Problem Solving in Electrochemical Impedance Spectroscopy

Preface xiii
Acknowledgments xvii
Why an Elephant? xxi

I Problems and Solutions 1

1 Complex Variables 3
2 Differential Equations 17
3 Statistics 25
4 Electrical Circuits 33
5 Electrochemistry 45
6 Electrochemical Instrumentation 55
7 Experimental Methods 61
8 Experimental Design 73
9 Equivalent Circuit Analogs 97
10 Kinetic Models 111
11 Diffusion Impedance 147
12 Impedance of Materials 171
13 Time-Constant Dispersion 179
14 Constant-Phase Elements 199
15 Generalized Transfer Functions 211
16 Electrohydrodynamic Impedance 217
17 Methods for Representing Impedance 223
18 Graphical Methods 235
19 Complex Nonlinear Regression 247
20 Assessing Regression Quality 255
21 Error Structure of Impedance Measurements 261
22 The Kramersâ"Kronig Relations 273
23 An Integrated Approach to Impedance Spectroscopy 285
24 Complex Integrals 289

II Application to Experimental Data 293

25 Measurement Model for Regression of Impedance Data 295
25.1 Introduction 295
25.2 Measurement Model 297
25.3 Brief Guide/Instructions 298
25.4 Experimental Methods 300
25.5 Data Conversion 300
25.6 Measurement Model Analysis 301
25.7 Stochastic Error Structure 305
25.8 Kramersâ"Kronig Relations 306
25.9 Interpretation Model Development 310
25.10 Discussion 317

26 Physical Properties of Aluminum Oxide 319
26.1 Initial Inspection 321
26.2 Interpretation Model Development 327
26.3 Regression Analysis 329
26.4 Regression of Integral Formula 336
26.5 Observations 338

27 Mass Transfer in Lithium Cobalt Oxide Coin Cells 339
27.1 Initial Inspection 341
27.2 Interpretation Model Development 352
27.3 Regression Analysis 357
27.4 Observations 360

28 Large Double-Layer Capacitance for Iron in the Presence of H2S 361
28.1 Introduction 361
28.2 Experimental Setup 361
28.3 Initial Inspection 362
28.4 Interpretation Model Development 366
28.5 Regression Analysis 368
28.6 Observations 373

29 Apparent Rotation-Speed Dependence of CPE Parameters 375
29.1 Initial Inspection 376
29.2 Interpretation Model Development 386
29.3 Regression Analysis 389
29.4 Observations 391

30 Model Development for Delamination of Coated Silver Mirrors 393
30.1 Experimental 393
30.2 Initial Inspection 394
30.3 Interpretation Model Development 405
30.4 Observations 410

III Reference Material 413

A Tables of Reference Material 415
A.1 Complex Variables 415
A.2 Statistics 419
A.3 Physical Properties 423
A.4 Selected Electrochemical Notation 425
A.5 Local Electrochemical Impedance Spectroscopy 427
A.6 Relationships for Impedance 431
A.7 Method to Identify Corrosion Model 436

B Computer Code 439
B.1 Fourier Analysis: Nonlinear 439
B.2 Fourier Analysis: Linear 442
B.3 Fourier Analysis with Noise 445
B.4 Single-Frequency Fourier Analysis with Noise 448
B.5 Convective Diffusion: Rotating Disk 450

List of Symbols 479
References 491
Author Index 503
Subject Index 507