VOLUME 2 MODERN ELECTROCHEMISTRY

Transcription

1 VOLUME 2 MODERN ELECTROCHEMISTRY

2 VOLUME 2 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 Boc... ris. John O'M Modllrn electrochemistry. Library 01 Congress Cataloging in Publication Data "A PienumfAO$IItt8!!dition." 1. Electrochemistry. I. A!!dctv. AmulY8 K. N.. joint 8uthor.11. Title B '.37 ISBN-13: : / e-isbn-13: ro A PlenumIRosetta Edition Published by Plenum Publishing Corporation 233 Spring Street, New York, N.v C 1970 Plenum Press, New York A Division of Plenum Publishing Corporation All rights reserved No part of this publication may be reproduced in any form without written permission from the publisher

4 CONTENTS 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 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 v

5 vi CONTENTS 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 's across a System of Interfaces Can and the Ll 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 What Would Represent Complete Structural Information Regarding an Electrified Interface? b The Concept of Surface Excess a 7.2.6c 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

6 CONTENTS vii 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 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

7 viii CONTENTS 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... 78:' 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. 8ll 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 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.... Appendix 7.1 Measurement of the Electrode-Solution Volta Potential Difference

8 CONTENTS ix CHAPTER 8 Electrodics 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 The Nernst Equation: Its Sphere of Relevance Looking Back 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 I The Interfacial Concentrations May Depend on Ionic Transport in the Electrolyte What Is the Physical Meaning of the Symmetry factor {3? 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

9 x CONTENTS 8.3.4d Is the (3 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 (3: 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 17 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 Multistep 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

10 CONTENTS xi Blockage of the Electrode Surface during Charge Transfer: The Surface-Coverage Factor Further Reading The Transient Behavior of Interfaces The Interface under Equilibrium, Transient, and Steady-State Conditions How an Interface Is Stimulated to Show Time Variations.... Some Ideas on the Understanding of Transients.... Intermediates in Electrodic Reactions and Their Effects on Potential- Time Transients Experimental Methods for the Determination of Partial Coverage, with Adsorbed Entities, of the Surface of Electrocatalysts a Radiotracer Method b Galvanostatic Transient Method c Potentiostatic Transients d The Potential-Sweep, or Potentiodynamic, Method Transport in the Electr.olyte Effects Charge Transfer at the Interface lonics Looks after the Material Needs of the Interface How the Transport Flux Is Linked to the Charge-Transfer Flux: The Flux-Equality Condition '" Appropriations from the Theory of Heat Transfer A Qualitative Study of How Diffusion Affects the Response of an Interface to a Constant Current A Quantitative Treatment of How Diffusion to an Electrode Affects the Response with Time of an Interface to a Constant Current The Concept of Transition Time Convection Can Maintain Steady Interfacial Concentrations The Origin of Concentration Overpotential The Diffusion Layer The Limiting Current Density and Its Practical Importance a Polarography: The Dropping-Mercury Electrode b The Rotating-Disc Electrode The Steady-State Current-Potential Relation under Conditions of Transport Control Transport-Controlled De-electronation Reactions What Is the Effect of Electrical Migration on the Limiting Diffusion- Current Density? Some Summarizing Remarks on the Transport Aspects of Electrodics 9.4 Determining the Stepwise Mechanism of an Electrodic Re action.... How One Tries to Determine the Reaction Mechanism.... Which Is the Rate-Determining Step in the Iron Deposition and Dissolution Reaction? The Transfer Coefficient a and Reaction Mechanisms Summarizing Remarks Concerning Mechanistic Studies Further Reading More on Mechanism Determination Why Review Mechanism Determination?

