Exciton migration in β-phase poly(9,9-dioctylfluorene)

Excitonmigrationin␤-phasepoly„9,9-dioctylfluorene…

M.Ariu,*M.Sims,*M.D.Rahn,J.Hill,A.M.Fox,andD.G.Lidzey†

DepartmentofPhysicsandAstronomy,TheUniversityofSheffield,HicksBuilding,HounsfieldRoad,SheffieldS37RH,UnitedKingdom

M.Oda‡

UniversityofPotsdam,InstituteofPhysics,AmNeuenPalais10,14469Potsdam,Germany

J.Cabanillas-GonzalezandD.D.C.Bradley†

TheBlackettLaboratory,ImperialCollegeLondon,PrinceConsortRoad,

SW72BZLondon,UnitedKingdom

͑Received21November2002;revisedmanuscriptreceived12March2003;published30May2003͒Wehavestudiedthedynamicsofopticallygeneratedexcitationsinspin-coatedglassyfilmsofpoly͑9,9-dioctylfluorene͒͑PFO͒andin␤-phasePFOfilmsusingpicosecondtimeresolvedphotoluminescence͑PL͒spectroscopy,performedbothatroomtemperature͑RT͒andat5K.WealsopresentmeasurementsofthePLemissionofPFOand␤-phasePFOatRTand5Kfollowingcontinuouswave͑cw͒excitation.Weshowthatthecwemissionfrom␤-phasePFOat5Kisveryhighlyresolved,permittingustomakeanassignmentofthedifferentvibrationalmodesofthemoleculethatcoupletotheS1→S0transition.Viatime-dependentspectros-copymeasurementsperformedat5K,weareabletofollowexcitondiffusionandrelaxationthroughanenergeticallybroadeneddensityofstatestopolymerchainshavingalongerconjugationlengthandlowerenergygap.Bycomparingtherelativeemissionintensityofthedifferentvibronictransitionsasafunctionoftime,weareabletodirectlydemonstratethatthelowerenergyemissivestatesareassociatedwithlongerconjugationlengthpolymericchainsthathaveenhancedrigidity.Atroomtemperature,wefindthattheserelaxationprocessesoccurfasterthantheresolutionofourdetectorduetothermallyassistedenergymigration.DOI:10.1103/PhysRevB.67.195333I.INTRODUCTIONANDOVERVIEW

PACSnumber͑s͒:78.55.Kz,78.47.ϩp,78.66.Qn,78.30.Jw

Conjugatedpolymersareanimportantclassoforganicsemiconductorthatwillfindapplicationinarangeoflow-costconsumerelectronics.1Recently,oneparticularclassofconjugatedpolymers;thepolyfluorenes,havereceivedworld-wideattentionduetotheirverypromisingperfor-manceinstate-of-the-artorganiclightemittingdiodes͑LED’s͒,2,3photovoltaicdevices,4andthinfilmtransistors.5Poly͑9,9-dioctylfluorene͒͑PFO͒isaprototypicalfluorene-basedhomopolymerwhosechemicalstructureisshowninFig.1.PFOisattractiveasanemissivematerialinorganicdisplaysduetoitshighphotoluminescencequantumeffi-ciency͑whichcanexceed50%͒6andhighholemobility.7PFOisathermotropicliquidcrystal,8andwhenalignedonsuitablypreparedsurfacescanemitbothpolarizedphotolu-minescenceandelectroluminescence,9–11thusmakingitapromisingmaterialforapplicationinliquid-crystaldisplaybacklights.Alignedsamplesalsoallowsignificantenhance-mentsinmobility12anddemonstratelargeopticalbirefringence13thatcanbeusedtoproducehighlypolarizedemissionfrommicrocavitiesandreducedgainthresholdswithinwaveguides.14Furthermore,poly͑9,9-dioctylfluorene͒isafascinatingsystemforthestudyoffundamentalphoto-physicalprocesses,asitcanbepreparedinanumberofdifferentmorphologicalphases.15Bymodifyingthephysicalmorphologyofthepolymerfilmwhilekeepingitschemicalcompositionconstant,wehavepreviouslyshown6thatchangesintheelectronicpropertiesofthedifferentphasescanbedirectlyrelatedtothenanostructureofthematerial.Thereaderisdirectedtoanumberofrecentreviews10,16,17of

0163-1829/2003/67͑19͒/195333͑11͒/$20.00

thestructuralandopticalpropertiesofpolyfluorenesforfurtherdetails.

Conjugatedpolymerthinfilmsareoftenstructurallydis-ordered,leadingtoalimitationoftheeffectiveconjugationlength.Forthisreason,conjugatedpolymerchainscanbethoughtofasbeingcomposedofanumberofdifferentseg-ments,eachhavingadifferentconjugationlengthandthusadifferentenergygap.Thedegreeofenergeticinhomogeneityinaconjugated-polymerthinfilmisafunctionofthelocalstateoforderandthustheStokesshiftresultingfromexcitonmigrationcanbeviewedasanextrinsiceffect.Suchadisor-dercanresultintheobservationofpronouncedenergymi-grationeffects,withexcitonsbeingabletomovebothalongandbetweenpolymerchains.Energytransferusuallyoccurstopolymerchainshavingalongerconjugationlengthandthuslowerenergygap.Thisprocesscanleadtothediffusion

FIG.1.ThechemicalstructureofPFOandasegmentofaPFOchaininthe␤-phaseconformation.In␤-phasePFO,therotationalanglebetweenmonomerunitsisfixedat180°.

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ofexcitonsinconjugatedpolymerfilmsoverdistancesthathavebeenestimatedtobebetween6and12nminthepoly-merPPV,18,1914nminLPPP,20and5nminPFO.21Themicroscopicprocessessurroundingexcitonmigrationarenotwellunderstood.Oneimportantmechanismforexcitonmi-¨rstertransfer͑dipole-dipolecoupling͒.22,23ThisgrationisFo

processcaneffectivelyaccountforthetransferofexcitonsbetweendifferentisolatedchromophoresbothinsolutionandinpolymerthinfilms.23,24Recentworkonpolymer/mesoporous-silicacompositeshasshownthattherateofex-citontransferbetweenpolymerchainsisovertwoordersofmagnitudefasterthanthemigrationofexcitonsalongapoly-merchain.25Asthetransitiondipolemomentofanexcitonisorientedparalleltothechainaxis,itwasarguedthatdipole-dipolecouplingbetweendifferentpolymerchainscanbeafastandefficientprocess,whilethesameprocesscannotrap-idlymoveanexcitonalongapolymerchain.Migrationofexcitonscanalsooccurviaothermechanismssuchastun-nelingandthermallyassistedhopping.26,27Excitontransferbytunnelingisanticipatedtoaccountforbothtransferbe-tweenpolymerchainsandbetweendifferentconjugatedseg-mentsonthesamechain.Disentanglingthesedifferentpro-cessesinadisorderedpolymerfilmisnotatrivialtask.Thisisbecausethetransferratesassociatedwitheachoftheseprocesseswillbehighlydependentonthelocalmicroscopicgeometryandthemolecularconformation.Suchconforma-tionsmayalsoundergothermallyinducedfluctuations,andthusenergy-transferchannelsbetweenoralongmoleculesmayopenandcloseinadynamicfashion.Thus,inallbutthemostsimplesystems,itbecomesasignificantchallengetofullydescribeexcitonmigrationatthemolecularscale.

