Electrochemistry

 

Mục Lục

 

1.1 – Introduction ……………………………………………………………………………………………………………….. 1
1.1.1 – Etymology……………………………………………………………………………………………………………. 1
1.1.2 – The historical development of ideas……………………………………………………………….. 2
1.1.3 – Socioeconimic importance……………………………………………………………………………….. 4
1.2 – Oxidation-reduction………………………………………………………………………………………………….. 7
1.2.1 – The modern notion of oxidation-reduction…………………………………………………… 8
The origins of the VOLTA battery …………………………………………………………………… 10
1.2.2 – Oxidation number ……………………………………………………………………………………………… 12
1.2.3 – How to write a redox half-reaction………………………………………………………………….. 14
1.3 – The notion of current………………………………………………………………………………………………… 17
1.3.1 – Macroscopic quantities defining the current ………………………………………………… 17
1.3.1.1 – Current density……………………………………………………………………………………………. 17
1.3.1.2 – Current………………………………………………………………………………………………………….. 17
1.3.1.3 – Electroneutrality and conservative current…………………………………………….. 18
1.3.2 – Conducting media……………………………………………………………………………………………… 19
1.3.2.1 – Different charge carriers ……………………………………………………………………………. 19
1.3.2.2 – Different classes of conductors ………………………………………………………………… 19
On electrodes ………………………………………………………………………………………………….. 21
1.3.3 – Electrodes and interfaces………………………………………………………………………………….. 22
1.4 – Description and operation of an electrochemical chain …………………………………….. 25
1.4.1 – General features …………………………………………………………………………………………………. 25
1.4.1.1 – Electrochimical cell and chain…………………………………………………………………… 25
1.4.1.2 – The polarity of the electrodes …………………………………………………………………… 26
1.4.1.3 – Sign convention for the current through an interface………………………….. 27
1.4.2 – Forced current flow: electrolyser mode …………………………………………………………. 30
Sign convention for current ………………………………………………………………………….. 31
1.4.3 – Spontaneous current flow: power source mode…………………………………………… 33
1.4.4 – Spontaneous or forced current flow……………………………………………………………….. 34
1.5 – Notions of potential – voltage – polarisation …………………………………………………………. 34
1.5.1 – Voltages and potentials in an electrochemical cell ………………………………………. 34
1.5.1.1 – Standard hydrogen electrode…………………………………………………………………… 35
1.5.1.2 – Reference electrodes………………………………………………………………………………….. 35
1.5.1.3 – The polarity of the electrodes …………………………………………………………………… 39
1.5.2 – Polarisations and overpotentials in an electrochemical cell ………………………. 39

