Modern Electrochemistry, 1970 An Introduction to an Interdisciplinary Area Volume 1

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 trans­ portation 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.

Volume 1.- 1 Electrochemistry.- 1.1 Introduction.- 1.2 Electrons at and across Interfaces.- 1.2.1 Many Properties of Materials Depend upon Events Occurring at Their Surfaces.- 1.2.2 Almost All Interfaces Are Electrified.- 1.2.3 The Continuous Flow of Electrons across an Interface: Electrochemical Reactions.- 1.2.4 Electrochemical and Chemical Reactions.- 1.3 Basic Electrochemistry.- 1.3.1 Electrochemistry before 1950.- 1.3.2 The Treatment of Interfacial Electron Transfer as a Rate Process: The 1950’s.- 1.3.3 Quantum Electrochemistry: The 1960’s.- 1.3.4 Ions in Solution, as well as Electron Transfer across Interfaces.- 1.4 The Relation of Electrochemistry to Other Sciences.- 1.4.1 Some Diagrammatic Presentations.- 1.4.2 Some Examples of the Involvement of Electrochemistry in Other Sciences.- 1.4.3 Electrochemistry as an Interdisciplinary Field, Apart from Chemistry?.- 1.5 Electrodics and Electronics.- 1.6 Transients.- 1.7 Electrodes are Catalysts.- 1.8 The Electromagnetic Theory of Light and the Examination of Electrode Surfaces.- 1.9 Science, Technology, Electrochemistry, and Time.- 1.9.1 Do Interfacial Charge-Transfer Reactions Have a Wider Significance Than Has Hitherto Been Realized?.- 1.9.2 The Relation between Three Major Advances in Science, and the Place of Electrochemistry in the Developing World.- 2 Ion—Solvent Interactions.- 2.1 Introduction.- 2.2 The Nonstructural Treatment of Ion—Solvent Interactions.- 2.2.1 A Quantitative Measure of Ion—Solvent Interactions.- 2.2.2 The Born Model: A Charged Sphere in a Continuum.- 2.2.3 The Electrostatic Potential at the Surface of a Charged Sphere.- 2.2.4 On the Electrostatics of Charging (or Discharging) Spheres.- 2.2.5 The Born Expression for the Free Energy of Ion—Solvent Interactions.- 2.2.6 The Enthalpy and Entropy of Ion—Solvent Interactions.- 2.2.7 Can One Experimentally Study the Interactions of a Single Ionic Species with the Solvent?.- 2.2.8 The Experimental Evaluation of the Heat of Interaction of a Salt and Solvent.- 2.2.9 How Good Is the Born Theory?.- Further Reading.- 2.3 Structural Treatment of the Ion—Solvent Interactions.- 2.3.1 The Structure of the Most Common Solvent, Water.- 2.3.2 The Structure of Water near an Ion.- 2.3.3 The Ion—Dipole Model of Ion—Solvent Interactions.- 2.3.4 Evaluation of the Terms in the Ion—Dipole Approach to the Heat of Solvation.- 2.3.5 How Good Is the Ion—Dipole Theory of Solvation?.- 2.3.6 The Relative Heats of Solvation of Ions on the Hydrogen Scale.- 2.3.7 Do Oppositely Charged Ions of Equal Radii Have Equal Heats of Solvation?.- 2.3.8 The Water Molecule Can Be Viewed as an Electrical Quadrupole.- 2.3.9 The Ion—Quadrupole Model of Ion—Solvent Interactions.- 2.3.10 Ion—Induced-Dipole Interactions in the Primary Solvation Sheath.- 2.3.11 How Good Is the Ion—Quadrupole Theory of Solvation?.- 2.3.12 The Special Case of Interactions of the Transition-Metal Ions with Water.- 2.3.13 Some Summarizing Remarks on the Energetics of Ion—Solvent Interactions.- Further Reading.- 2.4 The Solvation Number.- 2.4.1 How Many Water Molecules Are Involved in the Solvation of an Ion?.- 2.4.2 Static and Dynamic Pictures of the Ion—Solvent Molecule Interaction.- 2.4.3 The Meaning of Hydration Numbers.- 2.4.4 Why Is the Concept of Solvation Numbers Useful?.