电化学阻抗谱分析方法

Techniquesbasedonconceptsofimpedance•Wehavediscussedwaysofstudyingelectrodereactionsthroughlargeperturbationsonthesystem,forexample,potentialsweeps,potentialsteps,orcurrentsteps,theelectrodeisgenerallydriventoaconditionfarfromequilibriumandtheresponseisobserved,whichisusuallyatransientsignal.•Anotherapproachistoperturbthecellwithanalternatingsignalofsmallmagnitudeandobservethewayinwhichsystemfollowstheperturbationatsteadystate.I0E0I0+Isin(t+E0+EsintIEElectrochemicalImpedanceSpectroscopyFRA:FrequencyResponseAnalysisPotentiostaticorgalvanostaticmeasurementsReviewofaccircuits•Apurelysinusoidalvoltagecanbeexpressedas•Whereωistheangularfrequency,whichis2πtimestheconventionalfrequencyinhertz.•Thecurrentlagsthevoltage,itcanbeexpressedgenerallyas•Whereφisaphaseangle.sineEtsin()iItReviewofaccircuits•ApureresistanceR,E=IR,wherethephaseiszero.•ApurecapacitanceC,••WhereXcisthecapacitivereactance,1/ωC•AcomparisonofRandXcshowsthatXcmustcarrydimensionsofresistance,butthemagnitudeofXcfallswithincreasingfrequency.sin()2CEitXResistance:ZREIF0oCapacitance:ZC1IEF-90oElectrochemicalImpedanceSpectroscopyReviewofaccircuits•Componentsalongtheordinateareassignedasimaginaryandalongtheabscissaarereal,thus,wehandletheseparametersmathematicallyas“real”or“imaginary”.•AvoltageEisappliedacrossRandC•WhereZ=R-jXc,calledtheimpedance.CEjXI-()RCCEEEIRjXIZ-Reviewofaccircuits•ThemagnitudeofZandphaseanglearegivenbythefollowing,respectively•Theimpedanceisakindofgeneralizedresistance.Thephaseangleexpressesthebalancebetweencapacitiveandresistancecomponentsintheseriescircuit.Forapureresistance,φ=0;forapurecapacitance,φ=π/2;andformixtures,intermediatephaseanglesareobserved.221/2()1tanCCZRXXRRCFReviewofaccircuits•Forimpedancesinparallel,theinverseoftheoverallimpedanceisthesumofthereciprocalsoftheindividualvectors.Sometimesitisadvantageoustoanalyzeaccircuitsintermsoftheadmittance,Y,whichistheinverseimpedance1/Z.Equivalentcircuitofacell•Inageneralsense,weoughttobeabletorepresentitsperformancebyanequivalentcircuitofresistorsandcapacitorsunderagivenexcitation.•Theelementsofequivalentcircuitofacell:double-layercapacitanceCd,faradaicimpedanceZf,solutionresistanceRs,chargetransferresistanceRct,WarburgimpedanceZw.AResistanceandcapacitanceinseries-800x109-600-400-2000Zj,W500.00Zr,W108106104102|Z|,W106105104103102101Frequency,Hz-90-80-70-60Phase106105104103102101Frequency,HzNyquistBodefislow:fishigh:ZC1F90ZRF0Inelectrochemicalcell:R=Rs:solutionresistanceC=Cd:doublelayercapacitanceElectrochemicalImpedanceSpectroscopyAresistanceandcapacitanceinparallel(Randlescircuit)-300-250-200-150-100-500Zj,W3002001000Zr,W-50-40-30-20-100Phase106104102100Frequency,Hz24681002|Z|,W106104102100Frequency,HzNyquistBodeZ=RsathighfrequencyZ=Rct+RsatlowfrequencyElectrochemicalImpedanceSpectroscopyMixedkineticanddiffusioncontrol234567100|Z|,W104102100Frequency,Hz-40-30-20-100Phase104102100Frequency,Hz-200-150-100-500Zj,W200150100500Zr,WNyquistBodeCdlorCPERPRWZWZQn-1/()with0n1ElectrochemicalImpedanceSpectroscopy•Abstractthecellintoanequivalentcircuitmodel•Beforestartingtofit,getgoodinitialguessvaluesUse„findcircle“optionUselinearregressiontoevaluateaWarburgimpedance•Takecareof:NonuniquenessofequivalentcircuitmodelsWeightingthedataElectrochemicalImpedanceSpectroscopyDataAnalysis:复平面图1/2*1/2*01112AD2dBctOORRctctdDCCRADRTDCDCnFARTRnFiRC-0.20.40.60.8-10010E/VI/A13a0.20.40.60.80102030E/VI/A13bCyclicvoltammograms(a)anddifferentialpulsevoltammograms(b)ofdifferentconcentrationsofferroceneontheGCelectrode,C(mmol/L):(1)0.2,(2)0.5,(3)1;scanrate:100mV/s0.20.40.60.8-150153051E/VI/A0.10.20.30.45101520Ip,a/A1/2/(V،¤s-1£©Cyclicvoltammogramsof1mmol/LferroceneontheGCelectrode,Plotofoxidationpeakcurrent(Ip,a)vs.squarerootofscanrate(υ1/2)forferrocene0.30.60.901530Il/AE/V5168101218243036Il/A1/2/(s-1/2)Left:Voltammetriccurvesof1mmol/LferroceneontheGCeletrodewithdifferentrotationrate,rotationrate(r/min):(1)300,(2)600,(3)900,(4)1200,(5)1500;scanrate:5mV/s;Right:plotoflimitingdiffusioncurrent(Il)squarerootofangularvelocity(ω1/2)forferrocene0204060081624Z'/kWZ/kWLeft:Nyquistplotsof1mmol/LferroceneatdifferentpotentialsontherotatingGCelectrodeanditsfittingresults(solidline),E(V):■0.40,●0.45,▲0.50;rotationrate=900r/min;Right:thecorrespondingequivalentcircuit.整个电解池的电化学阻抗和双电层电容随电位变化。05101520250510152025Z/kWZ'/kWLeft:Nyquistplotsof1mmol/LferroceneontherotatingGCelectrodeanditsfittingresults(solidline),E=0.50V.Right:thecorrespondingequivalentcircuit.电化学极化控制的交流阻抗复平面图•反应粒子浓度高•施加于电极上的交流电信号的幅度低且频率高•通过电极的交流电流的振幅远小于极限电流值•此时电极附件不会出现可察觉的浓度变化•电极过程只受电化学极化控制。Diffusioncoefficientandstandardheterogeneousrateconstant1/2*1/2*01112AD2dBctOORRctctdDCCRADRTDCDCnFARTRnFiRC-