/2 information is unnecessary. The quasi-reference electrode may be used. Equations have been derived for simple, reversible diffusion-controlled processes which quantitatively compared relative sensitivity and resolution of regular and of first, second, and third derivative d.c. polarograms. On this basis, the resolution of d.c. polarography can be compared with that of other methods. Conventional d.c. regular and derivative polarograms can be rapidly obtained if a D.M.E. having a customary flow rate but a drop time of 0.5 sec or less (i.e., diffusion controlled) is used with fast circuits and scan rates. The specific resistance is low enough so that the tip need not be close to the D.M.E. Relationships between concentration and diffusion-current and concentrations and first derivative peak height are linear for cell concentrations from 5 × 10–6 to 1 × 10–4. By polarography in an organic solvents, there is also the possibility of determining species that are unstable in water.

11.1.1 Principle of Potentiostatic (Controlled-Potential) Electrolysis As late as in 1942, Kickling [8] developed a method for automatic electronic control of the potential of a working electrode with respect to that of a reference electorde, i.e., a potentiostal and many applications of this principle have since been described. In controlled-potential d.c. polarography, the command voltage is the sum of the initial and

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the scan voltages. In the potentiostat the command voltage is compared with the actual value of the voltage of the D.M.E. with respect to that of the reference electrode, and the difference between these, the error voltage, in the input signal at the summing point of the potentiostat. The output voltage of the potentiostat is applied between the counter electrode and ground. The D.M.E. is held at virtual ground potential with a current amplifier. In the polarography, the location of the potential difference that corresponds to the command voltage is thus the potential of the equipotential surface that passes through the tip of the reference electrode with respect to the potenital of the D.M.E. For being stable, the potentiostat should control the voltage between the working and reference electrode to within a few millivolts of the command voltage.

11.2 TIME-DERIVATIVE D.C. POLAROGRAPHY

2

dt

VALUE d 2T

PER CENT MAXIMUM

dT di VALUE

PER CENT MAXIMUM VALUE T

PER CENT MAXIMUM

The quantitative time-derivative d.c. polarography requires constant and reproducible scan rates, computation of average cell current, and computation and recording of time derivatives of average value of cell current. These conditions are easily obtained with simple electronic circuits. In nth derivative d.c. polarography, the object is to record a signal that is directly proportional to d n i (dE)n as a function of E (voltage). The nth derivative is obtained by n first derivative circuits in cascade. Thus only the instrumentation used to obtain the necessary conditions for first derivative polarography, needs attention. For higher derivatives, E, volts ΔE = 1 1 8 m V ½ E, volts ΔE = 77mV ½ degradation of signal to noise ratio has been circumvented by use of fast scan rates. This will be discussed later. The output of the polarograph is calibrated, for example, for first and for E, volts ΔE = 72mV second derivative d.c. ½ polarography respecFig. 11.1 : Relative resolution of regular, first derivative and tively, in µA min–1 and second derivative polarograms in µA min–27. Since the magnitude throughout an nth derivative wave is directly proportional to the nth power of dE/dt, it is essential that dE/dt be of a known, constant value. A wide range of highly reproducible values of dE/dt having very low noise levels are obtained by means of an electronic scan generating

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circuit that consists of an operational amplifier current-integrating system fed by a constant current of appropriate sign and magnitude [10]. In these circuits, an unstabilized operational amplifier is used. The constant current is derived from a voltage-reference zener diode. The basis of the analog method of computing the time derivative of a voltage signal is the fundamental property of a capacitor and that Q = CE (1), where Q is the charge, stared in a capacitor of capacities C and E is the voltage developed across the capacitor. Real capacitors are readily available whose properties, at frequencies of interest in derivative polarography, very closely appoximate those if an ideal capacitor. Consequently, if the signal voltage E, is impressed across a capacitor C, the current passing through the capacitor iC, is directly proportional to dE/dt as shown in the equation : dQ/dt = CdE/dt

...(1)

Simple (Ideal) Operational Amplifier Derivative Computer : Some improvement over the performance attainable above with only a passive RC network is possible by use of the above given In+++ amplifier. The common connection of Cd++ C and R is connected to the summing 0.1 μa/min. point of the amplifier and the free terminal of R is connected to the 0.5 μ a output terminal of the amplifier. The input signal E, is connected from ground to the free terminal C and the CONDITIONS : output, E0, is the voltage from ground O.R.N.L. model Q-1988-ES polarography to the output terminal of the amplifier. 1 × 10–4M IN++ and 2 × 10–4M Cd++ in 0.1 M KCI The output voltage of the amplifier, I.P. is –0.45 volts vs S.C.E. E0 is : 5 microamp. current range d E0 = – RC E dt

...(2)

Sargent 2 to 5 sec. Capillary Scan rate is 0.02 v/min., 0.04 v./ inch Regular : undamped Derivative : quad. parallel-T, RC current ave. filter 1-3-61

which shows that E 0 is the true derivative of the input signal, E. The advantages of the simple, ideal, 0.50 0.55 0.60 0.65 0.70 operational amplifier derivative E0 volts vs S.C.E. computer are as follows : There is no Fig. 11.2 : Qualitative comparison of resolution time lag because all of the input signal by regular and derivative polarography. is impressed across C. The value of RC may be high in order to obtain high sensitivity without the introduction of time log. Another advantage is that useful load current may be drawn from the amplifier without affecting the accuracy of the derivative computation. Additional Requirements for Optimum Resolution and Sensitivity : For optimum resolution, the recorded derivative wave must be of theoretical form, without distortion

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due to iR losses or to time lag CONDITIONS : broadening. The recorded wave O.R.N.L. model Q-1988-ES polarography forms must be dictated by the Quadruple parallel-T, RC l ave. filter reduction processes at D.M.E., Sargent 2 to 5 sec. capillary n = 90.5/ W½(mV) and be undistorted by circuitry Initial potential is –0.45 volts vs. S.C.E. (25°C) performance. This has been Current range is 2 microamperes n = 90.5/30.6 = 2.96 achieved at scan rates up to 300 Scan rate is 0.01 volts per min. 1×10–4M IN++ in 0.1 M KCI mV min–17, but even above this, W½ 30 Jan. 1961 dtave where some time lag distortion dt occurs, derivative polarograms are still highly reproducible H because the circuits are linear H 0.04 μ a/min. systems. The magnitudes of 2 these effects and the scan rate below which these magnitudes E½ IN+++ are negligible are readily predicted from the known time lags of the systems. For a –0.49 –0.53 –0.59 –0.45 –0.63 reversible wave, a sensitive E0 volts vs S.C.E. criterion is whether the recorded voltage at which tha peak occurs Fig. 11.3 : Determination of n by measurement of is independent of the direction derivative polarogram. of scan. Short Drop Time of D.M.E’s: It has been pointed out that a short drop time D.M.E. is needed in order to attain optimum resolution (at fast scan rates) and optimum sensitivity. It is also indicated that short drop time are less affected by vibration and are less noisy in aqueous and in organic solvents than the usual 2 to 5 sec D.M.E.’s. Signal to Noise Ratio : In practice, the sensitivity is limited to the signal to noise ratio (SN), of the cell current rather than by the magnitude of faradaic current, i.e., or the presence of a residual current, ires, whose magnitude [7] at low concentrations of depolarizer is larger than iF[7] i.e., rather than the ratio of iF to ires. This has been explained by a number of equations [9]. In case of nth derivative polarograph, the term in equations are each replaced by their nth derivative. The primary factor that limits the sensitivity of polarography is the noise (imperfect reproducibility) of the current at a D.M.E. The S/N and general usefulness of the D.M.E. is equal to or better than that of other kinds of polarized electrodes. In particular, the best S/N was obtained with small orifice and with smaller vertical orifice D.M.E.’s. It is anticipated that the S/N of derivative d.c. polarography will be highest with short drop time D.M.E.’s of these designs at fast scan rates with the new fast d.c. polarograph. The reproducibility of first derivative peak heights depends upon the reproducibility of the scan rate and also upon the reproducibility of the regular average current wave since the latter is the input signal to the derivative computer. In order to get best

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reproducibility results, the solution should be well sparged. The reproducibility of regular, wave heights and of first derivative peak heights is essentially the same.

11.2.1 Direct Proportionality of First Derivative Peak Heights to id Theoretically, for a simple reversible diffusion controlled process, with constant D.M.E. characteristics, temperature and scan rate, the first derivative peak heights should be directly proportional to id. This relationship has been verified for Tl+, Cd++, Pb++, etc. The results show that the heights of the derivative peaks have the same relationship to concentration as do the corresponding regular wave heights.

11.2.2 Relative Signal Levels in Regular and in First, Second, and Third Derivative D.C. Polarography The relative attainable sensitivities of regular and of first, second and third derivative d.c. polarography depends on the attainable S/N in each case. The degree of noise depends upon the specific hardware that is used and is best evaluated experimentally. It is possible to calculate the relative signal levels from the equations for a simple, reversible, diffusion controlled processes. This calculation serves as a guide to the relative sensitively limits under ideal conditions. New fast d.c. polarographs have been designed to record regular and first, second and third derivative d.c. polarograms. The ratio of the heights in µA min–1 of the peak of the first derivative d.c. polarogram to the diffusion current µA of the corresponding regular polarogram is : nF dE 4 RT dt

...(3)

where dE/dt is the scan rate in V min–1 and the other symbols have the same significance. The ratio of the height in µA min–2 of either peak of a second derivative d.c. polarogram to the diffusion current in µA of the corresponding regular polarogram is : 2

n 2 ⎛ F ⎞ ⎛ dE ⎞ ⎜ ⎟ ⎜ ⎟ 1 0.3 9 ⎝ RT ⎠ ⎝ dt ⎠

2

...(4)

The ratio of the height in µA min–3 of the middle peak of a third derivative d.c. polarogram to diffusion current in µA of the corresponding regular polarogram is : 3

n 3 ⎛ F ⎞ ⎛ dE ⎞ ⎜ ⎟ ⎜ ⎟ 8 ⎝ RT ⎠ ⎝ dt ⎠

3

...(5)

It is of interest to compare calculations made from the above equations [14]. The importance of attaining conditions allowing the use of fast scan rates is obvious from the above equation.

11.2.3 Criterion for Relative Resolving Power of Various Methods of Polarography The question arises of whether the concentration of all these species can be determined polarographically or the concentration of one of the species without error due to the

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reduction or otherwise. This may happen whenever several species reduce at successive voltage within the voltage range covered. It is well known that the E1/2’s of the waves can sometimes be shifted relative to each other by controlling pH or by complex formation of by other changes in the medium and that interference may be prevented by removing a species by solvent extraction. This may sometime solve a particular overlap problem. If there is no interaction between the primary species or between these and the products of electrolysis, the polarogram of the mixture is equal to the sum of a polarograms of the supporting electrotype and polarograms of each species that would be obtained if each were present separately in the supporting electrolyte : icell (E) = ires (E) + iF1 (E) + iF (E) + i F1 2

...(6)

The net polarogram =

polarogram of supporting electrolyte + polarogram of species 1 + polarogram of species 2 + ...

...(6)

Conditions under which regular and derivative d.c. polarograms of theoretical form can be recorded with polarographs. See ref. [14] for further details.

11.2.4 Geometrical Overlapping for Successive Waves In the case of first derivative d.c. polarography a first derivative wave has a maximum value at E1/2. In case where the two first derivative waves have a close E1/2’s, the position of one or both of the maximum values in the net first derivative programs are not necessarily at the corresponding E1/2 values. In severe overlapping, the net programme may have only one broad peak. This is a gemoetrical effect. Taking for example if the constituent derivative polarogram due to species 2 is increasing rapidly at the E1/2 ‘or species 1, the net derivative polarogram can continue to increase beyond the E1/2 for special. This means that measurements of geometrical overlapped derivative polarograms should be made at chosen constant voltages (usually at the E1/2) and not summit voltages of the net wave. This consequence of geometry is not unique to polarography. This is even important in absorption spectroscopy [13] and in gas chromatography [13].

RELATIVE RESOLUTION OF REGULAR AND OF FIRST, SECOND AND THIRD DERIVATIVE D.C. POLAROGRAPHY The equations for a simple, reversible, diffusion controlled process can be referred to [21]. The Fig. 11.4 are plotted for the following conditions : id is equal for two successive polarograms and n is 2 for both polarograms. In each case the percentage of the maximum value is plotted as a function E. The separation of E1/2’s that result in the second polarogram contributing 1% to the height of the first is shows in each case. This separation is explained as follows : regular polarogram Δ E/ 2 = 118 mV; first derivative polarogram, Δ E1/2 = 77 mV; second derivative polarogram, Δ E1/2 = 72 mV. The resolution of first derivative d.c. polarography is considerably better than that of regular d.c. polarography. The resolution of second derivative d.c. polarography is somewhat better than that of first derivative d.c. polarography. The Fig. 11.5 shows the improved resolution of the first derivative d.c. polarography over that of regular d.c. polarography.

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CONSTITUENT DERIVATIVE POLAROGRAM :

diave dt

1. 0.1 M KCl 2. 1×10–4M IN+++ in 0.1 M KCl 3. 2×10–4M Cd++ in 0.1 M KCl

4. NET DERIVATIVE POLAROGRAM : 1×10–4M In+++ and 2×1×10–4M Cd ++ in 0.1 0.1 M KCl

2

3

5. SUM OF CONSTITUENT DERIVATIVE POLAROGRAMS (Indicated by plotted points) CONDITIONS : O.R.N.L. model Q-1988-ES polarograph Quadruple parallel-T, RC current ave. filter Sargent 2 to 5 second capillary Initial potential –0.45 volts vs S.C.E Scan rate –0.02 volts per minute Supporting electrolyte is 0.1 M KCI Current range is 5 microamperes full scale

0.1 μ a/min.

1 1 –0.45 –0.49

16 Feb. 1961 E½

In +++

E½ C d ++ –0.65 E0 volts vs S.C.E.

Fig. 11.4 : Comparison of net derivative polarogram with sum of constitutent derivative polarograms.

The polarograms of In3+ and Cd2+ are shown in the Fig. 11.6. For more details relevant literature may be consulted. Relative resolution of sinusoidal a.c., square wave, and first derivative d.c. polarography. The evaluation of n by measurement of a first derivative d.c. polarogram is illustrated in Fig. 11.7. Breyer and Bauer [11] reported that the width of the sinusoidal a.c. polarographic wave at half-height in millivolts is given by 9 0.5 ...(7) n This is for simple diffusion controlled process that are considered reversible at the sinusoidal a.c. voltage frequency that is used. Barker [2] reported for a simple reversible wave, that at 25°C, the width of the square wave polarogram at half its maximum height in millivolts is 9 0.4 ...(8) n Also, for a peak to peak amplitude of the square wave voltage that is much less than RT/nF (condition being optimum). There is, however, no difference in the relative resolving power of these methods of polarography in case the working conditions are optimum for sinusoidal a.c., square wave, and first derivative d.c. polarography.

11.2.5 Mathematical Resolution of Overlapped First Derivative d.c. Polarograms In practice, there will be many cases where successive constituent first derivative d.c. polarograms overlap to the extent that the peaks in the net polarogram will be increased

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by the overlap even though the resolution of first derivative polarography exceeds that of regular polarography. If the recorded polarograms are of theoretical form, the amount of overlap is not being increased by the polarographic circuitry and depends only upon the relative n, F E1/2, and concentration values. The following conditions are required in order to use mathematical analysis to resolve overlapped first derivative d.c. polarograms. 1. The D.M.E. characteristics must be constant for the duration of the measurement. 2. The E1/2’s must be reproducible and independent of concentration. 3. The magnitude of a derivative polarogram at any fixed potential must be directly proportion to concentration over the concentration range involved as predicted by the equation [4]. The net derivative polarograms must be equal to the sum of the constituent derivative polarograms as predicted in the equation under reference [14]. Four experimental polarogram showing the additivity of polarogram of individual processes are reproduced as shown in Fig. 11.9. Polarogram No. 1, is a first derivative d.c. polarogram of the supporting electrolyte polarogram No. 2 is a first derivative d.c. polarogram of 1 × 10–4 M ln3+ in that supporting electrolyte. Polarogram No. 3 is a first derivative d.c. polarogram of 2 × 10–4 MCd2+ in that supporting electrolyte. Polarogram No. 4 is a first derivative d.c. polarogram of a solution containing both 1 × 10–4 M ln3+ and 2 × 10–4 MCd2+

...(9)

in that supporting electrolyte, the plotted points have been obtained by graphically summing polarograms No. 1, 2 and 3. It is seen that there is a good agreement between the experimental net polarogram, No. 4, and the actual sum of the constituent polarograms, the plotted points. It is to be noted that in the above figure the first peak of the net first derivative d.c. polarogram does not occur at the E1/2 for the first species. This is a geometrical effect and not a shift in E1/2 in solution containing both species. This illustrates the importance of measuring all of a series of net polarogram at the two chosen fixed potentials rather than at sumit potentials in the net polarograms.

11.2.6 Mathematical Resolution of Regular Polarography Compared to First Derivative d.c. Polarography The effects of n, Δ E1/2 and relative concentrations on the degree of resolution of two polarographic waves have been discussed by Müller [19]. Also it was pointed out that iR losses would degrade the resolution. He also concluded that, in the absence of iR distortion, the separation of the E1/2’s would have to be at least 180/n mV in order to measure the two wave heights independently. Even when two waves are so severely overlapped that the net polarogram looks like a single wave, the mathematical method can be applied to calculate the height of each of the two equivalent waves making up the net wave. The accuracy with which two overlapped regular polarograms can be resolved mathematically depends on tha precision with which the series of measurements can be made at the fixed potential E.

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11.2.7 D.C. Polarography in Non-aqueous Solvents and Particularly in Solvent Extracts Polarographic investigations and analyses have been made in great number of organic solvents, solvent mixtures and water-organic solvent mixtures. In the case of non-aqueous organic solvents one of the difficulties is that the specific resistance of such solutions, even after supporting electrolyte is added, can be high enough to result in large iR voltage in the solution. These can be prevented from affecting the forms of the recorded polarograms if a controlled-potential polarograph is used properly. The iRbulk losses are not seen by the potentiostat input of the tip of the reference electrode is located outside the current paths in the solution, and in cases where iR inner is of significant magnitude. In this case only a small portion of these losses is seen by the potentiostat input of the tip of the reference electrode is within about 0.1 of the radius of the D.M.E. drop from the surface of the D.M.E. drop. Controlled-potential d.c. polarography should, therefore, have special advantages for polarographic work in non-aqueous solvents. Some species are insoluble in water but undergo useful electrochemical reactions in non-aqueous solvents or in solvent mixtures. In some cases, certain ions cannot be determined in water polarographically because of specific solvent effects or interference from hydrogen wave or by catalytic hydrogen waves. The combination of polarography and a liquid chromatographic column by Kemula [9] is promising for gas-liquid chromatography for the analysis of complex mixtures of organic compounds. This is because it is difficult and in some cases impossible to find a stationary phase on which all the components of a mixture can be separated. Electrochemical Requirements for Polarography in Non-aqueous Solvents, Specially in Solvent-extracts : In the case of polarography, it is advantageous to have the presence of an excess of ionized supporting electrolyte [6]. The high dielectric constant, although favours the formation of ions and tends to increase the solubility of a supporting electrolyte. This is not a sufficient condition to ensure that an electrochemical reaction can be carried out. This fact is well known in the electrodeposition of metals from organic solutions [1]. Controlled-potential d.c. polarography of metal complexes in solvent extracts. The feasibility and usefulness of such complexed metals in solvent extracts has been investigated polarographically [4]. The method offers certain advantages over polarography in aqueous media. 1. The substance to be determined can be concentrated several told during the extraction step, thus increasing the sensitivity of the method and matrix elements that interfere are removed. 2. A separate stripping step is not required. Also, the possibility exists of performing polarographic analysis in an organic solvent with species that are not stable in aqueous solution.

11.3 THEORY, PRINCIPLES AND APPLICATIONS (a) Cyclic and Pulse Techniques : A belief review of a number of techniques which are regarded as offshoots of stationary-electrode voltammetry are being described in this section.

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In oscillographic or cathode-ray polarography [7], g a rapid linear voltage sweep is applied to a dropping electrode near the end of the drop life. The resulting current potential curve is displayed on the screen of an oscilloscope. Here the voltage applied to the electrodes is amplified and connected to the vertical deflecting plates. E However, in this application the oscilloscope merely replaces the galvanometer t t1 tk and bring no fundamental change in the polarographic Fig. 11.5 : Comparison of the time dependence of the instrumentation and because change in surface area of the drop q (upper curve) and of of this the term oscillographic the voltage sweep E (lower curve) applied to the electrode; polarography usually does not t k quiet period, t 1 drop time include the study of current time curves. A rather high sensitivity is attained as a cause of the large rate of change of potential that is needed to minimize variations of drop arcs and deviations from linear diffusion equations, but this, in turn, gives rise to rather large charging currents to the equation (11.8). ie /ip = 0.023v1/2 n 3/2 C0

...(1)

where i.e., is the charging current, by assuming typical values for x and D0. With v = 0.003 v/sec, n = 1, and C0 = 0.01 mM. The charging current is nearly 15% of the peak current and it would be even larger for an irreversible process.

11.3.1 Single Sweep Methods The shape of a current voltage curve depends on the nature of the depolarizing voltage. Starting with a simple linear voltage sweep, applied to the electrode (late in the life of the drop) when the growthrate of the drop-surface varies only slightly with time (see Fig. 11.5). The screen with a long afterglow is advantageous in this method. (a) Charging Current : In case only when pure supporting electrolyte is present in the experimental solution, the curve obtained shows the charging current ending in an electrolytic current due to reduction of the cation of the supporting electrolyte at a negative potentials, see Fig. 11.6. The formula

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Fig. 11.6 : Current-potential curves for the supporting electrolyte 1 N KOH : left : single sweep, right : multi-sweep

dQ ...(2) dt is generally used for the charging current, where Q is the total charge on the electrode at time t (Q can be expressed as product of the electrode area q and of the specific charge σ : (Q = qσ ). ic =

Hence

ic =

dQ dσ dq =q +σ dt dt dt

...(3)

arranging the equation takes the form : ic = q

d σ dE dq +σ dE dt dt

...(4)

where E denotes the electrode potential. The potential, in classical polarography may be regarded as constant during the life of a single drop. The first term is then zero and the following equation for the charging current is thus obtained : ic = EC '

dq 2 = 0.85EC ' m2/2 t –1/3 dt 3

...(5)

The surface of the electrode, in oscillographic methods may be considered constant during a single sweep. The second term in equation 3 may then be neglected, and one can obtain,

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ic = q

dσ dE dE dt

...(6)

for the charging current. The expression d σ /dE = d (CE)/dE = Cd, specific capacity. It is the capacity of 1 cm2 of the electrode surface at a given potential. It is called differential capacity so as to distinguish it with the integral capacity C, which aslo appears in polarographic charging current. The third coefficient in equation (6) is a constant and indicates the rate of change of the applied voltage v. Finally the equation for the charging current reads as : ic = Cdqv

...(7)

In principle, it then follows that the charging current shows the dependence of differential capacity on potential. The value of the differential capacity is an important parameter +i characterizing the electrode double-layer specially is cases when surface-active substances are adsorbed. The i=0 enables us to follow rapidly E the adsorption of surfaceactive substances at the electrode over a wide range of potentials. The adsorption of the substance usually occurs within a definite –i potential region. This changes the differential Fig. 11.7 : Charging current for 0.5 M Na2SO4 in the capacity of the electrode and presence of octyle alcohol. Multi-sweep method. The current consequently the charging peaks indicate adsorption and desorption of the surface film. current. A Sharp maximum Fig. 11.7 is characterize due to the instantaneous increase in differential capacity accompanying the rearrangemet of electrode double layer is the potential at which the substance adsorbs or desorbs. The foregoing equation (6) also holds for this peak for the charging current. The charging current rises as a linear function of the increasing slope v of the voltage sweep. Many substances specially, organic exhibit capacity phenomena. Hence oscillographic polarography opens additional possibilities for analysis as compared to classical polarography.

11.3.2 Electrolytic Current Reversible Electrode Processes : The presence of a depolarizer in the solution causes an increase in the electrolytic current with rising potential. The depolarizer is gradually

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exhausted by electrolyte process at the electrode surface. Fresh depolarizer is supplied by diffusion and the diffusion layer extends into the solution. The rate of the electrode process increases with rising electrode potential, but the transport of depolarizer is simultaneously retarded. Consequently, the current increases up to a certain maximum value from which it then decreases. Randles [8] and Sevik [9] independently solved problem for a reversible electrode process. The equation of the current is governed by linear diffusion of the substance towards an electrode, the potential of which is changing. The current potential curve can be expressed by a tabulated function passing through a maximum. This maximum or peak current is an important value in oscillographic polarography. Its significance corresponds to that of both the wave-height and the halfwave potential for classical polarographic current-voltage curve. The maximum current is given by the formula : imax = k1 qn3/2 cD1/2 v1/2 (A)

...(8)

where k1 is a combined constant depending on the electrode process; q, the electrode area (in cm2), which is considere constant during the voltage sweep, n the number of electrodes, c the depolarizer concentration in moles/cm3, D its diffusion coefficient (in cm2. sec–1) and v the rate of change of electrode potential (dE/dt, in V sec). According to previous workers, the ratio of the maximum current to the current on the falling part of the curves is given by imax = k 1n 2 i

...(9)

in reversible, and in irreversible electrode process by

( )

12 imax = k' α na ...(10) i The constants k and k′ depend solely on potential. From the ratio imax /i an empirical method for determining the number of electron for a reversible electrode process could be used. The condition being that the dictation of electrolysis does not exceed several seconds and the difference between linear and spherical diffusion is not significant. Reversible electrode processes are characterized by steep curve and sharp peaks (Fig. 11.8) right curve. The potential corresponding to these peaks is independent of concentration and by 29/n mV (at 25°C) more negative then E/2 is reductions of more positive in oxidations. Irreversible Electrode Processes : Delahay [3] was the pioneer to derive the corresponding mathematical function. According to which the expression for the peak height imax is stated as follows :

imax = k2qn (α n a)1/2 cD1/2 v1/2 (A)

...(11)

This formula is similar in form to the above equation (7) except that the term n (α n)½ replaces n 3/2. Here, α is the transfer coefficient (0 < α <1) and n a the number of electrons exchanged in the slowest step of the electrode process (0 < n a ≤ n). The value of the

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constant k2 is 2.99 at 105 at 25ºC. The product α n a decides the shape of the irreversible curve Fig. 11.6 The heterogeneous rate constant ke0 for the electrode process is responsible for the position of the curve on the potential axis. Since α is less than 1 and n a is often smaller than n, the peak for an irreversible process is lower than that for a reversible process. It loses sweep) : left its acute form Fig. 11.8 Fig. 11.8 : Oscillographic curve (linear 2voltage irreversible three-electron reduction (CrO 2– in 1 N KOH); right (left curve) but its reversible three electron reduction (Bi3+ in 1 N HCl) potential does not change with concentration. The whole curve is drawn out and is shifted to higher potentials i.e., to more negative ones in reduction and in oxidation to more positive ones with decreasing rate constant ke0 The character of the electrode process can be readily assessed from the appearance of the oscillographic curve. According to the character of the electrode process Matsuda and Ayabe [6] provide a general theoretical analysis of the oscillographic current-potential curves for simple electrode processes with a single potential-determining step under the conditions of linear diffusion. These authors distinguished three cases, according to the character of the electrode process and also mathematical equations were presented : 1. Reversible processes with a heterogeneous rate constant ke0 lager than 0.3

( nv ) cm.

sec–1 at 25°C;

2. a quasi-reversible process with ke0 ranging from 0.3 sec–1; and 3. Irreversible process for which ke0 is less than 2.10–5

( nv )

( nv )

to 2.10–5

( nv )

cm.

cm. sec–1.

It therefore follows from these equations that in a quasi-reversible processes the peak increases non-linearly with v1/2 in contrast to the other two types where this dependence is linear. The classification given shows that the term “reversibility” depends on the experimental condition. On increasing v, the number of processes that can be described as reversible decreases. The same effect is obtained by either decreasing the drop time or employing a streaming mercury electrode instead of the dropping mercury electrode in classical polarography.

Advances in D.C. Polarography

An oscillographic curve appears with two peaks on the screen, if the depolarizer is reduced in a twostep electrode process (Fig. 11.9). It was demonstrated by previous workers that both peaks behave as if they belonged to two independent processes, regardless of the rates of electrode processes for the two steps. The two peaks, when sufficiently apart, no mutual interactive of the peaks occur and they are directly proportional to the concentration and to the squareroot of the rate of variation of potential v.

149

a E

b

c

11.3.3 Kinetic Currents Oscillographic curves have a characteristic shape. These curves have the shape of conventional current voltage curve Fig. 11.10. The height of the curve is independent of v. The same relation holds as for polarographic kinetic currents. The oscillographic curve for the Brdicka [1] protein reaction show a striking similarity to the classical polarographic curve. Obviously the current is governed by the dependence of the catalytic reaction on potential.

d

e

f

11.3.4 Types and Forms of Voltage Sweeps Fig. 11.9 : Various types of

By comparing the potential of the peaks for rising voltage sweeps applied to the and falling sweeps, conclusions regarding the electrodes in oscillographic reversibility of the process can be drawn. Anodic polarography currents for the oxidation of substances in solution and for the dissolution of amalgams are more conveniently studied with polarization from negative to positive potentials. (Fig. 11.9 (b). The quiescent period of sweep is utilized for reducing the depolarizer from the solution at constant negative voltage, particularly for preparing the amalgam by depositing the metal on mercury. The cathodic and anodic maxima for perfectly reversible processes are 58/n mV apart. In order to study reversibility, an equilateral triangular voltage sweep is particularly advantageous (Fig. 11.9 (c)). The depolarizer, which is reduced in the first phase is immediately reoxidized in the next phase and vice-versa. The resultings current voltage curve has two branches : (i) cathodic and a reverse (ii) anodic one (Fig. 11.10). The reversibility of the peaks is indicated by the relative positions of the reduction and oxidation peaks.

11.4 MULTI-SWEEP METHODS An oscilloscope with a normal cathode ray like without after glow is used for the multisweep method. A stable curve appearing on the screen of the oscilloscope can be easily

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measured by alternating sawtooth. Voltage sweep is applied to the electrode either late in the life of the drop or during the whole period of its growth. This system resembles the single-sweep method. The triangular voltage sweeps can also be applied under the same conditions. The method can be utilized in analytical chemistry. In cases, where the alternating voltage sweep is applied to the electrodes during the growth of the drop, the current increases as a linear function of the drop surface-area and a series of increasing curves can be observed on the screen. These curves as already described are chiefly used in qualitative investigations due to the Fig. 11.10 : Reduction of Tl+ in difficulty in evaluation. 1 M Na2SO4 by an equilateralWith triangular voltage sweeps the oxidation and triangular voltage sweep reduction periods are of equal duration and hence both branches of the current-voltage curve are equally developed. As reported by previous authors in the course of several initial cycles of the triangular voltage sweep the cathodic current decreases somewhat and the anodic current increases at the constant electrode surface until an equilibrium between the cyclic electrode processes and diffusion is attained. Delahay [39] introduced a relay phase after each sweep of the saw-tooth voltage. During this period the condition in the electrode interface are restored.

