VOLUME 1

MODERN ELECTROCHEMIS TRY An Introduction to an Interdisciplinary Area

John O'M. Bockris Professor of Electrochemistry University of Pennsylvania, Philadelphia, Pennsylvania

and Amulya K. JV. Reddy Professor of Electrochemistry Indian Institute of Science, Bangalore, India

A Plenum/Rosetta Edition

CONTENTS

VOLUME 1

CHAPTER 1

Electrochemistry

1.1 Introduction 1

1.2 Electrons at and across Interfaces 3 1.2.1 Many Properties of Materials Depend upon Events Occurring at Their

Surfaces 3 1.2.2 Almost All Interfaces Are Electrified 3 1.2.3 The Continuous Flow of Electrons across an Interface: Electrochemical

Reactions 7 1.2.4 Electrochemical and Chemical Reactions 8

1.3 Basic Electrochemistry 12 1.3.1 Electrochemistry before 1950 12 1.3.2 The Treatment of Interfacial Electron Transfer as a Rate Processi

The 1950's 17 1.3.3 Quantum Electrochemistry: The 1960's 19 1.3.4 Ions in Solution, as well as Electron Transfer across Interfaces 22

1.4 The Relation of Electrochemistry to Other Sciences 26 1.4.1 Some Diagrammatic Presentations 26 1.4.2 Some Examples of the Involvement of Electrochemistry in Other Sciences 28 1.4.3 Electrochemistry as an Interdisciplinary Field, Apart from Chemistry? 29

1.5 Electrodics and Electronics 31

1.6 Transients 32

ix

x CONTENTS

1.7 Electrodes are Catalysts 34

1.8 The Electromagnetic Theory of Light and the Examination of Electrode Surfaces 35

1.9 Science, Technology, Electrochemistry, and Time 38 1.9.1 Do Interfacial Charge-Transfer Reactions Have a Wider Significance

Than Has Hitherto Been Realized? 38 1.9.2 The Relation between Three Major Advances in Science, and the Place

of Electrochemistry in the Developing World 39

CHAPTER 2

Ion-Solvent Interactions

2.1 Introduction 45

2.2 The Nonstructural Treatment of Ion-Solvent Interactions .. 48 2.2.1 A Quantitative Measure of Ion-Solvent Interactions 48 2.2.2 The Born Model: A Charged Sphere in a Continuum 49 2.2.3 The Electrostatic Potential at the Surface of a Charged Sphere 52 2.2.4 On the Electrostatics of Charging (or Discharging) Spheres 54 2.2.5 The Born Expression for the Free Energy of Ion-Solvent Interactions 56 2.2.6 The Enthalpy and Entropy of Ion-Solvent Interactions 59 2.2.7 Can One Experimentally Study the Interactions of a Single Ionic Species

with the Solvent? 61 2.2.8 The Experimental Evaluation of the Heat of Interaction of a Salt and

Solvent 64 2.2.9 How Good Is the Born Theory? 68 Further Reading 72

2.3 Structural Treatment of the Ion-Solvent Interactions 72 2.3.1 The Structure of the Most Common Solvent, Water 72 2.3.2 The Structure of Water near an Ion 76 2.3.3 The Ion-Dipole Model of Ion-Solvent Interactions 80 2.3.4 Evaluation of the Terms in the Ion-Dipole Approach to the Heat of

Soivation 88 2.3.5 How Good Is the Ion-Dipole Theory of Soivation? 93 2.3.6 The Relative Heats of Soivation of Ions on the Hydrogen Scale 95 2.3.7 Do Oppositely Charged Ions of Equal Radii Have Equal Heats of

