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APPLICATIONOFLISSAJOUSPLOTSTOIDENTIFYNON-STATIONARYBEHAVIORIN IMPEDANCESPECTROSCOPY By LIURUIDONGZOU ATHESISPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF MASTEROFSCIENCE UNIVERSITYOFFLORIDA 2020
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2020LiuruidongZou 2
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Dedicatedtomyfamily 3
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ACKNOWLEDGEMENTS Duringmy2yearsstudyattheUniversityofFloridaIlearnedtoappreciateallmembersof thefacultyandstaffintheDepartmentofChemicalEngineering,andIwouldliketoexpressmy specialappreciationtoProf.Orazemforhisguidancetomyresearch.IwouldliketothankYou ChenforhishelpaboutleadingmehowtouseGamry r Frameworkandanalyzingtheimpedance data.Finally,Iwouldliketoconveymydeepappreciationtomyparentswhomarealwaysbymy sidetoencouragemetofacethechallenges. 4
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TABLEOFCONTENTS page ACKNOWLEDGEMENTS.................................................................4 LISTOFSYMBOLS.......................................................................6 ABSTRACT...............................................................................7 CHAPTER 1INTRODUCTION.....................................................................8 1.1BriefHistoryofImpedanceSpectroscopy..........................................8 2BACKGROUND.....................................................................10 2.1APrimaryInsightofLissajousFigures............................................10 2.2BriefIntroductionoftheMeasurementModel.....................................10 2.3ExperimentalDesign.............................................................11 2.3.1VisualizationofimpedancedatabyLissajousplots...........................11 2.3.2Steeldiskelectrodeinsodiumchlorideelectrolyte...........................12 2.3.3Titaniumalloydiskelectrodeinsodiumchlorideelectrolyte..................13 2.3.4RedQuantum-LightEmittingDiode.........................................14 2.4AnalysisMethods................................................................14 2.4.1ImpedanceMeasurementProtocol...........................................15 2.4.2Kramers-Kronigrelations...................................................16 3RESULTSANDDISCUSSION.......................................................17 3.1ExperimentalResults............................................................17 3.1.1Metaldiskelectrodes.......................................................17 3.1.2Red5AQD-LED...........................................................18 3.1.3RedQD-LEDmodied.....................................................23 3.2SimulationModelResults........................................................23 3.2.1Steelelectrodemeasurementmodelresults..................................28 3.2.2Titaniumalloyelectrodemeasurementmodelresults.........................28 3.2.3Red5AQD-LEDdevicemeasurementmodelresults.........................28 4CONCLUSIONS.....................................................................34 REFERENCES............................................................................34 BIOGRAPHICALSKETCH...............................................................37 5
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LISTOFSYMBOLS Romans A Thecurrentnodeofelectricbridgecircuit,seeFigure1-1. B Thecurrentnodeofelectricbridgecircuit,seeFigure1-1. C Theparallelcapacitance,seeEquation2-1. C Thecurrentnodeofelectricbridgecircuit,see Figure1-1. CPE Constantphaseelements,seeFigure1-2. CE CounterelectrodeofPotentiostat,seeFigure1-2. D Thecurrentnodeofelectricbridgecircuit,seeFigure1-1. f frequency,f= w n 2 p ,Hz. I m Themeasuredcurrent,seeFigure3-2. j imaginarynumber,j=p )]TJ/F27 11.9552 Tf 9.289 0 Td [(1. REF ReferenceelectrodeofPotentiostat,seeFigure1-2. R e Controlohmicresistance,seeEquation2-1. R t Parallelohmicresistance,seeEquation2-1. R 1 Thecontrolohmicresistanceofconstantvalueinput,seeFigure1-2. R 2 Thecontrolohmicresistanceofoscillatinginput,seeFigure1-2. R 0 Theohmicresistanceparalleledwiththeamplier,seeFigure1-2. V + Thepotentialinputfromvoltageadder,seeFigure1-2. T Timevaluesrecordedduringexperiments,seeFigure3-2. V f Theforwardpotentialrecordedduringexperiments,seeFigure3-2. V supply Theappliedpotentialtotheelectricbridgecircuit,see Figure1-1. V out + ThepotentialvalueatnodeB,seeFigure1-1. WE WorkingelectrodeinPotentiostat,seeFigure1-2. V out )]TJ/F27 11.9552 Tf 35.845 -0.046 Td [(ThepotentialvalueatnodeD,seeFigure1-1. Z j Theimaginarypartofimpedance,seeFigure3-15. Z r Therealpartofimpedance,Figure3-15. Z j ; data Theoriginalexperimentalimpedance,seeFigure3-15. Z r ; data Theoriginalexperimentalimpedance,seeFigure3-15. Greeks a CPEexponent,seeEquation2-2,dimensionless. j phaselag,seeEquation2-16. w angularfrequency, w =2 p f,s )]TJ/F27 8.9664 Tf 6.967 0 Td [(1 . 6