- 2.4.5 On the Determination of Solvation Numbers.- Further Reading.- 2.5 The Dielectric Constant of Water and Ionic Solutions.- 2.5.1 An Externally Applied Electric Field Is Opposed by Counterfields Developed within the Medium.- 2.5.2 The Relation between the Dielectric Constant and Internal Counterfields.- 2.5.3 The Average Dipole Moment of a Gas-Phase Dipole Subject to Electrical and Thermal Forces.- 2.5.4 The Debye Equation for the Dielectric Constant of a Gas of Dipoles.- 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.- 2.5.6 The Local Electric Field in a Condensed Polar Dielectric.- 2.5.7 The Dielectric Constant of Liquids Containing Associated Dipoles.- 2.5.8 The Influence of Ionic Solvation on the Dielectric Constant of Solutions.- Further Reading.- 2.6 Ion—Solvent—Nonelectrolyte Interactions.- 2.6.1 The Problem.- 2.6.2 The Change in Solubility of a Nonelectrolyte Due to Primary Solvation.- 2.6.3 The Change in Solubility Due to Secondary Solvation.- 2.6.4 The Net Effect on Solubility of Influences from Primary and Secondary Solvation.- 2.6.5 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.- 3 Ion—Ion Interactions.- 3.1 Introduction.- 3.2 True and Potential Electrolytes.- 3.2.1 Ionic Crystals Are True Electrolytes.- 3.2.2 Potential Electrolytes: Nonionic Substances Which React with the Solvent to Yield Ions.- 3.2.3 An Obsolete Classification: Strong and Weak Electrolytes.- 3.2.4 The Nature of the Electrolyte and the Relevance of Ion—Ion Interactions.- Further Reading.- 3.3 The Debye—Hückel (or Ion-Cloud) Theory of Ion—Ion Interactions.- 3.3.1 A Strategy for a Quantitative Understanding of Ion—Ion Interactions.- 3.3.2 A Prelude to the Ionic-Cloud Theory.- 3.3.3 How the Charge Density near the Central Ion Is Determined by Electrostatics: Poisson’s Equation.- 3.3.4 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.- 3.3.5 A Vital Step in the Debye—Hückel Theory of the Charge Distribution around Ions: Linearization of the Boltzmann Equation.- 3.3.6 The Linearized Poisson—Boltzmann Equation.- 3.3.7 The Solution of the Linearized P—B Equation.- 3.3.8 The Ionic Cloud around a Central Ion.- 3.3.9 How Much Does the Ionic Cloud Contribute to the Electrostatic Potential ?r at a Distance r from the Central Ion?.- 3.3.10 The Ionic Cloud and the Chemical-Potential Change Arising from Ion-Ion Interactions.- Further Reading.- 3.4 Activity Coefficients and Ion-Ion Interactions.- 3.4.1 The Evolution of the Concept of Activity Coefficient.- 3.4.2 The Physical Significance of Activity Coefficients.- 3.4.3 The Activity Coefficient of a Single Ionic Species Cannot Be Measured.- 3.4.4 The Mean Ionic Activity Coefficient.- 3.4.5 The Conversion of Theoretical Activity-Coefficient Expressions into a Testable Form.- Further Reading.- 3.5 The Triumphs and Limitations of the Debye—Hückel Theory of Activity Coefficients.- 3.5.1 How Well Does the Debye—Hückel Theoretical Expression for Activity Coefficients Predict Experimental Values?.- 3.5.2 Ions Are of Finite Size, Not Point Charges.- 3.5.3 The Theoretical Mean Ionic-Activity Coefficient in the Case of Ionic Clouds with Finite-Sized Ions.- 3.5.4 The Ion-Size Parameter a.- 3.5.5 Comparison of the Finite-Ion-Size Model with Experiment.- 3.5.6 The Debye—Hückel Theory of Ionic Solutions: An Assessment.- 3.5.7 On the Parentage of the Theory of Ion-Ion Interactions.- Further Reading.- 3.6 Ion—Solvent Interactions and the Activity Coefficient.- 3.6.1 The Effect of Water Bound to Ions on the Theory of Deviations from Ideality.