Excitonmigrationinconjugatedpolymershasbeenstud-iedviasiteselectivefluorescencemeasurements.28–31Intheseexperiments,theexcitationenergyEistunedacrosstheabsorptionpeakanddownthroughthetailofthedensityofstates͑DOS͒,towardslowerenergy.Thecorrespondingpho-toluminescence͑PL͒spectraevolvefrominitiallybeingin-dependentofEtothenshiftingresonantlywithE.Thecriti-calenergyintheDOStailatwhichthischangeinbehavioroccursiscalledthelocalizationenergyEloc.ForEϽEloc,theemissiontendstooccurpredominantlyfromtheemissivecentresonwhichtheexcitonsarefirstcreatedi.e.,energytransferisblocked.Thisarisesbecausethereare,onanav-erage,nositesinthevicinitythathavelowerenergystates.Femtosecondandpicosecondtimeresolvedphotolumines-cencemeasurementshavealsobeenusedtostudyexcitonmigrationinconjugatedpolymers.PolymersthathavebeeninvestigatedincludePPV,33,32PPPV,34MEH-PPV,35,36CN-PPV,37LPPP,30,38andPFO.31Kerstingetal.32comparedthePLemissiondynamicsofPPVwiththoseofadistyryl-stilbenePPVoligomercomposedoftwophenylandtwophenyleneringsseparatedbythreevinylenemoities͑OPV3͒.Adynamicredshiftwasobservedforthepolymeremissionbutnotfortheoligomer,suggestingthattheshiftwasasso-ciatedwitharandomwalkoftheexcitonstowardslowerenergysiteswithintheDOS.Itwasalsoshownthatatroomtemperature͑RT͒,thetimerequiredforasingleexcitonhopbetweensiteswasр250fs.Understandingexcitonmigrationisimportantinthede-velopmentofefficientoptoelectronicdevicesbasedoncon-jugatedpolymers.Forexample,photovoltaicdevicesrelyonphotocurrentgenerationviaexcitondissociationintopairsofoppositelychargedpolarons.DissociationcanbepromotedataninterfacebetweentwodifferentmaterialsforwhichthepotentialoffsetsinHOMO͑highestoccupiedmolecularor-bital͒andLUMO͑lowestunoccupiedmolecularorbital͒lev-elsaresufficienttoovercometheexcitonbindingenergy.However,inmanypracticalcases,mostofthephotogener-atedexcitonsarecreatedatsomedistancefromtheinterfaceandhaveafinitelifetimetoreachthatinterfacebeforetheydecayradiatively.Itisthenimportantthatexcitonmigrationbeveryeffective.4InpolymerLEDshowever,excitonmi-grationisoftenresponsibleforreducingthequantumeffi-ciencyofthedevice.Itincreasestheprobabilityofexcitoncaptureatnonradiativetrapsandincreasestheeffectivewidthofthedeadzoneclosetothemetalcathodeswithinwhichtheexcitonscanbequenchedviadipole/image-dipoleinteractions.21,39Theexcitonmigrationprocesshasather-mallyassistedcomponent,26,27andthusexcitonquenchingisoftenreducedattemperaturesbelow200K.6,38

Thereareagrowingnumberofreportsthatdiscussul-trafastspectroscopymeasurementsonpolyfluorenes.31,40–43Herzetal.40investigatedtheroomtemperatureemissionfromorientedfilmsofPFO,annealedonarubbedpolyimidelayerbyPLup-conversionspectroscopy.Itwasshownthatatroomtemperature,excitonmigrationisresponsibleforthedynamicredshiftofthepolymeremissioninthefirst600psafterexcitationandforthefast͑3ps͒decayatthehigh-energysideofthePLemission.Itwasalsodemonstratedthatexcitonmigrationaccountsfortheincreaseinpolarizationratiothatoccurswithtimewhentheexcitationlaserispolar-izedperpendiculartotheaverageorientationofthePFOchains.Meskersetal.31studiedtheexcitationrelaxationatlowtemperatureinfilmsofpoly͑ethyl-hexylfluorene͒usingastreakcamerawithpicosecondresolution.At15K,theyob-servedadynamicredshiftofϳ45meVinthefirst400psfollowinglaserexcitationat3.08eV.Astheexcitationen-ergywasloweredbelowthelocalizationenergy(Elocϭ2.93eV),notime-dependentredshiftoftheemissionwasobserved.UsingaMonteCarlosimulationtheyshowedthat

¨rster-theredshiftofthePLcouldbedescribedassumingaFo

typeenergytransferwithacharacteristicradiusof3nm.

Inthispaper,wecomparetheemissiondynamicsofexci-tonsinPFOfilmsatbothRTand5K,preparedwithtwodifferentmorphologies,namely,spin-coated͑SC͒glassyfilmsandfilmscontainingafractionof␤-phasechains.44,45PFOintheso-called␤-phasemorphologyisparticularlyin-terestingforspectroscopicstudy.6,42,44,45IthasbeenshownthatwhenPFOisdrawnfromameltintotheformofafibreandthenconvertedintothe␤phase,thepolymerchainsarehighlyorderedandhaveaconjugationlengthofapproxi-mately30monomerunits.15Whether␤-phasechainsinthethinfilmsstudiedherearecharacterizedbysuchahighde-greeoforderisnotknown.However,itisclearfromthePLandabsorptionredshiftsobservedinboththeRTandthe5Kspectrathatthereisasignificantincreaseinconjugationlengthinthe␤phasecontainingfilmscomparedtoSC

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glassyfilms.Weshowthatthishighdegreeoforderresultsinverywell-resolvedPLemissionspectraat5K.Eachofthevibronicreplicasobservedinthe5KPLspectrumisrela-tivelynarrow(ϳ30meV)comparedtotheirenergeticspac-ing͑between40and110meV͒.Theresultingabsenceofsignificantoverlapbetweenthedifferentpeaksallowsmea-surementofthedecaysignaturesofexcitonmigrationacrossvirtuallytheentirePLspectrum.Thisisindistinctcontrastwithmostotherconjugatedpolymersystemsthathavebeenstudied.30,32–34,38Inthesematerials,stronginhomogeneousbroadening͑evenatlowtemperature͒masksalargepartofthediffusionprocess.Changesinthedecaydynamicsarethenonlyclearlyidentifiedatthehigh-energyendofthePLspectrum.Becauseoftheverywell-resolvedPLemissionspectrumof␤-phasePFO,weareabletoclearlyobserveeffectsthatareusuallymaskedbystronginhomogeneousbroadening.

Thepaperissplitintofivesections.AftertheIntroductionandtheExperimentalMethods,wedescribethecwPLemis-sionspectraofSCand␤-phasePFOinSec.IIIAandmakeinitialassignmentsofthevibrationalmodesofthepolymerthatcoupletotheelectronictransition.WethenpresentinSec.IIIBourresultsonthepicosecondPLemissiondynam-icsoftheSCand␤-phasePFOfilmsatbothroomtempera-tureand5K.WepresentcompellingevidenceforexcitonmigrationfromdynamicredshiftsoftheemissionandshowthattheenergeticDOSofanensembleof␤-phasechainsdispersedwithinaglassyPFOmatrixisaroundafactorof2narrowerthanthatfordisorderedspin-coatedfilms.TheDOSwidthsdeducedfromtheseexperimentsareconsistentwithspectrallinewidthsandwithestimatesfortransport-stateDOSwidthsestimatedfromtemperature-dependenttime-of-flightexperiments.EnergytransferoccursfromtheglassyPFOmatrixtothe␤-phasechainsinatimeshorterthanthetemporalresolutionofourdetector͑5ps͒.Theun-usuallywell-resolvedvibronicfeaturesobtainedfor␤-phasePFOsamplesatlowtemperatureallowtheexcitonmigrationtoalsoberevealedbyafastdecayofthePLatthehigh-energysideofeachofthevibronictransitionsandariseofintensitydetectedclosetoeachoftheirpeaks.Thefastcom-ponentarisesfromarapiddepletionofthehigherenergysites,whiletherisingcomponentindicatesthecorrespondingoccupationoflowerlyingsites.InSec.IV,weshowthatexcitonmigrationtoextendedpolymerchainswithalowerenergygapandhigherrigidityisfurtherrevealedbyatime-dependentdecreaseintheHuang-Rhysparameter.Finally,inSec.V,wepresentourconclusions.

