VOLUME 1 MODERN ELECTROCHEMISTRY

Transcription

1 VOLUME 1 MODERN ELECTROCHEMISTRY

2 VOLUME 1 MODERN ELECTROCHEMISTRY An Introduction to an Interdisciplinary Area John O'M. Bockris Professor of Electrochemistry University of Pennsylvania, Philadelphia, Pennsylvania and Amulya K. N. Reddy Professor of Electrochemistry Indian Institute of Science, Bangalore, India A Plenum/Rosetta Edition

3 6ockris, John O'M. Modern electrochemistry. Library of Congress Cataloging in Publication Data "A Plenum/Rosetta edition." 1. Electrochemistry. I. Reddy, Amulya K. N., joint author. II. Title ' A Plenum/Rosetta Edition Published by Plenum Publishing Corporation 227 West 17th Street, New York, N.Y Plenum Press, New York A DivisIOn of Plenum Publishing Corporation United Kingdom edition published by Plenum Press, london A Division of Plenum Publishing Company, ltd. Davis House (4th Floor),8 Scrubs lane, Harlesden, london, NW10 6SE, England All rights reserved ISBN-13: e-1sbn-13: DOl: /

4 PREFACE This book had its nucleus in some lectures given by one of us (J.O'M.B.) in a course on electrochemistry to students of energy conversion at the University of Pennsylvania. It was there that he met a number of people trained in chemistry, physics, biology, metallurgy, and materials science, all of whom wanted to know something about electrochemistry. The concept of writing a book about electrochemistry which could be understood by people with very varied backgrounds was thereby engendered. The lectures were recorded and written up by Dr. Klaus Muller as a 293-page manuscript. At a later stage, A.K.N.R. joined the effort; it was decided to make a fresh start and to write a much more comprehensive text. Of methods for direct energy conversion, the electrochemical one is the most advanced and seems the most likely to become of considerable practical importance. Thus, conversion to electrochemically powered transportation systems appears to be an important step by means of which the difficulties of air pollution and the effects of an increasing concentration in the atmosphere of carbon dioxide may be met. Corrosion is recognized as having an electrochemical basis. The synthesis of nylon now contains an important electrochemical stage. Some central biological mechanisms have been shown to take place by means of electrochemical reactions. A number of American organizations have recently recommended greatly increased activity in training and research in electrochemistry at universities in the United States. Three new international journals of fundamental electrochemical research were established between 1955 and In contrast to this, physical chemists in U.S. universities seem-perhaps partly because of the absence of a modern textbook in English-out of touch with the revolution in fundamental interfacial electrochemistry which has v

5 vi PREFACE occurred since The fragments of electrochemistry which are taught in many U.S. universities belong not to the space age of electrochemically powered vehicles, but to the age of thermodynamics and the horseless carriage; they often consist of Nernst's theory of galvanic cells (1891) together with the theory of Oebye and Hiickel (1923). Electrochemistry at present needs several kinds of books. For example, it needs a textbook in which the whole field is discussed at a strong theoreticallevel. The most pressing need, however, is for a book which outlines the field at a level which can be understood by people entering it from different disciplines who have no previous background in the field but who wish to use modern electrochemical concepts and ideas as a basis for their own work. It is this need which the authors have tried to meet. The book's aims determine its priorities. In order, these are: 1. Lucidity. The authors have found students who understand advanced courses in quantum mechanics but find difficulty in comprehending a field at whose center lies the quantum mechanics of electron transitions across interfaces. The difficulty is associated, perhaps, with the interdisciplinary character of the material: a background knowledge of physical chemistry is not enough. Material has therefore sometimes been presented in several ways and occasionally the same explanations are repeated in different parts of the book. The language has been made informal and highly explanatory. It retains, sometimes, the lecture style. In this respect, the authors have been influenced by The Feynmann Lectures on Physics. 2. Honesty. The authors have suffered much themselves from books in which proofs and presentations are not complete. An attempt has been made to include most of the necessary material. Appendices have been often used for the presentation of mathematical derivations which would obtrude too much in the text. 3. Modernity. There developed during the 1950's a great change in emphasis in electrochemistry away from a subject which dealt largely with solutions to one in which the treatment at a molecular level of charge transfer across interfaces dominates. This is the "new electrochemistry," the essentials of which, at an elementary level, the authors have tried to present. 4. Sharp variation is standard. The objective of the authors has been to begin each chapter at a very simple level and to increase the level to one which allows a connecting up to the standard of the specialized monograph. The standard at which subjects are presented has been intentionally