11.5 APPARATUS FOR APPLIED VOLTAGE OSCILLOGRAPHIC POLAROGRAPHY Matheson and Nichols [26] developed the first oscillographic assembly for studying the polarization of the dropping mercury electrode with voltage sweeps. They tested the polarization by sine-wave and sawtooth voltage sweeps by single sweeps on rapidly falling drops in the analysis of solutions containing several cations. The large charging current presented a disturbing factor in practical applications. In addition to distortion owing to the potential drop (iR), the characteristic peaks gradually decrease ans become rounded. This is because an increasing the resistance, the experimental conditions approach those for applied current oscillography. An oscillographic apparatus for studying polarization curves with a voltage step has been constructed by Vogel [31] as already indicated. The multisweep instruments with saw-tooth impulses are used more extensively. By decreasing the frequency sufficiently this method passes into single-sweep oscillography. This type of apparatus was described by Delahay [3]. Valenta [10] constructed a universal oscillograph giving voltage sweeps of all the types. This was used for studying electrode processes.

11.6 CONTROLLED CURRENT OSCILLOGRAPHIC POLAROGRAPHY The basic circuit is the same in the method for electrolysis with single current impulse and alternating current oscillography. A high voltage, i.e., several hundred volts is

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applied to the polarographic cell through a large resistance R from 10 to 100 megohms under these conditions the resistance in the cell and the electromotive force of polarization are negligible in comparison with other quantities in the circuit. The curent intensity given by the voltage source and by the resistance does not depend on the process occurring at the electrodes. These processes manifest themselves by variations in the electrode potentials. In polarography where the potential of one of the electrode remains constant, only the polarizable electrode changes its potential. The potential difference between the electrodes resulting from the passage of current is amplified and applied to the horizontal plates of the oscilloscope. The time base is connected to the other pair of deflecting plates. The resulting potential time curve on the screen shows the variation in potential of the polarizable B electrode for a given current as a function of time. Due to this dependence, the method is termed chronopotentiometry. The method is fully described in previous E O chapter. Alternating Current Rs A Oscillographic Polarography : The method was first of all introduced by Herovsky as early Z as 1941 [25]. The technique is analogous to polarization with Fig. 11.11 : Circuit for tracing potential-time curves alternating voltage. The time during polarization by alternating current : A–source dependence of the alternating of a.c. voltage; B–source of d.c. voltage; R –resistance; s current used may very triangular E–electrolysis cell; O–oscillograph; Z–time base and square wave alternating currents have been tested. (a) Potential-Time Curves : The current for following fundamental E – t curves is shown in the Fig. 11.11. In order to prevent the consumption of current only during alternate dissolution and deposition of mercury at the polarizable electrode, a direct current is superimposed on the alternating current. This allows polarization of the electrode up to the potential for deposition of cations of the supporting electrolyte. In case the direct and alternating voltages are of the same order (102V) and similarly the resistances in the circuit (105 to 106 Ω ), the conditions for the controlled current are maintained. With regard to the direction of the current two branches on the curve can be distinguished : the ascending cathodic branch and the descending anodic branch. In one half-period the electrode functions as a cathode and in the next half period as an anodie. The time-base Z is synchronized with the polarizing current so that s stationary fig. is obtained on the screen (Fig. 11.12).

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(b) Charging Currents : The supporting electrolyte is not electrolysed at the electrode and no depolarizer is present in the solution, the resulting curve depicts the charging current. The condition being the amplitude of the current is quite small. In a first approximation it may be regarded that the electrode capacity during a single cycle as constant and independent of potential : consequently it may be written for the charging current of the electrode as capacitor : ic =

dQ ⎛ dE ⎞ = C⎜ ⎝ dt ⎟⎠ dt

11.7 PULSE POLAROGRAPHY

...(12)

Fig. 11.12 : Potential time curve obtained by polarizing the electrode with a sinusoidal a.c. current Zn2+ in 1 M KOH

In pulse polarography [1,2] a single square-wave voltage impulse having a duration of about 40 m sec is applied to each drop at a predetermined instant after its birth, and the amplitude of the successive pulse are increased linearly with time. The charging current decays rapidly after the initial change of voltage. Since the duration of the pulse is much longer than in square wave polarography a much longer time can be allowed for the charging current to decay. The resistance of the cell is much less important, so that considerably more dilute supporting electrolytes can be employed. The relatively slowly decarying faradaic current that continues to flow during the second 20 m sec of the pulse is recorded against the pulse amplitude. The resulting curve has the same shape as an ordinary polarographic wave, and the limit of detection is improved to a level that is probably of the order of 10–5 mM. Noteworthy fact is that the limit of detection must be very nearly the same for irreversible processes as for reversible ones. Derivative pulse polarography may be called as a second kind of pulse polarography [32]. It yields curve which are essentially the derivatives of those obtained by the technique already described. A single square wave voltage pulse having a duration of about 40 m sec is again applied to each successive drop at a predetermined instant after the fall of its predecessor, but the pulses have a constant amplitude of about 50 mv and are superimposed on a relatively slow linear n potential sweep. During the first half of the pulse the charging current decays. During the second half the increase of current is recorded. The resulting increase of faradaic current produced by a fixed change of potential is plotted against the potential. Thus a peak is obtained at the inflection point of the dic or pulse polarogram. The height of the peak is proportional to the slope di/dE of the polarogram which is described by the eqn. [13]. Err/4 – Erf/4 = 3.76/n millivolts

...(13)

This is smaller for irreversible waves for which ν = α n a than for reversible ones for which ν = n, and consequently the sensitivity and limit of delection are poorer for

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irreversible waves. For a substance that undergoes a reversible two-electron reduction the limit of detection is of the order of 10–6 mM, roughly an order of magnitude lower than in “ordinary” pulse polarography. On the other hand, increasing-amplitude pulse polarography is better suited to work with irreversible waves because the height of the peak obtained in the derivative technique is affected by any change in the experimental conditions that results in a variation of α n a. The characteristics of all these techniques are briefly summarized for convenient reference in Fig. 11.13.

11.8 STRIPPING ANALYSIS There are two kinds of stripping analysis. Anodic stripping is used to determine metal ions that are reduced to methallic state during the preliminary electrolysis. This is based on anodic currents obtained when the metals are reoxidized. CYCLIC AND PULSE TECHNIQUE

Single-sweep oscillographic polarography Instant of drop fall

Signal applied

E

1

T

0.02 sec

2

0.5–2V

E

Multisweep oscillographic polarography

0.5–2V

Technique

3

5 sec 2 sec

Response obtained

0.001–0.1 sec

3

E

(a)

2 1 E

(b)

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Cyclic triangular-wave oscillographic polarography

Triangular-wave oscillographic polarography

E

0.5 –2V

E

0.001 – 1 sec.

Instant of drop fall

5 sec. T

T

3 E 1

+ne A

3

–ne

Reversible couple B

Irreversible couple

2 Reduction of C 1

E

1

E Cessation of reduction of A

2

Oxidation of B

(c)

E Cessation of catholic process Reoxidation of reduced form

(d)

Cathodic stripping is used to determine halides, thiols etc., which give anodic waves at metallic electrodes. The condition being that the half-reaction yields an insoluble salt that adheres to the electrode surface. A cathodic current is obtained from the reduction of the salt which accumulates there. Cathodic stripping has also been used to evaluate the thickness of tarnish films on such metals as iron, copper, and silver [35]. Not only this but both cathodic and anodic stripping have been used to investigate the adsorption of electroactive substances onto inert electrodes. Actually in conventional voltammetric analysis the measurement of a limiting or peak current which depends on the rate at which the substance being determined

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Alternating-current oscillographic polarography

Technique

Oscillopolarography

0.001 –0.2 sec. 100–1000 microamp

B C

C B

T

T

Signal applied A

D

A

D

F

E B

C

Supporting electrolyte alone

B A F

Response obtained

A

Cathodic Anodic transition transition Reversible couple

Cathodic transition Anodic transition

Supporting electrolyte alone

C E D

T

Reversible couple

E Irreversible couple Cathodic transition

Supporting electrolyte alone

Irreversible couple

dE dT

E Anodic transition

(e)

(f)

reaches the indicator electrode, and that also includes a residual current. As the concentration of this substance decreases, the rate at which it reaches the electrode surface also decreases, but the residual current remains the same. The residual current becomes a larger and larger fraction of the total current measured. The limit of detection is reached when the two become indistinguishable. If the substance being determined is deposited onto the indicator electrode at the plateau of the wave, prolonged electrolysis at such potentials will cause its reduction or oxidation product to accumulate at the electrode surface. As the accumulation proceeds, the supply of deposited material at the electrode surface may become very much larger than that of the substance being determined was initially present. In case the deposited

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Introduction to Polarography and Allied Techniques Alternating-current polarography E

Square-wave polarography

dEd.c. = 0.1 V./min dt

–0.02 sec.

interval of measurement

Instant of drop fall

Delay line ~2 sec. Ea.c. = 20 mV

~30mV. ~0.004 sec. dEd.c. = 0.1 V./min dt

ia.c. (rms)

iγ A B

G i

Cocay of charging current

Ed.c.

r

D C Variation of current during square-wave cycle Square wave polarogram

2.5 sec./drop

Ed.c.

(g)

(h)

Fig. 11.13 : Summary of the signals applied and the responses obtained in a number of cyclic and pulse techniques

substance can be re-oxidized or reduced it will yield a correspondingly larger limiting or peak current. Both the sensitivity and the limit of detection are considerably improved. This is the principle of the techniques called stripping analysis. The application of the analysis has been much extensively used and studied and is mainly devoted to anodic stripping in the determination of metal ions. Stripping electrodes, including hanging mercury drop electrodes, mercury pools, and solid electrodes of various, materials are quite suitable than dropping mercury electrode,

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where stripping analysis takes the form of oscillopolarography. Stripping analysis have been performed in many different ways. It can be discussed in two different ways ; (i) those in which the preliminary deposition is quantitative, and (ii) those in which it is not. The simplest technique is that in which the quantitative deposition is followed by quantitative stripping of the deposited material. Curve a of Fig. (11.14) shows the current-potential curve obtained with a large stirred mecrury pool electrode in a solution containing zinc (II). If the potential of the electrode is maintained at a value on the plateau of the cathodic wave, zine ions will be reduced as rapidly as they reach the electrode surface. Consequently quantitative reduction to zinc amalgam will result on allowing sufficient time. Curve b shows the current potential curve for amalgam electrode thus obtained. 60

Current in milliamperes

0 –60 –120 –180 –240

–0.3

–0.7

–1.1

–1.5

–1.9

Ew.e., volts vs. S.C.E.

Fig. 11.14 : Current-potential curves obtained with a large stirred mercury pool electrode for (a) the reduction of 0.6 mM zine (II) from 2 F ammonia– 1 F ammonia citrate, and ( ) the re-oxidation of the amalgam prepared by quantitative deposition of the zine in 50 ml of this solution into 25 ml of murcury at–1.45 V vs SCE

At any potential on the plateau of the anodic wave, zinc atoms are rapidly reoxidized. The quantity of zinc present in the original solution can be deduced from a measurement of the quantity of electricity consumed in the quantitative re-oxidation. Quantitative deposition is feasible even with a small electrode of the volume of the solution is small. Rogers [5] designed a cell in which a small amount like 0.02 ml of solution could be electrolyzed at a platinum working electrode. This is employed for the determination of silver by anodic stripping. Instead of measuring the quantity of electricity

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consumed in the stripping process at a potential on the plateau of the anodic wave, the current-potential curve may be recorded after the deposition is complete (Fig. 11.15). As a matter of fact, it is better and more convenient to use an electrode of small area in a substantial volume of solution. Quantitative deposition requires an inordinate length

5.3 × 10 –5 MCd

0 Cd Pb –1

Current

C urr ent, m icroa m p er es

Direction of polarization

–2

0.02 Micro Amp. 0

–1.0 +1.0

+0.5 E, volt vs. S.C.E

Fig. 11.15 : Current-potential curves for the anodic stripping of 5.6 mg of silver from a platinum electrode into dilute nitric or sulphuric acid and for the supporting electrolyte alone

0

–0.5 0 Volt vs. S.C.E

Fig. 11.16 : Anodic stripping voltammogram obtained with a small mercury pool electrode in a stirred solution containing Cd II

of time, and hence it is preferable to deposit only some reproducible fraction of the starting material. To maintain this the electrode at a potential on the plateau of the cathode wave for a measured length of time while stirring the solution at constant rate. This must be accurately reproduced in successive experiments. Stirring is necessary even with a stationary electrode like hanging mercury drop-stirring should be stopped, solution allowed to become quiet before measurements are taken. The quantity of metal deposited is proportional to the concentration of metal ion in the situation and also to the deposition time if it is not too great. It is not difficult to analyze mixure if the deposition can be carried out at such a potential that the substance being determined is the only one deposited. In case several substances are deposited together, the formation of an alloy or solid solution would

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make it impossible to strip any of them quantitatively without interference from the others. The technique has been applied to the determination of nickel [3] by anodic stripping from a platinum electrode into a thiocyanate solution, and to determine halides [6] by cathodic stripping after anodic deposition on to a silver or stationary mercury electrode. Carbon-paste and waximpregnated graphite electrodes have also been employed [4].

A A nod ic cu rren t

B

C

D

0

–0.4

–0.8

–1.2

Fig. 11.17 : Anodic stripping voltammograms obtained with hanging mercury drop electrodes in 0.1. potassium chloride after deposition for 2 min. : (A) the residual-current curve, (B) with 0.5 mM zinc(II), (C) with 0.5 mM zinc(II) and 0.5 mM nickel(II), (D) with 0.5 mM nickel(II). The scan rate was 6.7 mV/sec. The peak near–0.1 V on curve C is attributed to the oxidation of a nickel-zinc compound

Mercury electrodes have two advantages over solid ones for the determination of metals by anodic stripping. One is that amalgams do not create the problems arising from the variable activity of very thin layers of solid metals. This permits the measurement of the height of an anodic peak intead of the area under it. The other is that, if a mixed amalgam is sufficiently dilute, its different constituents can be reoxidized independently and a separate peak being obtained for each. This permits mixtures to be analyzed much more easily than with solid electrode. See Fig. 11.16. A very important characteristic of stripping procedures is that if all of the couples involved are reversible, the anodic peaks on the stripping curve occur in opposite order from the cathodic peaks on the voltammogram of the solution being analyzed. In the cadmium peak precedes the lead peak, although the cathodic peak of lead ion would precede that of cadmium ion. With such couples stripping analysis provides an easy solution to the wave order problems. If one or both of the couples is irreversible, no such generalization can be made. For example in dilute chloride media that half-peak potential of zinc ion is less negative than that of cobaltous ion, but on the contrary, the cobalt

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couple is so irreversible that cobalt does not give an anodic peak. Finally, the zinc peak occurs first on the anodic voltammogram as well as on the cathodic ones. Curves like those shown in Fig. 11.17 reveal the existence of such compounds in many amalgam containing two deposited metals. Compound formation with mercy may also occur those containing only one. The slowness of these reactions is very helpful in polarographic purposes. This is because if they were fast the half-wave potential of a metal ion would be altered by the presence of another whenever the two deposited metals reacted in the mercury phase. The practical applications of stripping analysis includes the determinations of metals and halides in reagent grade chemicals, of metals and halides in natural water, of lead in urine, and of copper in steels. For further details a review by Shain (6) should be consulted.

References 1. Campbell and U.B. Thomas, Trams Electrochem. Soc., 76, 303 (1939). 2. Erans, U.R. Bannister, L.C., Proc. Royal. Soc. London, A 125 (370) (1929), U.R. Evans and H.A. Hiley, Nature, 139, 283 (1937). 3. Nicholson M.M., J. Am. Chem. Soc., 29.7 (1957). 4. Perone S.P., Anal. Chem. 35, 2091 (1963); E.S. Jacobs, ibid, 35, 2112 (1963). 5. Rogers, L.B. and S.S. Lord, Jr. R.C., O’ Neill, Anal. Chem., 24, 209 (1952). 6. Shain, I. and Perone S.P., Anal. Chem. 33, 325 (1961). 7. Abner Brenner, J. Electrochem. Soc., 1956, 103, 652. 8. Barker, G.C., Anal. Chem. Acta, 1958, 18, 118. 9. Bartlet, J.C., and Smith D.M., Can. J., Chem. 1960, 38, 2057. 10. Belew, W.L., Applications of Controlled Potential...Specific Resistance Solutions, M.S., Thesis, Dept. of Chem. Univ of Tennesse, Dec. 1963. 11. Breyer B. and Bauer, H.H. Alternating Current Polarography and Tensammetry (Interscience New York 1963) p. 50. 12. Brener, Abner, J. Electrochem. Soc. 1956, 103, 652. 13. Charlot, G., Bandoz J. Lambing and B. Tremillan, Electrochemical Reactions (Elsevier, Amsterdam, N.Y. 1962) p. 125. 14. Cooke, W.D., Kelley M.T. and Fischer, D.J., Anal. Chem. 1961, 33, 1209. 15. Hickling A. Electrochem. Acta, 1961, 5 161. 16. Kemula, W. and Kublik, Z., Advances in Analytical Chemistry and Instrumentation, cd. Reilley C.N. (Inc. N.Y.) 1963, Vol. 2, pp. 123-177. 17. Kelley, M.T., and Fischer, D.J. and Jones H.C., Anal. Chem. 1960, 32, 1262. 18. Kortum G. and Bockris O’M. Text Book of Electrochemistry (Elsevier New York, Vol. II) 1951, pp. 364-365. 19. Muller, O.H., J. Chem. Edu. 1941, 18, 320. 20. Vandenbelt, J.M., and Henrich. C., Appl. Spectroscopy 1953, , 171. 21. Hills. G.J., Proceedings of Third International Congress, Southamption, Vol. 1 Macmillan, London. Ref. p. 115. 22. Brdicka R., : Z, Electrochem. 48, 278, 686 (1942). 23. Delahay, P. : J. Phys. and Colloid Chem. 53, 1279 (1949). 24. Delahay, P. : J. Am. Chem. Soc., 75, 1190 (1953). 25. Heyrovsky, J. Chem. Listy 35, 155 (1941).

Advances in D.C. Polarography 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.

Matheson, L.A., Nichols N : Trans. Electrochem., Soc. 73 93 (1938). Matsuda, H., Ayabe Y : Z., Electrochem. 59, 494 (1955). Randles, J.E.B., Trans. Faraday Soc., 44, 344 (1948). Randles, J.E.B., Analyst 72, S. 301 (1947). Valenta, P., Thesis Polarograph Institute Prabha (1955). Vogel J., Proc. 1st Internal Polarograph Congress Vol. III, p. 731 (1952). Barker, G.C., and Gardner A.W., Z. Anal. Chem. 173, 79 (1960). Boduy, V. 1., Kotlova, I.V. and U.S. Lyapikor, Zavodskaya lab, 28, 1042 (1963). Meites Louis Polarographic Technique P. 570. John Wiley & Sons New York. Maricle, D.L. Anal. Chem., 35 683, (1963).

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CHAPTER 12

VOLTAMMETRIC METHODS 12.1 VOLTAMMETRY Four electrochemical techniques-voltammetry (i.e., direct-current, alternating-current, fast-scan, and pulse polarography along with voltammetry at solid electrodes), coultometry (constant current and constant potential), potentiometric titration (includes

Differential Pulse Polarogrphy

Fast Scan Polarogrphy

A.C. Polarography Coulometry—(Constant I) Voltammetry—Solid Electrode D.C. Plarography Amperometry Potentiometry Coulometry—(Constant E) 10 ng/ml

100 ng/ml

1 μ g/ml

10 μ g/ml

100 μ g/ml

Fig. 12.1 : Range of practical usefulness of electroanalytical techniques.

the use of ion-specific electrodes), and amperometic titration are most commonly employed. Each of these electroanalytical techniques and their practical range of usefulness is presented in Fig. 12.1. Coulometric methods are ‘absolute’ and have been shown to be particularly useful since being absolute do not require chemical standards. More recently, fast scan and differential pulse polarography have become extremely useful for the measurements of drugs in biological fluids. However, the major limitation of these two highly sensitive polarographic techniques is the establishment of absolute specificity. To ensure specificity,

Voltammetric Methods

163

TLC separation is often coupled with polarographic measurements. A liquid chromatograph can be coupled directly to an electrochemical detector. A large number of pharmaceutical problems can be sorted out by this approach.

12.1.1 Coulometric Methods Controlled potential coulometry has been applied extensively to precision determinations [2] and to the establishment of n values for electrode reactions. The technique has also used for the elucidation of electrode reactions [1,6]. The technique is very useful when used in conjunction with a thin-layer cell where complete electrolysis is rapid. The technique involves the determination of the quantity of material electrolyzed from the amount of charges passed through an electrochemical cell during electrolysis. Faraday’s law relates the measured charge to the amount of material electrolyzed. N=

Q nF

...(1)

where, N is the number of moles of substance being electrolyzed, Q is the total charge passed (coulombs), n is the number of electrons transferred per molecule, and F is the Faraday’s constant. In controlled-potential coulometry the potential of a working electrode is applied at a value such that complete electrolysis of the desired species occur. The total charge passed during the exhaustive electrolysis is obtained by integrating (electronically) the current. The completion of electrolysis is indicated when the current becomes indistinguishable from the residual current. The charge due to the residual current must be substracted from the total measured charge in order to obtain the faradic charge for the electrode reaction of interest. This residual charge is estimated by repeating the experiment on supporting electrolyte and integrating the current over the same time interval. There is no guarantee, however, that the processes responsible for the residual currents are completely independent of the presence of sample and/or product. Maximizing the magnitude of the current during electrolysis and minimizes the time required for the complete electrolysis; besides the general technique of voltammetry there exist specific description regarding various factors which need attention. These are as such innumerated below. Thin Layer Voltammetry (TLV) : This is a very slow technique and this fact is used to a great advantage in quantitative studies of electrode reactions with small heterogeneous rate constants. Hubbard [4, 5] reviewed and pioneered this area. TLV is also applicable to examination of metal deposition and adsorption. Schmidt and co-workers [8] carried out this work. The technique has been helpful is mechanism studies of redox controlled solution chemistry. The number of coulombs to oxidize a substance R confined within a thin layer cell is given by Faraday’s Law, Q = nF VC R0

...(2)

where VCR0 is the initial (t = 0) concentration of R and V is the volume of the thin layer

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Introduction to Polarography and Allied Techniques

cavity. If the experiment is carried out slowly enough, CRi t will be uniform across the cell due to rapid diffusional mixing in thin solution films. The current at any time will be given by i=

dCR ,t dQ = nFV dt dt

...(3)

where nV (dCR, t/dt) is the number of equivalents consumed per second can be readily derivatized chemically to yield electroactive derivatives. The functional groups which show excellent voltammetric properties include the nitro, nitroso, quinone, azo, azoxy, azomethane, activated carbonyls, and activated double bonds [7]. For the most part, the voltammetric activity of a compound can be deduced from an examination of its functional groups. In case the compound under investigation is insoluble in aqueous media, then organic solvents such as alcohols, dioxane, acetonitrile, dimethyl sulphoxide and dimethyl formamide must be employed. Occasionally, pure non-aquous solvents of high dielectric constant, such dimethyl formamide, actonitrile, dimethyl sulphoxide, pyridine, or glacial acetic acid containing tetra alkyl salts may be required to attain highly negative potentials (greater than–1.8 V vs SCE) without supporting electrolyte decomposition. Voltammetric research is quite extensive in pharmaceutical compounds : The voltammetric analysis of drugs in pharmaceutical products is by for the most common use of electrochemistry for analytical-pharmaceutical problems. (10–3 – 10–8 M), any one method can readily be applied to the analysis of pharmaceuticals in bulk and in dosage forms. Solid electrode voltammetry (which excludes polarography) has an inherent detection limit of approximately 10–4 – 10–5 M and is consequently limited to these applications, small amplitude polarographic techniques (ac and pulse) can be applied to the measurement of impurities in bulk and dosage forms, and to the essay of drugs and metabolites in biological fluids following high-dose administration where levels are at least 10–6 M (1 – µg/mL sample). Only the techniques of fast-scan polarography and differential pulse polarography with limits of dection of approximately 100-200 and 10 – 20 ng/mL of biological fluids, respectively, are capable of measuring drugs in biological fluids following therapeutic administrative on a routine basis. The appeal of the voltammetric methods of analysis for organic compounds is attributable to their simplicity and rapidity. An extremely large number of organic compounds are either directly reducible at the DME or oxidizable at a solid electrode or can be readily reducible at the DME or oxidizable at a solid electrode.

12.1.2 Voltammetric Methods Potentiometric and coulometric titration methods are fairly universal and can be applied to a wide variety of problems, whereas voltametric methods are distinctly limited to easily reducible or oxidizable compounds. On the other hand, voltametric methods are clearly the most useful for low-level quantitation and have a wide linear dynamic range as given in Fig. 12.1 of the chapter. Here, voltammetry is defined as electrolysis at a microelectrode which is limited by the mass transfer rate at which molecules move from

Voltammetric Methods

165

the body of the solution to O+e→R ic the electrode. The current is followed as a function of the potential applied using three electrode cells of 150 ml working volume. For most reductions the working electrode is a dropping mercury electrode (DME) or a hanging mercury drop electrode E(+) O E0 (HMDE). Solid electrode voltammetry which is typically employed for E0+100 mV E0–100 mV (anodic oxidation) processes can use a rotating platinum electrode (RPE), a wax impregnated graphite electrode (WIGE), a carbon paste electrode (CPE), or a ia R–E–O glassy carbon electrode (GCE). Since the voltammetric Fig. 12.2 : Thin-layer voltammetry for a reversible onetechniques demonstrate a electron oxidation. large linear dynamic range. A plot of i vs E (eq. 4) defines the ideal thin-layer voltammogram as shown in Fig. 12.2. It is to be noted that the peak is symmetrical about E0, and that the current drops to zero after the potential passes through Ep, and that ip is directly proportional to scan rate 2

i=

(

n F VCR ν exp ⎡ ( nF / RT ) E − E ⎣ 2

0

{

(

'0

)}

RT 1 + exp ⎡( nF / RT ) E − E'0 ⎤ ⎣ ⎦

) ⎤⎦ 2

...(4)

The current is maximum at E = E0,, so ip =

0 n2 F 2VCR ν (v is the scan rate in V/s) 4RT

...(5)

The number of coulombs passed in fully traversing the peak is given by equation 0 Q = nF VCR , since the conversion of R to O is complete. In case when the scan direction is reversed, a reduction wave is obtained (as shown by dotted line) for the reverse reaction which is an exact mirror image of the oxidation wave. This result is obtained only for a fully reversible electrode reaction. When the

166

Introduction to Polarography and Allied Techniques

Current

heterogeneous rate constant is very slow, the forward and reverse waves will lose their symmetry and the peak potential will separate. Thin layer cyclic voltammetry is also sometimes used in conjunction with an optically transparent thin-layer electrode to obtain spectra, E0,, and n for redox couples by the “spectro potentiostatic” techniques and thin layer coulometry. Cyclic voltammetry is used initially to locate the redox couple and give an estimate of E0,. Stirred-Solution Voltammetry : This technique utilizes current-voltage relationships which are obtained at a stationary electrode immersed is a stirred solution. In this aspect it is extremely useful to consider a typical current-voltage curve (voltammogram) in terms of the concept of concentration-distance profiles. Hence the potential is considered as the controlled variable rather than current. The current resulting from an applied potential is determined by the slope of the concentration-distance profile of the reactant at the electrode surface. It can be further expressed in terms of Nernst diffusion layer concept. In the Fig. 12.3, a typical current voltage curve that would be obtained for a solution containing equal concentration of O and R. The shape of this curve can be understood by considering the slopes of the concentration-distance profiles that are depicted for several representative potentials. During oxidation current is determined by the slope of the profile for R, whereas the all concentration profiles are completely relaxed before the next pulse is applied and every pulse imitates a new chroamberometric experiment. The length of td required to accomplish this will depend on the chemical reversibility of the system, which would be shorter for ilc S CR reversible reactions and D D CR = CO S longer for irreversible CO= O reaction. A fully (chemically and O+e R electrochemically) reverCSR =C SO sible system is considered ic as an example. The reversible system gives the response to a ramp POTENTIAL E = E0, – E ref excitation as illustrated in ila the Fig. 12.3 and only three pulses are chosen R O+e for examination. S Response to pulse A : CO S Here the pulse amplitude CR = O is insufficient to initiate ia significant faradiac reaction and the sample concentration profiles not Fig. 12.3 : Voltammogram with representative concentrationdisturbed. The current distance profiles for a solution containing equal concentrations of response is then primarily O and R. DO = DR

Voltammetric Methods

167

due to charging and double-layer capacitance to the new potential (Ei + Δ E). The current sampled just between τ is negligible; for by that time the double layer is fully charged. Response to Pulse B : Now the pulse amplitude extends to the half-wave potential for the reactive species, concentration gradients will form and the significant faradiac current will be sampled. It is to be noted that the double-layer charging current will have decayed away when the sample is taken. This time-domain discrimination against idl is a principal advantage of pulse voltammetry profile for O is the determining factor during reduction. A limiting current (ie ) is reached when the surface concentration Cs of the controlling species becomes effectively zero.

12.2 LARGE-AMPLITUDE PULSE VOLTAMMETRY (LAPV) The technique is the normal pulse voltammetry where in the excitation wave form consists of successive pulses of gradually changing amplitude between which a constant “initial” potential is applied. The initial potential is usually chosen in a region where none of the sample components are electrochemically reactive. The current responses may be measured either during the forward step, after return to the initial condition, or both. Usually, the current is sampled only at the end of the forward step and the remainder of the response wave form is ignored. The sampled current is then plotted against the pulse heights (thus voltammetry). Sometimes the difference between successive sampled current is plotted as a function of potential. This results in a response having a derivative shape. It is important to recognize that all variations of LAPV are in essence a series of potential pulse chronoamperometry experiments. The Fig. 12.4 illustrates the simplest example of LAPV of a stationary electrodes. In this case it can be assumed that the time delayed between pulses is such that the initial condition is restored. This implies that the faradia current would thus follow a modified Cottrell equation : 1

i = nF

AC 0

⎛D ⎞ ⎜π ⎟ ⎝ t⎠

2

⎡ ⎛ CO ⎞ ⎤ ⎢1 + ⎜ ⎟⎥ ⎣⎢ ⎝ CR ⎠ ⎦⎥

−1

...(6)

where for a reversible systems X = 0. S

CO S CR

⎛ nF ⎜ ⎝ RT

=

⎞⎡ ⎟ ⎣( Ei + ΔE ) − E ⎠

⎤⎦

...(7)

In the case of pulse B, (Ei + Δ E) = E1/2.

(

S

S

So CO / CR

)

(

S S +C R = 1 and 1 + CO

)

−1

= 0.5

...(8)

Response to pulse C : It is the limiting case of chronoamperometry. The surface concentration becomes effectively zero and the response will follow the Cottrell equation. On plotting the sampled current versus the applied potential a complete pulse voltammogram results as shown in the last figure. When the difference between successive samples is plotted (Fig. 12.4) a peaked response is obtained.