II.EXPERIMENTALSECTION

A.Samplepreparation

swellingstresstobeappliedtothefilm,whichinducesanelongationinafractionofthepolymerchains,causingthemtoadopta21helixconformation.15Inthisconformation,theanglebetweentheplanesoftwoadjacentfluoreneunitsis180°͑seeFig.1͒,renderingthemhighlyplanar͑andeffec-tivelyribbonlike͒.WeestimatefromtheabsorptionspectrapresentedbelowthatϷ13%ofthePFOchainsadopta␤-phaseconformation.Becauseofthehighconjugationlengthofthe␤-phasechains,theyhaveasignificantlylowerenergygapthanthesurroundingamorphousPFOmatrix.Ithasbeenshown6,42,44,45thatfollowingexcitongenerationintheglassyPFOmatrix,efficientenergytransferoccurstothe␤-phasechains.Suchmaterialscanbeeffectivelyviewedasself-dopedpolymericsystems.

B.Methods

GlassySCfilmswerepreparedbydissolvingPFOat20mg/mlinchloroformandthenspincoatingontoaquartzsubstratetocreateafilmof350nmthickness.WehavefoundthatchloroformisagoodsolventforPFOandthatthereisvirtuallyno␤-phasechainformationinfreshspin-coatedglassyfilmspreparedfromit.The␤-phasechaincon-formationwasinducedinSCfilmsbyexposingthemtotolu-enevaporforaperiodof12h.Thisexposurecausesa

AllmeasurementswereperformedonPFOthinfilmsplacedinacontinuousflowheliumcryostat͑heldateitherroomtemperatureor5K͒.Continuouswave͑cw͒measure-mentsofthePLemissionweremadefollowingexcitationfromthe3-nmlineofaHeCdlaserandthendetectedusingacalibratedphotomultipliercoupledtoascanningmonochromator.AbsorptionmeasurementsweremadebyshiningthelightfromaxenonlampthroughthePFOfilmdepositedonaquartzsubstrate͑mountedonthecoldfingerinthecryostat͒.Thespectrumofthetransmittedlightwasmeasuredusingascanningmonochromatorandphotomulti-pliertubedetector.Thefilmwasthenreplacedbyablankquartzsubstrate,andtheopticaltransmissionwasthenre-measured.Bycomparingthetwospectra,therelativeabsorp-tionofthePFOwasdetermined.

Timeresolvedmeasurementsweremadebyexcitingthefilmsusing150-fspulsesfromthesecondharmonicofamode-lockedTi:sapphirelaseratawavelengthclosetothepeakofthePFOabsorption͑at365nm͒,ordirectlyintothe␤-phaseabsorptionmaxima͑at432nm͒.PLwascollectedwithalens,andimagedintoasubtractivedoublemonochro-mator.ThedynamicsofthePLdecay͑measuredataseriesofdiscretewavelengths͒werethendeterminedusingasyn-chroscanstreakcamera.Theexperimentalsetuphadatimeresolutionof5psandaspectrallydeoptimizedresolutionof3nmtoincreasethesignal.MeasurementsofthePLdecayweremadeevery3nmfrom430nmto0nm,whichcov-eredmostofthePFOemissionspectrum.ThePLspectraatdifferenttimes͑between5and900ps͒aftertheinitialexci-tationpulsewerethenreconstructedpointbypoint,bymea-suringtheemissionintensityforeachindividualwavelength.Thespectrometerandstreakcamerawerearrangedtohaveorthogonalslits,ensuringthatPLwasonlycollectedfromthecenteroftheexcitationregion.ControlmeasurementsdemonstratedthatthePLdecaykineticswereinsensitivetotheexcitationpower.

III.RESULTSA.cwspectra

Figure2͑a͒showstheabsorptionandcwPLemissionofaSCPFOfilmmeasuredatRT.Figure2͑b͒showsthesame

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FIG.2.ThecwabsorptionandPLofaspin-coated͑SC͒PFOfilmshownat͑a͒roomtemperature͑upperpanel͒and͑b͒at5K͑lowerpanel͒.ThePLwasexcitedat3nmusingaHeCdlaser.

FIG.3.TheabsorptionandPLofaPFOfilmcontaining␤-phasechainsat͑a͒roomtemperature͑upperpanel͒and͑b͒at5K͑lowerpanel͒.ThePLwasexcitedat3nmusingaHeCdlaser.

spectrameasuredat5K.ItcanbeseenthattheabsorptionspectrumischaracterizedbyaratherbroadbandthatdoesnotchangeverysignificantlyinwidthbetweenRTand5K.Theabsorptionbandoriginatesfromaseriesofinhomoge-neouslybroadenedvibronictransitionsfromthegroundS0tothefirstexcitedelectronicstateS1.TheRTPLspectrumischaracterizedbyaseriesoffeatureslocatedat423,447,476,and502nm.At5K,thewavelengthofeachofthetransi-tionsisredshiftedbybetween5and13nm͑beinglocatedat428,456,486,and515nm͒.Thepeakssharpenasthetem-peratureisreduced.Forexample,thewidthofthe423nmpeakis90meVatRTand60meVat5K.Thereisalsosomeredistributionofoscillatorstrength,withtherelativeinten-sityofthe428nmtransitionbeingalmosttwiceaslargeasthe455nmpeakat5K.

Figures3͑a͒and3͑b͒showtheabsorptionandthecwPLemissionofa␤-phasePFOfilmmeasuredatRTand5K,respectively.TheabsorptionspectrumischaracterizedatRTbyamainbandat390nmandanadditionalpeakat435nm.ThebroadbandoriginatesfrominhomogeneouslybroadenedS0→S1transitionsintheglassyPFOmatrix.Theabsorptionpeakat435nmhasbeenassigned44,45totheS0→S10-0transitionofthe␤-phasechains.Itappearsatalowerenergycomparedtothatoftheglassymatrix,asthe␤-phasechainsaremorehighlyconjugatedandthushavealowerenergygap.TheyarealsocharacterizedbyahigherstateoforderthantheglassyPFO,andthusthe0-0transitionisobservableinabsorptionasarelativelynarrowpeakhavingalinewidthof67meVat5K.Welargelydiscountthepossibilityofthisfeatureresultingfrominteractionsbetweenneighboringpolymerchains.Wecanreadilydetect␤-phaseemissionfromPFOthathasbeendilutedintoaninertpolystyrenematrixatlowconcentration͑equivalentto1partin104)andthenexposedtoatoluenevapor.Atsuchlowconcentrations,asignificantassociationbetweenindividualPFOmoleculesisratherunlikely,suggestingthatthe␤-phaseemissionorigi-natesfromanintrachainstateratherthananinterchainstate.