11 xii CONTENTS What Is Mechanism Determination? Stages in the Elucidation of a Reaction Mechanism The Elucidation of the Overall Reaction, the Entities in Solution, and the Surface Coverage Some Techniques for Mechanism Determination a The Determination of Reaction Order b The Determination of the Transfer Coefficients c The Determination of the Stoichiometric Number d Auxiliary Methods Mechanism Determination for Saturated Hydrocarbons.... Further Reading Current-Potential Laws for Electrochemical Systems The Potential Difference across an Electrochemical System The Equilibrium Potential Difference across an Electrochemical Cell The Problem with Tables of Standard Electrode Potentials The ph-potential Diagrams: A General Representation of Equilibrium Potential Differences across Cells Are Equilibrium Cell Potential Differences Useful? Electrochemical Cells: A Qualitative Discussion of the Variation of Cell Potential with Current Electrochemical Cells in Action: Some Quantitative Relations between IllS Cell Current and Cell Potential Further Reading The Grand Divide CHAPTER 10 Electrodic Reactions of Special Interest 10.1 Electrocatalysis A Chemical Catalyst and an Electrocatalyst At What Potential Should Electrocatalysts Be Compared? Electrocatalysis in Simple Redox Reactions a How Does the Electrocatalytic Rate Depend upon the Substrate Work Function at the Reversible Potential? b Can the Exchange-Current Density Depend upon the Work Function? Electrocatalysis in Reactions Involving Adsorbed Species.... 1O.1.4a Electrocatalysis in the Hydrogen-Evolution and -Dissolution Reaction.... 1O.1.4b The Electrocatalytic De-electronation of Hydrocarbons.... 1O.1.4c The Dependence of the Rate upon Substrate for the Oxidation of Ethylene.... 1O.1.4d The Special Position of Platinum as an Electrocatalyst Special Features of Electrocatalysis.... 1O.1.5a The Effect of the Electric Field.... 1O.1.5b Reactivity at Low Temperatures.... 1O.1.5c The Activation of an Electrocatalyst.... 1O.1.5d Increasing the Power Output by Changing the Reaction Path 1O.1.5e The Use of Porous Electrodes

12 CONTENTS xiii The Electrogrowth of Metals on Electrodes The Two Aspects of Electrogrowth.... The Reaction Pathway for Electrodeposition.... Stepwise Dehydration of an Ion; the Surface Diffusion of Adions... Mechanism Determination on Surfaces Which Change with Time... The Time Variation of the Average Adion Concentration in Response to the Switching on of a Constant Current The Contributions of Double-Layer Charging and Faradaic Reaction to the Total Deposition-Current Density The Time Variation of the Overpotential and the Rate-Determining Step in Electrodeposition The Contribution of Charge Transfer and Surface Diffusion to the Total Overpotential for Electrodeposition at Steady State From Deposition to Crystallization.... Some Devices for Building Lattices from Adions: Screw Dislocations and Spiral Growths Microsteps and Macrosteps.... How Steps from a Pair of Screw Dislocations Interact.... Crystal Facets Form.... Deposition on Single-Crystal and Polycrystal Substrates.... How the Diffusion of Ions in Solution May Affect Electrogrowth.,. Organic Additives and Electrodeposits.... The Simultaneous Deposition of More Than One Metal: Alloy De position The Sometimes Unavoidable Complication: Hydrogen Codeposit ion 1227 Further Reading The Hydrogen-Evolution Reaction Further Further A Reaction with a Special History.... What Are the Possible Paths for the Hydrogen-Evolution Reaction? What Mechanisms Are Possible in Hydrogen Evolution?.... How One Determines the Path and Rate-Determining Step of the Hydrogen-Evolution Reaction.... 1O.3.4a The Determination of the Exchange-Current Density.... 1O.3.4b The Determination of the Transfer Coefficient.... 1O.3.4c The Determination of Reaction Order with Respect to Hydrogen Ions in Solution.... 1O.3.4d The Stoichiometric Number v.... 1O.3.4e The Determination of Hydrogen Coverage.... 1O.3.4[ The Heat of Adsorption of Atomic Hydrogen on the Electrode 1O.3.4g Isotopic Separation Factors.... 1O.3.4h What Are the Probable Mechanisms for Hydrogen Evolution? Reading.... The Electronation of Oxygen.... The Importance of the Oxygen-Electronation Reaction.... The Evaluation of One of the Mechanisms of Oxygen Electronation.. Catalysis and the Oxygen Reaction.... Some Special Difficulties with Electrodic Reactions Having Small Exchange-Current Densities.... An Electrodic Method of Purifying Solutions.... Observing Very Slow Reactions near Equilibrium.... Reading