- 3.6.2 Quantitative Theory of the Activity of an Electrolyte as a Function of the Hydration Number.- 3.6.3 The Water-Removal Theory of Activity Coefficients and Its Apparent Consistency with Experiment at High Electrolytic Concentrations.- Further Reading.- 3.7 The So-Called “Rigorous” Solutions of the Poisson—Boltzmann Equation.- Further Reading.- 3.8 Temporary Ion Association in an Electrolytic Solution: Formation of Pairs, Triplets, etc.- 3.8.1 Positive and Negative Ions Can Stick Together: Ion-Pair Formation.- 3.8.2 The Probability of Finding Oppositely Charged Ions near Each Other.- 3.8.3 The Fraction of Ion Pairs, According to Bjerrum.- 3.8.4 The Ion-Association Constant KA of Bjerrum.- 3.8.5 Activity Coefficients, Bjerrum’s Ion Pairs, and Debye’s Free Ions.- 3.8.6 The Fuoss Approach to Ion-Pair Formation.- 3.8.7 From Ion Pairs to Triple Ions to Clusters of Ions.- Further Reading.- 3.9 The Quasi-Lattice Approach to Concentrated Electrolytic Solutions.- 3.9.1 At What Concentration Does the Ionic-Cloud Model Break Down?.- 3.9.2 The Case for a Cube-Root Law for the Dependence of the Activity Coefficient on Electrolyte Concentration.- 3.9.3 The Beginnings of a Quasi-Lattice Theory for Concentrated Electrolytic Solutions.- Further Reading.- 3.10 The Study of the Constitution of Electrolytic Solutions.- 3.10.1 The Temporary and Permanent Association of Ions.- 3.10.2 Electromagnetic Radiation, a Tool for the Study of Electrolytic Solutions.- 3.10.3 Visible and Ultraviolet Absorption Spectroscopy.- 3.10.4 Raman Spectroscopy.- 3.10.5 Infrared Spectroscopy.- 3.10.6 Nuclear Magnetic Resonance Spectroscopy.- Further Reading.- 3.11 A Perspective View on the Theory of Ion—Ion Interactions.- Appendix 3.1 Poisson’s Equation for Spherically Symmetrical Charge Distribution.- Appendix 3.2 Evaluation of the Integral $$\int_{r = 0}^{r \to \infty } {{e^{ - (\chi r)}}} (\chi r)d(\chi r)$$.- Appendix 3.3 Derivation of the Result $${f_ + } = {(f_ + ^{{\nu _ + }} + f_ - ^{{\nu _ - }})^{1/\nu }}$$.- Appendix 3.4 To Show That the Minimum in the Pr versus r Curve Occurs at r = ?/2.- Appendix 3.5 Transformation from the Variable r to the Variable y = ?/r.- Appendix 3.6 Relation Between Calculated and Observed Activity Coefficients.- 4 Ion Transport in Solutions.- 4.1 Introduction.- 4.2 Ionic Drift under a Chemical-Potential Gradient: Diffusion.- 4.2.1 The Driving Force for Diffusion.- 4.2.2 The “Deduction” of an Empirical Law: Fick’s First Law of Steady-State Diffusion.- 4.2.3 On the Diffusion Coefficient D.- 4.2.4 Ionic Movements: A Case of the Random Walk.- 4.2.5 The Mean Square Distance Traveled in a Time t by a Random-Walking Particle.- 4.2.6 Random-Walking Ions and Diffusion: The Einstein—Smoluchowski Equation.- 4.2.7 The Gross View of Non-Steady-State Diffusion.- 4.2.8 An Often Used Device for Solving Electrochemical Diffusion Problems: The Laplace Transformation.- 4.2.9 Laplace Transformation Converts the Partial Differential Equation Which Is Fick’s Second Law into a Total Differential Equation.- 4.2.10 The Initial and Boundary Conditions for the Diffusion Process Stimulated by a Constant Current (or Flux).- 4.2.11 The Concentration Response to a Constant Flux Switched on at t = 0.- 4.2.12 How the Solution of the Constant-Flux Diffusion Problem Leads On to the Solution of Other Problems.- 4.2.13 Diffusion Resulting from an Instantaneous Current Pulse.- 4.2.14 What Fraction of Ions Travels the Mean Square Distance ?x2? in the Einstein—Smoluchowski Equation?.