XI

XII ELECTROCHEMISTRY – THE BASICS, WITH EXAMPLES
1.6 – Experimentation in electrochemistry …………………………………………………………………….. 40
1.6.1 – Measurement devices ……………………………………………………………………………………….. 40
1.6.2 – Power supply and control devices…………………………………………………………………… 41
1.6.3 – Different types of electric control ……………………………………………………………………. 43
1.6.4 – Steady state…………………………………………………………………………………………………………. 44
Electrochemical devices ………………………………………………………………………………… 45
1.6.5 – Main electrochemical methods ……………………………………………………………………….. 46
Questions on chapiter 1…………………………………………………………………………………………………….. 48
2 – Simplified description of electrochemical systems………………………………….. 51
2.1 – Characteristics of systems in thermodynamic equilibrium ………………………………… 51
2.1.1 – Distribution of the electric potentials at equilibrium …………………………………… 51
2.1.2 – Potentiometry at equilibrium…………………………………………………………………………… 53
2.1.2.1 – NERNST’s law………………………………………………………………………………………………….. 53
Industrial production of aluminium in France……………………………………………. 56
2.1.2.2 – Apparent standard potential…………………………………………………………………….. 58
2.1.2.3 – The water redox couples……………………………………………………………………………. 59
2.2 – Characteristics of systems with a current flowing ……………………………………………….. 61
2.2.1 – Phenomena occurring when a current is flowing…………………………………………. 61
2.2.1.1 – Volume conduction ……………………………………………………………………………………. 61
2.2.1.2 – Phenomena occurring at interfaces ………………………………………………………… 64
2.2.2 – The faradic phenomena ……………………………………………………………………………………. 68
2.2.2.1 – Faradic current and capacitive current……………………………………………………. 68
2.2.2.2 – FARADAY’s law……………………………………………………………………………………………….. 68
2.2.2.3 – Faradic yield…………………………………………………………………………………………………. 69
The first electric vehicles ……………………………………………………………………………….. 71
2.2.3 – Cell voltage distribution ……………………………………………………………………………………. 72
2.2.4 – Ohmic drop in a conducting medium…………………………………………………………….. 75
2.2.4.1 – OHM’s law and the ohmic drop …………………………………………………………………. 75
2.2.4.2 – Movement direction via migration ………………………………………………………….. 77
2.2.4.3 – Molar conductivities and transport numbers ………………………………………… 80
2.2.4.4 – The supporting electrolyte………………………………………………………………………… 81
2.3 – The shape of the current-potential curves…………………………………………………………….. 83
2.3.1 – General characteristics………………………………………………………………………………………. 84
2.3.1.1 – Polarisation sign………………………………………………………………………………………….. 84
2.3.1.2 – Steady-state curves…………………………………………………………………………………….. 86
2.3.2 – Role of mass transport kinetics ………………………………………………………………………… 87
2.3.2.1 – Limiting current…………………………………………………………………………………………… 87
2.3.2.2 – Half-wave potential ……………………………………………………………………………………. 89
Regulating of fuel engines…………………………………………………………………………….. 91
2.3.3 – Role of redox reaction kinetics…………………………………………………………………………. 92
2.3.4 – Additivity of faradic currents or current densities ………………………………………… 94
2.3.5 – Water redox couples………………………………………………………………………………………….. 95
Energy storage: the Li-Metal-Polymer (LMP) batteries……………………………… 99
2.3.6 – Electrochemical window …………………………………………………………………………………… 100

CONTENTS XIII
2.4 – Predicting reactions ………………………………………………………………………………………………….. 102
2.4.1 – Spontaneous evolution of a system at open circuit……………………………………… 102
2.4.2 – Working points of a whole electrochemical system…………………………………….. 105
2.4.3 – Predicting reactions in electrolyser mode ……………………………………………………… 108
2.4.4 – Predicting reactions in power source mode ………………………………………………….. 110
2.4.5 – Various working conditions of an electrochemical system…………………………. 112
Questions on chapiter 2…………………………………………………………………………………………………….. 115
3 – Thermodynamic features…………………………………………………………………………………….. 119
3.1 – Concepts of potential ……………………………………………………………………………………………….. 119
3.1.1 – Electric potential ………………………………………………………………………………………………… 120
3.1.1.1 – Electric potential and electroneutrality…………………………………………………… 120
3.1.1.2 – VOLTA and GALVANI potentials ……………………………………………………………………. 121
3.1.2 – Chemical and electrochemical potentials………………………………………………………. 122
3.1.2.1 – Chemical potential……………………………………………………………………………………… 122
3.1.2.2 – Electrochemical potential………………………………………………………………………….. 124
3.1.2.3 – Convention for thermodynamic data tables ………………………………………….. 125
Fuel cells…………………………………………………………………………………………………………… 126
3.2 – Thermodynamic equilibrium in a monophasic system ………………………………………. 128
3.2.1 – Electrolytic solution……………………………………………………………………………………………. 129
3.2.1.1 – Mean activity and mean activity coefficient…………………………………………… 129
3.2.1.2 – Ionic strength………………………………………………………………………………………………. 130
3.2.1.3 – DEBYE-HÜCKEL’s model…………………………………………………………………………………. 132
3.2.2 – Metallic electrode ………………………………………………………………………………………………. 135
3.2.2.1 – Electrochemical potential………………………………………………………………………….. 135
3.2.2.2 – FERMI’s energy………………………………………………………………………………………………. 136
3.2.2.3 – Electron work function ………………………………………………………………………………. 136
3.3 – Thermodynamic equilibrium at an interface ………………………………………………………… 137
3.3.1 – Thermodynamic equilibrium at a non-reactive interface ……………………………. 137
3.3.2 – Thermodynamic equilibrium at a reactive interface…………………………………….. 139
Electrochemistry and neurobiology…………………………………………………………….. 142
3.3.3 – Thermodynamic equilibrium at a reactive interface
involving a single reaction between neutral species……………………………………. 144
3.3.4 – Thermodynamic equilibrium at a reactive interface
involving a single reaction between charged species…………………………………. 145
3.3.4.1 – Junction with the exchange of a single charged species …………………….. 145
3.3.4.2 – Reactive electrochemical interface with a single reaction …………………… 148
3.3.5 – Multi-reactive junction or interface…………………………………………………………………. 149
3.4 – Electrochemical systems in equilibrium ………………………………………………………………… 151
3.4.1 – Electrochemical cells with no ionic junction………………………………………………….. 151
3.4.1.1 – Thermodynamic reaction quantities ……………………………………………………….. 152
Corrosion of reinforced concrete …………………………………………………………………. 154
3.4.1.2 – NERNST’s law………………………………………………………………………………………………….. 156
3.4.1.3 – Considering multiple chemical equilibria……………………………………………….. 158

