Electrochemical impedance spectroscopy:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2008
|
| Series: | The Electrochemical Society series
|
| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Table of contents only Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. [495]-517) and index |
| Physical Description: | XXXI, 523 S. Ill., graph. Darst. |
| ISBN: | 9780470041406 |
Staff View
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| 100 | 1 | |a Orazem, Mark E. |e Verfasser |0 (DE-588)113615230X |4 aut | |
| 245 | 1 | 0 | |a Electrochemical impedance spectroscopy |c Mark E. Orazem ; Bernard Tribollet |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2008 | |
| 300 | |a XXXI, 523 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a The Electrochemical Society series | |
| 500 | |a Includes bibliographical references (p. [495]-517) and index | ||
| 650 | 4 | |a Impedance spectroscopy | |
| 650 | 0 | 7 | |a Impedanzspektroskopie |0 (DE-588)4161400-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Impedanzspektroskopie |0 (DE-588)4161400-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Tribollet, Bernard |d 1947- |e Verfasser |0 (DE-588)1136398473 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018000122 | ||
Record in the Search Index
| _version_ | 1804139998055759872 |
|---|---|
| adam_text | Contents
Contents...................................... v
Preface....................................... xv
Acknowledgments................................. xix
The Blind Men and the Elephant....................... xxi
History of Impedance Spectroscopy...................... xxv
I Background 1
1 Complex Variables.............................. 3
1.1 Why Imaginary Numbers?....................... 3
1.2 Terminology............................... 4
1.2.1 The Imaginary Number.................... 4
1.2.2 Complex Variables....................... 4
1.2.3 Conventions for Notation in Impedance Spectroscopy . . 5
1.3 Operations Involving Complex Variables.............. 5
1.3.1 Multiplication and Division of Complex Numbers..... 6
1.3.2 Complex Variables in Polar Coordinates........... 9
1.3.3 Properties of Complex Variables............... 13
1.4 Elementary Functions of Complex Variables............. 13
1.4.1 Exponential........................... 15
1.4.2 Logarithmic........................... 16
1.4.3 Polynomial ........................... 19
Problems................................. 20
Vl CONTENTS
2 Differential Equations............................ 23
2.1 Linear First-Order Differential Equations.............. 23
2.2 Homogeneous Linear Second-Order Differential Equations .... 26
2.3 Nonhomogeneous Linear Second-Order Differential Equations . . 28
2.4 Partial Differential Equations by Similarity Transformations ... 29
2.5 Differential Equations with Complex Variables........... 32
Problems.............,................... 34
3 Statistics.................................... 35
3.1 Definitions................................ 35
3.1.1 Expectation and Mean..................... 35
3.1.2 Variance, Standard Deviation, and Covariance....... 35
3.1.3 Normal Distribution...................... 36
3.1.4 Probability............................ 38
3.1.5 Central-Limit Theorem..................... 39
3.2 Error Propagation............................ 43
3.2.1 Linear Systems........................ . 43
3.2.2 Nonlinear Systems....................... 44
3.3 Hypothesis Tests ............................ 47
3.3.1 Terminology........................... 48
3.3.2 Student s t-Test for Equality of Mean............. 49
3.3.3 F-test for Equality of Variance................. 50
3.3.4 Chi-Squared Test for Equality of Variance.......... 56
Problems................................. 58
4 Electrical Circuits............................... 61
4.1 Passive Electrical Circuits....................... 61
4.1.1 Circuit Elements........................ 61
4.1.2 Parallel and Series Combinations............... 64
4.2 Fundamental Relationships...................... 66
4.3 Nested Circuits............................. 68
4.4 Mathematical Equivalence of Circuits................ 69
4.5 Graphical Representation of Circuit Response............ 70
Problems................................. 72
5 Electrochemistry................ ............... 73
5.1 Resistors and Electrochemical Cells.................. 73
5.2 Equilibrium in Electrochemical Systems............... 74
5.3 Polarization Behavior for Electrochemical Systems......... 76
5.3.1 Zero Current .......................... 76
5.3.2 Kinetic Control......................... 78
5.3.3 Mass-Transfer Control..................... 79
CONTENTS vü
5.4 Definitions of Potential......................... 80
