Modern Electrochemistry: An Introduction to an Interdisciplinary Area, Vol. 2

Modern Electrochemistry: An Introduction to an Interdisciplinary Area

7 The Electrified Interface.- 7.1 Electrification of an Interface.- 7.1.1 The Electrode-Electrolyte Interface: The Basis of Electrodics.- 7.1.2 New Forces at the Boundary of an Electrolyte.- 7.1.3 The Interphase Region Has New Properties and New Structures.- 7.1.4 An Electrode Is Like a Giant Central Ion.- 7.1.5 The Consequences of Compromise Arrangements: The Electrolyte Side of the Boundary Acquires a Charge.- 7.1.6 Both Sides of the Interface Become Electrified: The So-Called “Electrical Double Layer”.- 7.1.7 Double Layers Are Characteristic of All Phase Boundaries.- 7.1.8 A Look into an Electrified Interface.- Further Reading.- 7.2 Some Problems in Understanding an Electrified Interface.- 7.2.1 What Knowledge Is Required before an Electrified Interface Can Be Regarded as Understood?.- 7.2.2 Predicting the Interphase Properties from the Bulk Properties of the Phases.- 7.2.3 Why Bother about Electrified Interfaces?.- 7.2.4 The Need to Clarify Some Concepts.- 7.2.5 The Potential Difference across Electrified Interfaces.- 7.2.5a What Happens when One Tries to Measure the Absolute Potential Difference across a Single Electrode-Electrolyte Interface.- 7.2.5b The Absolute Potential Difference across a Single Electrified Interface Cannot Be Measured.- 7.2.5c Can One Measure Changes in the Metal-Solution Potential Difference?.- 7.2.5d The Extreme Cases of Ideally Nonpolarizable and Polarizable Interfaces.- 7.2.5e The Development of a Scale of Relative Potential Differences.- 7.2.5f Can One Meaningfully Analyze an Electrode-Electrolyte Potential Difference?.- 7.2.5g A Thought Experiment Involving a Charged Electrode in Vacuum.- 7.2.5h The Test Charge Must Avoid Image Interactions with the Charged Electrode.- 7.2.5i The Outer Potential ? of a Material Phase in Vacuum.- 7.2.5j What is the Relevance of the Outer Potential to Double-Layer Studies?.- 7.2.5k Another Thought Experiment Involving an Uncharged, Dipole- Covered Phase.- 7.2.5l The Dipole Potential Difference M?S? across an Electrode- Electrolyte Interface.- 7.2.5m The Sum of the Potential Differences Due to Charges and Dipoles: The Absolute Electrode-Electrolyte (or Galvani) Potential Difference.- 7.2.5n The Outer, Surface, and Inner Potential Differences.- 7.2.5o An Apparent Contradiction: The Sum of the ??fis across a System of Interfaces Can and the ?? across One Interface Cannot Be Measured.- 7.2.5p What Deeper Understanding Has Been Hitherto Gained Regarding the Absolute Potential Difference Across an Electrified Interface?.- 7.2.6 The Accumulation and Depletion of Substances at an Interface.- 7.2.6a What Would Represent Complete Structural Information Regarding an Electrified Interface?.- 7.2.6b The Concept of Surface Excess.- 7.2.6c Does Knowledge of the Surface Excess Contribute to Knowledge of the Distribution of Species in the Interphase Region?.- 7.2.6d Is the Surface Excess Equivalent to the Amount Adsorbed?.- 7.2.6e Is the Surface Excess Measurable?.- 7.2.6f The Special Position of Mercury in Double-Layer Studies.- Further Reading.- 7.3 The Thermodynamics of Electrified Interfaces.- 7.3.1 The Measurement of Interfacial Tension as a Function of the Potential Difference across the Interface.- 7.3.2 Some Basic Facts about Electrocapillary Curves.- 7.3.3 A Digression on the Electrochemical Potential.- 7.3.3a Definition of Electrochemical Potential.- 7.3.3b Can the Chemical and Electrical Work Be Determined Separately?.- 7.3.3c A Criterion of Thermodynamic Equilibrium between Two Phases: Equality of Electrochemical Potentials.- 7.3.3d Nonpolarizable Interfaces and Thermodynamic Equilibrium.- 7.3.4 Some Thermodynamic Thoughts on Electrified Interfaces.- 7.3.5 Interfacial Tension Varies with Applied Potential: Determination of the Charge Density on the Electrode.- 7.3.6 Electrode Charge Varies with Applied Potential: Determination of the Electrical Capacitance of the Interface.