Soivation? 96 2.3.8 The Water Molecule Can Be Viewed as an Electrical Quadrupole . . . 98 2.3.9 The Ion-Quadrupole Model of Ion-Solvent Interactions 99 2.3.10 Ion-Induced-Dipole Interactions in the Primary Soivation Sheath .. 102 2.3.11 How Good Is the Ion-Quadrupole Theory of Soivation? 103 2.3.12 The Special Case of Interactions of the Transition-Metal Ions with Water 108 2.3.13 Some Summarizing Remarks on the Energetics of Ion-Solvent Inter­

actions 113 Further Reading 116

2.4 The Soivation Number 117 2.4.1 How Many Water Molecules Are Involved in the Soivation of an Ion? 117

CONTENTS xi

2.4.2 Static and Dynamic Pictures of the Ion-Solvent Molecule Interaction 120 2.4.3 The Meaning of Hydration Numbers 123 2.4.4 Why Is the Concept of Solvation Numbers Useful? 124 2.4.5 On the Determination of Solvation Numbers 125 Further Reading 132

2.5 T h e Die lec t r ic C o n s t a n t of W a t e r a n d l o n i c S o l u t i o n s 132

2.5.1 An Externally Applied Electric Field Is Opposed by Counterfields Developed within the Medium 132

2.5.2 The Relation between the Dielectric Constant and Internal Counterfields 136 2.5.3 The Average Dipole Moment of a Gas-Phase Dipole Subject to Electrical

and Thermal Forces 139 2.5.4 The Debye Equation for the Dielectric Constant of a Gas of Dipotes 142 2.5.5 How the Short-Range Interactions between Dipoles Affect the Average

Effective Moment of the Polar Entity Which Responds to an External Field 145

2.5.6 The Local Electric Field in a Condensed Polar Dielectric 147 2.5.7 The Dielectric Constant of Liquids Containing Associated Dipoles . . . 152 2.5.8 The Influence of lonic Solvation on the Dielectric Constant of Solutions 155 Further Reading 158

2.6 Ion-Solvent-Nonelectrolyte Interactions 158 2.6.1 The Problem 158 2.6.2 The Change in Solubility of a Nonelectrolyte Due to Primary Solvation 159 2.6.3 The Change in Solubility Due to Secondary Solvation 160 2.6.4 The Net Effect on Solubility of Influences from Primary and Secondary

Solvation 163 2.6.5 The Case of Anomalous Salting in 164 Further Reading 168

Appendix 2.1 Free Energy Change and Work 168 Appendix 2.2 The Interaction between an Ion and a Dipole . . . 169 Appendix 2.3 The Interaction between an Ion and a Water Quad-

rupole 171

CHAPTER 3

Ion-Ion Interactions

3.1 Introduction 175

3.2 True and Potential Electrolytes 176 3.2.1 lonic Crystals Are True Electrolytes 176 3.2.2 Potential Electrolytes: Nonionic Substances Which React with the

Solvent to Yield Ions 176 3.2.3 An Obsolete Classification: Strong and Weak Electrolytes 177 3.2.4 The Nature of the Electrolyte and the Relevance of Ion-Ion Interactions 180 Further Reading 180

3.3 The Debye-Hückel (or Ion-Cloud) Theory of Ion-Ion Inter­actions 180

3.3.1 A Strategy for a Quantitative Understanding of Ion-Ion Interactions 180

xii CONTENTS

3.3.2 A Prelude to the lonic-Cloud Theory 183 3.3.3 How the Charge Density near the Central Ion Is Determined by Electro-

statics: Poisson's Equation 186 3.3.4 How the Excess Charge Density near the Central Ion Is Given by a Clas-

sical Law for the Distribution of Point Charges in a Coulombic Field .. 187 3.3.5 A Vital Step in the Debye-Hückel Theory of the Charge Distribution

around Ions: Linearization of the Boltzmann Equation 189 3.3.6 The Linearized Poisson-Boltzmann Equation 190 3.3.7 The Solution of the Linearized P-B Equation 191 3.3.8 The lonic Cloud around a Central Ion 193 3.3.9 How Much Does the lonic Cloud Contribute to the Electrostatic Po­

tential tpT at a Distance r from the Central Ion? 199 3.3.10 The lonic Cloud and the Chemical-Potential Change Arising from Ion-