ThepeaksintheRT␤-phasePLspectraarelocatedat440,468,500,and533nm.The440nmPLpeakhasbeenassigned44,45totheS1→S00-0transition.The␤-phase0-0PLemissionpeakisthusredshiftedby16nmcomparedtothe0-0peakdetectedfromtheSCPFO,consistentwithasmallerenergy-gapforthe␤-phasechains.Asthetempera-tureisloweredto5K,thepeaksat468and500nmeachsplitinto͑atleast͒threepeaks.Inthe5K␤-phasePLspec-trum,wethusidentify7peaksat444,459,471,478,501,509,and517nm.AswasobservedintheSCPFOfilm,weseeasignificantnarrowingofeachofthepeaksinthePLspectrumasthetemperatureislowered.Forexample,the0-0peakhasalinewidthof9nm͑56meV͒atRTand4nm͑25meV͒at5K.

InFig.4weshowasemilogarithmicplotofthe5K␤-phaseandSCPLspectra,plottedagainstphotonenergy.

FIG.4.Acomparisonbetweenthe5KPLspectrumofaspin-coated͑SC͒PFOfilmandthatofa␤-phasecontainingfilm.Bothspectrawereexcitedat3nmusingaHeCdlaserandareplottedonalogarithmicordinatescaletomoreclearlyshowthevibronicfeatures.Thethickarrowidentifiesafeatureinthe␤-phaseemis-sionspectrumthatisassumedtocomefromtheemissionofexci-tonsthatremaininthesurroundingglassyPFOmatrix.Weidentifytheenergyseparationsbetweenthedifferentvibronicpeaksinthe␤-phasespectrumandthe0-0peakasdiscussedinthetext.

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Asthe␤-phasePLspectrumisratherwell-resolved,weareabletomakeatentativeidentificationoftheoriginofthesefeatures:Thepeaksat2.697eV͑459nm͒,2.628eV͑471nm͒,and2.5eV͑478nm͒correspondtoenergiesof712,1255,and1580cmϪ1belowthatofthe0-0transitionpeakat2.788eV͑444nm͒.WemarktheenergyseparationsbetweenthepeaksinFig.4.InourpreviouslyreportedRamanstudies46of␤-phasePFO,weidentifiedstrongRamanmodesat735,1281,and1604cmϪ1.Thepeaksat2.471͑501nm͒eVand2.3eV͑517nm͒correspondtoenergiesoftwice1255and1580cmϪ1fromthe0-0peak,respectively.Thepeakat2.432eV͑509nm͒isseparatedfromthe0-0peakbyanenergyequivalentto2876cmϪ1.Itispossiblethatthisfeatureoriginatesfromasummodeinvolvingboth1255and1580cmϪ1vibrationalquanta͑where1255ϩ1580ϭ2835cmϪ1).

TounderstandtheoriginoftheseRamanmodes,abinitiomolecularorbitalcalculationswerecarriedoutusingtheGaussian98WsoftwarepackageonaPCwithaPentium4processor.47,48ThevibrationalspectrumofafluorenetrimerwasmodeledusingtheRestrictedHartree-Fockmethodanda‘‘splitvalence’’basisset͑6-31G͒.Forthisparticularmethodandbasissetchoice,thecalculatedfrequencieshavetobescaledbyafactor0.inordertomatchtheexperi-mentalvalues.48OuranalysisindicatesthateachoftheseRamanmodescorrespondstoadifferentbackbonestretchingmodeofthefluorenemonomerandthusitisanticipatedthatsuchvibrationalmodescancoupletotheelectronictransi-tionsofthepolymer.OurmodelpredictsthattheRamanmodeat735cmϪ1correspondstoanin-planedeformationofthefluoreneunit,themodeat1281cmϪ1correspondstoaC-Cinterunitstretch,andthe1604cmϪ1modeisassociatedwithaphenyl-ringquadrantstretch.

ItcanbeseenthattheenergeticcoincidencebetweentheRamanmodesandPLpeaksthatwedetectisveryreason-able.Itisclear,however,thatsuchRamanmeasurementscontaincontributionsfromchainsofdifferentconjugationlength,whilethevibrationalspectrumthatweinferfromthePLspectrumoriginatesfromlongerconjugation-lengthchainsduetotheeffectofexcitonmigration.Polymerchainsthathavelongerconjugationlengthsareoftenassociatedwithlower-frequencyRamanmodes.However,wecanlargelydiscounttheeffectofconjugationlengthascausingthesmalldifferencebetweentheenergeticlocationsoftheRamanmodesandthevibronicfeaturesseeninthe5KPLspectra.InPFO,wefindthatchangesintheRamanfrequen-ciesthatoccurasafunctionofconjugationlengthareveryweak.Forexample,wehavecomparedthestrongphenyl-ringquadrant-stretchmode͑locatedaround1600cmϪ1)measuredfromathinfilmofafluoreneoligomer͑adimer͒withthatofaspin-coatedfilmofPFOpolymer,andfindthatthefrequencyofthismodeisonlyaround3cmϪ1higherinthedimercomparedtothepolymer.WehavealsocomparedthefrequencyofthisRamanmodeinaspin-coatedfilmofPFOwithbotha␤-phasePFOfilmandaPFOfilmwhichhasbeendrivenintoacrystallinephasebyheatingto220°Cfollowedbyaslowcooltoroomtemperature͑seeRef.6fordetails͒.WefindthatthecharacteristicRamanmodesshifttohigherfrequenciesinthe␤-phaseandcrystallinePFOfilmsbyaround1to2cmϪ1.Asboththe␤-phaseandcrystallineformsofPFOareassumedtohavealongeraverageconju-gationlengththanpolymermoleculesinaspin-coatedglassy-film,itappearsthatitistheconformationandthelocalenvironmentinwhichthemonomerfindsitselfthathasthemostprofoundeffectontheRamanmodesratherthantheconjugationlengthofthepolymer.ItisperhapsthisgeneralinsensitivityoftheRamanfrequenciesontheconjugationlengththatallowsustoachievesuchagoodcorrelationbe-tweentheresultsofourRamanandPLspectroscopymea-surements.Theremainingsmalldiscrepancybetweentheen-ergyofthefeaturesdetectedintheRamanandthePLspectroscopy͑ofaround25cmϪ1)canprobablybeac-countedforbytheexistenceofaphononwingassociatedwiththeelectronicorigin.30Theconsequenceofthepresenceofaphononwingisthatthetrueelectronicoriginfromwhichthevibronicpeaksshouldbemeasuredwouldinfactlieonthehigh-energysideofthe0-0vibronicpeakobservedhere.Inadditiontothiscorrection,thereareinfactanumberofothermolecularvibrationalmodesthatcanalsocoupletotheelectronictransitions.Thus,thesmallshiftsbetweenthefeaturesthatweidentifyinRamanandinPLmightbealsoexpectedasaconsequenceofpartialmixingwithothervi-brationalmodesofthemolecule.