- 7.3.7 The Potential at Which an Electrode Has a Zero Charge.- 7.3.8 Surface Tension Varies with Solution Composition: Determination of the Surface Excess.- 7.3.9 Reflections on Electrocapillary Thermodynamics.- 7.3.10 Retrospect and Prospect in the Study of Electrified Interfaces.- Further Reading.- 7.4 The Structure of Electrified Interfaces.- 7.4.1 The Parallel-Plate Condenser Model: The Helmholtz-Perrin Theory.- 7.4.2 The Double Layer in Trouble: Neither Perfect Parabolas nor Constant Capacities.- 7.4.3 The Ionic Cloud: The Gouy-Chapman Diffuse-Charge Model of the Double Layer.- 7.4.4 Ions under Thermal and Electric Forces near an Electrode.- 7.4.5 A Picture of the Potential Drop in the Diffuse Layer.- 7.4.6 An Experimental Test of the Gouy-Chapman Model: Potential Dependence of the Capacitance, but at What Cost?.- 7.4.7 Some Ions Stuck to the Electrode, Others Scattered in Thermal Disarray: The Stern Model.- 7.4.8 A Consequence of the Stern Picture: Two Potential Drops across an Electrified Interface.- 7.4.9 Another Consequence of the Stern Model: An Electrified Interface Is Equivalent to Two Capacitors in Series.- 7.4.10 The Relative Contributions of the Helmholtz-Perrin and Gouy-Chapman Capacities.- 7.4.11 Some Questions Regarding the Sticking of Ions to the Electrode.- 7.4.12 An Electrode Is Largely Covered with Adsorbed Water Molecules.- 7.4.13 Metal-Water Interactions.- 7.4.14 The Orientation of Water Molecules on Charged Electrodes.- 7.4.15 How Close Can Hydrated Ions Come to a Hydrated Electrode?.- 7.4.16 Is It Only Desolvated Ions which Contact-Adsorb on the Electrode?.- 7.4.17 The Free-Energy Change for Contact Adsorption.- 7.4.18 What Determines the Degree of Contact Adsorption?.- 7.4.19 How Is Contact Adsorption Measured?.- 7.4.20 Contact Adsorption, Specific Adsorption, or Superequivalent Adsorption.- 7.4.21 Contact Adsorption: Its Influence of the Capacity of the Interface.- 7.4.22 Looking Back to Look Forward.- 7.4.23 The Complete Capacity-Potential Curve.- 7.4.24 The Constant-Capacity Region.- 7.4.24a The So-Called “Double Layer” Is a Double Layer.- 7.4.24b The Dielectric Constant of the Water between the Metal and the Outer Heimholtz Plane.- 7.4.24c The Position of the Outer Heimholtz Plane and an Interpretation of the Constant Capacity.- 7.4.25 The Capacitance Hump.- 7.4.26 How Does the Population of Contact-Adsorbed Ions Change with Electrode Charge?.- 7.4.27 The Test of the Population Law for Contact-Adsorbed Ions.- 7.4.28 The Lateral-Repulsion Model for Contact Adsorption.- 7.4.29 Flip-Flop Water on Electrodes.- 7.4.30 Calculation of the Potential Difference Due to Water Dipoles.- 7.4.31 The Excess of Flipped Water Dipoles over Flopped Water Dipoles.- 7.4.32 The Contribution of Adsorbed Water Dipoles to the Capacity of the Interface.- Further Reading.- 7.5 The Competition between Water and Organic Molecules at the Electrified Interfaces.- 7.5.1 The Relevance of Organic Adsorption.- 7.5.2 The Forces Involved in Organic Adsorption.- 7.5.3 Does Organic Adsorption Depend on Electrode Charge?.- 7.5.4 The Examination of the Water Flip-Flop Model for Simple Cases of Organic Adsorption.- 7.5.5 At What Potential Does Maximum Organic Adsorption Occur?.- Further Reading.- 7.6 Electrified Interfaces at Metals Other than Mercury.- Further Reading.- 7.7 The Structure of the Semiconductor-Electrolyte Interface.- 7.7.1 How Is the Charge Distributed inside a Solid Electrode?.- 7.7.2 The Band Theory of Crystalline Solids.- 7.7.3 Conductors, Insulators, and Semiconductors.- 7.7.4 Some Analogies between Semiconductors and Electrolytic Solutions.- 7.7.5 The Diffuse-Charge Region inside an Intrinsic Semiconductor: The Garrett-Brattain Space Charge.- 7.7.6 The Differential Capacity Due to the Space Charge.- 7.7.7 Impurity Semiconductors, n Type and p Type.- 7.7.8 Surface States: The Semiconductor Analogue of Contact Adsorption.- 7.7.9 Semiconductor Electrochemistry: The Beginnings of the Electrochemistry of Nonmetallic Materials.