Ion Interactions 201 Further Reading 202

3.4 Activity Coefficients and Ion-Ion Interactions 202 3.4.1 The Evolution of the Concept of Activity Coefficient 202 3.4.2 The Physical Significance of Activity Coefficients 204 3.4.3 The Activity Coefficient of a Single lonic Species Cannot Be Measured 206 3.4.4 The Mean lonic Activity Coefficient 207 3.4.5 The Conversion of Theoretical Activity-Coefficient Expressions into a

Testable Form 209 Further Reading 212

3.5 The Triumphs and Limitations of the Debye-Hückel Theory of Activity Coefficients 212

3.5.1 How Well Does the Debye-Hückel Theoretical Expression for Activity Coefficients Predict Experimental Values? 212

3.5.2 Ions Are of Finite Size, Not Point Charges 219 3.5.3 The Theoretical Mean Ionic-Activity Coefficient in the Case of lonic

Clouds with Finite-Sized Ions 222 3.5.4 The Ion-Size Parameter a 224 3.5.5 Comparison of the Finite-Ion-Size Model with Experiment 227 3.5.6 The Debye-Hückel Theory of lonic Solutions: An Assessment 230 3.5.7 On the Parentage of the Theory of Ion-Ion Interactions 237 Further Reading 238

3.6 Ion-Solvent Interactions and the Activity Coefficient 238 3.6.1 The Effect of Water Bound to Ions on the Theory of Deviations from

Ideality 238 3.6.2 Quantitative Theory of the Activity of an Electrolyte as a Function of

the Hydration Number 240 3.6.3 The Water-Removal Theory of Activity Coefficients and Its Apparent

Consistency with Experiment at High Electrolytic Concentrations . . . 243 Further Reading 246

3.7 The So-Called "Rigorous" Solutions of the Poisson-Boltz­mann Equation 246

Further Reading 250

3.8 Temporary Ion Association in an Electrolytic Solution: For­mation of Pairs, Triplets, etc 251

CONTENTS xii i

3.8.1 Positive and Negative Ions Can Stick Together: Ion-Pair Formation 251 3.8.2 The Probability of Finding Oppositely Charged Ions near Each Other 251 3.8.3 The Fraction of Ion Pairs, According to Bjerrum 253 3.8.4 The Ion-Association Constant KA of Bjerrum 257 3.8.5 Activity Coefficients, Bjerrum's Ion Pairs, and Debye's Free Ions . . . 260 3.8.6 The Fuoss Approach to Ion-Pair Formation 261 3.8.7 From Ion Pairs to Triple Ions to Clusters of Ions 265 Further Reading 266

3.9 The Quasi-Lattice Approach to Concentrated Electrolytic So­

lutions 267 3.9.1 At What Concentration Does the Ionic-Cloud Model Break Down? 267 3.9.2 The Case for a Cube-Root Law for the Dependence of the Activity

Coefflcient on Electrolyte Concentration 269 3.9.3 The Beginnings of a Quasi-Lattice Theory for Concentrated Electrolytic

Solutions -.. 271 Further Reading 272

3.10 The Study of the Constitution of Electrolytic Solutions 273 3.10.1 The Temporary and Permanent Association of Ions 273 3.10.2 Electromagnetic Radiation, a Tool for the Study of Electrolytic Solutions 274 3.10.3 Visible and Ultraviolet Absorption Spectroscopy 275 3.10.4 Raman Spectroscopy 276 3.10.5 Infrared Spectroscopy 278 3.10.6 Nuclear Magnetic Resonance Spectroscopy 278

Further Reading 279

3.11 A Perspective View on the Theory of Ion-Ion Interactions. 279

Appendix 3.1 Poisson's Equation for Spherically Symmetrica!

