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Corrosion of Copper in Deaerated Deionized Water and Geometry Induced Frequency Dispersion of the Ring Electrode

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Title:
Corrosion of Copper in Deaerated Deionized Water and Geometry Induced Frequency Dispersion of the Ring Electrode
Creator:
Cleveland, Christopher N
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[Gainesville, Fla.]
Florida
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University of Florida
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english
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1 online resource (110 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Chemical Engineering
Committee Chair:
ORAZEM,MARK E
Committee Co-Chair:
ZIEGLER,KIRK JEREMY
Committee Members:
CHAUHAN,ANUJ
MOGHADDAM,SAEED

Subjects

Subjects / Keywords:
comsol -- copper -- corrosion -- cpe -- electrochemistry -- electrode -- impedance -- kinetics -- mass-transfer -- matlab -- nyquist -- spectroscopy
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, Ph.D.

Notes

Abstract:
Copper is commonly regarded to be immune to corrosion in deaerated deionized electrolytes. The present work shows that, in the absence of hydrogen, copper will corrode on the order of 1 nm/day in deionized water with an oxygen concentration on the order of, or less than, 1 ppb. While a corrosion rate of this magnitude can normally be neglected, it may be catastrophic for nanoscale copper structures utilized in emerging applications to enhance energy transport at the solid-electrolyte interface, such as in cooling advanced electronics. This conclusion is supported by a set of experimental and analytical studies that encompass impedance spectroscopy, slow-scan linear sweep voltammetry, thermodynamic calculations for the environment under study, and kinetic simulations. The studies provide a comprehensive insight on details of the corrosion mechanism for copper in deaerated water. An extended kinetic model is developed and used to study the cumulative corrosion rate of copper after 15 years for a microelectrode and for bulk copper. The parameters varied for this study were the area to volume ratio, copper and hydrogen mass-transfer coefficients, equilibrium potentials and exchange current densities. After less than 60 days, the bulk copper in a closed system reached a limiting hydrogen partial pressure of 0.096 atm; whereas, the microelectrode continued to evolve hydrogen over the 15 years, reaching a value of 0.0013 atm. The corrosion rate for the bulk copper was calculated to be 0.35 nm/day and dropped precipitously to zero in less than 60 days; whereas, the calculated corrosion rate for the microelectrode was 1.1 nm/day and gradually reached a value of 0.74 nm/day after 15 years. Simulations were performed using refined kinetic model for a microelectrode validate the assumption that the hydrogen oxidation reaction can be neglected for the small electrode area to volume ratio and short times considered. The hydrogen oxidation reaction played an essential role in simulating the behavior of the bulk copper experiments with larger electrode area to volume ratio and longer exposure time. For both the open and closed systems, the cumulative corrosion was reduced for larger electrode area to volume ratios. The difference in estimated corrosion rates between the copper microelectrode and the Hultquist bulk copper experiments is shown in the present work to be the natural consequence of the manner in which kinetics, mass transfer, and electrode area to volume ratio influence the progression toward the equilibrium condition. A 2D axisymmetric mathematical model was developed to investigate frequency dispersion in a ring electrode. The finite element software COMSOL Multiphysics was used to solve Laplace's equation in cylindrical coordinates for the ring electrode with an applied perturbation potential as the boundary condition. Due to the singularities that arise near the ring electrode's edges, a nonuniform meshing scheme was implemented near the surface of the ring electrode. The presence of frequency dispersion is seen at frequencies greater than the dimensionless frequency equal to unity. The characteristic length for the ring electrode is shown to be a function of the geometric ratio of the inner to outer radius. ( en )
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In the series University of Florida Digital Collections.
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Includes vita.
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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 (Ph.D.)--University of Florida, 2017.
Local:
Adviser: ORAZEM,MARK E.
Local:
Co-adviser: ZIEGLER,KIRK JEREMY.
Statement of Responsibility:
by Christopher N Cleveland.

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CORROSIONOFCOPPERINDEAERATEDDEIONIZEDWATERAND GEOMETRYINDUCEDFREQUENCYDISPERSIONOFTHERINGELECTRODE By CHRISTOPHERN.CLEVELAND ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 201

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c r 201 Christopher N. Cleveland

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Idedicatethistomyfamilyandfriends.

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ACKNOWLEDGMENTSIwouldliketoextendmygratitudetoProfessorMarkOrazem,whosecombinedguidanceandexpertiseintheeldofelectrochemistryhavebeenessentialtomydevelopmentasascientistandengineer.ProfessorOrazem'sunwaveringcommitmenttohisstudentsandenthusiasmforresearchhavekeptmeengagedinmyresearchendeavorshereattheUniversityofFlorida.IalsooweagreatdealofgratitudetoProfessorsSaeedMoghaddam,AnujChauhan,andKirkJ.Zieglerfortheirextraordinarysupportasmycommittee.ThisworkwouldnothavebeenpossiblewithoutthenancialsupportofDARPAandMedtronic. 4

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TABLEOFCONTENTS Page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 7 LISTOFFIGURES .................................... 8 ABSTRACT ........................................ 10 CHAPTER 1INTRODUCTION .................................. 12 2REVIEWOFCOPPERCORROSION ....................... 16 2.1CopperNano-StructuresatRiskofCorrosion ................ 16 2.1.1CopperNanoWicks ........................... 16 2.1.2UniformCorrosion ........................... 17 2.1.3Galvanic(Coupling)Corrosion ..................... 18 2.1.4Electrokinetic-CurrentCorrosion .................... 18 2.1.5ThermogalvanicCorrosion ....................... 20 2.2InuenceofSolutionChemistry ........................ 20 2.2.1AcidicChlorideMedia ......................... 21 2.2.2AcidicSulphateMedia ......................... 21 2.2.3AlkalineMedia .............................. 22 2.2.4AlkalineChlorideMedia ........................ 23 2.3NuclearWasteStorage ............................. 25 3OVERVIEWOFELECTROCHEMICALIMPEDANCESPECTROSCOPY .. 26 4CORROSIONOFCOPPERINDEAERATEDWATER ............. 30 4.1HeatSinksusedtoCoolHighPerformanceElectronics ........... 30 4.2StabilityofCopperinDierentMedia .................... 31 4.3DisposalofSpentNuclearRods ........................ 32 4.4Experimental .................................. 33 4.4.1De-AerationProcedure ......................... 34 4.4.2Instrumentation ............................. 35 4.4.3Electrodes ................................ 35 4.5ExperimentalResults .............................. 37 4.5.1ImpedanceSpectra ........................... 37 4.5.2PolarizationCurves ........................... 40 4.6Simulations ................................... 41 4.6.1ThermodynamicAnalysis ........................ 41 4.6.2KineticSimulation ........................... 44 4.6.3ImpedanceRegressionAnalysis .................... 49 5

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4.7Discussion .................................... 53 4.8ConcludingRemarks .............................. 55 5REFINEDKINETICMODELFORCOPPERCORROSION .......... 56 5.1MathematicalDevelopment .......................... 56 5.2Mass-TransferCoecients ........................... 58 5.2.1Microelectrode .............................. 58 5.2.2HultquistFoils .............................. 59 5.3Results ...................................... 60 5.3.1OpenSystem .............................. 60 5.3.2ClosedSystem .............................. 65 5.4ControversySurroundingNuclearWasteStorage ............... 72 5.4.1ThermodynamicAnalysis ........................ 73 5.4.2TraceAmountsofOxygen ....................... 75 5.4.3ComparisontoWorkofHultquistetal. ................ 76 5.5ConcludingRemarks .............................. 76 6INFLUENCEOFRINGELECTRODEONEIS .................. 78 6.1FrequencyDispersioninElectrochemicalSystems .............. 78 6.2RotatingElectrodes ............................... 79 6.2.1SteadyStateResponse ......................... 79 6.2.2ImpedanceResponse .......................... 80 6.3MathematicalDevelopment .......................... 82 6.3.1RingElectrodePrimaryResistance .................. 82 6.3.2RingElectrodeImpedanceResponse .................. 84 6.4NumericalMethod ............................... 85 6.5ResultsandDiscussion ............................. 86 6.5.1ValidationofPrimaryResistancefortheRingElectrode ....... 87 6.5.1.1ThickRing,ThinRingandFEAResults .......... 88 6.5.1.2ThickRing,ThinRingandFEAResults .......... 89 6.5.2InterpretationofImpedanceResponse ................. 89 6.5.2.1Imaginary-Impedance-DerivedPhaseAngle ........ 91 6.5.2.2EmpiricalFormula ...................... 92 6.6ConcludingRemarks .............................. 97 7CONCLUSIONS ................................... 98 8FUTUREWORK ................................... 99 REFERENCES ....................................... 100 BIOGRAPHICALSKETCH ................................ 110 6

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LISTOFTABLES Table Page 2-1Reactionspresentin1MKOHwithassociatedthermodynamicequilibriumpotential. ....................................... 23 4-1ListofspeciesconsideredinthethermodynamicanalysispresentedinFigure4-6. ....................................... 43 4-2SummaryofthetimedependentreactionsconsideredformodelingCucorrosionkinetics. .................................. 45 4-3Kineticparametersusedforthesimulationandresults. .............. 46 4-4RegressionresultsforthedatapresentedinFigure4-8A ............. 50 4-5Estimatedvaluesforcoppercorrosionrates. .................... 53 5-1Summaryofequationsusedforthekineticstudy.Timesteppingusedforthissystemisshowninthelowerhalfofthetable. ............... 59 5-2Kineticparametersusedforthenumericalsimulations. .............. 62 6-1Parameters,values,anddescriptionusedfortheFEAsimulations. ........ 87 6-2Computedvaluesofprimaryresistanceasafunctionofthegeometricparametersr1andr2. ................................. 87 7

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LISTOFFIGURES Figure Page 1-1Heatsinkfoundinconsumerpersonalcomputers.Cross-sectionalareadepictingthecopperspongematrixwithintheheatpipe. ............. 13 1-2Schematicofahybridmicro/nanowickcoolingsystem. .............. 13 2-1Helicalhybridstructuresusedtoachieveenhancedheatremoval ......... 17 2-2Electricdoublelayerstreamingpotentialshownonananowick. ......... 19 3-1Sinusoidalperturbationofanelectrochemicalsystematsteadystate ....... 27 3-2Impedanceresponseofplatinum,goldplatedtungstenandtungstenmeasuredfrom0.1Hzto20kHz ................................ 28 3-3Analogouscircuitsofanelectrochemicalinterfacesusceptibletocorrosionattheopen-circuitpotential ............................. 29 4-1Schematicdiagramshowingthedeaerationprocessusedtoachieve1-2ppbgas-phaseO2concentrationlevels .......................... 34 4-2Cu,AuandPtworkingelectrodeswiththeexposed0.25mmdiskdiametershown.Theoutsidediameteroftheacrylictubewas6.5mm.1(Source:Photocourtesyofauthor.) ............................. 36 4-3Scaledimpedanceresponseofcopper,goldandplatinum0.25mmdiameterelectrodesindeaerateddeionizedwater ....................... 37 4-4Lowfrequencyimpedanceresponseofcopper,goldandplatinum0.25mmdiameterelectrodes .................................. 39 4-5PolarizationcurveforcopperdeaeratedwithN2andobtainedusingasweeprateof0.06mV/s ............................... 40 4-6Calculatedpotential-pH(Pourbaix)diagramforcopperindeaerateddeionizedwater.ThetitrantswereassumedtobeNaOHandHNO3 ....... 42 4-7Evansdiagramshowingsimulationresultsatt=0forhydrogenevolution,copperdissolution,andcopperelectrodepositionreactions ............ 48 4-8EquivalentelectricalcircuitmodelsfortheimpedancedatapresentedinFigure4-4 ....................................... 49 4-9Measurementmodelextrapolation(blueline)ofthecopperimpedance(circle)showingthepredictedzerofrequencylimit. ................ 51 5-1Calculatedopen{systemcorrosionratesasafunctionoftimewithmass{transfercoecientasaparameter .............................. 61 8

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5-2Calculatedopen{systemcumulativecorrosionasafunctionoftimewithmass{transfercoecientasaparameter ...................... 63 5-3Calculatedopen{systembulkconcentrationofcupricionasafunctionoftimewithmass{transfercoecientasaparameter ............... 64 5-4Calculatedclosed{systemcorrosionratesasafunctionoftimewithmass{transfercoecientasaparameter .............................. 66 5-5Calculatedclosed{systemcumulativecorrosionasafunctionoftimewithmass{transfercoecientasaparameter .................... 67 5-6Calculatedclosed{systembulkconcentrationofcupricionasafunctionoftimewithmass{transfercoecientasaparameter ............... 69 5-7Calculatedclosed{systembulkhydrogenpartialpressureasafunctionoftimewithmass{transfercoecientasaparameter ............... 70 5-8CalculatedcorrosioncurrentdensityasafunctionofpotentialfortheHultquistcellunderopenandclosedcondition ................... 71 5-9Calculatedpotential-pH(Pourbaix)diagramsforcopperindeaerateddeionizedwatergeneratedbyCorrosionAnalyzer2.0 ................ 74 6-1Schematicrepresentationofniteelementmeshusedfortheringelectrodesimulations ...................................... 86 6-2Computedvaluesofprimaryresistanceasafunctionofthegeometricparametersr1andr2obtainedfromEq.(6{10)andEq.(6{11) .......... 88 6-3Ringelectrodescaledmodulusimpedanceasafunctionoffrequency.Frequencydispersionisdependentonthegeometricparameterr1=r2. ...... 90 6-4Ringelectrodeimaginary-impedance-derivedphaseangleasafunctionoffrequency ...................................... 91 6-5Ringelectrodeimaginary{impedance{derivedphaseangleasafunctionofdimensionlessfrequency .............................. 93 6-6Characteristiclengthasafunctionofthegeometricratior1=r2 .......... 94 6-7Ringelectrodeimaginary{impedance{derivedphaseangleasafunctionofdimensionlessfrequency .............................. 95 6-8Ringelectrodeimaginary{impedance{derivedphaseangleasafunctionofdimensionlessfrequency .............................. 95 6-9Ratioofthecharacteristicfrequencyoftheringelectrodefc;ringtothecharacteristicfrequencyofthediskelectrodefc;disk ................ 96 9

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulfllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy CORROSIONOFCOPPERINDEAERATEDDEIONIZEDWATERAND GEOMETRYINDUCEDFREQUENCYDISPERSIONOFTHERINGELECTRODE By ChristopherN.Cleveland 201 Chair:MarkE.Orazem Major:ChemicalEngineering Copperiscommonlyregardedtobeimmunetocorrosionindeaerateddeionized electrolytes.Thepresentworkshowsthat,intheabsenceofhydrogen,copperwill corrodeontheorderof1nm/dayindeionizedwaterwithanO 2 concentrationonthe orderof,orlessthan,1ppb.Whileacorrosionrateofthismagnitudecannormallybe neglected,itmaybecatastrophicfornanoscalecopperstructuresutilizedinemerging applicationstoenhanceenergytransportatthesolid-electrolyteinterface,suchasin coolingadvancedelectronics.Thisconclusionissupportedbyasetofexperimental andanalyticalstudiesthatencompassimpedancespectroscopy,slow-scanlinearsweep voltammetry,thermodynamiccalculationsfortheenvironmentunderstudy,andkinetic simulations.Thestudiesprovideacomprehensiveinsightondetailsofthecorrosion mechanismforcopperindeaeratedwater. Anextendedkineticmodelisdevelopedandusedtostudythecumulativecorrosion rateofcopperafter15yearsforamicroelectrodeandforbulkcopper.Theparameters variedforthisstudyweretheareatovolumeratio,copperandhydrogenmass-transfer coecients,equilibriumpotentialsandexchangecurrentdensities.Afterlessthan60 days,thebulkcopperinaclosedsystemreachedalimitinghydrogenpartialpressureof 0.096atm;whereas,themicroelectrodecontinuedtoevolvehydrogenoverthe15years, reachingavalueof0.0013atm.Thecorrosionrateforthebulkcopperwascalculated tobe0.35nm/dayanddroppedprecipitouslytozeroinlessthan60days;whereas,the 10

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calculatedcorrosionrateforthemicroelectrodewas1.1nm/dayandgraduallyreachedavalueof0.74nm/dayafter15years.Simulationsperformedusingarenedkineticmodelforamicroelectrode,1validatetheassumptionthatthehydrogenoxidationreactioncanbeneglectedforthesmallelectrodeareatovolumeratioandshorttimesconsidered.Thehydrogenoxidationreactionplayedanessentialroleinsimulatingthebehaviorofthebulkcopperexperiments2withitslargerelectrodeareatovolumeratioandlongerexposuretime.Forboththeopenandclosedsystems,thecumulativecorrosionwasreducedforlargerelectrodeareatovolumeratios.Thedierenceinestimatedcorrosionratesbetweenthecoppermicroelectrode1andtheHultquistetal.2bulkcopperexperimentsisshowninthepresentworktobethenaturalconsequenceofthemannerinwhichkinetics,masstransfer,andelectrodeareatovolumeratioinuencetheprogressiontowardstheequilibriumcondition.A2-Daxisymmetricmathematicalmodelwasdevelopedtoinvestigatefrequencydispersioninaringelectrode.TheniteelementsoftwareCOMSOLMultiphysicswasusedtosolveLaplace'sequationincylindricalcoordinatesfortheringelectrodewithanappliedperturbationpotentialastheboundarycondition.Duetothesingularitiesthatariseneartheringelectrode'sedges,anonuniformmeshingschemewasimplementednearthesurfaceoftheringelectrode.Thepresenceoffrequencydispersionisseenatfrequenciesgreaterthanthedimensionlessfrequencyequaltounity.Thecharacteristiclengthfortheringelectrodeisshowntobeafunctionofthegeometricratiooftheinnertoouterradius. 11

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CHAPTER1INTRODUCTIONManagingthethermaldissipationinmicroelectronicsfoundinconsumerPCs,laptops,radarsystemsandsatelliteshasbecomeincreasinglymoredicultasthesizetransistordecreasesandtheproximitytooneanotherbecomesmorecompact.TraditionalheatsinkssuchastheoneseeninFigure 1-1 performwell,providingasucientheatuxremovalforthemicroelectronicdevicestomaintainoperation,3butaresimplytoolargeforthespatiallyconstrainedmicroelectronicpackagingschemesoftoday.Innovationsarerequiredthatdissipatethesamepowerdensitybutwithlessthermalresistance.4Overthepastdecade,anumberofmicrostructures,nanostructuresandvariouscombinationsofbothhavebeenimplementedaswickstoaddresstheheatgeneratedfromhigh-poweredelectronics.Coppermicro/nanowickshybridstructureaccomplishthisbyprovidingasignicantpressuredrop,loweringthepermeabilityandresultinginagreaterheatremovalwhencomparedtotraditionalheatsinks.Aschematicrepresentationofatwo-phaseheatsinkisprovidedinFigure 1-2 .TheelectroniccomponentactingasaheatsourceislocatedatthebottomofthesystemseeninFigure 1-2 .Thecoolantpassivelywickstheuidtowardshotelectronicsourcebycapillaryforces.Asthecoolantisheateditbeginstoevaporate.Thevaporphaseisforcedawayfromthecentralheatingsourcewhereitbeginstocoolandeventuallycondenses.Coppernanostructuresstructuresareknowntodegradeinperformancewithtime.Sincethecoolingperformanceofacoppersurfaceisintricatelyrelatedtohowtheliquid-vaporinterfaceformsandhowwelltheuidowsthroughastructure,5preventativemeasuresmustbetakentoensurecorrosion-basedstructuraldegradationdoesnotoccur.ReportbyJu,6microuidicchannelsusedinatwo-phasecoolingsystembecamelesseectiveovertimeduetocorrosionofthechannelwall.Thetendencyforcorrosionto 12

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Figure1-1. Heatsinkfoundinconsumerpersonalcomputers.Cross-sectionalareadepictingthecopperspongematrixwithintheheatpipe.(Source:Kristoferb,en.wikipedia.org/wiki/Heat pipe) Figure1-2. Schematicofahybridmicro/nanowickcoolingsystem.(Source:SchoolofMechanicalEngineering,PurdueUniversity) 13

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occurinthesecoppercoolingsystemscanbedetrimentaltoperformanceandcouldeventuallyleadtoacatastrophicfailureifnotconsideredoutright.ThemotivationforthisworkarisesfromtheneedforabetterunderstandingofcoppercorrosionindeaerateddeionizedwaterandistheprimaryfocusofthisworkdiscussedinChapters 2 through 6 .InChapter 2 ,potentialmodesofcoppercorrosionareintroducedforthenanowickheatsink.Next,isaliteraturereviewdescribingtheroledierentmediahasonhowquicklycoppercorrodes.RelevancetothenuclearwasteindustrywithsomeoftheprevailingcontroversysurroundingtheissueisraisedatnalpagesofChapter 2 .Abetterunderstandingofcoppercorrosionhasbeengainedwiththeaidofelectrochemicaltechniques.Ofparticularimportanceistheapplicationofatechniqueknownaselectrochemicalimpedancespectroscopy(EIS).Chapter 3 providesanoverviewofthetheorybehindEIS.AnexampleispresentedtodemonstratetheneedtodistinguishtheFaradaicandchargingcurrentwheninterpretingtheimpedanceresponse.Theexperimentalprocedure,electrochemicaltechniquestoquantifycorrosionofcopperinpuredeaeratedwater,thermodynamicsimulations,kineticsimulations,andinterpretationofimpedanceresponsearepresentedinChapter 4 .Theexperimentaltechniquesemployedinthisstudyincludeimpedancespectroscopyandlinearsweepvoltammetry.Fromthesemeasurements,corrosionratesweredeterminedandfurthervalidatedwiththeuseofkineticmodeling,andthermodynamicsimulations.ArenedkineticmodelispresentedinChapter 5 toexploretheinuencemasstransfer,surfaceareatovolumeratio,exchangecurrentdensityandequilibriumpotentialhaveonthecorrosionofcopperindeaeratedwater.Toexploretheinuenceofsystemparameters,thesimulationspresentedinChapter 5 areextendedinChapter 6 toincludetheoxidationofhydrogenanddiusionofdissolvedhydrogenawayfromtheelectrodesurface. 14

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Electrodegeometryhasbeendemonstratedtocausefrequencydispersionintheelectrochemicalimpedanceresponseforvarioussystemsofdierentelectrodegeometry.Chapter 6 providesdevelopmentofarelationforthecharacteristicdimensionassociatedwiththeimpedanceresponseofaringelectrode.Emphasisonthefrequencydispersionthatiscausedbytheringelectrodeandthecharacteristicdimensionwillallowpredictionofthefrequencyatwhichdispersionisseen.Edgeeectsfromanonuniformcurrentdistributionwillbeconsideredforprimaryresistanceandimpedance.Identicationofacharacteristicdimensioncanbeusedtoavoidfrequencydispersioninacarefullychosensystemmatchingasetofparameters.Chapter 7 containsconcludingremarksforeachofthechapterspresented.InChapter 8 futureworkisproposedthatcanbecarriedoutforcoppercorrosionandgeometryinducedfrequencydispersion. 15

