Electrochemical impedance spectroscopy and its applications

369 Pages·2014·13.18 MB·English

by  Lasia, Andrzej

Andrzej Lasia
Electrochemical
Impedance
Spectroscopy
and its
Applications
Electrochemical Impedance Spectroscopy
and its Applications

Andrzej Lasia
Electrochemical Impedance
Spectroscopy
and its Applications
AndrzejLasia
De´partementdechimie
Universite´deSherbrooke
Sherbrooke,Que´bec
Canada
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ISBN978-1-4614-8932-0 ISBN978-1-4614-8933-7(eBook)
DOI10.1007/978-1-4614-8933-7
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All impedances are complex, but some are more complex
thanothers.
MargarethaSluyters-Rehbach

Preface
My first practical contact with electrochemical impedance spectroscopy (EIS)
was during my postdoctoral training in the laboratory of Prof. Ron W. Fawcett
attheUniversityofGuelph,Ontario,Canada,in1975.AtthattimeIwasusingac
voltammetry on a dropping mercury electrode. Since then, the technique and
equipment have evolved significantly. I was continually using EIS in subsequent
years in the kinetics of the reduction of metal cations in nonaqueous solvents to
determine the kinetics of hydrogen evolution, adsorption and absorption into
metals, impedance of porous electrodes, and electrocatalytic reactions. After a
series ofseminarsonthe impedance spectroscopy inthe laboratory ofProf. Brian
ConwayinOttawain1994,heencouragedmetowriteareviewinModernAspects
ofElectrochemistry,whichwaspublishedin1999.Prof.Conwayhasalsoaskedme
to write a second chapter in Modern Aspects on the impedance of hydrogen
adsorption, absorption, and evolution (2002). Later, Prof. M. Schlesinger asked
metowriteyetanotherchapterontheimpedanceofporouselectrodes(2009).This
bookoriginatedfrommypreviousreviewsandlecturesatvariousuniversities.
The purpose of this book is to present the concept of impedance, impedance
ofelectricalandelectrochemicalsystems, itslimitations, andcertain applications.
The available books on EIS were written either by physicists or engineers, and I
wantedtopresentitfromthechemist’spointofview.Someknowledgeofelectro-
chemistryisnecessarytounderstandthedevelopmentsofkineticequations.Ihope
that it will be useful to students who are just starting to use this technique and to
othersalreadyusingitintheirresearch.Thebookcontainstheoryandapplications,
numerical examples shown in the text, and exercises with full solutions on the
Internet.
First, electrical circuits containing resistances only are presented, followed by
circuits containing R, C, and L elements in transient and ac conditions. To under-
stand the concept of impedance, the notions of Laplace and Fourier transforms
arepresentedandmustbeunderstoodthoroughly.Inthischapter,impedanceplots
arealsopresented,alongwithseveralexamplesforvariouscircuits.Next,methods
fordeterminingimpedances,includingfastFouriertransform-basedtechniques,are
discussed.
vii
viii Preface
Based on that knowledge, the impedance of electrode processes in the presence
ofdiffusioninvariousgeometriesandadsorptionismathematicallydeveloped.This
leadstothegeneralmethodofdeterminingtheimpedancesofcomplexmechanisms.
As an illustration, the impedance of electrocatalytic reactions involving hydrogen
adsorption,absorption,andevolutionispresented.
The next two chapters deal with impedance dispersion at solid electrodes and
the impedance of porous electrodes in the absence and presence of electroactive
species.
It is difficult to present all applications of EIS; some applications (such as
those to solid materials and PEM fuel cells, corrosion and passivity, batteries;
seeSect.1.3)maybefoundinavailablebooks.Asexamples,Mott-Schottkyplots
obtained for semiconductors, the impedance of coating and paints, and electro-
catalysisofhydrogenadsorption,absorptionandevolutionwerepresentedasthey
arewellknownintheelectrochemicalliterature.Additionally,neweranddevelop-
ing applications such as the impedance of self-assembled monolayers, biological
bilayers,andbiosensorswerealsoshown.
Finally, methods of verification of obtained impedances and the modeling of
experimental data are discussed. The last two chapters deal with applications
ofnonlinearmeasurementsandinstrumentallimitations.
Besides examples in the text, there are exercises at the end of certain chapters
that can be solved using Excel, Maple, or Mathematica and more specialized
programssuchasZViewandKKtransform,withsolutionsontheInternet.
This book contains a comprehensive approach to impedance, but there exist
morespecializedbooksonimpedancethatshouldalsobeconsulted;readingofthe
researchliteraturecannotbeavoided.Onehourinthelibrarymaysaveoneyearof
laboratoryresearch.
Sherbrooke,Que´bec,Canada AndrzejLasia
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 WhyImpedance?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 ShortHistoryofImpedance. . . .. . .. . . .. . . .. . . .. . . .. . . .. 3
1.3 PublicationsonImpedance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 DefinitionofImpedanceandImpedanceofElectricalCircuits. . . . . 7
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 ElectricalCircuitsContainingResistances. . . . . . . . . . . . . . . . . 7
2.2.1 Ohm’sLaw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2 Kirchhoff’sLaws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Capacitance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Inductance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 LaplaceTransform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.6 ComplexNumbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.7 FourierTransform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.7.1 Leakage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7.2 Aliasing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.8 ImpedanceofElectricalCircuits. . . . . . . . . . . . . . . . . . . . . . . . 32
2.8.1 ApplicationofLaplaceTransformtoDetermination
ofImpedances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.8.2 DefinitionofOperationalImpedance. . . . . .. . . . . . . .. 33
2.8.3 ApplicationofFourierTransformtoDetermination
ofImpedances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.8.4 DefinitionofImpedance. . . . . . . . . . . . . . . . . . . . . . . . 44
2.9 CircuitDescriptionCode. . .. . . .. . . .. . . . .. . . .. . . .. . . . .. 47
2.10 ImpedancePlots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.10.1 InterpretationofBodeMagnitudePlots. . . . . . . . . . . . . 55
2.10.2 CircuitswithTwoSemicircles. . . . . . . . . . . . . . . . . . . 58
2.10.3 CircuitsContainingInductances. . . . . . . . . . . . . . . . . . 62
2.11 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.12 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
ix