Charge Distribution 282

Appendix 3.2 Evaluation of the Integral ^0°° e-{«r)(xr) d{xr) .... 283

Appendix 3.3 Derivation of the Result / + = (/;+ + f"s)xl" 284 Appendix 3.4 To Show That the Minimum in the Pr versus r Curve

Occurs at r = A/2 284

Appendix 3.5 Transformation from the Variable r to the Variable

y = X/r 285

Appendix 3.6 Relation Between Calculated and Observed Activity Coefficients 285

CHAPTER 4

Ion Transport in Solutions

4.1 Introduction 287

4.2 Ionic Drift under a Chemical-Potential Gradient: Diffusion 289 4.2.1 The Driving Force for Diffusion 291 4.2.2 The "Deduction" of an Empirical Law: Fick's First Law of Steady-

State Diffusion 293

xiv CONTENTS

4.2.3 On the Diffusion Coefficient D 296 4.2.4 Ionic Movements: A Case of the Random Walk 299 4.2.5 The Mean Square Distance Traveled in a Time t by a Random-Walking

Particle 301 4.2.6 Random-Walking Ions and Diffusion: The Einstein-Smoluchowski

Equation 304 4.2.7 The Gross View of Non-Steady-State Diffusion 307 4.2.8 An Often Used Device for Solving Electrochemical Diffusion Problems:

The Laplace Transformation 309 4.2.9 Laplace Transformation Conyerts the Partial Differential Equation

Which Is Fick's Second Law into a Total Differential Equation 312 4.2.10 The Initial and Boundary Conditions for the Diffusion Process Stimu-

lated by a Constant Current (or Flux) 313 4.2.11 The Concentration Response to a Constant Flux Switched on at t = 0 317 4.2.12 How the Solution of the Constant-Flux Diffusion Problem Leads On to

the Solution of Other Problems 323 4.2.13 Diffusion Resulting from an Instantaneous Current Pulse 328 4.2.14 What Fraction of Ions Travels the Mean Square Distance <x2> in the

Einstein-Smoluchowski Equation? 332 4.2.15 How Can the Diffusion Coefficient Be Related to Molecular Quantities? 338 4.2.16 The Mean Jump Distance /, a Structural Question 339 4.2.17 The Jump Frequency, a Rate-Process Question 340 4.2.18 The Rate-Process Expression for the Diffusion Coefficient 342 4.2.19 Diffusion: An Overall View 342 Further Reading 345

4.3 Ionic Drift under an Electric Field: Conduction 345 4.3.1 The Creation of an Electric Field in an Electrolyte 345 4.3.2 How Do Ions Respond to the Electric Field? 349 4.3.3 The Tendency for a Conflict between Electroneutrality and Conduction 351 4.3.4 The Resolution of the Electroneutrality-versus-Conduction Dilemma:

Electron-Transfer Reactions 351 4.3.5 The Quantitative Link between Electron Flow in the Electrodes and

Ion Flow in the Electrolyte: Faraday's Law 353 4.3.6 The Proportionality Constant Relating the Electric Field and the Current

Density: The Specific Conductivity 354 4.3.7 Molar Conductivity and Equivalent Conductivity 357 4.3.8 The Equivalent Conductivity Varies with Concentration 360 4.3.9 How the Equivalent Conductivity Changes with Concentration: Kohl-

rausch's Law 363 4.3.10 The Vectorial Character of Current: Kohlrausch's Law of the Inde-

pendent Migration of Ions 364 Further Reading 367

4.4 The Simple Atomistic Picture of Ionic Migration 367 4.4.1 Ionic Movements under the Influence of an Applied Electric Field . . . 367 4.4.2 What Is the Average Value of the Drift Velocity? 368 4.4.3 The Mobility of Ions 369 4.4.4 The Current Density Associated with the Directed Movement of Ions

in Solution, in Terms of the Ionic Drift Velocities 371 4.4.5 The Specific and Equivalent Conductivities in Terms of the Ionic Mo-

bilities 373 4.4.6 The Einstein Relation between the Absolute Mobility and the Diffusion

Coefficient 374

CONTENTS xv

4.4.7 What Is the Drag (or Viscous) Force Acting on an Ion in Solution? . . 377 4.4.8 The Stokes-Einstein Relation 379 4.4.9 The Nernst-Einstein Equation 381 4.4.10 Some Limitations of the Nernst-Einstein Relation 382 4.4.11 A Very Approximate Relation between Equivalent Conductivity and