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AbstractofThesisPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofMasterofScience APPLICATIONOFLISSAJOUSPLOTSTOIDENTIFYNON-STATIONARYBEHAVIORIN IMPEDANCESPECTROSCOPY By LiuruidongZou May2020 Chair:MarkE.Orazem Major:ChemicalEngineering ElectrochemicalimpedancespectroscopyEISisapowerfultoolusedtoidentifythe propertiesofelectrochemicalsystems.Thetechniqueinvolvesmeasuringthe frequency-dependenttransferfunctionthatrelatestheinputpotentialandoutputcurrent.The impedancemeasurementcanbeinuencedbyartifactsincludingnon-stationarybehaviorthat causethedatatobeinconsistentwiththeKramers-Kronigrelations.Whilepost-processingof measureddatabyapplicationofthemeasurementmodelcandetectlackofconsistencywiththe Kramers-Kronigrelations,itwouldbeusefultohaveamethodthatcandetectnon-stationary behaviorasthemeasurementisbeingmade. Theobjectiveofthisthesiswastoexplorethesuitabilityofinstantaneouslymeasured Lissajousguresforidentifyingnon-stationarybehavior.AscriptwrittenbyProf.BurukUlgut wasusedtoobtainaveragedandinstantaneousLissajousplotsfortheimpedancemeasurements ofasteelelectrode,atitaniumalloyelectrode,andredquantum-dotlightemittingdiodes providedbyNanophotonica.TheinstantaneousLissajousplotswereshowntobesensitiveto nonstationarybehavior,evenwhentheaveragedLissajousplotsuggestedstationarybehavior. InstantaneousLissajousplotswereshowntoprovideasimplemannerbywhichnon-stationary behaviorcouldbedetectedduringthecourseofanimpedancemeasurement.Comparisontouse ofameasurementmodeltoassessconsistencywiththeKramers-Kronigrelationstomeasured spectrashowedthattheinstantaneousLissajousplotscoulddetectnon-stationarybehaviorunder conditionsforwhichthemeasurementmodelgaveinconclusiveresults. 7
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CHAPTER1 INTRODUCTION 1.1BriefHistoryofImpedanceSpectroscopy Theelectrochemicalimpedancespectroscopyisawidelyusedmethodtomeasureandto examinetheelectrochemicalpropertiesofdevices.Inthe19thcentury,theconceptofimpedance spectroscopywasrstintroducedbyOliverHeaviside[14]whodenedthetermsofinductance andcapacitance.In1894,Nernst[13]beganhisworksfocusedonmeasuringthedielectric constantsfortheliquidformselectrolyteswithelectricalbridgesdesignedbyWheatstone[16]. Figure1-1showsthefoundationofwheatstoneelectricalbridge. Afterdevelopmentforoveracentury,nowthepublicationsthatrefertoelectrochemical impedancespectroscopynumberalmost10,000peryear,showingtheincreasingimpactof impedancespectroscopy.Impedancespectroscopyhasbeenwidelyusedinavarietyofeldssuch asnewtypebatteryresearch,metalcorrosion,andmanyotherelds.Figure1-2showsthe universalschemeofimpedancemeasurementinstrumentationwhichcalledpotentiostat.The potentiostatforEISisdesignedtokeepthevoltagebetweentheworkingelectrodeandthe referenceelectrode,theexperimentaldesignwillbeintroducedinlaterchapters.Filderetal.[5] hadintroducedhisapplicationandoriginalinventionofpotentiostatinhispaper.Intheschemeof EISpotentiostatismadeupwiththreeparts:1thevoltageadderconnectedwiththevoltage controlstation,enablingtheexperimentaliststoapplysinusoidalsignalstotargetsdevices.2The mainpartofpotentiostat,thesignalproducedbythevoltageadderisbeensenttothenoninverting leadoftheamplier,theinvertleadoftheamplierisconnectedtothereferenceelectrode.3 Finallythesignalcomingoutfromtheworkingelectrodeandbeensenttothecurrentfollower whichmeasuringthecurrentvaluesusedforanalyzing,thecurrentfollowerconsistedwitha currentamplierandaparallelohmresistance. 8
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a Figure1-1.Theschematicofawheatstonebridgewhichappliedformeasuringanunknown electricalresistancebybalancingtheresistancesoftwoparallelcircuits. a b c Figure1-2.TheguresinseriesrepresentatypicalEISpotentiostatformlefttoright.Line2of voltageadderisconnectedtotheamplierofPotentiostatandtheoutletofworking electrodeislinkedtothenegativesideofamplierofthecurrentfollower. 9