6 PREFACE vii variable, depending particularly on the degree to which knowledge of the material appears to be widespread. 5. One theory per phenomenon. The authors intend a tcaching book, which acts as an introduction to graduate studies. They have tried to present, with due admission of the existing imperfections, a simple version of that model which seemed to them at the time of writing to reproduce the facts most consistently. They have for the most part refrained from presenting the detailed pros and cons of competing models in areas in which the theory is still quite mobile. In respect to references and further reading: no detailed references to the literature have been presented, in view of the elementary character of the book's contents, and the corresponding fact that it is an introductory book, largely for beginners. In the "further reading" lists, the policy is to cite papers which are classics in the development of the subject, together with papers of particular interest concerning recent developments, and in particular, reviews of the last few years. It is hoped that this book will not only be useful to those who wish to work with modern electrochemical ideas in chemistry, physics, biology, materials science, etc., but also to those who wish to begin research on electron transfer at interfaces and associated topics. The book was written mainly at the Electrochemistry Laboratory in the University of Pennsylvania, and partly at the Indian Institute of Science in Bangalore. Students in the Electrochemistry Laboratory at the University of Pennsylvania were kind enough to give guidance frequently on how they reacted to the clarity of sections written in various experimental styles and approaches. For the last four years, the evolving versions of sections of the book have been used as a partial basis for undergraduate, and some graduate, lectures in electrochemistry in the Chemistry Department of the University, The authors' acknowledgment and thanks must go first to Mr. Ernst Cohn of the National Aeronautics and Space Administration. Without his frequent stimulation, including very frank expressions of criticism, the book might well never have emerged from the Electrochemistry Laboratory. Thereafter, thanks must go to Professor B. E. Conway, University of Ottawa, who gave several weeks of this time to making a detailed review of the material. Plentiful help in editing chapters and effecting revisions designed by the authors was given by the following: Chapters IV and V, Dr. H. Wroblowa (Pennsylvania); Chapter VI, Dr. C. Solomons (Pennsylvania) and Dr. T. Emi (Hokkaido); Chapter VII, Dr. E. Gileadi (Tel-

7 viii PREFACE Aviv); Chapters VIII and IX, Prof. A. Despic (Belgrade), Dr. H. Wroblowa, and Mr. J. Diggle (Pennsylvania); Chapter X, Mr. J. Diggle; Chapter XI, Dr. D. Cipris (Pennsylvania). Dr. H. Wroblowa has to be particularly thanked for essential contributions to the composition of the Appendix on the measurement of Volta potential differences. Constructive reactions to the text were given by Messers. G. Razumney, B. Rubin, and G. Stoner of the Electrochemistry Laboratory. Advice was often sought and accepted from Dr. B. Chandrasekaran (Pennsylvania), Dr. S. Srinivasan (New York), and Mr. R. Rangarajan (Bangalore). Comments on late drafts of chapters were made by a number of the authors' colleagues, particularly Dr. W. McCoy (Office of Saline Water), Chapter II; Prof. R. M. Fuoss (Yale), Chapter III; Prof. R. Stokes (Armidale), Chapter IV; Dr. R. Parsons (Bristol), Chapter VII; Prof. A. N. Frumkin (Moscow), Chapter VIII; Dr. H. Wroblowa, Chapter X; Prof. R. Staehle (Ohio State), Chapter XI. One of the authors (A.K.N.R.) wishes to acknowledge his gratitude to the authorities of the Council of Scientific and Industrial Research, India, and the Indian Institute of Science, Bangalore, India, for various facilities, not the least of which were extended leaves of absence. He wishes also to thank his wife and children for sacrificing many precious hours which rightfully belonged to them.

8 VOLUME 1 CHAPTER 1 Electrochemistry Introduction.... Electrons at and across Interfaces.... Many Properties of Materials Depend upon Events Occurring at Their Surfaces.... Almost All Interfaces Are Electrified.... The Continuous Flow of Electrons across an Interface: Electrochemical Reactions.... Electrochemical and Chemical Reactions.... Basic Electrochemistry.... Electrochemistry before The Treatment of Interfacial Electron Transfer as a Rate Process: The 1950's.... Quantum Electrochemistry: The 1960's.... Ions in Solution, as well as Electron Transfer across Interfaces.... The Relation of Electrochemistry to Other Sciences.... Some Diagrammatic Presentations.... Some Examples of the Involvement of Electrochemistry in Other Sciences Electrochemistry as an Interdisciplinary Field, Apart from Chemistry? Electrodics and Electronics.... Transients ix

9 x 1.7 Electrodes are Catalysts The Electromagnetic Theory of Light and the Examination of Electrode Surfaces Science, Technology, Electrochemistry, and Time Do Interfacial Charge-Transfer Reactions Have a Wider Significance Than Has Hitherto Been Realized? \.9.2 The Relation between Three Major Advances in Science, and the Place of Electrochemistry in the Developing World CHAPTER 2 lon-solvent Interactions Introduction.... The Nonstructural Treatment of Ion-Solvent Interactions t A Quantitative Measure of Ion-Solvent Interactions The Born Model: A Charged Sphere in a Continuum The Electrostatic Potential at the Surface of a Charged Sphere On the Electrostatics of Charging (or Discharging) Spheres The Born Expression for the Free Energy of Ion-Solvent Interactions The Enthalpy and Entropy of Ion-Solvent Interactions Can One Experimentally Study the Interactions of a Single Ionic Species with the Solvent? The Experimental Evaluation of the Heat of Interaction of a Salt and Solvent How Good Is the Born Theory? Further Reading Structural Treatment of the Ion-Solvent Interactions The Structure of the Most Common Solvent, Water The Structure of Water near an Ion The Ion-Dipole Model of Ion-Solvent Interactions Evaluation of the Terms in the lon-dipole Approach to the Heat of Solvation How Good Is the Ion-Dipole Theory of Solvation? The Relative Heats of Solvation of Ions on the Hydrogen Scale Do Oppositely Charged Ions of Equal Radii Have Equal Heats of Solvation? The Water Molecule Can Be Viewed as an Electrical Quadrupole The Ion-Quadrupole Model of Ion-Solvent Interactions Ion-Induced-Dipole Interactions in the Primary Solvation Sheath How Good Is the Ion-Quadrupole Theory of Solvation? The Special Case of Interactions of the Transition-Metal Ions with Water Some Summarizing Remarks on the Energetics of Ion-Solvent Interactions Further Reading The Solvation Number How Many Water Molecules Are Involved in the Solvation of an Ion? 117