XIV ELECTROCHEMISTRY – THE BASICS, WITH EXAMPLES
3.4.1.4 – Particular cases involving acido-basic equilibria …………………………………… 159
3.4.2 – Experimental aspects…………………………………………………………………………………………. 161
3.4.2.1 – Ionic junctions …………………………………………………………………………………………….. 161
3.4.2.2 – Reference electrodes………………………………………………………………………………….. 161
Questions on chapiter 3…………………………………………………………………………………………………….. 167
4 – Current flow: a non-equilibrium process………………………………………………………. 169
4.1 – Mass balances…………………………………………………………………………………………………………….. 169
4.1.1 – Definitions for the macroscopic quantities related to the current …………….. 169
4.1.1.1 – Molar flux……………………………………………………………………………………………………… 169
4.1.1.2 – Current density……………………………………………………………………………………………. 170
4.1.1.3 – Transport numbers …………………………………………………………………………………….. 171
4.1.2 – Volume mass balance………………………………………………………………………………………… 172
4.1.3 – Interfacial mass balance ……………………………………………………………………………………. 176
4.1.3.1 – General case ………………………………………………………………………………………………… 176
4.1.3.2 – Adsorbed species ……………………………………………………………………………………….. 178
4.1.3.3 – Electrochemical interfaces ………………………………………………………………………… 178
4.1.4 – A demonstration of FARADAY’s law …………………………………………………………………… 180
4.2 – Current flow in a monophasic conductor……………………………………………………………… 183
Conservation of archaeological artefacts……………………………………………………. 184
4.2.1 – Conduction phenomena: a macroscopic approach……………………………………… 186
4.2.1.1 – Different driving forces for transport ………………………………………………………. 186
4.2.1.2 – Thermodynamics of linear irreversible processes …………………………………. 187
4.2.1.3 – Link between migration and diffusion ……………………………………………………. 189
4.2.1.4 – Expressing molar flux and current densities…………………………………………… 190
4.2.1.5 – General equations in a monophasic conductor…………………………………….. 192
4.2.2 – Conduction phenomena: mechanisms and orders of magnitude……………… 197
4.2.2.1 – Examples of conduction mechanisms …………………………………………………….. 197
Energy storage: supercapacitors ………………………………………………………………….. 200
4.2.2.2 – Conductivity measurements …………………………………………………………………….. 201
4.2.2.3 – Orders of magnitude for conduction parameters …………………………………. 203
4.2.2.4 – Models for solutions at infinite dilution ………………………………………………….. 203
4.2.2.5 – Case of concentrated solutions………………………………………………………………… 207
4.2.3 – Situations in which the ohmic drop
does not follow the macroscopic OHM law ……………………………………………… 208
4.3 – Current flow through an electrochemical interface…………………………………………….. 209
4.3.1 – Potential and concentration profiles at an interface ……………………………………. 209
4.3.1.1 – Potential profile…………………………………………………………………………………………… 209
4.3.1.2 – Concentration profiles……………………………………………………………………………….. 210
4.3.1.3 – Example of a transient state: semi-infinite diffusion …………………………….. 215
4.3.1.4 – Example of a steady state: the NERNST model…………………………………………. 218
4.3.1.5 – Directions of the various current densities …………………………………………….. 220
4.3.2 – Kinetic model for a heterogeneous reaction …………………………………………………. 221
4.3.2.1 – General …………………………………………………………………………………………………………. 221
4.3.2.2 – Rate of a heterogeneous reaction ……………………………………………………………. 222