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CHAPTER2 BACKGROUND 2.1APrimaryInsightofLissajousFigures LissajousgureswereintroducedbyJulesAntoineLissajoustocombinetwosimple harmonicmotions[10].HowellandPernicka[8]showedtheirmathematicaltrajectorystateswork towardstherestrictedthree-bodyproblems.Ingeneral[6],iftwovariablesareundergoingsimple harmonicmotions,toshowtherelationsbetweenweareabletouseLissajousgurestoclarifyit. FortheEISmeasurement,whenapplyingthealternatingcurrenttothesystem,duetothe directionschangingofthecurrentow,thealternatingcurrentshouldbeconsideredassimple harmonicmotions,sothatfortheanalyzingsteps,itisnecessarytouseLissajousgurestoshow therelationbetweenthealternatingcurrentandalternatingvoltage.HashimotoandNagano[7] hadshowedthegreatpotentialLissajousguresanalyzationowesincelldistributionresearch. Jiangetal.[9]alsomakeagreateffortaboutinvestigatingtheapplicationofLissajousguresin electricaldiagnosticsresearch. 2.2BriefIntroductionoftheMeasurementModel Sincetheelectrochemicalimpedancespectroscopymeasurementisnotreplicableduetothe currentowbehaviorcannotbepreciselycontrolled,themeasurementmodelcodewas introducedbyOrazemandhiscollaborators[1,2,3].Generallyspeaking,themeasurement model[17,18]isdesignedtomakearobustdescriptionofunknownsystemandtobuildaproper errorstructureofthesystemthatmakestheimpedancemeasurementresultsmorereliable.Unlike otherkindofmeasurementslikeopticalspectroscopyorelectricalspectroscopy,the electrochemicalimpedancespectroscopyisnotabletodoreplicableexperimentswhichareuseful Figure2-1.TheschematicofaVoigtseries,thetopcircuitsresistancesparalleledwith capacitancesaswellthebottomcircuitsparalleledwithCPEs. 10
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forthewholeerrorstructures.ThemeasurementmodelisinherentlyconsistentwiththeKramersKronigrelations,whichwillbeintroducedlater.Thecomplexcircuitmodelcanbesimpliedtoa moreordinaryoneswhichisrepresentedasVoigtseries.AseriesofVoigtmodelcanbe representedasaohmicresistancefollowedbymultinumbersofcircuitscomposedwithaohmic resistanceparallelwithacapacitanceoraconstantphaseelementCPE.Theimpedance representationofaseriesofVoigtelementscanberepresentedas: Z = R e + n = 1 R t 1 + j w R t C -1 or Z = R e + n = 1 R t 1 + j w a R t Q -2 Aftertheregressionmodelwassetup,tosuccessfullybuilduparegressionmodelaleast-squares regressioninvolvesminimizationcanbeintroducedasformat[14]: c = p S p = N dat i = 1 y i )]TJ/F74 11.9552 Tf 10.949 -0.882 Td [( N p k = 1 P k X k x i s i -3 wherewithageneralfunctionmodel y x = N p k = 1 P k X k x -4 SothatasEquation2-3shows,intheequationy i standsforthemeasuredvaluesand s i represents thepositivesquarerootofstandarddeviationofmeasurementi.Theleast-squaresequationlink themeasurementvaluesandsimulationmodels. 2.3ExperimentalDesign 2.3.1VisualizationofimpedancedatabyLissajousplots Theexperimentsweredesignedtoinducenonstationarybehavior.Forthemetalelectrodes, anonstationarybehaviorwasinducedbyapplyingacathodicpotentialthatwasintendedto reducethenativeoxidelayer.Impedancemeasurementswerethenperformedattheopen-circuit potentialasthesystemapproachedasteady-statebehavior. 11
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2.3.2Steeldiskelectrodeinsodiumchlorideelectrolyte Theexperimentaldevicecomprisedwithasteeldiskelectrodecoatedwithplasticcovering actedasworkingelectrode,aTimeshwhichworkingareawas1centimetersquareactedasthe counterelectrode.Boththeworkingandcounterelectrodesareplacedintothe1mol/Lsodium chloridesolutionwhichactedaspHneutralelectrolyte.Themainelectrochemicalreactionsfor thecathodicandanodicelectrodesare: Fe ! Fe 2 + + 2 e )]TJ/F27 11.9552 Tf 174.558 -4.937 Td [(-5 2 H 2 O + O 2 + 4 e )]TJ/F67 11.9552 Tf 10.121 -4.937 Td [(! 4 OH )]TJ/F27 11.9552 Tf 150.408 -4.937 Td [(-6 Equation2-5showsthemainanodicreactionandEquation2-6showsthemaincathodicreaction, respectively.Fortheopencircuitsystem,beforecathodicvoltagewasbeenaddedtotheworking electrode,duetotheformationofironionsandthehydroxidegroupsthesurfaceofthesteeldisk electrodewillbecoveredbyathinironoxidelm.Thecomponentsofoxidelmsarecomplex, butitcanstillbeconsideredasmadeupbyferricironoxide.Byapplyingcathodicvoltagetothe workingelectrode,theelectrochemicalreactionsseriesare: Fe x O y ! xFe + y 2 O 2 -7 Equation2-7canbeconsideredastworeactionsseparatedintheworkingandcounterelectrode: Fe 2 O 3 + 6 H + + 6 e )]TJ/F67 11.9552 Tf 10.122 -4.937 Td [(! 