10 xi Static and Dynamic Pictures of the Ion-Solvent Molecule Interaction The Meaning of Hydration Numbers Why Is the Concept of Solvation Numbers Useful? On the Determination of Solvation Numbers.... Further Reading The Dielectric Constant of Water and Ionic Solutions An Externally Applied Electric Field Is Opposed by Counterfields Developed within the Medium The Relation between the Dielectric Constant and Internal Counterfields The Average Dipole Moment of a Gas-Phase Dipole Subject to Electrical and Thermal Forces The Debye Equation for the Dielectric Constant of a Gas of Dipoles How the Short-Range Interactions between Dipoles Affect the Average Effective Moment of the Polar Entity Which Responds to an External Field The Local Electric Field in a Condensed Polar Dielectric The Dielectric Constant of Liquids Containing Associated Dipoles The Influence of Ionic Solvation on the Dielectric Constant of Solutions Further Reading Ion-Solvent-Nonelectrolyte Interactions The Problem The Change in Solubility of a Nonelectrolyte Due to Primary Solvation The Change in Solubility Due to Secondary Solvation The Net Effect on Solubility of Influences from Primary and Secondary Solvation The Case of Anomalous Salting in Further Reading Appendix 2.1 Appendix 2.2 Appendix 2.3 Free Energy Change and Work.... The Interaction between an Ion and a Dipole... The Interaction between an Ion and a Water Quadrupole CHAPTER 3 lon-ion Interactions Introduction.... True and Potential Electrolytes Ionic Crystals Are True Electrolytes Potential Electrolytes: Nonionic Substances Which React with the Solvent to Yield Ions An Obsolete Classification: Strong and Weak Electrolytes The Nature of the Electrolyte and the Relevance of Ion-Ion Interactions 180 Further Reading The Debye-Hiickel (or Ion-Cloud) Theory oflon-ion Interactions A Strategy for a Quantitative Understanding of Ion-Ion Interactions 180

11 xii A Prelude to the Ionic-Cloud Theory.... How the Charge Density near the Central Ion Is Determined by Electrostatics: Poisson's Equation.... How the Excess Charge Density near the Central Ion Is Given by a Classical Law for the Distribution of Point Charges in a Coulombic Field.. A Vital Step in the Debye-Hlickel Theory of the Charge Distribution around Ions: Linearization of the Boltzmann Equation.... The Linearized Poisson-Boltzmann Equation.... The Solution of the Linearized P-B Equation.... The Ionic Cloud around a Central Ion.... How Much Does the Ionic Cloud Contribute to the Electrostatic Po- tential 'Pr at a Distance r from the Central Ion? The Ionic Cloud and the Chemical-Potential Change Arising from Ion- Ion Interactions Further Reading Activity Coefficients and Ion-Ion Interactions The Evolution of the Concept of Activity Coefficient The Physical Significance of Activity Coefficients The Activity Coefficient of a Single Ionic Species Cannot Be Measured The Mean Ionic Activity Coefficient The Conversion of Theoretical Activity-Coefficient Expressions into a Testable Form.... Further Reading The Triumphs and Limitations of the Debye-Htickel Theory of Activity Coefficients How Well Does the Debye-Hiickel Theoretical Expression for Activity Coefficients Predict Experimental Values? Ions Are of Finite Size, Not Point Charges The Theoretical Mean Ionic-Activity Coefficient in the Case of Ionic Clouds with Finite-Sized Ions The Ion-Size Parameter a Comparison of the Finite-Ion-Size Model with Experiment The Debye-Hiickel Theory of Ionic Solutions: An Assessment On the Parentage of the Theory of Ion-Ion Interactions.... Further Reading Ion-Solvent Interactions and the Activity Coefficient The Effect of Water Bound to Ions on the Theory of Deviations from Ideality Quantitative Theory of the Activity of an Electrolyte as a Function of the Hydration Number... '" The Water-Removal Theory of Activity Coefficients and Its Apparent Consistency with Experiment at High Electrolytic Concentrations Further Reading The So-Called "Rigorous" Solutions of the Poisson-Boltzmann Equation Further Reading Temporary Ion Association in an Electrolytic Solution: Formation of Pairs, Triplets, etc

