OlgaWodoJacobusJvanFranekerAJJanssen andPeterABobbertMolecularMaterialsandNanosystemsEindhovenUniversityofTechnologyPOBox513NL5600MBEindhovenTheNetherlandsDepartmentofMaterialsDesignandIn ID: 833064
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SimulatingPhaseSeparationduringSpinCoati
SimulatingPhaseSeparationduringSpinCoatingofaFullereneBlend:AJointComputationalandExperimentalInvestigationVikasNegi,OlgaWodo,JacobusJ.vanFraneker,A.J.Janssen,andPeterA.BobbertMolecularMaterialsandNanosystems,EindhovenUniversityofTechnologyP.O.Box513,NL-5600MBEindhoven,TheNetherlandsDepartmentofMaterialsDesignandInnovationandDepartmentofMechanicalandAerospaceEngineering,UniversityatBualo,NewYork14260,UnitedStatesInstituteofComplexMolecularSystems,EindhovenUniversityofTechnology,P.O.Box513,NL-5600MBEindhoven,TheNetherlandsCenterforComputationalEnergyResearch,DepartmentofAppliedPhysics,EindhovenUniversityofTechnology,P.O.Box513,NL-5600MBEindhoven,TheNetherlandsSupportingInformationDuringspincoatingofthephotoactivelayerofabulkheterojunctionorganicsolarcell,phaseseparationbetweenthedonor(D)andacceptor(A)componentsistriggeredbysolventevaporation.Themorphologyoftheresultinglayerisoneofthemaindeterminantsofthedeviceeciencyandcriticallydependsonprocessingconditionssuchasthespinningspeed,DAmixingratio,andchoiceofsolvents.Itiscrucialtounderstandhowtheseconditionsinuencethenanostructureofthephotoactivelayer.Opticalexperimentshavealimitedspatialresolutionandcannotprobetheshortlengthscalesofphaseseparation.Inthiswork,wepresentthree-dimensionalsimulationsofevaporation-inducedphasesep-arationinadiketopyrrolopyrrolefullereneDAblend,wherewederivethesimulationparametersfr
ominsitulaserinterferenceandcontactangle
ominsitulaserinterferenceandcontactangleexperiments.Dependingonthedryingrate,phaseseparationinitiatesinerentregionsofthethinninglm.Fromalinearstabilityanalysis,weestimatetheearlystagelengthscaleofphaseseparationandcompareitwithsimulations.Thenormalizeddryingrateisshowntobethekeyparameter.Theexperimentallyfoundpowerlawdependenceofthecharacteristiclengthscaleofphaseseparationonthisparameterisreproducedwithamatchingexponent.organicphotovoltaicdevices,bulkheterojunction,processstructurerelationships,spincoating,phaseseparation,Cookequations1.INTRODUCTIONSolution-processedorganicphotovoltaics(OPV)aimstobeaectivealternativetothetraditionalsilicon-basedtech-nologythatcurrentlydominatesthesolarenergymarket.Otheradvantagesincluderoll-to-rollprocessingonexiblesubstrates,whichisappealingwithregardtoitspotentialforlarge-scaleThepowerconversioneciency(PCE)ofbothandmultijunctionOPVcellshassteadilyimprovedovertheyearsandrecentlyreachedthe13%mark.Inordertocompetewithsilicon-basedphotovoltaics,whichcanhaveaPCEcloseto26%,alotofprogressstillneedstobemade.OneofthekeyreasonsfortheriseinthePCEofsolution-processedOPVhasbeenthedevelopmentoflow-bandgapsemiconductingpolymers.Thesepolymerscontainalter-natingelectron-richandelectron-decientunitsinaso-calledSincetherstpublishedreportindiketopyrrolopyrrole(DPP)hasbecomeapopularcientunitforuseinlow-bandgappolymers.Suchpolymersallowne-tun
ingoftheiropticalandelectronicproper-tie