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CHAPTER2REVIEWOFCOPPERCORROSION 2.1CopperNano-StructuresatRiskofCorrosionCoppernanowicks,inthepresenceofanion-freedeaeratedelectrolyte,isoftenconsideredtobethermodynamicallystableandthereforeshouldnotcorrode.However,ithasbeenreported7thatcoppermicrocrystallineandnanocystallinestructureswillcorrodeundervariousconditions.Infact,deaeratedwatermayplayalargerroleincoppercorrosionthanpreviousthought.Usingelectrochemicalimpedancespectroscopythischapterexplorestheextenttowhichcorrosionisoccurring,underwhatconditionsitoccurs,andthenproposesanovelmethodforminimizingoreliminatingthecorrosionwhilemaintainingorimprovinguponthethermalandcapillaryeciencyofthecoppernanowicks. 2.1.1CopperNanoWicksManagingthethermaldissipationinmicroelectronicprocessorsfoundinconsumerPCs,laptops,radarsystemsandsatelliteshasbecomeincreasinglymoredicult.Traditionalheatsinksperformwell,providingasucientheatuxremovalforthemicroelectronicdevicestomaintainoperation,butaresimplytoolarge.3Innovationsarerequiredthatdissipatethesamepowerdensitybutwitharesistancelessthermalresistance.4Nanowicksaccomplishthisbyproducingasignicantpressuredrop,loweringthepermeabilityandresultinginanincreasedheatremovalwhencomparedtotraditionalheatsinks.Hybridmicro/nanoscalewickstructurescanbeusedtoprovideampleheatuxremovalbytheirtwophasecoolingsystem.Figure 2-1A depictsamicropillararrayattachedtoaplateincontactwiththeliquidphaseuid.HelicalhybridstructuresusedtoachieveenhancedheatremovalA)3DCADrenderedsideviewofCunanowicks;andB)SEMsideviewofregularhelicalSigrownonatungstensurface.3Attachedtoeachmicropillarisahelicalstructure.Itis 16

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A BFigure2-1. Helicalhybridstructuresusedtoachieveenhancedheatremoval:A)3DCADrenderedschematicsideviewofCunanowicks;andB)SEMsideviewofregularhelicalSigrownonatungstensurface.3(Source:Photocourtesyofauthor.) generallyunderstoodthatahybridwickstructurewillachievesuperiormasstransportwhencomparedtothatofhomogenousmicropillararraywicks. 2.1.2UniformCorrosionUniformcorrosionoccurswhenthemetalisnotimmunebutpartiallyresistanttoattackatthesurface.Inthismodeofcorrosion,themetalsurfaceundergoescorrosionatauniformrate.Asaresult,alloftheexposedareaofthemetalisequallysusceptibletocorrosion.Atthesurfaceofthemetaltherearespatiallyseparatedlocalanodicandcathodicsiteswherebothoxidationandreductionoccursimultaneously.Thenetcurrentofthesystemisequaltozerobutthereactionisnotequilibratedwhichprovidesasucientpotentialdierencefortheelectrochemicalreactiontooccur.Intheabsenceofoxygen,thereactionsinvolveanodicdissolutionofcopper Cu!Cu2++2e)]TJ /F1 11.955 Tf 168.23 -4.94 Td[((2{1)andwaterreductionatthecathode, H2O+e)]TJ /F2 11.955 Tf 10.4 -4.94 Td[(!1 2H2+OH)]TJ /F1 11.955 Tf 149.9 -4.94 Td[((2{2) 17

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Theseequationsrepresentthetwocompetingreactionrequiredforuniformcoppercorrosion. 2.1.3Galvanic(Coupling)CorrosionItiscommonlyobservedthatwhentwoormoremetalsareelectricallyconnectedinanelectrolyte,thelessnoblemetalcorrodesrapidly.8Thisphenomenaisknownasgalvaniccorrosionandoccurswhenthereexistsapotentialdierencebetweenthetwoormoredissimilarmetals.Galvaniccorrosionisfrequentlyobservedinplacessuchaschemicalplants,residentialhomesandoshoreplatforms.AnotableexampleisdescribedbyFontana9whereayachtcontainingaMonelhullaxedbysteelrivetsundergoesrapidcorrosionoftherivets.Notascommonlyobservedisthepotentialdierenceoccurringbetweentwoofthesamemetalshavingnearlythesamecompositionyetdierentmetallurgicalproperties.Pantazopoulos10attributestheleakageofacopperwatertubeattheelbowtofatiguecrackinginducedbystress. 2.1.4Electrokinetic-CurrentCorrosionTheerosivityofthecomponentsfoundinhighpressurehydraulicsystemsofairplaneswasinitiallyattributedtosimplewearandtear.Itwaslaterdiscoveredthatwhenuidsareforcedthroughchannelsastreamingpotentialisformed.Thestreamingpotentialprovidesanadequatedrivingforceforcorrosionattheuid-surfaceinterface.TheElectricdoublelayerstreamingpotentialshownonananowick.Astheuidmovesupbycapillaryforces(wicking),thedepletionofcationsatthebaseofthedeviceresultsinacorrosionreactionnecessarytoreplenishthecations.Coppernanowickshavea(-)chargeisprovidedinFigure 2-2 .Astheuidtraversesthediusedoublelayer,ionsaresweptawaytothebulkfasterthantheycanbereplenishedbythewallssurface.Thedepletionofionsresultingfromshearvariationissucienttoproduceanelectricalcurrentatthemetal-uidinterfacethuscorrodingthemetalsurface. 18

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Figure2-2. Electricdoublelayerstreamingpotentialshownonananowick.Astheuidmovesupbycapillaryforces(wicking),thedepletionofcationsatthebaseofthedeviceresultsinacorrosionreactionnecessarytoreplenishthecations.Coppernanowickshavea(-)charge. Nanodevices,bydesign,coolthemselvesbythecapillaryforcedrivingtheuidthroughthenanostructuredposts.ThepotentialdrivingforceistheelectriceldEzasafunctionofthepressuregradientdp dz, Ez=I2(R0) I1(R0)q2 edp dz(2{3)WhereI1andI2arethemodiedBesselfunctionoftherstandsecondkind,respectively.11R0istheratioofcapillaryradiustoDebyelength.Purewaterat25ChasaDebyelengthof=0:96m.Assumingasurfacechargeofq2=0:01C cm2withaneectiveconductivity=5:510)]TJ /F4 7.97 Tf 6.59 0 Td[(8S cmandaviscosityof=0:01g cm_s,theelectriceldcanbedeterminedby Ez=4:37510)]TJ /F4 7.97 Tf 6.59 0 Td[(6I2(R0) I1(R0)dp dz(2{4) 19

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Furthermore,ifthesystemisassumestohaveaporeradiusof100nmwhichcorrespondstotheratiooftheBesselfunctionsintheaboveexpress,I2(R0)=I2(R0),of0:0025thenthefollowingrelationbetweenthethevoltagepotentialVandthepressuredroppacrossachannelsizeofz, V=Ezdz=4:37510)]TJ /F4 7.97 Tf 6.58 0 Td[(6dp(2{5)Ascanbeseenfromthislinearrelationapressuredropof10kParesultsinavoltagepotentialof4.375V. 2.1.5ThermogalvanicCorrosionThermogalvaniccorrosionoccurswhenonepartofametalismaintainedatahighertemperaturerelativetotheotherparts.Inthepresenceofatemperaturegradientof20CRushing12describeshowcoppersolubilityinthe13variessucientlytoinducecorrosion. 2.2InuenceofSolutionChemistryThecorrosionofcopperinaeratedmediahasbeenthoroughlystudiedandisnowrelativelywellunderstood.Copperinthepresenceofacidchloride14,15,16,17takesplacesbyamechanismthatinvolvesformationofCuCl)]TJ /F4 7.97 Tf 6.59 0 Td[(12withnoevidenceindicatingthepresenceofaprotectiveoxidelayerCuO2.18ThereactionprocessisdiusioncontrolledratherthanactivationcontrolledwhichdemonstratesaTafelbehaviorwithcorrespondingTafelslopesof2:303RT=F.Acidicsulphatemedia19,20,21,22resultintheanodicdissolutionofcopperwhichisalsodiusioncontrolled,albeitadierentdiusingspecies.Additionalelectrochemicalstudies23,24,25demonstratetheeectsofalkalineenvironmentsoncopper.OfparticularinteresttoUSNavy,shipsusingcopperandcopperalloysasheatexchangersaresubjecttocorrosionunderhighowmarineenvironments.26,27,28,29Coppercorrosioninanalkalinechloridemediainvolveserosion-corrosionreactionwherebyhydrodynamicsheardisruptsthecopperoxideprotectivelayerthusrenderingthecopperexposedandsusceptibletocorrosion. 20

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2.2.1AcidicChlorideMediaMuchoftheliteraturediscussesthecorrosionofcopperinanacidicmediacontainingcorrosivespeciessuchassulphateorchlorideions.Anodicdissolutionofcopperinanacidicchloridesolutionhasbeenextensivelydiscussedintheliterature.14,15,16,17MuchofthisworkaimstoobtainkineticexpressionsbasedonNerst'sequationandFick'srstlaw.Forconstantanodiccurrentatvaryingchlorideconcentrationsupto1M,LalandThirsk14showpolarizationcurvesbasedontheTafelequation, dV dlog[Cl)]TJ /F1 11.955 Tf 7.09 -3.45 Td[(]=22:303RT F(2{6)wherethetemperaturedependent,T,changeinpotential,V,withrespecttothelogofthechlorideconcentrationisrelatedtoAvogadro'sconstant,RandFaraday'sconstant,F.Chlorideconcentrationhigherthan1Mchangesthecoecient2seeninEq.( 2{6 )to3.BacarellaandGriess18considertheanodicdissolutionofcopperinacidwithchlorideconcentrationrangingfrom0:124Mto1:24M.TheirresultsshowthatthisprocessisdiusioncontrolledratherthanactivationcontrolledwhichdemonstratesaTafelbehaviorwithcorrespondingTafelslopesof2:303RT=F.Furthermore,theTafelbehaviorconsistentashighas175CwhichispHindependentonthischlorideconcentrationrange.TheformationofCuCl)]TJ /F4 7.97 Tf 0 -7.88 Td[(2wastheprimaryproductobtainwithnoevidenceindicatingthepresenceoftheprotectiveoxidelayerCuO2. 2.2.2AcidicSulphateMediaWhensulphidesarepresentinsolutioncopperisseentocorrodeatfasterrates.Theoxidelmthatisseenonthecoppersurfacebecomessusceptibletoreductionofoxygeninthepresenceofsulphides.19Copperdissolutioninacidsolutionundervariousstirringconditions,acidstrengthandO2saturationlevelispresentedbyAndersen.20InthisworkitisfoundthattheanodicdissolutionofCuoccursfasterinanO2saturatedsolutionthaninaN2saturatedsolution.Underweaklyacidicconditionstheycomparethefastrate-determiningdiusioncontrolledstepfortheanodicdissolutionofCuinthepresence 21

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ofHCltothatofH2SO4.SlightlyacidsulfatesolutionreducethestabilityoftheCu+andareremovedbyformingtheCuO2precipitate.Astudyofcopperdissolutioninanacidicsulphatemediawasusedtoinvestigatewhethercopperdissolutionoccursthroughamonovalentordivalentstate.21Usingaquartzcrystalmicrobalance,impedancespectroscopyandelectrocoulometryitwasfoundthatcopperdissolvestothemonovalentCu+atlowcurrentdensities10)]TJ /F4 7.97 Tf 6.59 0 Td[(5A=cm2andtoCu2+athighercurrentdensities10)]TJ /F4 7.97 Tf 6.58 0 Td[(2A=cm2.TheinstabilityoftheCu+insolutiontransformsthemonovalentcopperbythefollowingdisproportionationreaction, 2Cu+!Cu2++Cu(2{7)WherethedominatingspeciesofCuandCu2+aredisproportionatelyfavored. 2.2.3AlkalineMediaInextremealkalineenvironmentselectrochemicallyformedanodiclmsactasabarrieronthecoppersurfaceprotectingthecopperfromcorrosion.In-situRamanspectroscopywasusedtostudy22thepassivatinglmsofcopperin1Mand6MKOHatdierentpotentials.Basedontheanodicvoltammetricpeaksinconjunctionwithin-situRamanspectroscopy,theauthorswereabletoidentifythecoppersurfacelmproductsasCu2O,Cu(OH)2andCuOrespectively.Onceformed,theanodicsurfacelmsbecomemorediculttoreduceanddoingsorequiresahighcathodicpotential.Alternatively,onecouldlowerthepHoftheelectrolytetofacilitateinthedissolutionofthepassivelmtorecoverthecoppersurface.Additionalelectrochemicalstudies23,24,27demonstratetheeectsofalkalineenvironmentsoncoppermetal.Severalstudiesofcoppercontainingintrauterine(IUD)devices31,32discussthepHdependentcoppercorrosionofsimulateduterinesolutionoveraphysiologicallyrelevantpHrangeof6:3to8:0.25Inthisstudythecharacterizationofthecorrosionproductsisobtainedusingabsorptionspectroscopy.Forthesimulateduterinesample,thehighestcorrosionratewasfoundatapH=5:0.Herethepresencehydrogen 22

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Table2-1. ReactionswereadoptedfromMayer22andthermodynamicvalueswerecalculatedbasedonPourbaix's30work. RedOxPotential(Vvs.Hg/HgO)CoupledReactionatEquilibrium -0.872H2O+2e)]TJ /F12 11.955 Tf 10.41 -4.33 Td[(H2+2OH)]TJ /F1 11.955 Tf -246.01 -18.78 Td[(-0.4962Cu+2OH)]TJ /F12 11.955 Tf 10.41 -5.01 Td[(Cu2O+H2O+2e)]TJ /F1 11.955 Tf -290.67 -18.82 Td[(-0.340Cu2O+6OH)]TJ /F12 11.955 Tf 10.4 -5.01 Td[(2Cu2O2)]TJ /F1 11.955 Tf 9.74 -5.01 Td[(+3H2O+2e)]TJ /F1 11.955 Tf -321.68 -18.78 Td[(-0.220Cu2O+2OH)]TJ /F12 11.955 Tf 10.4 -5.01 Td[(2CuO+3H2O+2e)]TJ /F1 11.955 Tf -305.63 -18.79 Td[(-0.189Cu2O+2OH)]TJ /F1 11.955 Tf 9.74 -5.02 Td[(+H2O$2Cu(OH)2+2e)]TJ /F1 11.955 Tf -319.5 -18.78 Td[(0.324OH)]TJ /F12 11.955 Tf 10.4 -5.01 Td[(H2O+O2+4e)]TJ ET q .936 w 24.23 -144.84 m 439.87 -144.84 l S Q BT /F1 11.955 Tf 0 -177.19 Td[(ionsplayanimportantroleinpromotingthecorrosionofcopperas, 2Cu+4H++O2!2Cu2++2H2O(2{8)AthigherpHtheyobserveasimilarpassivatingbehaviorasisreportedbyMayer,22attributingcupricoxideCu2Oastheprimarylmproduct.AproposedmechanismforcoppercorrosioninaUIDis, 8Cu+O2+2H2O!4Cu2O+4H++4e)]TJ /F1 11.955 Tf 107.48 -4.94 Td[((2{9) Cu2O+2H+!2Cu2++H2O+2e)]TJ /F1 11.955 Tf 115.94 -4.94 Td[((2{10)Thelmproductobservedforthecopperintrauterinedeviceagreeswiththeanodiccopperlmdescribedby.22 2.2.4AlkalineChlorideMediaOfparticularinteresttotheUSNavyaretheirshipswhichutilizecopperandcopperalloysasheatexchangers.Theseheatexchangersbecomesubjecttocorrosionunderhighowmarineenvironments.24,26,27,28,29Coppercorrosioninanalkalinechloridemediainvolveserosion-corrosionreactionwherebyhydrodynamicsheardisruptscopperprotectinglayer.Usinganaxisymmetricimpingingjetcoupledwithascanningellipsometer,theauthorsuseelectrochemicaltechniquestocomparethehighowconditionstothoseunderstaticconditionsof3:5%wtNaClinsolutionshavingpH8.5and9.8.Specically,the 23

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surfaceshearstresswasisolatedfromothercorrosion-erosionmechanismsandfoundnottobetheprimarysourceforcoppererosion-corrosionunderalkalinechlorideconditions. NeutralMedia.Ithasbeenreported19thatwateratpH=7and25oCwithdissolvedO2concentrationsaslowas8ppbcancontributetoaredoxpotentialof+0:76(vsSHE).Forthefollowingcoupledredoxreactionoxygenisbeingreduced O2+2H2O+4e)]TJ /F1 11.955 Tf 10.41 -4.93 Td[(=4OH)]TJ /F1 11.955 Tf 140.64 -4.93 Td[((2{11)OnthecoppersurfacethereductionofO2willbedependentonboththenumbercatalyticsitesavailableandthepotential.IthasbeenobservedatneutralconditionsthatthereductionofO2canresultinanincreaseintheinterfacialpHashighas10)]TJ /F1 11.955 Tf 11.7 0 Td[(1133fromtheformationofOH)]TJ /F1 11.955 Tf 7.09 -4.34 Td[(.Electrochemicalexperiments29showthatpurecopperinaneutralsolutionresultsintheformationofanoxidelmworkstoprotectthecopperfromcorrosion.Astimeprogressestheauthorsreportthattheoxidelmontheelectrodesurfaceincreasesbasedontheincreaseinthepolarizationresistance.Theimportanceoftheself-formingoxidelayerisapparentwhencomparingtheresultsofneutralpHtoanacidicenvironment.AtpH=1,withincreasedimmersiontime,thedissolutionofthenativeoxidelmatthecoppersurfaceoccursexposingthecoppersurface.Onceexposed,thecoppersurfaceissusceptibletocorrosionwheresolutioncomposition,pHandpotentialcanallplayaroleintheinterfacialelectrochemistry.Oncesuchcase,involvingthecorrosionofcopperinaeratedneutraltapwatersolution,isreportedtobecontrolledbythediusionofcopperionsinthecuprousoxidelm.34DiusioncontrolledWarbergimpedanceobservedintheirEISresultsindicatethattheanodicprocessdictatesthenetrateofcoppercorrosion.FromtheWarbergimpedanceonecanobtainthepolarizationresistancewhichincreaseswithimmersiontime.Theauthorsattributetheincreasingpolarizationresistancetotheproliferationofthenatantcopperoxidelm.Furthermore,ifexposedtoowconditionsinducedbyarotating 24

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discelectrodetheauthorsobserveanincreaseinanodiccurrentandlowerpolarizationresistancewhichcanbeattributedtothethinningoftheoxidelayer.AtpHlowerthan5theauthorssuggestthatmixeddiusion(diusionofcopperionsinoxidelmandinsolution)occurs.Unfortunately,thisclaim,underacidicconditions,lackthesupportXPSandcyclicvoltammetrydatathatwaspresentfortheneutralandalkalinestudies. 2.3NuclearWasteStorageCorrosionindeaerateddeionizedwaterislesswellunderstood.Theequilibriumpotentialforthecopperdissolutionreactionis0.377Vwithreferencetothehydrogenreaction,therefore,inneutraldeaeratedmedia,copperiscommonlybelievedtobeimmunetocorrosioninpurewater.Thestabilityofcopperindeaeratedenvironmentsmotivatedproposedstorageofnuclearwaste33,35,36,37,38,39,40incopper-linedcontainerstobeplacedinundergroundvaults.Hultquist2showed,however,thatcopperfoilstoredfor15yearsinaErlenmeyeraskwithpermeablemembraneselectivelypermittingtheegressofhydrogenrevealedsignicantcorrosion.Thiswasincontrasttoaaskthatwashermeticallysealedandshowednocorrosion. 25

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CHAPTER3OVERVIEWOFELECTROCHEMICALIMPEDANCESPECTROSCOPYElectrochemicalImpedanceSpectroscopy(EIS)isapowerfulnon-invasivetechniqueusedforstudyinginterfacialelectrochemistry.Havinggainedtremendouspopularityinrecentyears,EIShasbecomewidelyusedinelucidatingthecorrosionprocessesofvariousmetalsandalloys.EISmeasurementsareobtainedbyapplyingasmallamplitudesinusoidalperturbationsignalandmeasuringthesystemsresponseatmodulatedfrequency.Theoutputsignalismeasuredinthefrequencydomainandthereforecontainsbothrealandimaginarycomponents.ImpedanceisdenedastheratioofthechangeinpotentialVtothechangeincurrentI,41 Z=jVj jIjej=Zr+jZj(3{1)whereisthephasedierencebetweenpotentialandcurrent,jisacomplexnumberandZrandZjaretherealandimaginarycomponentsofthemeasuredimpedance.Whencurrentandpotentialareinphase,theimpedancecontainsonlytherealcomponentandisexpressedasresistance, Zres=R(3{2)Ifthereexistsaphaseshiftof90degreesbetweenthecurrentandpotentialcorrespondstoapureimaginarycomponentandisoftentimesdenedasthecapacitance, Zcap=1 j!C(3{3)Figure 3-1 showsthepotentialversuscurrentplotandillustratesthesmall-amplitudesinusoidalperturbationappliedtothesystemduringatypicalEISmeasurement.EISmeasurementscanbeusedtodirectlyinvestigatetheelectrochemistryoccurringontheelectrodesurface.Nyquistplotsshowingrealversusimaginaryareusedtorepresenttheimpedancedata.EISMeasurementsaretakensweepingfromhighfrequency(LHSofNyquistplot)tolowfrequency(RHSofNyquistplot).Considertheimpedance 26

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Figure3-1. Sinusoidalperturbationofanelectrochemicalsystematsteadystate,whereVandIrepresentthepotentialandcurrentoscillatingatthefrequency!withaphasedierenceof.42 resultsobtainedforPt,W,andAu(platedw/W)showninFigure 3-2 .TheresponseofthePtelectrodeislinearwhencomparedtothesemicircularimpedanceoftungsten.Electrochemically,thelinearbehavioroftheimpedancesuggeststhatthePtelectrodeisinerttoanycathodicoranodicreactionatopencircuitwhichisclassiedasblockingelectrodebehavior.Alternatively,thenitevalueofimpedanceobservedatlowfrequenciesforthetungstenmicroelectrodessuggeststhepresenceofFaradaicreactions.TheimpedanceresponseforthePtelectrodeshowsthebehavioronewouldexpectifnocorrosionwereoccurringintheCunanowick.Electricalcircuitanalogsarefrequentlyusedtoillustratethedistributionofpotentialinanelectrochemicalsystem.Thetypeofelectrochemistrybeingconsidereddictateshowoneconstructstheanalogouscircuit.Forexample,asystemhavingcontributionsfromonlytheOhmicresistanceoftheelectrolyteReandinterfacialimpedanceZ0correspondtoaninseriesanalogcircuitasseeninFigure 3-3A .Inseriescircuitsaremathematically 27

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Figure3-2. Impedanceresponseofplatinum,goldplatedtungstenandtungstenmeasuredfrom0.1Hzto20kHz.Theimpedanceresponseclearlydelineatestheblocking(nonreactive)behavioroftheplatinumelectrodefromtheFaradaicreactivebehaviorofthetwotungstenelectrodes.43 representedbythesumofthecomponents, U=Rei+V(3{4)Inordertounderstandtheinterfacialimpedance,wemustnotonlyconsiderthechargingcurrent,butwemustalsoaccountfortheFaradaiccurrentaswell.Attheopencircuitpotential(corrosionpotential)thesumoftheanodicandFaradaiccurrentsmustbezero, ia+ic=0(3{5)ThismeansthecurrentpathsshowninFigure 3-3B willbeaparallelsumofZaandZc.Furthermore,wemustconsiderthecontributionofthedoublelayercapacitanceCdlwhich 28

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A BFigure3-3. Analogouscircuitsofanelectrochemicalinterfacesusceptibletocorrosionattheopen-circuitpotential:A)electricalcircuitinseriestoaccountforOhmicresistanceandinterfacialimpedance;B)electricalcircuitshowinghowtheinterfacialimpedancecanberepresentedbytheadditionofimpedancesinparalleltoaccountforcurrentcontributionsassociatedwithchargingtheinterface,theanodic(corrosion)reaction,andthecathodicreaction.41 isaddedinparallel. Z0=1 1 Za+1 Zc+j!Cdl(3{6)TheanodicimpedanceofthecorrodingcoppernanowickZawillbesmallandeasilyseenintheimpedanceresponseZ0,thereforemakingimpedancespectroscopyaviabletechniqueforinvestigatingthemechanismsleadingtothecorrosionofthenanowicks. 29

