方波循环伏安法-经典

方波循环伏安法经典ANALCHEM2009,81,90419047CYCLICSQUAREWAVEVOLTAMMETRYOFSINGLEANDCONSECUTIVEREVERSIBLEELECTRONTRANSFERREACTIONSJOHNCHELFRICK,JRANDLAWRENCEABOTTOMLEYSCHOOLOFCHEMISTRYANDBIOCHEMISTRY,GEORGIAINSTITUTEOFTECHNOLOGY,ATLANTA,GEORGIA303320400INTHISREPORT,THEORYFORCYCLICSQUAREWAVEVOLTAMMETRYFORSINGLEANDCONSECUTIVEREVERSIBLEELECTRONTRANSFERREACTIONSISPRESENTEDANDEXPERIMENTALLYVERIEDTHEIMPACTOFEMPIRICALPARAMETERSONTHESHAPEOFTHECURRENTVOLTAGECURVEISEXAMINEDDIAGNOSTICCRITERIAENABLINGTHEUSEOFTHISWAVEFORMASATOOLFORMECHANISTICANALYSISOFELECTRODEREACTIONPROCESSESAREALSOPRESENTEDSINCETHISWAVEFORMEFFECTIVELYDISCRIMINATESAGAINSTCAPACITANCECURRENTS,CYCLICSQUAREWAVEVOLTAMMETRYWILLENABLEACQUISITIONOFMECHANISTICINFORMATIONATANALYTECONCENTRATIONLEVELSLOWERTHANTHATPOSSIBLEWITHCYCLICVOLTAMMETRYCYCLICVOLTAMMETRYHASBEENTHEELECTROCHEMICALMETHODOFCHOICEFORTHEEVALUATIONOFTHEMECHANISMOFELECTRONTRANSFERFORMORETHANFOURDECADES1,2ADVANTAGESOFTHISMETHODINCLUDETHEWIDEAVAILABILITYOFLOWCOSTINSTRUMENTATIONANDEXTENSIVETHEORYAVAILABLETOGUIDETHEEXPERIMENTALISTINTHEINTERPRETATIONOFEMPIRICALRESULTSTHESEADVANTAGESHAVECONTRIBUTEDTOITSWIDESPREADPOPULARITYESPECIALLYAMONGTHOSEWHOARENOTSPECIALISTSINELECTROCHEMISTRYNUMEROUSAPPLICATIONSOFTHISMETHODHAVEBEENPUBLISHEDHOWEVER,THISMETHODHASTWOSHORTCOMINGSFIRST,THEDETERMINATIONOFTHEMECHANISMOFTHESECONDOFTWOORMORECLOSELYSPACEDCHARGETRANSFERREACTIONSALONGTHEPOTENTIALAXISISOFTENDIFCULTTHISPOORRESOLUTIONISARESULTOFTHECURRENTVOLTAGEPEAKASYMMETRYSECOND,THECONCENTRATIONOFTHEANALYTEMUSTBEATLEAST10MFORTHEATTAINMENTOFRELIABLEMECHANISTICINFORMATIONEXCEPTWHENTHEANALYTEISCONNEDTOTHEELECTRODESURFACETHISLOWERCONCENTRATIONLIMITISNOTAREECTIONOFTHEPOORSENSITIVITYOFTHEMETHODBUTRATHERTHERESULTOFTHEHIGHCAPACITANCECURRENTRESULTINGFROMSWEEPINGTHEPOTENTIALLINEARLYWITHTIMESQUAREWAVEVOLTAMMETRYISANIMPORTANTELECTROANALYTICALMETHODINCOMPARISONTOBOTHLINEARSWEEPANDCYCLICVOLTAMMETRY,SQUAREWAVEVOLTAMMETRYHASAMUCHBROADERDYNAMICRANGEANDLOWERLIMITOFDETECTIONBECAUSEOFITSEFCIENTDISCRIMINATIONOFCAPACITANCECURRENTANALYTICALDETERMINATIONSCANBEMADEATCONCENTRATIONSASLOWAS10NMTHEAPPLICATIONOFSQUAREWAVETOPROBLEMSINANALYSISHASBEENCRITICALLYAUTHORTOWHOMCORRESPONDENCESHOULDBEADDRESSEDEMAILBOTTOMLEYGATECHEDU1ADAMS,RNELECTROCHEMISTRYATSOLIDELECTRODESMARCELDEKKERNEWYORK,19692BARD,AJFAULKNER,LRELECTROCHEMICALMETHODSFUNDAMENTALSANDAPPLICATIONS,2NDEDWILEYNEWYORK,2000101021/AC9016874CCC40752009AMERICANCHEMICALSOCIETYPUBLISHEDONWEB10/02/2009REVIEWED3,4THEORYTOGUIDEINTHEEVALUATIONOFCHARGETRANSFERMECHANISMSHASBEENDEVELOPEDBYODEA,OSTERYOUNG,ANDOSTERYOUNG58THEIRWORKDETAILSTHEEFFECTSOFRSTORDERKINETICCOMPLICATIONSANDNONPLANARORRESTRICTEDDIFFUSIONONTHESQUAREWAVEVOLTAMMOGRAMSTHEAPPLICATIONSOFTHISTHEORYFORMECHANISTICANALYSISHAVEBEENLIMITEDTHISMAY,INPART,BEDUETOBIASONTHEPARTOFNONSPECIALISTSAGAINSTTECHNIQUESTHATUTILIZEUNIDIRECTIONALPOTENTIALSWEEPSFORMECHANISTICANALYSISTHISBIASISBASEDONTHEPRESUMPTIONTHATTHESHAPEOFTHECURRENTVOLTAGECURVESISPRIMARILYDETERMINEDBYTHEELECTRODEREACTANTINTHISWORK,WEEXPLOREACOMPOSITEWAVEFORMFORTHEEVALUATIONANDIDENTICATIONOFELECTRONTRANSFERMECHANISMS,IE,CYCLICSQUAREWAVEVOLTAMMETRY9,10THISWAVEFORMUTILIZESASQUAREWAVEWHICHSTEPSTHROUGHTHEREGIONOFTHEFORMALPOTENTIALOFTHEELECTROACTIVESPECIESUNDERSTUDYINTWODIRECTIONSALTHOUGHTHEREISSTRONGLITERATUREPRECEDENTFORCYCLICPULSETECHNIQUES,1117ONLYAFEWREPORTSONCSWVHAVEAPPEARED9,10,16,1828WEBELIEVE3HAWLEY,MDINLABORATORYTECHNIQUESINELECTROANALYTICALCHEMISTRYKISSINGER,PT,HEINEMAN,WR,EDSMARCELDEKKERNEWYORK,1984PPCH17ANDREFERENCESTHEREIN4OSTERYOUNG,JGOSTERYOUNG,RAANALCHEM1985,57,101A102A,105A106A,108A,110A5ODEA,JJOSTERYOUNG,JLANE,TJPHYSCHEM1986,90,27616ODEA,JJOSTERYOUNG,JOSTERYOUNG,RAANALCHEM1981,53,6957017ODEA,JJOSTERYOUNG,JOSTERYOUNG,RAJPHYSCHEM1983,87,391139188ODEA,JJWIKIEL,KOSTERYOUNG,JJPHYSCHEM1990,94,362836369CHEN,XPU,GANALLETT1987,20,1511151910XINSHENG,CGUOGANG,PANALLETT1987,20,151111DRAKE,KFVANDUYNE,RPBOND,AMJELECTROANALCHEM1978,89,23124612ECCLES,GNPURDY,WCCANJCHEM1987,65,1795179913ECCLES,GNPURDY,WCCANJCHEM1987,65,1051105714MIAW,LHLBOUDREAU,PAPICHLER,MAPERONE,SPANALCHEM1978,50,1988199615MIAW,LHLPERONE,SPANALCHEM1979,51,1645165016RAMALEY,LTAN,WTCANJCHEM1987,65,1025103217RYAN,MDJELECTROANALCHEM1977,79,10511918CAI,PMIAO,WMO,JZHANG,RFENXICESHIXUEBAO1995,14,333819CAMACHO,LRUIZ,JJSERNA,CMOLINA,AGONZALEZ,JJELECTROANALCHEM1997,422,556020ECCLES,GNCRITREVANALCHEM1991