ingoftheiropticalandelectronicproper-tiesbyselectivelychangingthearomaticsubstituents,-conjugatedsegments,andthealkylsidechains.AnimportantfactorknowntolimitthePCEofDPP-basedsolarcellsisthenanostructureofthephotoactivelayer.iswell-establishedthatcharacteristicsofthephotoactivelayermorphologysuchasthedegreeofphaseseparation,thepresenceofpercolatingpathwaystowardtheelectrodesforelectronsandholes,thedonor(oracceptor)-richdomainsizes,andthedegreeofcrystallizationofthedonorpolymer,etc.,playacrucialroleNovember24,2017February2,2018February2,2018www.acsaem.orgCiteThis:ACSAppl.EnergyMater.2018,1,725©2018AmericanChemicalSocietyACSAppl.EnergyMater.2018,1,725indeterminingthenaldeviceeThemorphologyofthephotoactivelayer,inturn,iscriticallydependentonthedeviceprocessingorpostprocessingconditions.Solutionpro-cessingprovidesanelegantwaytofabricateabulkheterojunction(BHJ)typeofmorphologyforthephotoactivelayer.donor(D)andacceptor(A)componentsaredissolvedinavolatilesolventandspincoatedonarapidlyspinningsubstrate.Asthesolventevaporates,thetwocomponentsphaseseparateintodonor-richandacceptor-richdomains.Thedegreetowhichphaseseparationoccursdependsonavarietyoffactors,suchastherateofevaporation,thesolubilityoftheDandAcompo-nents,theDAmixingratio,andthetypeofsolventsused.Thus,foragivenDAcombination,thenumberofwaysinwhichadevicecanbefabricatedisextremelylarge,resultinginanenorm
ousoptimizationspace.Trial-and-error-bas
ousoptimizationspace.Trial-and-error-basedexper-imentalapproachescostalotoftimeandeort,hinderingtechnologicalprogress.Therefore,itisnecessarythatarationaldesignstrategytofabricateBHJdeviceswithwell-balancedmorphologiesisdeveloped.Toachievethisgoal,werstneedaclearunderstandingofhowphaseseparationleadstothefor-mationofthephotoactivelayernanostructure.VisualizingmorphologyevolutionofbulkheterojunctionsforOPVcellsinrealtimeischallengingbecauseoftherequiredtemporalandspatialresolution.Experimentaltechniquesbasedonlightscatteringareusuallylimitedbytheirspatialresolu-Inadditiontoopticalstudies,insituX-rayscat-teringanddiractionmeasurementshavealsobeenusedtoinvestigatethekineticsofmorphologyformationduringdrying,coveringsmallertolongerlengthscales.However,theX-raysignalisaveragedoveralargeareaandneedsfurtheranalysiswhenconvertingfromreciprocaltorealspace.SomestudieshaveuseddirectimagingtechniquestotracktheonsetofphaseseparationastheblendlmthinsovertimeduringspinInordertoobtainclearimages,thephaseseparatingcomponentsneedtohavesucientcontrast,whichlimitstheapplicabilityofsuchtechniques.Moreover,theearlylengthscalesassociatedwithphaseseparationaretoosmalltobetrackedwithopticalimagingmethods.Computersimulationscanaidexperimentstoovercometheselimitationsandhelpelucidatetheroleofprocessingcon-ditionsindeterminingthephotoactivelayermorphologyand,ultimately,thedeviceecienc
y.Theyfurtherenableustovisu-alizemorphol
y.Theyfurtherenableustovisu-alizemorphologyevolutioninthreedimensions,whichiscur-rentlybeyondexperimentalcapabilities.Theabilitytoperformautomatedhigh-throughputcomputationalanalysisisalsoexpectedtomakeOPVdevicemanufacturingcheaperandmuchmorecient.Duetothehighspatialresolutionrequiredtostudyphaseseparation,continuum-basedsimulationapproachesarethemostpracticaltouse.PhaseeldmethodsbasedonsolvingtheCahnCookequationsarequiteversatileintheirapplicabilityandcaneasilybeusedtorepresentcomplexmor-phologies.SomeprogresshasalreadybeenmadeusingthisHowever,thereportedsimulationshaveeithermadeuseofmodelparametersorhavebeenrestrictedtoa2Ddomain.SuchmorphologiesthereforecannotbedirectlycomparedwithrealisticOPVlms.Wepresentacomputationalframeworkbasedon3Dphaseeldsimulationsthatallowsustoaccesstheexperimentallengthandtimescalesassociatedwithphaseseparation.Thesimulatedmorphologiesarefurthervalidatedbycomparingtheirdominantfeatureswithcorrespondingimagingexperiments.Wefocusourattentiononmodelingphaseseparation,triggeredbysolventevaporationinaternaryblendconsistingofPDPP5T(diketopyrrolopyrrolequinquethiophene)andPC([6,6]-phenyl-C71butyricacidmethylester)dissolvedinchloro-form.Duetosolventremovalduringspincoatingofthephotoactivelayer,theblendenterstheunstableregionoftheternaryphasediagram.Inthisregion,thermaluctuationsinthecompositiongetampliedandresultintheformationofBM-richd
