Electrochemical Impedance Spectroscopy and its Applications

Preface......Page 8
Contents......Page 10
 1.1 Why Impedance?......Page 15
 1.2 Short History of Impedance......Page 17
 1.3 Publications on Impedance......Page 19
  2.2.1 Ohm´s Law......Page 20
  2.2.2 Kirchhoff´s Laws......Page 21
 2.3 Capacitance......Page 24
 2.4 Inductance......Page 25
 2.5 Laplace Transform......Page 26
 2.6 Complex Numbers......Page 31
 2.7 Fourier Transform......Page 33
  2.7.1 Leakage......Page 41
  2.7.2 Aliasing......Page 43
  2.8.1 Application of Laplace Transform to Determination of Impedances......Page 45
  2.8.2 Definition of Operational Impedance......Page 46
  2.8.3 Application of Fourier Transform to Determination of Impedances......Page 54
  2.8.4 Definition of Impedance......Page 57
 2.9 Circuit Description Code......Page 60
 2.10 Impedance Plots......Page 61
  2.10.1 Interpretation of Bode Magnitude Plots......Page 68
  2.10.2 Circuits with Two Semicircles......Page 71
  2.10.3 Circuits Containing Inductances......Page 75
 2.12 Exercises......Page 77
 3.1 AC Bridges......Page 80
 3.2 Lissajous Curves......Page 81
 3.3 Phase-Sensitive Detection, Lock-In Amplifiers......Page 82
 3.4 Frequency Response Analyzers......Page 83
 3.5 AC Voltammetry......Page 85
 3.6 Laplace Transform......Page 86
  3.7.1 Pulse or Step Excitation......Page 88
  3.7.3 Sum of Sine Wave Excitation Signals......Page 90
  3.7.4 Dynamic Electrochemical Impedance Spectroscopy......Page 92
 3.9 Conclusions......Page 96
 3.10 Exercises......Page 97
 4.1 Impedance of an Ideally Polarizable Electrode......Page 98
  4.2.1 General Case......Page 99
  4.2.2 DC Reversible Case......Page 105
  4.3.1 Randles Analysis......Page 110
  4.3.2 De Levie-Husovsky Analysis......Page 112
  4.3.3 Analysis of cot phiv......Page 113
 4.4 Finite-Length Linear Diffusion......Page 115
  4.4.1 Transmissive Boundary......Page 116
  4.4.2 Reflective Boundary......Page 119
 4.5 Generalized Warburg Element......Page 120
  4.6.1 Semi-infinite External Spherical Diffusion......Page 122
  4.6.2 Finite-Length Internal Spherical Diffusion......Page 125
 4.7 Cylindrical Diffusion......Page 126
 4.8 Diffusion to Disk Electrode......Page 129
 4.9 Rotating Disk Electrode......Page 130
 4.10 Homogeneous Reaction, Gerischer Impedance......Page 134
 4.11 Conclusions......Page 137
 4.12 Exercises......Page 138
 5.1 Faradaic Reaction Involving One Adsorbed Species, No Desorption......Page 139
 5.2 Faradaic Reaction Involving One Adsorbed Species with Subsequent Desorption......Page 143
  5.2.1 Determination of Impedance......Page 144
  5.2.2 Impedance Plots......Page 149
  5.2.3 Distinguishability of the Kinetic Parameters of the Volmer-Heyrovsky Reaction......Page 152
 5.3 Faradaic Reaction Involving Two Adsorbed Species......Page 153
 5.4 Exercises......Page 157
Chapter 6: General Method of Obtaining Impedance of Complex Reactions......Page 158
 7.1 Hydrogen Underpotential Deposition Reaction......Page 165
 7.2 Hydrogen Evolution Reaction......Page 169
 7.3 Influence of Hydrogen Mass Transfer on HER......Page 173
  7.4.1 Hydrogen Adsorption-Absorption Reaction in Presence of Hydrogen Evolution......Page 176
  7.4.2 Direct Hydrogen Absorption and Hydrogen Evolution......Page 181
  7.4.3 Hydrogen Absorption in Absence of Hydrogen Evolution......Page 182
