Kinetic Modeling of the Electric Field Dependent Exciton Quenching at the Donor − Acceptor Interface - Benatto et al. - 2021 - Unknown

《Kinetic Modeling of the Electric Field Dependent Exciton Quenching at the Donor − Acceptor Interface - Benatto et al. - 2021 - Unknown》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

pubs.acs.org/JPCCArticleKineticModelingoftheElectricFieldDependentExcitonQuenchingattheDonor−AcceptorInterfaceL.Benatto,*C.A.M.Moraes,M.deJesusBassi,L.Wouk,L.S.Roman,andM.Koehler*CiteThis:J.Phys.Chem.C2021,125,4436−4448ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Inthiswork,theelectricfielddependenceoftheexcitonquenchingefficiencyatthedonor/acceptor(D/A)heterojunctionwasstudied.TheconcentrationofsingletexcitonsandchargetransferstatesattheD/AinterfacewasmodeledbyasystemofcoupleddifferentialequationswithtransitionratesobtainedfromMarcustheory.Weappliedthenthemodeltodeterminetheangulardependence(expressedbyaparameter,θ)ofthelocalexcitonquenchinginducedbytheorientationofthedissociationprocessrelativetothedirectionoftheelectricfield(F).WefoundthattheexcitondiffusiontotheD/Aheterojunctionisnothomogeneousforeveryvalueofθ,butitishighertowardregionswherethedissociationrateisgreater.Theconsequenceofthiseffectisthatonlysmallvaluesofthisparameterwilleffectivelycontributetotheaveragequenchingefficiency.ThereisthenagradualincreaseofthequenchingefficiencywithF,afactthatwasverifiedexperimentally.Followingthisprinciple,wewereabletofittheexperimentaldatameasureinabulkheterojunctiondevice.Inaddition,westudiedthefielddependenceofthePLquenchinginabilayerdevicethatpresentsaveryusefulstructuretotestthetheory.Wefoundthatthemodelexplainsthefield-inducedquenchingefficiencynotonlywhenFhasafavorableorientationthatenhancesthechargetransferbutalsowhenFtendstoinhibitthisprocess.Inaddition,ouranalysismightgivesomehintsonthedegreeofmixingbetweenthedonorandacceptorintheactivelayerinthiskindofdevicearchitecture.WebelievethatthemodelmayclarifytheprocessesthatinfluencethedynamicsofexcitondissociationatD/Ainterfaces.Itisalsousefultoexploretheeffectsoftemperature,energydisorder,sitedisorder,andexcitonbindingenergyinthephotovoltaiceffectoforganicsolarcells.Overall,itopensthepossibilitytodeeplyunderstandtheeffectofanelectricfieldinnewD/Aheterojunctionswithlowdrivingforceandefficientexcitondissociation.DownloadedviaUNIVOFNEWMEXICOonMay16,2021at07:05:33(UTC).1.INTRODUCTIONphysicalprocessesthatallowelectronsorholestoescapefromSeehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.theCoulombpotentialwell(afterasuccessionofhoppingEfficientorganicsolarcells(OSCs)compromiseabulktransitionsbetweenlocalizedstates)andgeneratefreechargeheterojunction(BHJ)formedbyelectrondonor(D)and5−7carriers.Sincemanyaspectsofthoseprocessesarestillacceptor(A)componentssothatexcitonscreatedeitherattheunclear,excitonandchargeseparationdynamicsattheD/ADphaseorAphasecanefficientlyquenchattheD/A1,2interfacehasbeenthesubjectofintensestudiesusinginterface.Forasystemwithoptimizedchargetransportand8−13theoreticalandexperimentalapproaches.extraction,theOSCefficiencyisessentiallydeterminedbythe3Despitethoseintenseaffords,theroleplayedbytheelectricdissociationofthoseexcitonsattheheterojunction.Forthefield(F)toassistchargecarriergenerationattheBHJinsingledonorexcitation,thisdissociationoccursviaelectrontransfer14,15junctionOSCsremainselusive.DependingonthetoA.Ontheotherhand,aftertheexcitationoftheacceptor,theexcitondissociationoccursviaholetransfertoD.Inbothcases,itisbelievedthattheexcitonquenchingattheD/AReceived:December25,2020interfaceinvolvesachargetransfer(CT)stateformedbyaRevised:February10,2021Coulombicallyboundhole(atthedonor)andanelectron(atPublished:February23,20214theacceptor)thatmustbedissociatedtogeneratefreecharges.Hence,adeepunderstandingofthephotovoltaiceffectintheBHJinvolvesthedetaileddescriptionofthe©2021AmericanChemicalSocietyhttps://dx.doi.org/10.1021/acs.jpcc.0c114584436J.Phys.Chem.C2021,125,4436−4448

1TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure1.(a)Singleactivelayerbulkheterojunctionorganicsolarcell.b)Zoom-inactivelayerandasimplifiedschemeofexcitondissociationintwodifferentregionsoftheD/Ainterface.ThethetaangledefinestheorientationofmaterialsAandDintheinterfaceregioninrelationtotheelectricfield.combinationofDandAmaterialsandtheBHJmorphology,OtherkineticmodelswereproposedtodescribethechargephotogenerationcaneitherincreaseorbeindependentdynamicsoftheexcitondissociationattheD/Ahetero-16,17oftheF.Usually,whentheenergyoffsetbetweenDandAjunction.Inref36,amodelforthechargeseparationprocessesfrontierorbitals(drivingforce)ishigh,theefficiencyofexcitoninthosesystemswasproposed.Inthistheory,theformationofquenchingisnear100%withoutanyelectricfieldassistance.asingletexciton(S1)inoneoftheBHJphaseswasconsideredNevertheless,thisdependenceisextremelycomplexinlowasaprimaryevent.Byassumingallpossiblesecondary18,19drivingforceblends(LDFBs).ThosekindofBHJprocessesfortheexcitedcharge,thetime-dependentconstitutestheactivelayerofefficientOSCssincetheytendpopulationsofsingletexcitons(S1)andchargetransferstates20,21toreducetheopen-circuitvoltage(VOC)losses.Insome(CT)attheD/AinterfacewerequantifiedusingcoupledLDFBs,excitonquenchingbecomesstronglydependentonthedifferentialequations.Thetransitionratesforthoseprocesseselectricfield.ThiseffectwasobservedrecentlyforaD/AblendwereobtainedfromMarcus/Hushtheory.Analyticalex-containingthePffBT4T-2ODdonorcopolymerandthepressionswerethenderivedfortheexcitonquenching22PC71BMfullereneacceptor(FA).CombiningUV−visproducedbyselectiveexcitationofthedonor(QD)oracceptorabsorptionandultravioletphotoemissionspectroscopy(QA)underthesteady-stateapproximation.(UPS)measurements,thedrivingforceforelectrontransferThemodelwasabletoanticipatetheexcitonquenchinginthisblendwasfoundtobearound0.35eV.efficiencyoftwoD/AsystemsusingthepolymerPTB7-ThasHowever,otherLDFBshaddifferentdependenciesofthethedonorandthefullerenePC71BMorthenonfullerenephotovoltaiceffectonF.Forinstance,studyingdifferentD/A23derivativeITICastheacceptor.Uponthepolymerexcitation,blends,Niuetal.observedefficientexcitondissociationwiththeefficiencyofexcitonquenchingwas100%forbothblends,nearzerodrivingforce.Theysuggestedthatthiseffectwaswhichagreeswithexperiments.Thesamequenchingresultwasrelatedtolowervaluesofthebindingenergy(Eb)ofexcitonscalculatedfortheITICexcitationthatwasexperimentallyinnonfullereneacceptors(NFAs)inducedbystrongintra-observedaswell.Inaddition,themodelpredictedaquenchingmolecularandintermoleculardelocalization.Quitesurpris-efficiencyofonly30%upontheselectiveexcitationoftheingly,theyalsodemonstratedthattheexcitondissociationPC71BM.ThisvaluewasconfirmedbydirectPLmeasure-efficiencydidnotcorrelatewiththemagnitudeofthechargements.Fromthediscussionabove,itisthenexpectedthatthetransferratebetweenthedonorandacceptor.Otherstudiesalsofurtherhighlightedtheimportanceofexcitondelocaliza-QAofthePTB7-Th/PC71BMblendmighthaveadependenceontheF.Indeed,thiseffectwasobservedrecentlyinref34,tiontoallowefficientchargeseparationwithminimaldriving24−26whereitwasfoundthatquenchingefficiencyupontheforce.fullereneexcitationincreaseswithincreasingvaluesoftheOvertheyears,theanalysisoftheelectricfieldinfluenceonthephotoluminescence(PL)quenchinginorganicsemi-electricfield.conductorshasbeenapowerfultooltostudythechargeThosefindingsmotivatedustoextendthepreviousmodelingenerationprocessesinthosematerials.27−29Comparingtheref36toincludetheinfluenceoftheelectricfieldonthePLspectraofpristinematerials(DorA)withthePLspectraofkineticsofchargeseparationattheD/Ainterface.WealsoD/Ablends,theradiativepartofexcitonrecombinationcanberefinedthemodelbyconsideringtheeffectsofenergetic,investigated.30Todescribethisprocess,someworkshavepositional,andelectroniccouplingdisordersonthoseappliedtheOnsager−Braunmodel,31,32whichwasabletoprocesses.TheresultingtheorywasthenappliedtodescribereasonablyfittheelectricfielddependenceofthePLthevariationoftheexcitonquenchingwiththeFinthePTB7-quenchingmeasuredinsomeBHJactivelayers.33AnotherTh/PC71BMblend.Inaddition,westudiedthefieldapproachappliedaone-dimensionalhoppingapproximationdependenceofthePLquenchinginabilayerdevice(using37withdisordertomodelthefield-dependentluminescenceC70astheacceptor)thatpresentsaveryusefulstructureto34testthetheory.TheseanalysesprovidethennewinsightsonquenchinginOSCsystems.TheuseoftheMonteCarlomethodinthismodelshowedthatenergeticdisorderenhanceshowtooptimizethemorphologyoftheD/AstructureinorderexcitondissociationatlowelectricfieldsanddecreasesitattoenhanceQAandQDforthebuilt-inelectricfieldofaspecific35highfields.device.4437https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448

2TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticle2.COMPUTATIONALMETHODSwherethek’sineqs2and3aretheratesthatcharacterizesallpossibleelectronictransitionsaftertheformationofthesingletFigure1aillustratestheproblemunderconsideration.Itshowsstateeitherintheacceptor(eq2)orinthedonor(eq3).InaschematicrepresentationoftheOSCinaBHJstructure.Table1,wedetailallthoseratesineqs2and3withtheBetweentheactivelayerandtheanodeistheelectronblocklayer(EBL),andbetweentheactivelayerandcathodeistheTable1.RatesforHoleandElectronDynamicsholeblocklayer(HBL)(thoselayersarerepresentedinFigure1justforthesakeofcompletenessandarenotdiscussedinthisratetransitiondescriptionwork).Figure1bpresentstwopossiblearbitrarypathsforkA,SRLUMOA→recombinationrateforthesingletexcitonsintheexcitondiffusiontotheD/AinterfaceandtheconsequentHOMOAacceptor(S1,A)dissociation.Thespatialorientationoftheelectron−holepairkHTHOMOA→holetransferratetocreateaCTstaterelativetotheFproducedbythebuilt-involtageishighlighted.HOMODHerewegiveemphasisonθ,theanglethatdefinesthekHBHOMOD→holebackratetorecreateS1,AHOMOAorientationoftheD/Ainterfaceisrelativetotheelectricfield.kHSHOMOD(1)holejumpfromthenearestdonorchainadjacenttotheFormally,θisdefinedastheanglebetweentheFandthe→acceptor(chain1)tothenext-to-thenearestdonorvectornormaltothesurfaceformedbytheD/AinterfaceHOMOD(2)chain(chain2)adjacenttotheacceptor(orientedfromAtotheDphase)ateachpoint.ItessentiallykD,SRLUMOD→recombinationrateofsingletexcitonsinthedonorHOMOD(S1,D)determinesthepointattheheterojunctionwheretheexcitonskETLUMOD→electrontransferratetocreateaCTstatereachtheinterfacebetweenthetwomaterialsanddissociates.LUMOASeethatattheD/Ainterface,exciton-1andexciton-2presentkEBLUMOA→theelectronbackratetorecreateS1,Dopposingalignmentswiththebuilt-inelectricfield,sothatθ=LUMOD0°andθ=180°(respectively)forthoseexcitations.OnekESLUMOA(1)→electronjumpfromthenearestacceptormoleculeingredientofthepresentmodelistoinvestigatehowθLUMOA(2)adjacenttothedonor(molecule1)tothenext-to-thenearestacceptormolecule(molecule2)adjacenttomodulatesthevariationoftheexcitonquenchingatD/Athedonorinterface.Indeed,θrepresentstheangularconstrainsonthefield-inducedexcitonquenchingintroducedbythemorphol-ogyoftheD/AinterfacerelativetotheorientationoftheF.correspondingelectronictransitionsandthefrontiermolecularWiththisaim,weneglectedthecomplexityandthespecificorbitalsinvolved(HOMO,highestoccupiedmolecularorbital,detailsoftheheterojunctiongeometrytoassumethatθcanandLUMO,lowestunoccupiedmolecularorbitals).haveanyvaluebetween0°and180°withthesameprobability.kA,SRandkD,SRineqs2and3,respectively,aretheinverseofSomehintsabouttheunderlyingmeaningofθanditsrelationsingletexcitonrecombinationlifetimeandcanbeobtainedwiththeD/Amorphologywillbeobtainedafterthedirectfromexperimentaldataintheliterature.Here,theywere3839applicationofthemodeltofitexperimentaldata(seeSectionsassumedtobe600psforPC71BMand93psforPTB7-Th.3.1and3.2).TheotherratesinTable1areobtainedusingtheMarcus/ThepresentdescriptiontocalculatetheexcitonquenchingisHushequation:basedonasimpleone-electronpictureandassumesthatthe22ÄÅŇÉÑÑ4πβÅÅ−ΔGÑÑexcitonconcentrationinthepureacceptormaterialwask=expÅÅÑÑsubmittedtothesameilluminationconditionsoftheD/Ah4πλkTBÅÅÅÅÇkTBÑÑÑÑÖ(4)blend.Underthoseassumptions,theexcitonquenchingiswherekB,T,λ,andβaretheBoltzmannconstant,temperature,definedasreorganizationenergy,andelectroniccoupling(transfer[]Sintegral),respectively.TheactivationenergyforchargeQ=−11,A‡40Atransfer,ΔG,isrelatedtoλby[′S1,A](1)2‡()λ+ΔGΔG=where[S1,A]isthesingletstateconcentrationintheacceptor4λ(5)materialneartheD/Ainterface,and[S1,A′]isthesingletstatewhereΔGistheGibbsfreeenergy,theenergydifferenceconcentrationintheacceptormaterialintheabsenceofthebetweeninitialandfinalstates,commonlynamedasdrivingdonor.Notefromeq1thatifthedonorisnotefficienttoforce.WhenΔG<0,theprocessisthermodynamicallydissociatetheexcitons,then[S1,A′]≈[S1,A]andQA≈0.Thefavorable.Allthedrivingforcesinvolvedintheholeandsolutionofthemodel’sdifferentialequationsinsteady-state36electrontransitionsforthezeroelectricfieldarepresentedinapproximationgivesthequenchingefficiencyfortheacceptorTable2.Thereorganizationenergiesinthistableareassumedandthedonorexcitations(furtherdetailscanbefoundinrefindependentoftheF,asdemonstratedinref8.Inaddition,we36):considerthatthelocalexcited-stateenergy(ELE)andthekkkkA,SR()HS++HBHRchargetransferenergy(ECT)donotvarywiththeelectricfieldQ=−1aswell.AlthoughthoseenergieshaveasmalldependenceonA()kkkkkkA,SR++HT(HSHB+HR)−HTHBktheelectricfield,41,42thedisorderednatureoftheBHJhides(2)thiseffect.SincetheelectronicstatesinthosesystemstendtoberandomlyorientedrelativetotheF,theenergyvariationsandassociatedtothisdisordercanbedescribedbyaGaussian34kkkk()++distribution(moredetailswillbepresentedbelow).D,SRESEBERQ=−1Here,itisimportanttocallattentionforanimportantD()kk++(kkkk+)−kD,SRETESEBERETEBlimitationderivedfromtheuseofeq4.TheMarcusapproach(3)isderivedconsideringtheclassicalharmonicoscillation4438https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448

3TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleTable2.DrivingForcesforHoleandElectronDynamicsawithouttheInfluenceofanElectricFielddrivingforceparameterdefinitionholetransferΔGHT(eV)ECT−ELE,AholebackΔGHB(eV)−ΔGHTaholerecombinationΔGHR(eV)−(ECT−λh)holeseparationΔGHS(eV)Eb,A+ΔGHTelectrontransferΔGET(eV)ECT−ELE,DelectronbackΔGEB(eV)−ΔGETaelectronrecombinationΔGER(eV)−(ECT−λe)electronseparationΔGES(eV)Eb,D+ΔGETaλhandλearethereorganizationenergiesforholetransferandelectrontransfer(theoreticaldatainref36).assumption.Underthisapproximation,themoleculeisfirstexcitedtotheFranck−Condonelectronicstatesthatarecharacterizedbynonzerovibrationalpopulationswithlow41frequencies.Consequently,thisapproachignoresthetunnelingeffectsthatcanassisttheelectrontransfer.However,itisbelievedthattheelectronicexcitationofamoleculepopulatesvibrationallyhotstateswithhighfrequenciesFigure2.Simplifiedholedynamicsdiagrambetweenthematerialsof43comparedtotheaveragethermalenergy.DespitethistheD/AinterfaceandthevaluesofφHT,φHB,φHS,andφHRfor(a)θsimplification,ourapproachisalreadysoundenoughto=0°and(b)θ=180°.Asimplifiedelectrondynamicsdiagramexplainexperimentaldatameasuredindifferentsystems(asitbetweenthematerialsoftheD/AinterfaceandthevaluesofφET,φEB,willbedemonstratedbelow).φES,andφERfor(c)θ=0°and(d)θ=180°.ThedashedlinesThedependenceofthedrivingforcewiththeelectricfieldrepresentelectronicstatesHOMOandLUMO.Thefilledcirclecanbewrittenasfollows:representstheelectron,andtheemptycirclerepresentsthehole.ΔGGe=Δ0e−Fffr(6)distribution.Inaddition,weconsiderthattheenergeticwhereΔG0isthedrivingforcewithouttheelectricfield,eisdisordercanshiftthevaluesofELE,AandECT.Thoseshiftstheelementarycharge,risthespatialseparationbetweenaretakenatrandomfromaGaussiandistributioncenteredatadjacentsites,andFeffistheeffectiveelectricfieldcalculatedzeroandstandarddeviation,σ.viaFeff(F,φ)=Fcos(φ),whereφistheanglebetweentheFThedisordercanalsochangetherelativeorientationofdirectionandthedirectionofcarrierjumpoverthedistancer.adjacentmolecules,whichcaninducevariationsinelectronicInFigure2,wepresentedasimplifiedchargetransferdynamicscouplingbetweenthem.Thiseffectismodeledbymultiplyingdiagram,withalltheratesconsideredinourmodel.Thisfigureβ(calculatedforidealdimersintheface-onconfigurationalsoshowsthevaluesofφforthetwoextremevaluesofθ(0°(theoreticaldataisinref36))bythefactorcos(ω).ωisaand180°)fortheholeandtheelectrondynamics.Thesetworandomanglebetween0°and90°sothatω=0°wouldvaluesofθarerelatedtotheleftandrightinterfacesforexcitoncorrespondtoadimerintheface-onconfiguration,whereasωdissociationexemplifiedinFigure1.Forexample,ifφ=0°for=90°wouldcorrespondtothedimerintheedge-onholetransferandholeseparationprocesses,thenφ=180°forconfiguration.Thedrasticdecreaseinelectroniccouplingforholebackandholerecombinationprocesses.thedimerintheedge-onconfigurationiswellknownintheInthemodelfromref36,thedrivingforceforholeliterature42,44andcanbeseenclearlyinFigureS1andTable(electron)separationdependsonEbintheacceptor(donor)S2.Sincethedependenceofβontheelectricfieldissmaller(seeTable2).Therefore,itisalsonecessarytoconsiderthecomparedtotheshiftsproducedbyvariationsassociatedtothevariationofEbwiththeelectricfieldasfollows:orientationofthemolecules,hereweconsideredthatβisfieldEEebb=−,0Fcos()αd(7)independent.Indeed,weobservethatβisslightlyaffectedbytheelectricfieldinFigureS2andTableS3.whereEb,0istheexcitonbindingenergyintheabsenceofanAdditionally,weassumethatαineq7willbearandomelectricfield,disthedistancebetweentheelectronandhole,angleobtainedfromauniformdistribution,i.e.,allorientationsandαistheanglebetweentheFandthevectorthatforthecreatedelectron−holepairsareequallypossible.determinestheorientationoftheelectron−holepair(whichFinally,wewillconsiderthatthesecondchargejumpafterthehasthesameorientationofthedipolemomentvectorCTformation(associatedtothechargeseparationprocess)associatedtothepair).doesnotnecessarilyfollowthesamedirectionofthefirstjumpWefurtherconsiderthatpositionalandenergeticdisorders(associatedtothechargetransferprocess).Hence,weassumecaninducevariationsinthecharacteristicenergiesofthethatφHSisarandomanglebetweenφHT−ξandφHT+ξ,systemwithconsequentchangesinthequenchingefficiencies.whereξisthemaximumangulardeviationofthesecondjumpInthesequence,wedetailtheparametersthatareaffectedbyrelativetothefirstjump.Adescriptionoftheanglesinvolveddisordereffects.inthequenchingsimulationispresentedinTableS1withtheTosimulatesmallshiftsinthepositionofthestatesavailablerespectivedefinitionsandranges.forchargetransfer,thevalueofrineq6isdeterminedviar=Aftertheintroductionofdisorder,thequenchingefficiencyr0±δr,whereδrisrandomlychosenfromauniformwillbeafunctionoftheindividualparametersselectedforeach4439https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448

4TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlecreatedexciton.Theratesandquenchingefficienciesineqs2andrecombinationprocesses.Thosevariationsareinvertedand3arecalculatedbyassumingincreasingvaluesoftheFwhen90°<θ<180°.However,thebehaviorofkisessentiallyfrom0to2.0×108V/m.ForeachvalueofF,θisassumedtodeterminedbyrelativechangeof|ΔG|comparedtoλ.Whenvaryintheintervalfrom0°to180°.Theratesandquenching|ΔG|approachesλ,theactivationenergy(eq5)decreasesandefficienciesarethenobtainedafteraveraging104realizationsoftheratesincreasetotheirmaximumvalue.41ThisbehaviorwilltherandomparametersinTable3.definethevariationsofactivationenergiesinFigure4comparedtoΔG‡.Inthepresenceofanelectricfield,ΔG‡0Table3.ModelParametersCorrespondingtothethendecreasesforthetransferandbackprocesses(thea,b,c,d,e,f,grespective|ΔG|approachesλ),whereasitincreasesfortheTheoreticalQuenchingCurvesrecombinationandseparationprocesses(therespective|ΔG|valueordepartsfromλ)asθincreasesfrom0°to180°.Asaparameterdescriptionparameterdefinitionaconsequence,thekE(H)TandkE(H)BbecomehigherandkE(H)Sfirstlocalexcited-stateenergyoftheacceptorELE,A(eV)2.03aandkE(H)RbecomelowerthantherespectiveratesforF=0firstlocalexcited-stateenergyofthedonorELE,D(eV)1.92awhenθvariesfrom0°to180°.ThiseffectisconformedinchargetransferenergyECT(eV)1.63bFigure5whereweplotalltheratesasafunctionofθandtheenergeticdisorderparameterforELE,AandELE,DσLE(meV)30belectricfield.ThisfigurealsopresentsthequenchingenergeticdisorderparameterforECTσCT(meV)70aefficienciesobtainedfromeq2(holes)andeq3(electrons).reorganizationenergyforholetransfer(A→D),λh(eV)0.228back(D→A),andrecombination(D→A)Finally,astheintensityoftheelectricfieldincreases,thereorganizationenergyforholeseparation(D→D)λ(eV)0.240achangesinΔGandconsequentlyintheratesaregreater.h,sreorganizationenergyforelectrontransfer(D→λ(eV)0.239aFigure5a,calsoshowsthatthemagnitudesofkHT(kHR)areeA),back(A→D),andrecombination(A→D)muchhigher(lower)comparedtotheotherrates.Thus,QAisareorganizationenergyforelectronseparation(A→λe,s(eV)0.226mainlyinfluencedbythevariationsofkHBandkHS.ForA)instance,kbecomesfasterwiththeF,whilekisslowedcHSHBexcitonbindingenergyofacceptorEb,A(eV)1.0downbythefieldintherange0°<θ<90°.Hence,QisdAexcitonbindingenergyofdonorEb,D(eV)0.50enhancedinthisangularinterval.WiththeincreaseofkandeHBdielectricconstantofacceptorεA3.9thedecreaseofkwithθ,QbecomesextremelylowinthefHSAdielectricconstantofdonorεD4.0range90°<θ<180°(seeFigure5e).Forthoseangles,thedistancebetweenelectronandholede2/excitonquenchingattheacceptorcanbeeventotally4πεε0Ebspacialseparationbetweenadjacentsitesr(nm)0.50gsuppressedinthepresenceofstrongelectricfields.sitepositiondisorderδr(nm)0.10bTheelectrondynamicsdisplayedinFigure5b,d,ffollowsthemaximumdeviationangleofthesecondjumpinξ(degrees)30°samegeneraltrendsoftheholedynamicsdiscussedabove.Duerelationtothefirstjumptothesmallerexcitonbindingenergyinthedonor,theratekESaTheoreticaldatatakenfromapreviouswork.36bAtypicaldisorderissomeordersofmagnitudehighercomparedtotherespectiveparameterfororganicsemiconductorsinaccordancewithpreviousrateforholes(kHS).Asaresult,QD≈100%forthevariationof34,35c25,49works.Thetypicalvalueinaccordancewithpreviousworks.