Citation
Application of Lissajous Plots to Identify Non-Stationary Behavior in Impedance Spectroscopy

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Title:
Application of Lissajous Plots to Identify Non-Stationary Behavior in Impedance Spectroscopy
Creator:
Zou, Liuruidong
Place of Publication:
[Gainesville, Fla.]
Florida
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University of Florida
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english
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1 online resource (37 p.)

Thesis/Dissertation Information

Degree:
Master's ( M.S.)
Degree Grantor:
University of Florida
Degree Disciplines:
Chemical Engineering
Committee Chair:
Orazem,Mark E
Committee Co-Chair:
Ziegler,Kirk Jeremy
Graduation Date:
5/1/2020

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Subjects / Keywords:
impedance -- lissajous -- nonstationary
Chemical Engineering -- Dissertations, Academic -- UF
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bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Chemical Engineering thesis, M.S.

Notes

Abstract:
When examining properties of unknown devices spectrum of impedance are critical for overlooking the electrochemical properties of devices. Electrochemical impedance spectroscopy(EIS) measuring the transfer function which connecting the input potential and output current. Identification of non-stationary behavior in EIS requires post-processing by application of measurement model simulation based on Kramers-Kronig relations.The objective of this thesis was to explore the suitability of instantaneously measured Lissajous figures for identifying non-stationary behavior. Despite transmitting impedance spectrum a script written by Prof. Buruk Ulgut was used to obtain averaged and instantaneous Lissajous plots for the impedance measurements of steel electrode, titanium alloy electrode and red quantum-dot light emitting diodes provided by Nanophotonica. Comparison between the two Lissajous plots printing methods revealed that instantaneous Lissajous plots were shown to be sensitive to nonstationary behavior, even when the averaged Lissajous plot suggested stationary behavior. Instantaneous Lissajous plots were shown to provide a simple manner by which non-stationary behavior could be detected during the course of an impedance measurement. Comparison to use of a measurement model to assess consistency with the Kramers-Kronig relations to measured spectra showed that the instantaneous Lissajous plots could detect non-stationary behavior under conditions for which the measurement model gave inconclusive results. ( en )
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (M.S.)--University of Florida, 2020.
Local:
Adviser: Orazem,Mark E.
Local:
Co-adviser: Ziegler,Kirk Jeremy.
Statement of Responsibility:
by Liuruidong Zou.

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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 willclearlyshowingthe”mild”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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REFERENCES [1]PankajAgarwal,OscarDCrisalle,MarkEOrazem,andLuisHGarcia-Rubio, Application ofmeasurementmodelstoimpedancespectroscopyii.determinationofthestochastic contributiontotheerrorstructure ,JournaloftheElectrochemicalSociety 142 , no.12,4149. [2]PankajAgarwal,OscarDCrisalle,MarkEOrazem,andLuisHGarcia-Rubio, Application ofMeasurementModelstoImpedanceSpectroscopy:III.EvaluationofConsistencywiththe Kramers-KronigRelations ,JournaloftheElectrochemicalSociety 142 ,no.12,4159. [3]PankajAgarwal,MarkEOrazem,andLuisHGarcia-Rubio, Measurementmodelsfor electrochemicalimpedancespectroscopyi.demonstrationofapplicability ,Journalofthe ElectrochemicalSociety 139 ,no.7,1917. [4]PolinaOAnikeeva,JonathanEHalpert,MoungiGBawendi,andVladimirBulovi c, Electroluminescencefromamixedred-green-bluecolloidalquantumdotmonolayer ,Nano Letters 7 ,no.8,2196. [5]JohnCFidler,JamesPBobis,WilliamRPenrose,andJosephRStetter, Potentiostatic apparatusandmethods ,March301993,USPatent5,198,771. [6]ThomasBGreensladeJr, AllaboutLissajousgures ,ThePhysicsTeacher 31 ,no.6, 364. [7]ShigehiroHashimoto,NobumichiNagano,YoshinoriMurashige,andSatoshiYamauchi, MeasurementofcelldistributioninorganswithLissajousofimpedance ,Proceedingsofthe 5thWorldMulticonferenceonSystemics,CyberneticsandInformatics,vol.10,2001, pp.443. [8]KathleenCHowellandHenryJPernicka, NumericaldeterminationofLissajoustrajectories intherestrictedthree-bodyproblem ,CelestialMechanics 41 ,no.1-4,107. [9]HuiJiang,TaoShao,ChengZhang,WenfengLi,PingYan,XuekeChe,andEdl Schamiloglu, ExperimentalstudyofqvLissajousguresinnanosecond-pulsesurface discharges ,IEEETransactionsonDielectricsandElectricalInsulation 20 ,no.4, 1101. [10]JulesAntoineLissajous, M emoiresurl' etudeoptiquedesmouvementsvibratoires ,1857. [11]BenjaminSMashford,Tich-LamNguyen,GerardJWilson,andPaulMulvaney, All-inorganicquantum-dotlight-emittingdevicesformedvialow-cost,wet-chemical processing ,JournalofMaterialsChemistry 20 ,no.1,167. [12]BenjaminSMashford,MatthewStevenson,ZoranPopovic,CharlesHamilton,Zhaoqun Zhou,CraigBreen,JonathanSteckel,VladimirBulovic,MoungiBawendi,Seth Coe-Sullivan,etal., High-efciencyquantum-dotlight-emittingdeviceswithenhanced chargeinjection ,Naturephotonics 7 ,no.5,407. [13]WaltherNernst, Methodezurbestimmungvondielektrizit atskonstanten ,Zeitschriftf ur PhysikalischeChemie 14 ,no.1,622. 35

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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