,22,34538021MIAO,WMO,JCAI,PZHANG,RFENXICESHIXUEBAO1995,14,1522MO,JCAI,PLU,ZZHANG,RZOU,YFENXIHUAXUE1995,23,25025423MO,JMIAO,WCAI,PZHANG,RFENXICESHIXUEBAO1993,12,162024MO,JMIAO,WCAI,PZHANG,RFENXICESHIXUEBAO1995,14,1625MO,JZHANG,RLU,ZCAI,PZOU,YFENXIHUAXUE1995,23,25525826PU,GCHENG,XWANG,EYINGYONGHUAXUE1987,4,313627PU,GCHENG,XWANG,EYINGYONGHUAXUE1988,5,323728PU,GWU,SCHENG,XZHONGGUOKEXUEJISHUDAXUEXUEBAO1986,16,365366,364ANALYTICALCHEMISTRY,VOL81,NO21,NOVEMBER1,20099041FIGURE1CYCLICSQUAREWAVEVOLTAMMETRICWAVEFORMUSEDTHROUGHOUTTHISSTUDYTHEUSEOFTHISWAVEFORMMERITSCONSIDERATIONFORSEVERALREASONSFIRST,THEUTILIZATIONOFTHESQUAREWAVEPOTENTIALWAVEFORMANDTHEDISCRETECURRENTSAMPLINGREGI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COMPUTETHEORETICALVOLTAMMOGRAMSFORCSWV,WEMODIEDODEASSWVPROGRAMFORAREVERSIBLEREACTION,INCORPORATINGREVERSESWEEPPOTENTIALSCYCLICSQUAREWAVEVOLTAMMOGRAMSWERECALCULATED,ANDTHEEFFECTSOFTHESTEPTIME,STEPHEIGHT,SWITCHINGPOTENTIALANDPULSEHEIGHTONTHEPEAKCURRENTS,PEAKPOTENTIALS,PEAKWIDTHS,PEAKCURRENTRATIO,ANDPEAKSEPARATIONSWEREINVESTIGATEDANDAREITEMIZEDBELOWEFFECTOFSTEPTIMETHECURRENTONEACHSTEPORPULSEISRELATEDTOSTEPTIMEBYITTNFAD1/2COT1/24WHEREITISTHECURRENTATTIMETMA,TISTHECURRENTFUNCTIONATTIMET,NISTHENUMBEROFELECTRONSTRANSFERRED,FISTHEFARADAY,AISTHEELECTRODEAREACM2,DISTHEDIFFUSIONCOEFCIENTCM2/S,C0ISTHEBULKCONCENTRATIONOFOXMOL/L,ANDTISTHESTEPTIMESTHUS,THEPEAKCURRENTWILLDECREASEWITHT1/2SINCETHECURRENTISSAMPLEDATTHEENDOFTHESTEPANDTHESTEPTIMEISCONSTANTTHROUGHOUTTHESWEEP,THEPEAKCURRENTONTHEFORWARDANDREVERSESWEEPSWILLBEEQUALLYAFFECTEDTHEREFORE,THEPEAKRATIOWILLREMAINUNITYREGARDLESSOFSTEPTIMETHEPEAKWIDTHSATHALFHEIGHTAREALSOUNAFFECTEDWITHSTEPTIMELIKEWISE,THESTEPTIMEHASNOEFFECTONTHEPEAKPOTENTIALSTHUS,THESTEPTIMEISONEFACTORTHATCANBEUTILIZEDTOINCREASETHEPEAKCURRENTWITHOUTINCREASINGTHEPEAKWIDTHTHEREVERSIBLEMECHANISMISTHEONLYMECHANISMINWHICHTHEPEAKRATIO,POTENTIALS,ANDWIDTHSAREUNAFFECTEDBYTHESTEPTIMEEFFECTOFSTEPHEIGHTTHESWEEPRATEFORSQUAREWAVETECHNIQUESISGIVENBYSTEPHEIGHTDIVIDEDBYSTEPTIMEINCREASINGTHESTEPHEIGHTTHEREFOREINCREASESTHESWEEPRATEINCYCLICVOLTAMMETRYTHEPEAKCURRENTFORDIFFUSIONCONTROLLEDPROCESSESINCREASESWITHTHESQUAREROOTOFTHESWEEPRATEINCSWV,THEMAXIMUMOFTHEDIMENSIONLESSDIFFERENCECURRENT,PK,FORPK,R,DECREASESSLIGHTLYWITHINCREASINGSTEPHEIGHTANINCREASEINSTEPHEIGHTDECREASESTHEPOTENTIALDIFFERENCEBETWEENTHESTEPANDPULSEPOTENTIALSAND,CONSEQUENTLY,DECREASESTHEDIFFERENCECURRENTASILLUSTRATEDINFIGURE2FOREXAMPLE,WHENTHESTEPHEIGHTISVARIEDFROM230MVWHILETHEPULSEHEIGHTISHELDCONSTANTAT100MV,THEDECREASEINPK,FDECREASESFROM1344ATASTEPHEIGHTOF2MVTO1260AT25MVPK,RBEHAVESSIMILARLYTHEPEAKRATIOPK,R/PK,FREMAINSUNITYTHROUGHOUTTHERANGEOFSTEPHEIGHTSINVESTI35SMITH,DEANALCHEM1963,35,60260936NICHOLSON,RSOLMSTEAD,MLINELECTROCHEMISTRYCALCULATIONS,SIMULATIONANDINSTRUMENTATIONMATTSON,JS,MARKS,HB,MACDONALD,HC,EDSMARCELDEKKERNEWYORK,1972VOL2,PPCH5FIGURE2IMPACTOFPULSEA,STEPB,ANDDIFFERENCECCURRENTSASSTEPHEIGHTISINCREASEDSOLIDLINE5MVDOTTEDLINE15MVDASHEDLINE25MVFIGURE3EFFECTOFSTEPHEIGHTONTHENUMBEROFPOINTSDENINGPEAKPOTENTIALSGATEDTHISTRENDCOMPARESWITHTHATFOUNDINCVWHEREFORAREVERSIBLEMECHANISMTHEPEAKRATIOISUNITYREGARDLESSOFSWEEPRATE37OSTERYOUNG33HASSHOWNTHATTHEPEAKPOTENTIALSINSWVAREEQUALTOTHEFORMALPOTENTIALFORAREVERSIBLECHARGETRANSFERPROCESSSTUDIEDBYCSWV,BOTHTHEFORWARDANDBACKWARDPEAKPOTENTIALSAREINDEPENDENTOFPULSEAMPLITUDE,STEPTIME,ANDSWITCHINGPOTENTIALTHEPEAKPOTENTIALSAREALSOINDEPENDENTOFSTEPAMPLITUDESOLONGASASUFCIENTNUMBEROFSAMPLINGSARETAKENTOADEQUATELYDENETHECURRENTVOLTAGECURVETHUS,STEPHEIGHTISLIMITEDEXPERIMENTALLYTOABOUT2530MVATLARGERSTEPHEIGHTS,THENUMBEROFDATAPOINTSDENINGTHEPEAKBECOMESSMALLTHISISSHOWNGRAPHICALLYINFIGURE3ASWELLASBEINGAESTHETICALLYUNPLEASING,LARGESTEPHEIGHTSLEADTOGREATERUNCERTAINTYINPEAKCURRENTANDPOTENTIALMEASUREMENTFORTHE37NICHOLSON,RSSHAIN,IANALCHEM1964,36,706723ANALYTICALCHEMISTRY,VOL81,NO21,NOVEMBER1,20099043FIGURE4IMPACTOFPULSEHEIGHTONTHESHAPEOFTHECYCLICSQUAREWAVEVOLTAMMOGRAMPULSEHEIGHTAD100,80,60,AND40MV,RESPECTIVELYFIGURE5IMPACTOFPULSEHEIGHTONPEAKWIDTHFORBOTHTHEFORWARDAANDREVERSEBSWEEPSREVERSIBLEMECHANISM,EPK,FANDEPK,REQUALE0ANDAREINVARIANTWITHCHANGESINSTEPHEIGHTHOWEVER,THEPEAKWIDTH,W1/2,DECREASESSLIGHTLYFORTHEPEAKSONBOTHTHEFORWARDANDREVERSESWEEPSWITHINCREASINGSTEPHEIGHTFOREXAMPLE,THEW1/2ISONLYABOUT7MVASTHESTEPHEIGHTINCREASESFROM2TO20MVEFFECTOFPULSEHEIGHTASERIESOFCALCULATEDVOLTAMMOGRAMSINWHICHTHEPULSEHEIGHTISVARIEDISSHOWNINFIGURE4THEINDIVIDUALPEAKCURRENTSINCREASEPROPORTIONATELYWITHEPULSETHEPEAKCURRENTRATIOISEQUALTOUNITYANDINDEPENDENTOFEPULSEASLONGASEPULSEESTEPASEPULSEAPPROACHESESTEP,EPK,FSHIFTSTONEGATIVEPOTENTIALSANDEPK,RSHIFTSTOPOSITIVEPOTENTIALSEG,ATANEPULSEOF20MVANDANESTEPOF10MV,THESEPARATIONBETWEENEPK,FANDEPK,RISONLY4MVTHISTRENDHASBEENREPORTEDBYPREVIOUSWORKERSUSINGTHESAMETHEORY16WHENEPULSEESTEP,ASTAIRCASEPOTENTIALWAVEFORMRESULTSANDANONZEROPEAKSEPARATIONISEXPECTEDTHUS,EPULSESHOULDBEMAINTAINEDATASUFCIENTLYLARGEVALUEEPULSE5ESTEPTOENSURETHATANYPEAKPOTENTIALSEPARATIONISTHERESULTOFCHEMICALORELECTRONTRANSFERKINETICSUNDERTHATCONDITION,EPKFORTHEREVERSIBLEMECHANISMISINDEPENDENTOFEPULSEFIGURE5DEPICTSTHEDEPENDENCEOFW1/2ONEPULSEASEPULSEINCREASES,THEPOTENTIALOFTHEPULSECROSSESTHEFORMALPOTENTIAL9044ANALYTICALCHEMISTRY,VOL81,NO21,NOVEMBER1,2009FIGURE6EFFECTOFSWITCHINGPOTENTIALONSHAPEOFTHECYCLICSQUAREWAVEVOLTAMMOGRAMESWE0160MVA120MVB80MVC40MVDEARLIERINTHESWEEP,RESULTINGINLARGERPULSEANDSTEPCURRENTSANDTHEREFORELARGERIVALUESEARLIERINTHESWEEPCONSEQUENTLY,LARGEVALUESOFEPULSEINCREASESW1/2ANDMAYRESULTINPOORRESOLUTIONOFTWOCLOSELYSPACEDPEAKSALONGTHEPOTENTIALAXISVIDEINFRASINCETHEMAJOREFFECTOFCHANGESINEPULSEAREONIANDW1/2,THEMAINCONSIDERATIONWHENSELECTINGPULSEHEIGHTISTOOBTAINANADEQUATELYLARGESIGNALTONOISERATIOWHILEMINIMIZINGW1/2OSTERYOUNGANDODEAHAVEFOUNDTHATFORTHEREVERSIBLEMECHANISM,THEMAXIMUMPEAKCURRENTTOWIDTHRATIOOCCURSATAPULSEHEIGHTOF100MVFORA25,10,OR25MVSTEPANDAONEELECTRONTRANSFER33EFFECTOFSWITCHINGPOTENTIALASERIESOFVOLTAMMOGRAMSINWHICHTHESWITCHINGPOTENTIALISVARIEDISSHOWNINFIGURE6VARIATIONOFSWITCHINGPOTENTIALIMPACTSONLYTHEREVERSESWEEPNOTETHATIPK,FREMAINSCONSTANT,WHILEIPK,RHASDECREASEDBYLESSTHAN1WHENTHESWITCHINGPOTENTIALISONLY40MVPASTTHEFORMALPOTENTIALTHEPEAKRATIODECREASESBYLESSTHAN1WHENTHESWITCHINGPOTENTIALISASLITTLEAS20MVPASTTHEFORMALPOTENTIALSIMILARLY,THEPEAKPOTENTIALSAREINDEPENDENTOFSWITCHINGPOTENTIALATVALUESGREATERTHANONEHALFTHEPULSEHEIGHTTHUS,THESWITCHINGPOTENTIALMAYBEGREATERTHANOREQUALTOE0EP/2WITHOUTINTRODUCTIONOFARTIFACTSTHEREVERSIBLEMECHANISMISTHEONLYONEEXAMINEDINWHICHTHESWITCHINGPOTENTIALHASNOVISIBLEEFFECTONTHEVOLTAMMOGRAMSDIAGNOSTICCRITERIAFORTHEREVERSIBLEMECHANISMAREGIVENINTABLE1NOTETHATWEHAVEALSOEXAMINEDTHEIMPACTOFHETEROGENEOUSELECTRONTRANSFERKINETICSASWELLASTHEIMPACTOFCOUPLEDCHEMICALREACTIONSONBOTHSINGULARANDCONSECUTIVEELECTRONTRANSFERREACTIONSTHEMECHANISTICCRITERIAFORTHEIDENTICATIONOFTHESEELECTRONTRANSFERMECHANISMSFROMCSWVDATADIFFERSIGNICANTLYFROMTHATLISTEDINTABLE1MANUSCRIPTSDESCRIBINGTHESEWILLBEFORTHCOMING29EXPERIMENTALVERICATIONTWOWELLKNOWNREVERSIBLEREDOXCOUPLESWERESELECTEDTOCOMPARETHEORYANDEXPERIMENTTHEREDUCTIONOFTIIVTOTIIIIANDCDIITOCD0IN01MOXALICTABLE1DIAGNOSTICCRITERIAFORAREVERSIBLEELECTRODEREACTIONBYCSWVWAVEFORMPARAMETERSEMPIRICALVARIABLESTEPHEIGHT,ESSTEPTIMESWITCHINGPOTENTIAL,ESWPULSEHEIGHT,EPAPEAKCURRENTSIPK,FANDIPK,RDECREASEWITHINCREASINGESIPK,FANDIPK,RDECREASEWITHINCREASINGSTEPTIMEINDEPENDENTOFESWPEAKRATIOSAPEAKPOTENTIALSPEAKSEPARATIONPEAKWIDTHSEQUALSUNITYATALLESVALUESINDEPENDENTOFESEQUALSZEROATALLESVALUESINDEPENDENTOFESEQUALSUNITYATALLSTEPTIMESINDEPENDENTOFSTEPEQUALSZEROATALLSTEPTIMESINDEPENDENTOFSTEPTIMETIMEINDEPENDENTOFESWINDEPENDENTOFESWEQUALSZEROATALLESWVALUESEQUALSZEROATALLEPVALUESW1/2INCREASESWITHEPIPK,FANDIPK,RINCREASEWITHEPEQUALSUNITYATALLEPVALUESINDEPENDENTOFEPPEAKRATIOSFORCHEMICALLYCOUPLEDELECTRONTRANSFERREACTIONSDEVIATEFROMUNITYBPEAKPOTENTIALSEPARATIONSFORKINETICALLYCONTROLLEDELECTRONTRANSFERREACTIONSARELARGERTHANZEROFIGURE7THEORETICALLINEANDEXPERIMENTALSQUAREVOLTAMMOGRAMSFORTIIV/TIIIICOUPLEEP100A80B60C40MVDACIDATAHANGINGMERCURYDROP38TESTSOLUTIONSWERE001MMINEITHERTICL4ORCDNO32AND01MINOXALICACIDAPARCMODEL303AMERCURYELECTRODESTANDWASUSEDTOPROVIDEAHANGINGMERCURYDROPWORKINGELECTRODEFIGURE7SHOWSTHEEXCELLENTAGREEMENTFOUNDBETWEENEXPERIMENTALANDTHEORETICALVOLTAMMOGRAMSEACHVOLTAMMOGRAMDEPICTEDISTHERAWDATAOBTAINEDDURINGTHERSTSWEEPONANEWDROPDATACOLLECTEDFORBOTHREDOXCOUPLESWERECONSISTENTWITHTHEDIAGNOSTICCRITERIAPRESENTEDINTABLE1FORAREVERSIBLEELECTRODEREACTIONITSHOULDBENOTEDTHATOURTHEORETICALVOLTAMMOGRAMSARECOMPUTEDFROMAPLANARDIFFUSIONMODELATTHEHANGINGMERCURYDROPELECTRODE,HOWEVER,RADIALDIFFUSIONISTHEMODEOFTRANSPORTANDSLIGHTLYLARGERCURRENTSAREBOTHANTICIPATEDANDOBSERVEDWECHOSETHESEREDOXSYSTEMSSPECICALLYTOEVALUATETHEEMPIRICALPARAMETERTRE