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CHAPTER4CORROSIONOFCOPPERINDEAERATEDWATERTheneedforincreasinglymore-functionalelectronicsandtheindustry'sabilitytofabricatehighdensityintegratedcircuitshaveledtoanever-increasinggenerationofwasteheatinadvancedelectronicssystems.Theincreasesinpowergenerationhasoftenbeenhandledbyimprovementsinmaterialsorcomponentsconguration.However,itisnowgenerallyacknowledgedthatthecoolingrequirementsforadvancedelectronicsexceedtheheat-removalcapabilityofconventionalcoolingtechniques.Liquid-basedcooling44,45,46,47,48,49,50mayremedythermalmanagementissuesthathaveplagueddevelopmentanddeploymentofenhancedelectronicsystems. 4.1HeatSinksusedtoCoolHighPerformanceElectronicsDuetoitsexceptionalheattransfercharacteristics,particularlyinthephasechangeprocess,waterisconsideredtobeasuitablecoolinguid,solongasissuesrelatedtoitselectricalpropertiescanbeaddressed.Numerousstudieshavebeenconductedtodevelophighperformancewaterheatsinks.51,52,53,54,55,56Thesestudiesoftenutilizemicro-ornanostructurestoenhanceheattransferatthesolid-liquidinterface.Traditionally,copperhasbeenthematerialofchoiceinwaterheatexchangers,and,asitisgenerallyunderstoodthatcopperdoesnotcorrodeindeaerateddeionizedwater,coppermicro/nanostructuresareimplementedtobenetfromtheassociatedenhancedheattransfercharacteristics.Theperformanceofmicro/nanoscalecopperstructureshas,however,beenobservedtodegradewithtime.Juetal.6reportedthatcorrosionincoppermicrouidicchannelsusedinatwo-phasecoolingsystemcausedperformancedegradation.Sincethecoolingperformanceisintricatelyrelatedtofunctionalityoftheliquid-vaporinterfaceanduidowthroughastructure,5evensmallratesofcorrosioncanimpairperformanceofamicro/nanostructuredinterface.Thus,anabilitytopredictandmitigatecoppercorrosionisneeded. 30

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4.2StabilityofCopperinDierentMediaThecorrosionofcopperinaeratedmediaisrelativelywellunderstood.Inacidicchloridesolutions,forexample,thecorrosionofcoppertakesplacebyamechanismthatinvolvesformationofCuCl)]TJ /F4 7.97 Tf 6.59 0 Td[(12fromaCuClintermediate.17Thereactionprocessisreportedtobediusioncontrolledwithnoevidenceofaprotectiveoxidelayer.57Thismechanismhasbeenpresentedasvalidfortemperaturesashighas165C.18Incontrasttothemechanismacceptedforacidicchloridesolutions,directformationofCu+andCu2+hasbeenobservedforcorrosionofcopperinacidicsulphatemedia.20,21,22Jardyetal.21usedaquartzcrystalmicrobalance,impedancespectroscopy,andelectrocoulometrytoshowthatcopperdissolvestothemonovalentCu+atlowcurrentdensities(10)]TJ /F4 7.97 Tf 6.59 0 Td[(5A=cm2)andtothedivalentCu2+athighercurrentdensities(10)]TJ /F4 7.97 Tf 6.58 0 Td[(2A=cm2).TheCu+speciesisunstableandparticipatesinahomogeneousreactionaccordingto 2Cu+!Cu2++Cu(4{1)wheresolidanddivalentcopperaredisproportionatelyfavoredoverthelessstableCu+.21Inextremealkalineenvironments,electrochemicallyformedanodiclmsactasabarriertoprotectthecopperfromcorrosion.In-situRamanspectroscopywasusedtostudythepassivatinglmsofcopperin1Mand6MKOHatdierentpotentials.22Basedontheanodicvoltammetricpeaks,inconjunctionwithin-situRamanspectroscopy,theauthorsidentiedsurfacelmscomposedofCu2O,Cu(OH)2,andCuO.Onceformed,theanodicsurfacelmsbecomemorediculttoreduceanddoingsorequiresahighcathodicpotential.Alternatively,onecouldlowerthepHoftheelectrolytetofacilitatethedissolutionofthepassivelmtorecoverthecoppersurface.Inalkalinesolutions,therstandsecondoxidationstatesaretypicallyreportedbutinastudybyMiller,23asolubleCu3+specieswasidentiedintheanodicregionattheonsetofoxygenevolution.Ofparticularinteresttonavalvessels,copperandcopperalloyheatexchangerscooledwithseawateraresubjecttocorrosionunderhighvelocityow.28,29Thelargeshearstress 31

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attubeandinletwallswasfoundtoremovelooselyadherentsaltlms,causingformationofgalvaniccells.26,24,27Thiseecthasbeendescribedasresultingfromerosion-corrosion.58Bojinovetal.providedamechanisticstudyofcopperinteractionswithadeoxygenatedneutralaqueousboratebuersolution.60Theirpreliminaryconclusionswerethatnosustainedcorrosionofcopperwasfound,butthattheimpedanceresultswereconsistentwithanadsorbedCuOHintermediateassociatedwithreductionofCu(II)species.Inanearlierstudy,Bojinovetal.usedanon-lineresistanceprobetodiscoverthatcoppercorrodedatanappreciablerateof16m/yduringshort-timeexposureto1MNaClthatcontainedverysmallamountsofoxygen.61Afterlongerexposure,thecorrosionratedecreasedandback-depositionofcopperwasreported.Aspartoftheanalysisofthesuitabilityofcopperfornuclearwastestorage,Shari-AslaandMacdonald62haveperformedstudiesofthehydrogenevolutionreactiononcopperindeoxygenatedneutralaqueousboratebuersolutions.IncidenceofcoppercorrosionindeaerateddeionizedwaterhasalsobeenreportedintheheatexchangersusedtocoolthesynchrotronatArgonneNationalLabs.Astudyofcorrosionratesasafunctionofoxygencontentinneutraldeionizedwaterrevealedthatthecorrosionratewasgreaterthan8mg/m2/day(0.9nm/day),evenatdissolvedoxygenconcentrationsaslowas15ppb.63,64Theseresultswereconrmedbysubsequentanalysisbasedonanon-stationarynite-dierencesimulationusedtorepresenttheprocessesofcorrosion,erosion,dissolution,precipitationanddepositionforthelengthofa1-Dcoolingcircuit.Inthiswork,Parrofoundacorrosionrateof1g/m2/year(0.3nm/day).65Thesecorrosionrateswereconsideredtobesucientlysmallastoposenolong-termproblemswiththeoperationofthesynchrotron. 4.3DisposalofSpentNuclearRodsAsimilarbodyofworkdoesnotexistforcorrosionofcoppermicro/nanoscalestructuresinheatexchangers,thoughthisareamaybecloselyrelatedtothebodyofworkassociatedwithplansforencasingnuclearwasteincoppercladding.Thestandard 32

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equilibriumpotentialforthecopperdissolutionreactionhasavalueof0.337Vwithreferencetothehydrogenreaction;59therefore,copperiscommonlybelievedtobeimmunetocorrosioninneutraldeionizeddeaeratedmedia.Theproposedstabilityofcopperindeaeratedenvironmentshasmotivatedinvestigationofthefeasibilityforundergroundstorageofnuclearwasteincopper-linedcontainers.35,36,37,38,39,40,33ConcernhasbeenexpressedoverresultspresentedbyHultquist2whoshowedthatcopperfoil,storedfor15yearsinanErlenmeyerasklledwithdeaerateddeionizedwaterandcappedwithpermeablemembrane,selectivelypermittingtheegressofhydrogen,revealedsignicantcorrosion.Corrosionwasnotobservedforasimilarfoilenclosedinahermeticallysealedaskthatdidnotallowtheeusionofhydrogen(oranygas).Inacritique,KingandLiljaidentifysomeinconsistenciesandindicatethatothergroupshavebeenunabletoreproduceHultquist'sresults.MacdonaldandShari-Aslstate,however,thatHultquist'sresultsarenotatoddswiththermodynamics,providedthattheconcentrationofCu2+andthepartialpressureofhydrogenaresuitablylow.40Smallratesofcorrosionmay,however,besignicantforheatexchangersinwhichsurfacenano-structurepostsareutilizedtofundamentallychangethephysicsofliquid-surfaceinteractionsandtogreatlyenhancethephase-changeheattransferprocess.Smallratesofcorrosionmayalsocompromisesafestorageofnuclearwastewherestructuralintegritymustbeassuredforperiodsexceedingonemillionyears.Theobjectiveofthisworkistouseelectrochemicaltechniquestoquantifycorrosionofcopperinpuredeaeratedwater.Theexperimentaltechniquesemployedinthisstudyincludeimpedancespectroscopyandlinearsweepvoltammetry.Fromthesemeasurements,corrosionratesweredeterminedandfurthervalidatedwiththeuseofkineticmodeling,andthermodynamicsimulations. 4.4ExperimentalTheexperimentalprotocol,instrumentation,andelectrodesarepresentedinthissection. 33

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Figure4-1. Schematicdiagramshowingthedeaerationprocessusedtoachieve1-2ppbgas-phaseO2concentrationlevels,resultinginasubstantiallylowerconcentrationinthewater.1 4.4.1De-AerationProcedureAveport200mlglassvessel(GamryEuroCellr),showninFigure 4-2 ,wasusedastheelectrochemicalcell.Thevolumeofelectrolytewas30cm3.Thedeionizedwater(BarnsteadE-PureD4631)hadaresistivityof17.6Mcm.BIPrgradenitrogengas(Airgas),withguaranteed99.9999%puritywasusedtodeaeratethesystemthroughamicroporousglassfritforatleast1.5h.AHachOrbisphere3650micrologger,withasensitivityof0.1ppbO2,wasusedtomonitortheO2concentrationofthegasemanatingfromthecell,continuouslyuntilastable1-2ppbgas-phaseoxygenlevelwasachieved.Undertheseconditions,thelargeHenry'sLawconstantforoxygeninwaterensuredthattheoxygenlevelintheelectrolytewaslowerthan1ppb.Toensurethatmeasurementofgas-phaseO2concentrationreectedtheconcentrationsintheliquidphase,anexperimentwasdevisedinwhichthewaterfromtheelectrochemicalcellwasconveyedunderpressuretotheoxygendetector.Thewaterwasde-aeratedasdiscussedaboveuntilastable1-2ppbgas-phaseoxygenlevelwasachieved.Pressurefrom 34

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thenitrogentankwasusedtoforcethewaterfromthevesseltothedetectorthroughTygothanertubing(Saint-Gobain).Oxygenreadingsweretakenafterthe30minuteequilibrationperiodrecommendedbythemanufacturerforliquidshavingppblevelsofdissolvedO2.Thismeasurementwasrepeatedfourtimesandthemeasuredoxygenlevelsrangedfrom8ppbto18ppb.Thesevaluesrepresentanupperlimittotheoxygencontentachievedintheelectrolyteastheprocessintroducedthepotentialingressofsmallamountsofatmosphericoxygen.Indeed,theimpedanceresponseshowninasubsequentsectionindicatesthattheoxygenconcentrationinthewatermusthavebeenlessthan6.5ppb. 4.4.2InstrumentationElectrochemicalexperimentswereperformedforathree-electrodecongurationusingeitheraGamryReference3000oraGamryReference600potentiostat.Forimpedancemeasurements,opencircuitpotential(OCP)measurementswererecordeduntiltheOCPchangedlessthan0.1mV/min.Agroundedhome-builtFaradaycagewasusedtoreduceelectromagneticinterference.Impedancemeasurementswereperformedfrom100kHzto200mHzforexperimentsthatexploredthehigh-frequencydielectricresponsereportedinasubsequentsection.Forstudiesofelectrochemicalreactivity,measurementswereperformedfrom1kHzto50mHz.Theperturbationamplitudewas10mV.LinearsweepvoltammetrywasperformedwithaGamryReference3000usingasweeprateof0.06mV/s.Sweepswereperformedfromtheopencircuitpotentialinbothanodicandcathodicdirections.Theworkingelectrodeforthisexperimentwasa0.1mmdiameterannealed99.9%copper.ThereferenceelectrodeandcounterelectrodewereAg/AgClasreportedbelow. 4.4.3ElectrodesThecounterelectrodeandreferenceelectrodesweresolidAgClpelletsembeddedinaacrylictube,sealedwithepoxy,andattachedtoasilverwire.Twohourspriortoimpedancemeasurements,theAg=AgClelectrodeswereimmersedinpuredeionizedwater(witharesistivityof17.6Mcm)andshortedtogethertoreducepolarizingeects.The 35

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Figure4-2. Cu,AuandPtworkingelectrodeswiththeexposed0.25mmdiskdiametershown.Theoutsidediameteroftheacrylictubewas6.5mm.1(Source:Photocourtesyofauthor.) Ag/AgClelectrodeswereusedinthisapplicationtoavoidelectrochemicalreactionsthatwouldchangetheelectrolytepH.Theuseofsolidelectrodespreventedcontaminationoftheelectrolytebyllingsolutionsusedinconventionalreferenceelectrodes.Theworkingelectrodeswerecomposedofannealed99.9%copper,hard-tempered99.99+%gold,andannealed99.9+%platinum(Goodfellow,UK)wireswith0.25mmand0.1mmdiameters.Thewireswereembeddedinanepoxymoldtoexposeonlyadiskcross-section,asshowninFigure 4-2 .Electrodesurfaceswerepolishedmechanicallywiththenalpolishperformedusinganaluminasuspensionwitha0.1mparticlesizeuntilanemirror-likenishwasvisible.Aseriesoforganicsolventsinincreasingpolarity(methanol,isopropanol,andacetone)followedbydeionizedwaterwereusedtocleananddegreasethesurface.Theimpedanceresponseforelectrodesofdiameterexceeding0.5mmwasdominatedbyahigh-frequencyloopthat,asdiscussedinasubsequentsection,wasattributedtothedielectricresponseofwater.The0.25mmdiameterelectrodeswereusedinthepresentworktominimizetheportionofthemeasuredfrequencyrangeassociatedwiththehigh-frequencyloop,andtherebymaximizetheresponseassociatedwithchargingandfaradaiccurrentsattheelectrode. 36

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Figure4-3. Scaledimpedanceresponseofcopper,goldandplatinum0.25mmdiameterelectrodesindeaerateddeionizedwater.Thefrequencyrangewas100kHzto40mHz. 4.5ExperimentalResultsTheelectrochemicalmeasurementsincludedimpedancespectroscopyandlinearsweepvoltammetry.Impedancemeasurementsoncopperelectrodeswererepeatedwithinertgoldandplatinumelectrodesinordertorevealdierencesinelectrochemicalbehavior. 4.5.1ImpedanceSpectraScaledimpedanceresults,measuredattheopen-circuitcondition,arepresentedinFigure 4-3 withelectrodematerialasaparameter.Thedatashownwerecollectedonafrequencyrangeof100kHzto200mHz.ThedatawerescaledbytheapparentOhmicresistance,obtainedattheintersectionbetweenthehigh-frequencyandthelow-frequencyloops,toemphasizethesimilarityinthehigh-frequencyresponseforcopper,gold,and 37

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platinumelectrodes.Asthisfeatureisunaectedbytheelectrode,itcanbeattributedtothedielectricresponseofwater.Thevaluesoftheohmicresistanceobtainedfromtheimpedanceresponsewere15.0kcm2forthecopperelectrode,19.5kcm2forthegoldelectrode,and12.8kcm2fortheplatinumelectrode.Slightdierencesinthesevaluescanbeattributedtominuteleachingofionsfromtheglassware.FollowingtheformulafortheohmicresistanceofadiskelectrodepresentedbyNewman,66 Re= 4r0(4{2)thewaterresistivitywascalculatedtobe1.53,1.98,and1.30Mcm,respectively.Thisestimatedwaterresistivityisanorderofmagnitudelowerthantheinitial17.6Mcmwaterresistivity.Adecreaseinwaterresistivityisexpectedforexperimentsinhighlydeionizedwater.Asecondsetofexperiments,whichemphasizethelow-frequencybehavior,arepresentedinFigure 4-4 .Thefrequencyrange,chosentoeliminatetheinuenceofthehigh-frequencydielectricloop,is54.5Hzto46.5mHz.TheNyquistrepresentation,showninFigure 4-4A ,indicatesthatthegoldandplatinumelectrodeshadlowerelectrochemicalreactivitythanthecopperelectrode.TheimaginaryimpedanceispresentedonlogarithmicscaleasafunctionoffrequencyinFigure 4-4B .Theslopeoftheimaginaryimpedancewithrespecttofrequencyindicatesthattheimpedancedataforthegoldandplatinumelectrodesmayberepresentedbyaconstant-phase-elementmodel;whereas,thecopperdataindicatesthepresenceoftwotimeconstants.Asbothanodicandcathodicelectrochemicalreactionsarerequiredtohaveanimpedanceresponseatopencircuit,theimpedancedatapresentedforcopperinFigure 4-4 suggestthatcorrosionmaybetakingplace. 38

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A BFigure4-4. Lowfrequencyimpedanceresponseofcopper,goldandplatinum0.25mmdiameterelectrodesmeasuredfrom40mHzto100kHz(CuandAu)andfrom200mHzto100kHz(Pt):A)NyquistPlot,andB)imaginaryimpedanceasafunctionoffrequency.ThelinescorrespondtoregressionresultscorrespondingtothemodelsshowninFigure 4-8 39

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Figure4-5. PolarizationcurveforcopperdeaeratedwithN2andobtainedusingasweeprateof0.06mV/sfromtheopencircuitpotentialinbothanodicandcathodicdirections. 4.5.2PolarizationCurvesPolarizationcurvesresultingfromlinearsweepvoltammetryexperimentsarepresentedinFigure 4-5 foracopperelectrode.Theresultswereobtainedusingasweeprateof0.06mV/sfromtheopencircuitpotentialinbothanodicandcathodicdirections.Thepolarizationcurveintheanodicdirectionindicatesboththepresenceofcorrosionandtheabsenceofoxidelms.Thecompositionandresistivityoftheelectrolytechangedinresponsetotheelectrochemicalreactions.IRcompensationcouldthereforenotbeperformed,andareliableTafelslopecouldnotbeidentied,precludinguseofthepolarizationcurveforaccurateidenticationofthecorrosioncurrent.Thepolarization 40

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curveinthecathodicdirectionincludedreductionofspeciesresultingfromtheanodicreactionattheAg/AgClcounterelectrode.Themeasurementofpolarizationcurvescausedchangesinelectrolytecompositionthat,whilesmall,causedsignicantchangesinthepropertiesofthedeionizedwater.Themodicationstoelectrolytepropertieswereavoidedintheimpedancemeasurementsbyusingasmallperturbationamplitudeatopencircuit. 4.6SimulationsTheobservationofcorrosionissupportedbyaseriesofnumericalsimulations,includingcalculationofassociatedPourbaixdiagrams,kineticsimulationaccountingforpotentialreactions,andregressionanalysisoftheimpedanceresults. 4.6.1ThermodynamicAnalysisThepossibilityforcorrosionundertheconditionstestedwasexploredbycalculationofPourbaixdiagrams,presentedinFigure 4-6 ,forpurecopperindeaerateddeionizedwaterat25C.ThetitrantswereassumedtobeNaOHandHNO3.ThediagramsweregeneratedbyCorrosionAnalyzer2.0(Build2.0.16)byOLISystemsInc.ThecomputationalapproachisdescribedingreaterdetailbyAnderkoandco-workers.67,68ThespeciesconsideredinthethermodynamicanalysisarepresentedinTable 4-1 .ThePourbaixdiagramspresentedinFigure 4-6 areingoodagreementwiththePourbaixdiagramspresentedbyBeverskogandPuigdomenechforcopperat25C.69ThesolidcolormarkedCu(s)representstheregioninwhichcopperisstable.Thelinesmarkedaandbaretheequilibriumlinesforevolutionofhydrogenandoxygen,respectively,andtheregionbetweenaandbcanbedescribedasthestabilityregionforwater.ThenaturalpH,atwhichnotitrantsareadded,isequalto7.Theredoxpotentialforwater,showninFigure 4-6 bythelowerlledcircleatpH=7,isontheequilibriumlineaforhydrogenwhenthewaterissaturatedwithH2at1atmpressure.Thisfallswithinthestabilityregionforcopper.Foraeratedelectrolyte,theredoxpotentialforwaterliesontheequilibriumlinebforoxygen,theupperlledcircleatpH=7,wherecopperisnot 41

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A BFigure4-6. Calculatedpotential-pH(Pourbaix)diagramforcopperindeaerateddeionizedwater.ThetitrantswereassumedtobeNaOHandHNO3.ThemarkedpointscorrespondtothenaturalconditionforcopperdeaeratedwithN2(upper)andN2followedbysaturationbyH2(lower).ThediagramsweregeneratedbyCorrosionAnalyzer2.0(Build2.0.16)byOLISystemsInc. 42

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Table4-1. ListofspeciesconsideredinthethermodynamicanalysispresentedasFigure 4-6 AqueousSpeciesVaporSpeciesSolidSpecies H2OH2OCuCu+H2Cu2OCu(OH)2HNO3Cu(OH)2Cu+2O2Cu(NO3)25 2H2OCu(OH)+Cu(NO3)26H2OCu(NO3)+CuOCu(NO3)2NaOHCu(OH))]TJ /F4 7.97 Tf 6.58 0 Td[(24NaOHH2OCu(OH))]TJ /F4 7.97 Tf 6.58 0 Td[(13NaNO3H2Cu(NO3)2H+Cu(OH)OH)]TJ /F1 11.955 Tf -17.88 -18.79 Td[(NO)]TJ /F4 7.97 Tf 0 -7.88 Td[(3HNO3O2Na+NaNO3Na(OH)Na(OH)H2O stable.Fordeaeratedwaterintheabsenceofhydrogen,theredoxpotential,shownbythemiddlemarkedcircleinFigure 4-6 ,liesbetweenthelinesaandb.Theredoxpotentialisnotthecorrosionpotential;but,itmaybeusedasanindicatorforthestabilityofcopper.Whenhydrogenispresent,thesystemmaybeconsideredtobeatequilibrium,andcopperisindicatedtobestable.Intheabsenceofhydrogen,thehydrogenevolutionreactionmaytakeplaceuntilsucienthydrogenisformedtostabilizethecopper.ThethermodynamicsimulationssupporttheinterpretationthattheimpedanceandvoltammetryresultsshowcorrosionofcopperwhendeaeratedwithN2andthatcorrosionissuppressedbysaturationwithH2.TheseresultsareconsistentwiththeexperimentalobservationsreportedbyHultquist2andwiththethermodynamicanalysisreportedbyMacdonaldandShari-Asl.40 43

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4.6.2KineticSimulationKineticsimulationswereperformedtoexplorethemannerinwhichcoppermayreactindeaeratedwater.Intheabsenceofoxygen,thereactionswereassumedtoincludedissolutionofcopper Cu!Cu2++2e)]TJ /F1 11.955 Tf 168.23 -4.93 Td[((4{3)andhydrogenreductionatthecathode 2H++2e)]TJ /F2 11.955 Tf 10.41 -4.94 Td[(!H2(4{4)Astheconcentrationofcorrosionproductincreases,thecathodicreaction Cu2++2e)]TJ /F2 11.955 Tf 10.4 -4.93 Td[(!Cu(4{5)beginstoplayarole.Generationofhydrogenmaybeexpectedtoresultinhydrogenoxidation H2!2H++2e)]TJ /F1 11.955 Tf 171.24 -4.93 Td[((4{6)Thecorrespondingrateexpressionswereusedtoconstructatimedependentmodelforthesystem.AsimulationwasperformedusingthekineticexpressionsforreactionspresentedinEq.( 4{3 ),Eq.( 4{4 )andEq.( 4{5 ).59Atopencircuitpotentialthenetcurrentisequaltozero;thus, ia;Cu+ic;Cu+ic;H2=0(4{7)Theanodiccurrentdensityforcopperdissolutionisgivenby ia;Cu=i0;Cueba;Cu(V)]TJ /F6 7.97 Tf 6.59 0 Td[(V0;Cu)(4{8)whereV0;Cuistheequilibriumpotentialforthecopperreaction.Thecorrespondingcathodiccurrentdensitycanbeexpressedas ic;Cu=)]TJ /F3 11.955 Tf 9.3 0 Td[(i0;CucCu2+(0) cCu2+;refe)]TJ /F6 7.97 Tf 6.58 0 Td[(bc;Cu(V)]TJ /F6 7.97 Tf 6.58 0 Td[(V0;Cu)(4{9) 44