  7.4.4 Hydrogen Absorption in Spherical Particles......Page 184
 7.5 Conclusions......Page 185
 8.1 Constant Phase Element......Page 186
 8.2 Fractal Model......Page 192
 8.3 Origin of CPE Dispersion......Page 196
  8.3.1 Dispersion of Time Constants......Page 197
  8.3.2 Dispersion Due to Surface Adsorption/Diffusion Processes......Page 201
  8.4.1 Regularization Methods......Page 205
  8.4.3 Differential Impedance Analysis......Page 207
  8.4.4 Summary......Page 209
 8.5 Conclusion......Page 210
 9.1 Impedance of Ideally Polarizable Porous Electrodes......Page 211
  9.1.1 Cylindrical Pore with Ohmic Drop in Solution Only (idc=0, re=0, rs0)......Page 212
  9.1.2 Other Pore Geometry with Ohmic Drop in Solution Only......Page 218
  9.1.4 Porous Electrode with Ohmic Drop in Solution and in Electrode Material (idc=0, rs0, re0)......Page 222
  9.2.1 Ohmic Drop in Solution Only in Absence of DC Current (idc=0, rs0, re=0)......Page 225
  9.2.2 Ohmic Drop in Solution and Electrode Material in Absence of DC Current (idc=0, rs0, re0)......Page 229
   9.2.3.1 DC Solution......Page 230
   9.2.3.2 AC Solution......Page 234
   9.2.4.1 DC Solution......Page 238
   9.2.4.2 AC Solution......Page 242
   9.2.5.1 DC Solution......Page 249
   9.2.5.2 AC Solution......Page 251
 9.3 Distribution of Pores......Page 252
 9.4 Continuous Porous Model......Page 253
 9.6 Exercises......Page 258
 10.1 Semiconductors in Solution......Page 259
 10.2 Determination of Flatband Potential......Page 261
 11.1 Electrical Equivalent Models......Page 264
 11.2 Water Absorption in Organic Coating......Page 265
 11.3 Analysis of Impedances of Organic Coatings......Page 266
 11.4 Conclusions......Page 268
 12.1 Self-Assembled Monolayers......Page 269
 12.2 Lipid Bilayers......Page 272
 12.3 Biosensors......Page 274
 12.4 Conclusions......Page 276
 13.1 Kramers-Kronig Relations......Page 277
  13.1.1 Polynomial Approximation......Page 279
  13.1.2 Checking Kramers-Kronig Compliance by Approximations......Page 281
 13.2 Linearity......Page 286
  13.3.1 Drift......Page 287
  13.3.2 Dealing with Nonstationary Impedances......Page 288
  13.3.3 Stability of Electrochemical Systems......Page 289
  13.3.4 Nyquist Stability Criterion......Page 297
  13.3.5 Negative Dynamic Resistances and Their Origin......Page 300
 13.4 Z-HIT Transform......Page 305
 13.6 Exercises......Page 306
 14.1 Acquisition of ``Good´´ Data......Page 307
 14.2 Types of Modeling......Page 308
 14.3 Fitting the Experimental Data......Page 316
 14.5 Methods for Finding the Best Parameters......Page 317
  14.6.1 Statistical Weighting......Page 318
  14.6.3 Modulus Weighting......Page 319
  14.6.5 Weighting from Measurement Model......Page 320
  14.7.1 Chi-Square......Page 321
  14.7.2 Test F......Page 325
 14.9 Exercises......Page 326
 15.1 Simple Electron Transfer Reaction Without Mass Transfer Effects......Page 328
 15.2 Other Reaction Mechanism......Page 332
 15.3 Conclusions......Page 336
 16.1 Measurements of High Impedances......Page 337
 16.2 Measurements at High Frequencies......Page 338
 16.3 Measurements of Low Impedances......Page 340
 16.4 Reference Electrode......Page 342
 16.5 Conclusions......Page 343
Chapter 17: Conclusions......Page 344
Appendix: Laplace Transforms......Page 346
References......Page 348
Index......Page 367