θfromzerotoalmost90°.Asθfurtherincreasesfrom90tod62eThetypicalvalueforthePTBfamilyofpolymers.Obtainedfrom180°,QDdecreasesconsiderablyespeciallyforhighmagnitudes68fcapacitance−voltagemeasurements.Adielectricconstantof4.0wasoftheelectricfield.14,48gusedinthecalculationsinaccordancewithotherworks.AItisreasonabletoassumethatallvaluesofθmightbe69,70typicalvalueofπ−πstackingdistancefororganicsemiconductors.presentwiththesameprobabilityinordinaryBHJactivelayersofOSCs.FromthisassumptionandtheresultsshowedinFigure5e,theelectricfieldmakestheaveragevalueofQAonly3.RESULTSANDDISCUSSIONSslightlyhigherthantherespectivevaluewithouttheelectric3.1.TheBulkHeterojunctionStructure.Thevaluesoffield.ThiseffectwillhappenbecausetheincreaseofQAfortheparametersassumedforthecalculationsdevelopedinthissmallvaluesofθispartiallycompensatedbythedecreaseofitsectionaresummarizedinTable3withthecorrespondingasobservedforhighervaluesoftheangle.Inaddition,Figurereferences.Wetriedtoassumevaluestypicalofhetero-5findicatesthattheelectricfieldwilltendtomaketheaveragejunctionsbasedonthePTBfamilyofpolymersasthedonorvalueofQDsignificantlylowerthanitsvaluewithouttheandthePCBMfamilyofmoleculesastheacceptor.Theseelectricfield.ThereasonisbecausetheFalmostdoesnotmaterialswereconsideredinrefs34,36andarealsoemployedchangethequenchingfortherange0°<θ<90°(thatremainsheretotestourmodel(seeSection3.2).Nevertheless,wecloseto100%)butsignificantlydropsQDfortheallotherbelievethatourconclusionsaregeneralenoughtoexplainvaluesofθ.However,manymeasurementsreportedinthesomebasicmechanismsoffield-dependentexcitondissociationliteratureclearlydemonstratethattheelectricfieldindeed22,34,46inagreatvarietyofD/Aheterojunctions.increasestheexcitonquenchingefficiency.Thebehaviorofeachrate,k,withθwillbedefinedbytheOnepossibleexplanationtothisinconsistencybetween45exponentialtermoftheMarcus/Hushequation(λ+ΔG).theoryandexperimentmaybeduetothefactthattheresultsAlltheratescalculatedhereareintheso-calledMarcusinFigure5donotconsiderthefluxofexcitonsthatdiffusestoinvertedregionsothat|ΔG|>λ.InFigure3,weplottheΔGtheD/Aheterojunction.Thisdiffusionmaynotbevaluesofalltheratesasafunctionofθandtheelectricfield.Ashomogeneousforeveryvalueofθ.Forinstance,localexpected,theΔGvaluesdonotdependonθwhenF=0,butimbalancesintheefficiencyofexcitondissociationmaycreatethechangesinΔGaregreaterastheFincreases.Intheintervalassociatedvariationsintheexcitonfluxamongdifferentpoints0°<θ<90°,thepotentialenergyvariationcreatedbytheFoftheD/Ainterface.Asaconsequence,determinedvaluesofθalwaysdecreasesΔGrelativetoΔG0forthetransferandcanbemoreimportantthanothervalueswhentheaverageseparationprocesses,whereasitincreasesthemforthebackexcitonquenchingefficiency(Q̅A(D))iscomputed.Letusthen4440https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448

5TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure3.Dependenceofdrivingforceswiththeelectricfieldandtheta.(a)Drivingforceforholetransferandback(ΔGHTandΔGHB).(b)Drivingforceforelectrontransferandback(ΔGETandΔGEB).(c)Drivingforceforholeseparationandnonradiativerecombination(ΔGHSandΔGHR).(d)Drivingforceforelectronseparationandnonradiativerecombination(ΔGESandΔGER).Figure4.Dependenceofactivationenergieswiththeelectricfieldandtheta.(a)Activationenergyforholetransferandback(ΔG‡andΔG‡).HTHB(b)Activationenergyforelectrontransferandback(ΔG‡andΔG‡).(c)ActivationenergyforholeseparationandnonradiativerecombinationETEB(ΔG‡andΔG‡).(d)Activationenergyforelectronseparationandnonradiativerecombination(ΔG‡andΔG‡).HSHRESERassumethattheexcitonfluxateachθ,J(θ),canbecoefficientsoftheorganicmaterialsusedinOSCs),thisapproximatedbyJ∝−gradn(θ),wheren(θ)isthelocalmechanismhasthepotentialtoexplaintheparadoxicalresultsdensityofexcitonsattheD/Ainterface.Hence,regionswithreportedinFigure5.poorexcitonquenchingwillhavelowergradientsofn(θ)intheTotestthishypothesis,wefirstidentifythevaluesofθthatvicinitiesoftheD/Ainterface.Theexcitonfluxtothisregionwouldproducehighergradientsofn.Thisprocedurewouldtendtobesmall.Ontheotherhand,regionswithhigherinvolvethesolutionofadiffusionequationinpolarcoordinatesexcitonquenchingwillhavestrongergradientsofn(θ)sothatwiththeappropriatedboundaryconditions.However,wetheytendtohaveahigherfluxofexcitons.ConsideringthatJisoptedtofollowasimplerapproach.WewillassumethatthenotlimitedbytherateatwhichnewexcitonsarecreatedhigherexcitonfluxtowardtheD/Ainterfacewillhappenatthe(whichisareasonableassumptionduetothehighabsorptionangleswherethetotalratethatdecreasesthelocalpopulation4441https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448

6TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure5.DependenceofMarcusratesandquenchingefficiencywiththeelectricfieldandtheta.(a)Holetransferandbackrates(kHTandkHB).(b)Electrontransferandbackrates(kETandkEB).(c)Holeseparationandnonradiativerecombinationrates(kHSandkHR).(d)Electronseparationandnonradiativerecombinationrates(kESandkER).(e)Excitonquenchingefficiencyforacceptorexcitation(QA)and(f)excitonquenchingefficiencyfordonorexcitation(QD).Figure6.Dependenceofaveragequenchingefficiencywiththeelectricfieldandexcitonbindingenergyfor(a)acceptorexcitationand(b)donorexcitation.ResultsforT=300K.ofCTexcitonsishigher.Theideaisthatthedeactivationofsimpleone-dimensionalexcitondiffusion).Hence,thepointstheCTexcitonatonedeterminedpointoftheheterojunctionwherethekQ,A(D)valuesarehigherdeterminethevaluesofθ(specifiedbyθ)pavesthewaytothearrivalofanewexcitontowherethereisanincreasedprobability,Pθ,A(D),offindinganthatpoint.ThiseffectwouldthenincreaseJ(θ).Therefore,weexciton.ThoseangleswillhaveastrongerweightontheconsiderkQ,A=kHS+kHR(kQ,D=kHS+kHR),whichisthetotalaveragequenchingsothatCTexcitondeactivationrateforacceptor(donor)excitation.kQ,A(D)isthenthesumoftheseparationandthenonradiative180°recombinationrates(intheSupportingInformation,weQ̅A(D)()FP=∑θ,A(D)QA(D)(,)FθdemonstratetherelationbetweenJandkQ,Abyconsideringaθ=°0(8)4442https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448

7TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlewhereQAandQDareobtainedfromFigure5e,f.WeassumeresultsinFigure3bgiveQ̅D=96%,whichreproducesthethatPθisgivenbyexperimentalresultverywell.ThoseresultswerecalculatedusingthedisorderparameterinTable3,F=0andEb,D=0.50kQ,A(D)P=eV.FigureS4alsoshowsthattheQ̅A(D)becomeslowerwithθ,A(D)180°∑θ°kQ,A(D)(9)increasingdisorderwhentheelectricfieldisstrong.OnecanalsoseefromthisfigurethattheincreaseoftheenergeticPθiscalculatedusingthevaluesofkQ,A(D)fromFigure5c,d.disorder(σ)hasahigherinfluenceonQ̅A(D)thantheItisnotedfromFigure5c,dthatkHSandkESaremuchhigherpositionaldisorder(δr)ortheangulardisorderofthesecondthankHRandkER.ThismakeskQ,A≈kHSandkQ,D≈kESforthechargejump(ξ).Thisoccursbecausethedrivingforcesareparametersconsidered.InthepresenceoftheF,kHSandkESstronglyaffectedbythechangeinσthanδrandξ.havetheirhighestmagnitudesforlowervaluesofθ.Hence,InFigure6,wealsoshowQ̅A(D)calculatedfordifferentfasterdepletionoftheCTexcitonsforthoseanglesincreasePθvaluesofEb,A(Eb,D).ThosecurvesevidencetheroleplayedbysothatsmallvaluesofθwillhaveastrongerweightinthetheexcitonbindingenergytodeterminethePLquenching.IndeterminationofQ̅A(D).Thereisthenagradualincreaseofourmodel,lowervaluesofEb,A(Eb,D)impliesthatΔGHSQ̅A(D)astheelectricfieldrises,seeFigure6.Thisisthe(ΔGES)isclosetozero,whichincreasesthehole(electron)25,49separation.ThisresultemphasizesthedoublerolethattheimprovementoffilmmorphologycanhaveforthePLquenching:besidesimprovingQ̅A(D)byreducingthedisordereffects,well-orderedorcrystallinedomainsarefundamentaltoinducechargedelocalization,whichareknownfordecreasing26,50−53theexcitonbindingenergy.ForthePTB7/PC71BMblend,ithasbeenreportedthattheuseofsolventadditivescanimprovetheactivelayermorphology,leadingtoanincreasein54,55thephotocurrentgeneration.Here,itisimportanttomentionthatmeasurementsoffield-dependentexcitonquenchingbyPC71BMexcitationarevery18complexduetolowPLyieldofthisfullerene.However,theFigure7.DependenceofQ̅A,Fieldwiththeelectricfieldandexcitonfield-dependentexcitonquenchingobtainedfromtime-bindingenergyforacceptorexcitation.Experimentalresultsofref34resolvedPLmeasurementsintheITO/PTB7/PC71BM/Alobtainedfromtime-resolvedPLmeasurementsintheITO/PTB7/BHJdeviceinvacuumarereportedinref34.ThosespectraPC71BM/AlBHJdeviceinvacuum,afterPC71BMexcitationat400nmandT=290K.wereobtainedafterthePC71BMexcitationat400nmandT=290K.SincethemeasurementswereperformeddirectlyontheexpectedPLquenchingdependencewiththeelectricfieldforblend,onlytheinfluenceoftheelectricalfieldisobtainedfromBHJactivelayers.33−35,46Forstrongerelectricfields,k(k)thoseexperimentaldata.InordertocompareourmodelwithHSESbecomesevenfastersothatallexcitonsarechanneledtothem,wehavetoslightlymodifyourexpressionforQAandregionswereθ≈0°.Underthosecircumstances,Q̅A(D)tendsconsideronlytherelativevariationswiththeFineq2sothattosaturateforthevaluesofQA(D)ifθ=0°.Q̅A,Field=1−[S1,A(F)]/[S1,A(F=0)].ThenetinfluenceofAnotherimportantfeatureofthesimulationsinFigure6istheelectricfieldforeachcurveinFigure3acanthenbethatQ̅A(D)doesnotreachthevalueof100%evenforhigherobtained.ThecomparisonbetweenthetheoreticalQ̅A,Fieldwithmagnitudesoftheelectricfield.Thisisadirectconsequenceofexperimentaldatameasuredinref34isshowninFigure7.Thedisorder.35Forinstance,assumingroomtemperature,F=0,theoreticalresultsareabletoreproducethemeasurementswhenE=1.2eVfortheF<1.75×108V/m.ThisestimateandEb,D=0.50eV,QD=100%ifdisordereffectsareb,A36oftheexcitonbindingenergyinPCBMisslightlyhigherthanneglected.Indeed,steady-statemeasurementsofQDfor7136,47,48E≈1.0eVobtainedusingtheopticalgapmethodandDFTPTB7/PC71BMblendsshowresultsverycloseto100%.b,A25Thisisanexpectedbehaviorforblendswithhighfreechargecalculations.Thedeviationbetweentheexperimentaldatagenerationefficiency,whichoccursforsystemswithhighandcalculationsathighelectricfieldscanbeattributedtothe22,25drivingforceand/orlowexcitonbindingenergy.OurcontributionoftunnelingprocessestodissociatetheFigure8.Dependenceofexcitonquenchingefficiencywiththeelectricfieldandtemperaturefor(a)acceptorexcitationand(b)donorexcitation.ResultsforEb,A=1.00eVandEb,D=0.50eV.4443https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448

8TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure9.Dependenceofexcitonquenchingefficiencyfordonorexcitationwiththeelectricfieldandexcitonbindingenergyconsideringtherangeforθfrom(a)0toπ/2(reversebias)and(b)π/2toπ(forwardbias).ResultsforT=300K.Figure10.Bias-dependentPLspectraoftheITO/PTB7-Th/C70/Albilayerdeviceinair,afterPTB7-Thexcitationat635nmandT=300Kfor(a)reversebiasand(b)forwardbias.ExperimentalandtheoreticalresultsofQ̅D,Fieldfor(c)reversebiasand(d)forwardbias(Eb,D=0.5eV).56excitons.AsEb,Adecreases,thequenchingcurvegrowsfasterthathasalreadybeenstudiedintheliteratureandverified60thantheexperimentaldataandsaturatesforhighermagnitudesexperimentallybyGerhardetal.forlowerenergyCTstatesoftheelectricfield.andthePTB7/PC71BMmaterialsystem.UnfortunatelyThevariationoftheexcitonquenchingwiththetemperatureMarcus’stheoryisnottotallyvalidintherangeoftemperaturesarederivedfromthedependencewithToftheratescalculatedofthedatareportedinref60.Asaconsequence,weavoidedtousingMarcus’theory.Itiswellknownthatthistheoreticalapplyourmodeltoexplainthosemeasurements.frameworkisappropriatedtodescribethechargetransferrate3.2.TheBilayerStructure.Inthissection,wecompareathightemperatures,wherequantumeffectsassociatedtoourmodeltoPLmeasurementsperformedinabilayer(BL)41,57−59nuclearvibrationscanbeneglected.TheArrhenius-likedevice.Inprinciple,thosedevicesarecomposedbyarelativelytemperaturedependenceoftheratesderivedfromthistheoryplanarD/Aheterojunction.Hence,theyareveryusefultotest(seeeq4)inducesthermalactivationtothedissociationthetheorysincethisspecialstructureenablesmeasurementsofefficiency.TheriseofthetemperaturemakestheratesslightlyQ̅DwhentheFhastwoopposingorientationsrelativetothehigher.Sincetheexcitonquenchinginthesystemundersurfaceoftheheterojunction.Suchrefinedcontrolofθisnotconsiderationismainlylimitedbytheseparationrate,thepossibleinordinaryD/AblendsofBHJdevices.temperatureincreaseimprovesthequenchingefficiency.FigureInordertoadaptourresultstothisspecialmorphologyofa8presentsQ̅AandQ̅DasfunctionsoftheelectricfieldforBLdevice,wehavetolimittheangularvariationofthemodeldifferenttemperatures.OnecanseethattheeffectofTisdescribedinSection3.1.ConsideringaplanarD/Ainterfacestrongerfortheexcitonsgeneratedintheacceptor.Thisisawithacertaindegreeofroughness,therangeofθineq8isdirectconsequenceofthehighermagnitudeofEb,AinthislimitedforacertainangularintervalθL=nπ,wherenisamaterial,whichtendstolimitQ̅A.DuetothelowerEb,D,Q̅Dnumberbetween0and1.ThisparameterisrelatedtothesaturatesforF≈1.0×108V/msothatthequenchingdegreeofroughnessoftheD/Ainterface.ForanidealplanarefficiencyalmostdoesnotchangewithtemperatureforhigherD/Asurface,θ=0(reversebias)andθ=π(forwardbias)soelectricfields.ThethermallyinducedquenchingisaneffectthatθL=0(n=0).Ontheotherhand,θL=π(n=1)foran4444https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448

9TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleidealbulkheterojunction.Figure9a,bshowsthecalculationsquenchinginducedbythe(morphology-driven)orientationofforθbetween0andπ/2(reversebias)andbetweenπ/2andπthedissociationprocessrelativetothedirectionoftheelectric(forwardbias)(orθL=0.5π),whichwouldsimulatearoughfield.OursimpletheoreticalapproachsuggeststhatthereisanplanarinterfacebetweenthedonorandtheacceptormaterialsimbalanceoftheexcitonfluxalongtheD/AinterfacesothatinaBLstructure.NotethatthesimulationswerecarriedoutthisfluxishighertowardregionswherethedissociationusingthesameparametersinTable3.Asexpected,theQ̅D(representedbythefield-induceddissociationrate)isgreater.magnitudebecomeshigher(Figure9a)withtheincreasingFollowingthisprinciple,wewereabletofittheexperimentalmagnitudeoftheelectricfield(foranorientationthatfavorsdatameasureinBHJandbilayerdevices.Fromthisanalysis,theelectronseparation),whileitbecomeslowerfortheFinweobtainestimatesfortheexcitonbindingenergiesinthetheoppositeorientation(Figure9b).IntherangeofelectricPTB7-Th,PC71BMandC70.Moreover,wespecificallytestedfieldsshowedinthosefigures,theincreaseordecreaseofthethetheorybymeasuringthePLquenchinginabilayerPTB7-quenchingefficiencyisalmostlinear.Th/C70deviceasafunctionoftheFmagnitudeandABLdevicewasbuilttocompareourtheoreticalorientation.Wedemonstratethatthemodelisabletocalculationswithdirectmeasurements(experimentalmethodsreproducethefield-inducedquenchingefficiencynotonlyintheSupportingInformation).Figure10a,bshowsthebias-whentheFhasafavorableorientationthatenhancesthedependentPLspectra(obtainedafterthedonorexcitationatchargetransferbutalsowhentheFtendstoinhibitthis635nm)forabilayerdevicewiththestructureITO/PTB7-process.Moreover,themodelisabletogivesomehintsontheTh/C70/Al.Inbothfigures,thecurvesarenormalizedbythedegreeofmixingbetweenthedonorandacceptorintheactivepeakwiththehighestPLintensity.Increasingthebiasforalayerinthiskindofdevicearchitecture.reverse(forward)direction,themeasurementsshowthattheWebelievethatourcontributioncanproducevaluablePLintensitybecomesweaker(stronger).Theoverallshapeofinformationaboutthemainprocessesthatinfluencethethecurvesunderreverseandforwardbiasesissimilar,withthedynamicsoftheexcitondissociationattheD/Ainterfaces.InmaximumofPLintensityat770nm.Thosecurvesaresimilarparticular,itrevealssomeaspectsoftheroleplayedbythetothethePLspectrarecordedafter633nmexcitationofheterojunctionmorphologytoenhancethefield-induced61PTB7-Thfilms.chargegeneration.ItisalsousefultoexploretheeffectsofInFigure10c,d,wecomparethetheoreticalfielddepend-temperature,energydisorder,sitedisorder,andexcitonenceofthequenchingefficiencywiththeexperimentaldata.bindingenergyinthephotovoltaiceffectofOSCs.AsaForthiscomparison,weassumedthattheFcanbewrittenasFconsequence,theanalysiscanbeavaluabletooltotailorthe≈V−Vbi/L,whereVistheappliedvoltage,Vbiisthebuilt-inmorphologyofmoreefficientorganicsolarcells.Finally,itvoltage(−0.7eV),andListhethicknessoftheactivelayeropensthepossibilitytobetterunderstandtheexciton(100nm).InBLdevices,thereisaconsiderablefractionofdissociationprocessofnewcombinationsofD/AmaterialsexcitonsthatrecombinebeforereachingtheD/Ainterface.Towithlowdrivingforceforchargeseparationandefficient65−67excludetheinfluenceinthemeasurementsofthePLproducedexcitondissociation.bythoseexcitons,wehavethentoconsiderjusttherelativevariationofthequenchingefficiencywiththeelectricfield.■ASSOCIATEDCONTENTThisvariationwasobtainedbywritingQ̅D,Field=1−PL(F)/*sıSupportingInformationPLMax(F),wherethePL(F)istakenfromFigure10a,b.Likewise,therelativevariationofthetheoreticalQ̅DinFigureTheSupportingInformationisavailablefreeofchargeat10c,dwasassumedtobeQ̅D,Field=1−[S1,D(F)]/https://pubs.acs.org/doi/10.1021/acs.jpcc.0c11458.[S1,D,Max(F)].InFigure10c,d,weplottedQ̅D,FieldforafixedExperimentalmethods,definitionoftheanglesusedinvalueofEb,D,andusingθLasfittingparameter,onecanseethatthedescriptionofthetheoreticalmethod,electronictheagreementbetweentheoryandexperimentisobtainedforcouplingbetweeneachpairofmolecularorbitalsEb,D=0.50eVandθL=0.61π.ThemagnitudeofEb,Disininvolvedintheelectronandholetransferdynamics,agreementwiththemagnitudeofthebindingenergyestimatedrelationbetweenexcitonfluxandtheCTexciton62forsingletexcitonsinPTB7-Th.ThevalueofθLthatfitsthedeactivationrate,anddependenceofexcitonquenchingexperimentaldataindicatesthatthePTB7-Th/C70interfaceiswiththeelectricfieldchangingsomedisorderparame-notatrueplanarbilayer.Itmighthaveaconsiderabledegreeofters(PDF)surfaceroughnessproducedbysomemixturebetweenthedonorandacceptorphases.Indeed,itwasobservedforBLPSIF-DBT/C70devicesthattheroughnessofthepolymeric■AUTHORINFORMATIONsurfaceenhancestheD/AcontactareaandassiststhefullereneCorrespondingAuthors37,63diffusiondeeperinsidethepolymericlayer.ThiseffectL.Benatto−DepartmentofPhysics,FederalUniversityofleadstobettermixingbetweendonorandacceptorspeciesandParaná,CuritibaC.P19044,81531-980,PR,Brazil;createsaninterpenetratinglayerthatresemblesabulk64orcid.org/0000-0001-9976-3574;Email:lb08@heterojunction.Ourresultsheresuggestthatthesameeffectfisica.ufpr.brisalsopresentinthePTB7-Th/C70devices.M.Koehler−DepartmentofPhysics,FederalUniversityofParaná,CuritibaC.P19044,81531-980,PR,Brazil;4.CONCLUSIONSorcid.org/0000-0001-9935-5060;Email:koehler@Insummary,weproposedakineticmodeltodescribethefisica.ufpr.brelectricfield-inducedphotoluminescencequenchingatD/Aheterojunctions.ThistheoryisanimprovementoveraAuthors36previousmodelthatneglectedfieldanddisordereffects.InC.A.M.Moraes−DepartmentofPhysics,FederalUniversityaddition,weconsidertheangularvariationofthelocalexcitonofParaná,CuritibaC.P19044,81531-980,PR,Brazil4445https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448

10TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleM.deJesusBassi−DepartmentofPhysics,FederalUniversity(10)Athanasopoulos,S.;Bassler,H.;Kö̈hler,A.DisordervsofParaná,CuritibaC.P19044,81531-980,PR,BrazilDelocalization:WhichIsMoreAdvantageousforHigh-EfficiencyL.Wouk−DepartmentofPhysics,FederalUniversityofOrganicSolarCells?J.Phys.Chem.Lett.2019,10,7107−7112.Paraná,CuritibaC.P19044,81531-980,PR,Brazil;Center(11)deSousa,L.E.;Coropceanu,V.;daSilvaFilho,D.A.;Sini,G.ofInnovations,CSEMBrazil,BeloHorizonteC.P31035-OnthePhysicalOriginsofChargeSeparationatDonor−AcceptorInterfacesinOrganicSolarCells:EnergyBendingversusEnergy536,MG,Brazil;orcid.org/0000-0002-1843-0741Disorder.Adv.TheorySimul.2020,3,1900230.L.S.Roman−DepartmentofPhysics,FederalUniversityof(12)Cao,Z.;Yang,S.;Wang,B.;Shen,X.;Han,G.;Yi,Y.Multi-Paraná,CuritibaC.P19044,81531-980,PR,Brazil;ChannelExcitonDissociationinD18/Y6ComplexesforHigh-orcid.org/0000-0001-6567-5920EfficiencyOrganicPhotovoltaics.J.Mater.Chem.A2020,8,20408−Completecontactinformationisavailableat:20413.https://pubs.acs.org/10.1021/acs.jpcc.0c11458(13)Karki,A.;Vollbrecht,J.;Gillett,A.J.;Selter,P.;Lee,J.;Peng,Z.;Schopp,N.;Dixon,A.L.;Schrock,M.;Nadaźdy,V.;etal.UnifyinǧChargeGeneration,Recombination,andExtractioninLow-OffsetNotesNon-FullereneAcceptorOrganicSolarCells.Adv.EnergyMater.Theauthorsdeclarenocompetingfinancialinterest.2020,10,2001203.