CONTENTS XV
4.3.2.3 – Simplified kinetic model of the E mechanism (single step) …………………. 223
4.3.2.4 – Rate-limiting or determining step……………………………………………………………. 225
4.3.2.5 – Reversibility character of an elementary reaction step ………………………… 226
4.3.2.6 – Rapidity of a redox couple ………………………………………………………………………… 227
4.3.3 – Polarisation of an electrochemical interface at steady state ………………………. 228
4.3.3.1 – Concentration profiles and equation for the limiting currents …………… 229
Scanning electrochemical microscope ……………………………………………………….. 232
4.3.3.2 – Fast redox systems……………………………………………………………………………………… 234
4.3.3.3 – Slow redox systems ……………………………………………………………………………………. 235
4.3.3.4 – General case ………………………………………………………………………………………………… 240
4.4 – Complete electrochemical systems with a current flowing……………………………….. 242
4.4.1 – One-compartment cell………………………………………………………………………………………. 242
4.4.1.1 – Cases where all steady states correspond to zero-current…………………… 242
4.4.1.2 – Obtaining non-zero-current steady states ……………………………………………… 245
Electrodialysis………………………………………………………………………………………………….. 246
4.4.2 – Cell with two separate compartments……………………………………………………………. 248
4.4.2.1 – Different types of separation…………………………………………………………………….. 249
4.4.2.2 – Steady states with a non-zero current …………………………………………………….. 251
4.4.2.3 – Characteristics of the transient period: the HITTORF mass balance ……… 252
HITTORF’s mass balance experiment……………………………………………………………… 254
4.4.2.4 – Industrial applications ……………………………………………………………………………….. 256
Questions on chapiter 4…………………………………………………………………………………………………….. 257
Appendices………………………………………………………………………………………………………………………… 261
A.1.1 – Liquid ionic junction voltage without current…………………………………………………… 261
The HENDERSON equation and its impact in practical terms …………………………………… 261
Basic elements for demonstrating the HENDERSON equation ………………………………… 263
A.1.2 – Potentiostat and galvanostat……………………………………………………………………………….. 265
A.2.1 – General shape of the current-potential curve
for reducing water or protons: the role of mass transport kinetics ……………….. 267
A.2.2 – Different working points for an electrochemical system ………………………………… 272
A.3.1 – Electric potential: VOLTA and GALVANI potentials……………………………………………….. 275
A.3.2 – Mean activity of a solute in an electrolyte………………………………………………………… 277
Electrochemical chains with no ionic junction ……………………………………………………….. 277
Electrochemical chains with an ionic junction………………………………………………………… 278
A.3.3 – DEBYE-HÜCKEL’s model ……………………………………………………………………………………………. 280
A.3.4 – Thermodynamic equilibrium at a reactive interface
involving a single reaction between charged or neutral species…………………… 284
Exchange of neutral species M ………………………………………………………………………………….. 285
Exchange of cation M+ ………………………………………………………………………………………………… 285
Redox equilibrium at an electrochemical interface ……………………………………………….. 287

XVI ELECTROCHEMISTRY – THE BASICS, WITH EXAMPLES
A.4.1 – Highlighting the role of the supporting electrolyte in mass transport
and its impact on an electrolysis cell ………………………………………………………………….. 289
Solution with no supporting electrolyte (solution S1)……………………………………………. 291
Solution with a supporting electrolyte (solution S2)………………………………………………. 300
A.4.2 – Concentration profiles at an interface………………………………………………………………… 307
Chronopotentiometry with semi-infinite unidirectional diffusion………………………. 308
Chronopotentiometry with steady-state unidirectional diffusion ………………………. 310
Chronopotentiometry with diffusion-convection according to the NERNST model 311
Chronoamperometry with steady-state unidirectional diffusion ………………………… 312
Summary tables……………………………………………………………………………………………………………….

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