12 xiii Positive and Negative Ions Can Stick Together: Ion-Pair Formation The Probability of Finding Oppositely Charged Ions near Each Other The Fraction of Ion Pairs, According to Bjerrum The Ion-Association Constant KA of Bjerrum Activity Coefficients, Bjerrum's Ion Pairs, and Debye's Free Ions The Fuoss Approach to Ion-Pair Formation From Ion Pairs to Triple Ions to Clusters of Ions Further Reading... : The Quasi-Lattice Approach to Concentrated Electrolytic Solutions At What Concentration Does the Ionic-Cloud Model Break Down? The Case for a Cube-Root Law for the Dependence of the Activity Coefficient on Electrolyte Concentration The Beginnings of a Quasi-Lattice Theory for Concentrated Electrolytic Solutions Further Reading The Study of the Constitution of Electrolytic Solutions The Temporary and Permanent Association of Ions Electromagnetic Radiation, a Tool for the Study of Electrolytic Solutions Visible and Ultraviolet Absorption Spectroscopy Raman Spectroscopy Infrared Spectroscopy Nuclear Magnetic Resonance Spectroscopy Further Reading A Perspective View on the Theory of Ion-Ion Interactions. 279 Appendix 3.1 Poisson's Equation for Spherically Symmetrical Charge Distribution Appendix 3.2 Evaluation of the Integral f;:ct r(xr)(i<r) d(i<r) Appendix 3.3 Derivation of the Result 1+ = {fvt + 1':.._)I/v 284 Appendix 3.4 To Show That the Minimum in the P r versus r Curve Occurs at r = Al Appendix 3.5 Transformation from the Variable r to the Variable Y = Air Appendix 3.6 CHAPTER 4 Relation Between Calculated and Observed Activity Coefficients Ion Transport in Solutions 4.1 Introduction Ionic Drift under a Chemical-Potential Gradient: Diffusion The Driving Force for Diffusion.... The "Deduction" of an Empirical Law: Fick's First Law of Steady- State Diffusion

13 xiv On the Diffusion Coefficient D.... Ionic Movements: A Case of the Random Walk.... The Mean Square Distance Traveled in a Time t by a Random-Walking Particle.... Random-Walking Ions and Diffusion: The Einstein-Smoluchowski Equation.... The Gross View of Non-Steady-State Diffusion.... An Often Used Device for Solving Electrochemical Diffusion Problems: The Laplace Transformation.... Laplace Transformation Converts the Partial Differential Equation Which Is Fick's Second Law into a Total Differential Equation.... The Initial and Boundary Conditions for the Diffusion Process Stimulated by a Constant Current (or Flux).... The Concentration Response to a Constant Flux Switched on at t = 0 How the Solution of the Constant-Flux Diffusion Problem Leads On to the Solution of Other Problems Diffusion Resulting from an Instantaneous Current Pulse What Fraction of Ions Travels the Mean Square Distance <x 2 ) in the Einstein-Smoluchowski Equation? How Can the Diffusion Coefficient Be Related to Molecular Quantities? The Mean Jump Distance t, a Structural Question The Jump Frequency, a Rate-Process Question The Rate-Process Expression for the Diffusion Coefficient Diffusion: An Overall View.... Further Reading Ionic Drift under an Electric Field: Conduction The Creation of an Electric Field in an Electrolyte.... How Do Ions Respond to the Electric Field?.... The Tendency for a Conflict between Electroneutrality and Conduction The Resolution of the Electroneutrality-versus-Conduction Dilemma: Electron-Transfer Reactions.... The Quantitative Link between Electron Flow in the Electrodes and Ion Flow in the Electrolyte: Faraday's Law.... The Proportionality Constant Relating the Electric Field and the Current Density: The Specific Conductivity.... Molar Conductivity and Equivalent Conductivity.... The Ec;.uivalent Conductivity Varies with Concentration.... How the Equivalent Conductivity Changes with Concentration: Kohlrausch's Law The Vectorial Character of Current: Kohlrausch's Law of the Independent Migration of Ions.... Further Reading The Simple Atomistic Picture of Ionic Migration Ionic Movements under the Influence of an Applied Electric Field What Is the Average Value of the Drift Velocity? The Mobility of Ions The Current Density Associated with the Directed Movement of Ions in Solution, in Terms of the Ionic Drift Velocities The Specific and Equivalent Conductivities in Terms of the Ionic Mobilities The Einstein Relation between the Absolute Mobility and the Diffusion Coefficient