(14)Heiber,M.C.;Okubo,T.;Ko,S.-J.;Luginbuhl,B.R.;Ran,N.■A.;Wang,M.;Wang,H.;Uddin,M.A.;Woo,H.Y.;Bazan,G.C.;ACKNOWLEDGMENTSetal.MeasuringtheCompetitionbetweenBimolecularChargeThisworkhasbeensupportedbytheCompanhiaParanaenseRecombinationandChargeTransportinOrganicSolarCellsunderdeEnergia,COPELresearchandtechnologicaldevelopmentOperatingConditions.EnergyEnviron.Sci.2018,11,3019−3032.program,throughthePD2866-0470/2017project,regulated(15)Causa’,M.;Ramirez,I.;MartinezHardigree,J.F.;Riede,M.;byANEEL.ThisstudywasfinancedinpartbytheBanerji,N.FemtosecondDynamicsofPhotoexcitedC60Films.J.Phys.CoordenaçãodeAperfeiçoamentodePessoaldeNívelChem.Lett.2018,9,1885−1892.Superior-Brasil(CAPES),FinanceCode001.Research(16)Vandewal,K.;Albrecht,S.;Hoke,E.T.;Graham,K.R.;developedwiththeassistanceofCENAPAD-SP(CentroWidmer,J.;Douglas,J.D.;Schubert,M.;Mateker,W.R.;Bloking,J.NacionaldeProcessamentodeAltoDesempenhoemSaõT.;Burkhard,G.F.;etal.EfficientChargeGenerationbyRelaxedPaulo),projectUNICAMP/FINEP-MCT.SpecialthanksgotoCharge-TransferStatesatOrganicInterfaces.Nat.Mater.2014,13,63−68.CNPq(grant159897/2019-0)andtoLCNano/SisNANO2.0(17)Nakano,K.;Chen,Y.;Xiao,B.;Han,W.;Huang,J.;Yoshida,(grant442591/2019-5)forthefinancialsupport.H.;Zhou,E.;Tajima,K.AnatomyoftheEnergeticDrivingForceforChargeGenerationinOrganicSolarCells.Nat.Commun.2019,10,■REFERENCES2520.(18)Cha,H.;Wheeler,S.;Holliday,S.;Dimitrov,S.D.;Wadsworth,(1)Karuthedath,S.;Gorenflot,J.;Firdaus,Y.;Chaturvedi,N.;DeA.;Lee,H.H.;Baran,D.;McCulloch,I.;Durrant,J.R.InfluenceofCastro,C.S.P.;Harrison,G.T.;Khan,J.I.;Markina,A.;Balawi,A.BlendMorphologyandEnergeticsonChargeSeparationandH.;Archie,T.;etal.IntrinsicEfficiencyLimitsinLow-BandgapNon-RecombinationDynamicsinOrganicSolarCellsIncorporatingaFullereneAcceptorOrganicSolarCells.Nat.Mater.2020,1−7.(2)Kawashima,K.;Tamai,Y.;Ohkita,H.;Osaka,I.;Takimiya,K.NonfullereneAcceptor.Adv.Funct.Mater.2018,28,1704389.High-EfficiencyPolymerSolarCellswithSmallPhotonEnergyLoss.(19)Nikolis,V.C.;Dong,Y.;Kublitski,J.;Benduhn,J.;Zheng,X.;Nat.Commun.2015,6,10085.Huang,C.;Yüzer,A.C.;Ince,M.;Spoltore,D.;Durrant,J.R.;etal.(3)Wu,J.;Lee,J.;Chin,Y.-C.;Yao,H.;Cha,H.;Luke,J.;Hou,J.;FieldEffectversusDrivingForce:ChargeGenerationinSmall-Kim,J.-S.;Durrant,J.R.ExceptionallyLowChargeTrappingEnablesMoleculeOrganicSolarCells.Adv.EnergyMater.2020,10,2002124.HighlyEfficientOrganicBulkHeterojunctionSolarCells.Energy(20)Han,G.;Yi,Y.OriginofPhotocurrentandVoltageLossesinEnviron.Sci.2020,13,2422−2430.OrganicSolarCells.Adv.TheorySimul.2019,2,1900067.(4)Liu,X.;Li,Y.;Ding,K.;Forrest,S.EnergyLossinOrganic(21)Zhang,J.;Tan,H.S.;Guo,X.;Facchetti,A.;Yan,H.MaterialPhotovoltaics:NonfullereneVersusFullereneAcceptors.Phys.Rev.InsightsandChallengesforNon-FullereneOrganicSolarCellsBasedAppl.2019,11,No.024060.onSmallMolecularAcceptors.Nat.Energy2018,3,720−731.(5)Yang,C.;Zhang,J.;Liang,N.;Yao,H.;Wei,Z.;He,C.;Yuan,(22)Weu,A.;Hopper,T.R.;Lami,V.;Kreß,J.A.;Bakulin,A.A.;X.;Hou,J.EffectsofEnergy-LevelOffsetbetweenaDonorandVaynzof,Y.Field-AssistedExcitonDissociationinHighlyEfficientAcceptoronthePhotovoltaicPerformanceofNon-FullereneOrganicPffBT4T-2OD:FullereneOrganicSolarCells.Chem.Mater.2018,30,SolarCells.J.Mater.Chem.A2019,7,18889−18897.2660−2667.(6)Meredith,P.;Li,W.;Armin,A.NonfullereneAcceptors:A(23)Niu,M.-S.;Wang,K.-W.;Yang,X.-Y.;Bi,P.-Q.;Zhang,K.-N.;RenaissanceinOrganicPhotovoltaics?Adv.EnergyMater.2020,10,Feng,X.-J.;Chen,F.;Qin,W.;Xia,J.-L.;Hao,X.-T.HoleTransfer2001788.OriginatingfromWeaklyBoundExcitonDissociationinAcceptor-(7)Hinrichsen,T.F.;Chan,C.C.S.;Ma,C.;Palecek,D.;Gillett,A.;̌Donor-AcceptorNonfullereneOrganicSolarCells.J.Phys.Chem.Lett.Chen,S.;Zou,X.;Zhang,G.;Yip,H.-L.;Wong,K.S.;etal.Long-2019,10,7100−7106.LivedandDisorder-FreeChargeTransferStatesEnableEndothermic(24)Wang,X.;Yang,Y.;He,Z.;Wu,H.;Cao,Y.InfluenceoftheChargeSeparationinEfficientNon-FullereneOrganicSolarCells.AcceptorCrystallinityontheOpen-CircuitVoltageinPTB7-Th:Nat.Commun.2020,11,5617.ITICOrganicSolarCells.J.Mater.Chem.C2019,7,14861−14866.(8)Song,P.;Li,Y.;Ma,F.;Pullerits,T.;Sun,M.ExternalElectric(25)Benatto,L.;Marchiori,C.F.N.;MoysesAraujo,C.;Koehler,Field-DependentPhotoinducedChargeTransferinaDonor-AcceptorM.MolecularOriginofEfficientHoleTransferfromNon-FullereneSystemforanOrganicSolarCell.J.Phys.Chem.C2013,117,15879−Acceptors:InsightsfromFirst-PrinciplesCalculations.J.Mater.Chem.15889.C2019,7,12180−12193.(9)Vithanage,D.A.;Matheson,A.B.;Pranculis,V.;Hedley,G.J.;(26)Zhu,L.;Tu,Z.;Yi,Y.;Wei,Z.AchievingSmallExcitonBindingPearson,S.J.;Gulbinas,V.;Samuel,I.D.W.;Ruseckas,A.BarrierlessEnergiesinSmallMoleculeAcceptorsforOrganicSolarCells:EffectSlowDissociationofPhotogeneratedChargePairsinHigh-Perform-ofMolecularPacking.J.Phys.Chem.Lett.2019,10,4888−4894.ancePolymer-FullereneSolarCells.J.Phys.Chem.C2017,121,(27)Arkhipov,V.I.;Bassler,H.;Deussen,M.;Gö̈bel,E.O.;14060−14065.Kersting,R.;Kurz,H.;Lemmer,U.;Mahrt,R.F.Field-Induced4446https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448

11TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleExcitonBreakinginConjugatedPolymers.Phys.Rev.B1995,52,(46)Inal,S.;Schubert,M.;Sellinger,A.;Neher,D.TheRelationship4932−4940.betweentheElectricField-InducedDissociationofChargeTransfer(28)Arkhipov,V.;Bassler,H.;Emelyanova,E.;Hertel,D.;Gulbinas,̈ExcitonsandthePhotocurrentinSmallMolecular/PolymericSolarV.;Rothberg,L.ExcitonDissociationinConjugatedPolymers.Cells.J.Phys.Chem.Lett.2010,1,982−986.Macromol.Symp.2004,212,13−24.(47)Yi,X.;Gautam,B.;Constantinou,I.;Cheng,Y.;Peng,Z.;(29)Bakulin,A.A.;Xia,Y.;Bakker,H.J.;Inganas,O.;Gao,F.̈Klump,E.;Ba,X.;Ho,C.H.Y.;Dong,C.;Marder,S.R.;etal.ImpactMorphology,Temperature,andFieldDependenceofChargeofNonfullereneMolecularArchitectureonChargeGeneration,SeparationinHigh-EfficiencySolarCellsBasedonAlternatingTransport,andMorphologyinPTB7-Th-BasedOrganicSolarCells.PolyquinoxalineCopolymer.J.Phys.Chem.C2016,120,4219−4226.Adv.Funct.Mater.2018,28,1802702.(30)Vandewal,K.;Ma,Z.;Bergqvist,J.;Tang,Z.;Wang,E.;(48)Qian,D.;Zheng,Z.;Yao,H.;Tress,W.;Hopper,T.R.;Chen,Henriksson,P.;Tvingstedt,K.;Andersson,M.R.;Zhang,F.;Inganas,̈S.;Li,S.;Liu,J.;Chen,S.;Zhang,J.;etal.DesignRulesforO.QuantificationofQuantumEfficiencyandEnergyLossesinLowMinimizingVoltageLossesinHigh-EfficiencyOrganicSolarCells.BandgapPolymer:FullereneSolarCellswithHighOpen-CircuitNat.Mater.2018,17,703−709.Voltage.Adv.Funct.Mater.2012,22,3480−3490.(49)Zhu,L.;Yi,Y.;Wei,Z.ExcitonBindingEnergiesofNon-(31)Onsager,L.DeviationsfromOhm’sLawinWeakElectrolytes.FullereneSmallMoleculeAcceptors:ImplicationforExcitonJ.Chem.Phys.1934,2,599−615.DissociationDrivingForcesinOrganicSolarCells.J.Phys.Chem.C(32)Braun,C.L.ElectricFieldAssistedDissociationofCharge2018,122,22309−22316.TransferStatesasaMechanismofPhotocarrierProduction.J.Chem.