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Introduction to Polarography and Allied Techniques

Excitation Waveform

E(–)

td ΔE

(A)

tp

Time System response to selected pulses 0 CO = CO

(B)

PULSE B

PULSE A

PULSE C

at t = t p + r

at t = t p + r

no reaction

X

X

CO = 0

X

Current Response to Selected Pulses sample

(C)

sample sample tp

t

tp

t

tp

tp + r

LAPV

(D)

isampled

E(–) Derivative LAPV (E)

Δisampled E(–)

Fig. 12.4 : Introduction to stationary electrode LAPV

Voltammetric Methods

169

When LAPV is carried out with a DME, the technique is large amplitude pulse polarography (LAPP). This is usually referred to as “normal” pulse polarography. One pulse is applied per drop at a fixed time late in the life of the drop. The current is sampled just before the drop is dislodged by mechanical means, a time at which the rate of change of area is smallest. Because the pulse widths are usually in the 50-ms region, the electrode is effectively stationary and of fixed area during each pulse. Since each drop is a new electrode, the time between pulses td is made to be the drop time. The timing circuitry that is used to generate the pulses also functions to trigger an electrochemical “drop knocker” or a static mercury drop electrode. Sometimes it is useful to apply identical pulse to several drops before increasing the amplitude. This allows for time averaging and some improvement in the signal-tonoise ratio. LAPP is analytically useful, being sensitive to 10–6 M in some circumstances. In an interesting variation of LAPP originally described by Kalousek [9] the potential applied to DME is alternately switched from an initial potential E(–) (A) (which is sufficiently negative of the O →R E1/2 for a reducible species to cause Ei a limiting cathodic current) to a series of potential pulses changing in height from values more positive than E 1/2 toward more negative E½ values. The current is sampled late in the life of each pulse, as indicated sample taken here in the Fig. 12.5. At first the R →O reduction product formed at the Time td initial potential is oxidized during anodic wave Fig. 12.5. After the pulse heights pass through E1/2 and ic reach potentials for reduction, a O→R cathodic current is recorded. The forward reaction (B) relative values of i a and i c will depend on the reversibility of the ic reaction and the specific pulse i E(–) sampled widths and sampling times employed. In yet another variation the ia current is recorded at the initial potential following a series of pulses increasing in amplitude from the reverse reaction initial potential toward more ia R→O negative values (i.e., the same exilation as shown in Fig. 12.4 (a). Fig. 12.5 : In one of many possible variations of When the pulses reach sufficiently LAPP the current is sampled on a reverse step just negative potentials to cause prior to drop fall. (a) excitation, (b) response

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Introduction to Polarography and Allied Techniques

reduction of the species, the product of the reduction is oxidized at Ei, and the sampled anodic current is recorded unless the couple is totally irreversible. This is equivalent to a series of potential pulse chronoamperometry experiments with samples taken on the reverse step. Techniques of this type have been used, at times, in reversibility studies and for identification of unstable products of electrode processes [3].

12.3 DIFFERENTIAL AND DERIVATIVE VOLTAMMETRY This technique was originally devised by Semerano and Riccoboni. Two indicator electrodes at the same potential in different solutions are used, and the difference between the currents flowing through them is recorded as a function of their common potential. A simple circuit, that serves the purpose is shown in Fig. 12.6, where the magnitude of potential drop ER indicated by the recorder is given by ER = i1 R1 – i2 R2 ...(9) To polarizing circuit

ind.

ref. Cell 1

i1

R1

Recorder ind.

Cell 2

ref.

i2

R2

Fig. 12.6 : Schematic diagram of a simple circuit for differential voltammetry

A solution of the supporting electrode alone could be placed in cell 2 and an identical solution containing an electroactive substance may be placed in cell 1. In case the two indicator electrodes are exactly identical, the variation of i2 with potential will be exactly the same as the variation of the residual current included in i1. Hence, if R1 and R2 are equal, ER will be proportional to the current due to the electroactive substance alone. The resulting plot of ER against indicator electrode potential will provide an automatic correction for the residual current. This can be used to compensate for the final current to improve the shape of a cathodic wave occurring at potentials so negative that its plateau is too short to be measured on an ordinary voltammogram. Compensation can be achieved, not only for the residual current, but also for the current on the plateau of the prior wave. As an example a portion of the cadmium-zinc solution yielding the polarogram is shown in Fig. 12.7 might be placed in cell 1 while supporting electrolyte in cell 2. The circuit is then adjusted to provide a potential on

Voltammetric Methods

171

b

di/dt

a

di dt di dt

max

max

Potential

Fig. 12.7 : Schematic derivative voltammograms obtained with (a) a single reducible substance, illustrating the measurement of the peak height, and (b) a mixture of two such substances giving overlapping peaks, showing that the more difficulty reducible substance is more readily detected than determined

the plateau of the cadmium wave. A concentrated solution of cadmium ion might be added to cell 2 to decrease ER to zero. Difference between the concentration of cadmium ion in the solution, between the areas of two stationary or solid indicator electrodes, or between the values of m for two dropping electrodes, or between the values of m for two dropping electrodes can be compensated by suitable adjustment of the ratio R1/R2. As such the plot of Em against indicator electrode potential would then show only the zinc wave. The foregoing applications (both) are termed “subtractive” voltammetry. Some difficulty is involved in differential polarography, in which dropping electrodes are used as the indicator electrode. Because unless the cycles of drop growth and fall are exactly synchronized the difference of current will undergo wide periodic fluctuations even though the two electrodes yield the same average current. Kolthoff and Lingane called this as “beaded string” effect. Derivative voltammetry consists of recording the rate of change, di/dt, of the current flowing through a voltammetric cell against the potential E of the indicator electrode, which is varied at a constant rate dE/dt. The values of di/dE is small at potentials preceding the wave, increases to a maximum at the half-wave potential.

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Introduction to Polarography and Allied Techniques

This happens when the wave obeys either of the equations : d ( Ed e )

d [ log i / ( id − i )] Ed.e = E1/2 –

=−

005915 . n

i 00542 . log id − i αn

...(10)

...(11)

It then decrease again to a very small value on the plateau. The maximum deflection of the galvanometer or recorder occurs at the half-wave potential. It is proportional to the diffusion current (and hence to the concentration of the electroactive substance responsible for the maximum) and increases as the rate of polarization increase. It is larger for a reversible wave than for an irreversible one involving the same overall number of electrons, and it increases as n or α n a increases. For recording a derivative voltammogram, the simplest practical technique consists of connecting a condenser having a high capacitance in series with the galvanometer or the resistor across which the recorder is connected. On a derivative polarogram two clear peaks which can easily be identified are obtained. Peak heights in derivative polarography have to be measured by a base-line technique. If there is only one wave on the polarogram, the derivative curve has the typical shape as shown in Fig. 12.7 (a) and the height of the peak can be measured, though with uncertainty.

References 1. Bard, A.J. and Sonthanam K.S.V. in Electroanalytical Chemistry, Vol. 4, Marcel Dekkar, New York, 1970. 2. Harran, J.E., Electroanalytical Chemistry, Vol. 8 (A.J. Bard, ed.) Marcel Dekkar, New York, 1975. 3. Heinman William R. Dept. of Chemistry University of Cincinnati, Cincinnati and Ohio, Kissinger Peter T., Dept., of Chemistry Purdue University Inc. West Lafayette Indiana. 4. Hubbard A.T., and Anson F.O., in Electroanalytical Chemistry, Vol. 4. (A.J. Bard, ed.) Marcel Dekkar, New York, 1970. 5. Hubbard A.J. CRC Crit, Rev. Anal Chem. 3 : 201 (1973). 6. Janata, J. and Mark H.B., Jr. Electroanalytical Chemistry, Vol. 3. (A.J. Bard, ed.) Marcel Dekkar, New York, (1969). 7. Punger, E., Feher Z. and Nagy, G., Acta Chem. Hung. 70 : 207 (197) and Abstr. 23 : 747 (1972). 8. Schmidt E., Electrochim. Acta, 8, 23 (1963). 9. Kalousek M. Collection Czechoslov. Chem. Communs., 13, 105 (1948).

CHAPTER 13

CONTROLLED POTENTIAL ELECTROLYSIS 13.1 ELECTRO-ORGANIC SYNTHESIS AND THE TECHNIQUE There has been a vigorous expansion of the classical areas of organic electroanalysis and its applications to physical organic chemistry [9] as well as electrosynthesis and related mechanisms. Besides these many new fields have opened during this period. In brief may be included as research and applications of organic electrochemistry in fuel and solar cells [5], high energy batteries, corrosion inhibitors, electrodeposition of metals and paint, organic semiconductors, organic photo electric materials, etc. Recently interest is developing in the application of these techniques to the study of biological processes pharmacy and pharmacology and also the new branch-Bioelectrochemistry. Recent studies also involve the fabrication and testing of chemically modified and ion selective electrodes which have attracted unusual interest in electrocatalysis, electro synthesis, photosensitization and electrosensors [3]. Thus, for the production of a number of chemical, the electrochemical routes has an edge over the chemical methods specially in regard to ease of operation, enhanced product purity, pollution control and ease of operation. Besides a number of advantages, the technique has some limitations too. The main draw back is that the reactions are slow and thus consume more time. The choice of solvents is also restricted along with the limited choice of the supporting electrolyte. The organic electrode reactions can be classified as described below. However, these depend of the nature of final products and its formal mode of formation. Some important types of reactions are listed below :

13.1.1 Pure Electron Transfer Anodic and cathodic electron transfer is the elementary process underlying in all electrochemical reactions. These finally result in the formation of radical ions from neutral molecules (Eq. 1 and 2).

→ R – E'+ + e– R – E ⎯⎯ e−

R – Nu+ ⎯⎯→ R –Nu'– and neutral radicals from charged species (Eq. 2 and 3).

...(1) ...(2)

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Introduction to Polarography and Allied Techniques

R – E– → R – E' + e–

...(3)

R – Nu+ + e– → R – Nu' ...(4) In majority of cases, radical ions and neutral radicals are consumed as they are formed in very fast chemical follow up reactions giving rise to a wide variety of products.

13.1.2 Conversion of Functional Groups This type of reaction is similar to its chemical counter part in which a functional group is reduced or oxidized to another one for example, as given equations (5), (6 and 7) + e−

+2 e−

+4H

2H

⎯⎯⎯⎯ + → R – NHOH ⎯⎯⎯ + → R – NH2

R – NO2

+4e −

⎯⎯⎯⎯ + → R – CH2 OH

R – COOH

+4H

...(5)

...(6)

...(7) The oxidation of pyridine methanols to pyridine carboxylic acids has (eqn. 7) been carried cut in nickel oxide electrode [11].

13.1.3 Substitution Reactions A general expression for anodic substitution reactions is given in (Eq. 8). Here E is often hydrogen atom, which can also be another atom or group e.g., tbutyl, OCH3, CrCOO– R – E + Nu– → R – Nu + E+ + 2e–

...(8)

A general equation (9) conforms to the cathodic substitution e.g., R – Nu + E+ + 2e– → R – E + Nu–

...(9)

+

+

Here E , in most cases, is H or an equivalent proton donor. It can also be a neutral molecule, such as CO2 or methylbromide, whereas Nu is a leaving group of some kind e.g., halogen, RSO, RSO2, N+R3, etc.

13.1.4 Addition Reactions In an anodic addition, two nucleophilic molecules are added across a double bond (eq. 10) or in a system of double bonds with loss of two electrons. Nu Nu | | ...(10) R2 C = CR2 + 2Nu– → R2 C – CR2 + 2e– Similarly, in a cathodic addition reaction two electrophilic molecules add across a double bond (eq. 11) or in a system of double bonds with addition of two electrons. E E | | ...(11) R2 C = CR2 + 2E+ + 2e– → R2 C – CR2

Controlled Potential Electrolysis

175

The most important reaction is cathodic hydrogenation where E+ is a proton donor (eq. 11). For this reaction the authors [5] have tried electrocatalytic hydrogenation of amino benzoic acids at platinum cathode in 2N per chloric acid media giving rise to bicyclic lactams and ester (eq. 12). O

N H2 –

+ 6 e + 6H

NH

+

...(12)

– H2O

COOH

13.1.5 Elimination Reactions Anodic and cathodic elimination is simply the reverse of cathodic (eq. 11) and anodic (eq. 10) addition respectively.

13.1.6 Coupling Reactions Two simple versions of formal anodic coupling exist, namely coupling-elimination (eq. 13) and coupling addition (eq. 14) : 2R – E → R – R + 2E+ + 2e– –

2Nu + 2 C = C

...(13)

Nu – C – C – C – C – Nu + 2e

–

...(14)

The former type is best represented by the historical “Kolbe Reaction” (16) ...(16) 2R – COO– → R – R + 2CO2 + 2e– The cathodic counter parts of eq. (13, 14) are indicated in (eqs. 17 and 18) 2R – Nu + 2e– → R – R + 2Nu– ...(17) 2E + 2 C = C + 2e → E – C – C – C – C – E +

–

...(18)

Reaction (18) is of great importance in cases where E+ is a proton. The general designation for this mode of coupling is electro hydrodimerization. The best known case being the flag ship and grant swinger of electroorganic chemistry all over the world, “Monsanto’s” process (eq. 19) for making adiponitrile directly from acrylonitrile. 2CH2 = CH – CN + 2H+ + 2e– → NC (CH2 )4 CN

...(19)

13.1.7 Cyclization (Intramolecular and Intermolecular) [2, 11, 12] Oxidative intramolecular cyclization of 2-nitro aniline affording benzofuroan (eq. 20) in the presence of electrogenerated iodonium ions, which behave as catalytic oxidizing agent, and at the same time as an electron carrier. NH2 N O2

+

I

N O

+

...(20)

N O

–

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13.2 ELECTROCHEMICAL ACTIVITY IN HETEROCYCLIC SYSTEMS Heterocyclic compounds occupy a unique position in the field of organic chemistry. Electrochemical studies of nitrogen containing heterocycles are almost as old as the field of electrochemistry itself. The nitrogen containing heterocyclic compounds have been of much interest for electrochemistry as not all but many of them, in one way or the other are related to any biochemical pathway, energy transfer system, or medicinal significance. The electrolytic reaction pathways of N-heterocyclic reactions may be enumerated in general categories as shown below : Electrolytic Reduction Heterocyclic Systems: (i) Hydrogenation (ii) Dimerization (iii) Hydrodimerization (iv) Halogen elimination Electrolyte Oxidation Heterocyclic Systems: (i) Coupling (ii) Fragmentation (iii) Anodic substitution The electrolytic reactions in which a heterocyclic system is formed, may be classified in different ways according to the type of bond formation. These are described below : 1. Ring closure reactions 2. Ring contraction reactions 3. Ring expansion reactions

13.2.1 Ring Closure Reactions Suitably substituted molecules can undergo intra- and/or inter-molecular electrophilic and/or nucleophilic reaction utilizing otherwise unstable electrogenerated functional groups, giving rise to heterocyclic compounds [3, 4, 5, 6]. Thus, in these systems the role of current is to bring one or both the reaction centers to a suitable oxidation state. In a ring closure systems there is either. (a) Attack of an electrolytically formed nucleophile (e.g., alcohol, hydroxylamine, amine hydroazine, on an electrophilic center e.g.,) carbonyl, cyano, nitro and nitroso derivative groups, commonly termed as reductive cyclization sections. The reduction of compounds suitably substituted with reducible functional groups can be advantageously used for heterocyclic ring systems. The guiding principle for such a reaction is to form a nucleophilic center in the molecule by cathodic reduction of a functional group and then to get this to react with an electrophilic center (suitably which may also be formed in an electrochemical process or be present in the starting material) positioned for ring closure [3, 4]. Reductive cyclization reaction of amino benzoic acids have been chosen as model examples by the authors [5]. There give rise to bicyclic lactans and ester. Thus, the electrocatalytic hydrogenation and subsequent intramolecular cyclization of 4-amino benzoic acid afforded 2-azo bicyclic [2, 2, 2] octan-3-one (eqn. 12).

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181

The polarization study of a system (oxidation or reduction) is achieved by three electrode system consisting of working electrode auxiliary electrode, and reference electrode as shown in Fig. 13.4. The polarization curves are drawn between electrode potential ‘E ’ versus current density ‘i’ (the current passed per unit surface area of the working electrode) or log current density, in the absence and presence of depolarizer to find a suitable range of current density applicable to the system under study. Normally potentiostatic and galvanostatic techniques produce identical polarization curves with only one exception the sigmoid characteristic which can only reproduce in potentiostatic control, see Fig. 13.4. In this figure, the full line represents the potentiostatic method, while the dotted line represents the galvanostatic method). In order to understand the practical utility of polarization curves, in electrosynthesis, a systematic approach of this concept can be very well explained by taking a general example of electrolytic reduction as shown in Fig. 13.5. In Fig. 13.5, curve 1 represents the polarization curve obtained in the absence of depolarizer. The small current flowing between a and b may be due to the presence of a small amount of reducible material present in the solution or, to diffusion of hydrogen away from the cathode. Visible hydrogen evolution commences in the vicinity of b, which gives the so-called bubble over voltage potential. Beyond this the gas is evolved freely with little further polarization. If a depolarizer is present (curve II), the reduction of depolarizer will occur in preference to hydrogen evolution. If this reduction is relatively slow, the cathode potential will rise from a to b' as shown in curve II. Between a and b' the reduction efficiency is 100%, but at the potential b', which is close to b, appreciable hydrogen evolution will commence and the current efficiency will fall. For a rapid reduction process, the cathode potential rises slowly (curve III) until limiting current density is attained. After that a rapid increase of potential and hydrogen liberation occurs. Tafel Equation : An electrode process can be described by eq. (23). OX + Ze–

R

...(23)

where OX represents particles which are near the electrode and are subject to reduction by accepting Z electrons. R denotes particles formed immediately after the chargetransfer step. The rate of electrochemical reaction (eq. 30) expressed in the units of current density in the forward i → reduction and reverse i oxidation directions can be described by means of general kinetic equations (24, 25)

i = zF K1 COX

...(24)

i = zF K2 CR

...(25)

At equilibrium i.e., at the reversible potential of the system, E = Er 0 0 0 i = i = zF K1 COX = zF K 2 CR = i 0

...(26)

where i is the exchange current at the electrochemical stage. The Nernst equation (27) holds good

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Er = E0 +

COX RT ln CR zF

...(27)

where Er is the potential difference across the interface at equilibrium, E 0 is the standard potential of the redox couple COX /CR. When the electrode potential departs from the equilibrium value in the negative or positive direction, assuming the value Er reaction (23) will proceed predominantly in one direction at a rate iE determined by the equation (28) iE = i – i = zF (Ek1 COX – EK2 CR)

...(28)

and the relationship between current (current density) and potential is represented by the Butler-Volmer equation (35) for conditions where concentration at the interface and the bulk are the same :

(

s (1 −α) zF ηe − i = i – i = i e zF ηe RT − e

/ RT

)

...(29)

where ηe = E1 – Er , is the electrochemical over potential i, the equilibrium exchange current density, i, the net current. The distribution coefficient α characterizing the fraction of the double layer energy that effects the forward reaction is known as the transfer coefficient. Thus the fraction of the energy required for the forward reaction is α and that for the backward reaction is (1 – α ). The equation (29) can be simplified for making certain approximations. The equation : η = –

RT RT ln i0 + ln ia 1 − α zF ( ) (1 − α ) zF

...(30)

can be transformed into Tafel’s equation for the anodic process

η = aa + ba log i

...(31)

(–E), η

tan v=b

v a

–5

–4

–3

–2

–1

0

+1

Fig. 13.6 : Determining Tafel constants ‘a’ and ‘b’ from a semilogarithmic plot of overpotential η against current density ‘i’ at η 〈〈0 or η〉〉 0

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183

Thus, the overpotential is linearly dependent on the logarithm of the current density and obeys Tafel’s equation

η = a + b log i

...(32)

The Tafel constants ‘a’ and ‘b’ depend on the electrode material, temperature, the solution composition and current density and thus gains fundamental significance. The determination of relationship between current and potential assumes importance for electrochemical redox reaction of organic compounds. The value of i0 (exchange current) and α (transfer coefficient) for a single step electrochemical act can be found graphically in Fig. 13.6, by plotting η against log i in that region of overpotentials ((α zFn) > RT) where either equation

η=

RT RT ln i − ln ic αzF αzF

...(33)

(strong cathodic polarization) or equation (strong anodic polarization is satisfied. The slope b of the η is log i straight time in Fig. 13.6 is equal to 2.3RT/α zF, and hence

α = 2.3

RT zFb

...(34)

The exchange current i can be determined from the value of overpotential ‘a’, at log i = 0, i.e., at unit current density i0 = 10–aαzF/2.3RT = 10–a/b

...(35)

The more general expression of equation (29) can be rewritten as follows : ln

log

i 1−e

zFn RT

= ln i0

αzFn RT

...(36)

i 1–e zFη /RT

η=0

η = (V)

Fig. 13.7 : Graphical determination of the exchange current density ‘i0’ and transfer coefficient ‘α’ by substituting experimental data into Eqn. (36).

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185

References 1. Baizer, M.M., Organic Electrochemistry, Marcel Dekkar, New York (1973). 2. Bard, A.J., and Lund H., Encyclopedia of Electrochemistry of elements, Vol. 13, Marcel Dekkar, New York (1979). 3. Daniel, C.S., Kuwana, T. and Roger, G.P., J. Electroanal. Chem., 98, 345 (1979). 4. Lacan, M.K., Jakopac, V., Domani O. Rogic, and Tabokovic I., Synth. Commun. 4, 219 (1974). 5. Lund, H., Adv. Heterocyclic Chem., 12, 213 (1970). 6. Natarajan, P., Trans SAEST, 17, 145 (1982). 7. Eberson, L. and Nyberg, K. in Advances in Physical Organic Chemistry’, Vol. 12, Aca. Press (London) 1976. 8. Selley, N.J. in Experimental Approach to Electrochemistry Ch. 6, Edward Arnold, London, 1977. 9. Weinberg, L.L., Techniques of Electroorganic Synthesis, Part I & II, Wiley, New York, 1974. 10. Zuman, P., C.L. Perin, Organic Polarography, J.W. & Sons, New York (1969). 11. Zutshi R. Rastogi and G. Dixit, Trans, SAEST 17, 295 (1982). 12. Zutshi K., Rastogi R.J. Prakt. Chem. 325 (1983), Ext. Abstr. 33rd ISE Meeting, Lyon (France) P. 704, September 6-10, 1982.

CHAPTER 14

CORROSION PART A : PRINCIPLES AND CONTROL 14.1 CORROSION AND CONTROL The deterioration of a substance, usually the conversion of iron, steel and other alloys and metals into oxides, hydrated oxides, carbonates, or other compounds due to the action of air or water or both cause corrosion. The minor components present in the air or water are important factors in the rate of corrosion and produce the kind of corrosion products. Natural minor components such as carbon dioxide in air and water cause serious corrosion, but contaminates introduced by all types of air and water pollution usually accelerate corrosion. Salts, such as sea water, are serious causes of corrosion. Sulphur in fuels such as coal, oil, gasoline and natural gases and other fuels are also important source of corrosion, so that removal treatments are common except for coal, although the mode of treatment and the methods may be different. Electric currents from power sources, or from differences in composition of materials in ground or different parts of metal objects are also accelerators of corrosion. Corrosion Inhibitors–Conventionally are a synergistic combination of sodium nitrite– borax and organic inhibitors which are used, as the case may be, to prevent corrosion most commonly of ferrous and non-ferrous metal and alloy surfaces in low make up as well as closed cooling and heating systems. The efficiency of inhibitors in the control of corrosion can be evaluated reliably by the application of Tafel Intercept method and Linear Polarisation Resistance Techniques. As per recent developments these techniques have been successfully employed in the evaluation of ureas, thiourea and semithiocarbazide. Interesting results have been obtained with thiourea as inhibitor. Researches have been going on from time to time to over come the losses due to corrosion and also to improve the quality of the product specially with respect to safety. Corrosion has always been considered as one of the important subjects of electrochemistry and engineering for a long time as the destruction caused to materials, by this process has been increasing every year. In addition to this increase there has been growing use of metals in modern technology. Both these aspects together with the corrosive environment, the modern civilization has been generating, forces. The scientists and engineers are adopting methods to reduce this corrosion loss. Corrosion preventive techniques and protection methods have been evolved in recent years which require the immediate attention of industries.

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Anticorrosive paintings, epoxy coatings, galvanisation techniques etc. have been topics of great relevance in the present day technology. Hot corrosion of materials has been causing a great concern for immediate solution to the problem. Not only this, a similar problem is faced in micro corrosion. In the present text generalised aspects of corrosion are presented so also the preventive methods which present some basic instrumental and electronic aspects of electrochemical techniques specific to corrosion study and evaluation. Standard electroanalytical methods have been discussed, very briefly, stressing the devises used and the basic electrical circuits in use. Electrochemical instrumentation has undergone a major revolution after the introduction of operational amplifiers. The measurement, amplification, control of current or voltage have assumed new dimensions in accuracy. Introduction of these techniques have resulted in rapidity of measurement of current-voltage of EMF vs concentration plots. The instrumentation needed for the measurement of ionic concentrations has become increasingly sophisticated. Equally revolutionary has been the introduction of digital methods and the advert of microprocessors in measurement methods. This has resulted in intelligent instruments with programming capability and built-in sophisticated data analysis. Both research as well as corrosion testing laboratories have been benefited from these advancements terms. The ease of carrying out tests and data analysis and reliability of results. The first part discussion in the present text is limited to the following aspect regarding instrumentation in corrosion testing and research [2].

14.1.1 Ion Selective Electrodes These operate on the basis of membrane equilibrium [1]. When a membrane separates two solutions and assuming it is representing a thin selection of electrically conducting material. As such it develops a potential whose magnitude is controlled by the concentration of the ions. For the membrane, ideally a single ion specificity is preferred. Combining the membrane electrode with a non-polarizable reference electrode; it should be possible to measure cell emf. The most common membrane viz. the glass electrode is represented by : Ag/AgCl/HCl (0.01 m)/glass/HA, NaA, NaCl/AgCl/Ag ...(1) where Ag/AgCl is a reference electrode being used as bridge electrode. In a typical pH measurement, the commonly used reference is a saturated colonel electrode : Ag/AgCl (0.1 m)/ glass/H+ ← Test solution → KCl (satd.) HgCl2/Hg (SCE)

...(2)

The cell potential may be represented as E = const. +

RT ln an + (Solution) ZF

...(3)

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Introduction to Polarography and Allied Techniques TABLE 14.1 Typical potentials of Ion-Selective electrodes [3] (25°C) Ion

Output Potential (mV)

Calibration Range Range (m)

Anions F– Cl– Br– I–

–200 to + 200 0 to + 200 –120 to + 200 –390 to + 90

1 1 1 1

– – – –

Cations Cd++ Cu++ Pb++ Ca++ K+ Na+ H+ NH+4

–70 to – 280 +180 to – 20 +30 to – 160 +80 to – 60 +200 to – 200 +100 to – 400 +414 to – 414 +150 to – 100

1 – 1 – 1 – 1 1

– 10–8

10–10 5 × 10–5 5 × 10–6 5 × 10–6

Resistance (M) 0.20 30 30 30 1 1 1 25 250 100 200 50

– 10–10 – 10–7 – 10–14 – 10–4

where the EMF ‘E ’ depends on a constant, namely the standard electrode potential E 0 and a concentration dependent term RT/ZF. In aH+, (4). Thus the cell potential is directly proportional to the ionic concentration. Typical output potentials of ion selective electrodes with respect to Saturated Calomel Electrode (SCE) are given in (Table 14.1). As indicated in the table, these ion selective electrodes have high internal resistance and thus require for signal amplification–amplifiers with very high input impedance (Zi). For a measurement accuracy of 0.1%, the enquired Zi is at least three orders of magnitude higher than the electrode impedance. Thus for a glass electrode having typical impedance of 2 × 108 ohms, the amplifier should have Zi of 1011–1012 ohms. R

E Cell

Rload |Y loss|

+

Rp=106 ohms Ecell=1Volt

Fig. 14.1 : Effect of internal resistance of the measuring device on the accuracy of measurement

Figure 14.1 describes the equivalent circuit of an ion-selective electrode based cell having an impedance of Rp and the measurement amplifier impedance of Rload. The resulting error voltage Vloss manifests as error which diminishes with increase in Rload.

Corrosion

189

14.1.2 OPERATIONAL AMPLIFIERS Operational amplifiers are the building Rf blocks of most amplifiers. These have differential input terminals. The if operational amplifier (OA) can be used to implement either inverting or non– inverting amplifiers. An ideal OA has in Ri an infinite Zi, zero output impedance + ei (Z0), infinite gain and zero input bias e0 current (Fig. 14.2). The OA of the purpose of inverter with gain utilizes a feedback circuit as Fig. 14.2 : Operational amplifier. Its shown in Fig. 14.2. The current iin characteristics and inverting amplifier flowing through Ri is given by ei LRi. configuration Current flowing through Rf is 0 – e0/Rf . Since no current flows into the input of OA (bias current zero for ideal OA), iin = ii. Thus e0 = –eiRf / Ri if iin

..(4)

Rf – +

Fig. 14.3 : Current to voltage converter for zero resistance ammeter

Open loop gain of OA is typically 105–108 and the feedback establishes stability and the linearity of the amplifier. Current to voltage converters are usually implemented by dropping the current across a resistor and measuring the voltage dropped across it. OA can be used to implement a zero resistance ammeter (Fig. 14.3). Since iin has to flow through the feedback resistor Rf , the voltage dropped across the resistor is e0 = iin. Rf ...(5) Current to voltage converter circuits are used in potentiostats, galvanostats and polarography equivalent.

14.1.3 Potentiostat The figure given ahead shows the basic principle of a typical potentiostatic circuit highlighting its similarity to a typical OA based non-inverting amplifier. The potential difference between the reference electrode and the working electrode is controlled by OA. The potential differences between working a reference electrode is controlled independently of working and counter electrode polarization resistance and electrolyte resistance.

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14.1.4 Galvanostat Galvanostats are used in chronopotentiometry, plating and other applications where the current is required to be controlled via voltage control across a fixed resistance inserted between reference and working electrode terminals. A simple galvanostat is given in schematic diagram below :

Cell

or1 C d

R Vref

Cell = V ref/R

14.1.5 Polarography Polarography deals with obtaining the current potential curve with a dropping Fig. 14.4 : Use of operational amplifier to make mercury electrode (DME). Its use as an galvanostatic circuits analytical tool, for understanding mechanisms of electrode reactions and for the study of complexes has stimulated development of its theory and instrumentation polarography has assumed a significant place in electrochemical techniques after the introduction of AC polarography (ACP), pulse polarography (PP) and differential pulse polarography (DPP). The details of all these techniques have already been described in the foregoing chapters on polarography in this text.

14.1.6 Pulse Plating Sources However, information on wave forms and equipment for pulse plating is described briefly. Pulsed galvanostatic plating can lead to metal deposits of increased uniformity. The residence time at low and high potential may be chosen independently. Instrumentation for pulse plating depends on the power range as well as the pulse shape requirement. The figure (shows the various wave forms used in pulse plating). The voltage to current converter can be used to implement pulsed galvanostatic plating by employing a suitable wave form generator. Unipolar pulses can be generated by simple switching equipment while popular pulses require the use of complex switching schemes.

Unipolar pulses

Bipolar pulses

Pulsed pulse reverse

Pulse-on-pulse

Duplex pulses

Fig. 14.5 : Various pulse plating waveforms.

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191

14.1.7 Micro Processor Based Instrumentation Application of digital techniques and the advert of microprocessors has been a major change in the electrochemical instrumen-tation. Use of analog to digital convertor (ADC) and digital to analog converter (DAC) results in interfacing the analog signals to the digital domain of microprocessors. The task of ramp generation, setting of scan limits and super position of AC voltage is taken over by DAC and software. Signal processing is done by applying sophisticated mathematical algorithms to the digital data off-line. A typical digital potentiostat is shown in Fig. 14.6, wherein the building blocks have been indicated.

To AUX DAC

Voltage to current converter To AUX Power booster

Current to voltage Converter ADC

Analog multiplexer

From WE Buffer From REF

Digital computer

Fig. 14.6 : Block schematic of a microcomputer based potentiostat

14.1.8 Damage and Control Introduction : Hydrogen damage resulting from the entry of hydrogen into steel during production, fabrication and service conditions is a major problem. The mode of entry, uptake and subsequent interaction of hydrogen in steels, together with other phenomenological aspects of hydrogen damage are relevant to present day technology. The effects of hydrogen on the physical and mechanical properties of steels and other alloys are relevant to many technological and engineering application. As already indicated hydrogen damage is a major problem in present day technology, as it places higher demands on the performance of many steels under actual service conditions. In fact hydrogen embrittlement and hydrogen assisted cracking of steels limit their useful life and pose constraints in the selection of suitable steels for certain useful components. In one form or the other, hydrogen problems are encountered in (a) nuclear power plants, (b) thermal power stations, (c) fertilizer plants, (d) petroleum refineries, (e) aerospace and (f) hydrospace projects so also in fusion reactor technology.

