Analytical and physical electrochemistry

Cover Page......Page 1
Title: ANALYTICAL AND PHYSICAL ELECTROCHEMISTRY......Page 3
ISBN 0824753577......Page 4
PREFACE......Page 6
PREFACE TO THE ORIGINAL FRENCH VERSION: “ELECTROCHIMIE PHYSIQUE ET ANALYTIQUE”......Page 7
TABLE OF CONTENTS......Page 9
Thermodynamic definition......Page 12
Chemical potential in the gas phase......Page 14
Chemical potential in the liquid phase......Page 15
Mole fraction scale......Page 16
Molarity scale......Page 18
Application of chemical potentials......Page 19
The Gauss theorem......Page 20
Coulomb’s theorem......Page 21
Outer potential and the Volta potential difference......Page 22
Polarisation of matter......Page 23
Relative permittivity......Page 24
Electric displacement vector......Page 26
Surface of polar liquids......Page 27
Adsorbed ionised surfactants......Page 28
Metal surfaces......Page 29
1.1.5 The Galvani potential difference......Page 30
1.1.6 Electrochemical potential......Page 31
1.1.7 Chemical potential of a salt......Page 33
1.2.1 Band structure......Page 34
1.2.2 The Fermi-Dirac distribution......Page 36
1.2.3 Work function......Page 37
1.2.4 Contact between two metals......Page 38
1.2.5 The Kelvin probe......Page 39
1.2.6 Electrochemical potential of the electron in solution......Page 41
2.1.1 Galvani potential difference between an electrode and a solution......Page 44
Empirical approach......Page 46
A posteriori derivation of the Nernst equation......Page 47
Thermodynamic approach......Page 48
2.1.3 Standard redox potential......Page 49
Standard cell potential......Page 52
Measuring directly with a standard hydrogen electrode......Page 53
Measuring directly with a reference electrode......Page 55
Spectroelectrochemical measurements......Page 56
2.1.5 Absolute redox potential......Page 59
2.2.1 Voltaic cells......Page 61
2.2.2 Accumulators......Page 63
2.2.3 Fuel cells......Page 64
2.3 POURBAIX DIAGRAMS......Page 65
2.4.1 The Nernst equation for the distribution of ions between two phases......Page 68
2.4.2 Distribution potential......Page 69
2.4.4 Distribution diagrams......Page 71
2.4.5 Redox equilibria at the liquid | liquid interface......Page 73
Calomel electrode......Page 74
Silver | silver chloride electrode......Page 77
2.5.2 Potentiometric Titration......Page 78
Thermodynamic approach......Page 81
pH electrode......Page 84
The Nikolsky equation......Page 87
2.6.1 Structure......Page 89
2.6.2 Donnan potential......Page 90
APPENDIX : THE RESPIRATORY CHAIN......Page 93
3.1.1 Radial distribution function......Page 94
3.1.2 Water......Page 95
3.2 THERMODYNAMIC ASPECTS OF SOLVATION......Page 96
The Born-Haber cycle for NaCl(s)......Page 97
The Born-Haber cycle for HCl(aq)......Page 98
Electrochemical measurement of the standard formation enthalpies......Page 100
3.2.2 Standard enthalpies of ionic solvation......Page 102
3.2.3 The Born model......Page 104
3.2.5 Electrostatic Gibbs energy......Page 109
3.3.2 Solvation number......Page 111
3.3.3 Potential of a dipole......Page 113
3.3.5 Average ion-dipole interaction energy......Page 114
3.4.1 Electrostatic interaction energy and the activity coefficient......Page 116
3.4.2 The Debye-Hückel theory (1923)......Page 117
Calculation of the electric potential phi(r)......Page 120
Ionic atmosphere......Page 122
Calculation of the ionic activity coefficient......Page 124
Calculation of the average ionic activity coefficient of a salt......Page 126
Average ionic activity coefficient of a concentrated salt......Page 128
3.4.3 Electrochemical measurement of activity coefficients......Page 131
3.4.4 Kinetics of reactions between ions......Page 132
3.5.1 The Bjerrum theory (1923)......Page 134
3.5.2 Association constant......Page 136
3.5.3 The Fuoss theory......Page 138
