COMSOL-Based Numerical Analysis of Electric Field

1COMSOLCOMSOL--BasedNumericalAnalysisBasedNumericalAnalysisofElectricFieldDistributionduringofElectricFieldDistributionduringElectrospinningElectrospinningandandPiezoPiezo--ResponseResponseImagingofUltraImagingofUltra--FinePZTFibersFinePZTFibersYuWangandJorgeSantiago-AvilésDepartmentofElectrical&SystemsEngineeringUniversityofPennsylvaniaPresentedattheCOMSOLUsersConference2007Boston2OutlineOutlineI.BackgroundandMotivationI.1BackgroundI.2Piezo-responseimaging(PRI)I.3MotivationII.MathematicalModelsandEquationsIII.NumericalAnalysisResultsIII.1ElectrospinningpotentialandfielddistributionIII.2PRIpotentialandfielddistributionIV.PRIExperimentalResultsV.Conclusions3I.1I.1BackgroundBackgroundNano-fibers/wires•Lowestdimensionforefficientelectronstransportandopticalexcitations•Buildingblocksinbottom-upassemblyinnano-electronics&photonics•Possiblyovercomethefundamentallimitationsofconventionalmicro-fabricationbasedonlithography.Electrospinning•PatentedbyFormhalsin1934•Recentlyrevitalizedtofabricateultra-finefibers•Simple,inexpensive,flexibleanduniversalLeadzirconatetitanate,Pb(ZrxTi1-x)O3(PZT)nanofibers•PZTiswell-knownferroelectricmaterialofwideapplications•PZTfibershavepotentialforutilizationinhighperformancehydrophones&ultrasonictransducerapplications•WesynthesizedPZTmicro/nano-fibersusingtheelectrospinningtechnique•WeprobedelectrospunPZTfibersusingpiezoresponseimaging(PRI)techniques**Wangetal,Appl.Phys.A,78(2004):1043;Nanotechnology,15(2004):32SyringeStationarycollectorscreenHighvoltagesourceMetaltipPrecursorsolutionFilter4I.2I.2PiezoresponsePiezoresponseimaging(PRI)imaging(PRI)•Developedtocharacterizeferroelectricthinfilms,e.g.PZTthinfilms•Basedonscanningprobemicroscopy(SPM)+lock-inelectricalmeasurement•Sandwichedstructure:biasedSPMtip/PZTthinfilm/bottommetal(grounded)C.Harnagea,PhDdissertation,2001,•ApplyDCandACvoltagesbetweenthetipandthemetal,Vtip=VDC+VACcos(ωt),(1)setupelectricfieldandinducepiezoelectricoscillationonPZTsurfaceδ=δ0+δ1cos(ωt+φ1)+δ2cos(2ωt+φ2)+······,(2)wherethesubscriptistandsforthei-thorderharmoniccomponent,δ0reflectsthesurfacetopographyandVDCeffect;phaseφ1=0andπforpolarizationPinthelocaldomainisupanddown.δ1=d33·VAC,(3)whered33isthelocalpiezoelectricconstant,proportionaltothemagnitudeofpolarization(P)andtheirsignreflectthePdirection.•IfVDCisadditionallysweptandd33ismeasured,d33canbeplottedagainVDCasthelocalpiezoelectriccurveforeachtipposition.5I.3MotivationI.3MotivationSincebothelectrospinningandPRIworkbymeansofelectricfield,wewanttonumericallyanalyzethespatialdistributionofelectricpotential(u)andfield(E)in(1)ourelectrospinningsetupunderitstypicaloperatingconditions.(Previousreportsindicatedthatthedistributiondependsspecificallyonthesetupconfigurationanditsoperatingconditions.)(2)ourpiezo-responseimagingofPZTmicrofibersandhopefullyhelpstounderstandourPRIandlocalmeasurementresultsbetter.6OutlineOutlineI.BackgroundandMotivationI.1BackgroundI.2Piezo-responseimaging(PRI)I.3MotivationII.MathematicalModelsandEquationsIII.NumericalAnalysisResultsIII.1ElectrospinningpotentialandfielddistributionIII.2PRIpotentialandfielddistributionIV.PRIExperimentalResultsV.Conclusions7II.II.MathematicalModelsandEquationsMathematicalModelsandEquationsLaplaceequation∇2u=0,(4)withDiricheletboundaryconditions,u=Vtip,ontheelectrospinning/PRItip,(5a)u=0,onthegroundedmetal,(5b)u=0,atinfinity,(5c)Defined≡thetip-to-metaldistanceIntroduceanimaginarysphericalboundarycenteredatthetipendandwithradiumof10d,wheretheequi-potentialsareapproximatelyradial,PRIimaginarysphericalsurfaceandvonNeumannboundarycondition,∂u/∂n=0(5c’)Electrospinning:azimuthalsymmetry,canbereducedinto2DPRI:noazimuthalsymmetry,hastobesolvedin3DConictipfullconeangle=20°r≡curvatureradiumoftipapexEllipticalcrosssectionofPZTfibera≡semi-major/minoraxisb≡semi-major/minoraxis8OutlineOutlineI.BackgroundandMotivationI.1BackgroundI.2Piezo-responseimaging(PRI)I.3MotivationII.MathematicalModelsandEquationsIII.NumericalAnalysisResultsIII.1ElectrospinningfielddistributionIII.2PRIpotentialandfielddistributionIV.PRIExperimentalResultsV.Conclusions9III.NumericalAnalysisResultsNumericalAnalysisResultsuudistributiondistributionuu&&EEdistributionbetweentipandscreendistributionbetweentipandscreen•Potentialdecreasesrapidlyaroundthetip(likearoundapointsource)andlinearlywiththedistance(likebetweenflatplates)towardthemetalscreen;•Fieldisveryhigharoundthetipandlevelsofffarawayfromthetip;•Theshorterthetip-screendistance,thehigherfield.Implicationsforelectrospinningprocesscontrol(1)Electrostaticspinningforceisexertedmainlyaroundthetip(2)Thetip-metalscreendistancedisnotacriticalparametersolongasEislargeenoughtospinfiberfromthetipIII.1Electrospinningpotential/fielddistribution051015200.00.20.40.60.81.0u/Vz(cm)d=10cmd=15cmd=20cm051015200.00.20.40.60.80.00.10.20.30.40.50.20.40.60.8E(V/cm)z(cm)d=10cmd=15cmd=20cm10III.2PRIpotential/fielddistribution(1)III.2PRIpotential/fielddistribution(1)TipOverallpotentialandfielddistributionwithparameters