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Table4-2. SummaryofthetimedependentreactionsconsideredformodelingCucorrosionkinetics. ReactionNumberCaseI:AtTime=0NoO2CaseII:ForTime>0NoO2CaseIII:ForTime>0NoO2andH2Enriched ( 4{3 )Cu!Cu2++2e)]TJ /F1 11.955 Tf 27.23 -4.34 Td[(Cu!Cu2++2e)]TJ /F1 11.955 Tf 35.03 -4.34 Td[(Cu!Cu2++2e)]TJ /F1 11.955 Tf -374.6 -47.68 Td[(( 4{4 )2H++2e)]TJ /F2 11.955 Tf 10.4 -4.33 Td[(!H22H++2e)]TJ /F2 11.955 Tf 10.41 -4.33 Td[(!H22H++2e)]TJ /F2 11.955 Tf 10.41 -4.33 Td[(!H2( 4{5 )Cu2++2e)]TJ /F2 11.955 Tf 10.41 -4.34 Td[(!CuCu2++2e)]TJ /F2 11.955 Tf 10.41 -4.34 Td[(!Cu( 4{6 )H2!2H++2e)]TJ ET q .936 w 26.49 -211.55 m 441.51 -211.55 l S Q BT /F1 11.955 Tf 0 -243.9 Td[(wheretheconcentrationtermaccountsfortheconcentrationofcupricionattheelectrodesurface,cCu2+;refistheconcentrationatwhichtheexchangecurrentdensitywasobtained,andwasassignedavalueof0:75.Thecathodichydrogenevolutionreactionwasexpressedas ic;H2=)]TJ /F3 11.955 Tf 9.3 0 Td[(i0;H2e)]TJ /F6 7.97 Tf 6.59 0 Td[(bc;H2(V)]TJ /F6 7.97 Tf 6.59 0 Td[(V0;H2)(4{10)whereV0;H2istheequilibriumpotentialforthehydrogenevolutionreaction.Theconcentrationofcopperattheelectrodesurfacewasassumedtobecontrolledbysphericaldiusionfromtheelectrode,70thus, (ia;Cu+ic;Cu)=4nFDCu2+r0 A(cCu2+(0))]TJ /F3 11.955 Tf 11.95 0 Td[(cCu2+(1))(4{11)ThethreecasesshowninTable 4-2 wereconsidered.Case(I)correspondstoaninitialconditioninwhichcopperdissolutionisbalancedbyhydrogenevolution.ForCase(II),accumulationofcopperionsattheelectrodesurfaceallowscopperdissolutionandreductionreactionstooccurintandemwiththereductionofhydrogen.Case(III)accountsforsaturationbyH2gas.Thesetofequationswassolvedsimultaneouslyunderapseudo-steady-stateapproximationinwhichtheconcentrationcCu2+(1)wasincreasedincrementallyby 45

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Table4-3. ValuesfortheequilibriumpotentialforthecopperdissolutionreactionweretakenfromFigure1ofreference71andadjustedtobereferencedtotheNormalHydrogenElectrode.TheelectrolytepHforthehydrogenreactionreportedinreference62wasobtainedbyaddingNaOH.Corrosionratesrepresentcalculatedvaluesaveragedoveraone-yearperiod. ReactionpHpH2,atmE0,V(NHE)i0,A/cm2ba,V)]TJ /F4 7.97 Tf 6.59 0 Td[(1bc,V)]TJ /F4 7.97 Tf 6.58 0 Td[(1icorr,nm/day rxn( 4{3 )a)]TJ 42.62 0 Td[()]TJ /F8 10.909 Tf 50.15 0 Td[(-0.1876910)]TJ /F4 7.97 Tf 6.58 0 Td[(42053.56)]TJ ET q .585 w 6.4 -121.14 m 461.6 -121.14 l S Q BT /F8 10.909 Tf 12.82 -134.28 Td[(rxn( 4{4 )bA5.721-0.3313:4610)]TJ /F4 7.97 Tf 6.58 0 Td[(7)]TJ /F8 10.909 Tf 39.12 0 Td[(23.037:94B81-0.4656:7610)]TJ /F4 7.97 Tf 6.58 0 Td[(7)]TJ /F8 10.909 Tf 39.12 0 Td[(23.501.12C9.21-0.5351:0110)]TJ /F4 7.97 Tf 6.58 0 Td[(6)]TJ /F8 10.909 Tf 39.12 0 Td[(23.030.45D80.5-0.4565:4310)]TJ /F4 7.97 Tf 6.58 0 Td[(7)]TJ /F8 10.909 Tf 39.12 0 Td[(23.031.16E80.3-0.4504:7310)]TJ /F4 7.97 Tf 6.58 0 Td[(7)]TJ /F8 10.909 Tf 39.12 0 Td[(24.241.05F80.1-0.4363:2810)]TJ /F4 7.97 Tf 6.58 0 Td[(7)]TJ /F8 10.909 Tf 39.12 0 Td[(24.241.02 a)Theelectrolytewas0.7MCuSO4in1.5MH2SO4.Datatakenfromreference.71b)NaOHwastitratedtoachieveddesiredpHin0.03H3BO3.Theelectrolytetemperaturewas20C.Datatakenfromreference.62 amaterialbalance.ThekineticparametersusedforthesimulationsarepresentedinTable 4-3 .Asparametersfrompurewaterwerenotfoundintheliterature,dataweretakenforenvironmentsassociatedwithsimilarreactionmechanisms.FormationofCuClwasnotexpectedinthepresentsystem;therefore,parametersforthecopperdissolutionanddepositionweretakenfromareferencereportingexperimentsinasulphateelectrolyte.Theexchangecurrentdensityusedinoursimulationswasadjustedforthecupricionconcentrationatwhichtheexchangecurrentwasmeasured,asshowninEq.( 4{9 ).Bueredborateelectrolyteshavebeenusedasasurrogateforwatersassociatedwithnuclearrepositories.60,62Theparametersforthehydrogenevolutionreactionat20CweretakenfromShari-AslaandMacdonald,whoreportedresultsinaboricacidelectrolytewithpHadjustedbyadditionofNaOH.62Theresultingcalculatedcorrosionrates,averagedoveraoneyearperiod,areastrongfunctionofpH.Forthesystemunderinvestigation,undertheassumptionthathydrogenwasremovedbydeaeration,thecorrosionrateforparametersetAobtainedatapHof5.72wascalculatedtobe7.9 46

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nm/day.TheaveragecorrosionrateforparametersobtainedatapHof8(setsB,D,E,F)wascalculatedtobe1nm/day.ThecalculatedcorrosionrateforhydrogenparametersobtainedatapHof9.2was0.45nm/day.Inthepresenceofasaturatedpressureofhydrogen,thenetrateofcorrosion(notshowninTable 4-3 )wascalculatedtobeequaltozero.TheseresultsareinagreementwiththethermodynamicresultspresentedinFigure 4-6 .AnunderstandingoftheresultspresentedinTable 4-3 maybeobtainedfromtheEvan'sdiagrampresentedinFigure 4-7 thatwastakenfromthesimulationDatt=0,forwhichcCu2+(1)=0.Thesolidlinescorrespondtothetotalcathodiccurrent,ic;Cu+ic;H2,andtheanodiccurrentia;Cu.Thedashedlinesrepresentthecontributionsofic;Cuandic;H2.Theverticallineattheintersectionoftotalcathodicandanodiccurrent(point1inFigure 4-7 )yieldsthecorrosionpotentialVcorr=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:3399V.Atthecorrosionpotential,ia;Cu=2:58210)]TJ /F4 7.97 Tf 6.59 0 Td[(7A/cm2andthesumofcathodiccurrentdensitieshasthevalueic;Cu+ic;H2=)]TJ /F1 11.955 Tf 9.3 0 Td[(2:58210)]TJ /F4 7.97 Tf 6.58 0 Td[(7A/cm2.Thecathodiccopperdepositioncurrentdensity,seenatpoint2,hasthevalueic;H2=)]TJ /F1 11.955 Tf 9.3 0 Td[(2:20810)]TJ /F4 7.97 Tf 6.59 0 Td[(7A/cm2.Thecathodichydrogenevolutioncurrentdensity,seenatpoint3,hasthevalueic;H2=)]TJ /F1 11.955 Tf 9.29 0 Td[(3:74510)]TJ /F4 7.97 Tf 6.58 0 Td[(8A/cm2.Thecorrosioncurrentdensityobtainedfromthesumofcopperdissolutionanddepositioncurrentdensitiesisicorr=3:74510)]TJ /F4 7.97 Tf 6.58 0 Td[(8A/cm2,correspondingto1.2nm/day.ThecalculatedconcentrationattheelectrodesurfacewascCu2+(0)=2:64610)]TJ /F4 7.97 Tf 6.59 0 Td[(10mol/cm3.TheanodiccopperdissolutionreactionisbalancedatthecorrosionpotentialVcorrbythesumofhydrogenevolutionandcopperdepositionreactions.Thebackdepositionofcopperoccursduetotheaccumulationofcopperionsattheelectrodesurface.Thecopperdissolutionanddepositionreactionswerenotequalinmagnitudebecause,asshownbyEq.( 4{11 ),someofthecopperionsdiuseawayfromthesurface.IntheusualapplicationofEvan'sdiagrams,thecathodicreactiondoesnotinvolvemetaldepositionandthecorrosioncurrentwouldbefoundfromtheintersectionofthemetaldissolutioncurrentandthecathodiccurrent.Inthepresentcase,thecathodiccurrentcontainsadominant 47

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Figure4-7. correspondingtoparametersetDinTable 4-3 .Thesolidlinescorrespondtothetotalcathodiccurrent,ic;Cu+ic;H2,andtheanodiccurrentia;Cu.Thedashedlinesrepresentthecontributionsofic;Cuandic;H2.Theverticallineattheintersectionoftotalcathodicandanodiccurrent(point1)representsthecorrosionpotential.Thecathodiccopperdepositioncurrentdensityatthecorrosionpotentialisseenatpoint2.Thecathodichydrogenevolutioncurrentdensityisseenatpoint3.Thecorrosioncurrentdensity,obtainedfromthedierencebetweenthecopperdissolutioncurrentdensityatpoint1andthecopperdepositioncurrentdensityatpoint2,isequalinmagnitudetothecathodichydrogenevolutionreactionatthecorrosionpotential(point3). 48

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A B C DFigure4-8. EquivalentelectricalcircuitmodelsfortheimpedancedatapresentedinFigure 4-4 :A)generalmodelshowingtheparallelcontributionsofallpotentialreactions;B)reducedmodelcorrespondingtotheimpedancedataforgoldandplatinumelectrodes;C)modelcorrespondingtotheimpedancedataforgoldandplatinumelectrodesintermsofaneectiveresistance;D)modelforthecopperelectrode. contributionfromthereversereactiontometaldissolution.Thus,thecorrosioncurrentdensityisobtainedfromthedierence,measuredatthecorrosionpotential,betweenthecopperdissolutioncurrentdensityandthemagnitudeofthecopperdepositioncurrentdensity.Thecorrosioncurrentisequalinmagnitudetothecathodichydrogenevolutionreactionatthecorrosionpotential.Theoxidationofhydrogenformedbythecathodichydrogenevolutionreactionwasnotfoundtobesignicant,andinclusionofthisreactiondidnotchangetheresultspresentedinFigure 4-7 .Oncethehydrogenpartialpressureissucient,thecorrosionratewasfoundtobeequaltozero.TheseresultsareinagreementwiththeobservationsofMacdonaldandShari-Asl.40 4.6.3ImpedanceRegressionAnalysisAnimpedancemodelforthedatapresentedinFigure 4-8A shouldaccountforparallelcontributionsoftheimpedancesassociatedwiththechargingcurrentandtheotherreactionsoccurringforthissystem.AnelectricalcircuitthatprovidesaframeworkforsuchamodelispresentedcouldbeexpressedasFigure 4-8A 49

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Table4-4. RegressionresultsforthedatapresentedinFigure 4-8A ParameterAuPtCu Re,kcm25.850.074.930.059.60.5Q,F/s(1)]TJ /F6 7.97 Tf 6.58 0 Td[()cm227.60.327.60.39.60.2,dimensionless0.660.010.690.010.730.02Re,kcm2790210750170{Rt,kcm2{{9512kW,Ss1=2/cm2{{240.2Ce,F/cm210.911.23.9 Forthegoldandplatinumelectrodes,thefeasiblereactionsarehydrogenevolutionandoxidationofthehydrogenthusproduced.ThecircuitofFigure 4-8A isthereforereducedtoFigure 4-8B ,wherecharge-transferresistanceswereusedtodescribetheelectrochemicalreactions.Asthetworesistancesinparallelcannotbedistinguished,thecircuitofFigure 4-8B mustbeexpressedasFigure 4-8C where Re=RH2;aRH2;c RH2;a+RH2;c(4{12)Theimpedanceisexpressedas ZAu=Re+Re 1+(2jf)QRe(4{13)andthettingresultsarepresentedaslinesinFigure 4-8A .TheresultingparametersareprovidedinTable 4-4 .Severalmodelswereconsideredforthecopperelectrode.ThecircuitthatprovidedthebestrepresentationoftheexperimentaldataispresentedinFigure 4-8D ,i.e., ZCu=Re+Rt+1=kWp 2jf 1+(2jf)Q)]TJ /F3 11.955 Tf 5.48 -9.68 Td[(Rt+1=kWp 2jf(4{14)ThettingresultsarepresentedaslinesinFigure 4-8A ,andtheresultingparametersareprovidedinTable 4-4 .Thismodelsuggeststhattheimpedanceassociatedwiththecorrosionandhydrogenevolutionreactionsweretoolargetocontributetotheimpedanceresponse.ThediusioncontributionpresentedinthemodelgivenasFigure 4-8D may 50

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Figure4-9. Measurementmodelextrapolation(blueline)ofthecopperimpedance(circle)showingthepredictedzerofrequencylimit. beattributedtothedepositionofcopper,asshowninFigure 4-7 .ThishypothesisissupportedbyBojinovetal.,61whoobservedbackdepositionofcopper.Asthemeasuredfrequencyrangewasinsucienttoallowdeterminationofthediusiontimeconstant,thediusingspeciescouldnotbeidentied.Atthezero-frequencylimit,thepolarizationresistanceisrelatedtothecorrosiondensity,icorr,usingtheStern-Gearyequation,72 icorr=)]TJ /F3 11.955 Tf 9.3 0 Td[(H2Cu 2:303Rp(Cu)]TJ /F3 11.955 Tf 11.95 0 Td[(H2)(4{15)whereH2andCuaretheTafelslopeparametersobtainedfromliterature.62,71Aszero-frequencylimitcannotbereadilydiscernedfromtheimpedancedata,theregressionresultscannotprovideanestimateforthecorrosionrate.Anestimationofanupperboundtothecorrosionratemay,however,beprovided.Ameasurementmodel73extrapolationofthedataispresentedinFigure 4-9 .Theestimationofthepolarizationresistanceobtainedfromthemeasurementmodelforcoppersuggeststhatthecorrosionratemustbesmallerthan2.5nm/day.ThreeapproacheswereusedtoassignaphysicalmeaningtotheCPEparametersobtainedbyregression.Astheabsenceofpassivationbehaviorinthepolarizationcurve 51

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showninFigure 4-5 suggeststheabsenceofoxidelms,theBrugformula74 Ce=Q1=R(1)]TJ /F6 7.97 Tf 6.58 0 Td[()=e(4{16)wasusedtoestimatethecapacitanceassociatedwiththeCPEparametersQand.TheuseoftheBrugformulaisfurthersupportedbyanalysisofthegeometry-inducednonuniformcurrentandpotentialdistributionsexpectedfortheelectrode.Huangetal.75showedforadiskelectrodethat,aboveadimensionlessfrequency K=Q(2f)r0=1(4{17)nonuniformcurrentandpotentialdistributionsinuencetheimpedanceresponse.Theresultingimpedancewasdescribedasapseudo-CPEthatwasbestmodeledbytheBrugformula.76ThedimensionlessfrequencyKiswritteninEq.( 4{17 )asafunctionoftheCPEcoecientQ,theangularfrequency2fraisedtothepoweroftheCPEexponent,thediskradiusr0,andtheelectrolyteresistivity.Forthepresentsystem,thecharacteristicfrequencyobtainedfromEq.( 4{17 )was1.6Hz,meaningthatabovethisfrequency,theimpedancewasinuencedbyasurfacedistributionofohmicresistance.Thevaluesobtainedforgoldandplatinumelectrodes,showninTable 4-4 ,areingoodagreementwithexpectedvaluesforelectrodesindeionizedwater.Thecapacitanceobtainedforcopperwas,however,smallerthanexpectedforanelectrode-electrolyteinterface.Adierentsetofcalculationswereperformedtoexplorethehypothesisthatthecapacitanceshouldbeassociatedwithanoxidelm.IftheCPEbehavioriscausedbytheaxially-distributedpropertiesofanoxidelm,thepower-lawmodel77,78providesthebestmethodtoassociateCPEparameterstolmproperties.79UndertheassumptionthatthelmisCu2O(withadielectricconstantof7.6)80andthatthelowerlimitofthelmresistivityis1000cm,thelmthicknesswouldbeontheorderof190nm.UndertheassumptionthatthelmisCuO,withadielectricconstantof18.1,80thelmthickness 52

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Table4-5. Estimatedvaluesforcoppercorrosionrates. Methodicorr,mA=cm2icorr,nm/day Measurementmodelextrapolationofimpedance<7:910)]TJ /F4 7.97 Tf 6.59 0 Td[(5<2:5KineticSimulations3:210)]TJ /F4 7.97 Tf 6.59 0 Td[(51.1 wouldbeontheorderof350nm.Asoxidelmsoncopperarenotexpectedtobethickerthan6nm,81theinterpretationbasedontheBrugformulaseemsmostappropriate.AthirdapproachistoattributethecapacitanceobtainedfromtheBrugequationtoalm.Thelmthicknesssoobtainedwouldrangefrom1.7forCu2Oto4.1nmforCuO,whichiswithintherangeofexpectedvaluesforanoxideoncopper.Ifanoxidelmispresent,thepolarizationcurveindicatesthatitisnotprotective. 4.7DiscussionSeveralmethodswereemployedinthepresentworktoquantifytherateofcoppercorrosionindeaerateddeionizedwater.Theimpedanceanalysisshowedthatthecopperelectrodebehavedinamannerthatwasstrikinglydierentfromthegoldandplatinumelectrodes.Thus,theimpedanceresultssuggestthattheelectrochemistryofcoppermustplayarole.Asthegoldandplatinumresultswerealmostidentical,theimpedanceresponseforthesetwomaterialsshouldnotbeassociatedwiththerespectiveelectrochemistry.Theimpedancedata,therefore,supportthehypothesisthatcorrosionofcoppertakesplaceindeaerateddeionizedwater.Anextrapolationoftheimpedancediagramtothezero-frequencylimitsuggeststhatthecorrosionratemustbelessthan2.5nm/day(seeTable 4-5 ).ThepolarizationcurvespresentedinFigure 4-5 providedadditionalvericationfortheelectrochemicalactivityofcopper,butchangesintheelectrolyteduringtheexperimentprecludedaccurateassessmentofacorrosioncurrentdensity.AsshowninTable 4-5 ,thekineticsimulationssuggestacorrosionrateof1nm/day,wherekineticparameterswereobtainedfromelectrolytesthatmaybeconsideredsurrogatesfordeionizedwater.Thehypothesisthatcoppercorrodesindeaerateddeionizedwater 53

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isfurthersupportedbythePourbaixdiagramcalculatedfortheenvironmentunderinvestigation.Inthepresentwork,copperwasshowntobethermodynamicallyunstableindeaerateddeionizedwater;whereas,thermodynamicstabilitywaspredictedforcopperindeaerateddeionizedwaterequilibratedwithhydrogengasatapressureof1atm.Aslightincreaseintheconcentrationofdissolvedhydrogenattheelectrodesurfaceissuggestedbytheimpedanceresponsefortheinertgoldandplatinumelectrodes,butthiswasapparentlynotsucienttostabilizethecopper.Theresultofthekineticanalysisisthat,intheabsenceofhydrogen,acorrosionrateof1nm/dayispredictedunderanaerobicconditions.Theimpedancemeasurementsdidnotprovideanestimateofthecorrosionrate,butyieldedinsteadanupperboundof2.5nm/day.Ifoxygenwerepresentintheexperimentalsystem,theconcentrationassociatedwiththeupperboundof2.5nm/daywouldhavebeen6.5ppb.Thedissolvedoxygenconcentrationintheexperimentalsystemreportedherewasthereforelessthan6.5ppband,likely,basedonHenryslawarguments,substantiallyless.Theoxygenconcentrationyieldingacorrosionrateof1nm/day,equaltothatpredictedintheabsenceofoxygen,wouldbe2.5ppb.Thecorrosionrateinwatercontainingdissolvedoxygenconcentrationsmuchlowerthan2.5ppbwouldstillbe1nm/day,solongashydrogenisabsent.Thus,thepresentworkshowsthat,intheabsenceofhydrogen,copperwillcorrodeontheorderof1nm/dayindeionizedwaterwithanO2concentrationontheorderof,orlessthan,1ppb.Thecorrosionratesinthepresentwork(underanaerobicconditions)arecomparableinmagnitudetothecorrosionrateofthecopper(at15+ppbO2)coolingsystemusedattheArgonneNationalLaboratorysynchrotron.63,64Herewedemonstratethatadetectablecoppercorrosionrate(underanaerobicconditions)stilloccursanddoessotoameasurabledegree.Thepresentworkalsosupportstheclaimthatcopperindeaerateddeionizedwaterwillcorrodeifhydrogenisremovedfromtheelectrolyte,aswaspreviouslyobservedbyHultquist2anddiscussedasatheoreticalpossibilitybyMacdonaldandShari-Asl.40The 54

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estimatedcorrosionrateissucientlysmallthatitcanbeneglectedformosttechnologicalapplications.Thisrate,however,maybesucienttocausefailureofcoppernanowicksemployedinheatexchangersforhigh-performanceelectronics. 4.8ConcludingRemarksAcombinationofimpedanceandpolarizationexperimentsandthermodynamic,kinetic,andimpedancemodelswereusedtoassessthetendencyofcoppertocorrodeindeaerateddeionizedwaterthatdidnotcontainhydrogen.Thepresentworkshowsthatcopperwillcorrodeataverysmallrate.Kineticsimulationsindicatethat,forthepresentexperimentalconditions,theaveragerateoveraperiodofoneyearwouldbeontheorderof1nm/day.Theimpedanceanalysissuggeststhatthecorrosionrateislessthan2.5nm/day.Thiscorrosionratewilldecreaseastheconcentrationofhydrogenandcopperincreases.Whiletheestimatedcorrosionratemaybeinconsequentialformosttechnologicalapplications,thecorrosionrateislargeenoughtoinuencethefunctionalityofnanostructureutilizedinemergingapplications. 55