3.6.1 The Monte-Carlo method......Page 140
3.6.2 Molecular dynamics......Page 141
APPENDIX......Page 142
4.1.1 Gradient of electrochemical potential......Page 144
4.1.2 Fick’s law for diffusion......Page 146
4.1.3 Ohm’s law for migration......Page 147
4.2.1 Limiting molar conductivity......Page 149
4.2.2 Measurement of conductivities......Page 151
4.2.3 Measurement of acidity constants......Page 154
4.3.2 Thermodynamic approach......Page 156
4.3.3 Electrophoretic effect......Page 157
4.3.4 Relaxation effect of the ionic atmosphere......Page 159
4.4.1 Electric field created by a dipole......Page 163
4.4.2 Relaxation of the dielectrics......Page 164
4.4.3 Dielectric friction coefficient......Page 167
4.5.2 Diffusion potential......Page 171
4.5.3 The Planck-Henderson equation......Page 173
4.6.1 Random motion in one dimension......Page 174
4.6.2 One-dimensional random motion with an absorbent wall......Page 176
Langevin’s equation......Page 178
Einstein’s diffusion equation in one dimension......Page 180
Tensor constraint for a viscous fluid......Page 182
Flow friction of a liquid around a sphere......Page 184
5.1.1 Surface Gibbs energy......Page 188
5.1.2 How is the surface Gibbs energy density linked to the mechanical properties of the interface?......Page 190
5.2.1 The Gibbs adsorption equation......Page 191
5.2.2 Surface excess concentration......Page 193
5.3.1 Mercury | electrolyte interface......Page 195
5.3.2 Electrolyte | electrolyte interface......Page 202
5.4.1 Metal | electrolyte interface......Page 205
The Gouy–Chapman theory......Page 206
Influence of the metal and the inner layer......Page 211
Potential of zero charge......Page 214
The Gouy–Chapman theory......Page 216
Intrinsic and extrinsic semiconductors......Page 219
Junction between a p-type semiconductor and a n-type semiconductor......Page 220
Accumulation, depletion and inversion layers......Page 224
5.5.1 Monocrystal | electrolyte interface......Page 226
5.5.2 Electrolyte | electrolyte interface......Page 230
6.1.1 Definitions......Page 232
6.1.2 Electro-osmosis......Page 233
6.1.3 Electrophoresis of charged colloids......Page 236
6.1.4 Streaming potential......Page 237
6.1.5 Sedimentation potential......Page 239
6.2.1 Capillary electro-osmotic flow......Page 240
6.2.2 Zone electrophoresis in a capillary......Page 242
6.2.3 Micellar electrokinetic capillary chromatography......Page 244
6.2.5 Capillary separation techniques not using electro-osmosis......Page 245
Electrokinetic injection......Page 246
Electrokinetic sample loop......Page 247
Columns and the effect of temperature......Page 248
Detection methods......Page 249
6.3.1 Moving boundary......Page 250
6.3.2 Isotachophoresis......Page 253
6.3.3 Zone electrophoresis......Page 254
Protein separation......Page 255
Separation of nucleic acids and the sequencing of DNA......Page 256
Movement of an ideal chain......Page 257
Reptation......Page 258
Reptation in an electric field......Page 259
Biased reptation in an electric field......Page 260
6.4.3 Isoelectric focusing......Page 263
Titration of a protein in a pH gradient gel......Page 264
‘Off-gel’ isoelectric separation......Page 265
6.5.1 Ion exchange chromatography......Page 267
6.5.2 Chromatography by ionic exclusion......Page 269
6.5.3 Ion pair chromatography......Page 270
6.5.4 Experimental methods......Page 271
6.6.1 Electrodialysis......Page 272
6.6.2 Donnan dialysis......Page 273
6.6.3 Ion exchange dialysis......Page 274
7.1 ELECTROCHEMICAL KINETICS......Page 276
7.2.1 Standard case of an ideal solution......Page 279
7.2.2 General case......Page 282
7.3.1 Diffusion layer......Page 286
7.3.2 Limiting diffusion current......Page 288
7.3.3 Current-potential curve......Page 289
7.4.1 Rotating disc electrode......Page 291
