ElectrochemicalImpedance Spectroscopy 電化學(xué)阻抗譜分析方法

.,Techniquesbasedonconceptsofimpedance,Wehavediscussedwaysofstudyingelectrodereactionsthroughlargeperturbationsonthesystem,forexample,potentialsweeps,potentialsteps,orcurrentsteps,theelectrodeisgenerallydriventoaconditionfarfromequilibriumandtheresponseisobserved,whichisusuallyatransientsignal.Anotherapproachistoperturbthecellwithanalternatingsignalofsmallmagnitudeandobservethewayinwhichsystemfollowstheperturbationatsteadystate.,.,ElectrochemicalImpedanceSpectroscopy,FRA:FrequencyResponseAnalysis,Potentiostaticorgalvanostaticmeasurements,.,Reviewofaccircuits,ApurelysinusoidalvoltagecanbeexpressedasWhereistheangularfrequency,whichis2timestheconventionalfrequencyinhertz.Thecurrentlagsthevoltage,itcanbeexpressedgenerallyasWhereisaphaseangle.,.,Reviewofaccircuits,ApureresistanceR,E=IR,wherethephaseiszero.ApurecapacitanceC,WhereXcisthecapacitivereactance,1/CAcomparisonofRandXcshowsthatXcmustcarrydimensionsofresistance,butthemagnitudeofXcfallswithincreasingfrequency.,.,Resistance:,E,I,Capacitance:,I,E,ElectrochemicalImpedanceSpectroscopy,.,Reviewofaccircuits,Componentsalongtheordinateareassignedasimaginaryandalongtheabscissaarereal,thus,wehandletheseparametersmathematicallyas“real”or“imaginary”.AvoltageEisappliedacrossRandCWhereZ=R-jXc,calledtheimpedance.,.,Reviewofaccircuits,ThemagnitudeofZandphaseanglearegivenbythefollowing,respectivelyTheimpedanceisakindofgeneralizedresistance.Thephaseangleexpressesthebalancebetweencapacitiveandresistancecomponentsintheseriescircuit.Forapureresistance,=0;forapurecapacitance,=/2;andformixtures,intermediatephaseanglesareobserved.,.,Reviewofaccircuits,Forimpedancesinparallel,theinverseoftheoverallimpedanceisthesumofthereciprocalsoftheindividualvectors.Sometimesitisadvantageoustoanalyzeaccircuitsintermsoftheadmittance,Y,whichistheinverseimpedance1/Z.,.,Equivalentcircuitofacell,Inageneralsense,weoughttobeabletorepresentitsperformancebyanequivalentcircuitofresistorsandcapacitorsunderagivenexcitation.Theelementsofequivalentcircuitofacell:double-layercapacitanceCd,faradaicimpedanceZf,solutionresistanceRs,chargetransferresistanceRct,WarburgimpedanceZw.,.,AResistanceandcapacitanceinseries,fislow:fishigh:,Inelectrochemicalcell:R=Rs:solutionresistanceC=Cd:doublelayercapacitance,ElectrochemicalImpedanceSpectroscopy,.,Aresistanceandcapacitanceinparallel(Randlescircuit),Z=RsathighfrequencyZ=Rct+Rsatlowfrequency,ElectrochemicalImpedanceSpectroscopy,.,Mixedkineticanddiffusioncontrol,C,dlorCPE,RP,R,W,ZW,with0n1,ElectrochemicalImpedanceSpectroscopy,.,AbstractthecellintoanequivalentcircuitmodelBeforestartingtofit,getgoodinitialguessvaluesUsefindcircle“optionUselinearregressiontoevaluateaWarburgimpedanceTakecareof:NonuniquenessofequivalentcircuitmodelsWeightingthedata,ElectrochemicalImpedanceSpectroscopy,DataAnalysis:,.,Cyclicvoltammograms(a)anddifferentialpulsevoltammograms(b)ofdifferentconcentrationsofferroceneontheGCelectrode,C(mmol/L):(1)0.2,(2)0.5,(3)1;scanrate:100mV/s,.,Cyclicvoltammogramsof1mmol/LferroceneontheGCelectrode,Plotofoxidationpeakcurrent(Ip,a)vs.squarerootofscanrate(1/2)forferrocene,.,Left:Voltammetriccurvesof1mmol/LferroceneontheGCeletrodewithdifferentrotationrate,rotationrate(r/min):(1)300,(2)600,(3)900,(4)1200,(5)1500;scanrate:5mV/s;Right:plotoflimitingdiffusioncurrent(Il)squarerootofangularvelocity(1/2)forferrocene,.,Left:Nyquistplotsof1mmol/LferroceneatdifferentpotentialsontherotatingGCelectrodeanditsfittingresults(solidline),E(V):0.40,0.45,0.50;rotationrate=900r/min;Right:thecorrespondingequivalentcircuit.,.,Left:Nyquistpl