14 xv Further What Is the Drag (or Viscous) Force Acting on an Ion in Solution?.. The Stokes-Einstein Relation.... The Nernst-Einstein Equation.... Some Limitations of the Nernst-Einstein Relation.... A Very Approximate Relation between Equivalent Conductivity and Viscosity: Walden's Rule...,.. The Rate-Process Approach to Ionic Migration.... The Rate-Process Expression for Equivalent Conductivity.... The Total Driving Force for Ionic Transport: The Gradient of the Electrochemical Potential.... Reading The Interdependence of Ionic Drifts The Drift of One Ionic Species May Influence the Drift of Another A Consequence of the Unequal Mobilities of Cations and Anions, the Transport Numbers The Significance of a Transport Number of Zero The Diffusion Potential, Another Consequence of the Unequal Mobilities of Ions Electroneutrality Coupling between the Drifts of Different Ionic Species How Does One Represent the Interaction between Ionic Fluxes? The Onsager Phenomenological Equations An Expression for the Diffusion Potential The Integration of the Differential Equation for Diffusion Potentials: The Planck-Henderson Equation'.... Further Reading The Influence of Ionic Atmospheres on Ionic Migration The Concentration Dependence of the Mobility of Ions Ionic Clouds Attempt to Catch Up with Moving Ions An Egg-Shaped Ionic Cloud and the "Portable" Field on the Central Ion A Second Braking Effect of the Ionic Cloud on the Central Ion: The Electrophoretic Effect The Net Drift Velocity of an Ion Interacting with Its Atmosphere The Electrophoretic Component of the Drift Velocity The Procedure for Calculating the Relaxation Component of the Drift Velocity How Long Does an Ion Atmosphere Take to Decay? The Quantitative Measure of the Asymmetry of the Ionic Cloud Around a Moving Ion The Magnitude of the Relaxation Force and the Relaxation Component of the Drift Velocity The Net Drift Velocity and Mobility of an Ion Subject to Ion-Ion Interactions The Debye-Htickel-Onsager Equation The Theoretical Predictions of the Debye-Htickel-Onsager Equation versus the Observed Conductance Curves A Theoretical Basis for Some Modifications of the Debye-Htickel- Onsager Equation Further Reading Nonaqueous Solutions: A New Frontier in Ionics? Water Is the Most Plentiful Solvent

15 xvi Water Is Often Not an Ideal Solvent.... The Debye-Hilckel-Onsager Theory for Nonaqueous Solutions.... The Solvent Effect on the Mobility at Infinite Dilution.... The Slope of the A versus d Curve as a Function of the Solvent.... The Effect of the Solvent on the Concentration of Free Ions: Ion As sociation The Effect of Ion Association upon Conductivity Even Triple Ions Can Be Formed in Nonaqueous Solutions Some Conclusions about the Conductance of Nonaqueous Solutions of True Electrolytes Further Reading Appendix 4.1 The Mean Square Distance Traveled by a Random- Walking Particle Appendix 4.2 The Laplace Transform of a Constant Appendix 4.3 A Few Elementary Ideas on the Theory of Rate Processes Appendix 4.4 The Derivation of Equations (4.257) and (4.258) Appendix 4.5 The Derivation of Equation (4.318) CHAPTER 5 Protons in Solution The Case of the Nonconforming Ion: The Proton.... Proton Solvation What Is the Condition of the Proton in Solution? Proton Affinity The OveraIl Heat of Hydration of a Proton The Coordination Number of a Proton Further Reading Proton Transport The Abnormal Mobility of a Proton Protons Conduct by a Chain Mechanism Classical Proton Jumps and Proton Mobility Do Proton Jumps Obey Classical Laws? Quantum-Mechanical Proton Jumps and Proton Mobility Water Reorientation, a Prerequisite for Proton Jumps The Rate of Water Reorientation and Proton Mobility A Picture of Proton Mobility in Aqueous Solutions The Rate-Determining Water-Rotation Model of Proton Mobility and the Other Anomalous Facts Proton Mobility in Ice The Existence of the Hydronium Ion from the Point of View of Proton Mobility Why Is the Mechanism of Proton Mobility So Important? Further Reading

16 xvii 5.4 Homogeneous Proton-Transfer Reactions and Potential Electrolytes Acids Produce Hydrogen Ions and Bases Produce Hydroxyl Ions: The Initial View Acids Are Proton Donors, and Bases' Are Proton Acceptors: The Bronsted View The Dissolution of Potential Electrolytes and Other Types of Proton- Transfer Reactions An Important Consequence of the Bronsted View: Conjugate Acid Base Pairs.... The Absolute Strength of an Acid or a Base.... The Relative Strengths of Acids and Bases.... Proton Free-Energy Levels.... The Primary Effect of the Solvent upon the Relative Strength of an Acid A Secondary (Electrostatic) Effect of the Solvent on the Relative Strength of Acids.... Further Reading CHAPTER 6 Ionic liquids 6.1 Introduction The Limiting Case of Zero Solvent: Pure Liquid Electrolytes The Thermal Dismantling of an Ionic Lattice Some Features of Ionic Liquids (Pure Liquid Electrolytes) Liquid Electrolytes Are Ionic Liquids The Fundamental Problems in Pure Liquid Electrolytes Further Reading Models of Simple Ionic Liquids The Origin of Liquid Electrolyte Models Lattice-Oriented Models a The Experimental Basis for Model Building b The Need to Pour Empty Space into a Fused Salt c The Vacancy Model: A Fused Salt Is an Ionic Lattice with Numerous Vacancies d The Hole Model: A Fused Salt Is Full of Holes like Swiss Cheese Gas-Oriented Models for Liquid 'Electrolytes a The Cell-Theory Approach b The Free Volume Belongs to the Liquid and Not to the Particles: The Liquid Free-Volume Model A Summary of the Models for Liquid Electrolytes Further Reading Quantification of the Hole Model for Liquid Electrolytes An Expression for the Probability That a Hole Has a Radius between r and r + dr The Furth Approach to the Work of Hole Formation The Distribution Function for the Size of the Holes in a Liquid Electrolyte

