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Tafelequation663●TTTafel,Julius(CourtesyofDr.KlausMüller)(June,,Choindez,Switzerland–Sep.,,Mu-nich,Germany)Tafelwasanorganicchemist(associ-atedwithHermannEmilFischerandLudwigKnorr)andphysicalchemist(workingwithOstwald,F.W.)[i–iii].Hestudiedelectrochemistryoforganiccompoundsandtherelationbetweenratesofelectrochemicalre-actionsandappliedoverpotentials[iv].HeisbestrememberedfortheTafelequation,anempiricallyfoundrelationconnectingthecurrentgeneratedinanelectrochemicalsystemwiththeappliedoverpotential.Tafelintroducedahydrogencoulometertomeasurechargespassingthroughelectrochemicalsystems.Also,hedemonstratedthathydrocarbonswithisomerizedstructurescanbegenerateduponelectrochemicalre-ductionoftherespectiveacetoaceticesters(namedTafelrearrangement).Refs.:[i]MüllerK()JResInstCatal,HokkaidoUniv:;[ii]Bock-risJO’M,ReddyAKN,Gamboa-AldecoM()Modernelectrochem-istry,ndedn.Fundamentalsofelectrodics,vol.A.Kluwer,NewYork,p;[iii]EmmertB()BerDeutChemGes:;[iv]TafelJ()ZElektrochem:EKTafelequationTafelobservedanempiricalrelation-shipbetweentheoverpotentialandthefaradaiccur-rent:ηct=A+Blgjct.()Thisequation(Tafelequation)isoffundamentalim-portanceinstudiesofelectrodekinetics.ItisactuallyanapproximationoftheButler–Volmerequationatsufficientlylargeoverpotentialsη.TheButler–Volmerequation(fordetailsandmeaningofsymbolsButler–Volmerequation)underconditionswherethereisnoef-fectofconcentrationgradientjct=jcexpαnFRTηct−exp−(−α)nFRTηct`()canbesimplifiedifoneofthetwoexponentialtermsbe-comessufficientlysmall;e.g.,incaseofananodicprocessatlargevaluesofη(η.nmV)thesecondtermbecomesnegligible;incaseofacathodicprocessesatasufficientlylargevalueofηthefirsttermvanishes.Thecorrespondingsimplifiedequationsareinthefirstcasejct=jPexpαnFRTηctQ()andinthesecondcasejct=−jcexp−(−α)nFRTηct`.()Thedependenceofthechargetransferoverpotentialηctonthechargetransfercurrentdensityjctcanbedescribedinsemilogarithmicformηct=RTαnF.logj−RTαnF.logjct()andηct=RT(−α)nF.logj−RT(−α)nF.logjct.()ThisformisequivalenttotheTafelequation.ItcloselyresemblesthegeneraltypeofanEq.().ThetermBiscalledTafelslope.Incaseofaone-electrontransferprocess(n=)atT=Candα=.followsB=mV.ConvenientlytheTafelequationisalsodisplayedaslgjct=lgj+α.RTηctandlgjct=lgj+(−α).RTηct.Refs.:[i]TafelJ()ZphysChem:;[ii]TafelJ()ZphysChem:;[iii]InzeltG()Kineticsofelectrochemicalreactions.In:ScholzF(ed)Electroanalyticalmethods,Springer,Berlin,pRH664Tafelplot●TTafelplot—PlotoflogjversusEorη.Incaseofapurelycharge-transfercontrolledcur-rentattheelectrodeoneelectrodeprocesswilldom-inatewhereastherespectiveback-reactioncontributesonlyanegligiblefractiontothetotalcurrent.Assumingthiscontributiontobe%theback-reactioncanbene-glectedatηnmVwithslopesBdependingonnandα.Atsmallervaluesofηdeviationswillappear:Tafelplot—Figure.Calculatedchargetransfercurrentdensityjasafunctionofoverpotentialηassumingatransfercoefficientα=.andanexchangecurrentdensityj=.Acm,and,insimplifiedformfortheanodicandcathodicbranch,respectivelyThedeviationcausedbythesimplificationsintheTafelequationbecomesobviousonlyatsmalloverpo-tentials.Inalogarithmicdisplay(Tafelplot)adifferentandmoreusefuldisplayresults.Tafelplot—Figure.Calculatedlogarithmofchargetransfercur-rentdensityjasafunctionofoverpotentialηassumingatransferco-efficientα=.andanexchangecurrentdensityj=.Acm,insimplifiedformfortheanodicandcathodicbranch,respectivelyBecausevaluesofnaremostly,rarely,theslopeoftheTafelplotyieldsthevalueofthechargetransfercoef-ficientα,theintersectionyieldstheexchangecurrentdensityj.Ref.:[i]TafelJ()ZphysChem:RHTafelregion—Partofthecurrentdensityvs.electrodepotentialrelationshipwhichcanbedescribedinsuffi-cientlygoodapproximationwiththeTafelequation.Partofthecurrentdensityvs.electrodepotentialrela-tionshipwhichcanbedescribedinsufficientlygoodap-proximationwiththeTafelequation.RHTafelreactionhydrogenTafelslopeTafelequationTaguchisensor—Theso-calledTaguchisensor(Tagushisensor)isaconductimetricsensorthatisusedtodetectreducinggases,suchascombustiblegasesandvolatileorganicvaporsinair.TheTaguchisensorisbasedonann-typesemiconductor(SnO),theelectronicconductanceofwhichincreasesdramaticallyinpresenceofreducinggasesatanoperatingtempera-tureofca.C.Taguchisensorsarefrequentlyusedinwarningsystemsinbothindustrialandhouseholdapplications.Ref.:[i]GöpelW,HesseJ,ZemelJN()Sensors–acomprehensivesurvey,vol..VCH,WeinheimJBTate’slawdropweightmethodTaube,Henry(©TheNobelFoundation)(Nov.,,Neudorf,Saskatchewan,Canada–Nov.,,PaoloAlto,USA)TaubestudiedattheUniver-sityofSaskatchewan,Saskatoon(B.S.,M.S.).Temkinisotherm665●THeobtainedhisPh.D.degreeattheUniversityofCali-fornia,Berkeleyinwherehespenttwoyearsasaninstructor.HemovedtoCornellUniversity(–),thenheworkedfortheUniversityofChicago(–)wherehebecameprofessor.FromhewasprofessorofStanfordUniversity.HereceivedtheNobelPrizeinChemistry“forhisworkonthemechanismofelec-tr