- Further Reading.- 7.8 A Bird’s-Eye View of the Structure of Charged Interfaces.- 7.9 Double Layers between Phases Moving Relative to Each Other.- 7.9.1 The Phenomenology of Mobile Electrified Interfaces: Electrokinetic Properties.- 7.9.2 The Relative Motion of One of the Phases Constituting an Electrified Interface Produces a Streaming Current.- 7.9.3 A Potential Difference Applied Parallel to an Electrified Interface Produces an Electro-osmotic Motion of One of the Phases Relative to the Other.- 7.9.4 Electrophoresis: Moving Solid Particles in a Stationary Electrolyte.- Further Reading.- 7.10 Colloid Chemistry.- 7.10.1 Colloids: The Thickness of the Double Layer and the Bulk Dimensions Are of the Same Order.- 7.10.2 The Interaction of Double Layers and the Stability of Colloids.- 7.10.3 Sols and Gels.- Further Reading.- Appendix 7.1 Measurement of the Electrode-Solution Volta Potential Difference.- 8 Electrodics.- 8.1 Introduction.- 8.1.1 The Situation Thus Far.- 8.1.2 Charge Transfer: Its Chemical and Electrical Implications.- 8.1.3 Can an Isolated Electrode-Solution Interface Be Used as a Device?.- 8.1.4 Electrochemical Systems Can Be Used as Devices.- 8.1.5 An Electrochemical Device: The Substance Producer.- 8.1.6 Another Electrochemical Device: The Energy Producer.- 8.1.7 The Electrochemical Undevice: The Substance Destroyer and Energy Waster.- 8.1.8 Some Basic Questions.- 8.2 The Basic Electrodic Equation: The Butler-Volmer Equation.- 8.2.1 The Instant of Immersion of a Metal in an Electrolytic Solution.- 8.2.2 The Rate of Charge-Transfer Reactions under Zero Field: The Chemical Rate Constant.- 8.2.3 Some Consequences of Electron Transfer at an Interface.- 8.2.4 What Is the Rate of an Electron-Transfer Reaction under the Influence of an Electric Field?.- 8.2.5 The Two-Way Electron Traffic across the Interface.- 8.2.6 The Interface at Equilibrium: The Equilibrium Exchange-Current Density i0.- 8.2.7 The Interface Departs from Equilibrium: The Nonequilibrium Drift- Current Density i.- 8.2.8 The Current-Producing (or Current-Produced) Potential Difference: The Overpotential ?.- 8.2.9 The Basic Electrodic (Butler-Volmer) Equation: Some General and Special Cases.- 8.2.10 The High-Field Approximation: The Exponential i versus Law.- 8.2.11 The Low-Field Approximation: The Lineariversus ? Law.- 8.2.12 Nonpolarizable and Polarizable Interfaces.- 8.2.13 Zero Net Current and the Classical Law of Nernst.- 8.2.14 The Nernst Equation.- 8.2.15 The Nernst Equation: Its Sphere of Relevance.- 8.2.16 Looking Back.- Further Reading.- 8.3 The Butler-Volmer Equation: Further Details.- 8.3.1 The Need for a Careful Look at Some Quantities in the Butler-Volmer Equation.- 8.3.2 The Relation between Structure at the Electrified Interface and the Rate of Charge-transfer Reactions.- 8.3.3 The Interfacial Concentrations May Depend on Ionic Transport in the Electrolyte.- 8.3.4 What Is the Physical Meaning of the Symmetry factor ??.- 8.3.4a The Factor ? Is at the Center of Electrode Kinetics.- 8.3.4b A Preliminary to a Second Theory of ?: Potential-Energy- Distance Relations of Particles Undergoing Charge Transfer.- 8.3.4c A Simple Picture of the Symmetry Factor.- 8.3.4d Is the ? in the Butler-Volmer Equation Independent of Over- potential?.- 8.3.5 Summing-up of Further Details on the Butler-Volmer Equation.- Further Reading.- 8.4 The Current-Potential Laws at Other Types of Charged Interfaces.- 8.4.1 Semiconductor n-p Junctions.- 8.4.2 The Current across Biological Membranes.- 8.4.3 The Hot Emission of Electrons from a Metal into Vacuum.- 8.4.4 The Cold Emission of Electrons from a Metal into Vacuum.- Further Reading.- 8.5 The Quantum Aspects of Charge-Transfer Reactions at Electrode-Solution Interfaces.- 8.5.1 A Few Words on the Mechanics of Electrons.- 8.5.2 The Penetration of Electrons into Classically Forbidden Regions.- 8.5.3 The Probability of Electron Tunneling through Barriers.