17 xviii What Is the Average Size of a Hole? Further Reading Transport Phenomena in Liquid Electrolytes Some Simplifying Features of Transport in Fused Salts Diffusion in Fused Salts a Self-Diffusion in Pure Liquid Electrolytes: It May Be Revealed by Introducing Isotopes b Results of Self-Diffusion Experiments The Viscosity of Molten Salts What Is the Validity of the Stokes-Einstein Relation in Ionic Liquids? The Conductivity of Pure Liquid Electrolytes The Nernst-Einstein Relation in Ionic Liquids a The Nernst-Einstein Relation: Its Degree of Applicability b The Gross View of Deviations from the Nernst-Einstein Equation c Possible Molecular Mechanisms for Nernst-Einstein Deviations Transport Numbers in Pure Liquid Electrolytes a Some Ideas about Transport Numbers in Fused Salts b The Measurement of Transport Numbers in Liquid Electrolytes c A Radiotracer Method of Calculating Transport Numbers in Molten Salts d A Stokes' Law Approach to a Rough Estimate of Transport Numbers Further Reading The Atomistic View of Transport Processes in Simple Ionic Liquids Holes and Transport Processes What Is the Mean Lifetime of Holes in Fused Salts? Expression for Viscosity in Terms of Holes The Diffusion Coefficient from the Hole Model A Critical Test of a Model for Ionic Liquids Is a Rationalization of the Heat of Activation of 3.7 RTm for Transport Processes An Attempt to Rationalize En = E~ = 3.7RTm The Hole Model, the Most Consistent Present Model for Liquid Electrolytes Further Reading Mixture of Simple Ionic Liquids-Complex Formation Mixtures of Simple Ionic Liquids May Not Behave IdeaIly Interactions Lead to Nonideal Behavior Can One MeaningfuIly Refer to Complex Ions in Fused Salts? Raman Spectra, and Other Means of Detecting Complex Ions Further Reading Mixtures of Liquid Oxide Electrolytes The Liquid Oxides Pure Fused Nonmetallic Oxides Form Network Structures Like Liquid Water Why Does Fused Silica Have a Much Higher Viscosity Than Do Liquid Water and the Fused Salts?..., The Solvent Properties of Fused Nonmetallic Oxides

18 xix Ionic Additions to the Liquid-Silica Network: Glasses The Extent of Structure Breaking of Three-Dimensional Network Lattices and Its Dependence on the Concentration of Metal Ions The Molecular and Network Models of Liquid Silicate Structure Liquid Silicates Contain Large Discrete Polyanions The "Iceberg" Model Fused-Oxide Systems in Metallurgy: Slags Further Reading Appendix 6.1 The Effective Mass of a Hole Appendix 6.2 Some Properties of the Gamma Function Appendix 6.3 The Kinetic Theory Expression for the Viscosity of a Fluid Index..., xxxiii

19 VOLUME 2 CHAPTER 7 The Electrified Interface 7.1 Electrification of an Interface The Electrode-Electrolyte Interface: The Basis of Electrodics New Forces at the Boundary of an Electrolyte The Interphase Region Has New Properties and New Structures An Electrode Is Like a Giant Central Ion The Consequences of Compromise Arrangements: The Electrolyte Side of the Boundary Acquires a Charge Both Sides of the Interface Become Electrified: The So-Called "Electrical Double Layer" Double Layers Are Characteristic of All Phase Boundaries A Look into an Electrified Interface Further Reading Some Problems in Understanding an Electrified Interface What Knowledge Is Required before an Electrified Interface Can Be Regarded as Understood? Predicting the Interphase Properties from the Bulk Properties of the Phases Why Bother about Electrified Interfaces? The Need to Clarify Some Concepts The Potential Difference across Electrified Interfaces a What Happens when One Tries to Measure the Absolute Potential Difference across a Single Electrode-Electrolyte Interface 644 xxi