Viscosity: Walden's Rule 385 4.4.12 The Rate-Process Approach to lonic Migration 387 4.4.13 The Rate-Process Expression for Equivalent Conductivity 391 4.4.14 The Total Driving Force for lonic Transport: The Gradient of the

Electrochemical Potential 394 Further Reading 399

4.5 The Interdependence of lonic Drifts 399 4.5.1 The Drift of One lonic Species May Influence the Drift of Another . 399 4.5.2 A Consequence of the Unequal Mobilities of Cations and Anions, the

Transport Numbers 400 4.5.3 The Significance of a Transport Number of Zero 402 4.5.4 The Diffusion Potential, Another Consequence of the Unequal Mobil­

ities of Ions 406 4.5.5 Electroneutrality Coupling between the Drifts of Different lonic Species 410 4.5.6 How Does One Represent the Interaction between lonic Fluxes? The

Onsager Phenomenological Equations 411 4.5.7 An Expression for the Diffusion Potential 413 4.5.8 The Integration of the Differential Equation for Diffusion Potentials:

The Planck-Henderson Equation' 417 Further Reading 420

4.6 The Influence of lonic Atmospheres on lonic Migration . . . 420 4.6.1 The Concentration Dependence of the Mobility of Ions 420 4.6.2 lonic Clouds Attempt to Catch Up with Moving Ions 422 4.6.3 An Egg-Shaped lonic Cloud and the "Portable" Field on the Central Ion 423 4.6.4 A Second Braking Effect of the lonic Cloud on the Central Ion: The

Electrophoretic Effect 424 4.6.5 The Net Drift Velocity of an Ion Interacting with Its Atmosphere . . . . 425 4.6.6 The Electrophoretic Component of the Drift Velocity 427 4.6.7 The Procedure for Calculating the Relaxation Component of the Drift

Velocity 427 4.6.8 How Long Does an Ion Atmosphere Take to Decay? 428 4.6.9 The Quantitative Measure of the Asymmetry of the lonic Cloud Around

a Moving Ion 429 4.6.10 The Magnitude of the Relaxation Force and the Relaxation Component

of the Drift Velocity 430 4.6.11 The Net Drift Velocity and Mobility of an Ion Subject to Ion-Ion

Interactions 432 4.6.12 The Debye-Hückel-Onsager Equation 434 4.6.13 The Theoretical Predictions of the Debye-Hückel-Onsager Equation

versus the Observed Conductance Curves 435 4.6.14 A Theoretical Basis for Some Modifications of the Debye-Hückel-

Onsager Equation 438 Further Reading 439

4.7 Nonaqueous Solutions: A New Frontier in Ionics? 440 4.7.1 Water Is the Most Plentiful Solvent 440

xvi CONTENTS

4.7.2 Water Is Often Not an Ideal Solvent 441 4.7.3 The Debye-Hückel-Onsager Theory for Nonaqueous Solutions 442 4.7.4 The Solvent Effect on the Mobility at Infinite Dilution 443 4.7.5 The Slope of the A versus cl Curve as a Function of the Solvent . . . . 445 4.7.6 The Effect of the Solvent on the Concentration of Free Ions: Ion As­

sociation 447 4.7.7 The Effect of Ion Association upon Conductivity 448 4.7.8 Even Triple Ions Can Be Formed in Nonaqueous Solutions 450 4.7.9 Some Conclusions about the Conductance of Nonaqueous Solutions

of True Electrolytes 452 Further Reading 452

Appendix 4.1 The Mean Square Distance Traveled by a Random-

Walking Particle 453

Appendix 4.2 The Laplace Transform of a Constant 454

Appendix 4.3 A Few Elementary Ideas on the Theory of Rate

Processes 455

Appendix 4.4 The Derivation of Equations (4.257) and (4.258) . . 458

Appendix 4.5 The Derivation of Equation (4.318) 460

CHAPTER 5

Protons in Solution

5.1 The Case of the Nonconforming Ion: The Proton 461

5.2 Proton Solvation 462 5.2.1 What Is the Condition of the Proton in Solution? 462 5.2.2 Proton Affinity 466 5.2.3 The Overall Heat of Hydration of a Proton 467 5.2.4 The Coordination Number of a Proton 468 Further Reading 470