ItcanbeseenthatintheSCand␤-phasePFOspectra,alltheabsorptionandemissionpeaksredshiftbybetween5and13nmasthetemperatureisreducedfromRTto5K.Thismightbeexplainedasaconsequenceofanincreaseinthedensity͑andthusdielectricconstant͒ofthepolymer,anef-fectthathasbeendemonstratedbyhigh-pressurestudiesofPPV.49However,suchredshiftscanalsooriginatefromin-creasesintheconjugationlengthofthepolymerchains.Theincreaseintheintensityofthe0-0peakinbothPLandabsorptionatlow-temperatureseemstosuggestthatthepolymerchainsaremoreplanar,indicatingthatthecontribu-tionfromincreasedconjugationplaysamoresignificantrole.SimilarbehaviorhasbeenobservedinPPVpolymers28andhasbeenassociatedwiththefreezingoutofthelibrationalandrotationalmodesatlowtemperature.Wefindthatthelinewidthofthe␤-phase0-0PLpeakreducesasthetem-peratureislowered,being9nm͑56meV͒atRTand4nm͑25meV͒at5K.ThefreezingoflibrationalmodesisindirectaccordwiththelinewidthreductionofthePLspectrumthatweobserve,andwethusconcludethattheplanarityandconjugationlengthof␤-phasechainsincreasesasthetem-peratureisreduced.Interestingly,wefindthatat5K,thelinewidthofthe0-0PLpeakisoverafactorof2narrowerthanthe0-0absorptionpeak͑25meVcomparedwith67meV͒.Sucheffectsareoftenobservedindisorderedorganicsemiconductorsandoccurasaresultofexcitonmigrationtothemostorderedand,thus,thelowestenergy-gapregionsofthefilm.Itisclearthereforethatthereisstilladegreeofdisorderwithinthehighlyordered␤-phasechains.Atpresent,theoriginofsuchadisorderisnotclear.Inthehighlyextended␤-phaseensemble,therewillstillbesomedistributionofconjugationlengths.However,theelectronicpropertiesofasinglechainwillsaturate,oncetheconjuga-tionlengthexceedssomecriticallength.Therefore,adistri-butionof͑verylong͒conjugation-lengthpolymer-chainsmay

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notbereflectedinasimilardistributionofpolymer-chainenergygaps.Rather,thebroadeningofthe0-0PLpeakmaywelloriginatefromthefactthatthe␤-phasechainsarepresentwithinaheterogeneous,glassyPFOmatrix.Itmaywellbethislattersourceofdisorder͑ratherthanaconjugation-lengthdistribution͒whichultimatelydetermineswhich␤-phasepolymerchainshavethelowestenergygap.Asweshowbelow,wecanfollowthedynamicsoftheexci-tonmigrationprocessbothinglassySCPFOandinthe␤-phasechaincontainingsamples.

Wecanestimatethefractionof␤-phasechainspresentinthesolvent-treatedfilmbyfirstsubtractingtheabsorptionspectrummeasuredonthefreshlyspin-coatedfilmfromthatmeasuredaftersolventexposure.Thisrevealsthe␤-phaseabsorptionspectrum.44,45Boththe␤-phaseabsorptionspec-trumandtheabsorptionspectrumoftheremainingglassymatrixarethenintegratedtofindtheirrelativeareas.Com-paringtheintegrals͑assumingthatboththeSCglassyPFOand␤-phasePFOhavesimilaroscillatorstrengths͒allowsustocalculatethefractionof␤-phasechainsinthematrix.Inthefilmstudiedinthiswork,thefractionofchainsthatas-sumethe␤-phasemorphologywasϷ13%.Suchananalysishaspreviouslybeenreportedindetailfor␤-phasePFOfilmsatRT.45

FromthespectrapresentedinFigs.2͑a͒and3͑a͒,wees-timatethatattheexcitationwavelength(␭ϭ365nm),theopticalabsorptionoftheglassyPFOmatrixis13timesgreaterthanthatofthe␤-phasecomponent.Thus,morethan90%oftheexcitonsareexpectedtobephotogeneratedintheglassyPFOmatrix.Followingphotoexcitation,almostcom-pleteenergytransferoccursfromthismatrixtothe␤-phasechains.FromFig.4itisapparentinthe␤-phaseemissionthatthereisaveryweakemissionpeakat2.92eV͑markedwithanarrow͒,whichwebelieveoriginatesfromthe0-0emissionpeakofexcitonsthatremaininthesurroundingmatrixthroughouttheirlifetime.TheintensityofthisfeatureisϷ700timesweakerthantheintensityofthe0-0bandofthe␤-phasePL.Italsoappearstobeslightlyshiftedtohigherenergy͑40meV͒comparedtothe0-0PLemissionpeakoftheSCfilm.Webelievethatthisapparentenergyshiftoriginatesfromself-absorptioneffectsbythe␤-phasechains.Theabsorptionmaximumofthe␤-phasechainsco-incideswiththelow-energytailoftheSC0-0emissionpeak.Theeffectofthisself-absorptionistoshifttheapparentmaximumoftheemissiontoslightlyhigherenergy.Self-absorptiononlymakesasmallcontributiontoitsrelativeweakness,astheSC0-0PLpeakapproximatelycoincideswiththeminimuminthe␤-phaseabsorptionspectrumob-servedat425nm.Fromtheanalysisofthe␤-phaseabsorp-tionspectra,weinfactfindthattherelativelinearabsorptionofthefilmat2.9eV͑correspondingtothepeakoftheglassyPFOemission͒isonlyϷ20%greaterthanthatat2.8eV͑correspondingtothepeakofthe␤-phaseemission͒.Thus,aftercorrectingforthefactthatthe5Kfluorescencequan-tumyieldofSCPFOisafactorof2largerthanthatof␤-phasePFO,6weestimatethatϾ99%oftheexcitonsgen-eratedintheSCPFOmatrixtransferto␤-phasechains.

FIG.5.The5KPLspectraof͑a͒aSCPFOfilmand͑b͒a␤-phasefilmexcitedat365nmusingafrequency-doubled,mode-lockedTi:sapphirelaserandmeasuredat5ps,100ps,and900psfollowingexcitation.ThecwPLspectrumexcitedat3nmusingaHeCdlaserisalsoshownforreference͑asathickline͒,alongsidethe900psspectrum͑shownasopencircles͒.

B.TimeresolvedPL

WefirstpresentmeasurementsofthePLdecayfrom␤-phaseandSCPFOfilmsat5Kfollowingultrafastexci-tationat365nm.Figures5͑a͒and5͑b͒showthePLemissionspectra,fromtheSCand␤-phasefilmsrespectively,atthreedifferenttimesfollowing365nmexcitation.Foracompari-son,wealsoplotthecwPLemissionspectraforboththeSCandthe␤-phasefilmsmeasuredat5K͑fullline͒ontopofthespectrameasuredat900ps͑opencircles͒.Thecwspectraare,inboththecases,normalizedtothe900psdataatthepeakofthe0-0emissiontransition.Itcanbeseenthatinbothmorphologies,thecwspectraarealmostidenticaltothosemeasuredat900ps,and͑apartfromasmallredshiftandrelativechangeinintensityofthepeaks͒areverysimilartothosemeasuredat5ps.Themoststrikingobservationisthatatalltimesbetween5and900ps,theemissionspectrafromthe␤-phasefilmissignificantlydifferentfromthatob-servedfromtheSCfilm.Inaddition,wedonotdetect͑withinthestreakcameranoiselimit͒anyglassy͑SC͒PFOemissionfromthe␤-phasefilm͑expectedaround420to430nm͒evenat5ps.Thesekeyresultsindicatethatontimescalesfasterthantheresolutionofourstreakcamera,alltheexcitonsphotogeneratedintheglassymatrixofPFOfilmsurroundingthe␤-phasechainshavetransferredtothe␤-phasechains.