5.5 Rate Expressions ............................ 81
5.5.1 Law of Mass Action ...................... 81
5.5.2 Generalized Electrode Kinetics................ 83
5.6 Transport Processes........................... 85
5.6.1 Primary Current and Potential Distributions........ 87
5.6.2 Application to Blocking Electrodes.............. 88
5.6.3 Secondary Current and Potential Distributions....... 89
5.6.4 Tertiary Current and Potential Distributions........ 90
5.6.5 Mass-Transfer-Controlled Current Distributions...... 90
5.7 Potential Contributions......................... 90
5.7.1 Ohmic Potential Drop..................... 90
5.7.2 Surface Overpotential..................... 90
5.7.3 Concentration Overpotential................. 91
5.8 Capacitance Contributions....................... 91
5.8.1 Double-Layer Capacitance................... 91
5.8.2 Dielectric Capacitance..................... 95
Problems................................. 96
6 Electrochemical Instrumentation...................... 97
6.1 The Ideal Operational Amplifier ................... 97
6.2 Elements of Electrochemical Instrumentation............ 99
6.3 Electrochemical Interface........................ 101
6.3.1 Potentiostat........................... 101
6.3.2 Galvanostat........................... 102
6.3.3 Potentiostat for EIS Measurement.............. 103
Problems................................. 105
II Experimental Considerations 107
7 Experimental Methods............................ 109
7.1 Steady-State Polarization Curves................... 109
7.2 Transient Response to a Potential Step................ 109
7.3 Analysis in Frequency Domain.................... 110
7.3.1 Lissajous Analysis....................... Ill
7.3.2 Phase-Sensitive Detection (Lock-in Amplifier)....... 117
7.3.3 Single-Frequency Fourier Analysis.............. 119
7.3.4 Multiple-Frequency Fourier Analysis............ 121
7.4 Comparison of Measurement Techniques.............. 122
7.4.1 Lissajous Analysis....................... 122
7.4.2 Phase-Sensitive Detection (Lock-in Amplifier)....... 122
7.4.3 Single-Frequency Fourier Analysis.............. 123
7.4.4 Multiple-Frequency Fourier Analysis............ 123
vill CONTENTS
7.5 Specialized Techniques......................... 123
7.5.1 Transfer Function Analysis.................. 123
7.5.2 Local Electrochemical Impedance Spectroscopy...... 124
Problems................................. 128
8 Experimental Design............................. 129
8.1 Cell Design................................ 129
8.1.1 Reference Electrodes...................... 129
8.1.2 Flow Configurations...................... 131
8.1.3 Current Distribution...................... 132
8.2 Experimental Considerations..................... 133
8.2.1 Frequency Range........................ 133
8.2.2 Linearity............................. 134
8.2.3 Modulation Technique..................... 146
8.2.4 Oscilloscope........................... 147
8.3 Instrumentation Parameters...................... 147
8.3.1 Improve Signal-to-Noise Ratio................ 147
8.3.2 Reduce Bias Errors....................... 149
8.3.3 Improve Information Content................. 151
Problems................................. 152
III Process Models 153
9 Equivalent Circuit Analogs......................... 155
9.1 General Approach............................ 155
9.2 Current Addition............................ 156
9.2.1 Impedance at the Corrosion Potential............ 156
9.2.2 Partially Blocked Electrode.................. 157
9.3 Potential Addition ........................... 158
9.3.1 Electrode Coated with an Inert Porous Layer........ 158
9.3.2 Electrode Coated with Two Inert Porous Layers...... 159
Problems................................. 162
10 Kinetic Models................................ 163
10.1 Electrochemical Reactions....................... 163
10.2 Reaction Dependent on Potential Only................ 164
10.3 Reaction Dependent on Potential and Mass Transfer........ 169
10.4 Coupled Reactions Dependent on Potential and Surface Coverage 173
10.5 Reactions Dependent on Potential, Surface Coverage, and Transport 176
Problems................................. 180
CONTENTS ¡X
11 Diffusion Impedance............................. 183
11.1 Uniformly Accessible Electrode.................... 184
11.2 General Mathematical Framework.................. 185
11.3 Stagnant Diffusion Layer........................ 189
11.4 Diffusion through a Solid Film .................... 191
11.4.1 Region of Film Diffusion Control............... 191
11.4.2 Film Impedance Response................... 194
11.5 Coupled Diffusion Impedance..................... 198
11.6 Rotating Disk.............................. 198
11.6.1 Fluid Flow............................ 199