13 xiv CONTENTS CHAPTER 11 Some Electrochemical Systems of Technological Interest I I I Technological Aspects of Electrochemistry.... Corrosion and the Stability of Metals.... Civilization and Surfaces.... Charge-Transfer Reactions Are the Origin of the Instability of a Surface A Corroding Metal is Analogous to a Short-Circuited Energy-Producing Cell.... The Mechanism of the Corrosion of Ultrapure Metals.... What Is the Electronation Reaction in Corrosion?.... Thermodynamics and the Stability of Metals.... Potential-pH (or Pourbaix) Diagrams: Uses and Abuses.... The Corrosion Current and the Corrosion Potential.... The Basic Electrodics of Corrosion in the Absence of Oxide Films... An Understanding of Corrosion in Terms of Evans Diagrams.... Which Step in the Corrosion Process Controls the Corrosion Current? Metals, ph, and Air.... Some Common Examples of Corrosion.... Electrodic Approaches to Increasing the Stability of Metals a Corrosion Inhibition by the Addition of Substances to the Electrolytic Environment of a Corroding Metal I4b Corrosion Prevention by Charging the Corroding Metal with Electrons from an External Source.... Passivation: The Transformation from a Corroding and Unstable Surface to a Passive and Stable Surface.... The Mechanism of Passivation.... The Dissolution-Precipitation Model for Film Formation.... Spontaneous Passivation: Nature's Method of Stabilizing Surfaces... A Competition in Models for Passivation?.... The Thermodynamics of Passivation.... Hydrogen Diffusion into a Metal The Preferential Diffusion of Absorbed Hydrogen to Regions of Stress in a Metal.... Interstitial Hydrogen Can Crack Open a Metal Surface.... Surface Instability and the Internal Decay of Metals: Stress-Corrosion Cracking.... Surface Instability and Internal Decay of Metals: Hydrogen EmbrittIe ment Charge Transfer and the Stability of Metals The Cost of Corrosion A Bird's-Eye View of Corrosion Further Reading Electrochemical Energy Conversion I The Present Situation in Energy Consumption.... How Are the Hydrocarbon Fuels Used at Present?.... The Pollution of the Atmosphere with Products from Internal-Combustion Reactions and Its Possible Effect on World Temperature and Sea Levels a Products of Combustion Other than Carbon Dioxide.... II.3.3b Carbon Dioxide

14 CONTENTS xv c Uncertainties in Predicting the Future Pollution of the Atmosphere Thermal-Combustion Engines Waste the Chemical Energy Available from Burning Hydrocarbons in Air Direct Energy Conversion.... Direct Energy Conversion by Electrochemical Means.... The Maximum Intrinsic Efficiency in Electrochemical Conversion of the Energy of a Chemical Reaction to Electric Energy The Actual Efficiency of an Electrochemical Energy Converter.... The Physical Interpretation of the Absence of the Carnot Efficiency Factor in Electrochemical Energy Conversion Cold Combustion.... Making V near Ve Is the Central Problem of Electrochemical Energy Conversion The Electrochemical Quantities Which Must Be Optimized for Good Energy Conversion The Power Output of an Electrochemical Energy Converter The Electrochemical Engine Was the Wrong Path Taken in the Development of Power Sources at the End of the Nineteenth Century? Electrodes Burning Oxygen from Air The Special Configurations of Electrodes in Electrochemical Reactors Electrochemical Electricity Producers: The Two Basic Types Examples of Electrochemical Generators a The Hydrogen-Oxygen Cell b Reformer-Supplied Hydrogen-Air Cells c Hydrocarbon-Air Cells d Dissolved-Fuel Fuel Cells ge Natural Gas and CO-Air Cells The Relations between Electrochemical Energy Conversion and the Future Dominance of Atomic Energy as the Source of Power a Will Atomic Power Sources Compete for Any of the Uses Foreseen for Electrochemical Power Sources? b Will Electrochemical Means Be Used to Convert Nuclear Power to Electricity? c What Is the Relation between Electricity Storage and Atomic Energy? A Summary of the Direct Conversion of Chemical Energy to Electricity 1398 Further Reading Electricity Storage.... Conventional and Descriptive Terminology in Energy Conversion and Storage...,..., '".... The Important Quantities in Electricity Storage a Electricity Storage Density b Energy Density c Power d Desirable Trends.... Classical Electricity Storers a The Lead-Acid Storage Battery b A Dry Cell c Two Relatively New Electricity Storers