- 4.2.15 How Can the Diffusion Coefficient Be Related to Molecular Quantities?.- 4.2.16 The Mean Jump Distance l, a Structural Question.- 4.2.17 The Jump Frequency, a Rate-Process Question.- 4.2.18 The Rate-Process Expression for the Diffusion Coefficient.- 4.2.19 Diffusion: An Overall View.- Further Reading.- 4.3 Ionic Drift under an Electric Field: Conduction.- 4.3.1 The Creation of an Electric Field in an Electrolyte.- 4.3.2 How Do Ions Respond to the Electric Field?.- 4.3.3 The Tendency for a Conflict between Electroneutrality and Conduction.- 4.3.4 The Resolution of the Electroneutrality-versus-Conduction Dilemma: Electron-Transfer Reactions.- 4.3.5 The Quantitative Link between Electron Flow in the Electrodes and Ion Flow in the Electrolyte: Faraday’s Law.- 4.3.6 The Proportionality Constant Relating the Electric Field and the Current Density: The Specific Conductivity.- 4.3.7 Molar Conductivity and Equivalent Conductivity.- 4.3.8 The Equivalent Conductivity Varies with Concentration.- 4.3.9 How the Equivalent Conductivity Changes with Concentration: Kohlrausch’s Law.- 4.3.10 The Vectorial Character of Current: Kohlrausch’s Law of the Independent Migration of Ions.- Further Reading.- 4.4 The Simple Atomistic Picture of Ionic Migration.- 4.4.1 Ionic Movements under the Influence of an Applied Electric Field.- 4.4.2 What Is the Average Value of the Drift Velocity?.- 4.4.3 The Mobility of Ions.- 4.4.4 The Current Density Associated with the Directed Movement of Ions in Solution, in Terms of the Ionic Drift Velocities.- 4.4.5 The Specific and Equivalent Conductivities in Terms of the Ionic Mobilities.- 4.4.6 The Einstein Relation between the Absolute Mobility and the Diffusion Coefficient.- 4.4.7 What Is the Drag (or Viscous) Force Acting on an Ion in Solution?.- 4.4.8 The Stokes—Einstein Relation.- 4.4.9 The Nernst—Einstein Equation.- 4.4.10 Some Limitations of the Nernst—Einstein Relation.- 4.4.11 A Very Approximate Relation between Equivalent Conductivity and Viscosity: Walden’s Rule.- 4.4.12 The Rate-Process Approach to Ionic Migration.- 4.4.13 The Rate-Process Expression for Equivalent Conductivity.- 4.4.14 The Total Driving Force for Ionic Transport: The Gradient of the Electrochemical Potential.- Further Reading.- 4.5 The Interdependence of Ionic Drifts.- 4.5.1 The Drift of One Ionic Species May Influence the Drift of Another.- 4.5.2 A Consequence of the Unequal Mobilities of Cations and Anions, the Transport Numbers.- 4.5.3 The Significance of a Transport Number of Zero.- 4.5.4 The Diffusion Potential, Another Consequence of the Unequal Mobilities of Ions.- 4.5.5 Electroneutrality Coupling between the Drifts of Different Ionic Species.- 4.5.6 How Does One Represent the Interaction between Ionic Fluxes? The Onsager Phenomenological Equations.- 4.5.7 An Expression for the Diffusion Potential.- 4.5.8 The Integration of the Differential Equation for Diffusion Potentials: The Planck—Henderson Equation.- Further Reading.- 4.6 The Influence of Ionic Atmospheres on Ionic Migration.- 4.6.1 The Concentration Dependence of the Mobility of Ions.- 4.6.2 Ionic Clouds Attempt to Catch Up with Moving Ions.- 4.6.3 An Egg-Shaped Ionic Cloud and the “Portable” Field on the Central Ion.- 4.6.4 A Second Braking Effect of the Ionic Cloud on the Central Ion: The Electrophoretic Effect.- 4.6.5 The Net Drift Velocity of an Ion Interacting with Its Atmosphere.- 4.6.6 The Electrophoretic Component of the Drift Velocity.- 4.6.7 The Procedure for Calculating the Relaxation Component of the Drift Velocity.- 4.6.8 How Long Does an Ion Atmosphere Take to Decay?.- 4.6.9 The Quantitative Measure of the Asymmetry of the Ionic Cloud Around a Moving Ion.- 4.6.10 The Magnitude of the Relaxation Force and the Relaxation Component of the Drift Velocity.- 4.6.11 The Net Drift Velocity and Mobility of an Ion Subject to Ion—Ion Interactions.- 4.6.12 The Debye—Hückel—Onsager Equation.- 4.6.13 The Theoretical Predictions of the Debye—Hückel—Onsager Equation versus the Observed Conductance Curves.- 4.6.14 A Theoretical Basis for Some Modifications of the Debye—Hückel—Onsager Equation.- Further Reading.- 4.7 Nonaqueous Solutions: A New Frontier in Ionics?.- 4.7.1 Water Is the Most Plentiful Solvent.- 4.7.2 Water Is Often Not an Ideal Solvent.- 4.7.3 The Debye—Hückel—Onsager Theory for Nonaqueous Solutions.- 4.7.4 The Solvent Effect on the Mobility at Infinite Dilution.- 4.7.5 The Slope of the ? versus c½ Curve as a Function of the Solvent.- 4.7.6 The Effect of the Solvent on the Concentration of Free Ions: Ion Association.- 4.7.7 The Effect of Ion Association upon Conductivity.- 4.7.8 Even Triple Ions Can Be Formed in Nonaqueous Solutions.- 4.7.9 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).- 5 Protons in Solution.- 5.1 The Case of the Nonconforming Ion: The Proton.- 5.2 Proton Solvation.- 5.2.1 What Is the Condition of the Proton in Solution?.- 5.2.2 Proton Affinity.- 5.2.3 The Overall Heat of Hydration of a Proton.- 5.2.4 The Coordination Number of a Proton.- Further Reading.- 5.3 Proton Transport.- 5.3.1 The Abnormal Mobility of a Proton.- 5.3.2 Protons Conduct by a Chain Mechanism.- 5.3.3 Classical Proton Jumps and Proton Mobility.- 5.3.4 Do Proton Jumps Obey Classical Laws?.- 5.3.5 Quantum-Mechanical Proton Jumps and Proton Mobility.- 5.3.6 Water Reorientation, a Prerequisite for Proton Jumps.- 5.3.7 The Rate of Water Reorientation and Proton Mobility.- 5.3.8 A Picture of Proton Mobility in Aqueous Solutions.- 5.3.9 The Rate-Determining Water-Rotation Model of Proton Mobility and the Other Anomalous Facts.- 5.3.10 Proton Mobility in Ice.- 5.3.11 The Existence of the Hydronium Ion from the Point of View of Proton Mobility.- 5.3.12 Why Is the Mechanism of Proton Mobility So Important?.- Further Reading.- 5.4 Homogeneous Proton-Transfer Reactions and Potential Electrolytes.- 5.4.1 Acids Produce Hydrogen Ions and Bases Produce Hydroxyl Ions: The Initial View.- 5.4.2 Acids Are Proton Donors, and Bases Are Proton Acceptors: The Brönsted View.- 5.4.3 The Dissolution of Potential Electrolytes and Other Types of Proton-Transfer Reactions.- 5.4.4 An Important Consequence of the Brönsted View: Conjugate Acid-Base Pairs.- 5.4.5 The Absolute Strength of an Acid or a Base.- 5.4.6 The Relative Strengths of Acids and Bases.- 5.4.7 Proton Free-Energy Levels.- 5.4.8 The Primary Effect of the Solvent upon the Relative Strength of an Acid.- 5.4.9 A Secondary (Electrostatic) Effect of the Solvent on the Relative Strength of Acids.- Further Reading.- 6 Ionic Liquids.- 6.1 Introduction.- 6.1.1 The Limiting Case of Zero Solvent: Pure Liquid Electrolytes.- 6.1.2 The Thermal Dismantling of an Ionic Lattice.- 6.1.3 Some Features of Ionic Liquids (Pure Liquid Electrolytes).- 6.1.4 Liquid Electrolytes Are Ionic Liquids.- 6.1.5 The Fundamental Problems in Pure Liquid Electrolytes.- Further Reading.- 6.2 Models of Simple Ionic Liquids.- 6.2.1 The Origin of Liquid Electrolyte Models.- 6.2.2 Lattice-Oriented Models.- 6.2.2a The Experimental Basis for Model Building.