11.6.2 Mass Transfer.......................... 200
11.6.3 Classification of Models for Convective Diffusion..... 201
11.7 Submerged Impinging Jet....................... 205
11.7.1 Fluid Flow............................ 206
11.7.2 Mass Transfer.......................... 206
11.8 Rotating Cylinders........................... 207
Problems................................. 210
12 Semiconducting Systems .......................... 211
12.1 Semiconductor Physics......................... 211
12.1.1 Electrons and Holes as Species................ 212
12.1.2 Doping.............................. 214
12.1.3 Deep-Level States........................ 216
12.1.4 Shockley-Read-Hall Processes ................ 217
12.1.5 Interfaces ............................ 218
12.2 Steady-State Models .......................... 219
12.2.1 Mass Transfer.......................... 219
12.2.2 Space-Charge Region...................... 220
12.2.3 Application to Electrolyte-Semiconductor Junctions .... 221
12.3 Impedance Models........................... 223
12.3.1 Equivalent Electrical Circuits................. 223
12.3.2 Mott-Schottky Analysis.................... 225
Problems................................. 230
13 Time-Constant Dispersion.......................... 233
13.1 Constant-Phase Elements ....................... 233
13.1.1 2-D and 3-D Distributions................... 234
13.1.2 Determination of Capacitance................. 236
13.1.3 Limitations to the Use of the CPE............... 236
13.2 Convective Diffusion Impedance at Small Electrodes ....... 237
13.2.1 Analysis............................. 238
13.2.2 Local Diffusion Convective Impedance........... 239
13.2.3 Global Convective Diffusion Impedance .......... 242
X CONTENTS
13.3 Geometry-Induced Current and Potential Distributions...... 243
13.3.1 Mathematical Development.................. 244
13.3.2 Global and Local Impedances................. 246
13.4 Porous Electrodes............................ 252
13.5 Oxide Layers............................... 260
Problems................................. 263
14 Generalized Transfer Functions....................... 265
14.1 Multi-Input/Multi-Output Systems ................. 265
14.1.1 Current or Potential Are the Output Quantity....... 269
14.1.2 Current or Potential Are the Input Quantity ........ 270
14.1.3 Experimental Quantities.................... 272
14.2 Transfer Functions Involving Exclusively Electrical Quantities . . 273
14.2.1 Ring-Disk Impedance Measurements............ 273
14.2.2 Multifrequency Measurements for Double-Layer Studies . 275
14.3 Transfer Functions Involving Nonelectrical Quantities....... 278
14.3.1 Thermoelectrochemical (TEC) Transfer Function...... 278
14.3.2 Photoelectrochemical Impedance Measurements...... 282
14.3.3 Electrogravimetry Impedance Measurements........ 283
Problems................................. 284
15 Electrohydrodynamic Impedance...................... 285
15.1 Hydrodynamic Transfer Function................... 287
15.2 Mass-Transport Transfer Function .................. 290
15.2.1 Asymptotic Solution for Large Schmidt Numbers..... 293
15.2.2 Asymptotic Solution for High Frequencies......... 294
15.3 Kinetic Transfer Function for Simple Electrochemical Reactions . 295
15.4 Interface with a 2-D or 3-D Insulating Phase............. 296
15.4.1 Partially Blocked Electrode.................. 296
15.4.2 Rotating Disk Electrode Coated by a Porous Film..... 299
Problems................................. 306
IV Interpretation Strategies 307
16 Methods for Representing Impedance................... 309
16.1 Impedance Format........................... 311
16.1.1 Complex-Impedance-Plane Representation......... 312
16.1.2 Bode Representation...................... 314
16.1.3 Electrolyte-Resistance-Corrected Bode Representation . . 316
16.1.4 Impedance Representation.................. 317
16.2 Admittance Format........................... 319
16.2.1 Admittance-Plane Representation.............. 320
16.2.2 Admittance Representation.................. 321
CONTENTS X¡
16.2.3 Electrolyte-Resistance-Corrected Representation...... 324
16.3 Complex-Capacitance Format..................... 324
16.3.1 Complex-Capacitance-Plane Representation........ 325
16.3.2 Complex-Capacitance Representation............ 326
16.4 Effective Capacitance.......................... 328
Problems................................. 331
17 Preliminary Graphical Methods....................... 333
17.1 Application to a Randies Circuit ................... 334
17.1.1 Traditional Representation of Data.............. 334
17.1.2 Phase Angle and Modulus Corrected for Ohmic Resistance 337
17.1.3 Real and Imaginary Components............... 338