14.1.9 Sources of Hydrogen and Modes of Entry In general, steels come in contact with gaseous hydrogen or hydrogen producing environment. As such the following sources may be regarded as the main sources.

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(i) Hydrogen dissolved in molten steel during production picked up subsequently during casting, heat treatment and welding operations. (ii) Hydrogen absorbed by steel at elevated temperature an exposure to hydrogen containing environment. (iii) Hydrogen absorbed by the steel while in contact with high pressure hydrogen gas. (iv) Nascent hydrogen absorbed by steel during pickling and electroplating. (v) Hydrogen and its isotopes implanted by high dose charged particles or radiation in alloy steels used as shields in fission and fusion devices. (iv) Diffusion of hydrogen in steel occurs due to the gradient in the chemical potential of dissolved hydrogen. Fick’s laws are obeyed and interstitial diffusion is the predominant process. Diffusion of hydrogenation also be the consequence of a gradient in electric field (electron transport) or a gradient in temperature (thermotransport) or a gradient in stress. Duplex stainless steels have good resistance to localized corrosion and are widely used in severe corrosive environments like petroleum refineries, petrochemical industries, marine atmosphere etc. The high temperature, high pressure aqueous environment and the presence of radiation pose a variety of corrosion problems for materials used in Nuclear Power Plants. The corrosion problem of condensers is common to conventional power plants including stainless steel pipes, internal components and steam generators and off-shore sector. The degradation of materials takes place when exposed to high temperature. Degradation of mechanical properties, loss of metal due to corrosion/oxidation, DCscaling or spalling of protective layers, localized attack such as denting/heat spots etc. The high temperature corrosion problems are related to the aircraft power plants in aircraft industry. Engines and gas turbines operate at elevated temperature to realize maximum efficiency. Such applications require materials to withstand damages due to creep, fatigue, corrosion, erosionet. During the production of oil and gas from deep wells by combustion, carbon dioxide flooding etc., there is quite a possibility of encountering hydrocarbons associated with undesirable fluids mainly, carbon dioxide and H.S. Both these fluids result in severe corrosion in presence of even small amounts of water.

14.1.10 Mechanism of Corrosion of H2S CO2 H2S is a colourless transparent gas with rotten egg odour. Its sp. gr. is 1.92, and 2.9 volumes gas are soluble in one volume of water at 20°C. Nascent Hydrogen is produced in the electrochemical reaction of iron. Fe ↔ Fe2+ + 2e–

...(7)

H2S ↔ S2+ + 2H+

...(8)

Fe + H2 S ↔ FeS + H2 2H+

+

2e–

→ H + H → H2

...(9) ...(10)

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193

Normally both hydrogen atoms combine together at the metal surface to form molecular hydrogen. There are two distinct phenomena which may occur due to the penetration of hydrogen atom into steel lattice structure. (a) Sulphide stress corrosion cracking (hydrogen embrittlement) (b) Hydrogen induced cracking. (a) When H2S is introduced into a system both sulphide ion and atomic hydrogen are present in the electrolyte. Sulphide ions reduce the rate of combination of hydrogen atoms to form molecular hydrogen, thus creating a large cone of atomic hydrogen on metal surface. This results in migration of more atomic hydrogen through gain boundaries of metal making the metal brittle. When the metal is under stress, due to loss of ductility, it fails without being plastically deformed, resulting in sudden failure. (b) As already explained, atomic hydrogen is capable of penetrating any metal. When this atom migrates into steel, it gets lodged in the internal fissures and non-metallic inclusions. As more and more hydrogen is trapped, formation of molecular hydrogen occurs. This molecular hydrogen cannot diffuse out of steel and pressure in the gas pocket increases. The equilibrium pressure of atomic hydrogen with molecular hydrogen is several hundred thousand pounds and is capable of repuring any material.

14.2 MECHANISM OF CARBON DIOXIDE CORROSION When CO2 dissolves in matter it forms carbonic acid which is corrosive. CO2 + H2 O → H2 CO3

...(11)

The severity of CO2 corrosion depends on CO2 concentration, its partial pressure, water content, temperature, flow viscosity, pressure etc. This type of corrosion is generally weight loss type, but in the presence of CO2 it can result in stress corrosion. Pressure increases the solubility of CO2, while temperature decreases the same. In gas condensate wells, partial pressure of CO2 is used as yardstick to predict corrosiveness. Less than 3 psi partial pressure is non-corrosive, 3 to 30 psi may be corrosive and more than 30 psi is definitely corrosive. Partial pressure (in psi) =

totalpressure ( in psi) ×% by vol of CO2

100 Carbonic acid formed as above, reacts with iron to form iron carbonate. ...(12) Fe + H2 CO3 → FeCO3 + H2 CO2 and H2CO3 act as catalyst for evolution of hydrogen. Anode zone is corroded while cathode zone remains intact. Iron carbonate formed as above, forms a protective film against corrosion, mainly when the test is carried out under static conditions. Under dynamic conditions or in pipe under flow conditions, this layer is destroyed and fresh corrosion occurs. This exercise is continuously repeated until thick non-porous protective film is made on the surface. Normally CO2 results in uniform corrosion. But pitting or localised corrosion can also result under low flow or even at elevated temperature conditions.

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Inhibitors : Acid Corrosion Inhibitors. Generally, corrosion of metals in acidic environment is caused by the electrochemical process which occur on the metal surface and/or at the metal/solution interface. Due to severe environment restrictions, organic chemicals are widely accepted as better acid corrosion inhibitors. The function of these inhibitors is briefly described : (i) Chemosorption of organic molecule on metallic substrate with specific active sites like nitrogen sulphur, oxygen, hydroxyl group or as unsaturation in the molecule. This chemical adsorption constitutes a mono or multinuclear layer on the metal surface which is almost impermeable for ionic exchange. (ii) Complexing of the molecule with metal in which remains in a solid lattice. (iii) Neutralization of the corrodent. (iv) Absorption of the corrodent. The organic corrosion inhibitors which have been proved successful to a desirable extent in preventing corrosion of metals in acidic environments can be categorized in the following groups. These are : (a) Acetylene derivatives and aldehydes. (b) Alkyl/aryl arrives. (c) Sulphur based amide derivatives. (d) Long chain alkyl phenol ethoxylates. (e) Thiazoles/Priazoles. (f) Quaternary ammonium compounds (g) Organophosphorous compounds, and (h) Halogenated aromatics. However, ideal corrosion inhibitors do require certain ideal conditions. In order to fulfill these requirements they should exhibit the following specifications. They should be readily soluble which can easily be dispersed in acids and easy to monitor. At the same time they should remain stable in acids for several days and should not float on bath surface. They should withstand temperature of use without decomposition. No insoluble compounds should be formed with metallic salts. They should fully prevent or atleast significantly reduce the evolution of hydrogen. They should be easily removable from the surface by raising and at the same time hydrogen embrittlement of metals should not be caused. No pitting corrosion should take place as well as they should not be harmful to the environment and should not cause unnecessary pollution. Corrosion inhibition studies have been carried out from time to time. Moreover the subject of corrosion with regard to inhibition deals with engineering and allied technology. The author is specially thankful to the authors of the book on metallic corrosion principles and control published by New Age International Limited Publishers, New Delhi.

References 1. Koryta, J., ‘Ion selective Electrode’s Cambridge University Press, Cambridge (1975). 2. Khosla, N.K., Metallurgical Engineering, Indian Institute of Technology, Bombay-400 076.

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PART B : STABILITY OF METALS 14.3

THERMODYNAMICS AND THE STABILITY OF METALS

The real criterion for deciding the stability of an iron vessel is the magnitude of the rate of its dissolution. If it has a negligible rate of corrosion and sufficient strength, it is considered suitable for the purpose of construction or fabrication in a given environment. TABLE 14.2 Products and Overall Energetics of Spontaneous Corrosion Reactions* Hydrogen type, pH = 1.0 atm 2

Metal

Solid product

Silver Copper

Ag2O CuO Cu(OH)2 Cu2O PbO (red) Ni(OH)2 Cd(OH)2 Fe(OH)3 Fe(OH)2 Fe 3O4 Zn(OH)2(?) Cr(OH)3 Al(OH)3(?) Mg(OH)2

Lead Nickel Cadmium Iron

Zinc Chromium Aluminium Magnesium

Oxygen type, pO2 = 0.21 atm

Free-energy change at 25°C, cal g-mole–1 metal + 27,000 + 24,800 + 27,800 + 9,500 + 11,500 + 7,800 + 600 + 4,700 – 2,260 – 5,020 – 19,240 – 32,500 – 102,570 – 84,000

– 1,080 – 37,450 – 28,300 – 18,600 – 44,600 – 48,500 – 55,600 – 80,000 – 58,500 – 80,000 – 75,200 – 117,000 – 180,700 – 140,000

*F. L. La Que and H. R. Copson, eds., Corrosion Resistance of Metals and Alloys, Reinhold Publishing Corp., New York, 1963 (By courtesy).

Supposing, even before calculating or measuring the corrosion rate; the stability of steel vessel is under question as to whether the Fe → Fe++ + 2e de-electronation reaction and the electronation reaction, which together constitute the corrosion process, proceed spontaneously or not (equilibrium thermodynamics). Using thermodynamics such questions can be answered for example making use of the relation between free energy change and equilibrium potential in order to obtain free energy changes for the electronation and electronation reactions. The sum of the two free-energy changes yields the total free-energy change for the corrosion process

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Δ G = nFV

...(1)

Potential

If this total free-energy change is negative, then the corrosion of the metal will proceed spontaneously. Calculated (Table 14.2) free-energy changes for the corrosion reactions of different metals with hydrogen evolution and oxygen reduction as the electronation reactions. A shortcut approach based on the potential versus pH representation of equilibrium potentials is also available. The approach is as follows: Suppose the Mn+ + ne = M reaction does not involve proton transfer. Its equilibrium potential is then independent of pH and can therefore be represented on the potential pH diagram as a straight line parallel to the pH axis. Fig. 14.1. Next, one considers the electron acceptor A present in the solution which is in contact with the metal M and Potential calculates the equilibrium potential for its reaction. Suppose it does involves a proton transfer as well, i.e., xA + mH+ + ne = yD + zH2O. Since this reaction involves both electron xA +m + H +n transfer and proton transfer, its e = yD + zH2 O equilibrium potential will vary with pH and can be represented as a straight line sloping downward see potential pH diagram Fig. 14.8. Once one has a pH potential diagram with lines drawn for the n+ M=M +ne reaction Mn+ + ne = M reaction and for the xA + mH+ + ne = yD + zH2O reaction, all one has to do is to drawn line perpendicular to the pH axis at the particular value of pH corresponding to that of the solution (see pH last Fig). If that line intersects the pH of solution Mn+ + ne = M line at a more negative value of potential than the xA + mH+ Fig. 14.7 : The potential–pH diagram for the given + ne = yD + zH2O line, then a simple system of the metal-dissolution and electronation conclusion follows. The Mn+ + ne = M reaction reveals the tendency of the metal to corrode. reaction will tend to run spontaneously in the de-electronation direction and produces Mn+ from M, i.e., dissolution, and the other reaction will tend to proceed spontaneously as an electronation reaction (and thus absorb electrons supplied during de-electronation) if a path is provided for the electron flow from the sink for the de-electronation reaction to the source for the electronation reaction. The metal M will be said to corrode spontaneously. On this basis, it is clear from the Fig. 14.8 ahead that, if the solution in the mildsteel reaction vessel contains Fe++ ions at a concentration of unit activity and if the pH = 2, the material of the vessel must tend to dissolve. [It is to be noted that, at higher

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197

pH values, the potential of iron becomes pH dependent. This is because, with increasing OH– ion concentration, the Fe(OH)2 species is formed and controls the potential. Its concentration is of course pH dependent, and the excess ferrous ions originally present are precipitated]. It must, therefore, be rejected as an unsuitable material for holding a pH = 2 solution. Suppose, however, that the solution in the reaction vessel does not contain any ferrous ion. Then what is the concentration or activity that must be inserted in the Nernst expression for the equilibrium potential of the Fe++ + 2e = Fe reaction? What ++

value should be used for CFe in Fe, Fe++/Fe = E0

Fe

++

Fe

+

RT l n C ++ ( Fe 2F

)

The value for CFe+2 is obviously zero, in which case Nernst’s equation for electrode potential of the Fe++ + 2e = Fe equilibrium indicates a value which would be highly negative. Since this potential is negative with respect to the E equilibrium potential of any (volts) possible electronation reac2H ++ tion, the iron will start 2e 0 ++ H2 dissolving and building Fe concentration in the solution layer which is in contact with the electron sink area of the iron. If this layer is stagnant and the Fe ++ ions are not removed by a chemical reaction, e.g., precipitation, the 2+ 2+ Fe Fe +2e(Fe =1) Fe++ concentration will climb –0.441 up from zero clearly, the Fe++ ion concentration adjacent to the metal is determined by the amount of metal which has dissolved, and how fast 1 2 3 pH this diffuses away. How much iron must Fig. 14.8 : The potential–pH diagram for iron immersed dissolve to attain a given Fe++ in a ferrous-ion solution of unit activity. concentration? A ferrous ion concentration of 10–6 mole liter–1 corresponds to the dissolution of about 0.06 mg of iron per liter of solution. Hence a concentration of less than 10–4 mole liter–1, e.g., 10–8 mole liter–1, corresponds to the dissolution of around a microgram of iron per liter of solution in contact with the metal. On the other hand, a ferrous ion concentration of more than 10–6 mole liter–1, e.g., 10–4 mole liter–1, requires the dissolution of a few milligram of iron per liter of solution in contact with it i.e., the dissolution of a significant quantity of iron.

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Fe(OH)2

Potential

In view of these consideration one can adopt an arbitrary, criterion i.e., 2.0 A ferrousion concentration of 10 –6 mole liter –1 and FeO2– 4 higher implies the occurence of “considerable” dissolution, i.e., corrosion. Fe3+ Ox yg 1.0 en l i Putting these considerane tions in background, if conventional in using a potential–pH diagram for Fe2O3 deciding whether a metal 2+ 0 Fe can possibly corrode or not, Hydr ogen to calculate the equilibrium lin e n+ potential for the M + ne = Fe(OH)2 M reaction for a metal ion Fe concentration of 10–6 mole –1.0 liter–1. 0 2 4 6 8 10 12 14 A similar approach like pH corrosion of mild steel vessel not initially containFig. 14.9 : Example of potential–pH diagram for a system ing Fe++ ions can be used with a solid phase as a dissolution product. to inspect the potential–pH diagrams of other metals to decide whether they also tend to corrode spontaneously or not a solutions of a given pH.

14.4 POTENTIAL–pH (OR POURBAIX) DIAPHRAGMS: USES AND ABUSES It must not be imagined that the ultimate product of the metal dissolution reaction is always an ionic species, e.g., M → Mn+ + ne. Often it is a solid oxide or hydroxide. From the free energy considerations, one can calculate the reversible potentials for a metal that is in equilibrium with its simple hydrated ions or with its soluble product of hydrolysis or with its insoluble oxide. Such calculations give set of data (Table). Potential–pH diagrams are useful in this respect too. Potential and pH conditions are indicated under which a solid product is thermodynamically stable. Fig. 14.9. The regions of the potential–pH diagram in which oxide or hydroxide formation receives thermodynamic approval arise as follows: Considering the case of iron and assuming, that the immediate product of iron dissolutions is ferrous ions. The solution in contact with iron can dissolve ferrous ions only up to the limit which is given by applying the law of mass action to the reaction Fe(OH)2 + 2H+ = Fe++ + 2H2 O

...(1)

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199

According to the Law of Mass Action, for a constant concentration of Fe(OH)2 in equilibrium in a solid phase, CFe++ C2 H+

= K = 10 + 13.29

...(2)

or by CFe++ = 2log CH+ + 13.29 = 13.29 – 2pH

...(3)

++

If, as before, the minimum concentration of Fe ions corresponding to a piece corroding iron is arbitrarily taken as 10–6 mole liter–1, then pH =

13.29+6 = 9.6 2

which means that above a pH of 9.6, Fe(OH)2 is stable. Since the Fe(OH)2/Fe++ a equilibrium depends only on pH and not on potential i.e., it is a pure proton transfer reaction and does not involve electron transfer. The Fe(OH)2/Fe++ equilibrium is shown the potential –pH diagram as a vertical line parallel to the potential axis (Fig. 14.10) Above the indicated pH value, the concentration of Fe2+ ions is governed by the equation: log CFe++ = 2 log.CH+ + 13.29 ...(4) = 13.29 – 2 pH hence, the potential changes with increasing pH with a slope of RT/F. The question of how the corrosion of a metal is affected by the formation of a solid product of the dissolution reaction is rather complex. It is important however, that whereas the potential –pH diagram indicates that a particular hydroxide, e.g., can be formed only above a certain pH value. It is experimentally observed that the hydroxide is formed when the electrode is immersed in a solution with much lower pH value. This apparent contradiction 2.0 arises (1) because the FeO42– values of pH in a potential–pH diagram Fe 3+ 1.0 O x y g e n li ne always refer to the solution in the immediate vicinity of 0 F e 2O 3 the electrode and Hy d ro g e n l ine (2) because the local F e (O H )2 )2 OH pH near an electrode Fe ( can increase well above the bulk pH of –1.0 the solution if the 0 2 4 6 8 10 11 12 14 electronation reaction takes place at the Fig. 14.10 : Example of potential –pH diagram for a system electrode consumes with a solid phase as a dissolution product.

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hydrogen ions (e.g., 2H+ + 2e → H2) or generates hydroxyl ion (e.g., O2 + H2O + 4e → 4OH–). Therefore, in conclusion, potential–pH diagrams can be used to answer whether a particular corrosion process is thermodynamically possible or not. A compact pictorial summary is provided in diagrams indicating electron transfer, proton transfer, and electron and proton transfer reactions which are favoured in thermodynamic grounds when a metal is immersed in a particular solution. An example of lead is taken in contact with aerated water. The potential–pH diagram shows the equilibrium potential for the Pb++ + 2e = Pb reaction for a Pb++. Concentration of ~ 10–6 g liter–1 to be negative with respect to the equilibrium potential for the hydrogen reduction reaction at a pH less than about 5. This implies the tendency for lead to corrode in an aerated aqueous environment. In fact the rate of corrosion is so negligible that lead is used in pipes for carrying water.

14.5 ELECTRONATION REACTION IN CORROSION

Potential

A very important aspect of 2.0 the corrosion of metal ? concerns the electronation –6 reaction required to PbO 2 0 complete the corrosion –6 circuit by consuming the O xyg e n lin electrons transferred to the 1.0 e metal from the metal? 0 dissolution reaction. To Pb++ Pb3O 4 answer the question as to ? what is the electronation –6 H yd r og e n (cathodic) reaction? Theorel in e PbO 0 0 tically, “it can be any reaction with an equili–6 brium potential which is –6 more positive than the equilibrium potential of the Pb –1.0 metal-dissolution reaction. 0 2 4 6 8 10 12 14 In practice, it is a reaction pH of the type : A + ne = D, where A is an electronacceptor species present in Fig. 14.11 : The potential–pH diagram for lead. the electrolyte which is in contact with the corresponding metal. Considering the aqueous electrolytes, the electron acceptors invariably present are H3O+ ions and dissolved oxygen, and the corresponding electronation reaction being 2H3O+ + 2e → 2H2O + H2 [acid solutions] and

O2 + 4H+ + 4e → 2H2O

[acid solutions]

Corrosion

or

201

O2 + 2H2O + 4e → 4OH–

[alkaline solution]

The electrolyte may also contain species such as Fe3+ ions or nitric acid, in which case there can be additional electronation reaction of the type:

or

Fe3+ + e → Fe2+

...(5)

3H+ + NO −3 + 2e → HNO2 + H2 O

...(6)

The possibility where several electronation reactions are possible, i.e., their equilibrium potentials are positive with respect to the metal dissolution equilibrium potential. In such a case the one which yields the highest corrosion current is preferentially adopted. There is no new principle here; when parallel reactions can occur, the current is controlled by that reaction which yields the largest current corresponding to the given potential. This point is very clear when the increase in corrosion rate of iron in oxygenated solution. Compared with that in a deoxygenated one i.e., the rate in the latter case is decided by the 2H3O+ ± 2e = 2H2O + H2 electronation reaction while in the former case it is determined by oxygen reduction. The higher the pressure is of oxygen in gas phase, the higher is corrosion rate. This is due to the solubility of oxygen in the electrolyte is proportional to pressure. TABLE 14.3 Effect of Oxygen Pressure on Corrosion Rate of Iron in 3

1 % Sodium Chloride Solution 2

Oxygen pressure, atm 0.2 1 10 61

Corrosion rate, mmn–1 2.2 9.3 86.4 300

Upon addition of dilute nitric acid, the corrosion rate is increased even more because of the occurrence of reaction involving nitric acid.

14.6

THE CORROSION CURRENT AND CORROSION POTENTIAL

Considering a system consisting of a metal corroding is an electrolyte, the corrosion process involves a metal-dissolution de-electronation reaction at electron-sink areas on the metal and an electronation reaction at electron source areas. This is applicable to a metal’s corroding by a Wagner Traud mechanism. It has also been pointed out that the corroding metal, is equivalent to a short circuited energy producing all with the following specifications : (1) The electron sink (anodic) and electron source (cathodic) areas of the equivalent energy-producing cell are chosen equal to the corresponding areas on the corroding metal. Thus, the total metal-

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dissolution current IM and electronation current I S0 (not current densities) on the corroding metal are equal in magnitude but opposite in sign, just as they are in an energy producing cell. IM = I S 0

...(7)

The rate of corrosion of the metal is obviously given directly by the rate of metal dissolution. Hence the corrosion current Icorr is equal to the metal-dissolution current IM : Icorr = IM = – I S 0

...(8)

This is an important feature of a corroding system. However, there is another feature of a corroding system. This arises from the short-circuit condition of the corrosion cell and of the equivalent cell (Actually, it can be recalled that the electron sources and the sinks in the corroding metal are internally short-circuited, and the two electrodes in the equivalent to all are externally short-circuited). Hence the total potential difference V across the equivalent cell is zero. But this cell potential is composed of the absolute potential difference across the interfaces at the two electrodes and the potential drop IR in the electrolyte : V = 0 = Δφ S – Δφ M + IR ...(9) 0 Since both electrodes consist of the same metal, no potential difference arises owing to metal-metal contact. Thus when IR = 0, the potential Electron-source area difference across the metal-electrolyte Corroding interface at the electron-source electrode metal of the short-circuited equivalent cell is Glass walls virtually equal to that at the electronof probe sink electrode. The validity of the assumption IR = 0 in the corroding metal could be Electrolyte suggested that if the metal is homogeneous and is corroding according to Wagner-Traud mechanism, the sink and source areas are separated at any Area ‘seen’ by Electron probe ines one instant by a distance of the order of sinks sinks and sources a few angstroms. Further, the sink and source areas are shifting around and therefore smearing out the negligible Impurities potential difference in the solution adjacent to these areas. Thus IR = 0 is Fig. 14.12 : In heterogeneous systems, the quite true. distances between source (e.g., metallic inclusions) The validity of IR = 0 depends upon and sink points are so small that a probe cannot the separation of sink and source areas usually detect any potential difference in the and upon the conductivity of the electrolyte between them.

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203

electrolyte, when the metal has heterogeneties and is corroding by local cell action. This happens in special circumstances in which the distance apart of sink and source areas is to be considered (of the order of centimeters). Under these situations, IR = 0 and ΔφS 0 = Δφ M , implies a difference in the metal electrolyte potential difference at electron source and sink areas. Generally, the sink to source distance is of the order of microns or even less i.e., the conducing path in the solution, hence IR becomes negligible. Thus, the Δφ S is virtually equal to Δφ M , and any negligible difference that exists occurs over 0 distances which are too small to be resolved by a probe used to measure the potential difference between the metal and the solution. This uniform potential difference across the interface between a corroding metal and its electrolyte environment may be termed the corrosion potential Δφ corr. This is given by the expression: Δφ corr = Δφ S = Δφ M ...(10) 0 It, therefore, follows that the corrosion potential on a heterogeneous metal according to local cell action is virtually equal to the mixed potential at an electrode on which electronation and de-electronation reactions are occuring on separated sinks and sources by space. This is identical to a mixed potential when the metal is corroding by a WagnerTraud mechanism.

14.7 THE BASIC ELECTRODICS OF CORROSION IN THE ABSENCE OF OXIDE FILMS Firstly, the rate of corrosion, a quantity of great practical significance is given by the corrosion current Icorr which is equal to the metal dissolution, de-electronation current IM and to the negative of the electronation (cathodic) current I S0 at the electron source areas, i.e., Icorr = IM = – I S0

...(11)

The equation can be written as Icorr = IM = AM iM

...(12)

Since the metal dissolution current is equal to the product of the corresponding current density IM times the sink area AM and similarly, Icorr = – I S0 = – AS0 iS0

...(13)

Secondly, there is a uniform potential difference, e.g., the corrosion potential Δφ corr, all over the surface of the corroding metal. It is this corrosion potential which is associated with both the metal-dissolutions and electronation currents, i.e.,

Δφ corr = Aφ M = Δφ S

0

...(14)

In order to obtain quantitative expression for the corrosion current and the corrosion potential the proper expression for the metal dissolution and electronation current densities have to be substituted. In case when no oxide film is formed on the surface of the corroding metal and neither of the current densities is controlled by mass transport,

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it means that there is no concentration over potential, the Butler-Volmer expression for the de-electronation and electronation-current densities can be inserted. Thus, Icorr = IM = AM iM

...(15)

Also, it could be written for the relation between the corrosion current and the electronation current at the electron source area as : Icorr = – I S

0

...(16)

After elaborating the expressions and solving the equations it is made clear that the corrosion current depends upon the exchange currents (i.e. available areas and exchange current densities). The dependence of the corrosion current (the rate at which a metal destroys itself) on the exchange currents, Tafel slopes and equilibrium potentials of the metal-dissolution and electronation reaction is clearly brought out by solving the mathematical expressions. In general, the more positive the equilibrium potential of the electronation reaction is with respect to the equilibrium potential for the Mn+ + ne = M reaction and the larger the exchange currents (areas times exchange current densities) are, the greater is the rate of corrosion. The Tafel slopes also enter in the picture. A such high slopes diminish the enhancing effect which the exponential term has on the rate of the corrosive attack on the metal.

14.8 FACTORS AFFECTING THE RATE OF CORROSION AND EVANS DIAGRAMS Most of the factors affecting the rate of corrosion can be understood from the graphical presentation of the current-potential curves for the metal dissolution and electronation reactions. Considering the metal-dissolution reaction Mn+ + ne = M, A curve could be constructed as in Fig. 14.13 for the variation of potential of an electrode. M with the de-electronation current crossing the electrode-electrolyte interface. Such a curve could be obtained either experimentally or from a knowledge of the parameters which determine the overpotential associated with the de-electronation current density. For concentration overpotential, this parameter is the limiting current density. And, for activation overpotential, the parameters are the exchange-current density and the transfer coefficients. If on the same diagram, one can superimpose a curve for the variation of the potential of the M electrode. With the current associated with the electronation of electron acceptor present in the electrolyte. The current at which the metal dissolution and electronation are equal is, in fact, the corrosion current. Fig. 14.14. The potential corresponding to the corrosion current is the corrosion potential. Evans type of diagrams Fig. 14.15(a, b) could be obtained if only the magnitude of the de-electronation and electronation currents are used in the construction of Δφ versus I curves.

205

Potential, Δφ

Corrosion

M → Mn+ +ne

Δφ e,M

Metal dissolution current, I

Fig. 14.13 : The potential–current relation for the metal-dissolution reaction.

Positive potential

Δφ e,s0 Δφ corr

x A + m H ++ n e→ → y D + z H2O

Is 0

IM

M → M n++ n e

Δφ e,M

–I

Electronation current

De-electronation current

+I

Fig. 14.14 : The potential-current relation for the two reactions occurring at a corroding interface. The corrosion current and corrosion potential are defined by the point on the diagram at which the two currents IM and IS are equal. 0

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Actually, the Evans diagram obtained depend upon the current-potential curves for the metal dissolution and electronation reactions. Some of the common diagrams are, shown in Figs. 14.16–14.18. In these diagrams the exchange current for the metal dissolution reaction is much greater than that for the electronation, i.e. I >> I or in which I0,S0 >> I0,M. Evans diagrams can also be used to bring out the influence Tafel slopes. The influence of equilibrium potentials can be seen in Fig. The effect of mass transport control into electronation current from Figs. 14.15(a, b); also 14.17(a & b) & 14.18 ahead. The effect of an IR drop in the electrolyte between the electron-sink (anodic) and electron source (cathodic) areas can also be represented in an Evans diagram Fig. which then shows the inequality of the metal solution potential difference at the two areas, i.e., the anodic (or de-electronation) and the cathodic (or electronation areas).

14.9 SOME COMMON EXAMPLES OF CORROSION In this section some electrodic principles underlying some familiar instances of corrosion are being cited. In most cases, it is expected that the unprotected metal beneath the broken point spot (mostly in automobiles) which corrodes. The exposed metal has a better access to oxygen than the metal still covered with paint and is therefore the electron-source area. Actually it is the adjoining metal underneath the paint coating which corrodes. The situation is much worse since having a break in paint coatings which Moist Atmosphere lead to spreading of corroded area rather than to a restriction of corrosion to the exposed spot Fig. 14.19. O2 Paints and coatings of various kinds, as such are only partially useful in corrosion prevention. Often cracks or n+ M n+ M pinholes are developed resulting in exposed spots providing Paint access to oxygen giving rise to electronation reaction. This results in unseen corrosion of surrounding areas. Consequently, electronation reaction takes place due Metal to oxygen reduction and this known as the “principle of differential aeration”. To clarify the oxygen electronation Corrosion tends to occur at the oxygen rich area and the metal dissolution tends to occur at the oxygen poor area. In such cases the oxygen rich areas act as electron-sources (cathodes) and the oxygen-starved regions as electron sinks Fig. 14.19 : As the paint (anodes). Thus owing to the diffusion of oxygen on metal coating is damaged, the surface, a corrosion cell is produced in which electron source corrosion couple is established and sink areas are spatially separated. with the metal dissolving at Apart from corrosion due to differential aeration, the edges underneath the corrosion of underground metal structures and pipelines coating, while the exposed may also arise from stray currents. part is the place for the The presence of a current carrying cable in conducting electronation of oxygen (and soil results in stray currents passing through the soil. These thus not that which dissostray currents may set up a potential difference between lves).

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209

two portions of a pipeline. Therefore, an electron-source (cathodic) and sink (anodic) areas are developed and thus the pipelines tend to corrode when they pass near electric lines.