- 6.2.2b The Need to Pour Empty Space into a Fused Salt.- 6.2.2c The Vacancy Model: A Fused Salt Is an Ionic Lattice with Numerous Vacancies.- 6.2.2d The Hole Model: A Fused Salt Is Full of Holes like Swiss Cheese.- 6.2.3 Gas-Oriented Models for Liquid Electrolytes.- 6.2.3a The Cell-Theory Approach.- 6.2.3b The Free Volume Belongs to the Liquid and Not to the Particles: The Liquid Free-Volume Model.- 6.2.4 A Summary of the Models for Liquid Electrolytes.- Further Reading.- 6.3 Quantification of the Hole Model for Liquid Electrolytes.- 6.3.1 An Expression for the Probability That a Hole Has a Radius between r and r + dr.- 6.3.2 The Fürth Approach to the Work of Hole Formation.- 6.3.3 The Distribution Function for the Size of the Holes in a Liquid Electrolyte.- 6.3.4 What Is the Average Size of a Hole?.- Further Reading.- 6.4 Transport Phenomena in Liquid Electrolytes.- 6.4.1 Some Simplifying Features of Transport in Fused Salts.- 6.4.2 Diffusion in Fused Salts.- 6.4.2a Self-Diffusion in Pure Liquid Electrolytes: It May Be Revealed by Introducing Isotopes.- 6.4.2b Results of Self-Diffusion Experiments.- 6.4.3 The Viscosity of Molten Salts.- 6.4.4 What Is the Validity of the Stokes—Einstein Relation in Ionic Liquids?.- 6.4.5 The Conductivity of Pure Liquid Electrolytes.- 6.4.6 The Nernst—Einstein Relation in Ionic Liquids.- 6.4.6a The Nernst—Einstein Relation: Its Degree of Applicability.- 6.4.6b The Gross View of Deviations from the Nernst—Einstein Equation.- 6.4.6c Possible Molecular Mechanisms for Nernst—Einstein Deviations.- 6.4.7 Transport Numbers in Pure Liquid Electrolytes.- 6.4.7a Some Ideas about Transport Numbers in Fused Salts.- 6.4.7b The Measurement of Transport Numbers in Liquid Electrolytes.- 6.4.7c A Radiotracer Method of Calculating Transport Numbers in Molten Salts.- 6.4.7d A Stokes’ Law Approach to a Rough Estimate of Transport Numbers.- Further Reading.- 6.5 The Atomistic View of Transport Processes in Simple Ionic Liquids.- 6.5.1 Holes and Transport Processes.- 6.5.2 What Is the Mean Lifetime of Holes in Fused Salts?.- 6.5.3 Expression for Viscosity in Terms of Holes.- 6.5.4 The Diffusion Coefficient from the Hole Model.- 6.5.5 A Critical Test of a Model for Ionic Liquids Is a Rationalization of the Heat of Activation of 3.7RTm for Transport Processes.- 6.5.6 An Attempt to Rationalize ED = E? = 3.7 RTm.- 6.5.7 The Hole Model, the Most Consistent Present Model for Liquid Electrolytes.- Further Reading.- 6.6 Mixture of Simple Ionic Liquids—Complex Formation.- 6.6.1 Mixtures of Simple Ionic Liquids May Not Behave Ideally.- 6.6.2 Interactions Lead to Nonideal Behavior.- 6.6.3 Can One Meaningfully Refer to Complex Ions in Fused Salts?.- 6.6.4 Raman Spectra, and Other Means of Detecting Complex Ions.- Further Reading.- 6.7 Mixtures of Liquid Oxide Electrolytes.- 6.7.1 The Liquid Oxides.- 6.7.2 Pure Fused Nonmetallic Oxides Form Network Structures Like Liquid Water.- 6.7.3 Why Does Fused Silica Have a Much Higher Viscosity Than Do Liquid Water and the Fused Salts?.- 6.7.4 The Solvent Properties of Fused Nonmetallic Oxides.- 6.7.5 Ionic Additions to the Liquid-Silica Network: Glasses.- 6.7.6 The Extent of Structure Breaking of Three-Dimensional Network Lattices and Its Dependence on the Concentration of Metal Ions.- 6.7.7 The Molecular and Network Models of Liquid Silicate Structure.- 6.7.8 Liquid Silicates Contain Large Discrete Polyanions.- 6.7.9 The “Tceberg” Model.- 6.7.10 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.