17.1.4 Effective High-Frequency Capacity or CPE Coefficient . . 340
17.2 Application to Blocking Electrodes.................. 342
17.2.1 Nyquist and Bode Representations.............. 342
17.2.2 Imaginary Component..................... 344
17.2.3 Effective CPE Coefficient ................... 345
17.3 Overview................................. 348
Problems................................. 351
18 Model-Based Graphical Methods...................... 353
18.1 Mass Transfer.............................. 353
18.1.1 Scaled Plots of Impedance................... 353
18.1.2 Asymptotic Behavior at Low-Frequency........... 355
18.2 Reaction Kinetics: Arrhenius Relations................ 357
18.3 Mott-Schottky Plots........................... 360
Problems................................. 362
19 Complex Nonlinear Regression....................... 363
19.1 Concept.................................. 363
19.2 Objective Functions........................... 365
19.3 Formalism of Regression Strategies.................. 367
19.3.1 Linear Regression........................ 367
19.3.2 Nonlinear Regression ..................... 368
19.4 Regression Strategies for Nonlinear Problems............ 370
19.4.1 Gauss-Newton Method.................... 370
19.4.2 Method of Steepest Descent.................. 371
19.4.3 Levenberg-Marquardt Method................ 371
19.4.4 Downhill Simplex Strategies ................. 372
19.5 Influence of Data Quality on Regression............... 373
19.5.1 Presence of Stochastic Errors in Data............. 373
19.5.2 Ill-Conditioned Regression Caused by Stochastic Noise . . 375
19.5.3 Ill-Conditioned Regression Caused by Insufficient Range . 375
XII CONTENTS
19.6 Initial Estimates for Regression.................... 380
19.7 Regression Statistics .......................... 380
19.7.1 Confidence Intervals for Parameter Estimates ....... 381
19.7.2 Statistical Measure of the Regression Quality........ 382
Problems................................. 382
20 Assessing Regression Quality........................ 385
20.1 Methods to Assess Regression Quality................ 385
20.1.1 Quantitative Methods..................... 385
20.1.2 Qualitative Methods...................... 386
20.2 Application of Regression Concepts................. 386
20.2.1 Finite-Diffusion-Length Model................ 388
20.2.2 Measurement Model...................... 393
20.2.3 Convective-Diffusion-Length Model............. 395
Problems................................. 402
V Statistical Analysis 405
21 Error Structure of Impedance Measurements.............. 407
21.1 Error Contributions........................... 407
21.2 Stochastic Errors in Impedance Measurements........... 408
21.2.1 Stochastic Errors in Time-Domain Signals.......... 409
21.2.2 Transformation from Time Domain to Frequency Domain 411
21.2.3 Stochastic Errors in Frequency Domain........... 413
21.3 Bias Errors................................ 414
21.3.1 Instrument Artifacts...................... 415
21.3.2 Ancillary Parts of the System under Study......... 415
21.3.3 Nonstationary Behavior.................... 415
21.3.4 Time Scales in Impedance Spectroscopy Measurements . . 416
21.4 Incorporation of Error Structure.................... 418
21.5 Measurement Models for Error Identification............ 420
21.5.1 Stochastic Errors........................ 422
21.5.2 Bias Errors............................ 423
Problems................................. 425
22 The Kramers-Kronig Relations....................... 427
22.1 Mathematical Origin.......................... 427
22.1.1 Background........................... 428
22.1.2 Application of Cauchy s Theorem.............. 432
22.1.3 Transformation from Real to Imaginary........... 432
22.1.4 Transformation from Imaginary to Real........... 435
22.1.5 Application of the Kramers-Kronig Relations........ 436
22.2 The Kramers-Kronig in an Expectation Sense............ 439
CONTENTS xiü
22.2.1 Transformation from Real to Imaginary........... 439
22.2.2 Transformation from Imaginary to Real........... 440
22.3 Methods for Application........................ 442
22.3.1 Direct Integration of the Kramers-Kronig Relations .... 442
22.3.2 Experimental Assessment of Consistency.......... 443
22.3.3 Regression of Process Models................. 443
22.3.4 Regression of Measurement Models............. 444
Problems................................. 445
VI Overview 447
23 An Integrated Approach to Impedance Spectroscopy.......... 449
23.1 Flowcharts for Regression Analysis.................. 449
23.2 Integration of Measurements, Error Analysis, and Model..... 450
23.2.1 Impedance Measurements Integrated with Error Analysis 451
23.2.2 Process Models Developed Using Other Observations . . . 452
