Page 26 - MODERN ELECTROCHEMISTRY

CONTENTS xxv

4.2.1. The Driving Force for Diffusion ...................... 363
4.2.2. The “Deduction” of an Empirical Law: Fick’s First Law of Steady-State
Diffusion ....................................... 367
4.2.3. The Diffusion Coefficient D ........................ 370
4.2.4. Ionic Movements: A Case of the Random Walk .............. 372
4.2.5. The Mean Square Distance Traveled in a Time t by a Random-Walking
Particle ................................... 374
4.2.6. Random-Walking Ions and Diffusion: The Einstein–Smoluchowski
Equation ................................... 378
4.2.7. The Gross View of Nonsteady-State Diffusion .............. 380
4.2.8. An Often-Used Device for Solving Electrochemical Diffusion Problems:
The Laplace Transformation ........................ 382
4.2.9. Laplace Transformation Converts the Partial Differential Equation into a
Total Differential Equation ......................... 385
4.2.10. Initial and Boundary Conditions for the Diffusion Process Stimulated by a
Constant Current (or Flux) ......................... 386
4.2.11. Concentration Response to a Constant Flux Switched On at t = 0 . . . . . 390
4.2.12. How the Solution of the Constant-Flux Diffusion Problem Leads to the
Solution of Other Problems ......................... 396
4.2.13. Diffusion Resulting from an Instantaneous Current Pulse ......... 401
4.2.14. Fraction of Ions Traveling the Mean Square Distance in the Einstein-
Smoluchowski Equation .......................... 405
4.2.15. How Can the Diffusion Coefficient Be Related to Molecular Quantities? 411
4.2.16. The Mean Jump Distance l, a Structural Question ............. 412
4.2.17. The Jump Frequency, a Rate-Process Question .............. 413
4.2.18. The Rate-Process Expression for the Diffusion Coefficient ........ 414
4.2.19. Ions and Autocorrelation Functions .................... 415
4.2.20. Diffusion: An Overall View ........................ 418
Further Reading .................................. 420

4.3. Ionic Drift under an Electric Field: Conduction ........... 421
4.3.1. Creation of an Electric Field in an Electrolyte ............... 421
4.3.2. How Do Ions Respond to the Electric Field? ................ 424
4.3.3. The Tendency for a Conflict between Electroneutrality and Conduction . 426
4.3.4. Resolution of the Electroneutrality-versus-Conduction Dilemma: Electron-
Transfer Reactions ............................. 427
4.3.5. Quantitative Link between Electron Flow in the Electrodes and Ion Flow in
the Electrolyte: Faraday’s Law ....................... 428
4.3.6. The Proportionality Constant Relating Electric Field and Current Density:
Specific Conductivity ............................ 429
4.3.7. Molar Conductivity and Equivalent Conductivity . ............ 432
4.3.8. Equivalent Conductivity Varies with Concentration ............ 434
4.3.9. How Equivalent Conductivity Changes with Concentration: Kohlrausch’s
Law ..................................... 438
4.3.10. Vectorial Character of Current: Kohlrausch’s Law of the Independent
Migration of Ions .............................. 439