14.10 CONTROL OF CORROSION CURRENT IN THE CORROSION PROCESS On examining the Evans diagram, Fig. 14.15(a) it is observed that the corrosion current is controlled by the electronation (cathodic) reaction and as such the corrosion process is under electronation i.e., cathodic control. This is when I0M >> I0, 0. In another situation, i.e., I0, S0 >> I0,M it could be indicated that de-electronation (anodic) control takes place. It is also possible to have mixed control situation over the corroding system when the corrosion current is controlled by both the de-electronation and electronation reactions. It could also be called an ohmic control, where the corrosion current is determined by the IR drop in the electrolyte. The corrosion process can be looked upon as a consecutive reaction consisting to the following four steps say : (1) de-electronation, (2) electron flow in metal, (3) electronation, and (4) ion flow in the electrolyte. When a consecutive reaction attains a steady state, the net currents associated with the various steps are equal to each other and also equal to overall current. Considering the case of corroding metal, the overall current is the corrosion current and therefore: Icorr = IM = IS0 = I = Ii (where Ie and Ii are the currents due to electron. How in the metal and ion flow in the electrolyte.) Despite the equality of the currents in the various steps, the overall current in the consecutive reaction may be controlled by one of the four steps. One is left with the possibility of the three rate controlling steps. It is because the electronic conductivity of the metal will be high enough to prevent electron flow in the metal from controlling the corrosion current. It is in this way that the corroding system becomes subject to deelectronation control or electronation control or control by ion flow in electrolyte (i.e., the ohmic control). In order to identify the type of control over the corrosion current, one should know the rate-determining step in a multistep electrodic reaction.

14.11 VARIOUS FACTORS IN DETERMINING CORROSION First and foremost, is the fact that corrosion depends a great deal upon the particular metal involved. Sodium e.g., corrodes vigorously in aqueous solution and considerable heat is evolved, sparks are produced and the evolved hydrogen explodes. On the other hand gold does not corrode at all and hence its stability is the main reason for its used as a monetary standard. The standard equilibrium potential for the Na+ + e = Na reaction extremely negative (–2.71 V) with respect to the equilibrium potential of either the hydrogen evolution or oxygen-reduction reaction.

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For gold, the standard equilibrium potential for the reaction Au+++ + 3e = Au reading is +1.50 V. This is more positive than the equilibrium potential of either the hydrogen evolution or oxygen reduction reactions. Hence, if there is unit activity of ions in solution, gold cannot corrode. When metals are arranged according to decreasing standard electrode potentials, a table thus yields what is called the electrochemical series. All metals with E 0 values of negative with respect to hydrogen, which has an E 0 of zero, are known as “base metals” and are expected to corrode spontaneously. However, the corrosion rate is a question of kinetics and may prove to be negligible e.g., lead. Metals with positive E° values are known as “noble” metals and are in corrodible in deoxygenated solutions of pH = 0. The influence of air and pH upon the rate of corrosion of a metal is linked up with the fact that hydrogen evolution and oxygen reduction are the most common electronation reactions in corrosion. Whether oxygen reduction or hydrogen evolution becomes the predominant electronation reaction depends on several factors for instance. 1. The equilibrium potential for oxygen reduction : O2 + 2H2O + 4e = 4 OH– is given by ...(17) Ee . O2 /OH = 1.23 – 0.059 pH whereas that for hydrogen evolution 2H + + 2e = H2 is given by E

e

+

2

= – 0.059 pH

...(18)

Electrode potential

the former is always 1.2 V more positive than the latter Fig. 14.20 in a solution of the same pH. Since one of the factors determining the corrosion rate is m slope = – 2.303RT the difference between the n F equilibrium potentials of the aAx m E=E°+ 2.303RT log – 2.303RT pH electronation reaction at the aDy n nF F electron-source area and of the metal dissolution reaction. It is expected that the oxygen reduction reaction would always be preferred, the point being that thermodynamics is on such a side. 2. Kinetics generally favours the hydrogen-evolution reaction. The exchange-current densities for hydrogen evolution on the pH corrodible metals are generally Fig. 14.20 : The equilibrium potential for a reaction many order of magnitude higher involving H+ or OH– ions for any concentration ratio of than the exchange current acceptors and donors depends linearly on pH. densities for oxygen reduction.

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211 2

Taking the case of iron, the i0 for hydrogen evolution is about 10–14 < amp–cm . Thus in highly acidic solutions, hydrogen evolution is the preferred reaction. 3. The situation may be reversed as the pH increases. The main reaction for this reversal is that the exchange-current densities for hydrogen evolution reaction depends on the hydrogen ion concentration. This is it so long as the solution is sufficiently concentrated. As the pH increases, the hydrogen ion concentration decreases and so does the exchange-current density for hydrogen evolution. It is therefore concluded that the predominating electronation reaction depends upon the pH. Hydrogen evolution generally has a substantial role in highly acid reactions. But in neutral or alkaline solutions, oxygen reduction plays a predominant part in the reaction. 4. The oxygen molecules required for the oxygen electronation reaction originate from dissolved air. The solubility of oxygen in water is of the order of 10 –4 mole liter–1. This is quite a low concentration and implies that the limiting current density for oxygen reduction is of the order of 10–5 amp cm–2 in unagitated aqueous solutions. Hence when the electronation of oxygen molecules is the reaction associated with metal dissolution in a corrosion process. The transport of oxygen to the metal causes the maximum corrosion rate to be the value given by the limiting current density for oxygen reduction. Consequently, in such a situation of oxygen-reduction control, agitation of the solution is which corrosion is taking place leads to an increase of the limiting current for oxygen reduction and therefore to an increase of the corrosion rate. TABLE 14.4 Effect of at Atmospheric Temperatures*

Material

Acid

Mild steel Lead Copper Tin Nickel

Sulfuric Hydrochloric Hydrochloric Sulfuric Hydrochloric

N 1.2 1.1 1.1 1.2 1.1

HydrogenOxygensaturated acid saturated (no oxygen) acid Corrosion rate, mm yr–1 31 17 17 9 6

358 163 1380 1100 440

* F. L. La Que and H. R. Copson, eds., Corrosion Resistance of Metals and Alloys, Reinhold Publishing Corp., New York, 1963.

illustrates the extent of the effect that hydrogen and oxygen electronation reactions have on the rate of corrosion of different metals in different acid media.

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PART C : PASSIVATION 14.12 PASSIVATION : TRANSFORMATION FROM A CORRODING AND UNSTABLE SURFACE TO A PASSIVE AND STABLE SURFACE One of the ways of protecting a metal from corrosion is when the double-layer field is altered in such a way as to diminish the metal dissolution reaction which results in corrosion. The fact is that the unstable surface of an actively corroding metal can sometimes, be made passive and stable by increasing the potential in the positive direction. This of course depends on the metal and the solution conditions. When a metal is to be tested for corrosion, a piece of corrodible metal, the test electrode, is immersed in an electrolyte along with two other electrodes. One of these is non polarizable reference electrode and the other, an auxiliary electrode. An electronic device “Potentiostat is used for the purpose Fig. 14.21. The potentiostat measures the potential V of the test electrode under study and compares this with the selected value V* from the potential source (in the potentiostat). Actually, the, potentiostat controls the rate of charge transfer reactions at the metal-solution interface. By increasing the de-electronation or electronation current, pushes the electrode potential in the positive or negative direction to the pre-selected value. The use of potentiostat facilitates enables one to hold the potential of the electrode at chosen values and make measurements of the steady-state current density at each value of the potential. Different metals exhibit different passivation potentials e.g., see Table 14.5. Potentiostat Potential source

+ –

V V

I Ref electrode

T e s t Auxiliary electrodes

Fig. 14.21 : In a potentiostatic circuit, an imposed potential difference V * drives the current from the auxiliary electrode to the test electrode till the potential difference V becomes equal to V *, so that the total input into the potentiostat falls to zero.

Corrosion

213

Once the metal is passivated, the currents which flow are negligible. Usually 100 to 1000 times less than the dissolution current at the maximum in the current potential region in which the corrosion current increases with increasing potential. For all purposes, corrosion has ceased and the metal has been anodically protected. This is done by pumping electrons away from the metal instead of pumping electrons into the metal, as in cathodic protection. TABLE 14.5 Approximate Passivation Potentials of Some

Meta V, N-Hydrogen Sca Gold Platinum Iron Silver Nickel Chromium Titanium

+1.36 +0.91 +0.58 +0.40 +0.36 –0.22 –0.24

This method of stabilizing a metal is largely used in large tanks used for storing oil containing water and are acidic.

14.13 THE MECHANISM OF PASSIVATION On considering the enforced passivation of nickel in acid solution, it turns out that there comes a critical potential at which a film of Ni (OH)2. Suddenly forms on the metal surface. This film formation, cannot explain passivation because it occurs at potentials negative to the passivation potential. This film that is formed is called a prepassive film. It is, therefore, concluded that the mechanism of enforced passivation of nickel in acid solutions consists of the formation of a passive film at potentials negative to the passivation potential. This film is a necessary condition of passivation, though not sufficient. The passive film has to become an electronic conductor. In cases of spontaneous passivation if a metal is corroding spontaneously at a rate less than the minimum current density, it will corrode – and corrode. But suppose the dissolution–current density is greater (during corrosion) than the minimum current density, then a film will form by a dissolution precipitation mechanism and thus the metal will passivate spontaneously. Explanation for well-known fact that iron corrodes drastically in dilute nitric acid but becomes protected by a passive film in concentrated nitric acid.

14.14 THE THERMODYNAMICS OF PASSIVATION An important conclusion that is drawn on discussing the phenomenon of passivity is that the surface of a metal can under the appropriate environmental conditions be

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Potential

covered with oxide films. The potential pH diagrams Fig. 14.22 for metals indicate the conditions for the stability of a metal immunity from corrosion, of Corrosion ? its ions (corrosion), and its oxides the possibility of passivation. An important point is to be borne in Passivity Corrosion mind to understand oxide for while using possible potential–pH diagrams to understand oxide-film formation on electrodes. Also, Corrosion it is important to note that it is only the pH of the solution which is adjacent to Immunify the electrode which is relevant and not the pH if the bulk solution. Thus, e.g. the pH adjacent to an electron-source pH electrode may be increased to 9 by the removal of Hydrogen ion (2H+ + 2e → Fig. 14.22 : Complete potential–pH diagrams indicate the conditions of oxide formation at the H2O), whereas the bulk pH remains 3. surface which is a precursor to passivity. As such the potential–pH diagram must be examined at a pH of 9 and not at a pH of 3. The oxide formation does not necessarily imply passivation unless the oxide, films have the right properties i.e., the electronic conductivity. In such case only they can serve as excellent inhibitors of corrosion. The films must also satisfy other requirements too i.e., (i) The protective oxide films must be mechanically stable, (ii) they must not flakeoff or crack. and (iii) the films must be continuous. The corrosion, cells can be set up, if they are porous or full of pinholes. The cathodic reduction of oxygen could be one reaction occuring on the oxide, and metal dissolution, in the pores.

14.15 ROLE OF HYDROGEN IN CORROSION (i) Diffusion into a metal Sufficient emphasis has been laid as the fact that the instability of metal surfaces arises from an electrodic mechanism. In such a case an electronation reaction teams up with the metal-dissolution reaction to keep numerous micro corrosion cells running. Thus electrodic charge transfer reactions at the surface have far reaching implications for the strength of bulk metals. Considering a corroding metal where the hydrogen evolution be the electronation reaction. In the electrodic evolution of hydrogen, the formation of hydrogen atoms adsorbed on the metal surface is an essential intermediate step in electrodic evolution of hydrogen. But there is also a way in from the surface where the adsorbed hydrogen atoms can dissolve into the metal to form absorbed hydrogen. Since one has started off with zero concentration of absorbed hydrogen inside the bulk of the metal, a gradient of hydrogen concentration develops between the surface (where hydrogen enters) and the interior of the metal. It is this concentration gradient which makes the adsorbed hydrogen to

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215

diffuse into the metal. Thus the diffusion of hydrogen in the bulk of the metal is a fairly fast process. The penetration of hydrogen into the interior of a metal is quite simple. A thin metal membrane separates two vessels containing an electrolyte. Hydrogen is electrodically evolved on one side. The potential difference across the other membrane electrolyte interface is adjusted for the de-electronation (or ionization of any absorbed hydrogen: H ads → H+ + e, coming through the metal from the entry side of the membrane. Thus, the ionization current is the manifestation of the hydrogen penetration through the metal membrane from the surface on which hydrogen is evolved.

(ii) Preferential Diffusion of Absorbed Hydrogen to Regions of Stress in a Metal In a polycrystalline material, it is considered that the grain boundaries are irrigation channels for the diffusing hydrogen yet it is found that the diffusion coefficient for hydrogen is the same for polycrystalline and single crystal ion. Thus, the hydrogen would be diffusing through the lattice interstitial diffusion. When a hydrogen atom occupies an interstitial site, there is a certain displacement of the atoms around the interstitial atom. It appears that some atoms moved apart a little to accomodate the interstitial hydrogen atom. Hence it is expected that there is same change in volume due to the entry of hydrogen atom into the lattice. The net change in volume so resulting due to one gram atom of hydrogen, is the partial molar volume of hydrogen in the metal.

CHAPTER 15

CONVERSION AND STORAGE OF ELECTROCHEMICAL ENERGY SECTION A 15.1 PRESENT STATUS OF ENERGY CONSUMPTION: The thermal combustion of coal, oil and natural gas have been the main sources of energy which is being consumed by man. What is being consumed is energy capital and not energy income, and, therefore, a day might come when the reserves of fossil fuels are exhausted. Specially, the easily transportable and usable oil and natural gas. It is also important that, in energy conversion, the efficiency of the process of the thermal combustion of these fossil fuels be critically examined. The energy is produced when fossil fuels undergo chemical reaction with oxygen, at first in the form of heat. This is then converted in an engine to mechanical energy. The conversion of mechanical to electrical energy is a process in which the efficiency of conversion is almost unity. Hence it is the conversion of the heat energy given out in the chemical reaction of combustion to mechanical energy or work. The essence of heat engine is a piston or turbine rotor which is forced to move by the expansion of a gas. This actually occurs as a consequence of a rise of temperature due to heat given out in the chemical reaction taking place between the fuel and oxygen. The combustion process can take place either (i) outside the engine or (ii) inside the engine. In case (i) that is in an external-combustion engine, the fuel is burned outside the engine and the heat generated is transformed to the so-called “working substance”. This is then conducted into the cylinder or turbine and is allowed to expand. This then produces mechanical work. The example of such an external combustion engine is the steam engine, the essential instrument by which man made machines work for him. This has been continuing since nineteenth century. In the second case (ii) that is in the internal combustion engine, an approximate mixture of air and the fuel for example the hydrocarbon mixture gasoline is either ignited inside the cylinder by an electric spark or compression or continuously burned inside a gas turbine. The expansion of the gas there is due to the heat given out in the reaction of hydrocarbon and oxygen to carbon dioxide causes the piston or the rotor to move. The internal-combustion engine has been the basis of the transport revolution of the twentieth century. At present, electricity is generated mostly by utilizing mechanical energy from the external and sometimes the internal combustion of fossil fuels to drive generators.

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There is a common feature to both the external and internal combustion engine is: that the chemical energy contained in the fuel in first converted into heat and then this heat energy is used to produce mechanical power through the force associated with the expansion of a heated gas. Actually heat is essentially an intermediate form of energy in the conversion to mechanical work of the difference between the energy of the reactants and that of products in chemical reactions, hence its conversion by the generator to electricity. Spontaneous reaction between the two substances. The storers take in electricity when an electric current is passed through them from an outside source and give back electricity when required by allowing to run spontaneously in the forward direction the reaction which had been made to go backward during charging. In converters or so to say generators, the cost of substances undergoing reaction the fuels is of importance. It determines the cost of electricity and power produced. The cost of substrate by which the reactions are catalyzed is also of great importance in determining the initial cost of the converter. In storers, the cost of the substances undergoing the reactions at the electrodes determines the initial cost of the device but it only secondarily influences the cost of the electricity given back from the storage.

15.2 STATUS OF ENERGY CONSUMPTION Pollution Problems Some direct negative results arise from the present predominant form of energy conversion. (a) Products of combustion other than carbon dioxide. Gasoline and diesel oil which is being used in present internal combustion engines do not undergo 100% conversion to CO2. The organic compounds remaining incompletely burned are several dozens in number and include particularly unsaturated compounds. Oxides of carbon, nitrogen, sulphur and a lead containing compound [from the Pb (C2H5)4 added to fuels to break up chains in the combustion reactions] are also present in significant amounts. However, it is known that certain of these organic compounds undergo a photochemical reaction of oxides of nitrogen to produce a complex addition compound which is the origin of smog. Evidence suggests that some of the compounds from automobile exhausts are carcinogenic. The production of smog is favoured for production of smog are sunlight and a large concentration of exhaust gases like oxides of nitrogen and the unsaturated compounds from automobiles. Smog conditions would be expected to threaten many urban areas. Carbon Dioxide–This gas is an inevitable consequence of the method of obtaining mechanical energy by burning coal and oil. Absorbs radiant energy in the infrared. The temperature of the earth’s atmosphere is the net consequence of a number of influences which include the amount of solar radiation reflected back to space. The greater the concentration of CO2 in the atmosphere, the less of this reflected energy escapes. i.e., the more is stored in the earth’s atmosphere. The energy thus absorbed degrades to heat. All other things being equal, the average temperature of the atmosphere is expected to increase.

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Uncertainties in Predicting the future Pollution of the Atmosphere An assessment of the problem of time dependence of the growth of atmospheric pollution is difficult because of the unsaturated compounds produced in internal combustion engines and their distribution in the atmosphere. Whatever be the consequence predicted for the increase in carbon dioxide concentration resulting from burning hydrocarbons, they would seem to be difficult.

Thermal-Combustion Engines Waste the Chemical Energy Available from Burning the Hydrocarbons in Air Suppose that combustion engines can be so modified in design so that they do not pollute the atmosphere and even the effects of the absorption of reflected solar energy by CO2 can somehow be significantly delayed so that internal combustion could continue to be used till the end of the present century.

15.3 DIRECT ENERGY CONVERSION BY ELECTROCHEMICAL MEANS A chemical reaction produces heat which causes a gas to expand and thus push forward a part of a machine. This machine then drives another which produces the electricity. It would be preferable to attempt to devise a means of converting directly to electricity the energy released during most chemical reactions without involving a second machine and also preferably without moving parts for these are subject to erosion and mechanical failure. Several such methods, called direct energy-conversion methods, have been known since past. Compared with the conventional method, the present methods represent an improvement and give rise to much modern interest. However, rather than direct energyconversion methods, a better term would be direct heat to electricity conversion. What actually needed is a method in which the energy released in chemical reactions is indeed converted directly to electricity without moving parts, but also in a way which avoids the loss of energy due to the intrinsic Carnotlenitate.

15.4 DIRECT ENERGY CONVERSION BY ELECTROCHEMICAL MEANS Of the three types of electrochemical systems that are known, the energy producer, is a spontaneously working self-driving electrochemical system Fig. 15.1. In it there is a spontaneous occurence of a de-electronation reaction at the electronsink electrode and an electronation reaction at the electron-source electrode. If an external load is connected to the two electrodes, a current electrons flows in the external circuit. Thus, the electrode reaction at the two electrodes bring about the conversion of the difference in the chemical energy (Gibbs free energy) of the reactants and products directly into a flow of electricity (and thereafter, by a motor, to mechanical energy). There is no intermediate step in which the energy has to bring itself to power by expansion of a gas converting thereby only part of its thermal energy to mechanical work.

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Load e

e + OI ← R I

Electron sink electrode Solution

RII←O II+e

Electron source electrode

Fig. 15.1 : Schematic diagram of an electrochemical energy producer.

15.5 THE MAXIMUM INTRINSIC EFFICIENCY OF AN ELECTROCHEMICAL CONVERTER An essential thermodynamic equation is recapitulated e.g., – Δ G = Wrev – PΔ V

...(1)

This means that the change in free energy in a reaction is equal to the total reversible work obtainable from the reaction. This includes all kinds of work i.e., gravitational, electrical, surface, etc., and also the work of expansion diminished by the work of expansion, PΔ V. Hence – Δ G = W′ rev ...(2) where W′ rev stands for all the work obtainable from the reaction exclusive of any work which can be obtained from a possible volume change in the system. If a chemical reaction is carried out in an electrochemical way, then in the example of the reaction: 2H2 + O2 → 2H2 O there will be two partial reactions 2H2 → 4H+ + 4e

...(3) ...(4)

+ 4e → 2H2 O ...(5) In fact after carrying out the over all reaction 2H2 + O2 → 2H2O and hence, the normal change of free energy associated with this reaction at a given temperature and pressure has occurred.

and

O2 +

4H+

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15.6 THE ACTUAL EFFICIENCY OF AN ELECTROCHEMICAL ENERGY CONVERTER It has been already shown in the previous section that in an electrochemical energy converter, the maximum cell potential is the value Ve obtainable when the reaction in the cell is electrically balanced out to equilibrium. This means that no current is being drawn from the cell. As soon as the cell devices a current through the external circuit, the cell potential falls from the equilibrium value Ve to V. The value of the actual potential V at which the cell works when delivering a current i is always less than the equilibrium potential Ve Hence from equation: Emax = E0 =

ΔG −nFVe , =− ΔH ΔH nFVe V Δ H Ve

...(6)

...(7) or E0 = Emax Ep where Emax is the maximum efficiency given by the above equation* and Ep is known as the voltage efficiency given by Ep =

V Ve

...(8)

The picture is true if the overall reaction is fully accomplished and none of the electrons take part in some alternative reaction. Considering the current or faradaic efficiency Ef into account the incomplete conversion of reactants into products. The overall efficiency is then given as : E0 = (Emax Ep) Ef In many reactions that may be of interest, Ef is virtually unity.

15.7 PHYSICAL INTERPRETATION OF THE ABSENCE OF THE CARNOT EFFICIENCY FACTOR IN ELECTROCHEMICAL ENERGY CONVERTERS The mechanism of energy conversion, in the thermal reaction, may be visualized on a molecular scale in the way that the change in energy between products and reactants is released in the form of the heat or kinetic energy of the constituent gases. These then impact upon some mechanical and movable object (e.g., the piston in an internal – combustion engine), but in these collisions, there is a series of glancing angles of incident of the molecules on the cylinder and the transfer of momentum to the piston from the (hot) molecules is not complete. The degree of its completeness is measured by the change in the kinetic energy of the particles after they have struck the piston. The temperature of the gases initially i.e., before striking the piston is T1 or the kinetic

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221

energy per particle is 3/2 k T1. Afterwards, it is T2, or the kinetic energy per particle, 3/2 kT2. The point is that only a part of the kinetic energy, 3/2 kT2, or heat energy was transferred to the piston the rest of the energy escaped, i.e., remained as heat in the gas that was rejected to the heat sink (the products of the reaction are emitted from the reaction chamber at a lower temperature than the maximum but still containing much of the reactions energy, i.e., still hot) The efficiency of the conversion process is given by E =

3 2 k . T1 − 3 2 k . T2 Q1 − Q2 W T − T2 = = = 1 3 2 k T1 Q1 Q1 T1

...(9)

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 Curent density, amp cm –2

0.8

0.9

1.0

Fig. 15.2 : The power versus current-density and efficiency versus currentdensity relations for the electrochemical energy converter.

Power, watts

Efficiency

As a matter of fact these are no collisions, in the electrochemical converter, between the particles e.g., H2 and O2, which react to form H2O. They simply undergo electron supplying for the H2 and electron accepting for the O2 reaction on the electrodes. These electrons travel round an external circuit and, while doing so, pass through a load (e.g., the armature of a motor) and thereby do work. They complete the reaction and allow the product i.e., water to be formed. Hence there is no analog of any process of incomplete transfer of the energy difference between the two sides of a reaction to the outside of the convert. This is because there is in thermal conversion. The electrons thus pass

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through the entire potential difference generated by the cell reaction and not through a part of it only. The question arises as to why the electrochemical converter working under ideal conditions does not convert into electric energy all the energy released in a chemical reaction, Δ H, but only the free energy change in the reation, Δ F. This of course happens because the reaction taking place is still the same overall chemical reaction as in the thermal case i.e., the reaction is still 2H2 + O2 → 2H2O. The entropy change remains unaltered. A part of the Δ H is used up in the unavailable energy connected with the differences in order and disorder between the products and the reactants, and this unavoidably so, independent of any method of energy conversion.

15.8 THE POWER OUTPUT OF AN ELECTROCHEMICAL ENERGY CONVERTER When electrochemical energy converters are to be considered for use. As for example, in driving trucks it is the power output or the rate at which they are able to do work that has to be examined. The power P of an electrochemical energy converter is thus defined: P = IV from which it follows that the power is small when I is small even though V is near the maximum Ve. But the power output is also small when I is very large because of the sudden growth of concentration overpotential when the current density approaches iL tends to drive V to zero. Thus the P versus I curve should pass through a maximum. The distinction between the situation in which one wants high power becomes clear when one compares the P versus I and E versus I curves Fig. 15.2. When its efficiency is at a maximum, the electrochemical energy converter is a less good power source. As the current density is increased, the power output increases, but the efficiency decreases, of course, at highest current drains, both power and efficiency fall toward zero.

SECTION B Electrochemical Generators (Fuel Cells) Fuel cells are electrochemical batteries, in which the necessary reactants are supplied continuously from outside to non-consumable electrodes. From which the final products of current generating reactions are removed away continuously. By such a direct conversion (which avoids thermal energy) fuel cells are not limited by the Carnot factor prohibiting high conversion-efficiency. Easily oxidizable compounds such as hydrogen, hydrozine, and methanol and oxidants such as oxygen or air are preferred as fuels. Out of these technical development is most advanced in the case of hydrogen-oxygen cells operating at ambient temperature and low over atmospheric pressure. As already indicated different materials can be used as oxidants in fuel cells. Yet it is desirable, if possible, to use O2 from air at one electrode in every earth bound fuel cell

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because this avoids the necessity of carrying a second fuel for the cathodic reaction. Hence the cathodic reduction of O2 has a special importance in electrochemical reactors. The overall reaction is, in acid solution ...(1) O2 + 4H3 O + + 4e → 6H2 O and in alkaline solution, ...(2) O2 + 2H2 O + 4e → 4OH – There is a great disadvantage in this important electrode reaction. It has an i value in the region of 10–10 amp cm–2, and hence the reaction usually contributes considerably to the overpotential in the functioning of an air burning electrochemical converter. Electrocatalysis of this reaction is needed more than any other in energy converters. As already stated, among fuels already used in fuel cells, besides hydrogen, there are many hydrocarbons, several lower alcohols, hydrazine; and ammonia. A representative table is given here. Table 15.1. TABLE 15.1 Cells Using Fuels Other than Hydrogen* Fuel and type of cell

Electrolyte

Catalysts

Av. power density

Hydrocarbons CH4, C2H6, C3H8, etc., temp 100–200°C

Conc. H3PO4 solution with low vapor pressure

Anode, Pt; Cathode, Pt

10–60 mW cm–2 at 0.4–0.5 V

Alcohols CH3OH, C2H4(OH)2, and other alcohols and derivatives, temp 20–80°C

6N KOH

Anode, Pt, Pd, and Ni; Cathode, C, Ag, Pt, and Pd oxides Anode, Pt; Cathode, Pt

20–100 mW cm–2 at 0.6–0.7 V 10–50 mW cm–2 at 0.4–0.6 V

Nitrogen derivatives NH2–NH2, temp 20–60°C NH3, temp 200–400°C

6–12N KOH

Anode, Ni and Co; Cathode, C and Ag

60–200 mW cm–2 at 0.8–0.9 V

Molten hydroxides

Anode, Pt; Cathode, NiO + Li

100–200 mW cm–2 at 0.7–0.8 V

6 to 12N KOH

Anode, Steel; Cathode, C, Ag, etc.

100–300 mW cm–2 at 1.0–1.2 V

Special fuels and Alkali metals, 20–60°C

7N H2SO4

* Table based on Piles à combustible, Paris, 1965.

Cells using fuels other than Hydrogen These fuels are generally used as anodically reacting materials in combination with an oxygen cathode. A rough division of present electrochemical generators could be made depending on temperature. As such if this is below 150°C, the device is called a low temperature fuel cell and above about 500°C a high temperature fuel cells.

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Thus, for low temperature cells, the main problem is that of electrocatalysis i.e., how to raise the exchange current density for the oxidation of relatively cheap fuels by using electrode materials which do not make the initial cost of a device too high. The stability of construction material is not to critical. For the high temperature cells, the temperature alone causes the exchange current densities to be sufficiently high that there can be production of energy at a suitable rate without using expensive materials as catalysts. The counter problem could be the corrosive action of the electrolytes.

The Hydrogen-Oxygen Cell This is the best known of electrochemical generators, the first to reach meaningful practical power levels. Several types of hydrogen-oxygen fuel cells have been developed since the accomplishment by Bacon, of which the Gemini and Apollo systems of the American space programme are outstanding. A schematic diagram of a single Gemini cell is shown in the Fig. 15.3 below. Load e e

H2

O2 Titanium screen coated with Pt catalyst H 2O +

H2

Polystyrene sulfonic acid ion-exchange membrane

O 2 + H2O Wicks for maintaining water balance H2O

Fig. 15.3 : Schematic representation of a single Gemini hydrogen-oxygen fuel cell.

The unique feature of this cell is the use of a thin cation exchange membrane as electrolyte (polystyrene sulphonic acid intimately mixed with a Kel –F+ spine). Each side of this rectangular membrane is covered by a titanium screen coated with a platinum 1 mm. The reactions that are taking catalyst. The thickness of the entire cell is about 2 place are : at anode 2H2 → 4H+ + 4e ...(3) at cathode

O2 + 4H+ + 4e → 2H2 O

...(4)

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The conductivity of the membrane is strongly dependent on the water content. Hence the water balance is maintained by supplying water by capillary action. The performance of a single cell is shown in the figure below: 1.2

Cell potential, volt

1.0

0.8 0.6

0.4 0.2

0

0.02

0.04 0.06 0.08 Current density, amp cm –2

0.10

0.12

Fig. 15.4 : The cell-potential versus current-density relations for a Gemini hydrogen—oxygen fuel cell.

An important overpotential loss is, in these cells, due to membrane resistance also, as usual, to oxygen electrode. A storage system built of these cells, having an average power of about 900 W and a maximum power of 2 kW. At present, some hydrogenoxygen fuel cells have attained a power level of 1W cm–2.

Hydrogen Air cells Pure hydrogen is expensive, although it is an excellent fuel because of its large i0 value and the resulting possibility of catalyzing its dissolution well (i.e., with small over potential on cheap materials such as nickel. In order to overcome this situation, a series of fuel cells utilize a system in which a cheap hydrocarbon fuel is the origin of the hydrogen. This is produced in an adjoining apparatus, separated from other gases, and fed into the cell. The steam hydrocarbon process is as follows: CnH2n+2 + nH2 O → (2n + 1) H2 + nCO

...(5)

...(6) CO + H2 O → CO2 + H2 The CO2 may be removed by absorption in ethylamine or by hydrogen separated by diffusion through palladium or silver-palladium membranes. Apart from these ammonia or metal hydrides may also be used as chemicals since both are in fact hydrogen carriers.

CHAPTER 16

ELECTROCHEMICAL ENERGY STORAGE: THE IMPORTANT QUANTITIES IN ELECTRICITY STORAGE 16.1 ELECTRICITY STORAGE DENSITY The electricity storage density is the amount of electricity (Coulombs) per unit weight which the storer can hold. It states nothing concerning the energy (watts or kilowatthours) which it can store per unit weight. The electricity storage density actually refers to a measure of the maximum total amount of electricity which can be withdrawn from unit weight of a substance when (in conjunction with another substance in a cell) it undergoes an electrochemical reaction. Thus, let one formula weight mole of substance enter into an electrodic reaction in which they accept or reject n electrons to produce other substances in one of the two electrode reactions in a cell. Then, M [g of substance] = nF [Coulomb of electricity] ...(1) or

1 kg =

96,500 × 1000n [C ] M 6

96.5n10 ⎡ Electricity storage density is C k g -1 ⎤ ⎣ ⎦ M Suppose the potential difference through which the amount of electricity stored passed (the cell potential) was particularly small for a given system, then its electricity storage density could be high but the energy is stored (the coulombs flowing times the potential difference passed through) would be small. It is to be noted that the electricity storage density, e.g., says little of the actual behaviour of the substance at an electrode or the possibilities of making an electrode from it. Electricity storage density may be therefore only a paper parameter, useful as an indication of what might be possible with certain substances if they are made to react reversibly at electrodes which give the reaction large i0’s.