2 Fe + 3 H 2 O -8 H 2 O ! H + + e )]TJ/F76 11.9552 Tf 9.125 -4.938 Td [(+ O 2 -9 Inthemeasurementprocess,theapplicationofacathodicpotentialwasintendedtodisruptthe oxidelm.Thesubsequentmeasurementofimpedanceattheopen-circuitpotentialcouldbe envisionedasoccurringduringaregrowthoftheoxidelm.Asmeasurementatlower frequenciesrequiresalongerelapsedtime,theinuenceofnon-stationarybehaviorshouldbe 12
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moreapparentatlowerfrequencies.Thus,thelow-frequencydatashouldbeinconsistentwiththe Kramers-Kronigrelations. 2.3.3Titaniumalloydiskelectrodeinsodiumchlorideelectrolyte Asintroducedinpreviouschapter,forthesituationwhichmetaldisksaturatedinneutral solutionelectrolyte,mostlytheopencircuitelectrochemicalreactionsaremetalcorrosion, meaningtheoxidelmswillformafterthemetalbarelectrodebeenimmersedintothesolution foraperiodoftime.Butasironandtitaniumareindifferentpositionsofmetalreactivityseries, titaniummustberesistanttosodiumchlorideandtheoxidelmisalsomuchhardertoform duringthereactionprocess.Butafterall,theelectrochemicalreactionsforopencircuitno cathodicoranodicvoltageappliedcanbeasfollowed: Ti ! Ti 4 + + 4 e )]TJ/F27 11.9552 Tf 170.469 -4.937 Td [(-10 2 H 2 O + O 2 + 4 e )]TJ/F67 11.9552 Tf 10.121 -4.937 Td [(! 4 OH )]TJ/F27 11.9552 Tf 144.43 -4.937 Td [(-11 Generally,bycheckingthemetalreactivityseriesthatironismorereactivethantitanium,sofora sameperiodoftime,theoxidationdegreeofsteelelectrodewillbemuchhigherthantitanium alloyelectrode.Itisreasonablethatattheexperimentconditions,whichapplyingalso-1volt cathodicpotentialtotheworkingelectrodethethicknessoftitaniumalloyoxidelmmustbe thinnerandtheareasizemustbesmaller.Theelectrodereductionreactionseriesafterapplying cathodicpotentialtotheworkingelectrodearesimilarlyasequation2-7asfollowing: TiO 4 + 8 H + + 8 e )]TJ/F67 11.9552 Tf 10.122 -4.938 Td [(! Ti + 4 H 2 O -12 H 2 O ! H + + e )]TJ/F76 11.9552 Tf 9.125 -4.938 Td [(+ O 2 -13 Themeasurementprocessissimilartotheprevioussteelelectrodeexperimentmeasurement,but theresultswereslightlydifferentatlowfrequencies.Fortitaniumalloyelectrodeexperiment,the strongestnon-stationarybehaviorswasnotobservedatlowestfrequenciesregionapproximately 13
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10mHzbutwasobservedinsteadatfrequenciesaround12Hz.Thisresultwasnotexpected. 2.3.4RedQuantum-LightEmittingDiode Light-emittingdiodeLEDdevicesareplayingamuchmoreimportantroleinmodern sociallife.Thequantum-dotlight-emittingdiodeQLEDdevicesareespeciallypromisingdueto theirlowercostandhigherefciency.Anikeevaetal.[4]showedthesuperiorluminous performancewithrelativelylowenergyconsumption.AsshowninFigureZZ,thequantumdotis composedof3parts:theinnerkernel,themediumlayershellandtheouterligand.SongandLee [15]showedthattheperformanceofahybridredquantumdothadgoodluminescencewiththe combinationofanotherLEDdevice. SomeQLEDchemistriesarenotstable,leadingtoshortdevicelifetimes.TheEIS measurementwasintroducedinanefforttoimprovetheunderstandingofQLEDproperties.For thepresentwork,aredQLEDdevicewasexaminedafterithadreachedanestimated50percent remaininglifetime.Theimpedanceforthisdeviceshowsnon-stationarybehavioratlow frequency. 2.4AnalysisMethods Forallpotentiostatsystemswithalternatingsignalinput,theycanberepresentedasa sinusoidalformfunctiontypicallyconstitutewithasteadyconstantvalueplusanoscillating value: V = V + j4 V j cos w t -14 Bymathematicalexchange,equation2-14canberepresentedas: V = V + Re f V exp j w t g -15 Equation2-15istheequivalenttransformationofequation2-14whichmadeupwithrealand imaginarypart,sothattheoutputsignalshouldalsoberepresentedasasinusoidalfunctionwitha phaselag: I = I + j4 I j cos w t + j -16 14
