Monitoring Fast Thermal Dynamics at the Nanoscale through Frequency Domain Photoinduced Force Microscopy - Kim et al. - 2021 - Unknown

《Monitoring Fast Thermal Dynamics at the Nanoscale through Frequency Domain Photoinduced Force Microscopy - Kim 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/JPCCArticleMonitoringFastThermalDynamicsattheNanoscalethroughFrequencyDomainPhotoinducedForceMicroscopyBongsuKim,JunghoonJahng,AbidSifat,EunSeongLee,andEricO.Potma*CiteThis:J.Phys.Chem.C2021,125,7276−7286ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Inilluminatedtip−samplejunctions,theabsorptionoflightbythesampleisaccompaniedbylocalheatingandsubsequentthermalexpansionofthematerial.Inphotoinducedforcemicroscopy(PiFM)experiments,thermalexpansionisexpectedtoaffectthemeasuredphotoinducedforcethroughthethermallymodulatedvanderWaalsforce.EvidenceforsuchthermalcontributionsinPiFMmeasurementshasbeendemonstratedinthemid-infraredrange,wheretheprimaryexcitationsaremolecularvibrationalmodes.ForPiFMmeasurementsinthevis/NIR,wherelight-matterenergytransferismediatedthroughelectronicexcitations,clearexperimentalevidenceofthermalcontributionsremainselusive.BydevelopingafrequencydomainversionofPiFM,weretrievevariationsinthephotoinducedforceonthesub-μstime-scales,allowingadirectregistrationofthethermalrelaxationdynamicsofthesampleafterphotoexcitation.OurmeasurementsconfirmthepresenceofthethermalcontributiontothePiFMsignalinthemid-infraredrangeandprovidestrongexperimentalevidencethatthermalcomponentsalsoplayaroleintheforcesmeasuredinPiFMinthevis/NIRrangeofthespectrum.■INTRODUCTIONinfraredhasattemptedtoidentifythermalcontributionsin7Scanprobetechniquesthatuselightcoupledtothetip−photoinducedmicroscopy.Thedissipativevibrationalline-samplejunctiontakeadvantageoftheconfinedfieldsneartheshapesandthesignaldependenceonsamplethicknesshavetip’sapex.Inphotoinducedforcemicroscopy(PiFM),suchprovidedstrongindicationsofthepresenceofthermalnanofocusedfieldsexertanelectromagneticforceonthetip,contributionstotheforcemeasuredunderconditionsrelevant2,7whichcanbestrongenoughfordetectioninaconventionaltoPiFM.Inthiswork,weseektoestablishthepresenceofatomicforemicroscope.1,2Becausethelocalfieldsinthethermalcontributionsinanindependentfashion,namely,junctiondependonthepolarizabilityofboththetipandthethroughdetectingthepresenceofforcesinthePiFMsample,PiFMcanbeusedtogenerateimagesbasedonexperimentrelatedtothesamplerelaxationtime,afterthe3,4spectroscopiccontrastatthenanoscale.However,suchlaserilluminationhasbeenswitchedoff.electromagneticforcesareinevitablyaccompaniedbythermalThethermalandelectromagneticcontributionsaremanifesteffects,causedbythesample’sabsorptionofenergyfromtheondifferenttimescales.Whenthelightisswitchedoff,theDownloadedviaUNIVOFCALIFORNIASANTABARBARAonMay16,2021at10:45:01(UTC).Seehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.5localfieldsnearthetip−samplejunction.Thermalloadingatelectromagneticforcedisappearsinstantaneouslywhileex-thenanoscalecanproducelocalexpansionofthesample,pansioneffectsremainpresentonthetimescalesetbythefollowedbydiffusionofheatawayfromthesource.Sampleprocessofheatdissipation.Forinstance,foranobjectofexpansioncanaffectPiFMmeasurements,especiallywhenthicknessd,therelaxationorcoolingtimeτcafterlocalthermaloperatedincontactmode.Eveninnoncontactmode,thermallyloadingcanbeapproximatedasτ=4d2/(π2D),whereDisthecinducedmaterialexpansioncanaltertheforceexperiencedbythermaldiffusivity.6,11,12Forad=300nmlayerofathetip,suchasthroughthethermallymodulatedvanderWaalsrepresentativenonconductingorganicmaterialwithD∼1.0×6,7force,whichcanoverwhelmtheelectromagneticforce.10−7m2/s,thistranslatestoτ≈0.4μs,withshortercoolingcWhilenanoscalethermaleffectsaresometimesconsideredtimesforthinnersamples.Unfortunately,suchtimescalesareparasiticinPiFM,theyformthebasisforcontrastobservedinexpansionforcemicroscopy,suchasinphotothermal-inducedresonancemicroscopy(PTIR)andpeakforceinfraredReceived:January30,2021microscopy(PFIR).8,9AlthoughthephysicsoflocalRevised:March8,2021absorption,followedbythermalexpansionandheatdissipationPublished:March24,202110,11intothesurroundings,iswellunderstood,measurementofthecontributionsofsuchnanoscalethermaldynamicstothePiFMsignalhasbeennontrivial.Recentworkinthemid-©2021AmericanChemicalSocietyhttps://doi.org/10.1021/acs.jpcc.1c008747276J.Phys.Chem.C2021,125,7276−7286

1TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlebeyondthe∼1μslimitaccessiblethroughconventionaltime-Measurementsinthenear-IRareperformedonaVistascope13−15domainrecordingofcantileverdynamics,andspecializedmicroscope(MolecularVistaInc.,SanJose,US).ThetechniquesareneededtoimprovethetemporalresolutionofmicroscopeisinterfacedwithafemtosecondTi:sapphirethemeasurement.Severaladvancedtime-domainmethodslaser(MaiTaiDeepsea,Spectra-Physics),delivering200fshavebeendevelopedforrecordingfastprocessesinelectro-pulsesat80MHzrepetitionrate.Notethattheinterpulsestaticforcemicroscopy(EFM),approachingatimeresolutionseparationoftheTi:sapphirelaseris12.5ns,muchfasterthan16−18theexpectedcoolingtimes(0.1−1.0μs)ofthemolecularoftensofns.Inaddition,recentworkinforcedetectionthroughphotonicreadouthasenabledadirectmeasurementofsampleunderstudyhere.Thisimpliesthattheeffectivecooling11inbetweenpulsesisminor,andthustheincidentlightcanbenanoscalethermaldynamicsat∼10nsresolution.However,suchfasttime-domainmethodsarenoteasilycombinedwithconsideredasaquasi-continuousformofillumination.Thecantilever-basedPiFMmeasurements.Evenfasterdynamics,centerwavelengthistunedto809nm,whichcoincideswithdowntothefemtosecondtimescales,canbeaccessedthroughtheabsorptionmaximumofsilicon2,3naphthalocyaninepump−probetypeimplementationsofscanprobemicros-(SiNc).Thelaserlightisfocusedwithahighnumericalcopy.19−21Yet,pump−probemeasurementsarelesssuitableaperturelens(NA=1.42,Olympus)ontothesamplewithanforthesub-μstimescales,whererelevantthermaldynamicsaveragepowernotexceeding40μW.Acantileveredtipismanifestsitself.positionedinthefocalvolumeofthelens.Weuseagold-Toconfirmthepresenceofsub-μscoolingdynamicsaftercoatedsiliconcantilever(ACLGG,AppliedNanoStructures)photoinducedheating,wedevelopafrequencydomainforcewithafirstmechanicalresonanceatf0=150kHzandaseconddetectionmethodthatissensitivetotransientsampleresonanceatf1=950kHz.Thefirstresonancefrequencyisexpansion.RecentworkinEFMhasshownthatfrequencyusedformeasuringthephotoinducedforcedrivenbythedomaintechniquesrepresentanattractiveapproachtoaccessmodulatedlaserlightinthedirectmode(homodyne)22configuration,3implyingthattheamplitudeofthecantileversub-μscantileverdynamics.WeaimtomodifysuchafrequencydomainapproachtoassessforcedynamicsonthesemotionismeasuredatthemodulationfrequencyoritsshorttimescalesinPiFMmeasurementsusingaminimumharmonics.ThesecondmechanicalresonanceisusedastheamountofFouriercoefficients.SincesampleexpansionisAFMchannelbydrivingthecantilevermechanicallyatfd=f1.reflectedintheforcedynamicsthroughthethermallyThischannelprovidesamplitudefeedbackandisusedtomodulatedvanderWaalsforce,identifyingtheseforcesongeneratetopographicimages.Thesamecantileverconfig-sub-μstimescalesenablesanindependentverificationoftheurationisusedforboththeelectrostaticforcemicroscopypresenceofthermalcontributionstothePiFMexperiment.We(EFM)andPiFMmeasurements.InthePiFMmeasurements,usethissimplemethodtofirmlyconfirmthethermalthecantileverisdrivenwithanamplitudeof∼20nm.SimilarcomponentinMIR-PiFMmeasurements,wherethelight-totheMIRexperiments,thebeamispositionedsuchthatitsmatterheattransferoccursthroughvibrationalexcitations,andamplitudeatf1approaches90%ofitsmaximumvalue.Thistoexplorethepresenceofthermaldynamicsinvis/NIRPiFMpositioncorrespondstoasituationinwhichweexpectthermalexperiments,wheretheenergytransferismediatedthrougheffectstogrowinprominence.electronicexcitations.■MATERIALS■MATERIALSANDMETHODSThepolystyrene(PS)homopolymerisacquiredfromPolymerSourceInc.(Montreal,Canada).ThepolymerhasamolecularPhotoinducedForceMeasurements.PiFMmeasure-mentsareperformedonanatomicforcemicroscope(AFM)weightofMn=22.5kg/molandMw/Mn=1.08.ThePSpolymerisdissolvedintolueneanddropcastontoasiliconplatformcoupledtoaninvertedopticalmicroscope.Measure-substrate,formingawedge-likepatternattherimsofthementsinthemid-infrared(MIR)arecarriedoutonaVista-IRdepositupondrying.TheSiNcsampleisobtainedfromSigma-microscopesystem(MolecularVistaInc.,SanJose,US).TheAldrichanddissolvedintoluene.SiNcisdepositedona0.17microscopeiscoupledtoaMIRQCLsystem(MIRcatQCL,mmborosilicatecoverslipbydrop-castingthetoluenesolutionDaylightSolutionInc.,SanDiego,US)withatuningrangeof−1−1directlyontotheplasma-cleanedglasssurface,followedby1450to1810cm,aspectralresolutionof0.1cm,andovernightdryinginadesiccator.Theresultingdepositsvaryinvariablepulsewidth.Thesampleisside-illuminatedwiththeoheightfrom50to400nm.MIRbeamata40incidentanglerelativetothesamplesurfaceusingaparabolicmirrorwithanumericalaperture(NA)of∼0.4.TheaverageilluminationpoweroftheMIRbeamis■RESULTSANDDISCUSSIONapproximately∼3mWwithina21μmdiameterfocalspotonFrequencyDomainDetectionofCantileverDynam-thesamplesurface.Themicroscopeisoperatedinnoncontact/ics.Ourmethodisbasedondirectmode(homodyne)tappingmodewithagoldcoatedSicantilever(PPP-NCLAu,detectionofthePiFMsignal,wheretheforceiscommonlyNanosensorsInc.,Switzerland).Thefundamentalresonanceofdetectedatthemodulationfrequencyωoftheincidentlaserthecantileversusedisnearf0=150kHz,andthesecondlight.AstrongPiFMresponseisobtainedwhentheresonanceisf1=940kHz.TheQCLbeamismodulatedbymodulationfrequencyistunedtoamechanicalresonanceω0tuningitsrepetitionratetothefundamentaleigenmodeoftheofthecantileverbeam,i.e.,ω≈ω0.Theeffectivetimecantileveratfm=f0=150kHzawith50%dutycycle.Thefreeresolutionoftheexperimentcanbeimprovedbydetectingtheoscillatingnoncontact/tappingamplitudeistypicallyaround2forcealsoatovertonesofthemodulationfrequency,whichcannmatthesecondeigenmodeofthecantileverandthebeachievedbytuningthemodulationfrequencysuchthatω=experimentisperformedat88%ofthefreeoscillatingω/nwherenisthenthovertonefrequencyofω.0amplitude,wherethephaseisstillpositive,correspondingtoWebrieflydiscusshowthetime-varyingforcecanbewrittenthenoncontactregion.intermsofFouriercoefficients.Thedisplacementzofthe7277https://doi.org/10.1021/acs.jpcc.1c00874J.Phys.Chem.C2021,125,7276−7286

2TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure1.Frequencydomaindetectionofelectrostaticpotentialdynamics.(a)Schematicoftheexperiment.(b)Drivingvoltageacrossthetip−samplejunction.TheRCtimeiscontrolledbythepotentiometer.(c)TimedomainrecordingofvoltagetransientsatdifferentRCtimes(datapoints)alongwiththeirexponentialfits(solidlines).(d)Frequencydomainmeasurementofthepotential.Cantileveramplitudeisshownasthemodulationfrequency(fd)ischangedrelativetothecantileverresonancefrequency(f0).Insetshowsthecantileveramplitudeatfd=f0/2fordifferentRCtimes.(e)ExponentialdecaytimeversustheR2/R1ratiowithvaluesderivedfromthetime-domainexperiment(red)andcalculatedfromthefrequency-domainexperiment(black).AFMtipcangenerallybedescribedasadrivenharmonicω2/πωoscillatormodelbFm=∫()sin(tmωt)dtπ0(4)mzb̈+zk̇+=zFtd()(1)Wemayexpectthatthedrivingforcecanstronglycoupletowherem,b,karetheeffectivemass,dampingcoefficient,andthecantileverwhenaspecificnthfrequencycomponentspringconstantofthetip-cantileversystem,respectively.coincideswiththecantilever’sresonancefrequency(ω0),i.e.,BecausetheforceFd(t)thatdrivesthecantilevermotionisaω0=nω.Undertheseconditions,onlythenthcomponenttime-periodicfunction,itcanbeexpandedintoaFouriercouplestothecantilevermotion,whereasothercomponentsseries,asfollows(m≠n)areoff-resonantandcannotaffectthecantileverÄÅÅ∞ÉÑÑmotion.Thevariousn-componentsoftheforcecanbetunedÅÅaÑÑFt()=+FÅÅ0∑amcos(ωωtbm)+sin(t)ÑÑd0ÅÅnnÑÑintoresonanceone-by-onebychangingthedrivingfrequencyÅÅ2ÑÑÅÇm=1ÑÖ(2)ωandfulfillingtheconditionω=ω0/n.WecanthenrewritewiththeFouriercoefficientstheFouriercoefficientsasω2/πωω02/nπω0am=∫Ft()cos(mtdtω)an=∫Ft()cos(ω0td)tπ0(3)nπ0(5)7278https://doi.org/10.1021/acs.jpcc.1c00874J.Phys.Chem.C2021,125,7276−7286

3TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure2.FrequencydomainPiFMexperiment.(a)Schematicoftheexperiment.FortheMIRexperiments,lasermodulationisachievedbydirectlycontrollingthedutycycleofthesource.Forthevis/NIRexperiments,thelaserlightismodulatedwithanacousticopticmodulator.(b)Schematicrepresentationoftheevolutionofthephotoinducedforce,withthecharacteristicheatingtimeτhduringthe“on”periodandcoolingtimeτcduringthe“off”period.(c)Modulationscheme.Cantileverisdriventhroughthephoton-inducedforce,whichismodulatedateitherf0oratf0/2.ω02/nπω0FrequencyDomainDetectionofElectrostaticDy-bn=∫Ft()sin(ω0td)t(6)namics.Theprincipleandperformanceofthefrequencynπ0domainmethodisillustratedbyasimpleelectrostaticforcewherenlabelsthespecificFouriercoefficientofinterestthatismeasurement,asdepictedinFigure1a.Inthismeasurement,atunedintoresonancewiththecantilever.Withthesecantilevered,gold-coatedsilicontipwithafirstmechanicaldefinitions,wecanrewritethedrivingforceandsubstituteresonanceatf0=150kHzisplacedoveragoldcoatedglasstheresultingexpressionintotheequationofmotioncoverslipatatip−sampledistanceof0.3μm.Thepotentialbetweenthetipandthesampleistime-modulatedwithamzb̈+zk̇+=zRnncos(ωθ0t−)(7)square-wavepattern,wherethewavepatterniscontrolledbyadjustingtheRCtimewithapotentiometer.Thetimevaryingwheretheamplitudeofthetime-dependentforceispotentialV(t)isshowninFigure1b,andtheperiodicexponentialtailisdisplayedinFigure1cforvarioussettingsof22Rnn=+Fab0n(8)theRCtimeinthe50ns−1.4μsrange.Wemayexpectthefollowingtimeevolutionoftheelectrostaticforceanditsphaseisloo1∂Cts22/−tτ−1ijjbnyzzooooVe0,0<

4TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlecalculationbasedoneq10andR=+Fa22()ωωb()fordynamicswiththeeffectiveheating(τh)andcooling(τc)times,nnn0whicharebothderivedfromexponentialfunctionsasstatedinvarioussettingsoftheresponsetime.Theresultsareplottedineqs12;seeSupportingInformationformoredetails.WithinFigure1e,showinggoodagreement.Hence,usingasimpleR2/thismodel,theevolutionofthephotoinducedforceissketchedR1measurementinthefrequencydomainretrievestheinFigure2b.Notethatintheactualexperiment,dependingonexponentialresponsetimedowntoτ∼50ns.Whenthelevelofdissipativelossesandabsorptionsaturation,theapproachingτ∼50ns,theamplitudeofthephotoinducedheatingdynamicsmaydeviatefromthechosenfunctionalforceatf0/2reachesnoise-level,markingthistimelimitastheform.Nonetheless,thecurrentdescriptionissufficientforfastestprocessthatcancurrentlybeobservedwiththisestablishingthepresenceofdelayeddynamicsandformethod.providingan-order-of-magnitudeestimationofthecoolingFrequencyDomainDetectionofForceRelaxationtime.Ourgoalisthustoretrievetheτcandτhtimes,whichareDynamicsinPhotoinducedForceMeasurements.Theinthesub-μsrange,usingfrequencydomainPiFM.electrostaticmeasurementsdescribedaboveconfirmthatthisHavingdefinedthefunctionalformforthetime-periodicfrequencydomaindetectionprocedurecandeterminetheforce,theFouriercoefficientsdefinedineqs5and6canbepresenceoftime-delayedforcesexertedonthecantileverafterrewrittenasV0hasbeenswitchedoff.ThissimplemethodcanbereadilyappliedtoconditionsrelevanttoPiFMmeasurementsofFvdWω0an=[ff()ττch±()]molecularsampleswithopticalresonancesintheMIRorinthenπ(13)vis/NIRrange.WhenthePiFMsignalisdetectedbyÄÅÅÉÑÑ2heterodynedetection(alsocalledsidebandmode),theFvdWω0ÅÅÅÅ11±ÑÑÑÑmeasurementissensitivetoforcegradients,whichincreasesbn=−ÅÅ2+±ττccff()ττhh()ÑÑnπÅÅÇω0ÑÑÖ(14)thetechnique’ssensitivitytotheelectromagneticgradient3,24,25force.Inthecurrentwork,weusePiFMinthehomodynewherethefunctionfisdefinedasdetectionmode,whichincreasesthemeasurement’ssensitivity−nπτω/0τ(1±e)toothercontributionstotheforce,includingthetotalthermalf()τ=722expansionforce.Forthispurpose,wedevelopaprocedurefor1+τω0(15)extractingthelowestorderFouriercomponentstotheforceIneq13−15,theplus-minussignisdesignatedasplusunderhomodynedetection.Notethatthisdetectionmode(minus)whennisanodd(even)number.Thetwounknownsdiffersfromthedetectionstrategyusedinapreviouslydescribedfrequencydomainmethodforincreasingthetimeofinterestareτcandτh.FromthePiFMmeasurement,theresolutionofresolvingthecantileverdynamics.22amplitudeRnandphaseθncanberetrieved,allowingThesituationinPiFMisrelatedtotheelectrostaticdeterminationofthevaluesforanandbn.Thisallowsustomeasurementsabove,butnowtheforceexertedonthetipwriteτcandτhintermsofexperimentallyaccessiblevalues.Forthispurpose,wedefinetwonewvariables,namelyoriginatesfromthepresenceoflightcoupledtothetip−samplejunction,assketchedinFigure2a.ThelaserlightisamplitudeR2modulatedwithasquarewave,producingaphotoinducedR12≡R1(16)forcethatisperiodicallymodulated.ThemodulatedforcecanbesummarizedasandFt()=++Ftem()Ftth()FvdW()t(11)θθθ12≡−12(17)Toobtainanalyticalexpressions,wemayfurtherusethewhereFem(t)istheelectromagneticforce,Fth(t)isthethermalapproximatione−nπτω/0∼0,whichisreasonablewhenT/2≫expansionforce,andFvdW(t)isthethermallymodulatedvanderWaalsforce.Theelectromagneticforcefollowstheτ.Withthisapproximation,wecanwriteexpressionsforτcinmodulatedlaserlightinstantaneouslyandthusdoesnottermsofeitherR12orθ12,andthesameforτh.Byequatingthecontributetothemeasuredforceduringthe00,andtheminussignis0

5TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure3.FrequencydomainPiFMintheMIRrange.(a)Topographyofthesample,consistingofapolystyrene(PS)layeronaSiwafer.(b)PiFMsignalasafunctionofthefrequencyoftheincidentlight.ReddatapointsaremeasuredonthePS,whereastheblackdatapointsareobtainedontheSi.(c)On-resonancePiFMsignalofthePSlayerat1492cm−1andf=f.(d)Off-resonancePiFMsignalofthePSlayerat1530cm−1andfm0m=f.(e)On-resonancePiFMsignalofthePSlayerat1492cm−1andf=f/2.(f)Off-resonancePiFMsignalofthePSlayerat1530cm−1andf0m0m=f0/2.onthe(sub)-μstimescalesexaminedinthiswork.Thisdominantthermalcomponenttothedetectedforce,wewillappearsareasonableassumption,consideringthatthestartvalidatingourmethodusingMIR-resonantPiFMfirst.relaxationtimeofthe∼40nmAucoating(D=1.27×10−7ThesampleconsistsofaPSlayeratopaSisubstrate.Asshownm2/s)canbeestimatedasτ∼5ps,wellbelowtheeffectiveinFigure3a,thePSlayerdisplaysagradualchangeinctemporalresolutionofthemethoddiscussed.Shouldtip-thickness:fromtheonsetof∼100nmtoathicknessof∼600expansionplayaprominentroleintheexperiments,thenwenm.TheamplitudeofthePiFMsignalasafunctionofincidentmayexpectsignificantforcedynamicsduringthelaser“off”laserfrequencyisshowninFigure3b.WhenthePiFMsignalistimes,independentofthefeaturesofthesample.AswewillmeasuredoverthePSlayer,aclearincreaseofthePiFMamplitudeisseennear1492cm−1,correspondingtotheshow,nosuchsampleindependentdynamicsareobserved,fosteringconfidencethattheassumptionsmadearejustified.excitationofcarbon−carbonstretchingvibrationsoftheSeealsothediscussionontheeffectoftipexpansioninSectionaromaticring.WhenthePiFMsignaliscollectedovertheS2oftheSI.bareSisurface,noincreaseofthesignalduetovibrationalNanoscalecoolingdynamicsafterMIRexcitation.Weexcitationsisobserved.ThespatiallyresolvedPiFMsignalofwillusethefrequencydomainPiFMmethodandthemodelthePSlayerisshowninFigure3c,fortheon-resonancecase,describedintheprevioussectiontoconfirmthepresenceofaandinFigure3d,fortheoff-resonancecase,bothacquiredbyforcecontributionthatoriginatesfromtherelaxationdynamicstuningfmtof0.Notethattheon-resonancePiFMsignalafterthermalloadingofthesample.BecausePiFMmeasure-increaseswiththethicknessofthelayer:anindicationthat7mentsintheMIRrangehaveprovidedstrongevidenceofathermaleffectsmayplayarole.Figure3e,fshowsthesame7281https://doi.org/10.1021/acs.jpcc.1c00874J.Phys.Chem.C2021,125,7276−7286

6TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure4.HeatingandcoolingtimesextractedfromthefrequencydomainPiFMmeasurements.(a)Heatingtimemapat1492cm−1.(b)Coolingtimemapat1492cm−1.(c)Heatingtimemapat1530cm−1.(d)Coolingtimemapat1530cm−1.measurementwhenthemodulationfrequencyistunedtof0/2.Second,thecomputedvaluesforτcrangebetween300nsAtthisfrequencysetting,itisclearthattheon-resonancesignaland1μs,withthelayerthicknessvaryingbetween100and600nm.Forreference,usingD=1.17×10−7m2/sforstillrevealsthepresenceofthelayer,whereastheoff-resonance6signalhasreachedthenoisefloor.Wethusobservethatapolystyreneandalayerthicknessofd=400nm,weexpectmeaningfulPiFMsignalatf0/2isonlyobservedwhenthelightacoolingtimeofτc=0.55μs,whichisinthecorrectrangeoffieldresonantlydrivesthesample,i.e.,whenenergyisvaluesextractedfromthefrequencydomainPiFMmethod.Ittransferredfromthelaserexcitationfieldtothematerial.canalsobeseeninFigure4bthattheaveragevalueτcincreasesUsingthePiFMsignalcollectedatf0andf0/2,itisnowwiththicknessofthematerial.AlthoughthethicknesspossibletodetermineR12andθ12andcalculateτhandτcwithdependenceoftheretrievedτcvaluesdoesnotexactlytracktheexpected∝d2dependence,themethodprovidesagoodthemodeldescribedbefore.TheresultsarepresentedinFigure4forboththeon-resonantsignal(panelsaandb)andoff-order-of-magnitudeestimateofthecoolingtimewithintherelevantexperimentalrange.Weattributethediscrepancyresonantsignal(panelscandd).First,averagevaluesofτhandτthatarepositiveandnonzeroareonlyfoundfortheon-betweentheretrievedτcvaluesandtheexpectedtrendofthecthicknessdependenceonthesimplicityofthemodelfortheresonancesignal.Thevaluescomputedfortheoff-resonantthermaldynamicsandthelimitednumberofFouriersignalfluctuatearoundthenoiselevel.Thisisexpected,asnocoefficientsusedforreconstructingthetimedomaintime-dependentexpansionandrelaxationofthesampleisinformation.Nonetheless,evenwiththeapproximationspresentintheabsenceofenergyexchangebetweenthelightmadehere,themeasurementsclearlyreportthatforcefieldsandthematerial.Inaddition,thevaluescomputedfordynamicsonthe(sub)-μstimescalesisonlyobservedwhenthebaresiliconsurfacearealsoatnoiselevel.ThisisexpectedenergyistransferredtothePSlayeruponopticalexcitation.asSidoesnotstronglyabsorbattheMIRexcitationSincepreviousMIRPiFMmeasurementshaveunderlinedthefrequenciesusedhere.Thecombinationoflowabsorptiondominantcontributionofforcesrelatedtothermalexpansion,andthehighthermalconductanceofsilicon(140Wm−1K−1)weattributethepresenceof(sub)-μsforcedynamicsfoundinprecludesthepresenceofanydetectableexpansiondynamicsthecurrentexperimentstothethermalrelaxationdynamicsofoverthesubstratebeyondthe50nstimeresolutionofthethePSsample.Viceversa,thepresenceofsuchforcedynamics,method.Wemaythusconcludethatfinitevaluesofτhandτcaftertheilluminationhasbeenswitchedoff,providesanareonlyobservedwhenthemolecularsampledisplaysthermalindependentconfirmationofathermalcomponenttothedynamicsonthe(sub)-μstimescaleafterexcitationbythedetectedforce.laserfields.Notealsothatthisobservationunderlinesthattip-FrequencydomainPiFMmeasurementsinthevis/expansionisnotlikelytoplayasignificantroleintheNIR.TheMIRexperimentsdescribedintheprevioussectionmeasurements,asitwouldhavegivenrisetoobservedforcesuggestthatifforcedynamicsispresentduring“off”timesofdynamicsoverboththebareSisurfaceaswellasoverthePSthelaser,thenclearPiFMsignalsinthef0/2channelareunderoff-resonantconditions.Neitherareobservedhere.observedandreasonableestimatesofτcvaluescanbeextracted7282https://doi.org/10.1021/acs.jpcc.1c00874J.Phys.Chem.C2021,125,7276−7286

7TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure5.FrequencydomainPiFMofa100nmsilvernanoparticle.(a)Topographyimage.(b)PiFMrecordedwithfm=f0.The809nmlaserlightispolarizedalongthedirectionofthearrow.(c)Topographysignalwhenfmischangedtof0/2.(d)PiFMrecordedwithfm=f0/2.(e)Topographysignalwhenfmischangedtof0/3.(f)PiFMrecordedwithfm=f0/3.usingonlythefirsttwoFouriercoefficientsofthetime-mayexpectonlynonzerocontributionsfortheresonancedependentforce.Wemaynowattempttousethesameconditionfm=f0/ninthefrequencydomainwhennisanoddmethodtoexaminethepresenceoftentativethermalinteger.AfrequencydomainPiFMmeasurementconductedcomponentstotheforcedetectedinPiFMwhentheforevennshouldyieldnosignificantcontribution,whereastheilluminationisinthevis/NIR.Unliketheconvincingevidencecontributionsforoddnwouldstillbesignificant.forthermalcontributionstotheforceinMIRPiFM,aclearFigure5showsthePiFMsignalfroman∼100nmdiameterdemonstrationofthermaleffectsinvis/NIRPiFMmeasure-silvernanoparticlewhenilluminatedwitha200fslaserbeammentshasremainedelusive.Ourhypothesisisthatifclearwithacenterwavelengthof809nm.Theleftcolumnsignalsinthef0/2channelarefoundandthecorrespondingτcrepresentsthetopographysignalfordifferentmodulationvaluesaredeterminedtobeintherangerepresentativeoffrequenciesofthelaserlight.Eventhoughtheexcitationlightthermalcoolingdynamics,thenthermalexpansionforcesplayaismodulatedatdifferentfrequencies,thetopographysignalisroleinvis/NIRPiFMmeasurementsaswell.alwayscollectedinthef1frequencychannel.TheimagesintheWewillfirststudyacasewheretheexpansionforcesareleftcolumnthusunderlinethatachangeinlasermodulationnegligibleonthetimescalesrelevanttotheexperiment.Forfrequencydoesnotchangethenatureofthetopographysignal.thispurpose,wechoosesilvernanoparticles,whichexhibitaTherightcolumnshowsthePiFMdatacollectedatdifferenthighthermaldiffusivityconstantofD=1.66×10−4m2/sforfrequenciesf/nforthedifferentharmonicordersn=1,2,3.0bulksilver.Forad=100nmsilverparticle,wemayexpectaInFigure5b,thePiFMsignalisshownwhenfmistunedtof0coolingtimeoftheorderofseveraltensofpicoseconds,well(n=1),revealingtheexpectedPiFMresponseoftheenhancedbelowthetimeresolutionofourfrequencydomainPiFMlocalfieldsattheparticle.NotethatthedetectedPiFMsignalstechnique.Thisimpliesthatthetime-periodicforceappearsarestrongestalongthepolarizationdirectionoftheincidentsymmetriconthetimescaleofthemeasurement,andthuswelight,aclearindicationthatPiFMissensitivetothelocal7283https://doi.org/10.1021/acs.jpcc.1c00874J.Phys.Chem.C2021,125,7276−7286

8TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticle26−29electricfield.InFigure5d,thePiFMsignalisshownforn=2.Whilethesignalforn=1isstrong,thesecond-ordersignalisvirtuallynegligibleasthePiFMamplitudeisatthenoisefloorofthemeasurement.Whenn=3,theimagereappearsinFigure5f,albeitwithloweramplitude.Infact,theamplituderatioofthef0andf0/3measurementsisabout3:1.Theabsenceofasignalatf0/2andthe3:1ratiobetweenthefirstandthirdharmonicsoffindicatethatthemeasuredforceexhibitsasymmetric,time-periodicprofile,i.e.,asquarewave,atthetimescaleoftheexperiment.Thethermaldynamicsis,therefore,muchfasterthan50ns,asexpectedfor100nmsilvernanospheres.TheAgnanoparticlemeasurementsconfirmthatintheabsenceofforcedynamicson(sub)-μstimescalesduring“off”times,nosecond-orderPiFMsignalsaredetected,eventhoughthefirst-orderandthird-ordersignalsPiFMareregisteredathighsignal-to-noiseratios.InFigure6,weshowresultsofPiFMmeasurementsonalayerofSiNc,amolecularsamplethatexhibitsastrongelectronicabsorptionnear809nm.Thetopographyimageshowninpanel6arevealsalayerofSiNc,withathicknessvaryingbetween250and450nm.ThePiFMimagerecordedatthe809nmelectronicresonanceisshowninFigure6bforn=1,whereastheimagecollectedforn=2isshowninFigure6c.Itisclearthat,unliketheAgnanoparticle,theSiNclayergivesrisetoasignificantPiFMamplitudeinthen=2frequencychannel,adirectreflectionofthepresenceofforcedynamicsduringthe“off”period.Noticethatthesignalcollectedovertheglasscoverslipisatnoiselevelforbothfrequencycomponents,anindicationthatnoforcedynamicsaremeasuredintheabsenceofSiNcmolecules.Wealsonotethatthesignalinthen=2channelapproachesnoiselevelwhenthelaseristunedawayfromtheelectronicresonance(seeSectionS3oftheSI).SimilartotheMIRmeasurements,theseobservationsinthevis/NIRunderlinethatthef0/2isonlypresentwhen(1)thesignaliscollectedoverthemolecularlayerand(2)theexcitationwavelengthistunedintoresonancewiththesample.WeattributetheobservedforcedynamicsoftheSiNcsampletothethermalexpansionrelatedvanderWaalsforce.WeobservethatforthesampleshowninFigure6,theretrievedcoolingtimesvaryintherange0.2−1.2μs:valuesofthesameorderofmagnitudeasexpectedforanonconductingorganicmaterialwithD∼1.0×10−7m/s2andthicknessintheFigure6.FrequencydomainPiFMofalayerofsilicon250nm−450nmrange.SimilartotheresultsfoundintheMIRnaphthalocyanine(SiNc)depositedonglass,collectedwiththeexperiments,thesimilaritybetweenthetimescaleofthelaserwavelengthtunedto809nm.