16.2 ENERGY DENSITY This refers to the energy which may be extracted from a given weight of a substance or a device per unit weight. Electrical energy is measured by the quantity of electricity

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227

(current multiplied by time) multiplied by the potential difference through which such a quantity passes. Thus Energy density = Electricity storage density × cell potential ...(2) or Maximum energy density =

9.65× 107nVe Mole

...(3)

where Ve is the reversible electrode potential of the material in the reaction concerned. It is also to be noted that the energy density of a single electrode is fictitious quantity since Ve depends on the arbitrarily selected reference electrode (e.g., a normal hydrogen electrode). The value of the above equation is in coulomb volts per kilogram (if ‘Hole’ is expressed in kilograms). The same may be expressed as ampere – second – volt per kilogram = ampere volt – second per kilogram = watt second per kilogram. Hence, maximum energy density is, in kilowatt hours per kilogram, 9.65 × 107 nVe Ve ⎡ =26.8 n k Whkg –1 ⎤⎦ M 60×60×1000 Mole ⎣

...(4)

This maximum energy density for an electrode material undergoing an electrode reaction involving n electrons is only an indication of its ability to act as a vessel loaded with realizable electricity. Values of such maximum energy densities of certain materials in certain reactions are shown in the following Table (16.1). On the other hand the maximum energy density of the best combinations of electrode reactions are given in Table 16.2. The real energy densities of cells are less than the values given in Tables 16.1 & 16.2 and sometimes by a fraction e.g., some one fifth Table 16.3. TABLE 16.1 Idealized Maximum Energy-Density Values for Some Elements, at 25°C

Element Lithium Sodium Potassium Beryllium Magnesium Calcium Aluminum Manganese Iron Nickel

Reaction Li → Li+ + e Na → Na+ + e K → K+ + e Be → Be2+ + 2e Mg → Mg2+ + 2e Ca → Ca2+ + 2e Al → Al3+ + 3e Mn → Mn2+ + 2e Fe → Fe 2+ + 2e Ni → Ni2+ + 2e

Thermodynamic potential E0, V – – – – – – – – – –

3.045 2.714 2.925 1.847 2.363 2.866 1.662 1.18 0.440 0.250

Idealized maximum energy density,* kWh kg –1 11.76 3.16 2.00 10.98 5.21 3.83 4.95 1.15 0.42 0.23 Contd.

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Element

Thermodynamic potential E0, V

Reaction

Idealized maximum energy density,* kWh kg –1

Zinc Cadmium Lead Silver

Zn → Zn2+ + 2e Cd → Cd2+ + 2e Pb → Pb2+ + 2e Ag+ + e → Ag

– – – +

0.763 0.403 0.126 0.799

0.63 0.19 0.03 0.20

Mercury

Hg 2+ 2 + 2e → 2Hg

+ 0.789

0.11

Bromine Chlorine Fluorine

Br2 + 2e → 2Br– Cl2 + 2e → 2Cl– F2 + 2e → 2F–

+ 1.065 + 1.359 + 2.87

0.36 1.03 4.05

* In a hypothetical cell with the normal hydrogen electrode. TABLE 16.2 Idealized Maximum Energy Density of Hypothetical Electrode Couples at 25°C Reaction

Cell potential Ve, V2

Energy density, kWh kg –1

2Li + F2 → 2LiF

6.05

6.03

2Li + CuCl2 → 2LiCl + Cu

3.06

1.11

2Li + CuF2 → 2LiF + Cu

3.55

1.66

2Li + NiF2 → 2LiF + Ni

2.83

1.34

3Li + CoF3 → 3LiF + Co

3.64

2.12

2Li + CoF2 → 2LiF + Co

2.88

1.40

2Li + CuO → Li2O + Cu

2.25

1.30

Mg + CuF2 → MgF2 + Cu

2.92

1.25

3Mg + 2CoF3 → 3MgF2 + 2Co

2.89

1.52

Mg + AgO → MgO + Ag

2.98

1.08

Ca + CuF2 → CaF2 + Cu

3.51

1.33

Ca + CuO → CaO + Cu

2.47

1.11

Some of the reasons for this are obvious. The idealized maxima of the calculation of the hypothetical maximum power density take into account the weight of the active materials with no accounting for grid, container, solutions connections etc. In addition, the Ve value, must be reduced by the prevailing overpotential for the given conditions of the rate or current density at which it is desired to supply electricity. However, these factors do not alone account for the differences between the idealized maxima and the real energy density of electricity storers. In brief calculated maximum energy densities are indicative largely of what system to investigate in considering the development of future electricity storers. Values obtainable in practice Table 16.3 are at present one half to one-fifth the ideal values and

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must be established empirically. Once measured at a given current density, the energy densities can, even then be used only as rough guides. This is because the available potential is reduced by the overpotential which arises with increase of current density, [Equation representing a cell potential cell current relation be consulted for further details], so that, intrinsically a variation of energy density with power will tend to occur. TABLE 16.3 Realized and Idealized Energy-Storage-Density Parameters for Some Cell Systems

System

ThermoRealized dynamic energy density reversible (mean), potential Ve, V kWh kg –1

Idealized energy density, kWh kg –1

Single discharge M-O2–KOH–Zn m-DNB–MgBr2–Mg Ag2O2–KOH–Zn HgO–KOH–Zn

1.64 2.84 1.81 1.34

0.15 0.22 0.11 0.11

0.44 1.54 0.22 0.22

Hypothetical single discharge Li–F2 Mg–O2 Be–m-dinitrobenzene Be–nitrobutanol

6.0 3.1 2.6 2.3

– – – –

1.5 1.3 3.1 3.7

Multiple charge–discharge PbO2–H2SO4–Pb NiO(OH)–KOH–Cd Ag2O2–KOH–Zn

2.04 1.48 1.70

0.02 0.04 0.11

0.18 0.22 0.44

Hypothetical multiple charge-discharge Be–BeF2–F2 Al–AlCl3–Cl2

4.5 3.02

– –

3.30 2.20

Ratio of realized to idealized energy density 0.34 0.14 0.50 0.50

0.11 0.18 0.23

Power The criteria for a good electrically storer given above relates to the question as to how much electricity, or say electric energy, can the device hold and deliver per unit weight. This question is primary one of the device is for the storage of electricity. Another, different question which relates to the rate at which the storer would be able to release the energy again. In fact the power is the product (for each single cell) of the working potential of the cell i.e., the maximum potential diminished by the sum of the over potentials at and between the electrodes in the cell multiplied by the current of each cell, which is itself a function of over potential. The power increases with current density and passes through a maximum Fig. 16.1.

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Introduction to Polarography and Allied Techniques 0.9 0.8 0.7

Power, watts

0.6 0.5 0.4 0.3 0.2 0.1

0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 Current density, amp cm–2

0.8

0.9

1.0

Fig. 16.1 : The power versus current-density relations for an electrochemical energy converter (calculated for curve 1 of Fig. 11.71)

In fact Rate in the form of current times potential is the rate of delivering energy, i.e., the power. A device could be imagined which has an excellent energy storage density but can only release this energy at a slow rate. The disadvantage of such a device would be that only a situation requiring low power could be coped with by it. Hence the power density of a storer (the number of kilowatts, rather than kilowatt hours, it can put out per unit weight) is also an important index of its merit as a device. The difference in function between electricity storers and electrochemical energy converters has been represented in Figs. given; ahead. The electricity storer working in the supply mode and the electrochemical generator or converter are both electrochemical cells working as energy producers.

Electricity Storage In the electrochemical converters already described, the two reactants are stored outside the cell and are fed to each electrode respectively e.g., see Figs. 16.2 and 16.3. In case, instead of feeding the reactants to the electrodes continuously the reactants are placed on the electrodes. When cathode and anode are joined through an external circuit, the two fuels, each on one inert electrode, will react electrodically at the respective electrode solution interfaces and a current will flow, just as in an electrochemical

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231

converter. An example could be, on one inert electrode substrate, powdered cadmium had been placed (in analogy in the fuel of a converter) and, on the other electrode, an oxide of nickel (the other fuel). When the external circuit is closed as shown in Fig. 16.4(a) the electrode on which the cadmium has been placed undergoes an anodic reaction, if the de-electronates with the following overall charge transfer reaction. Load e e

H2

O2 Titanium screen coated with Pt catalyst H 3O +

H2

Polystyrene sulfonic acid ion-exchange membrane O 2 + H2O Wicks for maintaining water balance

H2O

Fig. 16.2. Schematic representation of a single Gemini hydrogen—oxygen fuel cell.

Cd + 2OH– → Cd(OH)2 + 2e ...(5) Correspondingly, at the electrodes on which the nickel oxide has been placed, an electronation reaction occurs and could be represented as an overall reaction: ...(6) 2NiOOH + 2H2 O + 2e → 2OH– + 2Ni(OH)2 In case when an external source of electric power is used to push electricity into the cell Fig. 11.88(b) in the opposite way to that in which it passes if this cell is allowed to function spontaneously. While dealing with an electrochemical converter with decane as the anodic fuel, the product of the overall cell reaction would be CO2 and H3O+. If the pH is acidic, CO2 is evolved and expelled from the system (in an alkaline solution, the CO2 would of course from carbonate and eventually precipitate in the cell). Thus in the case decane, when one uses the aid of an external power source to push a current in a direction opposite to that in which the generator has been functioning spontaneously, there is no chance of reversing the overall reaction of decane oxidation which means reducing CO2 to decane at the cathode, while evolving oxygen at the anode. Apart from other reasons, the CO2 has escaped from the system into the atmosphere. On the other hand nothing escapes from the system during the spontaneous functioning of the electrode reaction

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(the cell discharging). This happens in a device in which, as with the cell Fig. 16.4(a) whose electrodes contain Cd(OH)2 and Ni(OH)2, the products of spontaneous functioning of the cell are held on the electrodes. Load e e Stainless steel cathode current collector Porous Ni Ag paint

H2 +CO

Molten carbonates with MgO H2+CO CO2+O 2+N2 Carbon steel anode current collector CO2+O 2+N 2 Nickel catalyst

Water

Natural gas Purifier

Fig. 16.3 : Schematic representation of a high-temperature (500°C) natural-gas fuel cell.

Hence, on the cadmium electrode, the reaction in the electrode plate covered with cadmium hydroxide can be, when electricity is put into device, Fig. 16.4(b) Cd(OH)2 + 2e → Cd(OH)– and on the nickel electrode during corresponding circumstances, 2Ni(OH)2 + 2OH– → NiOOH + 2H2 O + 2e

...(7) ...(8)

The device is an electricity storer. On the one hand, the substances on its electrodes can react to electricity sent in from an external source by undergoing transformation. On the other hand, upon demand, the storer can allow its electrode reactions to occur spontaneously and send out through an external circuit (Fig. 16.4(a) the electricity which was put into it previously. Thus electricity is stored in chemicals on the electrodes because they have a certain form. In charging over to another, they give out electricity. The essential and considerable difference between electrochemical energy converters and electricity storers can be made clear. The converters take in substances, usually stored externally, and produce electric energy directly from the spontaneous reaction between the two substances.

Electrochemical Energy Storage the important Quantities in Electricity Storage

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Classical Batteries

– Source+

Load e

e

e

e

Inert electrodes

Inert electrodes Cd NiOOH

C d ( O H )2 N i ( O H )2

KOH solution

KOH solution

Porous separator

Porous separator

Fig. 16.4(a) : A nickel cadmium cell at the beginning of discharging. At the cathode, 2NiOOH + 2H2O + 2e → 2Ni(OH)2 + 2OH–; at the anode, Cd + 2OH– → Cd(OH)2 + 2e.

Fig. 16.4(b) : A nickel cadmium cell at the beginning of charging. At the cathode, Cd(OH)2 + 2e → Cd + 2OH–; at the anode, 2Ni(OH)2 + 2OH– → 2NiOOH + 2H2O + 2e.

(b)(i) Lead-Acid–Storage Battery. This electricity storer was invented by Plant’e as early as 1860 and it is the one most used storer at the present time, particularly for driving the electric motor by which internal cumbustion engine are made to fire. It consists of two electrodes of lead sheet and electrolytic solution H2SO4 saturated with PbSO4 between them. Upon charging, Pb++ is deposited on the lead sheet which is made cathodic by the application of a potential from an outside power source. That is electronation occurs. At the other electrode, the Pb2+ ions present in solution, during charging, yield electrons to the anodic lead plate and become Pb4+. Afterwards hydrolysis takes place to form crystalline PbO2, which deposits on the plate. Therefore, the electrode reactions during charging would be: at cathode,

Pb2+ + 2e → Pb

...(9)

2e ...(10) at anode, Pb + 6H2 O → PbO2 + 4H3 During discharge, the reverse of the above reactions occur. Relatively high current densities can be reached during discharge, i.e., the over potential developed during the reaction is small. The importance of the fact that the exchange-current density for the discharge of H3O+ on lead is low may be seen for, at the cathode (during charging) the 2+

O+ +

1 H2 + H2O (i.e., this 2 latter reaction occurs to a negligible extent because the relation i = i0e–αn/RT. Also because the exchange-current density for the reaction of hydrogen evolution on lead is low. reaction Pb2+ + 2e → Pb occurs and not the reaction H3O+ + e →

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There are two main difficulties which make it desirable to develop electricity storers other than the lead-acid storage system as quickly as possible. The important one is the weight of the cell per unit of energy produced which gives poor value of the real energy density. The practical value is 0.022 to 0.026 kWh kg–1. The second difficulty being; that the plates undergo a process called sulphanation. When the storer is not supplying electricity, spontaneous discharge takes place at the lead electrode: Pb + SO2– 4

→ PbSO4 + 2e

...(11)

2H3 O+ + 2e → 2H2 O + H2

...(12)

At the PbO2 electrode, PbO2 + H2 SO4 + 2e → PbSO4 + 2H2 O + SO2– 4 Pb + SO2– 4

→ PbSO4 + 2e

...(13) ...(14)

The life of the cell gets limited with such processes like gradual conversion of lead and lead dioxide to lead sulphate of large particle size takes place. The lead acid battery is used for so long, the reason being that the battery gives very high current densities per unit area, little power is needed to start an automotive engine, it is just what is needed.

Zinc Manganese Dioxide Dry cells are electrochemical energy storers in which the electrolyte is immobilized in the form of a paste. A typical of these cells is the Leclanche’ cell. A schematic diagram of the cell is shown in Fig. 16.5 Load e e Carbon rod Zinc can (MnO+C+NH 2 4Cl+H2O ) mix Porous partition Immobilized electrolyte (NH4 Cl+ZnCl2 + H2O)

Fig. 16.5 : Schematic diagram of a Leclanche’ cell.

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235

The reactions that occur in the cell during discharge are At anode

Zn + Zn2+ + 2e

...(15)

...(16) At cathode 2MnO2 + 2H3 O + 2e → Mn2 O3 + 3H2 O The following irreversible side reactions also occur since hydroxide ions are produced during working: ...(17) OH– + NH4 + → H2 O + NH3 +

Zn 2+ + 2NH3 + 2Cl– → Zn(NH3 )2 Cl2 Zn 2+ + 2OH– → ZnO + H2 O

...(18) ...(19)

...(20) ZnO + Mn2 O3 → Mn2 O3 . ZnO The cell is only partially rechargeable because of the above reactions and as such it is never done in practice. These cells are extensively used as primary batteries, inspite of this disadvantage. They have an energy density of about 0.14 kWh kg –1 if discharged at low current densities.

Relatively New Electricity Stores Silver Zinc Cell An electrochemical energy storer which is particularly noted for high power densities in practice is the silver-zinc cell. The materials used as fuels on the electrode substrates are zinc and AgO. Saturated KOH is the electrolyte. Schematic diagram is given below : Reactions occuring in the cell during charging are described as: Load e e

Ag AgO Zn Porous separator

KOH solution

Fig. 16.6 : Schematic diagram of a silver-zinc cell.

at anode at cathode

Ag + 2OH– → AgO + H2 O + 2e ZnO + H2 O + 2e → Zn + 2OH

–

...(21) ...(22)

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While discharging the reverse of the above reaction takes place. The exchange current densities of the cell reactions are relatively large and side reactions are comparatively slow in the rate. These cells have an energy density in the region of 0.1 kWh kg–1. The disadvantage being, the small number of charge-discharge cycles which this cell is able to stand before its reactant mass undergoes some form of deterioration. The advantage in having the highest energy density and power density of commercially available cells. It is to be noted that the number of cycles which the cell undergoes before breakdown is a function of the degree to which it is discharged.

Storers with Zinc in Combination with an Air Electrode Among the more active metals is zinc (Ve = – 0.76 V for the reaction Zn → Zn ++ + 2e. And in an alkaline solution coupled with an air electrode, the reversible thermodynamic cell potential is 1.62 V. A schematic diagram of such a cell is shown in the Fig. 16.7. The reaction upon charging would be 4OH– → 2H2 O + O2 + 4e

at anode, at cathode,

2Zn(OH)2 + 4e → 2Zn +

4OH–

...(23) ...(24)

Load e e Air in Air compressor Electrolyte reservoir

Insert electrodes Zn Porous Ni Air (from compressor)

Pump

Circulating electrolyte (KOH)

Fig. 16.7 : Schematic representation of a zinc air cell.

Those upon discharging would be the reverse. The deposition and dissolution of zinc is empirically well understood, largely from studies concerned with the silver-zinc cell (in comparison with which the zinc air cell would have an obvious economic advantage). In fact such zinc-air cells have been known for many years, but regarded as systems able to give rise only to low power. The difficulties that are faced on such systems are largely concerned with the difficulties arisen on repeating many times (i.e., the cell is charged) the electrocrystallization reaction associated with the cathodic formation of zinc. These are

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oxygen side of the storer makes the energy density of such a hypothetical storage device depend on the weight of the container material used to store hydrogen. If volume considerations are not important, the hydrogen could be stored at low pressure in relatively light containers. Even sometimes balloon storage could be favourable. The problem is largely one of the weight of a container with sufficient strength. One could also contemplate underground storage of hydrogen produced by electrolysis, perhaps of sea water. Another difficulty of the hydrogen-oxygen cell is the slow kinetics of the oxygen electrode. Doped non stoichiometric oxides of transition metals have been shown to have catalytic properties comparable with those of platinum. The favourable kinetics of the reaction 2H+ + 2e → H2 with high i0 value on cheap substrate material like nickel oxide or nickel for both anodic dissolution as well as cathodic evolution. The prospects for hydrogen approach to the storage of electricity have rather been favourable prospects due to the absence of crystallization or corrosion.

Storage by Using Alkali Metals Among the requirements of a desired energy storer are a high reversible cell potential and high i0 values for both the electrode reactions. An approach of this ideal can be obtained by combining the alkali metal-dissolution reactions e.g., M → M+ + e with halogen-dissolution reaction in a molten X2 + 2e → 2x–

...(25) ...(26)

salt Mx. Such a device not only fulfills the two criteria mentioned e.g., Li – LiCl –

1 Cl at 2 2

600°C has an open circuit potential of about 3.5 V and an i0 value of about 0.1 amp cm–2 (on carbon) for the Cl2 electrode, but also has a further unique property. There is no solution in normal sense in which the diffusion of a solute to and from the electrodes gives limiting mass-transport rates which define the maximum rate of charge and discharge of devices. In pure Mx e.g., liquid LiCl at 650°C, the supply of material to the electrodes is in effect governed by the ionic-conductance parameters. These are about ten times higher in molten salts in the region of the temperature mentioned than in the corresponding aqueous electrolyte at lower temperatures. Electricity storers involving alkali metals and halogens have advantages in power densities which is difficult to find in any other directions. The stability of material is very important and electrochemical reactions which are the origin of instability of the materials have to be looked after. Examples could be of nonconducting organic materials may provide stable substrates in a number of instances. The difficulty has been the thermal instability of substances arises above 250 to 300°C. However, the example could be of polyphenylene type of compounds give thermal stability into the range of 500 to 600°C.

Electrochemical Energy Storage the important Quantities in Electricity Storage

239

Storers involving Non-aqueous Solutions The aim for an electricity storer would be that its electrodes should have widely different and highly reversible electrode potentials i.e., the latter is equivalent to having high exchange-current densities. A reaction is used with oxygen at the cathodic discharge step and it should be free of the material instability and breakdown problems associated with the presence of high temperatures. The former condition is to avoid the weight of containers for a second fuel. The first requirements indicates the projected alkali metal cells, the use of the metals like that of Lithium and Beryllium group. The difficulty that arises is that these metals corrode violently in aqueous solutions to give hydrogen from the parallel cathodic reaction like 2H+ + 2e → H2, which must occur if the central corrosive reaction M → M+ + e is to take place. The explosion is caused by the heat engendered together with the presence of oxygen from air. Another solution could be obtained by the use of non-aqueous solvents. Acetonitrile could be an example in which the corrosion reaction and therefore the presence of evolved H2 are suppressed to zero velocity. A number of non-aqueous solvents are known. The aim is to discover a way of making oxygen to dissolve cathodically in a non-aqueous medium. Corrosion problems at room temperature are small so long as that of the alkali or alkaline earth metal is avoided by the use of a non-aqueous solution in which hydrogenevolution reaction is absent. An excellent hypothetical electricity storer would be a rechargeable cell of beryllium with air. Load e e

Ag mesh Li sheet CuF + Cu powder mix (sintered) Porous separation (glass filter paper) Solution of NaPF6 in propylene carbonate

Fig. 16.9 : Schematic diagram of an organic electrolyte energy storer.

Satisfactory functioning of an oxygen electrode in a non-aqueous solution has not yet been made. The cathodic reduction of O2 usually forms water, so that a solvent system would have to be devised to provide an analogous solvent-forming reaction. Then during charging, the anodic reaction would have to be the evolution of oxygen. The solubility

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of salts in non-aqueous solution is often less than that in aqueous solutions. A relatively small limiting current and hence power would be expected with devices using nonaqueous solutions. The basic advantage of electricity storers with non-aqueous solutions is that they can involve, high electricity storage capacity of the alkali and alkaline earth containers. With this the problem of the weight of containers for hydrogen or the material instability problems of high temperature cells. Developments in the past few years have led to the development of liquid ammonia cells which operates under high pressure and organic solvents like propylene carbonate, dimethyl formamide dimethyl sulphoxide, acetonitrile and methyl formate which contain dissolved organic and inorganic salts. A schematic diagram of an organic electrolyte electricity storer is given here. Fig. using these electrolytes, it is possible to operate systems in which theoretical energy densities are about five times higher than those of conventional cells operating in aqueous media. A hybrid situation could also be possible, where alkali metal in contact with a non-aqueous solution an oxygen electrode in contact with an aqueous one. The two being separated by some kind of membrane. This device may give the advantage of the large amount of electricity per unit weight characteristic of alkali metals. This may avoid carrying the cathodic cell. Correspondingly, the difficulty of finding a suitable reaction for a nonaqueous situation and oxygen dissolution, including corrosion-inhibtion problems of molten-salt cells would be avoided.

CHAPTER 17

KINETICS OF ELECTRODE PROCESS INTRODUCTION The branch of chemistry concerned with the interrelation of electrical and chemical effects is actually the electrochemistry. Most of the study in this field deals with the study of chemical charges caused by the passage of electric current and the production of electrical energy by chemical reactions. A huge array of different phenomena are begin displayed in this field. The examples are : electrophoresis and corrosion, electroanalytical sensors, batteries and fuel cells. The technologies are electroplating of metals and the large scale production of aluminium and chlorine. Many electrochemical methods have been devised. Their application requires an understanding of the fundamental principles of electrode reactions and the electrical properties of electrodesolution interfaces. In electrochemical systems therefore, the main concern is between the chemical phases for example between an electronic conductor (an electrode) and an ionic conductor (an electrolyte). As such the main feature remains with the electrode/ electrolyte interface and the events that occur when an electric potential is applied and current passes. Typical electrode materials used are solid metals e.g., Pt, Au and liquid metals like Hg, amalgams. Carbon (graphite) and semi conducts like indium-tin oxide and si. In the electrolyte phase, charge is carried by the movement of ions. The electrolytes, that are most frequently used, are liquid solutions containing ionic species such as H +, Na+, Cl– either in water or in non-queous solvents. For a useful electrochemical cell the solvent/electrolyte system must be so chosen which is of sufficiently low resistance i.e., it should be sufficiently conductive for the experiment chosen. Fused salts like molten NaCl-KCl (eulectic) and ionically conductive polymers like Nafion, polyethylene oxide – LiClO4 are less conventionally used electrolytes. In general, a difference in electric potential can be measured between the electrodes in an electrochemical cell, which is done with a high impedance voltmeter. This cell potential is measured in volts (V), where IV = 1 joule/coulomb (J/c). It is a manifestation of the collected differences in electric potential between all the various phases in the cell. The transition, in electric potential, in crossing from one conducting phase to another usually occurs almost entirely at the interface. The measurement and control of cell potential is one of the most important aspects of experimental electrochemistry. Taking an example of chemical reaction taking place in a cell is has been observed that it is made up of two independent half reactions, which describe the real chemical changes taking place at the two electrodes. Each half-reaction (and, consequently, the chemical composition of the system near the electrodes) respond to the interfacial

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potential differences at the corresponding electrode. The electrode at which it occurs is called the working electrode, or indicator electrode. Because, mostly one is interested in (one of these reactions), and the electrode at which it occurs. The other half cell is standardized by using an electrode known as reference electrode made up of phases having essentially constant composition. The internationally accepted primary reference is the standard hydrogen electrode (SHE), or normal hydrogen electrode (NHE), which has all components at unit activity : PH/H2 (a = 1) H+ a = 1, aqueous ...(1) Potentials are often measured and quoted with respect to reference electrodes other than the NHE. A common reference electrode is the saturated calomel electrode (SCE), which is Hg/Hg2Cl2/KCl (saturated in water) Its potential is 0.242 V vs. NHE. Another is silver – silver chloride electrode : with a Ag/AgCl/KCl (saturated in water) potential of 0.197 V vs. NHE.

Power supply

v

i

Ag

Pt AgBr 1 M HBr

Fig. 17.1 : Schematic diagram of the electrochemical cell Pt / HBr(1 M)/AgBr/Ag attached to power supply and meters for obtaining a current-potential (i-E) curve.

Since the reference electrode has a constant make up, its potential is fixed. Therefore any changes in the cell are ascribed to the working electrode only. Consider, a typical electrochemical experiment in Fig. 17.1 where a working electrode and a reference electrode are immersed in solution and the potential difference between

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where ia is the anodic component to the total current. Thus the net reaction rate is vnet = vf – vb = kf C0 (O, t) – k . CR(O, t) =

ia nFA

...(9)

and the overall equation is represented as : i = ie – ia = nFA[kf C0 (O, t) – kb CR(O, t)]

...(10)

It is to be noted that the heterogeneous reactions are described differently than homogeneous ones. Hence they have units of mols–1 cm–2. As such heterogeneous rate constants must carry units of cm/s, if the concentration in which they operate are expressed in mol/cm3. This is because the interface can respond only to its immediate surroundings, the concentration entering rate expressions are always surface concentrations which may differ from those of the bulk solution.

17.2 BUTLER – VOLMER MODEL OF ELECTRODE KINETICS R From experience it can be demonstrated that the potential of an electrode strongly affects the kinetics of reactions occuring on its surface. Hydrogen evolves rapidly at some potentials, but not at others. Copper dissolves from a metallic sample in a clearly defined potential range; yet the metal is stable outside that range. So it is for all faradiac processes. It is because the interfacial potential difference can be used to control reactivity and hence one can predict the exact way in which kf and kb depend on potential.

Effects of Potential on Energy Barriers The idea that reactions can be visualized in terms of progress along a reaction coordinate connecting a reaction configuration to a product configuration on an energy surface implies to electrode reactions too. But the shape of the surface turns out to be a function of electrode potential. By considering the reaction, Na+ + e +

Hg

Na(Hg)

...(11)

the effect can easily be seen where Na is dissolved in acetonitrile or dimethylformamide. The reaction coordinate can be taken as the distance of the sodium nucleus from the interface. It is then the free energy profile along the reaction coordinate would resemble the Fig. 17.2(a) To the right, Na+ + e can be identified. This configuration has an energy that depends little on the nuclear position in solution, unless the electrode is approached so closely that, the ion must be partially or wholly desolvated. To the left, the configuration corresponds to a sodium atom dissolved in mercury. Within the mercury phase, the energy depends only slightly on position. But if the atom leaves the interior, its energy rises as the favourable mercury – sodium interaction is lost. The curves corresponding

Kinetics of Electrode Process

245

Reduction

Oxidation

(a)

Standard free energy

Na(Hg)

Na+ + e

Oxidation

(b) Na(Hg) Na+ + e

Reduction

(c) Na+

+e

Na(Hg)

Amalgam

Solution Reaction coordinate

Fig. 17.2 : Simple representation of standard free energy changes during a faradaic process. (a) At a potential corresponding to equilibrium. (b) At a more positive potential than the equilibrium value. (c) At a more negative potential than the equilibrium value.

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Considering a special case in which the interface is at equilibrium with a solution in which C*O = C*R . In such a situation, E = E 0' and K C* = K C * , So that kf = kb.Thus E0 is the potential where the forward and reverse rate constants have the same value. That value is called standard rate constant, k05. The rate constant at other potentials can then be expressed simply in terms of K 0. kf = k0 exp[–α f (E – E 0 )]

...(19)

kb = k0 exp[(1 – α )f (E – E 0')] Insertion of these relations into equation :

...(20)

i = ic – ia = xFA = [kf C0 (O,t) – kb Cr (O,t)] Yields the complete current-potential characteristic

⎡ f i = F Ak 0 ⎢C0 (O ,t )e −α ⎣

(20')

( E– E 0) −CR (O,t ) e (1=α )f (E = E ) ⎤⎥⎦ 0

...(21)

This relation is very important since this or a variation derived from it is very useful for every problem requiring an account of heterogeneous kinetics. These results and the inferences derived from these are broadly known as Butler-Volmer formulation of electrode kinetics.

17.3 IMPLICATIONS OF THE BUTLER-VOLMER MODEL FOR THE ONE STEP, ONE ELECTRON PROCESS Equilibrium Conditions. The Exchange Current at equilibrium, the net current is zero, and the electrode is known to adopt a potential based on the bulk concentration of O and R as dictated by the Nernst equation. Since equilibrium applies, the bulk concentrations of O and R are found also at the surface; hence et(Eeq–E 0 )

CO*

...(22)

CR*

which is simply an exponential form of the Nernst relation Eeq = E 0 ' +

RT CO* ln F CR*

...(23)

Even though the net current is zero equilibrium the balanced faradic at activity that can be expressed in terms of the exchange current, i0. which is equal in magnitude to either component current i0 or ia. That is .

(

* i0 = FAK o C oc − αf Ee q − E o'

)

...(24)

If both sides of the equation are raised to the α power, what is obtained is e–αf

(Eeq

⎛ Co* ⎞ – E ) = ⎜ ⎟ ⎝ CR* ⎠ 0

−α

...(25)

Kinetics of Electrode Process

249

Substitution of above equation into gives * (1−α ) ** CR

i0 = Fak Co

...(26) 0

The exchange current is therefore proportional to k and can often be substituted for k0 in kinetic equations. For the particular case where C*o = C *R = C, i0 = Fak0 C ...(27) Often the exchange current is normalized to unit area to provide the exchange current density, j0 = i0A.