(50)Murthy,D.H.K.;Gao,M.;Vermeulen,M.J.W.;Siebbeles,L.Phys.1984,80,4157−4161.D.A.;Savenije,T.J.MechanismofMobileChargeCarrier(33)Kern,J.;Schwab,S.;Deibel,C.;Dyakonov,V.BindingEnergyGenerationinBlendsofConjugatedPolymersandFullerenes:ofSingletExcitonsandChargeTransferComplexesinMDMO-PPV:SignificanceofChargeDelocalizationandExcessFreeEnergy.J.PCBMSolarCells.Phys.StatusSolidiRRL2011,5,364−366.Phys.Chem.C2012,116,9214−9220.(34)Gerhard,M.;Arndt,A.P.;Bilal,M.;Lemmer,U.;Koch,M.;(51)Matheson,A.B.;Ruseckas,A.;Pearson,S.J.;Samuel,I.D.W.Howard,I.A.Field-InducedExcitonDissociationinPTB7-BasedHoleDelocalizationasaDrivingForceforChargePairDissociationinOrganicSolarCells.Phys.Rev.B2017,95,195301.OrganicPhotovoltaics.Mater.Horiz.2019,6,1050−1056.(35)Rubel,O.;Baranovskii,S.D.;Stolz,W.;Gebhard,F.Exact(52)Gélinas,S.;Rao,A.;Kumar,A.;Smith,S.L.;Chin,A.W.;SolutionforHoppingDissociationofGeminateElectron-HolePairsClark,J.;vanderPoll,T.S.;Bazan,G.C.;Friend,R.H.UltrafastinaDisorderedChain.Phys.Rev.Lett.2008,100,196602.Long-RangeChargeSeparationinOrganicSemiconductorPhoto-(36)Benatto,L.;deJesusBassi,M.;WoukdeMenezes,L.C.;voltaicDiodes.Science2014,343,512−516.Roman,L.S.;Koehler,M.KineticModelforPhotoluminescence(53)Upama,M.B.;Elumalai,N.K.;Mahmud,M.A.;Wright,M.;QuenchingbySelectiveExcitationofD/ABlends:ImplicationsforWang,D.;Xu,C.;Uddin,A.EffectofAnnealingDependentBlendChargeSeparationinFullereneandNon-FullereneOrganicSolarMorphologyandDielectricPropertiesonthePerformanceandCells.J.Mater.Chem.C2020,8,8755−8769.StabilityofNon-FullereneOrganicSolarCells.Sol.EnergyMater.Sol.(37)Benatto,L.;Marchiori,C.F.N.;Talka,T.;Aramini,M.;Cells2018,176,109−118.Yamamoto,N.A.D.;Huotari,S.;Roman,L.S.;Koehle,M.(54)Song,X.;Gasparini,N.;Baran,D.TheInfluenceofSolventComparingC60andC70asAcceptorinOrganicSolarCells:AdditiveonPolymerSolarCellsEmployingFullereneandNon-InfluenceoftheElectronicStructureandAggregationSizeontheFullereneAcceptors.Adv.Electron.Mater.2018,4,1700358.PhotovoltaicCharacteristics.ThinSolidFilms2020,697,137827−(55)Wan,Q.;Guo,X.;Wang,Z.;Li,W.;Guo,B.;Ma,W.;Zhang,137836.M.;Li,Y.10.8%EfficiencyPolymerSolarCellsBasedonPTB7-Th(38)Hedley,G.J.;Ward,A.J.;Alekseev,A.;Howells,C.T.;Martins,andPC71BMviaBinarySolventAdditivesTreatment.Adv.Funct.E.R.;Serrano,L.A.;Cooke,G.;Ruseckas,A.;Samuel,I.D.W.Mater.2016,26,6635−6640.DeterminingtheOptimumMorphologyinHigh-Performance(56)Wang,L.;Nan,G.;Yang,X.;Peng,Q.;Li,Q.;Shuai,Z.Polymer-FullereneOrganicPhotovoltaicCells.Nat.Commun.2013,ComputationalMethodsforDesignofOrganicMaterialswithHigh4,2867.ChargeMobility.Chem.Soc.Rev.2010,39,423−434.(39)Dimitrov,S.D.;Schroeder,B.C.;Nielsen,C.B.;Bronstein,H.;(57)Yao,C.;Peng,C.;Yang,Y.;Li,L.;Bo,M.;Wang,J.ElucidatingFei,Z.;McCulloch,I.;Heeney,M.;Durrant,J.R.SingletExcitontheKeyRoleofFluorineinImprovingtheChargeMobilityofLifetimesinConjugatedPolymerFilmsforOrganicSolarCells.ElectronAcceptorsforNon-FullereneOrganicSolarCellsbyPolymers2016,8,14.MultiscaleSimulations.J.Mater.Chem.C2018,6,4912−4918.(40)Oberhofer,H.;Reuter,K.;Blumberger,J.ChargeTransportin(58)Zhao,Y.;Liang,W.ChargeTransferinOrganicMoleculesforMolecularMaterials:AnAssessmentofComputationalMethods.SolarCells:TheoreticalPerspective.Chem.Soc.Rev.2012,41,1075−Chem.Rev.2017,117,10319−10357.1087.(41)Song,P.;Li,Y.;Ma,F.;Pullerits,T.;Sun,M.Photoinduced(59)Zong,H.;Wang,X.;Quan,J.;Tian,C.;Sun,M.PhotoinducedElectronTransferinOrganicSolarCells.Chem.Rec.2016,16,734−ChargeTransferbyOneandTwo-PhotonAbsorptions:Physical753.MechanismsandApplications.Phys.Chem.Chem.Phys.2018,20,(42)Bai,R.-R.;Zhang,C.-R.;Liu,Z.-J.;Chen,X.-K.;Wu,Y.-Z.;19720−19743.Wang,W.;Chen,H.-S.ElectricFieldEffectsonOrganicPhotovoltaic(60)Gerhard,M.;Arndt,A.P.;Howard,I.A.;Rahimi-Iman,A.;HeterojunctionInterfaces:TheModelCaseofPentacene/C60.Lemmer,U.;Koch,M.Temperature-andEnergy-DependentComput.Theor.Chem.2020,1186,112914.SeparationofCharge-TransferStatesinPTB7-BasedOrganicSolar(43)Song,P.;Zhou,Q.;Li,Y.;Ma,F.;Sun,M.VibronicQuantizedCells.J.Phys.Chem.C2015,119,28309−28318.TunnelingControlledPhotoinducedElectronTransferinanOrganic(61)Guo,Y.;Li,Y.;Awartani,O.;Zhao,J.;Han,H.;Ade,H.;Zhao,SolarCellSubjectedtoanExternalElectricField.Phys.Chem.Chem.D.;Yan,H.AVinylene-BridgedPerylenediimide-BasedPolymericPhys.2017,19,16105−16112.AcceptorEnablingEfficientAll-PolymerSolarCellsProcessedunder(44)Coropceanu,V.;Cornil,J.;daSilvaFilho,D.A.;Olivier,Y.;AmbientConditions.Adv.Mater.2016,28,8483−8489.Silbey,R.;Brédas,J.-L.ChargeTransportinOrganicSemiconductors.(62)Lu,L.;Yu,L.UnderstandingLowBandgapPolymerPTB7andChem.Rev.2007,107,926−952.OptimizingPolymerSolarCellsBasedonIt.Adv.Mater.2014,26,(45)Song,P.;Li,Y.;Ma,F.;Sun,M.InsightintoExternalElectric4413−4430.FieldDependentPhotoinducedIntermolecularChargeTransportin(63)Kekuda,D.;Lin,H.-S.;ChyiWu,M.;Huang,J.-S.;Ho,K.-C.;BHJSolarCellMaterials.J.Mater.Chem.C2015,3,4810−4819.Chu,C.-W.TheEffectofSolventInducedCrystallinityofPolymer4447https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448

12TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleLayeronPoly(3-Hexylthiophene)/C70BilayerSolarCells.Sol.EnergyMater.Sol.Cells2011,95,419−422.(64)Benatto,L.;Govatski,J.A.;deMoraes,C.A.M.;Gouvea,C.P.;̂Avila,H.C.;Marchiori,C.F.N.;Oliveira,C.K.B.Q.M.;Cremona,M.;Koehler,M.;Roman,L.S.UnderstandingtheEffectofSolventAdditiveinPolymericThinFilm:TurningaBilayerinaBulkHeterojunction-likePhotovoltaicDevice.J.Phys.D:Appl.Phys.2020,53,365101.(65)Zhang,G.;Chen,X.-K.;Xiao,J.;Chow,P.C.Y.;Ren,M.;Kupgan,G.;Jiao,X.;Chan,C.C.S.;Du,X.;Xia,R.;etal.DelocalizationofExcitonandElectronWavefunctioninNon-FullereneAcceptorMoleculesEnablesEfficientOrganicSolarCells.Nat.Commun.2020,11,3943.(66)Zhong,Y.;Causa’,M.;Moore,G.J.;Krauspe,P.;Xiao,B.;Günther,F.;Kublitski,J.;Shivhare,R.;Benduhn,J.;BarOr,E.;etal.Sub-PicosecondCharge-Transferatnear-ZeroDrivingForceinPolymer:Non-FullereneAcceptorBlendsandBilayers.Nat.Commun.2020,11,833.(67)Classen,A.;Chochos,C.L.;Lüer,L.;Gregoriou,V.G.;Wortmann,J.;Osvet,A.;Forberich,K.;McCulloch,I.;Heumüller,T.;Brabec,C.J.TheRoleofExcitonLifetimeforChargeGenerationinOrganicSolarCellsatNegligibleEnergy-LevelOffsets.Nat.Energy2020,5,711−719.(68)Constantinou,I.;Yi,X.;Shewmon,N.T.;Klump,E.D.;Peng,C.;Garakyaraghi,S.;Lo,C.K.;Reynolds,J.R.;Castellano,F.N.;So,F.EffectofPolymer−FullereneInteractionontheDielectricPropertiesoftheBlend.Adv.EnergyMater.2017,7,1601947−1601954.(69)Liu,S.;Yuan,J.;Deng,W.;Luo,M.;Xie,Y.;Liang,Q.;Zou,Y.;He,Z.;Wu,H.;Cao,Y.High-EfficiencyOrganicSolarCellswithLowNon-RadiativeRecombinationLossandLowEnergeticDisorder.Nat.Photonics2020,14,300−305.(70)Alessandri,R.;Uusitalo,J.J.;deVries,A.H.;Havenith,R.W.A.;Marrink,S.J.BulkHeterojunctionMorphologieswithAtomisticResolutionfromCoarse-GrainSolventEvaporationSimulations.J.Am.Chem.Soc.2017,139,3697−3705.4448https://dx.doi.org/10.1021/acs.jpcc.0c11458J.Phys.Chem.C2021,125,4436−4448