(a)Topography.(b)PiFMimagemeasuredforcedynamicsandtheexpectedcoolingtimesoftherecordedatfm=f0.(c)PiFMimagerecordedatfm=f0/2.sampleprovidesstrongevidencethatPiFMissensitivetothermalexpansionforcesviatheirimprintsonthevandertriviallyaccessedincantilever-basedscan-probemeasurements.Waalsforce.Withnootherphotoinducedforcesthatmanifestthemselvesonthistimescale,weassigntheobservedforcedynamicsto■CONCLUSIONthethermalrelaxationofthesample,inparticular,throughtheInthiswork,wehavestudiedthepresenceofforcedynamicsrelaxationofthethermallymodulatedvanderWaalsforce.onthe(sub)-μstimescalestoestablishanindependentThisnotionisfurthersupportedbytheabsenceofsuchexperimentalverificationofthermalexpansionforcesthathavedynamicswhenthetipisplacedoverthebaresubstrate(siliconbeensuggestedtoplayaroleinPiFMexperiments.Toenableorglass),whenthemolecularsampleisilluminatedunderoff-suchmeasurements,wehavedevelopedarelativelysimpleresonantconditionsorwhentheexpectedcoolingdynamicsfrequencydomainscanprobeversionofPiFM.Wefindthatbyareordersofmagnitudefasterthantheresolvingpowerofthecollectingonlythetwolowestorders(n=1,2)oftheFouriermethod(asinthecaseoftheAgnanoparticles).componentsofthephotoinducedforce,convincinginforma-OurexperimentsintheMIRrangeconfirmrecentfindingstionontheexistenceof(sub)-μsforcedynamicscanbethatthethermalexpansionforcecanplayadominantroleinobtained.Usingthismethod,theextracteddynamicsarefoundforcemeasurementscarriedoutunderconditionsrelevanttotobeinthetemporalrangeexpectedfortherelaxationofthePiFMtechnique,fosteringconfidencethattheforcethermalsampleexpansion,atimescalethatisotherwisenotdynamicscanbeascribedtotheexpectedrelaxationofthe7284https://doi.org/10.1021/acs.jpcc.1c00874J.Phys.Chem.C2021,125,7276−7286

9TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlesample’sexpansionafterlight-inducedthermalloading.Inforcesinphotoinducedforcemicroscopy.Phys.Rev.B:Condens.addition,ourmeasurementsinthevis/NIRrangeprovideMatterMater.Phys.2014,90,155417.independentexperimentalevidencethatthethermalexpansion(4)Jahng,J.;Fishman,D.A.;Park,S.;Nowak,D.B.;Morrison,W.forcecanalsoplayanimportantroleinPiFMmeasurementsA.;Wickramasinghe,H.K.;Potma,E.O.Linearandnonlinearopticalwhenthesampleisdrivenviaelectronicresonances,especiallyspectroscopyatthenanoscalewithphotoinducedforcemicroscopy.Acc.Chem.Res.2015,48,2671−2679.inthelimitwhenthesampleisthick(d>100nm).(5)Yang,H.U.;Raschke,M.B.Resonantopticalgradientforce■interactionfornano-imagingand-spectroscopy.NewJ.Phys.2016,ASSOCIATEDCONTENT18,053042.*sıSupportingInformation(6)Jahng,J.;Potma,E.O.;Lee,E.S.Tip-EnhancedThermalTheSupportingInformationisavailablefreeofchargeatExpansionForceforNanoscaleChemicalImagingandSpectroscopyhttps://pubs.acs.org/doi/10.1021/acs.jpcc.1c00874.inPhotoinducedForceMicroscopy.Anal.Chem.2018,90,11054−11061.Discussiononthevalidityofthethermaldynamics(7)Jahng,J.;Potma,E.O.;Lee,E.S.NanoscalespectroscopicmodelandadditionalfrequencydomainPiFMexperi-originsofphotoinducedtip−sampleforceinthemidinfrared.Proc.mentsonmolecularsamples(PDF)Natl.Acad.Sci.U.S.A.2019,116,26359−26366.(8)Dazzi,A.;Prater,C.B.;Hu,Q.;Chase,D.B.;Rabolt,J.F.;■Marcott,C.AFM−IR:combiningatomicforcemicroscopyandAUTHORINFORMATIONinfraredspectroscopyfornanoscalechemicalcharacterization.Appl.CorrespondingAuthorSpectrosc.2012,66,1365−1384.EricO.Potma−DepartmentofChemistry,Universityof(9)Wang,L.;Wang,H.;Wagner,M.;Yan,Y.;Jakob,D.S.;Xu,X.G.California,Irvine,California92697,UnitedStates;NanoscalesimultaneouschemicalandmechanicalimagingviapeakDepartmentofElectricalEngineering&ComputerSciences,forceinfraredmicroscopy.Scienceadvances2017,3,No.e1700255.UniversityofCalifornia,Irvine,California92697,United(10)Dazzi,A.;Glotin,F.;Carminati,R.TheoryofinfraredStates;orcid.org/0000-0003-3916-6131;nanospectroscopybyphotothermalinducedresonance.J.Appl.Phys.Email:epotma@uci.edu2010,107,124519.