- 8.5.4 The Distribution of Electrons among the Energy Levels in a Metal.- 8.5.5 Under What Conditions Do Electrons Tunnel between the Electrode and Ions in Solution?.- 8.5.6 The Tunneling Condition and the Proton-Transfer Curve.- 8.5.7 Electron Tunneling and the De-electronation Reaction.- 8.5.8 A Perspective View of Charge-Transfer Reactions at an Electrode.- 8.5.9 The Symmetry Factor ?: A Better View.- 8.5.10 Quantifying the Charge-Transfer Picture.- 8.5.11 Some Desirable Refinements and Generalizations.- 8.5.12 Surveying the Progress.- Further Reading.- 8.6 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.- 9 Electrodics: More Fundamentals.- 9.1 Multistep Reactions.- 9.1.1 The Question of Multistep Reactions.- 9.1.2 Some Ideas on Queues, or Waiting Lines.- 9.1.3 The Overpotential ? Is Related to the Electron Queue at an Interface.- 9.1.4 A Near-Equilibrium Relation between the Current Density and Over- potential for a Multistep Reaction.- 9.1.5 The Concept of a Rate-Determining Step.- 9.1.6 Rate-Determining Steps and Energy Barriers for Multistep Reactions.- 9.1.7 How Many Times Must the Rate-Determining Step Take Place for the Overall Reaction to Occur Once? The Stoichiometric Number v.- 9.1.8 The Order of an Electrodic Reaction.- 9.1.9 Blockage of the Electrode Surface during Charge Transfer: The Surface-Coverage Factor.- Further Reading.- 9.2 The Transient Behavior of Interfaces.- 9.2.1 The Interface under Equilibrium, Transient, and Steady-State Conditions.- 9.2.2 How an Interface Is Stimulated to Show Time Variations.- 9.2.3 Some Ideas on the Understanding of Transients.- 9.2.4 Intermediates in Electrodic Reactions and Their Effects on Potential- Time Transients.- 9.2.5 Experimental Methods for the Determination of Partial Coverage, with Adsorbed Entities, of the Surface of Electrocatalysts.- 9.2.5a Radiotracer Method.- 9.2.5b Galvanostatic Transient Method.- 9.2.5c Potentiostatic Transients.- 9.2.5d The Potential-Sweep, or Potentiodynamic, Method.- Further Reading.- 9.3 Transport in the Electrolyte Effects Charge Transfer at the Interface.- 9.3.1 Ionics Looks after the Material Needs of the Interface.- 9.3.2 How the Transport Flux Is Linked to the Charge-Transfer Flux: The Flux-Equality Condition.- 9.3.3 Appropriations from the Theory of Heat Transfer.- 9.3.4 A Qualitative Study of How Diffusion Affects the Response of an Interface to a Constant Current.- 9.3.5 A Quantitative Treatment of How Diffusion to an Electrode Affects the Response with Time of an Interface to a Constant Current.- 9.3.6 The Concept of Transition Time.- 9.3.7 Convection Can Maintain Steady Interfacial Concentrations.- 9.3.8 The Origin of Concentration Overpotential.- 9.3.9 The Diffusion Layer.- 9.3.10 The Limiting Current Density and Its Practical Importance.- 9.3.10a Polarography: The Dropping-Mercury Electrode.- 9.3.10b The Rotating-Disc Electrode.- 9.3.11 The Steady-State Current-Potential Relation under Conditions of Transport Control.- 9.3.12 Transport-Controlled De-electronation Reactions.- 9.3.13 What Is the Effect of Electrical Migration on the Limiting Diffusion- Current Density?.- 9.3.14 Some Summarizing Remarks on the Transport Aspects of Electrodics.- Further Reading.- 9.4 Determining the Stepwise Mechanism of an Electrodic Reaction.- 9.4.1 How One Tries to Determine the Reaction Mechanism.- 9.4.2 Which Is the Rate-Determining Step in the Iron Deposition and Dissolution Reaction?.- 9.4.3 The Transfer Coefficient a and Reaction Mechanisms.- 9.4.4 Summarizing Remarks Concerning Mechanistic Studies.- Further Reading.- 9.5 More on Mechanism Determination.- 9.5.1 Why Review Mechanism Determination?.- 9.5.2 What Is Mechanism Determination?.- 9.5.3 Stages in the Elucidation of a Reaction Mechanism.- 9.5.4 The Etucidation of the Overall Reaction, the Entities in Solution, and the Surface Coverage.- 9.5.5 Some Techniques for Mechanism Determination.- 9.5.5a The Determination of Reaction Order.- 9.5.5b The Determination of the Transfer Coefficients.- 9.5.5c The Determination o...