ropletsinaPDPP5T-richphase.Theseisolated
ropletsinaPDPP5T-richphase.TheseisolateddropletsstayuntilthelmdriesandareclearlyvisibleindrylmTEMimages.Insituexperimentshaverevealedthatforaternarysystemwithchloroformasthesolvent,liquidliquid(L-L)phaseseparationinitiatesaroundasolventcontentof80vol%.Polymeraggregationforsuchblendshappenslater,closetoasolventcontentof50vol%.Insuchascenario,thedominantlengthscaleinthedrylmismainlydeterminedbythePCrichdropletsthatformattheonsetofL-Lphaseseparation.Polymeraggregationhasbeenshowntoinuencephasesep-arationinblendswithcosolventssuchasHowever,simulationswithcosolventsareoutsidethescopeofthisworkwherewepresentamodelforaternarysystem.We,therefore,exclusivelyprobetheoriginandevolutionofthedominantlengthscaleduetoformationofPCBM-richdomains.Earlierworkbasedontheternaryphasediagramforasystemofadonor,anacceptor,andasolventareastartingpointforourKouijzeretal.havemadeimportantobservationsregardingthephaseseparationprocessusingtwo-dimensional(2D)phaseeldsimulationsonthePDPP5T:PCBMsystem.However,theirstrategytosimulateaneective2Dtopviewbyremovingsolventuniformlyfromtheentiresimulationdomainerssubstantiallyfromtheactuallmthinningprocess.Itisalsodicult,ifnotimpossible,toimplementsubstrateorairsurfaceinteractionsinthefollowedapproach.Also,verticalcation,ifpresent,wouldnotberevealed.Inthiswork,wepresentresultsobtainedusingarealisticdescriptionofthesolventevaporationprocesswhere
wemakeuseofanite-element-basedapproachto
wemakeuseofanite-element-basedapproachtomodelthegoverningCook(CHC)equationsinthreedimensionsThehomogeneousfreeenergyoftheternarymixtureisdescribedusingtheFloryHugginsformulation,whiletheinterfacialenergyisobtainedusingasquare-gradientapprox-AsshowninFigure1,thekineticinputparametersforoursimulationsareobtainedfrominsitulaserinterferencewhereasthethermodynamicparametersarebasedonsurfaceenergydata.Solventisremovedfromthetopsur-faceataratethatisconsistentwithexperimentalspinningspeeds.Oursimulationsshowthatdependingontherateofevaporation,phaseseparationinitiateseitherinthetoplayersoruniformlyacrossthethicknessofthedryinglm.UsingfastFouriertrans-form(FFT)-basedautocorrelationfunction(ACF)methods,weareabletodeterminetheaveragesizeofPCBMdomainsinoursimulatedmorphologies.Weaccuratelyreproducethescal-inglawbetweenthedominantlengthscaleandthenormalizedevaporation,ordryingrate,reportedpreviouslyfromexperi-Usinglinearstabilityanalysis,weestablishthatuctuationsareresponsibleforsettingtheearlystagelengthscalesofphaseseparationasthesystemcrossesthespinodalboundary.2.DISCUSSIONANDRESULTS2.1.TernaryPhaseFieldModel.Oursimulationsfocusonaternarysystemconsistingofanelectrondonor(thecon-jugatedpolymerPDPP5T),anelectronacceptor(thefullerenederivativePCBM),andasolvent(chloroform).Weassumethatthesystemisincompressible.ThevolumefractionsofeachACSAppliedEnergyMaterialsACSAppl.Ene
rgyMater.2018,1,725ofthecomponentsateve