5.3 Proton Transport 470 5.3.1 The Abnormal Mobility of a Proton 470 5.3.2 Protons Conduct by a Chain Mechanism 474 5.3.3 Classical Proton Jumps and Proton Mobility 476 5.3.4 Do Proton Jumps Obey Classical Laws? 478 5.3.5 Quantum-Mechanical Proton Jumps and Proton Mobility 480 5.3.6 Water Reorientation, a Prerequisite for Proton Jumps 481 5.3.7 The Rate of Water Reorientation and Proton Mobility 482 5.3.8 A Picture of Proton Mobility in Aqueous Solutions 484 5.3.9 The Rate-Determining Water-Rotation Model of Proton Mobility and

the Other Anomalous Facts : 485 5.3.10 Proton Mobility in Ice 486 5.3.11 The Existence of the Hydronium Ion from the Point of View of Proton

Mobility 487 5.3.12 Why Is the Mechanism of Proton Mobility So Important? 487 Further Reading 488

CONTENTS xvii

5.4 Homogeneous Proton-Transfer Reactions and Potential Elec-trolytes 488

5.4.1 Acids Produce Hydrogen Ions and Bases Produce Hydroxyl Ions: The Initial View 488

5.4.2 Acids Are Proton Donors, and Bases Are Proton Acceptors: The Brönsted View 489

5.4.3 The Dissolution of Potential Electrolytes and Other Types of Proton-Transfer Reactions 491

5.4.4 An Important Consequence of the Brönsted View: Conjugate Acid-Base Pairs 493

5.4.5 The Absolute Strength of an Acid or a Base 494 5.4.6 The Relative Strengths of Acids and Bases 495 5.4.7 Proton Free-Energy Levels 500 5.4.8 The Primary Effect of the Solvent upon the Relative Strength of an Acid 504 5.4.9 A Secondary (Electrostatic) Effect of the Solvent on the Relative

Strength of Acids 507 Further Reading 511

CHAPTER 6

lonic Liquids

6.1 Introduction 513 6.1.1 The Limiting Case of Zero Solvent: Pure Liquid Electrolytes 513 6.1.2 The Thermal Dismantling of an lonic Lattice 514 6.1.3 Some Features of lonic Liquids (Pure Liquid Electrolytes) 515 6.1.4 Liquid Electrolytes Are lonic Liquids 517 6.1.5 The Fundamental Problems in Pure Liquid Electrolytes 518 Further Reading 522

6.2 Models of Simple lonic Liquids 522 6.2.1 The Origin of Liquid Electrolyte Models 522 6.2.2 Lattice-Oriented Models 523

6.2.2a The Experimental Basis for Model Building 523 6.2.2b The Need to Pour Empty Space into a Fused Salt 523 6.2.2c The Vacancy Model: A Fused Salt Is an lonic Lattice with

Numerous Vacancies 526 6.2.2d The Hole Model: A Fused Salt Is Füll of Holes like Swiss Cheese 527

6.2.3 Gas-Oriented Models for Liquid Electrolytes 529 6.2.3a The Cell-Theory Approach 529 6.2.36 The Free Volume Belongs to the Liquid and Not to the Particles:

The Liquid Free-Volume Model 530 6.2.4 A Summary of the Models for Liquid Electrolytes 532 Further Reading 533