7.4.2 Microelectrodes......Page 293
Microhemispheres......Page 294
Recessed microdiscs......Page 295
7.4.3 Band electrode in a laminar flow......Page 296
7.4.4 Membrane-covered electrode......Page 297
7.4.5 Liquid | liquid micro-interfaces......Page 298
7.5.1 Current-potential curve......Page 299
7.5.3 Comments on the experimental measurement of rate constants......Page 303
7.6 IRREVERSIBLE SYSTEMS: CURRENT LIMITED BY KINETICS AND DIFFUSION......Page 305
7.7 QUASI-REVERSIBLE SYSTEMS: CURRENT LIMITED BY DIFFUSION, MIGRATION AND KINETICS......Page 306
7.8.1 Ohmic drop at a planar electrode......Page 307
7.8.2 Ohmic drop at a hemispherical electrode......Page 309
7.8.3 Compensating for the ohmic drop......Page 310
8.1.1 Chronoamperometry with semi-infinite linear diffusion for a complete interfacial oxidation......Page 312
8.1.2 Chronoamperometry with spherical diffusion for a complete interfacial oxidation......Page 316
8.1.3 Chronocoulometry with semi-infinite linear diffusion for complete interfacial oxidation......Page 318
8.1.4 Chronoamperometry with semi-infinite linear diffusion for a partial interfacial oxidation......Page 319
8.2.1 Dropping mercury electrode......Page 322
8.2.2 Staircase polarography with sampling (TAST Polarography)......Page 323
8.2.3 Normal pulse polarography......Page 325
8.2.4 Differential pulse polarography......Page 326
8.3.1 Superposition principle......Page 330
8.3.2 Constant amplitude alternate pulse voltammetry......Page 334
8.3.3 Staircase voltammetry......Page 337
8.3.4 Square Wave Voltammetry......Page 340
8.4.1 Anodic stripping voltammetry......Page 342
8.4.2 Cathodic stripping voltammetry......Page 343
8.5.1 Chronoamperometry in finite linear diffusion for complete interfacial oxidation......Page 344
8.5.2 Electrode covered with a thin membrane......Page 346
8.6 AMPEROMETRIC DETECTORS FOR CHROMATOGRAPHY......Page 348
9.1.1 AC response......Page 350
9.1.2 Linear Systems......Page 351
9.1.3 Impedance and admittance......Page 352
9.1.4 The Nyquist diagram......Page 353
9.2.1 Resistor......Page 354
9.2.2 Capacitor......Page 355
9.2.3 Resistor – capacitor in series......Page 356
9.2.4 Resistor – capacitor in parallel......Page 358
9.2.5 Resistor in series with a parallel resistor-capacitor circuit......Page 360
9.3.1 Impedance of a redox reaction......Page 362
9.3.2 Charge transfer impedance......Page 363
9.3.3 Concentration impedance......Page 364
9.3.4 Warburg impedance......Page 367
9.3.5 The Randles-Ershler circuit......Page 369
9.3.6 Concentration impedance for a diffusion layer of a fixed thickness......Page 371
9.3.7 Concentration impedance for diffusion in a thin layer cell......Page 376
9.4.1 Voltammetry using a superimposed sinusoidal potential difference......Page 379
9.4.2 Potential-modulated reflectance (fluorescence) spectroscopy......Page 382
SYMBOLS......Page 0
10.1.1 Integration method......Page 386
10.1.2 Convoluted current......Page 392
10.2.1 Electrochemically quasi-reversible reactions......Page 393
10.2.3 Electrochemically irreversible reactions......Page 395
10.3.1 ECr reactions......Page 396
10.3.2 ECi reactions......Page 399
10.3.3 ECcat reactions......Page 402
10.4 ELECTRON TRANSFER AT LIQUID | LIQUID INTERFACES......Page 407
10.5 ASSISTED ION TRANSFER AT LIQUID | LIQUID INTERFACES......Page 410
10.6.1 Thin layer cell......Page 413
10.7 HEMI-SPHERICAL DIFFUSION......Page 415
10.8 VOLTABSORPTOMETRY......Page 418
10.9 SEMI-INTEGRATION......Page 419
1 COORDINATE SYSTEMS......Page 422
2 CIRCULATION OF THE FIELD VECTOR......Page 423
3 THE VECTOR GRADIENT......Page 424
5 THE GREEN-OSTROGRADSKI THEOREM......Page 425
ANNEX B: WORK FUNCTIONS AND STANDARD REDOX POTENTIALS......Page 428
SYMBOLS......Page 436
INDEX......Page 440
Back Page......Page 443