Fasttransferprocesseshavebeenobservedviapump-probemeasurementsofexcitontransferfromPFOtothemo-leculardyetetraphenylporphyrin͑TPP͒indopedpolymerfilms.50Itwasfoundthatthetransfertimewashighlydepen-

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dentontherelativeconcentrationofTPPacceptormoleculesintheblendanditwasarguedthatenergytransferoccurred

¨rstertransfer.24Itwasshownthatat1.5%TPP͑byviaFo

mass͒,transferoccurredinatimeof3psthatdecreasedto1.5psataTPPconcentrationof8%.WhethertransferfromtheglassyPFOmatrixtothe␤-phasechainsoccursvia¨rstertransferisnotknown.ThefasttransfertimesthatweFo

¨rstertransfer.WeseearecertainlynotinconsistentwithFo

estimatethat13%ofthePFOchainsadopta␤-phasemor-phology,andthus͑onthebasisofthefasttransferfromPFOtoTPP͒itisnotunreasonablethatexcitontransfercould

¨rstertransfertothe␤-phasechainsintimeslessoccurviaFo

than5ps.Indeed,thealmostcompletetransferofexcitonstothe␤-phasechains͑evidencedfromthecwPLspectra͒indi-catesthatthetransferprocessislikelytobeveryfastcom-paredtonormalspontaneousemission.However,itisdiffi-culttoruleoutotherexciton-transferprocess,e.g.,excitontunnelingbetweenneighboringchains,whichalsomightbeveryfast.

Itisinstructivetodiscussourresultsinthecontextofotherpolymericsystems.Inparticular,energytransferhasbeenstudiedfromPFOtothepolymerpoly͑9,9-dioctylfluorene-co-benzothiadiazole͒͑BT͒.26Hereitwas

¨rstertransferoccurredfromnearest-proposedthatFo

neighborsitesbetweenPFOandBTpolymerchains.Suchanexcitontransferoccurredoveratimescaleofaround12ps.

¨rstertransferisafunctionofthede-TheeffectivenessofFo

greeofspectraloverlapbetweentheabsorptionoftheguestmaterialandthefluorescenceemissionofthehostmatrix.22,23Wefindthatthedegreeofspectraloverlapbe-tweenaBTguestandaSCPFOhost,andbetweena␤-phasePFOguestandaSCPFOhostareequal,towithin10%.Onthisbasis,wearenotabletoquantitativelyexplainwhytransfertothe␤-phasechainsproceedssignificantlyfasterthanitdoestoBTguestmolecules.Itisprobablethatthedifferenceintransferratesisrelatedtothenanoscalestruc-tureofthefilms.OurrecentstructuralstudiesonblendfilmsofBTandPFOindicatethatatlengthscalesoverwhichexcitontransferandmigrationoccur͑i.e.,10nmandbelow͒,thereisacomplexsubstructurethatweassociatewithfine-scalephaseseparation.Suchaphaseseparationmighteffec-¨rstertransfer,tun-tivelyhinderexcitontransfer͑eitherbyFo

neling,orhopping͒betweenPFOandBTmolecules.InthePFO—␤-phasePFOsystemstudiedhere,theremaybeamuchmorehomogeneousmixofthe␤-phaseguestmol-eculeswithintheglassyPFOhostwhichcouldaccountfortheenhancedenergytransferratesthatweobserve.

Ithasbeenshown31,32,35thatexcitonmigrationeffectscanbeidentifiedbytime-dependentredshiftsofPLemission.SimilareffectsarefoundforSCand␤-phasePFOfilms.Theenergyshiftsofthepeaksobservedinthecwspectraofthe␤-phasefilmat446nm͑the0-0peak͒andat471nm͑the0-11255cmϪ1vibronicpeak͒areshowninFigure6͑a͒.ThecorrespondingshiftsinthepeaksobservedinthespectraoftheSCfilmat428nm͑the0-0peak͒andat456nm͑the1stvibronicpeak͒areshowninFigure6͑b͒.Toidentifythepeakwavelength,wefittedthespectraldatawiththeGaussianfunctions.TheenergeticlocationEofeachofthefeaturesfollowsalogarithmiclawasexpected32withEϳln(time),

FIG.6.͑a͒Thetemporalenergyshiftsofthepeaksdetected͑inthecwspectra͒at446nm͑filledcircles͒and471nm͑opencircles͒fora␤-phasefilm.͑b͒Thetemporalenergyshiftsofthepeaksdetected͑inthecwspectra͒at428nm͑solidsquares͒and456nm͑opensquares͒foraSCPFOfilm.Bothsetsofdatawereexcitedat365nmusingaTi:sapphirelaserandarefittedtoafunctionoftheformEϳln(t)͑solidline,seetextfordetails͒.Notethattheordinatescaleusedtoplottheenergy-shiftobservedintheSCPFOismorethanafactorof2largerthanthatusedforthe␤-phase.Thisisbecausethetime-dependentenergyshiftsobservedintheSCPFOweremorethanafactorof2largerthanthoseseeninthe␤-phasefilms.

indicatingthatweareindeedobservingadynamicrelaxationoftheexcitonsthroughtheinhomogeneouslybroadenedDOS.Itcanbeseenthatinthe␤-phasefilm,the0-0peakredshiftsbyapproximately(25Ϯ5)meVbetween0and900ps,withtheshiftmainlyoccurringinthefirst400psfollow-ingexcitation.AsenergytransferfromtheglassyPFOtothe␤-phasechainshasalreadyoccurredinthetimeintervalbe-fore5ps,itappearsthattherelaxationprocessweareob-servingiscausedbyexcitonmigrationthroughanensembleofhighlyconjugated␤-phasechains.Itcanbeseencon-verselythatthe0-0peakintheSCfilmshiftsinenergyshiftby(55Ϯ7)meVbetween0and900ps—avalueincloseaccordwithothermeasurementsonpolyfluorenes.31Wecanuseourresultstocomparetherelativeamountofdisorderin␤-phaseandSCPFOfilms.WefindthattheenergyshiftobservedinSCfilmsisapproximatelyafactorof2largerthanthatobservedin␤-phasefilms.WeproposethatthelargerenergyshiftthatweobserveintheSCfilmoriginatesfromtheeffectofdisorderthatbroadenstheDOS.Thisisentirelyconsistentwiththeobserveddifferencesinresolu-tionforthespectralfeaturesinSCand␤-phasePFOfilms;thelinewidthsofthe␤-phaseandSC͑0-0͒PLemissionpeaksat5Kare25and60meV,respectively.IfweequatetheenergyshiftobservedintheSCfilmfollowingexcitation͑55meV͒withthewidthoftheDOS͑ashasbeendonefollowingsiteselectivefluorescencemeasurements,29͒wefindthattheenergyshiftisconsistentwithestimatesofthetransportstatesDOSwidthfromtemperature-dependenttime-of-flightdata51thatwerefittedtotheGaussiandisorder

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model.52Inthesemeasurements,aGaussianwidthofϳ80meVwasfoundfor1to3␮mthickSCfilmsofPFO.AsexpectedwithintheGaussiandisordermodel,52thetrans-portDOSwidthissome1.5timestheDOSforneutralex-citedstates.Time-of-flightdataarenotavailablefor␤-phasesamplesanditwillbeinterestingtoseehowheterogeneoussamplesofthistypebehavewithregardtochargecarriertransport.

Intheaboveanalysis,wehaveassumedthattherelaxationobservedisnotduetovibronicrelaxationwithintheS1manifold.ThisisconsistentwiththedemonstrationthatinPPVanditsoligomers,sucharelaxationoccursonatimescaleshorterthan100fs.32Inaddition,commontoallphenyl/phenylenebasedpolymers,thevibrationalmodesthatcouplemoststronglywiththeelectronictransitionsofPFOareC-Cstretchmodesthathaveanenergybetween0.2and0.16eV.28,46Thisisanorderofmagnitudelargerthantheredshiftthatweobservein␤-phasePFO.