6.3 Quantification of the Hole Model for Liquid Electrolytes.. 533 6.3.1 An Expression for the Probability That a Hole Has a Radius between r

and r + dr 533 6.3.2 The Fürth Approach to the Work of Hole Formation 536 6.3.3 The Distribution Function for the Size of the Holes in a Liquid Elec­

trolyte 537

xviii CONTENTS

6.3.4 What Is the Average Size of a Hole? 539 Further Reading 541

6.4 Transport Phenomena in Liquid Electrolytes 541 6.4.1 Some Simplifying Features of Transport in Fused Salts 541 6.4.2 Diffusion in Fused Salts 542

6.4.2a Self-Diffusion in Pure Liquid Electrolytes: It May Be Revealed by Introducing Isotopes 542

6.4.26 Results of Self-Diffusion Experiments 544 6.4.3 The Viscosity of Molten Salts 547 6.4.4 What Is the Validity of the Stokes-Einstein Relation in lonic Liquids? 550 6.4.5 The Conductivity of Pure Liquid Electrolytes 553 6.4.6 The Nernst-Einstein Relation in lonic Liquids 555

6.4.6a The Nernst-Einstein Relation: Its Degree of Applicability . . . 555 6.4.66 The Gross View of Deviations from the Nernst-Einstein Equa-

tion 557 6.4.6c Possible Molecular Mechanisms for Nernst-Einstein Deviations 560

6.4.7 Transport Numbers in Pure Liquid Electrolytes 564 6.4.7a Some Ideas about Transport Numbers in Fused Salts 564 6.4.76 The Measurement of Transport Numbers in Liquid Electrolytes 566 6.4.7c A Radiotracer Method of Calculating Transport Numbers in

Molten Salts 571 6.4.Id A Stokes' Law Approach to a Rough Estimate of Transport

Numbers 572 Further Reading 573

6.5 The Atomistic View of Transport Processes in Simple lonic Liquids 574

6.5.1 Holes and Transport Processes 574 6.5.2 What Is the Mean Lifetime of Holes in Fused Salts? 576 6.5.3 Expression for Viscosity in Terms of Holes 577 6.5.4 The Diffusion Coefficient from the Hole Model 577 6.5.5 A Critical Test of a Model for lonic Liquids Is a Rationalization of the

Heat of Activation of 3.1RTm for Transport Processes 580 6.5.6 An Attempt to Rationalize ED = Er, = 3.7RTm 581 6.5.7 The Hole Model, the Most Consistent Present Model for Liquid Elec­

trolytes 584 Further Reading 587

6.6 Mixture of Simple lonic Liquids—Complex Formation . . . 587 6.6.1 Mixtures of Simple lonic Liquids May Not Behave Ideally 587 6.6.2 Interactions Lead to Nonideal Behavior 588 6.6.3 Can One Meaningfully Refer to Complex'Ions in Fused Salts? 589 6.6.4 Raman Spectra, and Other Means of Detecting Complex Ions 590 Further Reading 593

6.7 Mixtures of Liquid Oxide Electrolytes 594 6.7.1 The Liquid Oxides 594 6.7.2 Pure Fused Nonmetallic Oxides Form Network Structures Like Liquid

Water 594 6.7.3 Why Does Fused Silica Have a Much Higher Viscosity Than Do Liquid

Water and the Fused Salts? 597 6.7.4 The Solvent Properties of Fused Nonmetallic Oxides 601

CONTENTS xix

6.7.5 Ionic Additions to the Liquid-Silica Network: Glasses 603 6.7.6 The Extent of Structure Breaking of Three-Dimensional Network Lat-

tices and Its Dependence on the Concentration of Metal Ions 604 6.7.7 The Molecular and Network Models of Liquid Silicate Structure . . . . 606 6.7.8 Liquid Silicates Contain Large Discrete Polyanions 610 6.7.9 The "Iceberg" Model 615 6.7.10 Fused-Oxide Systems in Metallurgy: Slags 616 Further Reading 618

Appendix 6.1 The Effective Mass of a Hole 619

Appendix 6.2 Some Properties of the Gamma Function 620

Appendix 6.3 The Kinetic Theory Expression for the Viscosity of

a Fluid 621

Index xxxin