Electrochemical Systems

Preface To The Fourth Edition xv Preface To The Third Edition xvii Preface To The Second Edition xix Preface To The First Edition xxi 1 Introduction 1 1.1 Definitions 2 1.2 Thermodynamics and Potential 3 1.3 Kinetics and Rates of Reaction 6 1.4 Transport 8 1.5 Concentration Overpotential and the Diffusion Potential 15 1.6 Overall Cell Potential 18 Problems 20 Notation 21 Part A Thermodynamics of Electrochemical Cells 23 2 Thermodynamics In Terms of Electrochemical Potentials 25 2.1 Phase Equilibrium 25 2.2 Chemical Potential and Electrochemical Potential 27 2.3 Definition of Some Thermodynamic Functions 30 2.4 Cell with Solution of Uniform Concentration 36 2.5 Transport Processes in Junction Regions 39 2.6 Cell with a Single Electrolyte of Varying Concentration 40 2.7 Cell with Two Electrolytes, One of Nearly Uniform Concentration 44 2.8 Cell with Two Electrolytes, Both of Varying Concentration 47 2.9 Lithium–Lithium Cell With Two Polymer Electrolytes 49 2.10 Standard Cell Potential and Activity Coefficients 50 2.11 Pressure Dependence of Activity Coefficients 58 2.12 Temperature Dependence of Cell Potentials 59 Problems 61 Notation 68 References 70 3 The Electric Potential 71 3.1 The Electrostatic Potential 71 3.2 Intermolecular Forces 74 3.3 Outer and Inner Potentials 76 3.4 Potentials of Reference Electrodes 77 3.5 The Electric Potential in Thermodynamics 78 Notation 79 References 80 4 Activity Coefficients 81 4.1 Ionic Distributions in Dilute Solutions 81 4.2 Electrical Contribution to the Free Energy 84 4.3 Shortcomings of the Debye–Hückel Model 87 4.4 Binary Solutions 89 4.5 Multicomponent Solutions 92 4.6 Measurement of Activity Coefficients 94 4.7 Weak Electrolytes 96 Problems 99 Notation 103 References 104 5 Reference Electrodes 107 5.1 Criteria for Reference Electrodes 107 5.2 Experimental Factors Affecting Selection of Reference Electrodes 109 5.3 The Hydrogen Electrode 110 5.4 The Calomel Electrode and Other Mercury–Mercurous Salt Electrodes 112 5.5 The Mercury–Mercuric Oxide Electrode 114 5.6 Silver–Silver Halide Electrodes 114 5.7 Potentials Relative to a Given Reference Electrode 116 Notation 119 References 120 6 Potentials of Cells With Junctions 121 6.1 Nernst Equation 121 6.2 Types of Liquid Junctions 122 6.3 Formulas for Liquid-Junction Potentials 123 6.4 Determination of Concentration Profiles 124 6.5 Numerical Results 124 6.6 Cells with Liquid Junction 128 6.7 Error in the Nernst Equation 129 6.8 Potentials Across Membranes 131 6.9 Charged Membranes Immersed in an Electrolytic Solution 131 Problems 135 Notation 138 References 138 Part B Electrode Kinetics and Other Interfacial Phenomena 141 7 Structure of The Electric Double Layer 143 7.1 Qualitative Description of Double Layers 143 7.2 Gibbs Adsorption Isotherm 148 7.3 The Lippmann Equation 151 7.4 The Diffuse Part of the Double Layer 155 7.5 Capacity of the Double Layer in the Absence of Specific Adsorption 160 7.6 Specific Adsorption at an Electrode–Solution Interface 161 Problems 161 Notation 164 References 165 8 Electrode Kinetics 167 8.1 Heterogeneous Electrode Reactions 167 8.2 Dependence of Current Density on Surface Overpotential 169 8.3 Models for Electrode Kinetics 170 8.4 Effect of Double-Layer Structure 185 8.5 The Oxygen Electrode 187 8.6 Methods of Measurement 192 8.7 Simultaneous Reactions 193 Problems 195 Notation 199 References 200 9 Electrokinetic Phenomena 203 9.1 Discontinuous Velocity at an Interface 203 9.2 Electro-Osmosis and the Streaming Potential 205 9.3 Electrophoresis 213 9.4 Sedimentation Potential 215 Problems 216 Notation 218 References 219 10 Electrocapillary Phenomena 221 10.1 Dynamics of Interfaces 221 10.2 Electrocapillary Motion of Mercury Drops 222 10.3 Sedimentation Potentials for Falling Mercury Drops 224 Notation 224 References 225 Part C Transport Processes In Electrolytic Solutions 227 11 Infinitely Dilute Solutions 229 11.1 Transport Laws 229 11.2 Conductivity, Diffusion Potentials, and Transference Numbers 232 11.3 Conservation of Charge 233 11.4 The Binary Electrolyte 233 11.5 Supporting Electrolyte 236 11.6 Multicomponent Diffusion by Elimination of the Electric Field 237 11.7 Mobilities and Diffusion