(11)Chae,J.;An,S.;Ramer,G.;Stavila,V.;Holland,G.;Yoon,Y.;AuthorsTalin,A.A.;Allendorf,M.;Aksyuk,V.A.;Centrone,A.NanophotonicBongsuKim−DepartmentofChemistry,UniversityofAtomicForceMicroscopeTransducersEnableChemicalComposi-California,Irvine,California92697,UnitedStatestionandThermalConductivityMeasurementsattheNanoscale.JunghoonJahng−HyperspectralNano-imagingLab,KoreaNanoLett.2017,17,5587−5594.ResearchInstituteofStandardsandScience,Daejeon34113,(12)Katzenmeyer,A.M.;Holland,G.;Chae,J.;Band,A.;Kjollerc,K.;Centrone,A.Mid-infraredspectroscopybeyondthediffractionSouthKorealimitviadirectmeasurementofthephotothermaleffect.NanoscaleAbidSifat−DepartmentofElectricalEngineering&2015,7,17637−17641.ComputerSciences,UniversityofCalifornia,Irvine,California(13)Bak,W.;Sung,B.;Kim,J.;Kwon,S.;Kim,B.;Jhe,W.Time-92697,UnitedStatesresolvedobservationofthermallyactivatedruptureofacapillary-EunSeongLee−HyperspectralNano-imagingLab,Koreacondensedwaternanobridge.Appl.Phys.Lett.2015,106,013102.ResearchInstituteofStandardsandScience,Daejeon34113,(14)Chim,Y.H.;Mason,L.M.;Rath,N.;Olson,M.F.;Tassieri,SouthKorea;orcid.org/0000-0001-9444-1824M.;Yin,H.Aone-stepproceduretoprobetheviscoelasticpropertiesCompletecontactinformationisavailableat:ofcellsbyAtomicForceMicroscopy.Sci.Rep.2018,8,1−12.(15)Wang,L.;Wang,H.;Vezenov,D.;Xu,X.G.Directhttps://pubs.acs.org/10.1021/acs.jpcc.1c00874MeasurementofPhotoinducedForceforNanoscaleInfraredSpectroscopyandChemical-SensitiveImaging.J.Phys.Chem.CNotes2018,122,23808−23813.Theauthorsdeclarenocompetingfinancialinterest.(16)Giridharagopal,R.;Rayermann,G.E.;Shao,G.;Moore,D.T.;Reid,O.G.;Tillack,A.F.;Masiello,D.J.;Ginger,D.S.■ACKNOWLEDGMENTSSubmicrosecondTimeResolutionAtomicForceMicroscopyforTheauthorsthankfinancialsupportfromtheNationalScienceProbingNanoscaleDynamics.NanoLett.2012,12,893−898.Foundation,grantCHE-1414466andCMMI-1905582.JJand(17)Dwyer,R.P.;Nathan,S.R.;Marohn,J.A.MicrosecondESLthanksupportfromtheNanoMaterialTechnologyphotocapacitancetransientsobservedusingachargedmicrocantileverasagatedmechanicalintegrator.ScienceAdvances2017,3.DevelopmentProgram(2016M3A7B6908929),fundedbythe(18)Mascaro,A.;Miyahara,Y.;Enright,T.;Dagdeviren,O.E.;NationalResearchFoundationofKorea(NRF)andtheGrütter,P.Reviewoftime-resolvednon-contactelectrostaticforceCommercializationPromotionAgencyforR&DOutcomes(-microscopytechniqueswithapplicationstoionictransportmeasure-COMPA)(1711123356)fundedbytheMinistryofSciencements.BeilsteinJ.Nanotechnol.2019,10,617−633.andICT(MSIT).(19)Jahng,J.;Brocious,J.;Fishman,D.A.;Yampolsky,S.;Nowak,D.;Huang,F.;Apkarian,V.A.;Wickramasinghe,H.K.;Potma,E.O.■REFERENCESUltrafastpump-probeforcemicroscopywithnanoscaleresolution.(1)Rajapaksa,I.;Uenal,K.;Wickramasinghe,H.K.ImageforceAppl.Phys.Lett.2015,106,083113.microscopyofmolecularresonance:Amicroscopeprinciple.Appl.(20)Schumacher,Z.;Spielhofer,A.;Miyahara,Y.;Grutter,P.ThePhys.Lett.2010,97,073121.limitoftimeresolutioninfrequencymodulationatomicforce(2)Nowak,D.;Morrison,W.;Wickramasinghe,H.K.;Jahng,J.;microscopybyapump-probeapproach.Appl.Phys.Lett.2017,110,Potma,E.;Wan,L.;Ruiz,R.;Albrecht,T.R.;Schmidt,K.;Frommer,053111.J.etal.Nanoscalechemicalimagingbyphotoinducedforce(21)Schumacher,Z.;Rejali,R.;Pachlatko,R.;Spielhofer,A.;Nagler,microscopy.ScienceAdvances2016,2.P.;Miyahara,Y.;Cooke,D.G.;Grütter,P.Nanoscaleforcesensingof(3)Jahng,J.;Brocious,J.;Fishman,D.A.;Huang,F.;Li,X.;Tamma,anultrafastnonlinearopticalresponse.Proc.Natl.Acad.Sci.U.S.A.V.A.;Wickramasinghe,H.K.;Potma,E.O.Gradientandscattering2020,117,19773−19779.7285https://doi.org/10.1021/acs.jpcc.1c00874J.Phys.Chem.C2021,125,7276−7286

10TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticle(22)Borgani,R.;Haviland,D.B.Intermodulationspectroscopyasanalternativetopump-probeforthemeasurementoffastdynamicsatthenanometerscale.Rev.Sci.Instrum.2019,90,013705.(23)Martin,Y.;Abraham,D.W.;Wickramasinghe,H.K.High-resolutioncapacitancemeasurementandpotentiometrybyforcemicroscopy.Appl.Phys.Lett.1988,52,1103−1105.(24)Jahng,J.;Kim,B.;Lee,E.S.;Potma,E.O.Quantitativeanalysisofsidebandcouplinginphotoinducedforcemicroscopy.Phys.Rev.B:Condens.MatterMater.Phys.2016,94,195407.(25)Yamanishi,J.;Naitoh,Y.;Li,Y.J.;Sugawara,Y.Heterodynetechniqueinphotoinducedforcemicroscopywithphotothermaleffect.Appl.Phys.Lett.2017,110,123102.(26)Huang,F.;AnanthTamma,V.;Mardy,Z.;Burdett,J.;KumarWickramasinghe,H.ImagingNanoscaleElectromagneticNear-FieldDistributionsUsingOpticalForces.Sci.Rep.2015,5,10610.(27)Tumkur,T.U.;Yang,X.;Cerjan,B.;Halas,N.J.;Nordlander,P.;Thomann,I.PhotoinducedForceMappingofPlasmonicNanostructures.NanoLett.2016,16,7942−7949.(28)Tumkur,T.;Yang,X.;Zhang,C.;Yang,J.;Zhang,Y.;Naik,G.V.;Nordlander,P.;Halas,N.J.Wavelength-DependentOpticalForceImagingofBimetallicAl−AuHeterodimers.NanoLett.2018,18,2040−2046.(29)Rajaei,M.;Almajhadi,M.A.;Zeng,J.;Wickramasinghe,H.K.Near-fieldnanoprobingusingSitip-Aunanoparticlephotoinducedforcemicroscopywith120:1signal-to-noiseratio,sub-6-nmresolution.Opt.Express2018,26,26365−26376.7286https://doi.org/10.1021/acs.jpcc.1c00874J.Phys.Chem.C2021,125,7276−7286