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CHAPTER5REFINEDKINETICMODELFORCOPPERCORROSIONInthischapterarenedkineticmodelisdevelopedtoexploretheinuenceofmasstransfer,surfaceareatovolumeratio,exchangecurrentdensityandequilibriumpotentialhaveonthecorrosionofcopperindeaeratedwater.Toexploretheinuenceofsystemparameters,thesimulationspresentedinChapter 4 areextendedinheretoincludetheoxidationofhydrogenanddiusionofdissolvedhydrogenawayfromtheelectrodesurface. 5.1MathematicalDevelopmentThereactionsconsideredatthecopperelectrodeweredissolutionandelectroplatingofcopper CuCu2++2e)]TJ /F1 11.955 Tf 168.23 -4.94 Td[((5{1)andhydrogenevolutionandoxidation 2H++2e)]TJ /F12 11.955 Tf 10.41 -4.93 Td[(H2(5{2)KineticparameterswereobtainedfromStankovicandVukovic82andShari-AslaandMacdonald.62Theanodiccurrentdensityforreaction( 5{1 )wasexpressedas ia;Cu=i0;Cuexp(ba;Cu(V)]TJ /F3 11.955 Tf 11.96 0 Td[(V0;Cu))(5{3)whereV0;Cuistheequilibriumpotentialforthecopperreaction.Thecorrespondingcathodiccurrentdensitywasexpressedas ic;Cu=)]TJ /F10 11.955 Tf 11.29 16.86 Td[(cCu2+(0) cCu2+(ref)Cui0;Cuexp()]TJ /F3 11.955 Tf 9.3 0 Td[(bc;Cu(V)]TJ /F3 11.955 Tf 11.95 0 Td[(V0;Cu))(5{4)wheretheconcentrationtermcCu2+(0)accountsfortheconcentrationofcupricionattheelectrodesurfaceandcCu2+(ref)representstheconcentrationofcupricionatwhichtheexchangecurrentdensitywasobtained.TheanodichydrogenoxidationinEq.( 5{2 )was 56

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expressedas ia;H2=cH2(0) cH2(ref)H2i0;H2exp(ba;H2(V)]TJ /F3 11.955 Tf 11.95 0 Td[(V0;H2))(5{5)wherecH2(0)istheconcentrationofdissolvedhydrogenattheelectrodesurfaceandcH2(ref)representstheconcentrationofhydrogenatwhichtheexchangecurrentdensitywasobtained.Thecorrespondingcathodicreactionwasexpressedas ic;H2=)]TJ /F3 11.955 Tf 9.3 0 Td[(i0;Cuexp()]TJ /F3 11.955 Tf 9.3 0 Td[(bc;H2(V)]TJ /F3 11.955 Tf 11.96 0 Td[(V0;H2))(5{6)whereV0;H2istheequilibriumpotentialforthehydrogenevolutionreaction.Thenetrateofreaction( 5{1 )wasexpressedintermsoftheconcentrationsattheelectrodesurfaceandfarfromtheelectrodesurfaceby ia;Cu+ic;Cu=nFkCu2+(cCu(0))]TJ /F3 11.955 Tf 11.95 0 Td[(cCu(1))(5{7)wherekCu2+isthemasstransfercoecientforcupricions.Thenetrateofreaction( 5{2 )wasexpressedas ia;H2+ic;H2=nFkH2(cH2(0))]TJ /F3 11.955 Tf 11.96 0 Td[(cH2(1)):(5{8)wherekH2isthemasstransfercoecientfordissolvedhydrogen.Thetotalcurrentforthesystemwassetequaltozero,i.e., ia;Cu+ic;Cu+ia;H2+ic;H2=0(5{9)ThenonlinearsetofequationsEq.( 5{3 )toEq.( 5{9 )weresolvedateachtimestepforvariablesia;Cu,ic;Cu,ia;H2,ic;H2,cCu2+(0),cH2(0),andV.Anopensystemisdenedheretobeoneinwhichtheowofinertgasremovesthehydrogenformedbyreaction( 5{2 ).Foranopensystem,theconcentrationofhydrogenfarfromtheelectrodeattimestepkwasobtainedfromthecorrespondingvalueattimestepk)]TJ /F1 11.955 Tf 11.95 0 Td[(1from ckH2(1)=ck)]TJ /F4 7.97 Tf 6.59 0 Td[(1H2(5{10) 57

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Astheinitialhydrogenconcentrationwasequaltozero,Eq.( 5{10 )ensuredthattheconcentrationfarfromtheelectrodewasxedtoazerovalue.Aclosedsystemallowedtheaccumulationofhydrogen.Fortheclosedsystem,theconcentrationofhydrogenfarfromtheelectrodeattimestepkwasobtainedfromthecorrespondingvalueattimestepk)]TJ /F1 11.955 Tf 12.11 0 Td[(1from ckH2(1)=ck)]TJ /F4 7.97 Tf 6.59 0 Td[(1H2(1))]TJ /F3 11.955 Tf 13.15 9.45 Td[(ik)]TJ /F4 7.97 Tf 6.59 0 Td[(1a;H2+ik)]TJ /F4 7.97 Tf 6.59 0 Td[(1c;H2 nFA Vt(5{11)Forbothopenandclosedsystems,theconcentrationofcupricionsfarfromtheelectrodeattimestepkwasobtainedfromthecorrespondingvalueattimestepk)]TJ /F1 11.955 Tf 11.95 0 Td[(1from ckCu2+(1)=ck)]TJ /F4 7.97 Tf 6.59 0 Td[(1Cu2+(1)+ik)]TJ /F4 7.97 Tf 6.59 0 Td[(1a;Cu+ik)]TJ /F4 7.97 Tf 6.58 0 Td[(1c;Cu nFA Vt(5{12)Atimestepof1000secondswasusedforthesesimulations.Fortheclosedsystem,thepartialpressureofhydrogeninequilibriumwithcH2(1)wasobtainedusingHenry'slaw,i.e., pH2=cH2(1) kH(5{13)wherekH=0:00078mol/kgbar.83Thekineticstudywascarriedoutusingthe7equationssummarizedinTable 5-1 5.2Mass-TransferCoecientsMass{transfercoecientswereobtainedfrompublishedcorrelationsforthemicroelectrodeusedinourwork1andthecopperfoilsusedintheworkbyHultquistetal.2Therelationshipbetweenthemass{transfercoecientforcupricionsanddissolvedhydrogendieredforthetwocasesbecausetransportforthemicroelectrodewasassumedtobecontrolledbydiusionandtransportforthefoilswasassumedtobecontrolledbynaturalconvection. 5.2.1MicroelectrodeForthemicroelectrodethemasstransfercoecientwasobtainedfromtheexpression84 Shi=kiddisk Di=8 (5{14) 58

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Table5-1. Summaryofequationsusedforthekineticstudy.Timesteppingusedforthissystemisshowninthelowerhalfofthetable. DescriptionEquationRef. AnodicCurrent,Cuia;Cu=i0;Cueba;Cu(V)]TJ /F6 7.97 Tf 6.59 0 Td[(V0;Cu) 5{3 CathodicCurrent,Cuic;Cu=)]TJ /F10 11.955 Tf 11.29 13.27 Td[(cCu2+(0) cCu2+(ref)Cui0;Cue)]TJ /F6 7.97 Tf 6.58 0 Td[(bc;Cu(V)]TJ /F6 7.97 Tf 6.59 0 Td[(V0;Cu) 5{4 AnodicCurrent,H2ia;H2=cH2(0) cH2(ref)H2i0;H2eba;H2(V)]TJ /F6 7.97 Tf 6.59 0 Td[(V0;H2) 5{5 CathodicCurrent,H2ic;H2=)]TJ /F3 11.955 Tf 9.3 0 Td[(i0;H2e)]TJ /F6 7.97 Tf 6.58 0 Td[(bc;H2(V)]TJ /F6 7.97 Tf 6.59 0 Td[(V0;H2) 5{6 MassTransfer,Cuia;Cu+ic;Cu=nFkCu2+(cCu2+(0))]TJ /F3 11.955 Tf 11.96 0 Td[(cCu2+(1)) 5{7 MassTransfer,H2ia;H2+ic;H2=nFkH2(cH2(0))]TJ /F3 11.955 Tf 11.96 0 Td[(cH2(1)) 5{8 ZeroNetCurrentia;Cu+ic;Cu+ia;H2+ic;H2=0 5{9 k-thTimeStep,OpenH2(1)ckH2(1)=ck)]TJ /F4 7.97 Tf 6.59 0 Td[(1H2 5{10 k-thTimeStep,ClosedH2(1)ckH2(1)=ck)]TJ /F4 7.97 Tf 6.59 0 Td[(1H2(1))]TJ /F6 7.97 Tf 13.15 8.27 Td[(ik)]TJ /F11 5.978 Tf 5.75 0 Td[(1a;H2+ik)]TJ /F11 5.978 Tf 5.76 0 Td[(1c;H2 nFA Vt 5{11 k-thTimeStep,Cu(1)ckCu2+(1)=ck)]TJ /F4 7.97 Tf 6.58 0 Td[(1Cu2+(1)+ik)]TJ /F11 5.978 Tf 5.76 0 Td[(1a;Cu+ik)]TJ /F11 5.978 Tf 5.76 0 Td[(1c;Cu nFA Vt 5{12 whereShiisthedimensionlessSherwoodnumber,kiisthemasstransfercoecientofspeciesi,ddiskisthediameterofthedisk,andDiisthediusivityofspeciesi.ThemasstransportrepresentedinEq.( 5{14 )ismathematicallyequivalenttosphericaldiusionforamicroelectrode.Thus,themasstransfercoecientsforcupricionsanddissolvedhydrogenwererelatedby kH2=kCu2+DH2 DCu2+(5{15)Theelectrodediameterwas0.025cmandthevolumeofwaterwas30cm3yieldinganareatovolumeratioofA=V=1:6410)]TJ /F4 7.97 Tf 6.58 0 Td[(5cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1.FromEq.( 5{14 ),themasstransfercoecientforcupricionscanbeestimatedtohaveavalueofkCu2+=7:3310)]TJ /F4 7.97 Tf 6.59 0 Td[(4cm/s. 5.2.2HultquistFoilsTheexperimentalsystemsreportedbyHultquistetal.2consistedofcopperfoilswithanexposedareaof85cm2placeduprightinasealedvesselandimmersedinanoxicwaterwithavolumeof50cm3.Suchasystemmaybeexpectedtobedrivenbynaturalconvection.Acorrelationfornaturalconvectiontoaverticalplateisgivenas85 Shi=kiL Di=0:677(ScGr)1=4(5{16) 59

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whereListhelengthoftheplate,Sc==DiistheSchmidtnumber,andisthekinematicviscosityoftheelectrolyte.ThetermGristheGrashofnumberdenedfor(0)>(1)as Gr=gL3 21)]TJ /F3 11.955 Tf 13.15 8.09 Td[((1) (0)(5{17)wheregisgravitationalacceleration,representstheaverageelectrolytekinematicviscosity,(1)istheelectrolytedensityfarfromtheelectrode,and(0)istheelectrolytedensityattheelectrodesurface.Thus,forasystemcontrolledbynaturalconvection,themasstransfercoecientsforcupricionsanddissolvedhydrogenwererelatedby kH2=kCu2+DH2 DCu2+3=4(5{18)TheelectrodeareatovolumeratiowasA=V=1:7cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1.Undertheassumptionthatthedimensionlessdensitydierence1)]TJ /F3 11.955 Tf 12.31 0 Td[((1)=(0)isontheorderof10)]TJ /F4 7.97 Tf 6.59 0 Td[(9,themasstransfercoecientforcupricionscanbeestimatedtohaveavalueofkCu2+=110)]TJ /F4 7.97 Tf 6.59 0 Td[(5cm/s. 5.3ResultsThecalculatedresultsarepresentedforbothopenandclosedsystems.Intheopensystem,hydrogenisremovedbytheowofinertgassuchthatthebulkconcentrationofdissolvedhydrogenmaybeassumedtobeequaltozero.Intheclosedsystem,theaccumulationofhydrogenresultsinthebuildupofhydrogenpartialpressure.ParametersusedinthesimulationarepresentedinTable 5-2 5.3.1OpenSystemThecorrosionratecalculatedforthemicroelectrodeiscomparedtothatobtainedfortheHultquistcellinFigure 5-1 withmass{transfercoecientasaparameter.ForboththemicroelectrodeandtheHultquistcell,resultsarepresentedaswellformass{transfercoecientsthatareanorderofmagnitudelargerandsmallerthanthecorrespondingcalculatedvalue.Thecalculatedcorrosionrateforthemicroelectrodewas1.1nm/dayandreachedavalueof0.74nm/dayafter15years;whereas,fortheHultquistcell,thecalculatedcorrosionratewasinitiallyabout0.37nm/dayandreachedavalueof0.053 60

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A BFigure5-1. Calculatedopen{systemcorrosionratesasafunctionoftimewithmass{transfercoecientasaparameter:A)forthemicroelectrodewithA=V=1:6410)]TJ /F4 7.97 Tf 6.58 0 Td[(5cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1;B)fortheHultquistcellwithA=V=1:7cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1. 61

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Table5-2. Mass{transfercoecientsusedinthesimulationsarepresentedaslegendsintherespectivegures.ValuesfortheequilibriumpotentialforthecopperdissolutionreactionweretakenfromFigure1ofStankovic82andadjustedtobereferencedtotheNormalHydrogenElectrode.ThekineticparametersforthehydrogenevolutionreactionweretakenfromShari62forpH=0andpH2=0:1atm.SeeTableIIIinClevelandetal.1 ParameterValueUnits V0;Cu-0.1876V(NHE)i0;Cu910)]TJ /F4 7.97 Tf 6.58 0 Td[(4A/cm2ba;Cu201/Vbc;Cu53.561/VCu0.75V0;H2-0.436V(NHE)i0;H23.2810)]TJ /F4 7.97 Tf 6.59 0 Td[(7A/cm2ba;H238.381/Vbc;H224.241/VH21 nm/dayafter15.2years.Thecorrosionrateisshowntodependontheelectrodeareatovolumeratioandonthemass{transfercoecients.ThecumulativecorrosionispresentedasafunctionoftimeinFigure 5-2 forthemicroelectrodeandHultquistcells.Afteranelapsedtimeof15years,thecumulativecorrosionforthemicroelectrodewasestimatedtobe4700nm;whereas,thecumulativecorrosionfortheHultquistcellwascalculatedtobe390nm.Thus,usingthesamemodelforthekinetics,thecalculationforcumulativecorrosionthataccountedformasstransferandtheelectrodeareatovolumeratioyieldedacumulativecorrosionforthemicroelectrodethatwas12timeslargerthanfortheHultquistcell.TheinuenceofelectrodeareatovolumeratioisevidentintheconcentrationofcupricionpresentedinFigure 5-3 forthemicroelectrodeandHultquistcells.Thecalculatedbulkconcentrationofcupricionreachedavalueof9.3mol/cm3after15yearsintheHultquistcell.Incontrast,thecalculatedbulkconcentrationofcupricionforthemicroelectrodereachedavalueof1.0nmol/cm3after15yearsintheHultquistcell,whichis10,000timessmallerthanthatobtainedfortheHultquistcell.Thedierence 62

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A BFigure5-2. Calculatedopen{systemcumulativecorrosionasafunctionoftimewithmass{transfercoecientasaparameter:A)forthemicroelectrodewithA=V=1:6410)]TJ /F4 7.97 Tf 6.58 0 Td[(5cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1;B)fortheHultquistcellwithA=V=1:7cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1. 63

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A BFigure5-3. Calculatedopen{systembulkconcentrationofcupricionasafunctionoftimewithmass{transfercoecientasaparameter:A)forthemicroelectrodewithA=V=1:6410)]TJ /F4 7.97 Tf 6.58 0 Td[(5cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1;B)fortheHultquistcellwithA=V=1:7cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1. 64

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canbeattributedtothedierentelectrodeareatovolumeratiosandtothedierenceinmass{transfercoecients.Fortheopensystem,thebulkconcentrationofdissolvedhydrogenwasassumedtobeequaltozero.Thus,thecorrosioncontinuesinboththemicroelectrodeandHultquistsystems,evenafteraperiodof15years. 5.3.2ClosedSystemThebehaviorofanopensystemmaybeexpectedtodierfromthatofaclosedsystem,inwhichtheconcentrationofdissolvedhydrogenandthecorrespondinghydrogenpartialpressureincreaseswithtime.Theclosed{systemcorrosionratecalculatedforthemicroelectrodeiscomparedtothatobtainedfortheHultquistcellinFigure 5-4 withmass{transfercoecientasaparameter.ForboththemicroelectrodeandtheHultquistcell,resultsarepresentedaswellformass{transfercoecientsthatareanorderofmagnitudelargerandsmallerthanthecorrespondingcalculatedvalue.Thecalculatedcorrosionrateforthemicroelectrodewas1.1nm/dayandreachedavalueof0.74nm/dayafter15years,essentiallyunchangedfromtheresultsoftheopensystemshowninFigure 5-1A .Incontrast,thecorrosionratecalculatedfortheHultquistcellwasinitiallyabout0.35nm/dayanddroppedtoavaluenearzeroinlessthan60days.Theinsensitivitytotheopenorclosedconditionforthemicroelectrodemaybeattributedtothesmallelectrodeareatovolumeratio.ThesharpdecreaseinthecorrosionrateintheclosedHultquistcellcanbeattributedtothelargerelectrodeareatovolumeratio.ThecorrespondingcumulativecorrosionispresentedasafunctionoftimeinFigure 5-5 forthemicroelectrodeandHultquistcells.Afteranelapsedtimeof15years,thecumulativecorrosionfortheclosed{systemmicroelectrodewasunchangedfromthatintheopensystem;whereas,thecumulativecorrosionfortheHultquistcellwascalculatedtobe2.7nm.Thus,usingthesamemodelforthekinetics,thecalculationforcumulativecorrosionthataccountedformasstransferandtheelectrodeareatovolumeratioyieldedacumulativecorrosionforthemicroelectrodethatwas1700timeslargerthanfortheHultquistcell. 65

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A BFigure5-4. Calculatedclosed{systemcorrosionratesasafunctionoftimewithmass{transfercoecientasaparameter:A)forthemicroelectrodewithA=V=1:6410)]TJ /F4 7.97 Tf 6.58 0 Td[(5cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1;B)fortheHultquistcellwithA=V=1:7cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1. 66

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A BFigure5-5. Calculatedclosed{systemcumulativecorrosionasafunctionoftimewithmass{transfercoecientasaparameter:A)forthemicroelectrodewithA=V=1:6410)]TJ /F4 7.97 Tf 6.58 0 Td[(5cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1;B)fortheHultquistcellwithA=V=1:7cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1. 67

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TheinuenceofelectrodeareatovolumeratioisevidentintheconcentrationofcupricionpresentedinFigure 5-6 forthemicroelectrodeandHultquistcells.ThecalculatedbulkconcentrationofcupricionintheHultquistcellreachedavalueof75nmol/cm3,muchsmallerthanthe9.3mol/cm3reachedintheopensystemafter15years.Incontrast,thecalculatedbulkconcentrationofcupricionforthemicroelectrodeafter15yearswasunchangedascomparedtotheopensystem.ThedierenceinbehaviorbetweenthemicroelectrodeandHultquistsystemsisduetothedierenceinelectrodeareatovolumeratio.Themajordierencebetweentheopenandclosedsystemisthatthehydrogenpartialpressureisallowedtoincreaseinaclosedsystem.Thehydrogenpartialpressure,calculatedfromthebulkconcentrationofdissolvedhydrogen,ispresentedinFigure 5-7 asafunctionoftimeforthemicroelectrodeandHultquistcells.TheHenry'slawconstantusedforthiscalculationwereobtainedfromSander.83Afterlessthan60days,thecalculatedclosed{systemhydrogenpartialpressurereachedalimitingvalueof0.096atm;whereas,intheclosedmicroelectrodesystem,thehydrogenpartialpressuredidnotreachalimitingvalueand,after15years,reachedavalueof0.0013atm.Thelimitingvalueofhydrogenpartialpressurewasfoundtobeindependentofmass{transfercoecientandexchangecurrentdensity,butdiddependontheequilibriumpotentialused.Aclearerunderstandingofthecalculationsperformedinthepresentworkmaybeobtainedfromthecalculatedcorrosioncurrent{potentialrelationshippresentedinFigure 5-8 fortheHultquistcellunderopenandclosedcondition.Fortheclosedsystem,thecorrosioncurrentdensityapproachesavalueofzeroatapotentialof-0.284V(NHE).Thisvalueisindependentofmass{transfercoecientandisingoodagreementwiththePourbaixdiagramspresentedinFigure 5-9 .Fortheopensystem,thecorrosioncurrentdensitydecreasesasthepotentialincreases.Theequilibriumconditionisnotachievedastheaccumulationofhydrogenisprevented. 68

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A BFigure5-6. Calculatedclosed{systembulkconcentrationofcupricionasafunctionoftimewithmass{transfercoecientasaparameter:A)forthemicroelectrodewithA=V=1:6410)]TJ /F4 7.97 Tf 6.59 0 Td[(5cm)]TJ /F4 7.97 Tf 6.58 0 Td[(1;B)fortheHultquistcellwithA=V=1:7cm)]TJ /F4 7.97 Tf 6.58 0 Td[(1. 69

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A BFigure5-7. Calculatedclosed{systembulkhydrogenpartialpressureasafunctionoftimewithmass{transfercoecientasaparameter:A)forthemicroelectrodewithA=V=1:6410)]TJ /F4 7.97 Tf 6.58 0 Td[(5cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1;B)fortheHultquistcellwithA=V=1:7cm)]TJ /F4 7.97 Tf 6.59 0 Td[(1. 70

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Figure5-8. CalculatedcorrosioncurrentdensityasafunctionofpotentialfortheHultquistcellunderopenandclosedconditionwithmass{transfercoecientasaparameter. Thecalculatedlimitinghydrogenpartialpressureof0.096atmissubstantiallylargerthanthevalueof0.45mbarreportedbyHultquistetal.86Inaddition,thecorrosionrateestimatedinthepresentworkfortheHultquistsystemissmallerthantheratereportedbyHultquistetal.86Thisdiscrepancymaybeattributedtoexperimentalissuesortotheneedtomodifythemodelparameters.Themodelreportedinthepresentworkdidnotaccountforthecontributionoftheheadspace.Thehydrogenpressurewasassumedtobethatinequilibriumwiththebulkconcentrationofdissolvedhydrogen.Thus,themeasuredhydrogenpressuremaybeexpectedtobelowerthanthatcalculated.Thepresenceofalargeheadspacewouldcausethesystemtobehaveasanopensystematshorttimesandasaclosedsystemasthepartialpressureofhydrogenincreasesintheheadspace.TheagreementbetweenthesimulationsperformedinthepresentworktothosepresentedinClevelandetal.1validatetheassumptionmadethatthehydrogenoxidationreactioncouldbeneglectedforthesmallelectrodeareatovolumeratioandshorttimesconsidered.Thehydrogenoxidationreactionplaysanessentialroleinsimulating 71

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thebehavioroftheHultquistcellwithitslargerelectrodeareatovolumeratioandexperimentsoflongerduration.Forboththeopenandclosedsystems,thecumulativecorrosionisreducedforlargerelectrodeareatovolumeratios.Thedierenceinestimatedcorrosionratesbetweenourwork1andthatHultquistetal.2isshowninthepresentworktobethenaturalconsequenceofthemannerinwhichkinetics,masstransfer,andelectrodeareatovolumeratioinuencetheprogressiontowardtheequilibriumcondition. 5.4ControversySurroundingNuclearWasteStorageProponentstothestorageofspentnuclearwastebelievethatcopperprovidesasuitablewastecontainmentforperiodsexceedingamillionyears.OneoftheseproponentsraisedconcernstothecoppercorrosionworkdiscussedinChapter 4 .TherevisedkineticmodelprovidedinthischapterwascarriedouttoaddresstheconcernsraisedbyK.SpahiuandI.PuigdomenechattheSwedishNuclearFuelandWasteManagementCompany.ThissectionwillhighlighttheobjectionsraisedbySpahiuandPuigdomenechandaddresstheseobjectionswiththeresultsfromtherevisedkineticmodel.IntheirCommentonNanometer-scalecorrosionofcopperinde-aerateddeionizedwater[J.Electrochem.Soc.,161,C107(2014)],SpahiuandPuigdomenechraisethreeprincipalobjections: 1. Figure5inClevelandetal.1doesnotproperlyrepresentthedependenceofline"b"onthepartialpressureofoxygen.Inaddition,themiddleredoxpotential(ORP)presentedinFigure5diersfromthevaluecalculatedbySpahiuandPuigdomenech; 2. SpahiuandPuigdomenechsuggestthattraceamountsofoxygenintheexperimentmaybesucienttoexplainthederivedcorrosionratesfromtheexperimentsperformed; 3. SpahiuandPuigdomenechexpressconcernthattheobservedcorrosionratebyClevelandetal.1isaroundthreeordersofmagnitudehigherthantheratethatmaybederivedfromtheobservationspublishedbyHultquistetal.2,86Fromthesecriticisms,SpahiuandPuigdomenechpositthattheworkofClevelandetal.1\maynotbeconsideredtosupporttheclaimthatcopperwillcorrodeindeaerated 72