20 xxii 7.2.5b The Absolute Potential Difference across a Single Electrified Interface Cannot Be Measured c Can One Measure Changes in the Metal-Solution Potential Difference? d The Extreme Cases of Ideally Nonpolarizable and Polarizable Interfaces e The Development of a Scale of Relative Potential Differences / Can One Meaningfully Analyze an Electrode-Electrolyte Potential Difference? g A Thought Experiment Involving a Charged Electrode in Vacuum h The Test Charge Must Avoid Image Interactions with the Charged Electrode i The Outer Potential tp of a Material Phase in Vacuum j What is the Relevance of the Outer Potential to Double-Layer Studies? k Another Thought Experiment Involving an Uncharged, Dipole- Covered Phase / The Dipole Potential Difference MLlsX across an Electrode- Electrolyte Interface m The Sum of the Potential Differences Due to Charges and Dipoles: The Absolute Electrode-Electrolyte (or Galvani) Potential Difference n The Outer, Surface, and Inner Potential Differences An Apparent Contradiction: The Sum of the Ll<p's across a System of Interfaces Can and the Ll<p across One Interface Cannot Be Measured p What Deeper Understanding Has Been Hitherto Gained Regarding the Absolute Potential Difference Across an Electrified Interface? The Accumulation and Depletion of Substances at an Interface a What Would Represent Complete Structural Information Regarding an Electrified Interface? b The Concept of Surface Excess c Does Knowledge of the Surface Excess Contribute to Knowledge of the Distribution of Species in the Interphase Region? d Is the Surface Excess Equivalent to the Amount Adsorbed? e Is the Surface Excess Measurable? / The Special Position of Mercury in Double-Layer Studies Further Reading The Thermodynamics of Electrified Interfaces c The Measurement of Interfacial Tension as a Function of the Potential Difference across the Interface Some Basic Facts about Electrocapillary Curves A Digression on the Electrochemical Potential a Definition of Electrochemical Potential b Can the Chemical and Electrical Work Be Determined Separately? A Criterion of Thermodynamic Equilibrium between Two Phases: Equality of Electrochemical Potentials d Nonpolarizable Interfaces and Thermodynamic Equilibrium Some Thermodynamic Thoughts on Electrified Interfaces

21 xxiii Interfacial Tension Varies with Applied Potential: Determination of the Charge Density on the Electrode Electrode Charge Varies with Applied Potential: Determination of the Electrical Capacitance of the Interface The Potential at Which an Electrode Has a Zero Charge Surface Tension Varies with Solution Composition: Determination of the Surface Excess Reflections on Electrocapillary Thermodynamics Retrospect and Prospect in the Study of Electrified Interfaces Further Reading The Structure of Electrified Interfaces.... The Parallel-Plate Condenser Model: The Helmholtz-Perrin Theory The Double Layer in Trouble: Neither Perfect Parabolas nor Constant Capacities.... The Ionic Cloud: The Gouy-Chapman Diffuse-Charge Model of the Double Layer.... Ions under Thermal and Electric Forces near an Electrode.... A Picture of the Potential Drop in the Diffuse Layer.... An Experimental Test of the Gouy-Chapman Model: Potential Dependence of the Capacitance, but at What Cost?.... Some Ions Stuck to the Electrode, Others Scattered in Thermal Disarray: The Stern Model.... A Consequence of the Stern Picture: Two Potential Drops across an Electrified Interface.... Another Consequence of the Stern Model: An Electrified Interface Is Equivalent to Two Capacitors in Series.... The Relative Contributions of the Helmholtz-Perrin and Gouy-Chapman Capacities.... Some Questions Regarding the Sticking of Ions to the Electrode.... An Electrode Is Largely Covered with Adsorbed Water Molecules... Metal-Water Interactions.... The Orientation of Water Molecules on Charged Electrodes.... How Close Can Hydrated Ions Come to a Hydrated Electrode?.... Is It Only Desolvated Ions which Contact-Adsorb on the Electrode? The Free-Energy Change for Contact Adsorption.... What Determines the Degree of Contact Adsorption?.... How Is Contact Adsorption Measured?.... Contact Adsorption, Specific Adsorption, or Superequivalent Adsorption Contact Adsorption: Its Influence of the Capacity of the Interface... Looking Back to Look Forward.... The Complete Capacity-Potential Curve.... The Constant-Capacity Region a The So-Called "Double Layer" Is a Double Layer b The Dielectric Constant of the Water between the Metal and the Outer Helmholtz Plane c The Position of the Outer Helmholtz Plane and an Interpretation of the Constant Capacity The Capacitance Hump How Does the Population of Contact-Adsorbed Ions Change with Electrode Charge? The Test of the Population Law for Contact-Adsorbed Ions The Lateral-Repulsion Model for Contact Adsorption