Coefficients 238 11.8 Electroneutrality and Laplace’S Equation 240 11.9 Moderately Dilute Solutions 242 Problems 244 Notation 247 References 247 12 Concentrated Solutions 249 12.1 Transport Laws 249 12.2 The Binary Electrolyte 251 12.3 Reference Velocities 252 12.4 The Potential 253 12.5 Connection with Dilute-Solution Theory 256 12.6 Example Calculation Using Concentrated Solution Theory 257 12.7 Multicomponent Transport 259 12.8 Liquid-Junction Potentials 262 Problems 263 Notation 264 References 266 13 Thermal Effects 267 13.1 Thermal Diffusion 268 13.2 Heat Generation, Conservation, and Transfer 270 13.3 Heat Generation at an Interface 272 13.4 Thermogalvanic Cells 274 13.5 Concluding Statements 276 Problems 277 Notation 279 References 280 14 Transport Properties 283 14.1 Infinitely Dilute Solutions 283 14.2 Solutions of a Single Salt 283 14.3 Mixtures of Polymers and Salts 286 14.4 Types of Transport Properties and Their Number 295 14.5 Integral Diffusion Coefficients for Mass Transfer 296 Problem 298 Notation 298 References 299 15 Fluid Mechanics 301 15.1 Mass and Momentum Balances 301 15.2 Stress in a Newtonian Fluid 302 15.3 Boundary Conditions 303 15.4 Fluid Flow to a Rotating Disk 304 15.5 Magnitude of Electrical Forces 307 15.6 Turbulent Flow 310 15.7 Mass Transfer in Turbulent Flow 314 15.8 Dissipation Theorem for Turbulent Pipe Flow 316 Problem 318 Notation 319 References 321 Part D Current Distribution and Mass Transfer In Electrochemical Systems 323 16 Fundamental Equations 327 16.1 Transport in Dilute Solutions 327 16.2 Electrode Kinetics 328 Notation 329 17 Convective-Transport Problems 331 17.1 Simplifications for Convective Transport 331 17.2 The Rotating Disk 332 17.3 The Graetz Problem 335 17.4 The Annulus 340 17.5 Two-Dimensional Diffusion Layers in Laminar Forced Convection 344 17.6 Axisymmetric Diffusion Layers in Laminar Forced Convection 345 17.7 A Flat Plate in a Free Stream 346 17.8 Rotating Cylinders 347 17.9 Growing Mercury Drops 349 17.10 Free Convection 349 17.11 Combined Free and Forced Convection 351 17.12 Limitations of Surface Reactions 352 17.13 Binary and Concentrated Solutions 353 Problems 354 Notation 359 References 360 18 Applications of Potential Theory 365 18.1 Simplifications For Potential-Theory Problems 366 18.2 Primary Current Distribution 367 18.3 Secondary Current Distribution 370 18.4 Numerical Solution by Finite Differences 374 18.5 Principles of Cathodic Protection 375 Problems 389 Notation 396 References 397 19 Effect of Migration On Limiting Currents 399 19.1 Analysis 400 19.2 Correction Factor for Limiting Currents 402 19.3 Concentration Variation of Supporting Electrolyte 404 19.4 Role of Bisulfate Ions 409 19.5 Paradoxes with Supporting Electrolyte 413 19.6 Limiting Currents for Free Convection 417 Problems 423 Notation 424 References 426 20 Concentration Overpotential 427 20.1 Definition 427 20.2 Binary Electrolyte 429 20.3 Supporting Electrolyte 430 20.4 Calculated Values 430 Problems 431 Notation 432 References 433 21 Currents Below The Limiting Current 435 21.1 The Bulk Medium 436 21.2 The Diffusion Layers 437 21.3 Boundary Conditions and Method of Solution 438 21.4 Results for the Rotating Disk 440 Problems 444 Notation 446 References 447 22 Porous Electrodes 449 22.1 Macroscopic Description of Porous Electrodes 450 22.2 Nonuniform Reaction Rates 457 22.3 Mass Transfer 462 22.4 Battery Simulation 463 22.5 Double-Layer Charging and Adsorption 477 22.6 Flow-Through Electrochemical Reactors 478 Problems 482 Notation 484 References 486 23 Semiconductor Electrodes 489 23.1 Nature of Semiconductors 490 23.2 Electric Capacitance at the Semiconductor–Solution Interface 499 23.3 Liquid-Junction Solar Cell 502 23.4 Generalized Interfacial Kinetics 506 23.5 Additional Aspects 509 Problems 513 Notation 514 References 516 24 Impedance 517 24.1 Frequency Dispersion at a Disk Electrode 519 24.2 Modulated Flow With a Disk Electrode 522 24.3 Porous Electrodes for Batteries 526 24.4 Kramers–Kronig Relation 528 Problems 530 Notation 531 References 532 Appendix A Partial Molar Volumes 535 Appendix B Vectors and Tensors 537 Appendix C Numerical Solution of Coupled, Ordinary Differential Equations 543 Index 567