rgyMater.2018,1,725ofthecomponentsateveryposition)inthesystemaretheorderparameters(ofpolymer),(offullerene),and(ofsolvent),respectively,andsatisfy=1.Hence,weonlyneedtokeeptrackoftwoindependentorderparameters,e.g.,,andput.Wenowhavetospecifyfortheternarysystem.Initsbasicform,consistsofanintegraloverthefreeenergydensityofmixing,,andtheinterfacialfreeenergydensity,=+FfIV[(,)(,)]dpfpf,alsoknownasthehomogeneousfreeenergydensity,iscon-structedusingalattice-basedapproachpioneeredbyFloryandwidelyusedforpolymermixtures:=+++++fVNNN(,,)ln()ln()ln()pfspfpfpspsfsfsisthegasconstant,isthetemperature,theeectivedegreeofpolymerization,withbeingthemolarvolumeofcomponent),andistheFlorybinaryinteractionparameterbetweencomponents.Therstthreetermsineq2describetheentropicandthelastthreetermstheenthalpiccontributionstothefreeenergydensityofmixing.TheFloryHugginsinteractionparametershavebeenestimatedbyanapproachpreviouslyusedbyMoonsetal.Wemakeuseofthevalues(seeTable1)asgiveninliter-areestimatedbasedonthemolarvolumesofthepolymerandfullerenewithrespecttothesolvent.Theinter-facialenergydensityisdescribedusingasquare-gradient=I(,)ipfInthiswork,wesettheinterfacialparametersThereislittleexperimentalinformationaboutinterfacesbetweenPDPP5TandPCBM.Wethereforetakethevalue=10whichiscommonlyusedfororganicsystems.nedtheorderparametersandthefreeenergyofthesystem,wec
annowsetupthegoverningequationsforthetwo
annowsetupthegoverningequationsforthetwoindepen-,whiletheisknownthroughtheincompressibilityassumption.Masstransportisdrivenbygra-dientsinchemicalpotentialsofthepolymerandfullerenecom-ponents.Thechemicalpotentialsforthepolymerandfullerenearedenedas.UsingFickslawfordiandthecontinuityequation,=0for,wegetthefollowingCHCequations:+htz(,)+htz(,)Intheseequations,)linksthemobilityofacomponenttoits(self-)di,withbeingthefreeenergydensityofanidealsolutionwherethehavebeenputequaltozero.Thesecondterm(advectionterm)attheleft-handsidesineqs3accountsforthechangeinheightTable1.FloryHugginsInteractionParametersandDegreesofPolymerizationCalculatedforthePDPP5T:PCSystem87511.00.10.9WenotethatKouijzeretal.tobearound0.4butreportresultsusing=0.1,inwhichcasetheentropiccontributionisnotconsidered(seeeq7inref).Forafaircomparison,wealsouse=0.1inthiswork.Wetested=0.4andfoundthatthisdoesnotaecttheconclusionsfromoursimulations.Figure1.Summaryofexperimentalandcomputationaltechniquesusedinthiswork.(a)Schematicillustrationofaninsitulaserinterferencesetupusedtodeterminetherateofchangeoflmheightasthelmthinsovertime.ThisratedeterminestheBiotnumber,whichisacrucialinputparameterforourphaseeldmodel.(b)ContactanglemeasurementsprovidingsurfaceenergydatausedtoestimatetheFloryHugginsinteractionparameters.Thisimage(usedasanexamplehere)hasbeenreproducedwithpermissionfromref.Copyright2018
TheRoyalSocietyofChemistry.(c)Simulation
TheRoyalSocietyofChemistry.(c)Simulationsnapshotshowingsolventremovalfromthetopofthelmasimplementedinthephaseeldmodel,resultinginareductionoftheheightofthelm.Evaporation-inducedphaseseparationleadstoformationofPCBM-richdropletssuspendedinthePDPP5Tmatrix.ThecolorscaledepictsthePCBMvolumefraction,withdeepredrepresentingthehighestconcentration.Theothercomponentsarerenderedtransparentforclarity.ACSAppliedEnergyMaterialsACSAppl.EnergyMater.2018,1,725(thickness)ofthelmassolventevaporatesfromthetopsurface.Thefraction)equalszeroatthebottomsurface=0)andoneatthetopsurface()),with)beingtheheightofthelmattime.Therateofchangeofheightis.Thelasttermsontheright-handsidesofeqs3aretheLangevinforceterms,whicharerelatedtothemobilitiesofthecomponentsbythedissipationtheorem.WefollowtheimplementationoftherandomLangevinforcesbyShenetal.inthecaseofspaceandtimediscretization.Theserandomforcesareknowntoplayanimportantroleintheearlystagesofspinodaldecomposition.2.2.ModelingSolventEvaporationUsinginSituLaserInterferenceData.Intheexperiments,aslightlydefocusedlaserbeamisincidentonaspinningsubstrateduringspincoating.Thereectedsignaliscollectedbyaphotodiodepositionedataspecularangle(seeFigure1a).Theoscillatingspecularsignalisduetotheinterferencebetweenthereectionsfromthetopandbottomsurfaceofthelm.Asthelmheightdecreasesduetosolventevaporation,itsthicknesssatisesconditionsforcon-structiv
eanddestructiveinterferencerepeatedly.Th
eanddestructiveinterferencerepeatedly.Thenalthick-ness()ofthedrylayerismeasuredindependentlyusingalometer.Thethicknessofthelmcanthenbeback-calculated,thusprovidingtherateofdecreaseofdasshowninFigure2Weassumethatsolventistheonlycomponentlostfromthelm.Inourmodel,itisremovedfromthetopsurfaceofthelmatauniformrateasshowninFigure1c.Thisleadstoadecreaseofthelmheightovertime.Insitulaserinterferenceexperimentsmeasureaninitialrapiddecreaseinlmheightthatisattributedtoradiallyoutwardowonthespinningsub-lmthinningoccursduetoevaporationwithalinearrateofchangeofheight.Ourassumptionofacon-stantsolventevaporationrateisthereforevalid.Assolventisremovedfromthetoplayer,thelayerbecomesenrichedinpolymerandfullerenecomponents.Solventfromthebulkofthelmwillthereforemovetothetoplayertoreplenishthesolventlostduetoevaporation.Theeectivenessofthisprocessdependsontherateofdiusionofthesolventtowardthetoplayercomparedtotherateofsolventremoval.Toquantifythiscom-petition,weintroducethemassBiotnumber,nedasd/dwheredistherateofchangeoflmheight,usivityofthesolvent,andacharacteristiclength,whichwetaketobetheinitialheightofthe=0).AsshowninFigure2a,weestimatedbydeterminingtheslopeoftheexperimentaldryingcurveinthelinearregime.Westartoursimulationswhenthesolventcontentis90vol%whichliesoutsidethespinodalregionoftheternaryphasediagramasshownFigure3.Thedryingcurvesindicatethatthelmthicknessiscloseto10
00nmatthispoint.Using=1000nmandforchloro
00nmatthispoint.Using=1000nmandforchloroform,wecalculatetheBiotnumbersfordierentdryingspeeds;seeTable2.TherelativeusivitiesofPDPP5TandPCBMaresetto0.001and=0.005respectively.Furtherdetailscanbefoundinsection1oftheSupportingInformation(SI)ThegoverningCHCequationsaresolvedusingaapproach.Technicaldetailsregardingthenumericalmethodscanbefoundinsection2ofthe.Wehaveperformed3Dand,forcomparison,also2Dsimulations;seesection3ofthe.Asmentionedabove,thestartingsolventfractionis=0.90,xesthesumofpolymerandfullerenefractionsduetotheincompressibilityassumption.Experimentsindicatethatafullereneweightratioof1:2(w/w)leadstodevicesFigure2.(a)(Top)DryingcurveofaPDPP5T:PClmforaspinningspeedof6000rpm.Theinitialdecreaseinheightisduetoradialowoftheuidonthespinningsubstrate.Thereafter,lmthinningoccursprimarilyduetoevaporation.Therateofchangeofheightdobtainedfromalineart.Thestartingheight=0)inoursimulationboxis1000nm.(Bottom)Laserinterferencesignalsmeasuredasthethinsovertime.Knowingthelmthickness,theheightofthelmatanyinstantisback-calculated,resultinginthedryingcurveforagivenevaporationrate.(b)Transmissionelectronmicroscopy(TEM)imagesofdrylmsobtainedusingaspinningspeedof6000rpm(top)and500rpm(bottom).PCBMregionsappeardarkerandformdroplet-likestructuresembeddedinthePDPP5Tmatrix.(c)Chemicalstructureofthepolymerandfullerenederivativeused.ACSAppliedEnergyMaterialsACSAppl.EnergyMater.20