23.2.3 Regression Analysis in Context of Error Structure..... 453
23.3 Application ............................... 453
Problems................................. 459
VII Reference Material 461
A Complex Integrals............................... 463
A.I Definition of Terms........................... 463
A.2 Cauchy-Riemann Conditions..................... 465
A.3 Complex Integration.......................... 467
A.3.1 Cauchy s Theorem....................... 467
A.3.2 Improper Integrals of Rational Functions.......... 471
Problems................................. 473
B Tables of Reference Material........................ 475
C List of Examples ............................... 477
List of Symbols.................................. 481
References..................................... 495
Index........................................ 518
|
| any_adam_object | 1 |
| author | Orazem, Mark E. Tribollet, Bernard 1947- |
| author_GND | (DE-588)113615230X (DE-588)1136398473 |
| author_facet | Orazem, Mark E. Tribollet, Bernard 1947- |
| author_role | aut aut |
| author_sort | Orazem, Mark E. |
| author_variant | m e o me meo b t bt |
| building | Verbundindex |
| bvnumber | BV035723392 |
| callnumber-first | Q - Science |
| callnumber-label | QD116 |
| callnumber-raw | QD116.I57 |
| callnumber-search | QD116.I57 |
| callnumber-sort | QD 3116 I57 |
| callnumber-subject | QD - Chemistry |
| classification_rvk | UP 5000 VE 6300 VG 8930 |
| classification_tum | CHE 140f MSR 220f |
| ctrlnum | (OCoLC)144517368 (DE-599)BVBBV035723392 |
| dewey-full | 543.422 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 543 - Analytical chemistry |
| dewey-raw | 543.4 22 |
| dewey-search | 543.4 22 |
| dewey-sort | 3543.4 222 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik Chemie Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik |
| format | Book |
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| id | DE-604.BV035723392 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:52:59Z |
| institution | BVB |
| isbn | 9780470041406 |
| language | English |
| lccn | 2008300311 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018000122 |
| oclc_num | 144517368 |
| open_access_boolean | |
| owner | DE-20 DE-11 DE-703 DE-92 DE-91 DE-BY-TUM DE-384 DE-1043 DE-573 |
| owner_facet | DE-20 DE-11 DE-703 DE-92 DE-91 DE-BY-TUM DE-384 DE-1043 DE-573 |
| physical | XXXI, 523 S. Ill., graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Wiley |
| record_format | marc |
| series2 | The Electrochemical Society series |
| spelling | Orazem, Mark E. Verfasser (DE-588)113615230X aut Electrochemical impedance spectroscopy Mark E. Orazem ; Bernard Tribollet Hoboken, NJ Wiley 2008 XXXI, 523 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier The Electrochemical Society series Includes bibliographical references (p. [495]-517) and index Impedance spectroscopy Impedanzspektroskopie (DE-588)4161400-8 gnd rswk-swf Impedanzspektroskopie (DE-588)4161400-8 s DE-604 Tribollet, Bernard 1947- Verfasser (DE-588)1136398473 aut http://www.loc.gov/catdir/enhancements/fy0902/2008300311-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0902/2008300311-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0902/2008300311-t.html Table of contents only HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018000122&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Orazem, Mark E. Tribollet, Bernard 1947- Electrochemical impedance spectroscopy Impedance spectroscopy Impedanzspektroskopie (DE-588)4161400-8 gnd |
| subject_GND | (DE-588)4161400-8 |
| title | Electrochemical impedance spectroscopy |
| title_auth | Electrochemical impedance spectroscopy |
| title_exact_search | Electrochemical impedance spectroscopy |
| title_full | Electrochemical impedance spectroscopy Mark E. Orazem ; Bernard Tribollet |
| title_fullStr | Electrochemical impedance spectroscopy Mark E. Orazem ; Bernard Tribollet |
| title_full_unstemmed | Electrochemical impedance spectroscopy Mark E. Orazem ; Bernard Tribollet |
| title_short | Electrochemical impedance spectroscopy |
| title_sort | electrochemical impedance spectroscopy |
| topic | Impedance spectroscopy Impedanzspektroskopie (DE-588)4161400-8 gnd |
| topic_facet | Impedance spectroscopy Impedanzspektroskopie |
| url | http://www.loc.gov/catdir/enhancements/fy0902/2008300311-b.html http://www.loc.gov/catdir/enhancements/fy0902/2008300311-d.html http://www.loc.gov/catdir/enhancements/fy0902/2008300311-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018000122&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT orazemmarke electrochemicalimpedancespectroscopy AT tribolletbernard electrochemicalimpedancespectroscopy |