Cyclicvoltammetryonelectrodesurfacescoveredwithpor

SensorsandActuatorsB133(2008)462–466ContentslistsavailableatScienceDirectSensorsandActuatorsB:Chemicaljournalhomepage::Ananalysisofelectrontransferkineticsatsingle-walledcarbonnanotubemodifiedelectrodesIanStreeter,GregoryG.Wildgoose,LidongShao,RichardG.Compton∗PhysicalandTheoreticalChemistryLaboratory,OxfordUniversity,SouthParksRoad,OxfordOX13QZ,UnitedKingdomarticleinfoArticlehistory:Received21January2008Accepted5March2008Availableonline22March2008Keywords:CarbonnanotubesThinlayerdiffusionCyclicvoltammetryHeterogeneousrateconstantsNumericalsimulationabstractCyclicvoltammetryisrecordedoftheoxidationofferrocyanideonaglassycarbonelectrodemodifiedwithmultiplelayersofsingle-walledcarbonnanotubes.Thecurrentresponseisinterpretedintermsofsemi-infiniteplanardiffusiontowardsthemacro-electrodesurfaceandintermsofoxidationoftheelectroactivespeciestrappedinpocketsinbetweenthenanotubes.Athinlayermodelisusedtoillustratetheeffectsofdiffusionwithinaporouslayer.Itisfoundthatasemi-infiniteplanardiffusionmodelaloneisnotappropriateforinterpretingthekineticsoftheelectrontransferatthiselectrodesurface.Inparticular,cautionshouldbeexercisedinrespectofcomparingvoltammetricpeak-to-peakpotentialseparationsbetweennakedelectrodesandnanotube-modifiedelectrodesfortheinferenceofelectrocatalysisviaelectrontransferviathenanotubes.©2008ElsevierB.V.Allrightsreserved.1.IntroductionThepioneeringworkofWangetal.[1]hasledtoextensivelit-erature[2–21]inwhichelectrodes,often,butnotalways,madeofglassycarbon,aremodifiedwithlayersofcarbonnanotubes,andusedtostudytheredoxbehaviourofmoleculesofinterest.TheuseofthesemodifiedelectrodeshasbeenreviewedinRefs.[22–24].Typically‘fasterelectrodekinetics’arereportedonthemodifiedelectrodesandthisiscommonlyinterpretedintermsof‘electro-catalysis’causedbythenanotubes.Thediagnosticcriterionforthefasterelectrodekineticsisoftensimplybasedonthepeak-to-peakpotentialseparationoftheforwardandreversewavesinthecyclicvoltammetricexperiment.However,suchacomparisonisonlyvalidifthemasstransportregimeforthenakedandmodifiedelectrodeisthesame.Typicallyitisnotandthepurposeofthepresentpaperistoexploretheimplicationsofthiscontrastfordeductionsof‘electrocatalysis’.Inthisworkweconsiderasubstrateglassycarbonelectrodemodifiedwithmultiplelayersofsingle-walledcarbonnanotubes(SWCNTs).SEMimageshaveshownthatmultiwalledcarbonnanotubesformbundleswhenlargequantitiesareabrasivelyimmobilisedonanelectrodesurface[25].Thesurfacecanthere-forebethoughtofasaporouslayerinwhichpocketsofsolution∗Correspondingauthor.Tel.:[phone];fax:[phone].E-mailaddress:[e-mail](R.G.Compton).aretrappedinbetweenmultiplelayersofnanotubes.Weproposethattheoxidationofelectroactivespecieswithintheporouslayercanbeapproximatelybutilluminatinglydescribedusingthemodelofathinlayercellofhighelectrodeareareflectingthelargesur-faceareaofthenanotubeswithintheporouslayer.Oxidationatthenakedelectrodecanbemodelledusingasemi-infiniteplanardiffusionmodel.ThesetwomodelsaredescribedindetailinSec-tion2,andwejustifytheirapproximateusetomodeltheSWCNTmodifiedGCelectrode.Fig.1showsacomparisonofcyclicvoltam-metrysimulatedusingthetwomodels.Bothsimulationsusethesamevaluesofheterogeneousrateconstant,k0,transfercoefficient,˛,diffusioncoefficient,D,potentialscanrate,,andspeciescon-centration,c,withinaButler–VolmermodelforelectrontransfercoupledtoFickiandiffusion.Thethinlayermodelpredictsasmallerpeak-to-peakseparationthanthesemi-infinitediffusionmodel.Ifthecurrentmeasuredatthenanotube-modifiedelectrodehasasig-nificantcontributionfromoxidationofspecieswithintheporouslayer,asmallerpeakseparationmaybeobserved.Thiscouldleadana¨ıveelectrochemistusingthesemi-infinitemodeltoinferanerroneouslylargek0fortheelectrontransfer.2.Theoryofthinlayerdiffusionandsemi-infinitediffusionThevoltammetricresponseofanaked,planarmacro-electrodeiswellknownandreadilyinterpretedusingasemi-infiniteplanardiffusionmodel[26,27].Inthisdiffusionalregime,thepeak-to-peakseparationisequalto2.218RT/Fforafastreversibleprocess,0925-4005/$–seefrontmatter©2008ElsevierB.V.Allrightsreserved.doi:10.1016/j.snb.2008.03.015I.Streeteretal./SensorsandActuatorsB133(2008)462–466463Fig.1.Comparisonoflinearsweepvoltammetryusingasemi-infiniteandthinlayerplanardiffusionmodels.Forbothmodels,k0=10−4cms−1;D=10−5cm2s−1;=0.1Vs−1;c=10−6molcm−3.Semi-infinitediffusionelectrodearea,A=1cm2;thinlayerarea,A=30cm2;thickness,l=1m.whereaslargerpeakseparationsareobservedwithsluggishelectrodekinetics.Inthelimitofelectrochemicalirreversibility,analyticalequationsdescribethedependenceofpeakseparationonk0.Forquasi-reversibleelectrontransfers,commercialsimulationpackagesareusedtomodelthepeakseparation[28].Inathinlayercell,aplanarworkingelectrodeandaplanarinsu-latingsurfaceareseparatedbyasmalldistance,l.Asmallvolumeofsolutionistrappedbetweenthesesurfacesinathinlayer.Inapotentialsweepexperiment,currentisdrawnastheelectrontrans-ferbecomeskineticallyandthermodynamicallyfavourable.Ifthelayerofsol