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Andalsobeentransformedinto: I = I + Re f I exp j w t g -17 2.4.1ImpedanceMeasurementProtocol ThemeasurementdevicewasaGamry r Reference3000potentiostat,andthemeasuring scriptswereprovidedbyProf.BurakUlgutDepartmentofChemistry,BilkentUniversity, Turkey.Inthespecicexperimentalcases,theimpedancemeasurementprotocolmaybedivided into3mainsteps. 1.Opencircuitpotentialmeasurement.Thisstepisusedforwarmingupthemeasurement device,Usuallywedesigna200secondsand0.5secondperperiodmodustomakesurethe machineisworkingproperly,theresultsisintheformofaI-Vplot.Ifthedeviceis workingproperlytheI-Vplotgenerallyshowedaconstantoutputvalue. 2.Cathodicpretreatment.A-1Vpotential,referencedtotheopen-circuitpotential,was appliedforthesteelandtitaniumalloyelectrodesforaperiodof600sminutes.This stepwasintendedtoremovetheoxidelmsontheelectrode. 3.PotentiostaticEIS.Thisisthelastandmostsignicantstepforthewholeexperimentwork, includingasub-stepforprintingtheLissajousgures.Asingle-sinemethodwasusedin whichtheimpedancewasmeasuredforonefrequencyatatime,steppingfromhigh frequencytolowfrequency.Thefrequencyregimeforsteeldiskelectrode,titaniumalloy diskelectrodeandredQD-LEDdeviceareallbeensetfrom100kHzhighestvalueto 20mHzthelowestvalue.Thelowfrequencyregimeisbeenselectedinpurposewiththe limitationofmeasurementdeviceandinfrequencydomainaround20mHzwearesupposed toobservetypicalnon-stationarybehaviors. 4.PrintingofLissajousplots.Thisisthesub-stepofstep3.Separatescriptswereusedto generateeitherinstantaneousLissajousplotsoraveragedLissajousplots.Thus,the procedurehadtoberepeatedtoobtainbothinstantaneousandaveragedLissajousplots.It 15
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shouldbenotedthattheGamryinstrumentuseddisplaysaveragedLissajousplotsasthe experimentisperformed.TherecordingofinstantaneousandaveragedLissajousplotswas possibleonlythroughuseofthescriptprovidedbyProf.Ulgut. 2.4.2Kramers-Kronigrelations Kramers-KronigrelationswasrstintroducedbyKramersandKronigseparatel.,Themain ideaofKramers-Kronigrelations,whichmakesittightlybondingtoimpedancemeasurement spectroscopyisthattheKramers-Kronigrelationslinktherealpartsandimaginarypartsofa seriesofdata.Aswecanshowthattheoscillatinginputandoutputsignalcanbemathematically exchangedintorealandimaginaryparts,withtheoutputsignalweareabletogeneratetheuseful impedancedatausedformeasurement,andKramers-Kronigrelationsisperfectlyusefulfor investigatingtherelationsbetweenrealandimaginarydata.Theequationsbelowispartiallyshow someusefulequationsforinquiringintotheafliationofrealandimmaginarydata. Z j w = 2 w p Z + 0 Z r x x 2 )]TJ/F64 11.9552 Tf 10.95 0 Td [(w 2 dx -18 Z r w = Z r )]TJ/F27 11.9552 Tf 12.922 8.094 Td [(2 p Z + 0 xZ j x x 2 )]TJ/F64 11.9552 Tf 10.95 0 Td [(w 2 dx -19 AftertheapplicationofEquation2-18andEquation2-19,theconnectionbetweentherealand imaginarypartofimpedancehasbeensetupandmeasurementmodelsimulationplotsareableto comeout. 16
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CHAPTER3 RESULTSANDDISCUSSION 3.1ExperimentalResults InthissectionwemainlydiscussabouttheEISresultsoftheelectrochemicaloxideand reductionreactionsandtheredQD-LEDluminescenceprocessEISresultsandtrytondout valuableinformationbehindthedata.Asdiscussedinpreviouschaptersthemechanismsofoxide andreductionreactionsofmetaldiskelectrodesareinchargeofthenon-stationarybehaviorsin lowcurrentfrequenciesregimeduetotheunstablereactionconditions.Sothatitispredicable thattheLissajousplotsareabletoclearlyshowthenon-stationarybehaviors,fornon-stationary electrochemicalsystems,theamplitudesofthecurrentandpotentialvalueswouldbeoscillating insteadofkeepingasteadyvaluesduringtheexperimentalprocesses,whichwouldshowmultiple valuesofloopsonLissajousgurespresentationplotsofthei-Vguresduetotheamplitudesof thesinusoidalcurvesofcurrentandpotentialvalueswerenotoverlapping.Alsothe non-stationarybehaviorsofthetwoexperimentalelectrochemicalsystemswouldalsobe presentedbythesimulationworksdonebytheMeasurementModels,theresultswillbe introducedinlatersections. ForRedQD-LEDluminescencesystem,thenon-overlappingcurvesofLissajousplotsin lowfrequenciesregimeshowthatthenon-stationarybehaviorsofluminescenceprocesscanbe perfectlypresented. 3.1.1Metaldiskelectrodes Thepreviouschaptershadshownthatnon-stationarybehaviorswillbeobservedduetothe reductionreactionswillhappenatthetimethecathodicvoltagewasbeenapplyingtotheworking metalelectrodeforbothsteelandtitaniumalloy,butthenon-stationarybehaviorswillnotlast longaftertheoxidelmsformedbeforeitwaseliminated,sothatthesectionsandguresbelow willclearlyshowingtheâ€mildâ€non-stationarybehaviors. 3.1.1.1Steeldiskelectrode TheimpedanceresponseofthesteelelectrodeinNaClelectrolyteispresentedinFigure 3-1.Theexperimentalresultsofsteelelectrodewasn'tshowingrelativelyobviousnon-stationary behaviorsbecausethereductionreactionprocessisshortwhichcanbeseeninFigure3-2a 17
