e電化學(xué)阻抗譜分析方法

TechniquesbasedonconceptsofimpedanceWehavediscussedwaysofstudyingelectrodereactionsthroughlargeperturbationsonthesystem,forexample,potentialsweeps,potentialsteps,orcurrentsteps,theelectrodeisgenerallydriventoaconditionfarfromequilibriumandtheresponseisobserved,whichisusuallyatransientsignal.Anotherapproachistoperturbthecellwithanalternatingsignalofsmallmagnitudeandobservethewayinwhichsystemfollowstheperturbationatsteadystate.第1頁ElectrochemicalImpedanceSpectroscopyFRA:FrequencyResponseAnalysisPotentiostaticorgalvanostaticmeasurements

第2頁ReviewofaccircuitsApurelysinusoidalvoltagecanbeexpressedasWhereωistheangularfrequency,whichis2πtimestheconventionalfrequencyinhertz.Thecurrent

lagsthevoltage,itcanbeexpressedgenerallyasWhereφisaphaseangle.第3頁ReviewofaccircuitsApureresistance

R,E=IR,wherethephaseiszero.Apurecapacitance

C,

WhereXcisthecapacitivereactance,1/ωCAcomparisonofRandXc

showsthatXcmustcarrydimensionsofresistance,butthemagnitudeofXcfallswithincreasingfrequency.第4頁Resistance:ZR=EIF=0oCapacitance:ZC=1wIEF=-90oElectrochemicalImpedanceSpectroscopy第5頁ReviewofaccircuitsComponentsalongtheordinateareassignedasimaginaryandalongtheabscissaarereal,thus,wehandletheseparametersmathematicallyas“real”or“imaginary”.AvoltageEisappliedacrossRandCWhereZ=R-jXc,calledtheimpedance.第6頁ReviewofaccircuitsThemagnitudeofZandphaseanglearegivenbythefollowing,respectivelyTheimpedanceisakindofgeneralizedresistance.Thephaseangleexpressesthebalancebetweencapacitiveandresistancecomponentsintheseriescircuit.Forapureresistance,φ=0;forapurecapacitance,φ=π/2;andformixtures,intermediatephaseanglesareobserved.第7頁ReviewofaccircuitsForimpedancesinparallel,theinverseoftheoverallimpedanceisthesumofthereciprocalsoftheindividualvectors.Sometimesitisadvantageoustoanalyzeaccircuitsintermsoftheadmittance,Y,whichistheinverseimpedance1/Z.第8頁EquivalentcircuitofacellInageneralsense,weoughttobeabletorepresentitsperformancebyanequivalentcircuitofresistorsandcapacitorsunderagivenexcitation.Theelementsofequivalentcircuitofacell:double-layercapacitance

Cd,faradaicimpedance

Zf,solutionresistance

Rs,chargetransferresistance

Rct,Warburgimpedance

Zw.第9頁AResistanceandcapacitanceinseriesfislow:fishigh:Inelectrochemicalcell:R=Rs:solutionresistanceC=Cd:doublelayercapacitanceElectrochemicalImpedanceSpectroscopy第10頁Aresistanceandcapacitanceinparallel(Randlescircuit)Z=RsathighfrequencyZ=Rct+RsatlowfrequencyElectrochemicalImpedanceSpectroscopy第11頁MixedkineticanddiffusioncontrolCdlorCPERPRWZWwith0n1ElectrochemicalImpedanceSpectroscopy第12頁AbstractthecellintoanequivalentcircuitmodelBeforestartingtofit,getgoodinitialguessvaluesUse?findcircle“optionUselinearregressiontoevaluateaWarburgimpedanceTakecareof:NonuniquenessofequivalentcircuitmodelsWeightingthedataElectrochemicalImpedanceSpectroscopyDataAnalysis:第13頁Cyclicvoltammograms(a)anddifferentialpulsevoltammograms(b)ofdifferentconcentrationsofferroceneontheGCelectrode,C(mmol/L):(1)0.2,(2)0.5,(3)1;scanrate:100mV/s第14頁Cyclicvoltammogramsof1mmol/LferroceneontheGCelectrode,Plotofoxidationpeakcurrent(Ip,a)vs.squarerootofscanrate(υ1/2)forferrocene

第15頁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)

forferrocene第16頁Left:Nyquistplotsof1mmol/LferroceneatdifferentpotentialsontherotatingGCelectrodeanditsfittingresults(solidline),E(V):■0.40,●0.45,▲0.50;rotationrate=900r/min;Right:thecorrespondingequivalentcircuit.

第17頁Left:Nyqui