22 xxiv Flip-Flop Water on Electrodes Calculation of the Potential Difference Due to Water Dipoles The Excess of Flipped Water Dipoles over Flopped Water Dipoles The Contribution of Adsorbed Water Dipoles to the Capacity of the Interface Further Reading The Competition between Water and Organic Molecules at the Electrified Interfaces The Relevance of Organic Adsorption The Forces Involved in Organic Adsorption Does Organic Adsorption Depend on Electrode Charge? The Examination of the Water Flip-Flop Model for Simple Cases of Organic Adsorption At What Potential Does Maximum Organic Adsorption Occur? Further Reading Electrified Interfaces at Metals Other than Mercury Further Reading The Structure of the Semiconductor-Electrolyte Interface How Is the Charge Distributed inside a Solid Electrode? The Band Theory of Crystalline Solids Conductors, Insulators, and Semiconductors Some Analogies between Semiconductors and Electrolytic Solutions The Diffuse-Charge Region inside an Intrinsic Semiconductor: The Garrett-Brattain Space Charge The Differential Capacity Due to the Space Charge Impurity Semiconductors, n Type and p Type Surface States: The Semiconductor Analogue of Contact Adsorption Semiconductor Electrochemistry: The Beginnings of the Electrochemistry of Nonmetallic Materials Further Reading A Bird's-Eye View of the Structure of Charged Interfaces Double Layers between Phases Moving Relative to Each Other The Phenomenology of Mobile Electrified Interfaces: Electrokinetic Properties The Relative Motion of One of the Phases Constituting an Electrified Interface Produces a Streaming Current A Potential Difference Applied Parallel to an Electrified Interface Produces an Electro-osmotic Motion of One of the Phases Relative to the Other Electrophoresis: Moving Solid Particles in a Stationary Electrolyte.. Further Reading Colloid Chemistry Colloids: The Thickness of the Double Layer and the Bulk Dimensions Are of the Same Order The Interaction of Double Layers and the Stability of Colloids Sols and Gels.... Further Reading.... Appendix 7.1 Measurement of the Electrode-Solution Volta Potential Difference

23 xxv CHAPTER 8 Electrodics 8.1 Introduction The Situation Thus Far Charge Transfer: Its Chemical and Electrical Implications Can an Isolated Electrode-Solution Interface Be Used as a Device? Electrochemical Systems Can Be Used as Devices An Electrochemical Device: The Substance Producer Another Electrochemical Device: The Energy Producer The Electrochemical Undevice: The Substance Destroyer and Energy Waster Some Basic Questions The Basic Electrodic Equation: The Butler-Volmer Equation The Instant of Immersion of a Metal in an Electrolytic Solution The Rate of Charge-Transfer Reactions under Zero Field: The Chemical Rate Constant Some Consequences of Electron Transfer at an Interface What Is the Rate of an Electron-Transfer Reaction under the Influence of an Electric Field? The Two-Way Electron Traffic across the Interface The Interface at Equilibrium: The Equilibrium Exchange-Current Density io The Interface Departs from Equilibrium: The Nonequilibrium Drift- Current Density i The Current-Producing (or Current-Produced) Potential Difference: The Overpotential 1] The Basic Electrodic (Butler-Volmer) Equation: Some General and Special Cases The High-Field Approximation: The Exponential i versus 1] Law The Low-Field Approximation: The Linear i versus 1] Law Nonpolarizable and Polarizable Interfaces Zero Net Current and the Classical Law of Nernst The Nernst Equation I 5 The Nernst Equation: Its Sphere of Relevance Looking Back Further Reading The Butler-Volmer Equation: Further Details The Need for a Careful Look at Some Quantities in the Butler-Volmer Equation The Relation between Structure at the Electrified Interface and the Rate of Charge-transfer Reactions The Interfacial Concentrations May Depend on Ionic Transport in the Electrolyte What Is the Physical Meaning of the Symmetry factor f3? a The Factor f3 Is at the Center of Electrode Kinetics b A Preliminary to a Second Theory of f3: Potential-Energy- Distance Relations of Particles Undergoing Charge Transfer c A Simple Picture of the Symmetry Factor

24 xxvi 8.3.4d Is the fj in the Butler-Volmer Equation Independent of Overpotential? Summing-up of Further Details on the Butler-Volmer Equation Further Reading The Current-Potential Laws at Other Types of Charged Interfaces Semiconductor n-p Junctions The Current across Biological Membranes The Hot Emission of Electrons from a Metal into Vacuum The Cold Emission of Electrons from a Metal into Vacuum Further Reading The Quantum Aspects of Charge-Transfer Reactions at Electrode-Solution Interfaces A Few Words on the Mechanics of Electrons.... The Penetration of Electrons into Classically Forbidden Regions... The Probability of Electron Tunneling through Barriers.... The Distribution of Electrons among the Energy Levels in a Metal... Under What Conditions Do Electrons Tunnel between the Electrode and Ions in Solution? The Tunneling Condition and the Proton-Transfer Curve Electron Tunneling and the De-electronation Reaction A Perspective View of Charge-Transfer Reactions at an Electrode The Symmetry Factor fj: A Better View Quantifying the Charge-Transfer Picture Some Desirable Refinements and Generalizations Surveying the Progress Further Reading Electrodic Reactions and Chemical Reactions Further Reading Appendix 8.1 The Number of Electrons Having Energy EF Striking the Surface of a Metal from the Inside CHAPTER 9 Electrodics: More Fundamentals Multistep Reactions.... The Question of Multistep Reactions.... Some Ideas on Queues, or Waiting Lines.... The Overpotential 'Y) Is Related to the Electron Queue at an Interface A Near-Equilibrium Relation between the Current Density and Overpotential for a Multistep Reaction.... The Concept of a Rate-Determining Step.... Rate-Determining Steps and Energy Barriers for Multisfep Reactions. How Many Times Must the Rate-Determining Step Take Place for the Overall Reaction to Occur Once? The Stoichiometric Number v.... The Order of an Electrodic Reaction