Inaseparatecontrolexperiment,wehavemeasuredthePLredshiftfrom␤-phasePFOat5Kfollowingresonantexcitationofthe␤-phasecomponentofthefilmwiththelasertunedto432nm.Thiswavelengthcorrespondstoapositionclosetothepeakofthe␤-phase0-0absorptionmaximumwhichat5Kpeaksat435nm.Inthiscase,weexpectalloftheexcitonstobedirectlycreatedon␤-phasechainsastheabsorptionoftheglassymatrixisverylowatthiswavelength.Followingresonantexcitation,wefindthattheenergyshiftfollowingexcitationisreducedtoϷ6meV.Hence,bydirectlypumpingclosetothepeakofthe␤-phase0-0absorptionmaximum,wepopulateareducedsubsetof␤-phasechainshavingalongerthanaverageelectroniccon-jugationlengthandthuslowerenergygap.Thisisincontrasttothecaseofexcitationstransferredto␤-phasechainsfromtheglassyPFO.Hereany␤-phasechaincanbe,inprinciple,populatedandthustheenergyspreadoftheexcitonstatesthatareexcitedismuchlarger,resultinginalargerredshift͑25meV͒.

Tohighlighttheroleofexcitondiffusionon␤-phasechains,weplotinFig.7aseriesofdecaytracesmeasuredbothatthehigh-energysideofeachvibronicreplica͑labeledA,C,E,andG)andattheirpeakpositions͑labeledB,D,F,andH).Forreference,wealsoreplotthecwPLemissionspectrummeasuredat5K͑followingexcitationat3nm—i.e.,nonresonantexcitation͒andindicatethepositionsofthevariousmeasurementswitharrowsandcorrespondingalpha-beticallabels.Openarrowsdelineatevibronicpeakmeasure-mentsandfilledarrowsmeasurementsonthehigh-energysideofeachpeak.Itisfoundthatatallofthesewavelengths,thePLdecaycannotbedescribedbyasingleexponentialfunction.Ratherwefindthateachtraceisbetterfittedbytwoexponentialfunctionseitherhavingtheformof͑a͒bothafastandaslowdecaylifetimeorhavingtheformof͑b͒aninitialriseinintensityfollowedbyaslowdecay.Toquanti-tativelydescribethetime-dependentPL,thedatawerefittedtoafunctionoftheformM1eϪt/␶1ϩM2eϪt/␶2,whereMistherelativeweightingofeachexponentialand␶isadecaylifetime.Inthecase,wherewedetectaninitialriseinPLintensity,oneoftheexponentialprefactorshasanegativevalue.

FIG.7.ThePLdecaysmeasuredfora␤-phasefilmat5Kfollowingexcitationat365nmusingaTi:sapphirelaserareshownplottedonalogarithmicordinatescale.Measurementsmadeatwavelengthscorrespondingtothehigh-energysideofeachofthevibronicpeaksaremarkedA,C,E,andG.Thefilledarrowsidentifythewavelengthatwhichthemeasurementsweremadewithrespecttothe5KcwPLspectrum͑plottedonalogarithmicscaleintheleft-handpanel͒.DecaytracesB,D,F,andHweremeasuredatthepeakofeachofthevibronictransitions.Thecorrespondingwave-lengthsareidentifiedbytheopenarrowsintheleft-handpanel.

Specifically,wefindthatcase͑a͒͑fastandslowdecaycomponents͒areonlyobservedatthehigh-energysideofeachvibronictransition.Forexample,at439nm͑corre-spondingtothehigh-energysideofthe0-0peak͒,thePLdecayswithafastcomponentof25ps(Mϭ0.8)andaslowcomponentof150pslifetime(Mϭ0.2).Thefastdecaycomponentbecomesprogressivelylongeratwavelengthsclosetothepeakofthevibronictransition͑e.g.,itisϷ100psat441nm͒.Wealsoobservethatthefastriseandslowdecay͓case͑b͔͒isonlyobservedclosetothepeakofthetransition.Forexample,at444and477nm͑closetothepeakofthetransitionsobservedat445and478nm͒,therisetimesarebetween60and70ps,respectively,whicharethenfollowedbyslowdecaysof700and480ps,respectively.

IV.DISCUSSION

Weareabletoqualitativelydescribethisbehaviorbasedonamodelinvolvingexcitonmigration.Followinginitialexcitation,excitonstransferfromsitesofhigherenergytothoseoflowerenergy,losingexcessenergytothesurround-ingthermalreservoir.WhiletheargumentspresentedbelowapplyequallytotheSCandthe␤-phasecontainingPFOfilms,westressthatinthecaseofthe␤-phasecontainingfilm,weareonlyatthispointconcernedwiththeprocessesthatoccuraftertheexcitonshavebeentransferredfromtheglassyPFOmatrixtotheensembleof␤-phasechains.ThetransferratektfromasiteofenergyEiisproportionaltothenumberofsitesintheDOSwithenergylowerthanEiac-cordingto

kt͑Ei͒ϰ

͵Ei

Ϫϱ

k͑E͒␳͑E͒dE,͑1͒

whereEiistheexcitonenergy,␳(E)istherelativedensityofstates,andk(E)expressesthefactthatenergytransferbe-tweenstatesofdifferingenergymaybeafunctionoftheirenergeticseparation.Itcanbeseenthatastheenergyofthe

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excitondecreases,thetransferratealsodecreases.Theob-servedlifetime␶totatanyvalueofenergyEcanbeex-pressedusing

␶totϭ

1

,

krϩknrϩkt͑t,E͒͑2͒

wherekr,knr,kt(t,E)indicatetheradiative,nonradiative,andtheexcitontransferrates,respectively.Asmigrationpro-ceeds,thetransferratekt(t,E)approacheszeroandthusthepopulationdecaytimeincreases.TheenergyoftheexcitoneventuallyreachesaminimumenergyvalueofElocfromwherenofurthertransfertositesoflowerenergycanbeachieved.Thus,asindicatedbyEq.͑2͒,weobserveanin-creaseinthepopulationlifetimeastheexcitonsbecomelo-calizedinthetailoftheDOS.Suchexcitonsfindthatthenumberofsitesoflowerenergyontowhichtheycantransferissignificantlyreduced,resultinginanincreaseofthedecaylifetime.

ThedecayoffluorescencehavingalifetimesummarizedbyEq.͑2͒takestheformofasingleexponentialgivenbyN(t)ϭN0eϪt/␶tot.However,asitwasshowninFig.7thePLdynamicsatthehigh-energysideofeachvibronicpeakcanbedescribedusingtwoexponentialfunctionshavingafastandaslowdecaylifetime.Todescribethebiexponentialde-caythatweobserve,wemakethesimpleassumptionthattheexcitonpopulationNtotiscomposedoftwoessentiallyinde-pendentpopulations,whereNtotϭN1ϩN2.ThesolutionofthisequationhastherequiredbiexponentialformNtot(t)ϭM1eϪt/␶1ϩM2eϪt/␶2.Weassociatethefast͑25ps͒decaycomponentofthePLthatweobserveatthehigh-energysideofthevibronicpeakswithexcitonsthatareundergoingrapidenergytransfertolower-lyingstates.Theslower͑150ps͒decaycomponentismostlikelytooriginatefromtheradia-tivedecayofexcitonsthathavebecomelocalizedandareunabletoundergofurthertransfertolower-lyingstates.WeobservesuchfastinitialdecaysofPLatthehigh-energysideofeachofthevibronicpeaks,althoughitislesspronouncedwherethepeaksoverlaponeanother͑e.g.,forthepeaksat471and478nm͒.Transferofexcitonstolower-lyingenergystatescanalsobeinferredbythefastgrow-in͑60-70ps͒ofthePLthatisobservedaroundeachvibronicpeak.Thefactthatallofthevibronicpeaksredshiftatapproximatelythesamerateindicatesthatweareindeedobservingtherelax-ationofexcitonsthroughanensembleofdiscretestates.In-creasesindecaylifetimehaveonlypreviouslybeenobservedformeasurementsacrossthe0-0vibronictransitionsofcon-jugatedpolymers.30,32–34,38Thefactthatwehavebeenabletodetectsuchlifetimevariationsacrossallofthevibronictransitionsisafurthertestamenttotheunusuallywell-resolvedemissionspectraof␤-phasePFOfilms.Withthesesamples,itispossibletoobserveeffectsthatareusuallymaskedbyinhomogeneousbroadeningofthevibronicpro-gression.