17.4 THE CURRENT OVERPOTENTIAL EQUATION An advantage of working with io rather than k0 is that the current can be described in terms of the deviation from the equilibrium potential, that is, the overpotential, η, rather than the formal potential E 0'.

(C

* o

The ratios

C*R

) and (C

* o

C*R

)

−(1 −α )

can easily be evaluated from the equation ef (Eeq – E0) =

Co* and CR*

−α

⎛ Co* ⎞ the equation e (Eeq – E ) = ⎜ ⎟ , ⎝ CR* ⎠ and by substitution what is obtained is –αft

0'

⎡ Co (O,t ) −αfn CR (O,t ) (1−α )fn ⎤ i = io ⎢ e e − ⎥ CR * ⎣ Co * ⎦

...(28)

where η = E – Eeq. This equation is known as the current-overpotential equation. It is to be noted that the first term describes the cathodic component current at any potential, and the second gives cathodic contribution8.

17.5 THE STANDARD RATE CONSTANT The physical interpretation of k0 is straight forward. It is simply a measure of the kinetic facility of a redox couple. A system with a large k0 will achieve equilibrium in a short time scale but a system with small k0 will be sluggish. The largest measured standard rate constants are in the range of 1 to 10 cm/s and are associated with particularly simple electron transfer processes. The standard rate constants for reduction and oxidation of many aromatic hydrocarbons, such as substituted anthracenes, pyrene and perylene to the corresponding anion and cation radicals fall in this range(Ref.1-4). These processes involve only electron transfer and resolution. These are no significant alterations in the molecular forms. Similarly, some electrodes processes involving the formation of amalgam e.g., the couples Na+/Na(Hg), Cd2+/Cd (Hg), and Hg22+ / (Hg) are rather facile [25,26] R. It is to be noted that kf and kb can be made quite large, even if k0 is small. This is possible by using a sufficiently extreme potential relative to E0.

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17.6 THE TRANSFER COEFFICIENT The transfer coefficient, α is a measure of the symmetry of the energy barrier. This idea can be implied by considering α in terms of the geometry of the intersection region as shown in the Fig 17.4.

Standard free energy

E=0

(1–α)FE

O+ e θ

φ

E=E

θ Length=x

R αFE

Reaction coordinate

Fig. 17.4 Relationship of the transfer coefficient to the angles of intersection of the free energy curves.

If the curves are locally linear, then the angles θ and φ are defined by tan θ = α FE/x when φ = (1–α ) FE/x

(29) (30)

hence

α =

tan θ tan φ + tan θ

(31)

1 1 1 , otherwise 0 ≤ α or < αS1, , (32) 2 2 2 as shown in Fig. 17.5 (next page) in most systems α turns out to be between 0.3 and 0.7, and it can usually be approximated by 0.5 in the absence of actual measurements. Fig. 17.5 The transfer coefficient as an indicator of the symmetry of the barrier to reaction. The dashed lines show the shift in the curve for O + e as the potential is made more positive. The free energy profiles are not likely to be linear over large ranges of the reaction co-ordinate, thus the angles θ and φ can be expected to change as the intersection between reactant and product curves shifts with potential. Consequently α should generally be a potential dependent factor. However, in the great majority of experiments, If the intersection is symmetrical, φ = θ and α =

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251

Standard free energy

α appears to be constant, if only because the potential range over which kinetic data can be collected are fairly narrow. α=

1 2

α<

O+e

1 α> 2

1 2

O+e

O+e

R

R

R

Reaction coordinate

Fig. 17.5

In a typical chemical system, the free energy of activation are in the range of a few electron volts, but the full range of measurable kinetics usually correspond to a change in activation energy of only 50-200 meV, or a few percent of the total. Thus, the intersection point varies only over a small domain, such as the boxed region Fig. 17.3 where the curvature in the profiles can hardly be seen. The kinetically operable potential range is narrow in most systems because the rate constant for electron transfer rises exponentially with potential. Not far beyond the potential where a process first produces i/il 1.0

il

0.8 0.6 0.4 ic

Total current

0.2 –100

400

300

200

–200

–300

–400 η. mV

100 –0.2

Eeq i0 –i a

–0.4 –0.6 –0.8

–i l

–1.0

Fig. 17.6. Current-overpotential curves for the system O + e R with α = 0.5, T = 298 K, il, c = –il, a = il and i0 / il = 0.2. The dashed lines show the component currents ic and ia.

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a detectable current, mass transfer becomes rate-limiting and the elecrtron transfer kinetics no longer controls the experiment. In few systems, mass transfer is not an issue and kinetics can be measured over very wide range of potential. In cases involving surface-bound electroactive species, large variation of α with potential have also been observed. The behaviour predicted in the last equation is depicted in the ensuing Fig. 17.6 The solid curve shows the actual total current which is the sum of the components ic and ia, as are shown in dashed traces. For large negative overpotentials, the anodic component is negligible. Hence the total current curve merges with that for ic . At large positve overpotentials, the cathodic component is negligible, and the total current is essentially the same as ia. In going either direction from Eeq, the magnitude of the current rises rapidly, because exponential factors dominate the behaviour, but at extreme η, the current levels off. In these level regions, the current is limited by mass transfer rather than heterogeneous kinetics. The exponential factors in the forgoing equation are then moderated by the factors C0 (o,t)/ C*o and CR (O, t)CR*, which manifest the reactant supply.

17.7 APPROXIMATE FORMS OF THE i–η EQUATION (a) No Mass-Transfer Effects If the solution is well stirred or currents are kept so slow that the surface concentrations do not differ appreciably from the bulk valves, then the previous equation becomes (1−α ) f η ⎤ ⎡ i = io ⎢e −αf η− e ⎥ ⎣ ⎦

...(33)

which is historically known as the Butler-Volmer equation. Since mass-transfer effects are not included here, the overpotential associated with any given current serves solely to provide the activation energy required to drive the heterogeneous process at the rate reflected by the current. The lower the exchange current, the more sluggish the kinetics. Hence the larger this activation overpotential must be for any particular net current.

(b) Linear characteristic at small η For small values of x; the exponential ex can be approximated as 1 + x, hence for sufficiently small η, the above equation can be expressed as i = –i0 + f η ...(34) which shows that the net current is linearly related to overpotential in a narrow potential range near Eeq.The ratio –η/i has units of resistance and is often called the charge transfer resistance, Rct Rct =

RT Fi0

...(35)

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253

j,μA/cm2

0.8 (b)

0.6 (a) 0.4

(c)

0.2 400

300

200

–100

100

–200

–300

–400 η . mV

–0.2 –0.4 –0.6 –0.8

Fig. 17.7 : Effect of exchange current density on the activation overpotential required to deliver net current densities. (a) jo = 103 A/cm2 (Curve is indistinguishable from the current axis), ⎯⎯ → R with α = 0.5 (b) j0 = 10–6 A/cm2, (c) j0 = 10–9 A/cm2. For all cases the reaction is O +e ←⎯ ⎯ and T = 298 K

This parameter is the negative reciprocal slope of the i–n curve where that curve passes through the origin (η = 0, i = 0). It can be evaluated directly in some experiments, and it serves as a convenient index of kinetic facility. For very large K 0, it approaches zero Fig. 17.7.

(c) Tafel Behaviour at Large η For large values of η (either negative or positive), one of the bracketed terms in equation becomes negligible. For example at large negative overpotentials, exp (–afη) >> exp[(1–α )f η] and the equation Fig. 17.8 becomes: i = io e −α f η

...(36)

or

η=

RT RT lnio − lni αF αF

...(37)

A successful model of electrode kinetics must explain the frequent validity of the above equation, known as Tafel equation. The empirical tafel constants : equation η = a + b logi can be identified from theory as

α=

2.3RT log io αF

b=

−2. 3RT αF

...(38)

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The tafel form can be expected to hold whenever the back reaction (i.e., the anodic process, when a net reduction is considered, and vice versa) contributes less than 1% of the current. Tafel relationships cannot be observed fro such cases, because they require the absence of mass-transfer effects on the current. When electrode kinetics are sluggish and significant activation over potentials are required, good Tafel relationships can be seen. This point explains the fact that Tafel behaviour is an indicator of totally irreversible kinetics. Systems in that category allow no significant current flow except at high overpotentials, where the faradaic process is effectively unidirectional and, therefore, chemically irreversible.

(d) Tafel Plots A plot of log i. vs. η, known as Tafel plot, is a useful device for evaluating kinetic parameters. In general, there is an anodic branch with a slope (1–α )F/2.3RT and a cathodic branch with slope –α F/2.3RT. As shown in Fig. 17.8 both linear segments extrapolate to an intercept of log i0.

(1–α )F Slope = 2.3RT

log |i| –3.5

–αF Slope = 2.3RT

–4.5 log i0 –5.5

–6.5 200

150

100

50

–50

–100

–150

–200

η, mV

Fig. 17.8 : Tafel plots for anodic and cathodic branches of the current-overpotential curve for R with –α = 0.5, T = 298 K, and j0 = 10-6 A/cm2. O+e

Note that for –α = 0.5, b = 0.118 V, a value that is sometimes quoted as ‘typical’ Tafel slope. 9

The plots deviate sharply from linear behaviour as η approches zero, this is because the back reactions can no longer be regarded as negliglible. The transfer co-efficient α and the exchange current, i0 are obviously readily accessible from this kind of presentation when it can be applied.

Exchange Current Plots (Tafel Plots) This kind of plot is useful for obtaining from experiments in which i0 is measured essentially directly. From the equations it recognized that the exchange current can be related as :

Kinetics of Electrode Process

255

log io = log FAk o + log C*o +

αF αF Eo' − Ee q 2.3RT 2.3RT

...(39)

Therefore, a plot of log i0 vs. Eeq at constant C* should be linear with a slope of −αF / 2. 3 RT . The equilibrium potential Eeq can be varied experimentally by changing the bulk concentration of species R, while that of species O is held constant. This kind of plot is useful for obtaining α from experiments in which i0 is measured essentially directly.

17.8 EFFECTS OF MASS TRANSFER A more complete 1-η relation can be obtained from

⎡ Co ( o,t ) −αf η CR ( O,t ) (1 −α )f η ⎤ i = io ⎢ e e − ⎥ * C*R ⎣⎢ Co ⎦⎥

...(40)

(where η = E – Eeq) by substituting for C o (O,t ) C *o and C R (O,t )C *R

(x = 0)R

According to

Co

Co

*

( x = 0)

and

CR

CR* i ⎛ i ⎞ = ⎜1 − io ⎝ il,c ⎟⎠

e −αη

i il

...(41)

i il,a

...(42)

1 –

=1 −

⎛ i ⎞ (1−α ) f η e − ⎜1 − ⎝ il,a ⎟⎠

...(43)

This equation can be rearranged easily to give i as an explicit function of η over the whole range of η. For small overpotentials, a linearized relation can be used. In the Tafel regions, other useful forms of the above equation can be obtained. For the cathodic branch at high η values, the anodic contribution is insignificant and as such this equation becomes i ⎛ i ⎞ −αf η ⎛ i ⎞ = ⎜1 − − ⎜1 − e ⎟ e ( 1 − α) fn ⎟ io ⎝ il ,c ⎠ il,a ⎠ ⎝

...(44)

This equation can be useful for obtaining kinetic parameters for systems in which the normal Tafel plots are complicated by mass-transfer effects.

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References 1. B.E. Conway, “Theory and Principles of Electrode Processes,” Ronald, New York, 1965, Chap. 6. 2. H.R. Thirsk, “A Guide to the Study of Kinetics,” Academic, New York, 1972, Chap. 1. 3. J. O’m. Bockris and A.K.N. Reddy, “Modern Electrochemistry,” Vol. 2, Plenum, New York, 1970, Chap. 8. 4. K. J. Vetter, “Electrochemical Kinetics,” Academic, New york, 1967, Chap. 2. 5. C.N. Reilley in “Treatise on Analytical Chemistry,” Part I, Vol. 4, I.M. Kolthoff and P.J. Elving Eds., Wiley-Interscience, 1963, Chap. 42. 6. T. Erdey-Gr•uz, “Kinetics of Electrode Processes,” Wiley-Interscience, New York, 1972, Chap.1 & 4. 7. W.J. Albery, “Electrode Kinetics,” Clarendon, Oxford, 1975. J.E.B. Randles, Trans. Faraday Soc., 48,828 (1952). H. Kojima and A.J. Bard, J. Am. Chem. Soc., 97, 6317 (1975). 8. M. E. Peover, Electroanal. Chem., 2, 1 (1967). N. Koizumi and S. Aoyagui, J. Electroanal. Chem., 55,452 (1974).

CHAPTER 18

BIOELECTRODICS INTRODUCTION Electrochemistry as we have come to know it consists in the study of ionic solutions, and electrodes where ions and electrons combine and separate. Galvani from Bologna, Italy, in 1791, put forth that bio electrochemistry has been a part of electrochemistry. It would be not too much to say that there are electrochemical events going on in living systems where ever you pry into them. The nervous system is certainly based on the flow of electric currents and it is not of all fanciful to see nerves as the wires that run between the enzymes, the electrodes of the body. Bodies are full of membranes, 100, and so are electrochemical cells. Some reactions in the body baffle chemists by going up tree energy gradients, but again that is just what happens in electrolysis, in electrochemical reactors. We can study electrochemical phenomena in the immense complexity of living systems when all we know is how to explain simple systems like fuel cells and corrosion seems to be the crassest arrogance. The science of biology is a truly gigantic edifice, so big, in fact, that it includes all of organic chemistry and uses it to explore very very complicated interactions.

USEFUL PRELIMINARIES The aminoacid glycine i.e., NH3+–CH2–COO– would be simplest example excluding of course H3O+, H2O, and O2 of an entity that takes part in bioreactions, A Structural element within the amino acid is the peptide group

− N− C − | | H O which is important because when many of these groups occur in a chain, and such chains form a polymer, one has a protein. Proteins form skin, nails, and skeletal structures. Enzymes biocatalysts are proteins, Hemoglobin, which carries O2 around the body is a protein. Proteins can have molecular weights as law as 10,000 but some are really very large with molecular weights of 50 × 106. The corresponding radii of the larger of these entities (when they get formed spherically), would be in the hundreds of angstorms. Examples of some amino acids are shown in the Fig. 18.1. Structures that

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H | H2N—C—COOH | H

Glycine (gly)

H | H2N—C—COOH | CH2

CH2CH3

H | H2N—C—COOH | CH2 | OH

Isoleucine(ile)

Serine (ser)

H | H 2N—C—COOH | CH2 | COOH

H | H2N—C—COOH | (CH2)4 | NH2

H | H2 N—C—COOH | CH CH3

N H

Tryptophan (trp)

Aspartic acid (asp)

Lysine (lys)

Fig. 18.1 Examples of some amino acids. (Reprinted with permission from Accounts of Chemical Research 21 copyright 1989, Fig. 1, American Chemical Society)

a protein, for example in glycine. The proteins found in nature are made up of only about 20 different individual amino acids. On the other hand, a typical protein consists of several hundreds of these 20 distinguishable amino acids. These proteins (containing several hundreds of the 20 special amino acids) might be thought at first to be long, long chains containing repeated peptide groups (see last fig.) 18.2 which can be written more R R | | H—N—C—C—N—C—C—OH | | || | | || H H O H H O

Peptide Fig. 18.2 Peptide

explicitly as where the R’s may be hydrocarbon chains on other peptide elements and the shaded area denotes the bond between the two peptides. However these long flexible chains are neither linear nor random in shape. They coil and stretch in a way that greatly affects the properties of the protein i.e., how it does its work. Among the most important of these structures is an arrangement called the α -helix (according to pauling and Corey 1951) but of the elements in cells, the mitochondrion. These mitochondria are the entities in cells where energy is made from the oxidation of organics derived from intake of food and oxygen.

Bioelectrodics

259

Membrane Potentials The measurement and interpretation of the protentials across biological membranes has been going on for about a century. A remarkable suggestion was put forward by Bois-Raymond in 1868, whose concept was that a cell surface could be well looked at as though it were an electrode. The principal elements in biological cells is shown in Fig. 18.3. A Section of a yeast cell with its membrane is shown in Fig. 18.4.

nucleus nucleolus

mitochondrium

endoplasmatic reticulum

1 μm

Golgi complex

Cytoplasmic membrane

Lysosome approx. 10 μm

Fig. 18.3 : The scheme of an animal cell. reprinted from J. Koryta, Ions, Electrodes And Membranes Fig. 69. Copyright © J. Wiley & Sons, Ltd. 1991. Reproduced with permission of J. Wiley & Sons, Ltd.)

Fig. 18.4 : Electron micrograph of a section from a yeast cell. The outer envelope is the cell wall. The inner double line is the cytoplasmatic membrane. (Reprinted from J. Koryta, Ions, Electrodes and Membranes, Fig. 70. Copyright © J. Wiley & Sons, Ltd. 1991. Reproduced with permission of J. Wiley & Sons, Ltd.)

From these two figures it is inferred that the animal cells are rather complex, each one containing the heriditary material and in particular the entities known as mitochondria. It is infact the energy producing properties of these are discussed in forthcoming sections. Membranes, the subject of this section, can be relatively thick (0.1mm) of made chemically). Biological membranes are very much thinner (50–100Å) of the same (3–5 nm) range as that of passive oxide. The figure shows the essential constituents of the biological membranes. These are lipids and proteins. In myetin membrane the lipid content is 80% while at the other end the range, in mitochondria there is an inner membrane containing only about 20% lipid. There are many kinds of lipids as well as very many kinds of proteins. In membranes are usually phospholipids Fig 18.5. The

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IB1

IN

IM

IB2

O || O H2C—O—C—R || | O R—C—O—CH ′ | || H 2C—O—P—O—X | O

Teflon septum window (a)

aqueous solution drop of lipid solution

IC P

Fig. 18.5: Typical biological membrane structures. A liquidmosaic model in the form proposed by A. Kortya with different types of disposition of membrane protein) (phospholipids are shown as dark circles with two wavy tails); IB1, integral, membrane-bridging protein, with a single polypeptide span; IB2, the same with several spans; IN and IC, integral noncytoplasmic and cytoplasmic proteins; IM, integral buried proteins; P, peripheral protein. (Reprinted from J. Koryta, Ions, Electrodes and Membranes, Fig. 81. Copyright © Ltd. 1991. Reproduced with permission of J. Wiley & Sons, Ltd.)

polar head Hydrophobic end

(b) Plateau-Gibbs boundary

Fig. 18.5(a): A scheme of the bilayer lipid membrane. The black circles indicate the polar heads (the hydrophilic part) consisting of phosphoric acid, ethanol amine, and anlogue derivatives. The wavy lines are the long alkyl chains of fatty acids (the hydrophobic part) (Reprinted from J. Koryta, ions, Electrodes and Membranes, above. Copyright © J. Wiley & Sons Ltd. 1991.

(c)

BLM

Fig. 18.6: Preparation of a bilayer lipid membrane. (Reprinted from J. Koryta, Ions, Electrodes and Membranes, Fig. 84. Copyright © J. Wiley & Sons Ltd. 1991. Reproduced with permission of J. Wiley & Sons, Ltd.)

structure often contains an H atom and this allows the phosphoric acid element to ionize. In the membrane structure, the alkyl groups R and R′ are directed inward while the popular groups are on the surface. A scheme of bilayer and lipid membrane. The black circles indicate the polar heads (the hydrophilic part) consisting of phosphoric acid, ethanol amine; and analogue derivatives. The wavy lines are the long alkyl chains of fatty acids (the hydrophoblic part). [Taken from J. Koryta, Ions Electrodes and Membranes.] The most common model system to act as a smiplified biological membrane is the “bilayer Lipid membrane” (BLM) which was first prepared Mueller in 1962. It consists of two lipid molecules tail to tail Fig. 18.6 with the polar groups oriented to face the solution. In the basic BLM individual, compounds of a biological system can be built and examined.

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261

The BLMs, although very thin exhibit very high resistance, up to 10 10 ohms. Nevertheless, some pores do develop in these membranes and water, followed by ions, enters there and reduces the resistance. Application of a potential increases the flow of ions through the pores and the number of pores. This further reduces the resistance. Teflon septum window (a)

aqueous solution drop of lipid solution

(b) Plateau-Gibbs boundary (c)

BLM

Fig. 18.7 : Preparation of a bilayer lipid membrane [Taken from J. Koryta Ions, Electrodes and Membranes.

The method of measuring a membrane potential is simple. A calomel electrode is placed in a solution (if the solution contains Cl–) on either side of membrane, which usually occupies a hole about 1 mm in diameter in a teflon sheet. Since the potential of the calomel electrode is accurately known and varies accoding to Nernst potential with logdCl-, the difference in potential arising from the two different Cl– concentrations in each side of the membrane is easily known and can be subtracted from the total potential difference registered between the two electrodes to give the value due to the membrane. Most of the membrane potentials recorded in the literature lie within values of tens to hundreds of milli volts.

Simplistic Theory The theory of an equilibrium on one species between each side of the membrane was formulated by Donnan in 1925 until 1955, it reigned as the theory of membrane potentials. Its demise came when radiotracer measurements showed that all relevant ions (e.g., K+, Na+, and Cl–) permeated more than a dozen actual biological membranes, although each ion had a characteristic permeability coefficient in each membrane according to Hodg kin and Keynes 1953. Until 1950s Some bio-electrochemists confidently explained membrane potentials by assuming that only one ion like K+ in KCl permeated the membrane. If so, then ui−α = μ + nF ϕ* = ic + RT In aiα + nF ϕ α

(1)

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Introduction to Polarography and Allied Techniques

would be the expression for electrochemical potential of the permeable ion i, on one side, α , on the other side β, the corresponding expression for electrochemical potential of the same ion, there would be −β

bi

β

β = μ + η F ϕβ = boj σ + RTln α i + nF ϕ

As long as equilibrium can be assumed between permeating ions, i on each side e.g, on the α and the β side respectively −β

bi−α = bi Hence

αΔ R ϕ =

αβ RT ln i ηF ααi

...(2)

Being developed in parallel with the rise and fall of the Donan equilibrium theory of membrane potentials was the application of liquid function. Potential theory to membranes. This was proposed as far back as 1888 by great Nernst himself. The theory grew by application of the Nernst-Planck equation to take into account the driving forces due to concentration and potential gradients.

Modern Approaches to the Theory of Membrane Potentials According to (Jahn, 1962) there is found to be a poor match between theory and experiment. Ionic concentration differences alone, then, do not completely determine membrane potentials in living systems. Membrane Some membrane potentials are affected by light, just as if the membranes were semi-conductors. This is entirely outside the capabilities of A B theories that depend on the interplay of potential and concentration gradients in 1949 Albert Szent-Gyogyi made a EA–A• = E R•1 e Ea' – 2 = E R•3 suggestion that some biomaterials might be regarded as semiconductors. This was criticized and another view was that A• B• biomaterials could be thought of as possible electronic conductors and hence E1 E2 electrodes. This was consistent with the idea that the first step in photosynthesis is the photo-electrochemical decomposition of water, and it would account in Fig. 18.8: Schematic diagram showing the oxidation principle, for the photosensitivity of and reduction reactions occuring at a membrane solution interface on sides 1 and 2 of the membrane. membranes. (Reprinted from M.A. Habibi and O’M. Bockris, In case Szent Gyorgyi’s concept is J. Bioelectricity 2:66 (1984). Reprinted by accepted to interpret the electronic permission of Marcel Dekker.)

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conduction of some biomaterials, the To To idea that arose was that electronic Instruments Instruments transfer at the solid/solution interface could occur with the solid E A Outer We being a biomaterial. Jahn in 1962 Inner Aqueous Aqueous was the first to come up with Solution (1) Solution different theory of membrane (SCE) (SCE)(2) potentials. Jahn’s concepts pictured AE (SCE) the membrane as a bioelectrode, μ1 , μ1 μ2 , μ2 s s [Red]1 with each side the site 1 differing [Red]2 [Red]1 A– D [Red]2 (but coupled) redox reactions, the membrane itself acting somewhat 0 0 e E1 E2 like the membrane in a fuel cell Fig. A more detailed view, due to Tien is D + [OX]2 [OX]1 A shown in Fig. 18.8. Electron s Conducting s [OX]2 The equations deduced for the [OX]1 BLM s two reactions making up a corrosion ψ1 , ψ ψ2 , ψs 1 2 0 a i couple are specialized in the sense E a Ea E a that the cathodic reaction is taken to be hydrogen evolution and the anodic one, metal dissolution. The α values being assumed to be one half, but one can drop these assumptions Fig. 18.9 : Transmembrane electron movement and and assume that the membrane redox reactions. Also shown schematically are potentials is simply that of a electrodes and circuit diagram for cyclic voltammetry. WE, working electrode; SCE, saturated calomel bioelectrode. Somewhat similar reasoning can electrode; AE, auxiliary electrode. μ, and μ are be applied to the comings and goings chemical and electrochemical potentials, respectively. of the Na+, K+ and Cl– ions which Bulk concentrations of reduced (RED) and oxidized (in this view) determine the (OX) species on either side of the membrane as indicated by subscripts 1 and 2; interface potential of the membrane. Koryta concentrations are designated by a superscripts has for mulated this theory by (Reprinted from H.T. Tien, Aspects of Membrane writing electrode kinetic equation Chemistry, Kluwer Academic Publishers, 1991.) similar to those that lie behind the Butler-Volmer equation. The movement of ions occurs across the membrane of working electrochemical cells and in these cases certainly the ions are driven by two interfacial cooperating processes. Such movements occur as a result of events elsewhere. The differences in concentration in which they originate are not the causes of the potentials with which they are associated. These causes are surface electron-transfer reactions that occur at the interfaces, i.e., at interfaces on either side of the membranes. Such sites of electron transfer are probably at enzymes absorbed at the membrane surfaces. Thus in this view, the actual origin of membrane potentials lies in the free-energy changes in redox reactions occuring respectively, on each of the two membrane surfaces.

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Electrical Conduction in Biological Organisms Electronic. The initial reaction to the proposition that electronic currents flow in biological organisms understandably negative. In early investigations of this subject, the common view seemed to be justified for proteins that were crystallised out from the dissolved form and thoroughly dried show an extremely high resistivity. In 1960’s, some evidence of a significant 10–4 electrical conductance in biomaterials was Fully Hydrated Hemoglobin available. Significant conductance was found 1.2 eV Fully Hydrated Cholesterol in crustaceans. Indirect support also came from –6 Dry Palmitate 0.9 eV 10 Synthetic mechanisms involving electron flow which Partially Hydrated Melanin Synthetic Melanin 1.5 eV seemed necessary to explain phenomena in 1.2 eV photosynthesis, in enzyme reactivity and in the 10–8 energy producing activities in mitochondria. All Trans βCarotene Rosenberg and Postow realized that 1.5 eV Dry Sheep Root 2.3 eV proteins in the body are far from dry, and a 10–10 nearer approximation to the in vitro situation would be to find out the electronic conductivity Retinal- Aniline Protonated –12 of wet proteins. However, the difficulty that Schiff’s Base 10 Complex 2.1 eV arose was that since protein is wet, the Dry Hemoglobin Dry Cholesterol conductance measured may be partly ionic. 2.4 eV Palmitate 3.6 eV –14 Rosenberg and Postow managed to separate 10 2.7 3.0 3.5 4.0 out the ionic component of conductivity. They 1000 found that the energy of activation for the T°K electronic part of the conductance went linearly downward as the water content of the protein Fig. 18.10 The log of current plotted increased. It appeared as though water, or its against 1/T(K) for a variety of biological ionized constituents acted like doping agent in substances. The activation energies are increasing the electrical conductance of intrinsic calculated from the slopes of the lines. semi-conductors. Thus an increase of ~108 times (Reprinted with permission from B. Rosenbergh and E. Postow, Ann.N.Y. in conductance can arise in this way. Fig. 18.10. Acad. Sci. 158:61, 1969, p. 162, Fig. 1.) However, in respect to the mechanism for the reduction of O2 in biosystems. Szent-Gyorgyi suggested that methyl glyoxal, rather than O2 accepts electrons from enzyme H – C = O | C = O | CH3 surfaces and thereafter reduces O2 homogeneously. This kind of biochemical approach to cancer predated the recognition of DNA, which redirected the attention from biochemistry to genetics. In the account of electrical conductance in biological organisms, it is important to stress: the usefulness of examining semiconduction by means of the Hall effect. Thus,

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265

if an electric current flows through a body in the x direction, and a magnetic field is applied normal to the body in the z direction, an extra electric field is caused to exist in the y direction. From measurements made, then, on the effect of applying this magnetic field to a current flowing through a body, it is possible to determine the charge carrier concentration in the body. Moreover, the sign of the charge carriers, whether electrons (negative) or holes, (positive) can be determined. Knowing the conductance, the applied field strength and the concentration and sign of the charge carriers, it is possible to calculate their mobility values range between 0.01 cm 2/V s to 10 cm 2/Vs at room temperature. The carrier concentration varies over a range of 108 – 1018 sec. The biological materials measured (a comprehensive data set was gathered for the first time by Gutmann Lyons and Keyzer in 1983) show a wide variety of behaviours as to conductance in which either electrons or holes predominate. How does electronic conductance occur in biological materials in this respect, the basic mechanism of conductance in an impurity-containing protein is similar to that of a doped semiconductor such as silicon. However, complications occur in respect to the distance between sites from which electrons originate and those in which they may be received. Basically, electrons tend to transfer through energy barriers within the structure by quantum mechanism tunneling. However, a rough rule the maximum jump length for the tunneling electron is about 20Å. If there is no receiver state for an electrons within that distance, the probability of a successful tunnel transfer will be so slow that the dominant mechanisms of transport may change from that of a tunneling to that of electron hopping between neighboring atoms. Systems that allow tunneling will generally show a much higher value of charge-carrier mobility than those in which atom-to-atom electron hopping is the preferred mode. Another factor is crystallographic and concerns the shape and size of ordered areas in the protein in which there are respective groups, giving rise to band formation, which then enhances the concentration of electrons able to travel under a field gradient.

ELECTRICAL CONDUCTION IN BIOLOGICAL ORGANISMS PROTONIC There are possibilities in biological structures in which the charge carrier is neither an electron nor a hole, but a proton as per Nagle and Morowiz in 1978 and Pething in 1998. Because quantum mechanical tunneling is a frequent mode of transport with electrons, it may be asked if it is likely that proteins could also tunnel. Thus, the Gamow factor for the probability of tunneling is given by the equation. PT αe −

4π l 2mE η

...(3)

where m is the mass tunneling particle, l is the transfer distance, and E is the energy of the entity tunneling. The proton is ~ 1840 times heavier than the electron. Assuming that the distance of transfer for the proton is about one tenth that for the electron, and the E value is the same, the tunneling probability for individual proteins will be about e–4 that for electrons. However, in proteins even if they are wet, so that the activation energy for electrical conductance is only ~0.5eV, the probability of activating an electron to the conductance band will be as little as about 10–7 at room temperature. Particularly,

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Introduction to Polarography and Allied Techniques

it proteins, it may i.e., that the proton concentration exceeds that of conductance-band electrons so that conductance via proton tunneling mechanism becomes likely. Detailed investigation suggests that the rate deterimining step is usually some comformal charge rather than the tunneling step. This would be similar to the situation of protons conducting in aqueous solutions, where the rotation of a water molecule under the field of the approaching proton, is rate determining, not the rate of proton tunneling. Similar conformational changes are necessary in a protein structure, in which electron and proton transfer are the R O C C important steps in electrical | R | H conductance. A possible proton O H O=C C H | N conducting pathway within a H O – H N O N H C H H cytoplasmic membrane is | | H O N C shown in the Fig. 18.11. H H C H R O O Specific conductance in R | C C biological organisms covers the R enormous range of 1015. It is Direction of proton flow possible to understand why the Fig. 18.11 : A series of H bonds (...) serving as a protonrange is so large. The specific conducting pathway within a cytoplasmic or intramemconductance will depend on the brane protein. (Reprinted with permission from J.F. Nagle proteins’ structure. Is it and H.J. Morowitz, proc. Nat. Acad. Sci. U.S.A. 78, 298, suitable for band formation as 1978, p. 299, Fig.3.) it seems to be in many proteins. However, it will also depend on the degree and type of doping, not the intentional addition of trace additives as in the organic semiconductors, but the presence of other entities (water, extra organic substances, fragments etc.) in the structure. Finally, protons may add to the transport because although the probability of tunneling of the individual proton is much smaller than that of an electron, the number of available.