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3-3a3-4aandthenon-stationarybehaviorscanonlybeclearlyobservedviatheLissajousplots inFigure3-2b3-3b3-4bsothattheLissajousplotshadshowedtheirvaluesforthe visualizationofthequalityofimpedance. 3.1.1.2Titaniumalloydiskelectrode TheimpedanceresponseofthesteelelectrodeinNaClelectrolyteispresentedinFigure 3-5.Theexperimentalresultsoftitaniumalloyelectrodealsojustshowedthatthenon-stationary behaviorsduringthereductionreactionprocesswasabletoexamine,butthereductionprocess stillbeenclearlyrepresentedintheI-VplotsandLissajousguresinFigure3-63-73-8by examiningtheplateausandthesuddendropsofcurrentcurvesinthei-Vplotsisobviousto differentiateandthetailsofLissajousgures. 3.1.2Red5AQD-LED TheprocessowoffabricationofcolloidalQuantumDotshadbeenwelldevelopedduring pastdecades,nowthecostandluminanceofQD-LEDdevicesarecheaperandhigher[11][12]. DuetotheglowingmechanismofQD-LEDdevices,wemayconcludethattheextravoltage shouldactasexcitationofthechargetransferlayerswhichplaysanimportantrolein luminescence.Sothatthestrongertheoutsideapplyingpotentialthemoreobviousnon-stationary performanceofimpedance.Figure3-9hadshowntheimpedancespectraofRedQD-LED luminescence.Actuallyinexperimentprocess,theI-VresponseplotsandLissajousplotsresults Figure3-1.Theimpedancespectraofsteelelectrodeexperiment. 18
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a b Figure3-2.Thisplotseriespresentsfrequencyequalsto10kHz.Theshortperiod,highfrequency resultshadshownthetypicalstationaryreductionreactionswithsteadyampliesof currentandvoltageintensityintheformsofai-VplotsandbLissajousplots a b Figure3-3.Thisplotsseriespresentsfrequencyequalsto12.6Hz.Themediumvalueperiod, mediumvaluefrequencyresultshadshownthatthetypicalnon-stationarybehaviors duringthereductionbehaviorsduetotheplateauoftheI-Vplotsandtheloopsof Lissajousplotswerenotsuperposed. 19
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a b Figure3-4.Thisplotsseriespresentsfrequencyequalsto0.02Hz.Thelowfrequencyregimewill performalongperiodcyclereaction,whichmeansthereductionreactionprocess shouldbethoroughlycompletedandthelargerplateauofI-Vplotandthelongertail ofLissajousgurehadshowntheconclusion. Figure3-5.Theimpedancespectraoftitaniumalloyexperiment. 20
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a b Figure3-6.Thisplotseriespresentsfrequencyequalsto100,000Hz.Thehighfrequencyvalue resultsshowedthatthesuperposedofcurrentandpotentialcurves,whichmeansthat therewasnophaseshiftforcurrentandpotentialathighfrequenciesregime,butstill beforecheckingtheLissajousgurewecouldn'tmakeaassertionaboutwhetherthe non-stationarybehaviorshadoncehappened. a b Figure3-7.Thisplotseriespresentsfrequencyequalsto12.6Hz.Thenon-stationarybehaviorsis clearlyshowninbothgures,thepeaksofcurrentcurveinI-Vplotsisoscillatingand theloopsofLissajousguresarehighlynon-overlapping. 21
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a b Figure3-8.Thisplotseriespresentsfrequencyequalsto0.02Hz.Themediumfrequencies domainoftitaniumalloyelectrodeexperimentalresultshadshownthestrongest non-stationaryinsteadofthelowfrequenciesregime,thepeaksofcurrentcurvesis merelysharingthesameheight,althoughthetailofLissajousgureswasshowingthe non-stationarybehaviorsdoexistbutnotasobviousasprevious12.6Hzones,the Lissajousplotsstilldonewellinshowingthequalityofimpedance. inFigure3-103-11hadprovedthesuperiorpropertyofLissajousplotsinvisualizationof non-stationarybehaviorinlowfrequenciesimpedance,themultinumbersofloopsinLissajous plotsandinequivalentvaluesofampliesinI-Vplotswereallproventhat. Figure3-9.TheimpedancespectraofQD-LEDdevice. 22