15 xvi CONTENTS The Large Gap between the Maximum Feasible and the Present Actual Energy Densities of Electricity Storers Outlines of Some Possible Future Electricity Storers a Electricity Storage in Hydrogen b Storage by Using Alkali Metals c Storers Involving Nonaqueous Solutions d Storers with Zinc in Combination with an Air Electrode The Respective Realms of Applicability of Electrochemical Energy Converters and Electricity Storers Electrochemical Electricity Storage in a Nutshell Further Reading Index XXIX

16 CONTENTS VOLUME 1 CHAPTER 1 Electrochemistry 1.1 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 xvii

17 xviii CONTENTS \.9.1 \.9.2 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?.... 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 A Quantitative Measure of lon-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? 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 lon-solvent Interactions.... Evaluation of the Terms in the Ion-Dipole Approach to the Heat of Solvation.... How Good Is the lon-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 lon-quadrupole Model of Ion-Solvent Interactions.... Ion-Induced-Dipole Interactions in the Primary Solvation Sheath., How Good Is the lon-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 lnter actions Further Reading The Solvation Number.... How Many Water Molecules Are Involved in the Solvation of an Ion?

18 CONTENTS xix 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 ~oment 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 2.6 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 Free Energy Change and Work Appendix 2.2 The Interaction between an Ion and a Dipole Appendix 2.3 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 of Jon-Jon Interactions A Strategy for a Quantitative Understanding of lon-ion Interactions

19 xx CONTENTS 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 Potential1f!r at a Distance r from the Central Ion? The Ionic Cloud and the Chemical-Potential Change Arising from lon~ Ion Interactions 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 The Triumphs and Limitations of the Debye-Hlickel Theory of Activity Coefficients How Well Does the Debye~Hlickel 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 lon-size Parameter a Comparison of the Finite-Ion-Size Model with Experiment The Debye~Hlickel Theory of Ionic Solutions: An Assessment On the Parentage of the Theory of Ion~lon Interactions 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

20 CONTENTS xxi 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;:;:ooo e-exr)(xr) d(xr) Appendix 3.3 Derivation of the Result f+ = (f~+ + 1':_-)1Iv Appendix 3.4 To Show That the Minimum in the P r versus r Curve Occurs at r = A Appendix 3.5 Appendix 3.6 CHAPTER 4 Transformation from the Variable r to the Variable Y = Air Relation Between Calculated and Observed Activity Coefficients 285 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

21 xxii CONTENTS 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') in the Einstein-Smoluchowski Equation? How Can the Diffusion Coefficient Be Related to Molecular Quantities? The Mean Jump Distance I, a Structural Question The Jump Frequency, a Rate-Process Question The Rate-Process Expression for the Diffusion Coefficient Diffusion: An Overall View 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 Equivalent Conductivity Varies with Concentration.... How the Equivalent Conductivity Changes with Concentration: Koh1- rausch's Law.... The Vectorial Character of Current: Kohlrausch's Law of the Inde pendent 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

22 CONTENTS xxiii 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 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-HUckel-Onsager Equation The Theoretical Predictions of the Debye-HUckel-Onsager Equation versus the Observed Conductance Curves A Theoretical Basis for Some Modifications of the Debye-HUckel- Onsager Equation Further Reading Nonaqueous Solutions: A New Frontier in Ionics?.... Water Is the Most Plentiful Solvent

23 xxiv CONTENTS Water Is Often Not an Ideal Solvent.... The Debye-Hlickel-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 Overall 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?