THE ELECTROCHEMICAL MECHANISMS OF THE NERVOUS SYSTEM AN UNFINISHED SECTION Electrical activities are an integrated part of the activity of the brain, but there the amplitude of the encephalographic oscillations is in the microvolt region, whereas tens of millivolts are needed to trigger passage of a pulse through the nervous system. Bernstein, in 1962 first focused attention on the alleged importance of the ratios of the Na+ and K+ concentrations of the intra and extracellular fluids of the nerve axon and related them via a Nernst type equation to the electrical potential measured across it. Thus the theoretical approach to the passage of electricity through nerves become electrochemical. Hodgkin and Huxley, Nobel prize winners published seminal experiments on the current potential relation across the membrane of the nerve sheath during 1952. Attached to the original and elegant expeirments they described was a phenomenological theory of the surprising results were reported the result inferred the interpretation of the variation of potential across the membrane containing the intracellular fluid when the

Bioelectrodics

267

passage of current through a nerve was triggered and this confirmed as to what has been found experimentally and was expressed impressively mathematically also. The Hodgkin-Huxley (H-H) theory of the nervous system was an example of bioeletrochemistry glillering with the virtue, a work truly to be compared in status with the best known piece of electrochemistry the Debye-Hickel theory of ionic solutions. It appeared later that the theory was untestable. The electrophysiologists still use the HH theory.

ENZYMES AS ELECTRODES Enzymes: Enzymes are catalysts for reactions in the body in fact they serve to make the nature of biochemical activities different and faster. Enzymes are proteins and their molecular weight varies greatly, from 103 to 106: Apart from their acceleration of a reaction brought about by enzymes, there is their astounding specificity: They are turned on and of by tiny changes in the structure of the entities taking part in the bioreaction being catalysed. Apart from this there are ‘coenzymes’, by which is meant another substance, mostly a vitamins, that has to be present to make the enzyme work. Enzyme catalysts have yet another, puzzling feature, reactions catalyzed by them do indeed increase in rate, with temperature. However, proteins tend to unfold at certain temperature known as denaturation, when this occurs, the enzyme loses its activity. They still retain their extraordinary activity and specificity for reaction with a substance in solution that it is meant to catalyze.

Electrodes Carrying Enzymes: The 1980s were spent in discovering what not to do if one wished to carry enzymes in electrode and use their powers as electrocatalysts. 1. Single electron tunneling jumps greater than about 20Å do not happen, although much can be alone (Heller and Delgani, 1987) to facilitate successive jumps. 2. Even partial decomposition of an enzyme upon adsorption must be prevented because the fragments produced from a passive layer on the electrode and in activate any enzymatic activity there. 3. Far-reaching decomposition of the enzyme upon adsorption must obviously be avoided, for it occurs, it destroys the enzymes catalytic power. There are only two ways to obtain a successful, adsorbed enzyme acting as an electrocatalyst (Rusling 1997). 1. The enzyme itself and the electrode system upon which it is to adsorb must be highly purified. 2. The most important point (much applied by Eddowes and Hill at the University of Oxford) is to have a suitable promotors as the electrode. It is this prelayer that encourages complicated large bimolecules to adsorb and still retain some of the properties as catalysis that they show in solution. It has been known that one way to make model membranes is to use bilayers of phospholipids placed tail to tail and insert proteins is to them. Fig: 18.12.

Bioelectrodics 10 Current, μA

active in electron exchanges in chlorophyll and bacteria, and resulting in the production of H. Why is it that the pre adsorbed surfactant layer on the electrode (e.g., the DDAB), has such a helpful effect in facilitating the reactions of enzyme electrode? For one thing, the surfactant is a good, adsorber on the metal or graphite electrode. Correspondingly, if, upon adsorption, there is some partial dissociation of the complex enzyme, the pre adsorbed surfactant makes it difficult for such fragments to build up passive layers on the electrode layers that could diminish electron transfer. Another factor that has to be controlled, in case one wishes to obtain the maximum reaction rate, is pH. At a pH <4.6, MB is partly unfolded and can be reduced directly. However, at a pH > 9, the reduction involves protonation. The rates of these reactions are very high, a rate constant of 8000m-1cc-1, equivalent to an i0 of –10–5 A cm–2 if the reactant concentration is 10–3 M.

269

Fe(III)

c

Fe(II) ba

5 0 –5 Fe(II)

–10

0.40

0.20

Fe(III) 0.00 –0.20 –0.40 E, V vs SCE

Fig. 18.14 : Cyclic voltmmograms at 100mVs-1 inpH 5.5 buffer. a, pH 5.5 buffer on bare pyrolytic graphite (PG); b, 0.5 mMMB (horse, from Sigma) in buffer on bare PG; c, MB-DDAB film on PG in buffer, no MB in solution. (reprinted from J.F. Rusling, “Electrochemical Enzyme Catalysis,” Interface, 6(4): 26-312, Fig. 2 1997. Reproduced with permission from the Electrochemical Society, Inc.)

The Electrochemical Enzyme-Catalyzed Oxidation of Styrene Styrene is a phenyl ethylene, C–C6H11 – Ch = CH2, a compound important in a number of polymerization. In the body the cytochrome P450 enzyme in the liver can form styrene oxide, which then may react with organisms’ DNA, i.e., become a carcinogen. The use of MB in lipid films to oxidize styrene has been achieved by Rusting et.al. (1997) in a series of reactions that can be written as follows: X-MB Fe(III) + e– X-MB Fe(II) (at electrode) X-MB Fe(II) + O2 → X – MB Fe(II) – O2 X-MB Fe(II) – O2 + 2e– + 2H+ → X – MB Fe(II) + H2O2 (at electrode) H2O2 + X – MB Fe(III) → X – MB Fe(IV) = O + H2O 2X – MB Fe(IV) = O + H2O2 → 2HX – MB Fe(IV) = O + O2 Styrene + X – MB Fe(IV) = O → X – MB Fe(III) + styrene oxide It can resonably be concluded that the inclusion of enzyme proteins in SAMs provokes fast electrode reactions.

APPENDIX Table 1 : Values of Important Constants (N, F and R for the chemical mole) Avogadro’s Number N = (6.023 0 ± 0.000 2) × 1023 mole–1 Charge on the Electron e = (4.802 94 ± 0.000 08) × 10–10 e.s.u. = (1.602 09 ± 0.000 03) × 10–20 e.m.u. = (1.602 09 ± 0.0003 03) × 10–19 coulomb Faraday Constant F = (9,649.3 ± 0.2) e.m.u. equivalent–1 = (96,493 ± 2) coulomb equivalent–1 Gas Constant R = (8.3147 ± 0.000 05) joule deg.–1 mole–1 = (1.987 2 ± 0.000 01) cal. deg.–1 mole–1 = (0.082 057 ± 0.000 000 5) l.atm.deg.–1 mole–1 Boltzmann’s Constant k = (1.380 49 ± 0.000 05) × 10–16 erg deg.–1 Ice Point T0ºC = (273.150 0 ± 0.000 2) ºK Velocity of Light C = (2.997 928 ± 0.000 004) × 10 10 cm sec–1 Planck’s Constant h = (6.6254 ± 0.000 2) × 10–27 erg sec Standard Atmosphere 1 atm. = 1,013,250 dyne cm–2 Standard Gravitational Acceleration g 0 = 980.665 cm sec–1 Defined Calorie 1 cal. = 4.1840 joules Relation between Chemical and Physical Mole 1 phys. mole = 1.000 275 chem. mole Relation between Litre and Cubic Centimetre 11. = (1,000.028 ± 0.004) cm3

Appendix

271 TABLE 2 Electron Affinities of the Atoms

The electron affinity of an atom or radical is the energy absorbed in converting the particular ion shown into the neutral atom or radical. Values under I are those given by Fritchard (Chem. Rev. 52 (1953) 529); values under II are those given in LandoltBörnstein, I Band, 1 Teil, p. 213. Ion

I kcal/mole

H– Li– Na– K– Hg– C– C4– N–

17.22 12.5 28 16 35.4 48 ± 20 –708 –16

N 3– Bi– O– O2– S–

> 47 ? > 17 ? 53.8 ± 0.8 – 210 > 24

II kcal/mole

II eV

Ion

I kcal/mole

II kcal/mole

16.5 10

0.72 0.5

S2– Se– Se2– Te–

–80 > 40? –97 50?

–90

28

1.2

F– Cl– Br–

83.5 ± 2 88.2 ± 1.5 81.6 ± 1.5

94 87 81

4.1 3.78 3.52

Γ

74.6 ± 1.5

72 70 45 60

3.12 3 2 2.5

53.5 – 150 60

2.34 – 6.5 2.5

CN– OH– HS–

II eV –4

TABLE 3 The Work of Extraction of an Electron from various Metals in Electron Volts Ag Al

4.70 4.20

Cu Fe

4.48 4.63

Nb Nd

3.99 3.3

Si Sm

3.59 3.2

As Au B Ba Be Bi C Ca Cd Ce Co Cr Cs

4.79 4.71 4.6 2.52 3.92 4.34 4.36 3.20 4.04 2.88 4.25 4.45 1.94

Ga Ge Hf Hg Ir K La Li Mg Mn Mo Na

4.16 4.62 3.53 4.53 4.57 2.25 3.3 2.46 3.70 3.95 4.24 2.28

Ni Os Pb Pd Pr Pt Rb Re Rh Ru Sb Se

4.91 4.55 4.04 4.98 2.7 5.36 2.13 4.97 4.65 4.52 4.56 4.87

Sn Sr Ta Te Th Ti Tl U V W Zn Zr

4.39 2.74 4.13 4.73 3.47 4.16 4.05 3.45 4.11 4.53 4.27 3.93

272

Introduction to Polarography and Allied Techniques TABLE 4 Dielectric Constant of Aqueous Solutions at 25°C ε = 78.54 – 2Ac (valid c = 0.5 – 2.0) Solute

A

Solute

A

HCl LiCl NaCl KCl RbCl NaF KF

10 7 5.5 5 5 6 6.5

NaI KI MgCl2 BaCl2 LaCl3 NaOH Na2SO4

7.5 8 15 14 22 10.5 11

TABLE 5 Dielectric Constants (∈ ∈ ) of some Inorganic Solvents

Reproduced from Harned and Owen, Physical Chemistry of Electrolyte Solutions, First Edition, by courtesy of Reinhold Book Division Solvent

∈

tºC

Solvent

∈

tºC

AsCl3

12.8

20

NH3

16.9

25

D2O

77.94

25

N 2H2

51.7

25

HCN

106.8

25

N 2O4

2.4

18

83.6

25

NOCl

18.2

12

HF H2SO4

101

25

POCl3

13.3

22

9.8

240

SO2

14.1

20

I2

11.1

118

SOCl2

09.25

20

IF5

36.2

25

SO2Cl2

09.2

20

SeOCl2

46.2

20

HgBr2

TABLE 6 Dielectric Constants of Mixtures of Water and Organic Solvents at 25ºC Non-aqueous

Weight % of Non-aqueous Component

Component

10

20

30

40

50

60

70

80

90

100

CH3 CH 2OH CH3 CH 2CH 2OH

72.8 71.8

67.0 64.9

61.1 57.7

55.0 50.3

49.0 43.0

43.4 36.4

38.0 30.7

32.8 26.1

28.1 22.7

24.3 20.1

(CH 3) 2CHOH

71.4

64.1

56.9

49.7

42.5

35.3

28.7

23.7

20.3

18.0

(CH3 ) 3COH

70.0

61.3

52.6

43.9

35.4

27.9

21.4

16.5

12.4

9.9

CH 2OH.CH 2OH

75.6

72.8

69.8

66.8

63.2

59.4

54.7

49.3

43.7

37.7

Appendix

273 TABLE 7 Polarographic Half-Wave Potentials (in Volts vs. the normal Calomel Electrode) in Aqueous Solution

Ion

N

+

Li

A

B

– 2.31

– 2.31

Ca

– 2.23

– 2.23

K+

– 2.17

– 2.17

Na+

– 2.15

– 2.15

2+

– 2.13

– 2.13

+

– 2.09

– 2.09

+

Rb

– 2.07

NH+4

– 2.08

NH3CH+3

– 2.8a

NH2(CH3)+2

– 2.09a

NH(CH3)+3

– 2.27

N(CH3)+4

– 2.7

N(C2H5)+4

– 2.71

+ 7 4

– 2.56

+ 9 4

– 2.61

2+

Sr

Cs

N(C3H ) N(C4H )

– 2.07 – 2.15b

Rare Earth Metals – 1.90

– 1.94

2+

– 1.89

– 1.89

Ra Sc

– 1.9 to – 2.0

2+

Ba

– 2.29

3+

– 1.96

– 1.84

Zr4+

– 1.7 TABLE 8 Anodic Depolarization Potentials

Process

Solution

Hg + Cl− → HGCl Hg

+ N −3

E1/2 + 0.21

→ HgN 3

+ 0.21

−

Hg + CNS → HgCNS

+ 0.14

Hg + Br − → HgBr

+ 0.10

Hg + 2OH− → HgO

Anion concentration

+ 0.04

274

Introduction to Polarography and Allied Techniques Process

Solution

E1/2

Hg + 2SO23 − → Hg(SO3 )2

= 0.001 M

– 0.05

Hg + Γ → HgI Hg

+ 2S2O23−

– 0.07

→ Hg(S2O3 ) 22−

– 0.18

Hg + 2CN− → Hg(CN)2

– 0.4

Hg + S2 − → HgS

– 0.6

Fe II → Fe III II

Fe → Fe

III

II

Mn → Mn I

III

II

Re → Re

0.1 N KHF2

+ 0.08

C

– 0.38

2 N KOH, tartrate

– 0.40

1 N HCiO4

– 0.54

II

III

1 N HCiO4

– 0.42

III

V

Re → Re

1 N HCiO4

– 0.26

→

1 N HCiO4

0.0

→

Cr III

0.1 N Na2SO4

– 0.62

ReV CrII

→ Re

ReVII

Re

II

IV

HCl

– 0.06

SnII

→ SnIV

tartrate pH = 2.3

– 0.18

SnII

→ SnIV

tartrate pH =7

– 0.48

SnII

→ SnIV

tartrate pH =13

– 0.75

SnII

→ SnIV

1 N KOH

– 0.77

Sn → Sn

SnII → SnIV

F

– 0.24

SbIII

→ SbV

0.5 N KOH

– 0.34

AsIII

AsV

0.5 N KOH

– 0.25

Ti III → Ti IV

HCl

– 0.18

VIV

pH = 6.8

+ 0.07

C

– 0.36

1 N KOH

– 0.46

IV

V

→

→

VV V

→V

VIV → VV

TABLE 9 Inorganic Oxidation Reduction Potentials Process CuI

CuII

I

II

Cu

Cu

Solution

E1/2

0.1 N Na2SO4

– 0.06

C

– 0.25

Appendix

275

Process CuI

CuII

II

III

Solution

E1/2

Citrate buffer pH = 7.0

– 0.21

Cu

Cu

Saturated CaCl2

– 0.55

CuII

CuIII

D

– 1.42

MnII

MnIII

Triethanolamine, 0.5 N NaOH

– 0.49

Fe

III

1 N Sodium oxalate

– 0.30

Fe

III

Citrate buffer pH = 4.0

– 0.04

Fe II

Fe III

Citrate buffer pH = 7.0

– 0.49

Fe II

Fe III

Tartrate buffer pH = 10.0

– 0.9

II

III

1 N KOH

– 0.9

Tii

Saturated CaCl2

– 0.15

TiIII

TiiIV

0.1 N KCNS

– 0.49

TiIII

TiiIV

Citric or tartaric acid

– 0.48

1 N H2SO4

– 0.55

1 N oxalate, pH = 4.5

– 1.16

1 N HCl

– 0.93

Fe

II

Fe

II

Fe Ti

Fe

III

IV

VII

VIII

II

III

V

U

V

III

U

IV

NpIII

NpIV

1 N HCl

– 0.10

PuIII

PuIV

1 N HClZ

+ 0.65

TABLE 10 Electrode Potentials and Electrical Conductivities Electrode

Electrode reaction

Volts

Li = Li+ + e–

+ 3.045

Acid Solution Li/Li+ +

+

K/K

K=K + e ++

Ba/Ba

++

Ca/Ca

++

++

Ba = Ba

++

Ca = Ca

+

–

+ 2.925

+ 2e

–

+ 2.906

+ 2e

–

+ 2.866

–

Na/Na

Na = Na + e

Mg/Mg++

Mg = Mg++ + 2e–

+ 2.363

Al/Al3+

Al = Al3+ + 3e–

+ 1.662

Mn/Mn++

Mn = Mn++ + 2e–

+ 1.180

+ 2.7142

276

Introduction to Polarography and Allied Techniques Electrode

Electrode reaction

Volts

Zn/Zn++

Zn = Zn++ + 2e–

+ 0.762 8

Cr/Cr

3+

Fe/Fe

++

Cr = Cr

3+

Fe = Fe

++

+ 3e

–

+ 0.744

+ 2e

–

+ 0.440 2

Cd/Cd++

Cd = Cd++ + 2e–

+ 0.440 9

Pb/PbSO4/SO4–

Pb + SO4– = PbSO4 + 2e–

+ 0.358 8

++

Pb/Pb

Pb = Pb +

++

+ 2e

+

–

+ 0.126

–

Pt/H2/H

H2 = 2H + 2e

Ag/AgBr/Br–

Ag + Br– = AgBr + e–

– 0.071 3

Cu/CuCl/Cl

Cu + Cl– = CuCl + e–

– 0.137

+

Pt/Cu , Cu

++

+

++

Cu + Cu + e

–

0.000 0

–

– 0.153

–

–

Ag/AgCl/Cl

Ag + Br = AgBr + e

Pt/Hg/Hg2Cl2/Cl–

2Cl– ± 2Hg = Hg2Cl2 + 2e–

– 0.267 6

Cu/Cu++

Cu = Cu++ + 2e–

– 0.337

Pt/I2/I–

31 = I3– + 2e–

– 0.536

++

Pt/Fe , Fe

3+

Fe

+

++

= Fe

3+

+

+e

–

– 0.771

–

Ag/Ag

Ag = Ag + e

Au/AuCl4–, Cl–

Au + 4Cl– = AuCl4– + 3e–

Pt/Cl2/Cl–

2Cl– = Cl2 + 2e–

++

Pt/Mn , MnO

– 4

++

Mn

–

– 0.799 1 – 1.00 – 1.359 5 – 4

+

+ 4H2O = MnO 8H + 5e

–

Pt/F2/F

– 0.222 5

2F = F2(g) + 2e

–

–

– 1.51 – 2.87

TABLE 11 Ionic Properties of Water Temperature °C

0

10

20

25

Specific conductivity, ohm–1 cm–1 × 108

1.2

2.3

4.2

5.5

Ionic product KW × 1015

1.14

2.92

6.81

10.08

30

50

100

7.0

17

—

14.7

56

513

Appendix

277 TABLE 12 Ionisation Constants of Acids (at 25°C)

Acid

–log K

Acetic Benzoic Boric Bromacetic n-Butyric Carbonic

K1 K2

Chloroacetic Chromic Cinnamic (cis) Cinnamic (trans) Citric

K1 K2 K3

Dichloroacetic Formic Fumaric

K1 K2

Glutaric Glycine Hydrocyanic Hydrofluoric Hydrosulphuric (H2S)

K1

Acid

4.76 4.20 9.24 2.87 4.82 6.37 10.25 2.86 6.49 3.88 4.43 3.06 4.74 5.40 1.30 3.75 3.03 4.47 4.34 9.78 9.14 3.14 7.24

Nitrous Oxalic Phenol Phosphoric

Phosphorus Phenolphthalein o-Phthalic Picric Propionic Salicylic Silicic Succinic Sulfanilic Sulphuric Sulphurous

K2 14.92 K1 2.00 K2 6.26 K1 2.85 K2 6.10

Maleic Malonic

–log K

Tartaric Trichloroacetic Uric

K1 K2 K1 K2 K3 K1 K2 K1 K2

Ca K1 K2 K1 K1 K1 K2 K1 K2

4.47 1.19 4.21 9.89 2.12 7.21 12.32 1.80 6.15 9.70 2.89 5.41 0.38 4.87 2.97 9.7 4.19 5.57 3.19 0.40 1.92 1.76 7.20 3.02 4.54 0.89 3.89

TABLE 13 Buffer Mixtures Buffer Compositions (After Clark and Lubs) 4.85 20.75 8.3 5.3

ml ml ml ml

0.2 0.2 0.2 0.2

N N N N

HCl HCl HCl HCl

+ + + +

25 25 25 25

ml ml ml Ml

0.2 0.2 0.2 0.2

KCl KCl KCl KCl

pH (20°C) diluted diluted diluted diluted

to to to to

100 100 100 100

ml ml ml ml

1.0 1.4 1.8 2.0

278

Introduction to Polarography and Allied Techniques Buffer Compositions (After Clark and Lubs)

pH (20°C)

46.70 32.95 20.32 9.90 10.40 22.15 6.95 43.00

ml ml ml ml ml ml ml ml

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

N N N N N N N N

HCl + 50 ml 0.1M KHC8H4O4 diluted to 100 ml HCl + 50 ml 0.1M KHC8H4O4 diluted to 100 ml HCl + 50 ml 0.1M KHC8O4 diluted to 100 ml HCl + 50 ml 0.1M KHC8H4O4 diluted to 100 ml NaOH + 50 ml 0.1M KHC8H4O4 diluted to 100 ml NaOH + 50 ml 0.1M KHC8H4O4 diluted to 100 ml NaOH + 50 ml 0.1M KHC8H4O4 diluted to 100 ml NaOH + 50 ml 0.1M KHC8H4O4 diluted to 100 ml

2.2 2.6 3.0 3.4 4.0 4.6 5.2 5.8

5.70 17.80 39.50 45.20

ml ml ml ml

0.1 0.1 0.1 0.1

N N N N

NaOH NaOH NaOH NaOH

+ + + +

50 50 50 50

ml ml ml ml

0.1M 0.1M 0.1M 0.1M

KH2PO4 KH2PO4 KH2PO4 KH2PO4

6.0 6.6 7.4 7.8

2.61 8.50 21.30 36.85 43.90

ml ml ml ml ml

0.1 0.1 0.1 0.1 0.1

N N N N N

NaOH NaOH NaOH NaOH NaOH

+ + + + +

50 50 50 50 50

ml ml ml ml ml

0.1M 0.1M 0.1M 0.1M 0.1M

H3BO3 H3BO3 H3BO3 H3BO3 H3BO3

diluted diluted diluted diluted

diluted diluted diluted diluted diluted

to to to to

to to to to to

100 100 100 100

100 100 100 100 100

ml ml ml ml

ml ml ml ml ml

7.8 8.4 9.0 9.6 100

QUESTIONS Chapter 1 1. 2. 3. 4. 5.

Describe Polarography giving applications. What is a Polarographic cell? Describe the experimental set up of Polarographic circuit. Describe the Half-wave potential and its significance. Describe ionic strength and also give the influence of ionic strength on halfwave potentials. 6. What are the factors which affect the half-wave potentials?

Chapter 2 1. 2. 3. 4.

Describe Dropping Mercury Electrode (D.M.E.). What are the advantages of D.M.E.? What particular cell is used in Polarography? What are its advantages? Describe the various electrodes giving their uses. (a) Hanging Mercury Drop Electrodes. (b) Carbon Electrodes. (c) Carbon Paste Electrodes. (d) Glassy Carbon Electrodes. (e) Mercury Pool Electrode. (f) Calomel cell. 5. Which reference electrodes mostly used in Polarography? Why? 6. How would you distinguish between working electrode and a reference electrode?

Chapter 3 1. 2. 3. 4. 5.

Describe the Polarographic circuit. What is the significance of diffusion in classical Polarography? What solvents are mostly used in Polarography? Why supporting electrolytes are used in Polarography? What is Polarographic maxima? What various types of maxima are being observed in Polarography? 6. Innumerate various non-aqueous solvents. 7. Which are useful in Polarography?

280

Introduction to Polarography and Allied Techniques

Chapter 4 1. 2. 3. 4. 5.

Describe the Ilkovic equation? What are its consequences? Describe the cathodic and anodic waves. What are reversible and irreversible electrode processes? What is the significance of reversible polarographic wave? Describe the coupled chemical reactions and chemical reversibility.

Chapter 5 1. 2. 3. 4. 5.

What are the various currents that have some significance in Polarography? Describe the diffusion current and its significance in Polarography. What are diffusion-controlled currents? Describe the diffusion coefficient and its significance. What are the various factors that affect the diffusion current?

Chapter 6 1. What is the Polarization of the D.M.E.? Give an account of the depolarization process. 2. What is hydrogen over voltage and give an account of the reduction of hydrogen ions? 3. Describe double layer. How double layer affects the reduction process? 4. Give a brief account of the reduction of cation giving two examples.

Chapter 7 1. 2. 3. 4. 5. 6. 7.

Describe the theory of amperometry. Describe the types of amperometric titrations. What are redox titrations? What are complexometric and chelometric titrations? Give an account of amperometric titrations with two polarized electrodes. Describe the experimental set up of amperometric titrations. What is chronoamperometry?

Chapter 8 1. How metal complexes are determined by Polarographic method? 2. What is the significance of reversible, diffusion-controlled system in metal complex? 3. How the formulae and stability constants of metal complexes are determined by polarography? 4. What methods are employed in studying mixed ligand complexes? 5. How the co-ordination number of metal complex could be determined?

281

Chapter 9 1. 2. 3. 4.

Which bond types are reducible at D.M.E.? Which functional groups are reducible at D.M.E.? Can Polarography be used to detect and follow intermediates in some reactions? Describe the utility of Polarographic methods in the electrosynthesis of organic compounds. 5. What are the advantages of electro-organic syntheses?

Chapter 10 1. What conditions are required in order to use mathematical analysis to resolve overlapped first derivative D.C. polarograms? 2. What are the advantages of using Non-aqueous solvents or solvent extracts in D.C. Polarography? 3. Describe in brief theory, principles and applications of cyclic and pulse techniques. 4. What is stripping analysis? Describe the electrodes used in these techniques. 5. Give a brief account of voltammetric methods. Also the differential and derivative voltammetry.

Chapter 11 1. Innumerate various types of organic electrode reactions giving examples. 2. What are the various categories of electrolytic reaction pathaways of N-heterocyclic reactions in general? Give examples. 3. Describe the experimental technique for running an electrochemical experiment with an organic system. 4. Give a circuit diagram for galvanostatic method (constant current). 5. Also give circuit for potentiostatic method. 6. What is Polarization study? How is it done?

PART II. ALLIED TECHNIQUES Chapter 10 1. Define Kalousek’s commutator method. How is the method related to the square wave and pulse-polarographic techniques. 2. What are charging currents? 3. Give an account of the sinusoidal A.C. Polarograph? 4. Does the A.C. Polarograph constructed from operational amplifier provide some advantages? 5. What is the disadvantage of operational amplifier employed in most existing electroanalytical instruments?

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6. What arrangement is named as milli- or microcoulometry? 7. Innumerate the various methods for determining ‘n’ by electrolysis.

Chapter 11 1. Describe chronopotentiometry in brief. What are its analytical applications? 2. What are the advantages of chronopotentiometry over polarography for a particular type of experiment? 3. What type of cells are used for chronopotentiometry? 4. What is the significant use of pulse polarography and differential pulse polarography with D.C. Polarography? 5. Give an account of electrolytic currents and kinetic currents. 6. Give brief account of pulse polarography and oscillographic Polarography.

Chapter 12 1. What is voltammetry? 2. Describe in brief coulometric methods. 3. Distinguish between differential and derivative voltammetry.

Chapter 13 1. 2. 3. 4. 5. 6.

Give a brief account of the technique applied in electro-organic synthesis. What are the main reactions that take place in electro-organic synthesis? What is the main electrochemical activity in heterocyclic systems? Describe the experimental technique. How is the current efficiency determined? What is polarization study?

Chapter 14 1. 2. 3. 4. 5. 6. 7. 8.

What are ion selective electrodes? What part is played by hydrogen in corrosion? How is corrosion controlled? Give an account of potential-pH diagrams applied in corrosion processes. What are electronation reactions in corrosion? What are the factors that affect the rate of corrosion. Give some common examples of corrosion? What is passivation?

Chapter 15 1. 2. 3. 4. 5.

What pollution problems arise from the predominent form of energy conversion? What uncertainties are there in predicting the future pollution of the atmosphere? What is the power output of an electrochemical energy converter? What are fuel cells? Give a brief account of some important fuel cells?

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Chapter 16 1. 2. 3. 4. 5.

Describe energy density. Electricity storage density. Give an account of some important storage batteries. What are new electricity storers? Describe lead-acid storage battery.

Chapter 17 1. 2. 3. 4. 5.

Distinguish between faradic and non-faradic processes. What is an ideal polarised electrode? Describe briefly the electrical double layer. What are the factors which affect the rates of electrode reactions and current? Give a brief account of the following given one example of each. (i) Formal potential (ii) Electrochemical potentials (iii) Absolute potential (iv) Cell potential (v) Liquid junction potential. 6. Give the current over potential equation. 7. What are the implications of Butler-Volmer equation?

General Question 1. Define Faraday’s laws of electrolysis. 2. Define EMF of a cell. 3. Describe Fick’s laws of diffusion and their use in the study of polarography.

Describe: 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

Nern’st equation. Activity and activity coefficient. Ionic strength and ionic equlibrium. Boltzman’s constant. Avogadro’s number. Elcovic equation. Solubility and solubility product. Buffer solutions. Give two examples. Polarity of an electrode. Half wave potential. D.M.E. its advantages and disadvantages. Electrode potential and standard electrode potential. Indicator electrode and reference electrode. Liquid junction. Reversible and irreversible electrode reactions.

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19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.

Introduction to Polarography and Allied Techniques

Double layer and its part played during electrolysis. Over voltage. Free energy. Concentration polarization. Hydrogen over-voltage. Current efficiency. How it is determined? Advantages and disadvantages of D.M.E. Dielectric constant. Why there are no standard potentials more negative than about –3 volts and more positive than about +2 volt, in aqueous solution? What is pH? How can one determines pH of solution? How does a three electrode system differs from the two electrode system? What are these named as? Give advantages of choosing the three electrode system. What is the significance for the use of normal hydrogen electrode? Differenciate between D.C. and A.C. polarography. Why in polarographic experiments, it is desirable to remove dissolved oxygen from the electrolyte by bubbling an inert gas through it? Why is it necessary to add an inert electrolyte to the experimental solution of polarography before carrying out the actual experiment? When Ed. vs log iid-i , is plotted, the linear plot for reaction that behaves

reversibly under diffusion controlled conditions. What would be the value of the slope of this linear plot and what would be the expression and its value at the intercept? Explain giving an example. 35. Describe the various types of currents that have some significance in polarography and allied techniques.