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a b Figure3-10.Thisplotseriespresentsfrequencyequalsto200Hz.Highfrequenciesalternating voltageappliedtotheQD-LEDdeviceishardtoexcitetheelectronssothatthe chargetransferlayerswillnoactivatedandoutputcurrent,whichareclearlyshown inthelissajousplotthatthecurrentvaluesareconstantlyzero. 3.1.3RedQD-LEDmodied AsintroducedbeforeanewLissajousguresmeasuringmethodhadbeenintroducedto evaluatethedifferencesbetweenEISordinaryLissajousplotsprintingandEISaveraged Lissajousplotsprintingsothatanewseriesofexperimentshadcomeouttovisualizethe discrepancies.Tomakethecomparisonmoreobviouseachplotsseriescontainsthecomparisions betweentwoLissajousprintingmethodsinsameimpedancefrequencies,asFigure3-12d 3-13d3-14dshowedthattheaveragedLissajousplotprintingwasabletogenerateplotswith shortperiodandaveragedvaluesofpotentialandcurrentresponsebutdifculttovisualizethe non-stationarybehaviorsandnon-averagedLissajousplotprintingwasabletogenerategures thatobviouslyvisualizethenon-stationarybehaviors. 3.2SimulationModelResults Theresultsabovehadgenerallyshowntherelationsbetweentheinputpotentialandthe outputcurrent,thenextsectionshouldintroducedthebondingbetweenpotentialandcurrent, whichisimpedance.Makingcomparisonswiththeexperimentalworksandsimulationworks helpsusmakingbetterestimationandbetterunderstandingaboutthequalityoftheimpedance measurements.Asmentionedinpreviouschaptersthemeasurementmodelhadcreateda 23
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a b c d Figure3-11.Thisplotseriespresnetsfrequenciesequalto0.05and0.04Hz.Lowfrequencies regimeresultshadpresentedthatthelowfrequencies,highperiodsalternatinginput potentialhaddonewellinactivatingthechargetransferlayer,sothattheincreasing trendofampliesofcurrentcurvesshownthatthenon-stationarybehaviorswould appear,thethreeseparatedloopsofLissajousguresprovedtheconclusionsaswell. 24
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a b c d Figure3-12.ComparisonbetweenaveragedLissajousprintingandnon-sveragedLissajous printing.Inhighfrequenciesregimeclearlythattheaveragedmethodwasableto clarifythecurrent-potentialbehaviorsinashorterperiodoftime,whichmeansa moreprecisedescriptionofthebehaviors.Butinotherwordstheaveragedplotshad lostthedescriptionforthewholeprocessasnon-averagedplotsdid. 25
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a b c d Figure3-13.Inmiddlerangefrequenciesregimethecomparisonbetweenaveragedand non-averagedmethodarealsomanifest.Butwhatweshouldrealizeisthatduetothe longermeasuringperiodthenon-stationarybehaviorsoftheluminescenceprocess wasbeenclearlyemergedthroughthemultiloopsbuttheaveragedplotsonlyshown asingleloopwhichcontainedlimitedinformation. 26
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a b c d Figure3-14.Inlowrangefrequenciesregimethecomparisonbetweenaveragedandnon-averaged methodarealsomanifest.TheinstantaneouslymeasuredLissajousguresclearly showedthenon-stationarybehaviorsinsteadaveragedLissajousplotscouldn't. 27
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equivalentcircuitswhichttedthetargetdevicesimpedancespectrabyaddingVogitelements intotheequivalentcircuits.Sothatthemainpurposeofthesimulationworksistocerticatethe relationsbetweentherealandimaginarypartsoftheimpedancesothattheresultsarevaluablein examiningthequalityofimpedance.Thesimulationworksresultsshowedbelowaremadeup withthettingplotsofNyquistimpedanceplots,thestandarddeviationandcondenceinterval structuresplotsfortherealandimaginarypartsofimpedanceaswellasatablecontainsthe circuitparametersofthesystems. 3.2.1Steelelectrodemeasurementmodelresults TheNyquistplotinFigure3-15aofhadshownperfectlyttinginhighfrequenciesregime bythesuperposingoftheexperimentaldatadotsandthesimulationcurvesbutasthelow frequenciesregimethecurveisdeviatingthedots,whichsuggestingthemeasurementresults mightinaccurate.Figure3-15b3-15careshowingresidualerrorstructureofrealand imaginarypartsofimpedancehadprovedtheconclusions,althoughtherealpartttingwith imaginarydataarenotviolatedthecondenceintervalregionspresentedbythereddashedlines butstilltheimaginarypartttingdidn'tcomeoutgoodresultsespeciallyinlowfrequencies regions. 3.2.2Titaniumalloyelectrodemeasurementmodelresults Figure3-16ashowstheexperimentalimpedancespectraandmeasurementmodel simulation.Comparingtotheresultsmeasuredfromsteelelectrodetheresultsfromtitaniumalloy electrodeowedmoreconsistence,Figure3-15b3-16cshowtheresidualerrorstructures, whichhadprovedthatalltheexperimentaldataareinthecondenceintervalregionandthe Nyquistplotsalsomadewellttingtothedata,onlyonedatapointexceptional. 3.2.3Red5AQD-LEDdevicemeasurementmodelresults. Thesimulationresultsforthissectionarebeendividedintotwopartsduetotheunsatised ttingimpedancettingresultsshowninFigure3-17aandFigure3-17b.Tomakeabetter ttingresultswedeletedtheimpedancein20mHzto100mHzbecausethispartofimpedanceis hardtobewellmeasuredsothatitisalsohardtousetheVoigtelementsttingtomakeagood 28