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deionizedwaterifhydrogenisremoved."Ourresponsetothesecritiquesarepresentedbelow. 5.4.1ThermodynamicAnalysisSpahiuandPuigdomenecharecorrecttoobservethatline(b)showninFigure5ofourworkdoesnotproperlyrepresentthethreecasesdiscussed.OurpresentationofasinglePourbaixdiagramwiththreeoxidation/reductionpotentialsoverlaidwasintendedtoshowthatcopperisstableinanoxicwaterinthepresenceofhydrogenbuthasatendencytocorrodeinwatercontainingoxygenorinanoxicwaterthatisfreeofhydrogen.Clevelandetal.agreethatpresentationofthreePourbaixdiagramsindividuallywouldhavelessenedcauseforconfusion.TheoriginalPourbaixdiagramsforthethreecases,generatedbyCorrosionAnalyzer2.0(Build2.0.16)byOLISystemsInc.,67,68areshowninFigure 5-9 .AsSpahuiandPuigdomenechstate,thepotentialfortheoxygenline(b)isdependentonthepHandpartialpressureofO2following ESHE=1231mV)]TJ /F1 11.955 Tf 11.96 0 Td[(59:16pH+59:16(logpO2)=4(5{19)Line(b)movesinthenegativedirectionasthepartialpressureofO2isdecreased.Ourcalculationsshowthepotentialis1.185V(NHE)atapHof0whenthepartialpressureofO2isminimizedbyaN2blanket.Atapartialpressureof0.21atm,thepotentialis1.219V(NHE)atpH=0.Themodelusedtoproducethe(b)lineisinagreementwithEq.( 5{19 ).ItisimportanttounderstandthedistinctionbetweentheORPandthelinesrepresentedbytheletters(a)and(b).TheORPisamixedpotentialwithsimultaneousforwardandbackwardcomponentswithcontributionsfromthemetal/metalion/multiplemetalionoxidationstates(e.g.Cu/Cu[I]/Cu[II]),H2/H+,andsomeadditionalO2/OH)]TJ /F1 11.955 Tf 7.09 -4.34 Td[(/H2Oreactions.Thelines(a)and(b)describeonlyonehalf-reactioneach,and,therefore,describeonlyathermodynamiclimitintheabsenceofpolarization.TheORPisthe 73

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A B CFigure5-9. Calculatedpotential-pH(Pourbaix)diagramsforcopperindeaerateddeionizedwatergeneratedbyCorrosionAnalyzer2.0(Build2.0.16)byOLISystemsInc:67,68A)inthepresenceof8ppmdissolvedO2;B)intheabsenceofdissolvedH2andO2;andC)intheabsenceofdissolvedO2andinthepresenceofdissolvedH2.ThetitrantswereNaOHandHNO3. 74

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potentialassociatedwiththeequilibriumstatebetweenseveralsuchreactionssuchthatthechargeisbalancedamongallparticipatingreactions.TheORPofthesystemcalculatedbytheOLIsoftwareincludeseectsofthecoppermetalactivityaswellasthepartialpressuresofO2andH2.TheORPshownascirclesinFigure 5-9 includestheeectsoftheredoxreactionrequiredtogetthesolutiontothestatedCuactivity(110)]TJ /F4 7.97 Tf 6.59 0 Td[(6Mbydefault)andincludestheinuenceofthegeneratedH2and/orO2.Intheabsenceofdissolvedoxygenandhydrogen,asshowninFigure 5-9B ,theORPhasavalueof0.403V(NHE).SpahiuandPuigdomenechcorrectlypointoutthatthespeciesCu+identiedintheupperleftcornerinourPourbaixdiagramwasinerror.AsshowninFigure 5-9 ,thecorrectspeciesisCuNO+3whenusingNaOHandHNO3astitrants.Insummary,theconcernsraisedbySpahiuandPuigdomenechthattheuseofasinglePourbaixdiagramoversimpliedthethermodynamicsandthataspecieswasincorrectlylabeledarejustied.ThecalculationoftheORPinourwork,however,iscorrect.ThecalculationoftheORPinthePourbaixdiagramswasusedtodemonstratethat,intheabsenceofhydrogen,coppermaycorrodeinanoxicwater.TheconcernsraisedbySpahiuandPuigdomenechdonotinvalidatetheresultspresentedinClevelandetal.1 5.4.2TraceAmountsofOxygenThecoppermicroelectrodesystemwasmaintainedunderpositivepressurewithhigh-puritynitrogenandtheoxygencontentofthegasphaseleavingthesystemwasmeasuredtobeontheorderof1ppb.TheHenry'sconstantforthissystem(seereferenceSander83)wouldsuggestthat,underequilibriumconditions,thedissolvedoxygenconcentrationinwatershouldbelessthan1ppt.Nevertheless,itiswidelyrecognizedthatitisdiculttoachieveperfectanoxicconditions. 75

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ThemainfeaturesoftheexperimentalresultsfoundinClevelandetal.1canbesummarizedasfollows: 1. Impedancediagramsshowedreactivitythatwasnotpresentforgoldorplatinumelectrodes. 2. Theimpedancediagramscouldnotbeusedtoextractacorrosionrate.Onlyanupperboundforthecorrosionratecouldbeestimated. 3. Thehigh-frequencypartoftheimpedancespectrumwasanalyzedtoshowthattheconstant-phaseelementevidentintheimpedanceresponsecouldnotbeattributedtoanoxidelmonthecopper.Theconstant-phaseelementparameterswereshowntobeconsistentwithasurfacedistribution.Theimpedanceresultsmotivatedthekineticanalysisthatwasusedtoestimateacorrosionrate.Theimpedancewasnotusedtoquantifyacorrosionrate.Theabsenceofanoxidelmandtheinabilitytoquantifyacorrosionratesuggests,however,thatdeaerationwasachievedtoahighdegree.Insummary,theconcernontraceamountsofoxygenexpressedbySpahiuandPuigdomenechhavenobearingontheconclusionsdrawninourpaper. 5.4.3ComparisontoWorkofHultquistetal.TheconcernexpressedbySpahiuandPuigdomenechwasthatourestimatedcorrosionrateisaroundthreeordersofmagnitudehigherthanthatderivedfromtheobservationspublishedbyHultquistetal2,86Thisdiscrepancymaybereadilyunderstoodbyrecognizingthattheapproachtotheequilibriumconditionisgovernedbykineticparameterssuchasrateconstants,mass-transfercoecients,andtheelectrodeareatovolumeratio.Toexploretheinuenceofsystemparameters,thesimulationspresentedinourpaper1wereextendedtoincludetheoxidationofhydrogenanddiusionofdissolvedhydrogenawayfromtheelectrodesurface. 5.5ConcludingRemarksWeconsiderthecommentonthethermodynamicanalysistobejustiedinthesensethat,whileourthermodynamicanalysiswascorrect,itcouldhavebeenpresentedmoreclearly.Thecommentonthepossiblepresenceofoxygeninourexperimentsdoesnot 76

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inuencetheconclusionofourpaperasourconclusionwasbasedonsimulationresultsusingparametersextractedfromtheliterature.Theimpedanceresultswereusedonlytoshowthatanoxidelmwasnotpresentonthecopperelectrodeandtoprovideanupperboundforthecorrosionrateof2.5nm/day.ThecommentthatthedierenceinestimatedcorrosionratesbetweenoursystemandthatofHultquistsomehowinvalidatesourresultsisshowninthepresentworktobewithoutbasis.Thedierenceinestimatedcorrosionratesisthenaturalconsequenceofdierencesbetweenthetwosystems. 77

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CHAPTER6INFLUENCEOFRINGELECTRODEONEIS 6.1FrequencyDispersioninElectrochemicalSystemsElectrodegeometryhasbeendemonstratedtocausefrequencydispersionintheelectrochemicalimpedanceresponseforvarioussystemsofdierentelectrodegeometry.87In1970,Newman88showedfrequencydispersionwaspresentforthediskelectrodesystem.Frequencydispersionhasbeenshowntobeassociatedwithsurfaceroughness89andwithdistributionofelectrodeproperties.Ithasbeenshownthatthereisacharacteristicdimensionassociatedwiththeelectrodegeometrythatindicatesthefrequencyatwhichdispersionisseen.Foradiskelectrodethecharacteristicdimensionistheradiusofthedisk.87,90,91Forroughness,thecharacteristicdimensionisafunctionoftherugosityandtheperiodoftheroughness.89Fordistributionofthecapacitanceithasbeenshowntobeperiodofthecapacitancedistribution.92Frequencydispersionarisesinasystemwithanonuniformcurrentdistributionacrosstheelectrodesurface.Forthecaseofadiskworkingelectrodeembeddedinaninniteinsulateplanewithahemisphericalcounterelectrodelocatedatinnity,Alexanderetal.89deneacharacteristicfrequencytobe K= 4!C0r0 :(6{1)whereC0istheinterfacialcapacitance,isthesolutionconductivityandr0istheradiusofthedisk.Thecharacteristiclengthofthediskelectrodemaybeexpressedas `c;disk= 4r0(6{2)TheusefulnessofEq.( 6{1 )becomesapparentwhendeterminingthecharacteristicfrequencyatwhichdispersioninuencestheimpedanceresponseforadiskelectrode.Huangetal.87showedthecharacteristicfrequencyforadiskelectrodeoccursnear 78

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K=1.ForK>1frequencydispersionoccursduetoanonuniformcurrentdistribution.Therefore,frequencydispersionmaybeeliminatedinadesiredfrequencyrangebychoosingtheappropriateparametersC0,r0andtoensureK<1.Thecharacteristicdimensionforaroughelectrodeisexpressedas89 `c;rough=f2rP(6{3)wherePisdenedastheperiodoftheroughness.Alexanderetal.92showedthatacapacitancedistributiongaverisetofrequencydispersion,butthattheeectwasseenatfrequencieshigherthanthatassociatedwiththediskgeometry.Thecharacteristiclengthforaperiodicdistributionasafunctionoftheradialcoordinatewastheperiodofthedistributionsuchthat `c;cap=P(6{4)and,astheperioddecreased,thefrequencydispersionoccurredathigherfrequencies.Theobjectiveofthisworkistodeveloparelationforthecharacteristicdimensionassociatedwiththeimpedanceresponseofaringelectrode.Edgeeectsfromanonuniformcurrentdistributionwillbeconsideredforprimaryresistanceandimpedance.Identicationofacharacteristicdimensioncanbeusedtoavoidfrequencydispersioninacarefullychosensystemmatchingasetofparameters. 6.2RotatingElectrodes 6.2.1SteadyStateResponseRotatingdiskelectrodes(RDE),rotatingringelectrodes(RRE),androtatingring-diskelectrodes(RRDE)allplayanimportantroleinthestudyofelectrochemicalsystems.Originsofthering-diskelectrodecanbetracedbacktoexperimentsperformedbyFrumkinetal.93andFrumkinandNekrasov94wherearotatingdiskelectrodettedwithanisolatedmetalringwasfoundtobeasuitablemodicationforinvestigatingtheformationofintermediateelectrochemicalproducts.Underconvective-diusionconditions,reductionofoxygenwascarriedoutinanalkalinesolution.Thepurposeoftheseearly 79

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experimentswastodetectandidentifytheelectroactiveintermediatespeciesandnalproducts.SubsequenttheorywasdevelopedbyIvanovandLevich95thatexpressedthelimitingcurrentdensitydistributionontheringelectrode.AlberyandBruckenstein96improveduponthesolutionforthecollectioneciencyofaring-diskelectrodesystemusingdierentboundaryconditions.SmyrlandNewman97investigatedtheerrorinvolvedintreatingthering-disksystemasasectionedelectrodeformeasuringthecurrentdistribution.Integralswereevaluatedfortherotatingring-diskelectrodeforthreecasesandtheconcentrationandcurrentdistributionswerederivedforeachregionontheRRDEsurface.MiksisandNewman98calculatedtheprimarycurrentdistributionforthering-disksystem.Inthisworktheyprovidedthethreeprimaryresistancesforthering-disksystemasafunctionoftwogeometricratios.PieriniandNewman99investigatedthecurrentdistributionandconcentrationprolesonaRRDEbelowthelimitingcurrent.ThelimitingbehaviorforathickringelectrodewasobservedbyGregoryandRiddiford100,101whichwasinitiallyinvestigatedbyblockingoacenterportionofadiskelectrode.Levich102(p.107)derivedthediusionaluxtothesurfaceofaringelectrode(diskelectrodewithalacquercoatedcenter)remarkingthatthesolutionsareanalogoustothoseforthesemi-inniteplate.PieriniandNewman103presentedtheprimaryandsecondarycurrentdistributionsforthe"isolated"ringorRREsystem. 6.2.2ImpedanceResponseEarlyACtheoryforthering-diskelectrodewasdevelopedbyAlberyetal.104ThephaseshiftandamplitudefactorwasstudiedatdierentrotationalspeedsandACfrequencies.Atthetimeexperimentalresultsforthering-disksystemunderACmodulationcouldonlybeachievedforfrequenciesupto70Hz.105SincethenverylittletheoreticalworkhasbeendonefortheimpedanceresponseofRREorRRDE.Numerousexperimentalstudiesarepresentedintheliterature.AbsorptionofreactingintermediateswerestudiedusingACimpedanceatdierentpotentialsinthe 80

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active-to-passivetransitionrangeofFe-Crin0.5MH2SO4.106,107ThecyclingbehaviorofLi-ionbatterieswasstudiedusinga3-electrodesystem.108Ringcounterandworkingelectrodeswerealignedconcentricallytoadiskreferenceelectrodeandtheimpedanceresponsewasmeasured.Goldrotatingring-diskelectrodeswereusedtodeterminethediusioncoecientoftheborohydrideanioncommonlyusedastheanalyteinDirectBorohydrideFuelCells(DBFC).109Gabriellietal.110investigatedthedissolutionmechanismofcopperinachloridemediumusingaRRDEtosimultaneouslymeasureimpedanceandmasschangesusingaquartzmicrobalance.Cimenti111,112investigateddistortionsintheimpedancebasedoncellgeometry,electrodereactivityandrelaxationtimesinSOFC.Twoparalleldiskelectrodeswerearrangedconcentricallytoathinringreferenceelectrode.Thinconcentricringelectrodeswereusedtomodelepidermalandsubdermalimpedances.113Resultsfromthisstudywereusedindevelopingprotocolforconcentricringexperimentsandintherejectionofresultsbasedonthepresenceofartifacts.Ring-shapedinterdigitalelectrodes(RSIDEs)wereusedasanelectrochemicalbiosensorformeasuringtheconcentrationofHbA1clevelsindiabeticpatients.114Impedancesimulationsofsegmentedcylindricalelectrodeswereusedtostudyedgeeectsandedge-to-edgecurrentinteractions.115Usinganiteelementmodeltheauthorswereabletoquantifytheeectsgeometryhadoncurrentandpotentialdistributionsforsegmenteddeepbrainstimulationelectrodesusedfortargetingneuronalexcitationduringtherapy.ThermallyandelectrochemicallyinducedinterfacialsurfacealterationswerestudiedbyJiang116usingaring-disksystem.Inthisworktheringwastreatedasthereferenceelectrode.Kovacsetal.117demonstratedthatacperturbationbaseddetectionispossibleforthering-diskelectrodes.Inthisworktheauthorscorrelatethecapacitancechangesofagoldringtothepolarizationofthethinpolymerlmonthedisk.Frequencydispersioneectsduetocurrentdistributionresultinginerrorofthereactionresistanceweremodeledusingring-diskelectrode.118AcomparisoninRef.118 81

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toRef.87ismadewheretheauthorsindicatethatthefrequencydispersioncannotbedescribedasCPEbehaviorsincethephaseangleischangingcontinuouslyintheintermediatefrequencyrange.NoalternativetotheuseofapparentConstant-Phase-Elementbehaviorisprovided. 6.3MathematicalDevelopmentInthissectionexpressionsaredevelopedfortheprimaryresistanceoftheringelectrode.Presentedhereisanempiricalexpressiondescribingthedimensionlessfrequencyoftheringelectrodeintermsthegeometricparametersr1andr2.TheexpressionforthedimensionlessfrequencyofaringisanalogoustothediskdimensionlessfrequencyinEq.( 6{1 ).Theringservesastheworkingelectrode,whichisembeddedinaninnite,insulatedplanewithahemisphericalcounterelectrodelocatedatinnity. 6.3.1RingElectrodePrimaryResistanceForthepresentwork,theringelectrodeismostnaturallydescribedusinganaxisymmetriccylindricalcoordinatesystemwherethesolutionisdependentontheradialpositionralongtheelectrodesurfaceandthenormaltotheelectrodesurface,y.Theringelectrodehasaninnerandouterradiusofr1andr2,respectively.ThecurrentdistributiononaringproposedbyMiksisandNewman98varieswiththeradialpositionandisdescribedby ir iave=2 p 1)]TJ /F3 11.955 Tf 11.95 0 Td[(x2(6{5)where x=r)]TJ /F3 11.955 Tf 11.95 0 Td[(r1)]TJ /F3 11.955 Tf 11.95 0 Td[(r2 r2)]TJ /F3 11.955 Tf 11.96 0 Td[(r1(6{6)TotalcurrenttotheringelectrodeisobtainedbydirectlyintegratingEq.( 6{5 )fromr1tor2 Ir=2iaver2Zr1irrdr=2iave(r22)]TJ /F3 11.955 Tf 11.96 0 Td[(r21)(6{7) 82

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Thepotentialintheplaneoftheringisexpressedas 0(r)=2 r2Zr1ir(r0)K(m) r+r0r0dr0(6{8)whereirisdenedinEq.( 6{5 ),Kisthecompleteellipticalintegraloftherstkind98andmistheellipticparameter.Thecompleteellipticalintegraloftherstkind,K,showninEq.( 6{8 )isdenedby K(m)= 2Z0d )]TJ /F1 11.955 Tf 5.48 -9.69 Td[(1)]TJ /F3 11.955 Tf 11.96 0 Td[(msin21=2(6{9)whereistheeccentricity.TheratioofthepotentialshowninEq.( 6{8 )tothetotalcurrentshowninEq.( 6{7 )isoftendenedastheprimaryresistance.Forthissystemtheprimaryresistancecanbeexpressedintermsoftwolimitingcases.Theprimaryresistanceforathickringwhere0r1 r2<0:909 r2Rring= 824cos)]TJ /F4 7.97 Tf 6.59 0 Td[(1r1 r2+ 1)]TJ /F10 11.955 Tf 11.96 16.86 Td[(r1 r22!1=2tanh)]TJ /F4 7.97 Tf 6.58 0 Td[(1r1 r235)]TJ /F4 7.97 Tf 6.58 0 Td[(11+0:0143r1 r2tanh31:28r2 r1)]TJ /F4 7.97 Tf 6.59 0 Td[(1(6{10)Theprimaryresistanceforathinringwhere0:909r1 r21 r2Rring=1 21+r1 r2)]TJ /F4 7.97 Tf 6.59 0 Td[(1ln16 1+r1 r2 1)]TJ /F6 7.97 Tf 13.15 4.81 Td[(r1 r2!(6{11)equation 6{10 andequation 6{11 representtheprimaryresistanceforthetwolimitingcasesoftheringelectrode.Theseequationsaccountfortherealcomponentoftheimpedanceassociatedwiththeringelectrodeseenathighfrequency.SimilarlimitingexpressionshavebeendevelopedbyMiksisandNewman98andPieriniandNewman103wherethedimensionlessresistanceofthethickringapproachesthe 83

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dimensionlessresistanceofthediskelectrode. r2Rring=0:25(6{12)MiksisandNewman98useathinringlimitthatisassumedtoapproachthebehaviorofthenitelengthplaneelectrodeembeddedinaninsulator. r2Rring+1 22ln1)]TJ /F3 11.955 Tf 13.15 8.09 Td[(r31 r32=ln96 22(6{13)BruckensteinandMartinchek119provideanexpressionforthelimitingbehavioroftheprimaryresistancewithoutassuminganitelengthplaneelectrode.TheexpressionsforthelimitingprimaryresistancefortheringelectrodeareequivalenttothosepresentedbyBrucksteinandMartinchek119andcanbeveriedwiththephysicshandbookGray.120 6.3.2RingElectrodeImpedanceResponseThepotentialdistributionofanelectrolytewithuniformconductivityisgovernedbyLaplace'sequation r2=0:(6{14)Onthesurfaceadiskworkingelectrodeembeddedinaninnite,insulatedplanewithahemisphericalcounterelectrodelocatedatinnity.Thediskismostnaturallydescribedusinganaxisymmetriccylindricalcoordinatesystemwherethesolutionisdependentontheradialpositionralongtheelectrodesurfaceandthenormaltotheelectrodesurface,y.Thepotentialiszerofordistancesfarawayfromthedisk, !0asr2+y2!1(6{15)andbecausethecurrentdensityontheinsulatingplaneembeddingtheringiszero,thenormalofthepotentialgradientmustalsobezero, @ @yy=0=08r>r1(6{16) 84

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Thepotentialcanbeexpressedintermsofsteady-stateandoscillating~components =+Ref~ej!tg:(6{17)Similarly,thepotentialappliedattheelectrodesurfacecanbeexpressedintermsofsteady-stateVandoscillating~Vcomponents V=V+Ref~Vej!tg:(6{18)Forablockingelectrode,Huangetal.87showtheuxconditionatthesurfaceofadiskelectrodecanbeexpressedas, i=C0@(V)]TJ /F1 11.955 Tf 11.96 0 Td[(0) @t=)]TJ /F3 11.955 Tf 9.3 0 Td[(@ @yy=0(6{19)whereC0istheinterfacialcapacitanceandisthesolutionconductivity.UsingequationsEq.( 6{17 ),Eq.( 6{18 )andEq.( 6{19 )theuxboundaryconditionfortheblockingelectrodesurfacecanbeexpressedinthefrequencydomainas ~i=j!C0~V)]TJ /F1 11.955 Tf 13.26 3.02 Td[(~(6{20)wheretheoscillatingcomponent~Vrepresentstheappliedpotentialperturbationattheelectrodetoasystemwithanoscillatingpotentialintheelectrolyterepresentedby~. 6.4NumericalMethodTheniteelementanalysis(FEA),solverandsimulationsoftwareCOMSOLMultiphysicswasusedtosolveLaplace'sequationincylindricalcoordinatesfortheringelectrode.ThegoverningequationisprovidedinEq.( 6{14 )andissubjecttotheboundaryconditionsatinnityshowninEq.( 6{15 ).TheboundaryconditionfortheinsulatingplaneisprovidedinEq.( 6{16 )andtheboundaryconditionsattheelectrodesurfaceshowninEq.( 6{20 ).Duetothesingularitiesthatariseneartheringelectrode'sedges,anonuniformmeshingschemewasimplementednearthesurfaceoftheringelectrode.Aschematic 85