Wenowdiscusstheevolutionoftheintensityofthedif-ferentfeaturesmeasuredinthePLspectraasafunctionoftimefollowingopticalexcitation.Forthesakeofsimplicity,weconcentrateourdiscussiononmeasurementsof␤-phasefilms;however,similarresultsarealsoobtainedfromSC

FIG.8.The5K␤-phasePLemissionintensityofthepeaksat459and471nmrelativetothatat446nm͑0-0peak͒plottedasafunctionoftimefollowingexcitationat365nmusingaTi:sapphirelaser.

films.Figure8showstherelativeintensityofthevibronicpeaksat459nmand471nmrelativetothe0-0peak͑at445nm͒measuredat5Kasafunctionoftimefollowingexcita-tionat365nmwiththepulsedTi:sapphirelaser.Itcanbeseenthatbothofthepeaksfallinintensityto25%and35%,respectively,oftheirinitialvaluesoverthetimeintervalbe-tween5and900ps.Weconsiderthatthiseffectisafurthermanifestationofexcitonmigrationtolowerenergysites.Rigidapolarmolecules͑as␤-phasePFOchainsareexpectedtobeatlowtemperature͒areoftencharacterizedbyverysimilargroundandexcitedstategeometries.Iftheconfigu-rationforthegroundandexcitedstatesisthesame,theor-thogonalityoftheeigenstatesmakesthe0-0transitiontheonlyallowedone.Vibronicallycoupledtransitionsbecomemoreallowedastheconfigurationcoordinatesbetweenthegroundandexcitedstatesdiverge.TheweightinggofthevibronicpeakscanbedescribedbyaPoissondistributiong(n)ϭSneϪS/n!,wherenisthevibrationalquantumnum-berandSistheHuang-Rhysparameterthatdescribesthemostprobablevibrationallevelexcitedduringtheelectronictransition.Extendedpolymerchainsareexpectedtobemorerigidandarealsomoreconjugated,i.e.,theyhavelowerenergygaps.Thus,asexcitonrelaxationproceeds͑towardssmallerenergygaps͒,theemissionincreasinglyoccursfrommorerigidpolymerchainsforwhichSisexpectedtobesmaller.Correspondingly,theweightingshiftstothelowernvibronicpeakswiththe0-0,ultimatelygainingalltheoscil-latorstrengthwhenSϭ0͑nodisplacementbetweengroundandexcitedstateconfigurationcoordinates͒.ThisbehaviorisshownschematicallyinFig.9with⌬Qtheshiftinconfigu-rationcoordinatebetweengroundandexcitedstategeom-etries.

AtRT,wefindthatatallwavelengthsbetween400and490nm,the␤-phasePLdecayswithanaveragelifetimeof(400Ϯ50)ps.Overthiswavelengthrange,weobservethatthePLemissionstartstodecayoveratimescalethatisshorterthanthetemporalresolutionofourdetectorandthatnogrow-inofintensityisobserved.ThePLemissionspec-trummeasuredat5psissimilartothesteady-statecwemis-sion,andnoenergyshiftinthepositionofthevibronicpeaksisobserved.ItappearsthatatRT,theexcitonmigrationis

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FIG.9.Aschematicrepresentationoftheexcitonmigrationpro-cess.⌬Qindicatesthechangeintheequilibriumconfigurationbe-tweenexcitedandgroundstates.

muchfasterthanthetemporalresolutionofourdetector,con-firmingotherreports,26,27thatsuchprocesseshaveather-mallyactivatedcomponent.

V.CONCLUSIONS

Weareabletomonitortheprocessesofexcitonmigrationinourfilmsusingthedynamicredshiftofemissionfollowingexcitation.TheDOSwidthsdeducedfromtheseexperimentsareconsistentwithspectrallinewidthsandwithestimatesfortransportstateDOSwidthsestimatedfromtemperature-dependenttime-of-flightexperiments.ExcitonmigrationisalsorevealedbyafastdecayofthePLatthehigh-energysideofeachofthevibronictransitionsdetectedinemission,andariseofintensitydetectedclosetotheirpeak.Thefastcomponentindicatesarapiddepletionofthehigherenergysites,whiletherisingcomponentindicatesthecorrespondingoccupationoflower-lyingsites.Excitonmigrationtoex-tendedpolymerchainswithalowerenergygapandhigherrigidityisfurtherrevealedbyatime-dependentdecreaseintheHuang-Rhysparameter.

ACKNOWLEDGMENTS

Wehaveperformedcwandtime-resolvedspectroscopyexperimentsonspin-coatedand␤-phasePFOfilmsat5Kandatroomtemperature.Wefindthatduetotherigidandextendednatureof␤-phasePFO,the5KPLspectraarecharacterizedbyaseriesofverywell-resolvedvibronicpeaks.ByacomparisonwiththepublishedRamandata,wehavebeenabletomakeatentativeassignmentofthevi-bronicmodesofthePFOmoleculethatcouplewiththeelec-tronictransition.Byfollowingthetime-resolvedPLemissionafterultrafastexcitation,wefindthatenergytransferoccursfromtheglassyPFOmatrixtothe␤-phasechainsinatimeshorterthanthetemporalresolutionofourdetector͑5ps͒.

WeacknowledgetheU.K.HEFCEforitssupportofthisresearchviatheJREIgrant‘‘Ultrafastfluorescencemeasure-mentsinphysics,chemistryandbiology’’andtheU.K.EPSRCviaresearchgrants‘‘Femtoseconddynamicsinnovelorganicandinorganicsemiconductors’’͑GrantNo.͒GR/M22529,‘‘Electronicstructureofphenyl-basedconjugatedoligomersandpolymers’’͑GrantNo.͒GR/M21201and‘‘Polymerblendsemiconductordevices’’͑GrantNo.͒GR/R261.M.A.acknowledgesboththeEPSRCandtheSar-dinianRegionalGovernmentofItalyforfinancialsupport.D.G.L.acknowledgestheEPSRCforfinancialsupport.TheauthorsalsothankRobertFletcherandJimO’BrienoftheDowChemicalCompany͑USA͒forprovidingthePFOpoly-merusedinthisworkandPaulLaneforacriticalreadingofthismanuscript.

*Presentaddress:TheBlackettLaboratory,ImperialCollege

London,PrinceConsortRoad,SW72BZ,London,UK.

Correspondingauthors.Electronicaddress:d.g.lidzey@sheffield.ac.ukElectronicaddress:d.bradley@ic.ac.uk‡

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