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a b c Figure3-15.ThesimulationworkofsteelelectrodeexperimentaldataconsistswithaNyquist plotbresidualerrorstructureofrealpartcresidualerrorstructureofimaginarypart. 29
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a b c Figure3-16.Thesimulationworkoftitaniumalloyelectrodeexperimentaldataconsistswith aNyquistplotbresidualerrorstructureofrealpartcresidualerrorstructureof imaginarypart. 30
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ttingresults.Thedifferencesbetweentheoriginalimpedanceandthedeletedonesarealso obviousinFigure3-18thatthemeasurementmodelsuggestslackofconsistencywiththe Kramers-KronigrelationsfortheQLED,butisconfoundedbythelargecondenceintervalfor thepredictions.TheLissajousplotswereunequivocal. 31
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a b Figure3-17.NyquistplotsofaOriginalimpedanceof5AQD-LEDbLowfrequencies impedancedeleted. 32
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a b c d Figure3-18.Residualerrorstructureplotsofarealpartttingusingimaginarypartdata.breal partttinglowfrequenciesimpedancedeletedcimaginaryttingusingrealpart data.dimaginaryttinglowfrequenciesimpedancedeleted. 33
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CHAPTER4 CONCLUSIONS Tosumupthewholeexperimentalandsimulationworkweareabletoconcludethatthe applicationofLissajousguresinvisualizethequalityofimpedanceisillustrious.The applicationofLissajousguresishelpfulinidentifyingthenon-stationarybehaviorsinboth electrochemicaloxidationandreductionreactionseries.AnotherwellapplicationofLissajous guresisthepresentationofnon-stationarybehaviorsduringtheluminescenceprocessof differentlifetimeredQD-LEDdevices.Anothermethodforanalyzingthequalityofimpedance spectraismeasurementmodelbasedontheKramers-Kronigrelations.Boththetwomethodsall showinggoodusageoftheirapplications.TheLissajousguresareabletoclarifythe non-stationarybehaviorsbypresentingthenon-overlappingloopsoftheplots.Alsothe measurementmodelsimulationsofthewholeexperimentalworkhadshownvariousresults,the steeldiskelectrodeexperimentalworkshownthatthelowfrequenciesregimeimpedancewere notconsistentwiththeKramers-Kronigrelationsespeciallyfortheimaginaryt,theresultsfrom thetitaniumalloydiskelectrodeareconsistentwiththeKramers-Kronigrelationsforall frequencydomain,alsofortheredQD-LEDdevicewhichlifetimeislargerthan50percentthe lowfrequencyregimealsoshownmildinconsistentwiththeKramers-Kronigrelations,by deletingpartofthelowfrequenciesimpedancethettingresultsweremuchbetterbypresenting theconsistencyofcondenceinterval.AnotherredQD-LEDdeviceresultsshownthe comparisonbetweenthetwoLisssajousplotsprintingmethods,oneisordinaryLissajousplots printingEISforthewholeluminescenceperiodandtheotherwasaveragedLissajousplots printing,theaveragedLissajousprintingwouldprobablyprintoutmiddlestageperiodoftimeof thereactionandtheordinaryLissajousprintingwouldtruthfullyreectthewhole current-potentialrelationsduringthemeasurements. 34
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[14]MarkEOrazemandBernardTribollet, Electrochemicalimpedancespectroscopy ,John Wiley&Sons,2017. [15]HongjooSongandSeonghoonLee, Redlightemittingsolidstatehybridquantum dot–near-uvganleddevices ,Nanotechnology 18 ,no.25,255202. [16]CharlesWheatstone, Anaccountofseveralnewinstrumentsandprocessesfordetermining theconstantsofavoltaiccircuit ,AbstractsofthePapersPrintedinthePhilosophical TransactionsoftheRoyalSocietyofLondon,no.4,TheRoyalSocietyLondon,1843, pp.469. [17]B.Hirschorn,B.Tribollet,andM.E.Orazem, OnSelectionofthePerturbationAmplitude RequiredtoAvoidNonlinearEffectsinImpedanceMeasurements ,IsraelJournalof Chemistry, 48 ,133-142. [18]B.HirschornandM.E.Orazem, OntheSensitivityoftheKramers-KronigRelationsto NonlinearEffectsinImpedanceMeasurements ,JournalofTheElectrochemicalSociety, 156 ,C345-C351. 36
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BIOGRAPHICALSKETCH LiuruidongZouisfromZhuhai,Guangdong,China.AsmasterstudentinChemical EngineeeringDepartmentfortwoyears,itisgreatsuccessthatnallythethesisiscompleted. 37
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