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Figure6-1. Schematicrepresentationofniteelementmeshusedfortheringelectrodesimulations:a)entiredomain;b)enlargedregiondepictingthetwoinsulatingsurfacesandtheringelectrodesurface. representationofniteelementmeshusedfortheringelectrodesimulationsisprovidedinFigure 6-1 detailing:a)entiredomain;b)enlargedregiondepictingthetwoinsulatingsurfaceswithboundaryconditionnJ=0andtheringelectrodesurfacewithboundarycondition~i=j!C0~V)]TJ /F1 11.955 Tf 13.26 3.02 Td[(~.Thecounterelectrodeingure 6-1 (a)forthesesimulationsatadistance500-1000timesthatoftheouterringradiusastoavoiderrorsassociatedwithanonuniformcurrentdistribution.Anonuniformfreetriangularmeshwaschosenwherethemeshdensityincreasestheclosertotheringelectrode.Theringelectrodeconsistsoftwoedgesr1andr2.Theexposedringelectrodesurfaceiscoplanartotheinnerandouterinsulatingsurfaces. 6.5ResultsandDiscussionTheresultsoftheCOMSOLsimulationsarepresentedtoshowtheinuencegeometryhasontheimpedanceresponsefortheringelectrode.Anapproximatecharacteristicdimensionisproposedandthenimprovedupontoachievegreateraccuracywith 86

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Table6-1. Parameters,values,anddescriptionusedfortheFEAsimulations. ParameterValueDescription C00.02F=m2interfacialcapacitance2S/melectricconductivity~V0.01Vpotentialperturbationr1=r2Table 6-2 ringinnerradiustoouterradius Table6-2. Computedvaluesofprimaryresistanceasafunctionofthegeometricparametersr1andr2. r1=r2r2Rthickring(Eq. 6{10 )r2Rthinring(Eq. 6{11 )r2Rrr(Ref.98)Zr(!!1)(FEA) 0.100000.24998-0.25000.249970.250000.25034-0.25030.250290.333330.25109--0.251100.400000.25215-0.25230.252190.500000.25485--0.254900.600000.25944-0.25900.259460.666670.26402--0.263970.750000.27229--0.272310.800000.27932-0.27850.279250.90--0.3045-0.90909-0.30873-0.308710.95--0.3343-0.95238-0.33661-0.336610.97561-0.36757-0.367570.98--0.3770theintroductionofacorrectionfactorcorr.TheparametervaluescharacterizingtheelectrochemicalsystemusedforthesimulationsareprovidedinTable 6-1 6.5.1ValidationofPrimaryResistancefortheRingElectrodeThepurposeofthissectionistovalidatetheprimaryresistancescalculatedwiththatfoundintheliterature.OurcontributionsareprovidedinFigure 6-2 whichincludetheFEAsimulationsandtheoryresultinginthelimitingcasesprovidedinEq.( 6{10 )andEq.( 6{11 ).TheseresultsarecomparedwiththeworkofMiksisandNewman.98AllofthesevaluesaresummarizedinTable 6-2 87

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Figure6-2. Computedvaluesofprimaryresistanceasafunctionofthegeometricparametersr1andr2obtainedfromEq.( 6{10 )andEq.( 6{11 ).PrimaryresistancesinTable 6-2 6.5.1.1ThickRing,ThinRingandFEAResultsComputedvaluesofprimaryresistanceasafunctionofthegeometricparametersr1andr2areprovidedinTable 6-2 .Columns2and3representthetheoreticalresultsobtainedfromEq.( 6{10 )andEq.( 6{11 )whichareinexcellentagreementwiththeFEAsimulationsathighfrequencyshownincolumn5ofTable 6-2 .TheresistancevaluescalculatedfromEq.( 6{10 )andEq.( 6{11 )andshowninTable 6-2 areinagreementfor4to5signicantdigitswiththeFEAsimulationsperformedfortheringelectrode.JusticationfortheuseoftwolimitingcasesforthethickandthinringresistancesisprovidedinFigure 6-2 .ThebluelinerepresentsthethinringprimaryresistanceslimitingsolutioncalculatedusingEq.( 6{10 )andisvalidfor0:909r1 r21.TheredlinerepresentsthethickringprimaryresistanceslimitingsolutioncalculatedusingEq.( 6{11 )andisvalidfor0r1 r2<0:909.OurCOMSOLsimulationsdemonstratetheneedfor 88

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thetwolimitingcasesconsideredinEq.( 6{10 )andEq.( 6{11 ).Thebluethinlineisinexcellentagreementwithoursimulationresults.However,whenthinringapproximationisusedforthickrings(r1=r2<0:909),thebluelineisnolongervalidwhichisclearfromthedeviationinFigure 6-2 .Similarly,thethickringlimitingbehaviorisonlyrepresentativeoftheFEAresultsforr1 r20:909. 6.5.1.2ThickRing,ThinRingandFEAResultsMiksisandNewman98tabulateprimaryresistancevaluesasdimensionlesscorrelationsasfunctionsoftheratioofradiiforthediskandringelectrode.ItshouldbenotedthatthevaluesinTable 6-2 column4fromtheworkofMiksisandNewmanareforaringelectrodewiththepresenceofaverysmalldisk.Thediskissucientlysmalltohaveanegligibleeectonaringelectroderesistancevaluesusedforthiscomparison.Forthickrings(r1=r2=0:1;0:25)theresistancevaluescalculatedfromEq.( 6{10 )andtheFEAsimulationsareinagreementforthe4signicantgurestabulatedbyMiksisandNewman.98Forringshavingintermediatethicknesses(r1=r2=0:4;0:6;0:8)theresistancevaluescalculatedfromEq.( 6{10 )andtheFEAsimulationsareinagreementfor3signicantgurestothosetabulatedbyMiksisandNewman.98ThethinringworkofMiksisandNewman98isnotdirectlycomparablesincetheparameterratiosr1=r2arenotexactlythesame.Forourworkweusethickringratiosofr1=r2=0:90909;0:95238;0:97561whereasMiksisandNewmanuser1=r2=0:90;0:95;0:98.Nonetheless,thickringswiththicknesses(r1=r2=0:90909;0:95238;0:97561)haveresistancevaluescalculatedfromEq.( 6{11 )andtheFEAsimulationsareinagreementfor2signicantgurestothosetabulatedbyMiksisandNewman.98 6.5.2InterpretationofImpedanceResponseImpedancesimulationsarepresentedtoshowtheinuencegeometryhasonringelectrodesembeddedwithinaninsulatingplane.Impedanceresultsareshownforaringelectrodeasafunctionoffrequencyandasafunctiondimensionlessfrequency.Dimensionlessresultsareusedtodeterminethecharacteristiclengthsandfrequencies 89

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Figure6-3. Ringelectrodescaledmodulusimpedanceasafunctionoffrequency.Frequencydispersionisdependentonthegeometricparameterr1=r2. associatedwithdispersion.Characteristicfrequenciesfortheringelectrodearecomparedtothecharacteristicfrequenciesforthediskelectrode.Theimpedanceofaringelectrodewassimulatedtoshowtheeectofgeometricparametersr1andr2hasonthenonuniformcurrentdistributionsresultingfromringgeometry.ThedimensionlessscaledmodulusimpedancewascalculatedasafunctionofdimensionalfrequencyisprovidedinFigure 6-3 .Thedimensionlessmodulusimpedanceforthickestringelectrodesatlowfrequencywassmallerthantheimpedanceofthethickerringelectrodes.Thesmallerimpedanceofthethickringelectrodescanbeattributedtothelargersurfacearea.Furthermore,thethickringdimensionlessmodulusimpedanceshouldapproachtheimpedanceseenforadiskelectrode.Foraxedouterradiusr2andasr1!0(ier1=r2!0)theimpedanceofthethickringapproachedtheimpedanceofthediskelectrode.Similarly,theringelectrodedimensionlessmodulusimpedanceincreasesasr1!r2(ier1=r2!1). 90

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Figure6-4. Ringelectrodeimaginary-impedance-derivedphaseangleasafunctionoffrequencyshownfortheratioofradii,r1=r2. 6.5.2.1Imaginary-Impedance-DerivedPhaseAngleTheimaginary-impedance-derivedphaseanglewasdenedbyAlexanderetal.89as 'dZj=dlog(Zj) dlog(f)90:(6{21)Whencomparedtootherdenitionsofphaseangle,theimaginary-impedance-derivedphaseangleismoresensitivetotheonsetoffrequencydispersion.Theringelectrodeimaginary-impedance-derivedphaseangleasafunctionoffrequencyispresentedinFigure 6-4 .Frequencydispersionisdependentonthegeometricparameterr1=r2.Atfrequencieslessthan1000Hzthegeometryoftheringdoesnotintroduceanyfrequencydispersion.However,theonsetoffrequencydispersionforfrequenciesgreaterthan1000Hzoccursrstforthethickestringwithr1=r2=0:1.Astheringbanddistancedecreasestheobservedonsetoffrequencydispersionoccursatahigherfrequency.Thistrendisconsistentwithimaginary-impedance-derivedphaseresultpresentedinFigure 6-4 andthescaledmodulusimpedancepresentedinFigure 6-3 91

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6.5.2.2EmpiricalFormulaBasedstrictlyontheobservationthattheonsetoffrequencydispersionvariesaccordingtotheringelectrode'sthicknessdividedbyafactoraccountingforcurvature,weproposethefollowingempiricalformula.Thisispresentedasanapproximationforthedimensionlessfrequency K= 4!C0 r2)]TJ /F3 11.955 Tf 11.95 0 Td[(r1 1+r21=r22(6{22)wherer1andr2aretheinnerandouterradiusofthering,respectively.ComparingthedimensionlessfrequencyfortheringinEq.( 6{25 )tothatofthediskinEq.( 6{1 )itcanbeseenthatthegeometricparameterr0hasbeenreplacedbytheestimatedcharacteristiclength `c;ring= 4r2)]TJ /F3 11.955 Tf 11.95 0 Td[(r1 1+r21=r22:(6{23)TheestimatedcharacteristiclengthinEq.( 6{23 )isaratiooftheringthickness(r2)]TJ /F3 11.955 Tf 10.05 0 Td[(r1)toafactoraccountingfortheratiooftheradii(1+r22=r21).Theimaginary-impedance-derived-phaseangleasafunctionofdimensionlessfrequencyforringelectrodeispresentedinFigure 6-5 andisshownforveradiiratios,r1=r2andadiskelectrodewithr2=1:0cm.Figure 6-5A isshownforthedimensionlessfrequencyrange10mHzto10HzandFigure 6-5B isshownforthedimensionlessfrequencyrange100mHZto1.8Hz.InFigure 6-5B atK=1,all5ringelectrodeshaveanimaginary{impedance{derivedphaseanglegreaterthanthatofthediskelectrode(limitingcaseofr1!0).AttheedgeofthediskelectrodethepresenceofanonuniformcurrentandpotentialdistributionresultsinafrequencydispersionforK>1.Foraringelectrodetheedgeeectsareenhancedbythecontributionoftheinnerringedgeandouterringedge.ThepresenceofmoreedgedistancealongbothcircumferencesoftheringwhencomparedtothediskresultsinahighercontributiontofrequencydispersionatlowerfrequenciesasisseeninFigure 6-5 .TheoppositetrendisobservedwhenplottedforadimensionalfrequencyasisseeninFigure 6-4 .Whenplottingthedimensionalfrequency,asisdoneinFigure 6-4 ,itis 92

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A BFigure6-5. Ringelectrodeimaginary{impedance{derivedphaseangleasafunctionofdimensionlessfrequencyillustratingthefrequencydispersionfordimensionlessfrequencyK>1.Impedanceisshownforveradiiratios,r1=r2andadiskelectrodewithr2=1:0cmfordimensionlessfrequencyrange:(A)10mHzto10Hz;(B)100mHZto1.8Hz diculttocompareringgeometriesdirectlyasthisdoesnotaccountforthephysicalandgeometricparametersforeachcase.TheapproximatecharacteristiclengthshowninEq. 6{23 canbefurtherimproveduponbyintroducingacorrectionfactor.Thecorrectionfactor g=)]TJ /F1 11.955 Tf 9.3 0 Td[(2:2755x6+5:1002x5)]TJ /F1 11.955 Tf 11.96 0 Td[(3:4095x4)]TJ /F1 11.955 Tf 11.96 0 Td[(0:5242x3+1:6789x2)]TJ /F1 11.955 Tf 11.96 0 Td[(0:7333x+1(6{24)wherex=r1=r2.Thiscorrectionfactorwasobtainedbyttingapolynomialtothedatafordierentgeometricratiosr1=r2versusthecharacteristiclength.Figure 6-6 showshowtheapproximatecharacteristiclengthEq.( 6{23 )(red)comparestothesimulatedringdata(blue)andthepolynomialtofthesimulatedringdata(black).Usingthecorrectionfactorobtainedfromthepolynomialt,amoresuitabledimensionlessfrequencyisprovidedbyK*.Dividingthecharacteristiclengthbygallowsforthedeningofareviseddimensionlessfrequency K= 4!C0 r2)]TJ /F3 11.955 Tf 11.96 0 Td[(r1 1+r21=r22`c;ring g(6{25) 93

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Figure6-6. Characteristiclengthasafunctionofthegeometricratior1=r2.COMSOLsimulationresultsareshowninblue,empiricalapproximationEq.( 6{23 )isinred,andpolynomialtisinblack. Theringelectrodeimaginary-impedance-derivedphaseangleasafunctionofdimensionlessfrequency,K,isprovidedinFigure 6-7 .Similartothepreviousgures,theserepresentimpedanceresponseandillustratingthefrequencydispersionfordimensionlessfrequencyK>1.Unlikethepreviousgures,theseprovideforamorereasonablecomparison.Specically,theonsetoffrequencydispersioncanbeseentooccurforadimensionlessfrequencyK>1usinganestablishedcharacteristiclengthof`c;ring.AcharacteristicfrequencyoftheringelectrodeforeachgeometricratioforthesimulatedratiosprovidedinTable 6-2 wasfoundtorangefrom1to100.Figure 6-8A showsratioofthecharacteristicfrequencyoftheringelectrodefc;ringtothecharacteristicfrequencyofthediskelectrodefc;diskasafunctionofthecharacteristiclength`c;ringplottedonalog-scale.Intheseresultstheringelectrodehasacharacteristicfrequencygreaterthanthecharacteristicfrequencyofthediskforallgeometricratios. 94

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A BFigure6-7. Ringelectrodeimaginary{impedance{derivedphaseangleasafunctionofdimensionlessfrequencyillustratingthefrequencydispersionfordimensionlessfrequencyK>1. A BFigure6-8. Ringelectrodeimaginary{impedance{derivedphaseangleasafunctionofdimensionlessfrequencyillustratingthefrequencydispersionfordimensionlessfrequencyK>1. Anotherwaytoconsiderthesamesetofdataistoplotitscaledbytheouterradiiofthedisk,r2.Figure 6-8B showstheratioofthecharacteristicfrequencyoftheringelectrodefc;ringtothecharacteristicfrequencyofthediskelectrodefc;diskasafunctionofthecharacteristiclength`c;ringandthecorrectedcharacteristiclength`c;ringscaledbytheouterradiiofthedisk,r2.Theresultisastraightlineforboththeapproximatecharacteristiclength`c;ringandthecorrectedcharacteristiclength`c;ring. 95

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Figure6-9. Ratioofthecharacteristicfrequencyoftheringelectrodefc;ringtothecharacteristicfrequencyofthediskelectrodefc;diskassociatedwiththecharacteristiclength`c;ringandthecorrectedcharacteristiclength`c;ringscaledbytheouterradiiofthedisk,r2. Figure 6-9 providesratioofthecharacteristicfrequencyoftheringelectrodefc,ringtothecharacteristicfrequencyofthediskelectrodefc,diskassociatedwiththecharacteristiclength`c;ringlc,ringandthecorrectedcharacteristiclength`c;ringscaledbytheouterradiiofthedisk,r2. 96

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6.6ConcludingRemarksTheextentringelectrodegeometryhasonthefrequencydispersionathighfrequencywasstudiedusingniteelementanalysisforconstantinterfacialcapacitance,electrolyteconductivity,andpotentialperturbation.Ratiosofradiiusedinthenumericalsimulationswerechosentoprovidearangeofresultstoassesstheeectringelectrodegeometryhasontheimpedanceresponse.Thesescenariosincludedthelimitingcasesofathinringr1!r2,athickringr1!0andintermediategeometricratios.Finite-elementsimulationswereperformedfordierentring-electrodecongurationstoidentifythefrequencyatwhichtheelectrodegeometrycausesfrequencydispersion.Calculationswereperformedforuniforminterfacialcapacitanceandelectrolyteconductivity.Anexpressionwasdevelopedforthecharacteristicdimensionoftheringelectrode.Thefrequencyatwhicharingelectrodecausesfrequencydispersionwasfoundtobelargerthanthefrequencyatwhichadiskofradiusequaltotheouterringradiuscausesfrequencydispersion.Thisworkprovidesguidancetothedevelopmentofimpedance-basedsensorsemployingringgeometries. 97

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CHAPTER7CONCLUSIONSAcombinationofimpedanceandpolarizationexperimentsandthermodynamic,kinetic,andimpedancemodelswereusedtoassessthetendencyofcoppertocorrodeindeaerateddeionizedwaterthatdidnotcontainhydrogen.Thepresentworkshowsthatcopperwillcorrodeataverysmallrate.Kineticsimulationsindicatethat,forthepresentexperimentalconditions,theaveragerateoveraperiodofoneyearwouldbeontheorderof1nm/day.Theimpedanceanalysissuggeststhatthecorrosionrateislessthan2.5nm/day.Thiscorrosionratewilldecreaseastheconcentrationofhydrogenandcopperincreases.Whiletheestimatedcorrosionratemaybeinconsequentialformosttechnologicalapplications,thecorrosionrateislargeenoughtoinuencethefunctionalityofnanostructureutilizedinemergingapplications.Simulationsperformedforamicroelectrodeandcopperfoilshowedthatdierencesinestimatedcorrosionratesistheconsequenceofthedierentmasstransferratesanddierentelectrodeareatoelectrolytevolumeratios.Finite-elementsimulationswereperformedfordierentring-electrodecongurationstoidentifythefrequencyatwhichtheelectrodegeometrycausesfrequencydispersion.Calculationswereperformedforuniforminterfacialcapacitanceandelectrolyteconductivity.Anexpressionwasdevelopedforthecharacteristicdimensionoftheringelectrode.Thefrequencyatwhicharingelectrodecausesfrequencydispersionwasfoundtobelargerthanthefrequencyatwhichadiskofradiusequaltotheouterringradiuscausesfrequencydispersion.Thisworkprovidesguidancetothedevelopmentofimpedance-basedsensorsemployingringgeometries. 98

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CHAPTER8FUTUREWORKThecorrosionofcoppermicroelectrodesatroomtemperatureindeaeratedwaterispresentedinChapter 4 .Furtherworkintheareaofthermalcorrosioncouldprovideadditionalinsightintothemechanismbywhichcorrosionoccurs.ExperimentstomeasuretheextentofcoppercorrosionunderthermalcyclingconditionswereattemptedbymonitoringtheOCP.Theseexperimentswereunsuccessfulduetostabilityofthesystemathightemperate.TheuseofSEMimagesveriedthepresenceofcorrosion,howeverquantifyingthecorrosionratewasnotpossiblebythismethod.InChapter 5 arenedkineticmodelisdevelopedtoinvestigatetheinuenceofmasstransfer,surfaceareatovolumeratio,exchangecurrentdensityandequilibriumpotential.Forboththeopenandclosedsystemkineticmodelsonlyconsidertheliquidphasedissolvedgasconcentration.Incorporatingtheliquid-gasequilibriumfortheclosedsystemandthedynamicsoftheliquid-gasexchangeintheopensystembyaccountingforthevolumeofoverheadspacewouldbeinterestingtoinvestigate.ThegeometricinuenceontheimpedanceresponseofaringelectrodearepresentedinChapter 6 .Thepresenceoffrequencydispersionintheringelectrodesystemisobservedfordimensionlessfrequencygreaterthanone.Fromtheseresultsasemi-impericalcharacteristiclengthwasdeterminedbasedontheringbandthicknessandacorrectionfactor.Aclosedformexpressionthatholdsforallgeometricparameterscouldnotbefound.Itwouldbeconvenienttodevelopanexpressionthatisvalidforallgeometricparameters. 99

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REFERENCES [1] C.Cleveland,S.Moghaddam,andM.E.Orazem,\Nanometer-ScaleCorrosionofCopperinDe-AeratedDeionizedWater,"JournaloftheElectrochemicalSociety,161(2014)C107{C114. [2] G.Hultquist,P.S.I.Szakalos,M.J.Graham,G.I.Sproule,andG.Wikmark,\DetectionofHydrogeninCorrosionofCopperinPureWater,"inProceedingsofthe2008InternationalCorrosionCongress,Paper3884(2008)1{9. [3] Y.Zhao,D.Ye,G.Wang,andT.Lu,\Designingnanostructuresbyglancingangledeposition,"inProceedingsofSPIE,volume5219(Citeseer,2003)59{73. [4] A.Majumdar,R.Karnik,andW.Kim,\NANOSTRUCTUREDMICROHEATPIPES,"(2006).USPatentApp.12/063,226. [5] J.P.McHale,S.V.Garimella,T.S.Fisher,andG.A.Powell,\PoolBoilingPerformanceComparisonofSmoothandSinteredCopperSurfaceswithandWithoutCarbonNanotubes,"NanoscaleandMicroscaleThermophysicalEngineering,15(2011)133{150. [6] Y.S.Ju,M.Kaviany,Y.Nam,S.Sharratt,G.Hwang,I.Catton,E.Fleming,andP.Dussinger,\PlanarVaporChamberwithHybridEvaporatorWicksfortheThermalManagementofHigh-Heat-FluxandHigh-PowerOptoelectronicDevices,"InternationalJournalofHeatandMassTransfer,60(2013)163{169. [7] S.TaoandD.Y.Li,\Nanocrystallizationeectonthesurfaceelectronworkfunctionofcopperanditscorrosionbehaviour,"PhilosophicalMagazineLetters,88(2008)137{144. [8] K.Amaya,J.Togashi,andS.Aoki,\InverseAnalysisofGalvanicCorrosion-UsingFuzzya-PrioriInformation,"JSMEInternationalJournalSeriesA:MechanicsandMaterialEngineering,38(1995)541{546. [9] M.G.Fontana,CorrosionEngineering,3rdedition(NewYork:McGrawHill,1986). [10] G.Pantazopoulos,\MetallurgicalObservationsonFatigueFailureofaBentCopperTube,"JournalofFailureAnalysisandPrevention,9(2009)270{274. [11] J.NewmanandK.Thomas-Alyea,ElectrochemicalSystems(WileyHoboken,NJ,2004). [12] J.C.RushingandM.Edwards,\Theroleoftemperaturegradientsinresidentialcopperpipecorrosion,"CorrosionScience,46(2004)1883{1894.Temperaturegradients;Thermogalvaniccurrents;. [13] D.S.CarrandC.F.Bonilla,\ThermogalvanicPotentials,"JournaloftheElectro-chemicalSociety,99(1952)475{482. 100

