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Ultramicroelectrode(UME)687●UUUltracapacitor—Electrolyticcapacitorsofverylargecapacityemployinghigh-surface-areaelectrodema-terials(e.g.,activatedcarbonswithsurfaceareasofmg−orhigherorcarbonaerogelswithevenhigherspecificsurfacearea)arecalledsupercapaci-torsor–incaseofevenhighervolumetricand/orgravi-metriccapacity–ultracapacitor.Asbothtypesofcapaci-torsareessentiallybaseduponthecapacitivepropertyoftheelectrochemicaldoublelayertheonlydistinctivepropertyistheactualcapacityofadevice;whilesu-percapacitorhavetypicalcapacitiesintherangeofafewhundredmF,ultracapacitorshavecapacitiesofseveralF.Becauseoftheoperatingprinciplethevoltagewhichmightbeappliedtoanultracapacitormustremainbe-lowthedecompositionvoltageoftheelectrolytesolu-tion,oroftheemployedelectrodes,typicalvaluesare.to.V.Dependingontheelectrodematerialandtheelectrolytesolutionconstituentsbeyondmerecharg-ing/dischargingofthedouble-layerredoxprocessesin-volvingsaidmaterialmayoccur,thisresultsinapseu-docapacitancewhichcontributestotheoverallcapacityofthedevice.Becausetheredoxprocessesmayproceedatratessignificantlydifferentfromdouble-layercharg-ing,thebehaviorofthedevicebecomesmorecompli-catedintermsofcharging/dischargingtimes.Refs.:[i]DelnickFM,TomkiewiczM(eds)()Electrochemicalca-pacitors–proceedingsvolume–.TheElectrochemicalSociety,Pen-nington;[ii]ConwayBE()Electrochemicalsupercapacitors:scien-tificfundamentalsandtechnologicalapplications.Springer,NewYork;[iii]AshtianiC,WrightR,HuntG()JPowerSources:;[iv]ChuA,BraatzP()JPowerSources:RHUltramicroelectrode(UME)—anelectrodehavingacharacteristicdimensionlessthanμm.Thischar-acteristicdimensionreferstoadiameterforadisk,asphere,ahemisphere,andacylinder,andawidthforabandUME,forexample.Conceptually,thelowerlimitofthecharacteristicdimensionofaUMEisaboutnm,whichcorrespondstothethicknessofthedoublelayerorthesizeofmolecules.Electrodesofsuchdimensionsaresometimesreferredtoasnanoelectrodesornan-odes.Electrodeswithacharacteristicdimensionrang-ingfromμmuptoapproximatelymmarereferredtoasmicroelectrodes.Electrodeswithdimensionsofmillimeters,centimeters,ormetershavebeenreferredtoUltramicroelectrode(UME)—Figure.DiffusionregimesataninlaiddiskUMEfollowingapotentialstep.Fromlefttoright:lineardiffusionatshorttimes,quasi-hemisphericaldiffusionatintermediatetimes,hemisphericaldiffusionatlongtimesas“normal”,“conventional”,ormacroelectrodes.UMEsareabletoreadilyachievediffusionlayerswhicharelargerthantheircharacteristicdimensionandthisfea-tureconceptuallydistinguishesthemfrommicro-andmacroelectrodes.UMEsenjoyeaseoffabricationandcharacterization,andtheorydescribingtheirbehaviorunderavarietyofexperimentalconditionsiswelldevel-oped.Unlikemacroelectrodeswhichoperateundertran-sient,semi-infinitelineardiffusionconditionsatalltimes,UMEscanoperateinthreediffusionregimesasshownintheFigureforaninlaiddiskUMEfol-lowingapotentialsteptoadiffusion-limitedpotential(i.e.,theCottrellexperiment).Atshorttimes,wherethediffusion-layerthicknessissmallcomparedtothedi-ameteroftheinlaiddisc(left),thecurrentfollowstheCottrellequationandsemi-infinitelineardiffusionapplies.Atlongtimes,wherethediffusion-layerthick-nessislargecomparedtothediameteroftheinlaiddisk(right),hemisphericaldiffusiondominatesandthecur-rentapproachesasteady-statevalue.ThecharacteristicdiffusiontimeforanyUMEgeom-etrywherethetransitionfromsemi-infinitelineardiffu-sion(transient)tohemisphericalorsphericaldiffusion(steadystate)occursmaybegivenastdiffusion(criticaldimension)D688Ultrasound●UwhereDisthediffusioncoefficientoftheelectroactivespecies.Whentheexperimentaltimeismuchlessthantdiffusion,theUMEbehavesasaconventionalelectrodeandalltheoriesdevelopedforelectrochemicalmethodsatmacroelectrodesapply.Whentheexperimentaltimeismuchgreaterthantdiffusion,theoriesdevelopedforsteady-statetechniquesapply.Thetransitionregionbe-tweenthesetwolimitingregimesinvolvesmorecom-plicatedtheory,offersnoadvantage,andisgenerallyavoided.Thediffusion-limitedsteady-statecurrentatUMEsmaybewrittengenerallyasiss=nFAmOCOwherenisthenumberofelectronspassedpermoleofoxidizedspeciesO,FisFaraday’sconstant,COisthebulkconcentration,Aisthegeometricarea,andmOisthemasstransfercoefficient.ThefunctionalformofmOdependsontheUMEgeometryandis,forexam-ple:inlaiddisc,Dπro;hemisphere,Dro;sphere,Dro;whereDisthediffusioncoefficientandroistheradius.ThefluxofOtoaUMEbydiffusionisDCOroandquitelargeduetotheinversedependenceontheUMEradius.Thus,thecurrentatUMEsisrelativelyimmunetoconvectiveeffectssuchasstirringinthesolution.Asshownabove,thecurrentataUMEalsoreachesasteadystateinarelativelyshorttime(roD).Forexample,a-μmradiusdiskwillattainasteadystateinafractionofasecond.Becauseofthesmallcurrents,generallypAtonA,thatcharacterizemostexperimentswithUMEtips,resistivedropsinthesolutionduringthepassageofcur-rentaregenerallynegligible.Refs.:[i]BardAJ,MirkinMV(eds)()Scanningelectrochemicalmi-croscopy.MarcelDekker,NewYork,chap;[ii]BardAJ,FaulknerLR()Electrochemicalmethods,ndedn.Wiley,NewYork,chap;[iii]ZoskiCG(ed)(