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[14] H.LalandH.R.Thirsk,\TheAnodicBehaviourofCopperinNeutralandAlkalineChlorideSolutions,"JournaloftheChemicalSociety(Resumed),(1953)2638{2644. [15] T.Hurlen,\DissolutionofCopperbyOxidationAgentsinAcidChlorideSolution,"Acta.Chem.Scand,15(1961)1239{1245. [16] N.Berry,\"Thermogalvanic"corrosion,"NanostructuredMaterialsandNanotechnol-ogyIi,2(1946)261{267. [17] M.BraunandK.Nobe,\ElectrodissolutionKineticsofCopperinAcidicChlorideSolutions,"JournaloftheElectrochemicalSociety,126(1979)1666{1671. [18] A.L.BacarellaandJ.J.C.Griess,\TheAnodicDissolutionofCopperinFlowingSodiumChlorideSolutionsBetween25and175C,"JournaloftheElectrochemicalSociety,120(1973)459{465. [19] F.King,M.Quinn,andC.D.Litke,\OxygenReductiononcopperinneutralNaclsolution,"JournalofElectroanalyticalChemistry,385(1995)45{55. [20] T.N.Andersen,M.H.Ghandehari,andH.Eyring,\ALimitationtotheMixedPotentialConceptofMetalCorrosion,"JournaloftheElectrochemicalSociety,122(1975)1580{1585. [21] A.Jardy,A.L.Lasalle-Molin,M.Keddam,andH.Takenouti,\CopperDissolutioninAcidicSulphateMediaStudiedbyQCMandRRDEunderACSignal,"Elec-trochimicaActa,37(1992)2195{2201. [22] S.T.MayerandR.H.Muller,\AnInSituRamanSpectroscopyStudyoftheAnodicOxidationofCopperinAlkalineMedia,"JournaloftheElectrochemicalSociety,139(1992)426{434. [23] B.Miller,\Split-RingDiskStudyoftheAnodicProcessesataCopperElectrodeinAlkalineSolution,"JournaloftheElectrochemicalSociety,116(1969)1675{1680. [24] C.B.Diem,TheInuenceofVelocityontheCorrosionofCopperinAlkalineChlorideSolutions,Ph.D.dissertation,UniversityofVirginia,Charlottesville,Virginia(1990). [25] N.Mora,E.Cano,E.M.Mora,andJ.M.Bastidas,\InuenceofpHandOxygenonCopperCorrosioninSimulatedUterineFluid,"Biomaterials,23(2002)667{671. [26] C.B.DiemandM.E.Orazem,\TheInuenceofVelocityontheCorrosionofCopperinAlkalineChlorideSolutions,"NanostructuredMaterialsandNanotechnol-ogyIi,50(1994)290{300. [27] C.B.DiemandM.E.Orazem,\TheCorrosionofCopperinFlowingAlkalineChlorideSolutions,"inVelocityEnhancedCorrosion,K.J.Kennelley,R.H.Hausler,andD.Silverman,editors(Houston,Texas:NationalAssociationofCorrosionEngineers,1991)23:1{23:15. 101

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[28] C.H.Bongkio,H.C.Albaya,andO.A.Cobo,\TheKineticsoftheAnodicDissolutionsofCopperinAicdChlorideSolutions,"Corr.Sci.,13(1973)717{724. [29] P.Agarwal,O.C.Moghissi,M.E.Orazem,andL.H.Garca-Rubio,\ApplicationofMeasurementModelsforAnalysisofImpedanceSpectra,"NanostructuredMaterialsandNanotechnologyIi,49(1993)278{289. [30] M.Pourbaix,AtlasofElectrochemicalEquilibriainAqueousSolutions(Houston,Texas,USA:NACEInternational:TheCorrosionSociety,1974). [31] D.M.Bastidas,E.Cano,andE.Mora,\InuenceofOxygen,AlbuminandpHonCopperDissolutioninaSimulatedUterineFluid,"EuropeanJ.ofContraceptionandReproductiveHealthcare,10(2005)123{130. [32] J.Zhu,N.Xu,andC.Zhang,\Characteristicsofcoppercorrosioninsimulateduterineuidinthepresenceofprotein,"Advancesincontraception,15(1999)179{190. [33] F.King,L.Ahonen,C.Taxen,U.Vuorinen,andL.Werme,Coppercorrosionunderexpectedconditionsinadeepgeologicrepository,TechnicalReportTR-01-23,SwedishNuclearFuelandWasteManagementCo,SwedishNuclearFuelandWasteManagementCo,Box5864,SE-10240StockholmSweden(2001). [34] Y.Feng,W.-K.Teo,K.-S.Siow,K.l.Tan,andA.-K.Hsieh,\Thecorrosionbehaviourofcopperinneutraltapwater.PartI:Corrosionmechanisms,"Cor-rosionScience,38(1996)369{385. [35] G.Hultquist,G.Chuah,andK.Tan,\Commentsonhydrogenevolutionfromthecorrosionofpurecopper,"CorrosionScience,29(1989)1371{1377. [36] G.Hultquist,M.Graham,P.Szakalos,G.Sproule,A.Rosengren,andL.Grasjo,\HydrogenGasProductionDuringCorrosionofCopperbyWater,"Corros.Sci.,53(2011)310{319. [37] G.Hultquist,P.Szakalos,M.Graham,A.B.Belonoshko,G.Sproule,L.Grasjo,P.Dorogokupets,B.Danilov,T.AAstrup,G.Wikmark,etal.,\Watercorrodescopper,"CatalysisLetters,132(2009)311{316. [38] F.KingandC.Lilja,\Scienticbasisforcorrosionofcopperinwaterandimplicationsforcanisterlifetimes,"CorrosionEngineering,ScienceandTechnol-ogy,46(2011)153{158. [39] P.Szakalos,G.Hultquist,andG.Wikmark,\Corrosionofcopperbywater,"ElectrochemicalandSolid-StateLetters,10(2007)C63{C67. [40] D.D.MacdonaldandS.Shari-Asl,IsCopperImmunetoCorrosionWheninContactwithWaterandAqueousSolutions,TechnicalReportTR-01-23,SwedishRadiationSafetyAuthority,SwedishNuclearFuelandWasteManagementCoBox5864SE-10240StockholmSweden(2011). 102

PAGE 103

[41] M.E.OrazemandB.Tribollet,ElectrochemicalImpedanceSpectroscopy(Hoboken,NJ:JohnWiley&Sons,2008). [42] S.-L.Wu,InuenceofDiskElectrodeGeometryonLocalandGlobalImpedanceResponse,Ph.D.dissertation,UniversityofFlorida,Gainesville,FL(2010). [43] E.Patrick,M.E.Orazem,J.C.Sanchez,andT.Nishida,\CorrosionofTungstenMicroelectrodesusedinNeuralRecordingApplications,"JournalOfNeuroscienceMethods,198(2011)158{171. [44] A.Bar-CohenandP.Wang,\ThermalManagementofOn-ChipHotSpot,"J.HeatTransfer,134(2012). [45] S.V.GarimellaandC.Sobhan,\RecentAdvancesintheModelingandApplicationsofNonconventionalHeatPipes,"AdvancesinHeatTransfer,35(2001)249{308. [46] S.P.Gurrum,S.K.Suman,Y.K.Joshi,andA.G.Fedorov,\Thermalissuesinnext-generationintegratedcircuits,"DeviceandMaterialsReliability,IEEETransactionson,4(2004)709{714. [47] M.Groll,M.Schneider,V.Sartre,M.ChakerZaghdoudi,andM.Lallemand,\ThermalControlofElectronicEquipmentbyHeatPipes,"Revuegeneraledethermique,37(1998)323{352. [48] C.Zhang,AnalyticalandExperimentalInvestigationofCapillaryForcesInducedbyNanopillarsforThermalManagementApplications,Ph.D.dissertation,UniversityofTexas(2010). [49] R.Chen,M.-C.Lu,V.Srinivasan,Z.Wang,H.H.Cho,andA.Majumdar,\NanowiresforEnhancedBoilingHeatTransfer,"NanoLett.,9(2009)548{553. [50] A.S.Kousalya,J.A.Weibel,S.V.Garimella,andT.S.Fisher,\MetalFunctionalizationofCarbonNanotubesforEnhancedSinteredPowderWicks,"Int.J.HeatMassTran.,59(2013)372{383. [51] R.W.Knight,D.Hall,J.Goodling,andR.Jaeger,\HeatSinkOptimizationwithApplicationtoMicrochannels,"Components,Hybrids,andManufacturingTechnology,IEEETransactionson,15(1992)832{842. [52] D.B.TuckermanandR.Pease,\High-PerformanceHeatSinkingforVLSI,"ElectronDeviceLetters,IEEE,2(1981)126{129. [53] M.BowersandI.Mudawar,\HighFluxBoilinginLowFlowRate,LowPressureDropMini-ChannelandMicro-ChannelHeatSinks,"Int.J.HeatMassTran.,37(1994)321{332. [54] R.CheinandG.Huang,\AnalysisofMicrochannelHeatSinkPerformanceUsingNanouids,"ApplThermEng,25(2005)3104{3114. 103

PAGE 104

[55] S.P.JangandS.U.Choi,\CoolingPerformanceofaMicrochannelHeatSinkwithNanouids,"ApplThermEng,26(2006)2457{2463. [56] C.-J.Ho,L.Wei,andZ.Li,\AnExperimentalInvestigationofForcedConvectiveCoolingPerformanceofaMicrochannelHeatSinkWithAl2O3/WaterNanouid,"ApplThermEng,30(2010)96{103. [57] O.E.Barcia,O.R.Mattos,N.Pebere,andB.Tribollet,\Mass-TransportStudyfortheElectrodissolutionofCopperin1MHydrochloricAcidSolutionbyImpedance,"JournaloftheElectrochemicalSociety,140(1993)2825{2832. [58] K.D.Erd,\EectofFluidDynamicsontheCorrosionofCopper-BasedAlloysinSeawater,"NanostructuredMaterialsandNanotechnologyIi,33(1977)3{8. [59] J.S.NewmanandK.E.Thomas-Alyea,ElectrochemicalSystems,3rdedition(Hoboken,NJ:JohnWiley&Sons,2004). [60] M.Bojinov,I.Betova,andC.Lilja,\AMechanismofInteractionofCopperwithaDeoxygenatedNeutralAqueousSolution,"CorrosionScience,52(2010)2917{2927. [61] M.Bojinov,T.Laitinen,K.Mkel,M.Snellman,andL.Werme,\CorrosionofCopperin1MNaClunderStrictlyAnoxicConditions,"MRSProceedings,807(2003)459{464. [62] S.Shari-AslaandD.D.Macdonald,\InvestigationoftheKineticsandMechanismoftheHydrogenEvolutionReactiononCopper,"JournaloftheElectrochemicalSociety,160(2013)H382{H391. [63] R.DortwegtandE.Maughan,\TheChemistryofCopperinWaterandRelatedStudiesPlannedattheAdvancedPhotonSource,"inParticleAcceleratorConfer-ence,2001.PAC2001.Proceedingsofthe2001,volume2(IEEE,2001)1456{1458. [64] R.Dortwegt,C.Putnam,andE.Swetin,\MitigationofCopperCorrosionandAgglomerationinAPSProcessWaterSystems,"in2ndIntlWorkshoponMechan-icalEngineeringDesignofSynchrotronRadiationEquipmentandInstrumentation(MEDSI2002)(2002)462{468. [65] M.Parro,P.Karditsas,A.Caloutsis,D.Iglesias,B.Bra~nas,andA.Abanades,\CorrosionandActivationAnalysisoftheLIPACBeamDumpCoolingCircuit,"FusionEng.Des.,(2013). [66] J.S.Newman,\ResistanceforFlowofCurrenttoaDisk,"JournaloftheElectro-chemicalSociety,113(1966)501{502. [67] A.AnderkoandP.J.Shuler,\AComputationalApproachtoPredictingtheFormationofIronSuldeSpeciesUsingStabilityDiagrams,"Computers&Geo-sciences,23(1997)647{658. 104

PAGE 105

[68] A.Anderko,S.J.Sanders,andR.D.Young,\RealSolutionStabilityDiagrams:AThermodynamicToolforModelingCorrosioninWideTemperatureandConcentrationRanges,"Corrosion,53(1997)43{53. [69] B.BeverskogandI.Puigdomenech,\RevisedPourbaixDiagramsforCopperat25to300C,"JournaloftheElectrochemicalSociety,144(1997)3476{3483. [70] P.MahonandK.Oldham,\Diusion-controlledchronoamperometryatadiskelectrode,"AnalyticalChemistry,77(2005)6100{6101. [71] Z.StankovicandM.Vukovic,\TheInuenceofThioureaonKineticParametersontheCathodicandAnodicReactionatDierentMetalsinH2SO4Solution,"Electrochim.Acta,41(1996)2529{2535. [72] M.SternandA.L.Geary,\ElectrochemicalPolarization:I.ATheoreticalAnalysisoftheShapeofPolarizationCurves,"JournaloftheElectrochemicalSociety,104(1957)56{63. [73] P.Agarwal,M.E.Orazem,andL.H.Garca-Rubio,\MeasurementModelsforElectrochemicalImpedanceSpectroscopy:1.DemonstrationofApplicability,"JournaloftheElectrochemicalSociety,139(1992)1917{1927. [74] G.J.Brug,A.L.G.vandenEeden,M.Sluyters-Rehbach,andJ.H.Sluyters,\TheAnalysisofElectrodeImpedancesComplicatedbythePresenceofaConstantPhaseElement,"JournalofElectroanalyticalChemistry,176(1984)275{295. [75] V.M.-W.Huang,V.Vivier,I.Frateur,M.E.Orazem,andB.Tribollet,\TheGlobalandLocalImpedanceResponseofaBlockingDiskElectrodewithLocalCPEBehavior,"JournaloftheElectrochemicalSociety,154(2007)C89{C98. [76] B.Hirschorn,M.E.Orazem,B.Tribollet,V.Vivier,I.Frateur,andM.Musiani,\DeterminationofEectiveCapacitanceandFilmThicknessfromCPEParameters,"ElectrochimicaActa,55(2010)6218{6227. [77] B.Hirschorn,M.E.Orazem,B.Tribollet,V.Vivier,I.Frateur,andM.Musiani,\Constant-Phase-ElementBehaviorCausedbyResistivityDistributionsinFilms:1.Theory,"JournaloftheElectrochemicalSociety,157(2010)C452{C457. [78] B.Hirschorn,M.E.Orazem,B.Tribollet,V.Vivier,I.Frateur,andM.Musiani,\Constant-Phase-ElementBehaviorCausedbyResistivityDistributionsinFilms:2.Applications,"JournaloftheElectrochemicalSociety,157(2010)C458{C463. [79] M.E.Orazem,B.Tribollet,V.Vivier,S.Marcelin,N.Pebere,A.L.Bunge,E.A.White,D.P.Riemer,I.Frateur,andM.Musiani,\DielectricPropertiesofMaterialsshowingConstant-Phase-Element(CPE)ImpedanceResponse,"JournaloftheElectrochemicalSociety,160(2013)C215{C225. [80] W.M.Haynes,T.J.Bruno,andD.R.Lide,editors,CRCHandbookofChemistryandPhysics,94thedition(CRCPress,2014). 105

PAGE 106

[81] R.Bogdanowicz,J.Ryl,K.Darowicki,andB.B.Kosmowski,\EllipsometricStudyofOxideFormationonCuElectrodein0.1MNaOH,"JournalofSolidStateElectrochemistry,13(2009)1639{1644. [82] Z.D.StankovicandM.Vukovic,\TheInuenceofThioureaOnKineticParametersontheCathodicandAnodicReactionatDierentMetalsinH2SO4Solution,"ElectrochimicaActa,41(1996)2529{2535. [83] R.Sander,\Henry'sLawConstants,"inNISTChemistryWebBook,NISTStandardReferenceDatabaseNumber69,P.LinstromandW.Mallard,editors(GaithersburgMD:NationalInstituteofStandardsandTechnology)http://webbook.nist.gov.RetrievedNovember4,2015. [84] H.C.Hottel,J.J.Noble,A.F.Sarom,G.D.Sikox,P.C.Wankat,andK.S.Knaebel,\HeatandMassTransfer,"inPerry'sChemicalEngineers'Handbook,D.W.GreenandR.H.Perry,editors,8thedition(NewYork,NY:McGraw-Hill,2007)5:1{5:84. [85] C.R.Wilke,M.Eisenberg,andC.W.Tobias,\CorrelationofLimitingCurrentsunderFreeConvectionConditions,"JournalofTheElectrochemicalSociety,100(1953)513{523. [86] G.Hultquist,M.Graham,O.Kodra,S.Moisa,R.Liu,U.Bexell,andJ.Smialek,\CorrosionofCopperinDistilledWaterwithoutO2andtheDetectionofProducedHydrogen,"CorrosionScience,95(2015)162{167. [87] V.M.-W.Huang,V.Vivier,M.E.Orazem,N.Pebere,andB.Tribollet,\TheApparentCPEBehaviorofaDiskElectrodewithFaradaicReactions,"JournaloftheElectrochemicalSociety,154(2007)C99{C107. [88] J.S.Newman,\FrequencyDispersioninCapacityMeasurementsataDiskElectrode,"JournaloftheElectrochemicalSociety,117(1970)198{203. [89] C.L.Alexander,B.Tribollet,andM.E.Orazem,\ContributionofSurfaceDistributionstoConstant-Phase-Element(CPE)Behavior:1.InuenceofRoughness,"ElectrochimicaActa,173(2015)416{424. [90] V.M.-W.Huang,V.Vivier,M.E.Orazem,N.Pebere,andB.Tribollet,\TheApparentCPEBehaviorofanIdeallyPolarizedDiskElectrode:AGlobalandLocalImpedanceAnalysis,"JournaloftheElectrochemicalSociety,154(2007)C81{C88. [91] C.Blanc,M.Orazem,N.Pbre,B.Tribollet,V.Vivier,andS.Wu,\TheOriginoftheComplexCharacteroftheOhmicImpedance,"ElectrochimicaActa,55(2010)6313{6321. [92] C.L.Alexander,B.Tribollet,andM.E.Orazem,\ContributionofSurfaceDistributionstoConstant-Phase-Element(CPE)Behavior:2.Capacitance,"ElectrochimicaActa,(2015)submitted. 106

PAGE 107

[93] A.Frumkin,L.Nekrasov,B.Levich,andJ.Ivanov,\DieAnwendungderrotierendenScheibenelektrodemiteinemRingezurUntersuchungvonZwischenproduktenelektrochemischerReaktionen,"JournalofElectroanalyticalChemistry(1959),1(1959)84{90. [94] A.FrumkinandL.Nekrasov,\OntheRing-DiskElectrode,"inDokl.Akad.Nauk.SSSR,volume126(1959)115{118. [95] I.IvanovandV.Levich,\InvestigationofUnstableIntermediaryProductionoftheElectrodeReactionbyMeansofaRotatingDiskElectrode,"DokladyAkademiiNaukSSSR,126(1959)1029{1032. [96] W.AlberyandS.Bruckenstein,\Ring-discelectrodes.Part2.TheoreticalandExperimentalCollectionEciencies,"TransactionsoftheFaradaySociety,62(1965)1920{1931. [97] W.H.SmyrlandJ.S.Newman,\Ring-DiskandSectionedDiskElectrode,"JournaloftheElectrochemicalSociety,119(1972)212{219. [98] J.JosephJ.MiksisandJ.S.Newman,\PrimaryResistancesforRing-DiskElectrodes,"JournaloftheElectrochemicalSociety,123(1976)1030{1036. [99] P.PieriniandJ.S.Newman,\CurrentDistributiononaRotatingRing-DiskElectrodebelowtheLimitingCurrent,"JournaloftheElectrochemicalSociety,124(1977)701{706. [100] D.GregoryandA.Riddiford,\DissolutionofCopperinSulfuricAcidSolutions,"JournaloftheElectrochemicalSociety,107(1960)950{956. [101] D.GregoryandA.Riddiford,\TransporttotheSurfaceofaRotatingDisc,"JournaloftheChemicalSociety,(1956)3756{3764. [102] V.G.Levich,PhysicochemicalHydrodynamics(EnglewoodClis,NJ:PrenticeHall,1962). [103] P.PieriniandJ.S.Newman,\RingElectrodes,"JournaloftheElectrochemicalSociety,125(1978)79{84. [104] W.Albery,J.Drury,andA.Hutchinson,\RingDiscElectrodes.Part15.AlternatingCurrentMeasurements,"TransactionsoftheFaradaySociety,67(1971)2414{2418. [105] W.Albery,A.Davis,andA.Mason,\AlternatingCurrentandRing-DiscElectrodes,"FaradayDiscussionsoftheChemicalSociety,56(1973)317{329. [106] I.Annergren,M.Keddam,H.Takenouti,andD.Thierry,\ModellingofthePassivationMechanismofFe-CrBinaryAlloysfromACImpedanceandFrequencyResolvedRRDE:I.BehaviourofFe-CrAlloysin0.5MH2SO4,"Electrochimicaacta,41(1996)1121{1135. 107

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[107] I.Annergren,M.Keddam,H.Takenouti,andD.Thierry,\ModelingofthePassivationMechanismofFe-CrBinaryAlloysfromAcImpedanceandFrequencyResolvedRRDE:II.BehaviorOfFe-CrAlloysIn0.5MH2SO4withanAdditionofChloride,"ElectrochimicaActa,42(1997)1595{1611. [108] C.Bunzli,H.Kaiser,andP.Novak,\ImportantAspectsforReliableElectrochemicalImpedanceSpectroscopyMeasurementsofLi-IonBatteryElectrodes,"JournalofTheElectrochemicalSociety,162(2015)A218{A222. [109] M.Chatenet,M.Molina-Concha,N.El-Kissi,G.Parrour,andJ.-P.Diard,\DirectRotatingRing-DiskMeasurementoftheSodiumBorohydrideDiusionCoecientinSodiumHydroxideSolutions,"ElectrochimicaActa,54(2009)4426{4435. [110] C.Gabrielli,M.Keddam,F.Minouet-Laurent,andH.Perrot,\SimultaneousEQCMandRing-DiskMeasurementsinACRegimeApplicationtoCopperDissolution,"Electrochemicalandsolid-stateletters,3(2000)418{421. [111] M.Cimenti,A.Co,V.Birss,andJ.Hill,\DistortionsinElectrochemicalImpedanceSpectroscopyMeasurementsUsing3-electrodeMethodsInSOFC:1.EectofCellGeometry,"FuelCells,7(2007)364{376.3-electrodeconguration;Area-specicpolarisationresistances;Electrodegeometry;Impedancedistortions;Referenceelectrodes;. [112] M.Cimenti,V.Birss,andJ.Hill,\DistortionsinElectrochemicalImpedanceSpectroscopyMeasurementsUsing3-electrodeMethodsInSOFC:2.EectofElectrodeActivityandRelaxationTimes,"FuelCells,7(2007)377{391.3-electrodeconguration;Planarcells;Referenceelectrodes;. [113] W.BesioandA.Prasad,\AnalysisofSkin-ElectrodeImpedanceusingConcentricRingElectrode,"inEngineeringinMedicineandBiologySociety,2006.EMBS'06.28thAnnualInternationalConferenceoftheIEEE(IEEE,2006)6414{6417. [114] K.-M.Hsieh,K.-C.Lan,W.-L.Hu,M.-K.Chen,L.-S.Jang,andM.-H.Wang,\GlycatedHemoglobin(HbA1c)AnityBiosensorswithRing-ShapedInterdigitalElectrodesonImpedanceMeasurement,"BiosensorsandBioelectronics,49(2013)450{456. [115] X.F.WeiandW.M.Grill,\CurrentDensityDistributions,FieldDistributionsandImpedanceAnalysisofSegmentedDeepBrainStimulationElectrodes,"JournalofNeuralEngineering,2(2005)139. [116] S.P.Jiang,\ThermallyandElectrochemicallyInducedElectrode/ElectrolyteInterfacesinSolidOxideFuelCells:AnAFMandEISStudy,"JournalofTheElectrochemicalSociety,162(2015)F1119{F1128. [117] N.Kovacs,M.Ujvari,G.G.Lang,P.Broekmann,andS.Vesztergom,\CharacterizationoftheCapacitanceofaRotatingRing-DiskElectrode,"In-strumentationScience&Technology,(2015). 108

PAGE 109

[118] J.NielsenandT.Jacobsen,\CurrentDistributionEectsinACImpedanceSpectroscopyofElectroceramicPointContactandThinFilmModelElectrodes,"ElectrochimicaActa,55(2010)6248{6254. [119] S.BruckensteinandG.Martinchek,\AClosedFormExpressionforthePrimaryResistanceataRingElectrode,"JournalofTheElectrochemicalSociety,126(1979)1307{1309. [120] D.E.Gray,AmericanInstituteofPhysicsHandbook(McGraw-Hill,1972). 109

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BIOGRAPHICALSKETCH Christopher Cleveland matriculated at the University of St. Thomas in St. Paul, Minnesota, in August of 2005, where he graduated with honors earning his Bachelor of Science in chemistry and Bachelor of Arts in mathematics in May of 2008. Following this, Chris attended Carnegie Mellon University where he received his Master of Science in chemical engineering in May of 2010. Under the direction of Professor Mark E. Orazem, Chris has investigated the corrosion of copper in deaerated water and will receive his Doctor of Philosophy from the University of Florida in 201 110