Insights on the Coupling of Plasmonic Nanoparticles from Near- Field Spectra Determined via Discrete Dipole Approximations - Barr et al.

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pubs.acs.org/JPCCArticleInsightsontheCouplingofPlasmonicNanoparticlesfromNear-FieldSpectraDeterminedviaDiscreteDipoleApproximationsJamesW.Barr,SagharGomrok,EliseChaffin,XiaohuaHuang,andYongmeiWang*CiteThis:J.Phys.Chem.C2021,125,5260−5268ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Couplingbetweenplasmonicnanoparticles(NPs)inNPassemblieshasbeeninvestigatedextensivelyviafar-fieldproperties,suchasabsorptionandscattering,butveryrarelyvianear-fieldproperties,andaquantitativeinvestigationofnear-fieldpropertiesshouldprovidegreatinsightsintothenatureofthecoupling.Wereportanumericalproceduretoobtainreliablenear-fieldspectra(QNF)aroundsphericalgoldNPs(AuNPs)usingdiscretedipoleapproximation(DDA).ThereliabilityofthemethodwastestedbycomparingQNFfromDDAcalculationswithexactresultsfromtheMietheory.WethenappliedthemethodtoexamineAuNPsassembledindimers,trimers,anduptopentamersinalineararrangement.Forthewell-studieddimersystem,weshowthattheQNFenhancement,duetocouplinginlongitudinalmode,ismuchgreaterthantheenhancementinQext.ThereisalinearcorrelationbetweentheQNFandQextpeakpositions,withtheQNFpeakred-shiftedfromtheQextpeakbyanaverageofapproximately12nm.Inthecaseofthemultimers,QNFspectrafromindividualsphereswerenotalwaysidenticalandbecomedependentonthespherelocation.Inthelongitudinalmodel,thecenterspherehasthestrongestQNFspectra.Forthetransversemode,wedifferentiatetwodifferentscenarios:transverse-Y,wherebothelectricfield(E)andlightpropagationvector(k)areperpendiculartothechainaxis,andtransverse-X,wherekisparalleltothechainaxis.Inthetransverse-Ymode,couplingleadstoreducedQNFspectraandthecenterspherehasthelowestQNFintensity.Inthetransverse-Xmode,thereisaretardationeffectfromthefrontspheretothebacksphere.TheQNFfromthefrontsphereisstrongerthanfromthebacksphere.Inaddition,duetothephaselaginthek-direction,theQNFintransverse-Xcandifferquitesignificantlyfromthatintransverse-Yforlargeparticles.TheseresultsprovidenewinsightsintothecouplingpropertiesofAuNPs.Collectively,theseresultscanbeunderstoodwhenoneconsidershowtheelectricfieldfrominduceddipolesonneighboringNPsaddswith,orsubtractsfrom,theincidentE-field.TheseresultsprovidenewinsightsintothecouplingpropertiesofAuNPs.DownloadedviaUNIVOFNEWMEXICOonMay16,2021at12:37:11(UTC).■couplinghasbeenperformedbyDolinnyi20,21whocompiledINTRODUCTIONAssembliesofplasmonicgoldnanoparticles(AuNPs)intoextensiveexperimentalstudiesandsupplementedthemwithdimers,trimers,andmultimershavebeenunderextensivecomplementarycomputationalresultsobtainedusingtheSeehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.studiesforthelast2decadesduetotheirfascinatingpropertiesgeneralizedMietheory.Theresultsofhiscompilationshowed1−17thattheearliersuggestedscalingdependencebyJainetal.14anddiversepotentialapplications.Agreatwealthofknowledgehasbeenaccumulated.Forexample,itiswell-doesnotalwaysholdandneedstobemodified.knownthatwhentheincidentelectricfieldisalignedparalleltoMostofthestudiesthatinvestigatecouplingbetweenNPsinthemultimeraxis,theresultingplasmonicresonancepeakinassemblieshavereliedonthefar-fieldpropertiessuchastheextinctionspectraisred-shiftedasthegapdistanceextinctionorscatteringspectra.22−24Thesefar-fieldpropertiesdecreases.Thisphenomenoncanbeexplainedeitherbycanbemeasuredquantitatively,andgoodagreementbetweenapproximatingtheparticlesaspointdipolesinteractingwiththeoryandexperimentalresultshasbeenobtained,yetitisthedipolarcouplingorbymakinguseoftheplasmonhybrid-near-fieldpropertiesthatarehighlyintriguing.Near-field9,18izationmodel.AscalinglawdependencebetweenthefractionalshiftofthepeakpositionandparticlegapdistancehasbeenproposedbyJainetal.14basedonexperimentalReceived:February4,2021resultsandnumericaldataobtainedviathediscretedipoleRevised:February16,2021approximation(DDA).SuchphenomenonhasbeencalledaPublished:March2,2021“plasmonicruler”andhasbeensuggestedthatitcouldbeusedtomeasuredistanceatthenanometerscalebasedontheshift19intheplasmonicpeak.Amorerigorousanalysisofthedimer©2021AmericanChemicalSocietyhttps://dx.doi.org/10.1021/acs.jpcc.1c010715260J.Phys.Chem.C2021,125,5260−5268

1TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleproperties,suchastheenhancedelectricfieldneartheparticleincidentelectricfield.ThepresentedQ=C/πa2isaextexteffsurface,canleadtosurface-enhancedRamanspectra(SERS)dimensionlessnumber,whereaeffistheeffectiveradiusofthefromRamanreportermoleculesadsorbedonthemetalsurface.givenNPassembly.ForaNPassemblyofn-spheres,ofasingleSERSnanoprobes,atermusedformetalNPscoatedwithmaterial,withthesameradiusr,a=n1/3r.FortheassemblyeffRamanreportermolecules,havebeendevelopedforavarietyofNPs,wehaveusedtheSPHERESmoduletogeneratetheofbiomedicalapplications.Itiswell-knownthatthegapassembledNPsystems.AllDDAcalculationsonNPassembliesbetweentheNPscanleadtohotspotsandthatthesehotspotsareperformedinamediumwithrefractiveindexm=1.33,cangiverisetostrongSERSsignals.Gap-enhancedSERSrepresentingtheaqueoussolution.WhenwecompareQextfordetectionsystemshavebeendevelopedandappliedformultimersystems,wenoticedthatweneedtoapplya25−28sensitivedetectionsinavarietyofsettings.Itiscriticallycorrectiontoaccountforthenumberofparticles.Ifthereisnoimportanttounderstandhowcouplingaffectsthenear-fieldcouplingbetweenthemultimers,onemayapproximatepropertiesinordertodevelopawell-informedgap-enhancedCext(multimers)=nCext(monomer).KnowingthatSERSdetectionsystem.Unfortunately,experimentalmeasure-Q(multimers)=C(multimer)/πa2extexteffmentsofthenear-fieldpropertiesofcoupledplasmonic7,13,16,29nC(monomer)systemsarequitechallenging.SERSspectrameasuredext1/3Q(multimer)==nQ(monomer)directlyfromexperimentalsystemscouldbesubjectedtoaextπ()nr1/32extnumberofexperimentaluncertainties,suchasunknown(2)numberofRamanreportermoleculesnearthesurface.Numericalcalculationsofnear-fieldpropertiesareusefulbutThiscorrectionwasappliedwhenwecompareQextforhavesufferedfromerrorsassociatedwithdiscretizationusedinmultimersystemswithadifferentnumberofparticles.30,31thenumericalmethods.Numericalnear-fieldresultshaveThenear-fieldspectraarecalculatedaccordingtoQNF(ω)=mostlybeenusedtovisualizetheelectricfieldenhancement⟨|E(ω)|2⟩/|E(ω)|2,whereEistheelectricfieldofincident00patternsbutarerarelyusedforquantitativecomparisons.lightandE(ω)istheelectricfieldnearthemetalsurface.Inthiswork,weprovideaproceduretocalculatetheelectricSpecifically,E(ω)istheresultaftertheDDSCATcalculationisfieldaroundasphericalmetalNPbasedonDDAcalculations.convergedandtheelectricfieldwithintheextendedvolumeWedemonstratethatanaccuratecalculationoftheelectriccoveringtheparticlesisobtainedforagivenfrequency,ω,offieldenhancementspectra,QNF,withinthecurrentimplemen-light.36Here,the⟨⟩representsthenumericalaveragetationofDDSCAT7.3,consistentwiththenear-fieldspectraperformedoverallsurfacepointsoftheNP(s).ThecalculatedproducedbytheMietheoryforasinglesphericalNP,canbeQNFspectraareusefulwhenelucidatingtheexperimentalSERSobtained.Thisisachievedbyevaluatingtheelectricfieldataenhancementfactor,whichisnormallydeterminedbygivendistanceawayfromthesphericalNPsurface,alongwithcomparingtheRamanintensityfromthesameamountofanappropriatechoiceofdipoledistanceusedinDDAdyemoleculesfreeinsolutiontotheRamanintensityofthesecalculations.Wethenappliedournear-fieldcalculationmethoddyemoleculesadsorbedonthemetalsurface.28IfoneassumestothecouplingofNPsfromdimerstopentamersofNPsinathatdyemoleculesmakeasinglemonolayeronthesurfaceoflinearchain.Thenear-fieldspectraaroundeachindividualNPs,thentheSERSenhancementfactorisapproximatetothesphere,ofaparticularmultimer,areobtainedandresultsrevealsquareofQ(SERSEF=Q2).InDDSCAT7.3,thetargetNFNFsalientfeaturesofcouplingthathavenotbeenreportedbefore.isrepresentedbydiscretedipoleslocatedonasimplecubicForexample,thenear-fieldspectraaroundanindividualspherelatticegrid.Thefinerthegrid,thesmallerthedipoledistance,inalinearchainofmultimersarenotofthesamestrengthandandthebettertherepresentationofthetarget.InourpreviousdependontheparticlepositionandpolarizationoftheE-field.study,37welocatedallsurfacesitesthatareonelatticepointEvidenceofcouplingbetweenNPsbeyondthenearestmetalawayfromtheparticlesurfaceandtheQNFisobtainedbyNPneighborisobserved.Thecomputednear-fieldspectraalsoaveragingall|E|2valuesoverthesesurfacesites.Thisapproach,revealtheretardationeffectandphaselageffect.Theseresultshowever,ledtoQNFspectrawithaspuriousshoulderpeak.providenewinsightsintothecouplingofmetalNPs.ThiscorrelatedtotheimperfectrepresentationoftheNPspherebythecubiclatticegrid,especiallywhentheQNFis■METHODScalculatedrightnearthesurfacepoints.WeusedtheDDAmethodasimplementedintheDDSCATInthecurrentstudy,wehavedevelopedanewalgorithmto32−347.3softwarepackageforallcalculations.TheDDAisancalculatetheQNFspectraataparticularradialdistance(Rsurf)approximationmethodusedtosolveMaxwell’sequationsawayfromtheNPsurface.Thiswasachievedby,first,markingwhereexactsolutions,suchastheMietheory,arenotavailableallthegridpointswiththeradialdistanceRNF=R+Rsurffromduetotheshapeofthetargetmaterial.TheDDAmethodhasthecenteroforiginofthesphere,whereRisthesphereradius.33,35beenwidelyusedandisdiscussedindetailelsewhere.TheAfterward,electricfieldswerecalculatedatthemarkedpointsfar-fieldpropertiessuchasextinction,absorption,andalongradialdistanceRNF.IfthemarkedpointisnotpreciselyscatteringarecalculatedasdiscussedintheDDSCATmanual.atRNF,alinearextrapolationbetweengridpointswasappliedTheextinctionspectra,Qext,arecalculatedfromtheextinctionsuchthatthecalculatedelectricfieldwouldbethevaluecrosssection,Cext,accordingtothedefinitionasimplementedexpectedatexactlyRNF.SupportingInformationFigure1inDDSCATshowsanexampleoftheQNFspectracalculatedforasphericalNAuNPwithDDSCATusingasmalldipoledistance(dd=0.34πkCext=2∑Im(EPinc,*jj·)nm)whenRsurfisvariedfrom0.3,0.5,1.0,and1.2nmaway||Eincj=1(1)fromthesurface.Ascanbeseen,theQNFobtainedimmediatelyneartheNPsurfacehasthespuriousshoulderwheretheindexjrunsoveralldipolesrepresentingthetarget,peak(∼670nm);however,asRsurfisincreased,theresulting2πPjistheinduceddipoleatthesitej,k=,andEincisthespectrumnolongerhasthisshoulderpeak.Thetrade-offisthatλ5261https://dx.doi.org/10.1021/acs.jpcc.1c01071J.Phys.Chem.C2021,125,5260−5268

2TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure1.Comparisonofextinction(Qext)andnear-field(QNF)spectraforMietheory(A,Bsolidlines)andDDAcalculations(C,Ddashedlines).TheDDAisperformedwithdipoledistancesof0.3nm(for15nmNPs)and0.4nm(for20,50,and80nmNPs).AllcalculationsusethedielectricconstantsofJohnsonandChristy.Figure2.Spectra(QextandQNF)for20nmAuNPdimers(A,B)and80nmAuNPdimers(C,D)withagapseparationof2,5,and10nm.TheE-fieldisparalleltotheinterparticleaxisasshownintheillustration(thelongitudinalmode).ThedashedlinesaretheQextandQNFforthemonomer,respectively.DDSCATcalculationsweredonewithdipoledistancesof0.2nm(for20nmNPs)and0.4nm(for80nmNPs).theoverallintensitydecreasessincetheelectricfieldisknownawayfromthemetalsurface.FluctuationsinQNFspectratodecreaseradiallyfromthemetalNPsurface.SupportingobtainednumericallyfromDDSCATaresmallaslongastheInformationFigure2showshowtheDDSCAT-calculatedQNF,dipoledistancesarekeptbelow0.5nm.evaluatedatRsurf=1.0nm,dependsonthegridresolutionInthecurrentstudy,wefocusonAuNPsofdiameters15,(from0.1to0.5nm)andcomparestheseresultstothoseof20,50,and80nm.ThesizesconsideredrepresenttwotheMietheory.TheQNFfromtheMieresultsistheanalyticalregimes:forthesmallersizeAuNPs(15and20nm),thesolutionevaluatedattheNPmetalsurfacelimitaccordingtoplasmonicpropertycontainsmostlydipolarcontribution,while37theequationgiveninourpreviouswork.ItisexpectedthatthelargersizeAuNPs(50and80nm)containcontributionsthespectraobtainedviatheanalyticalMieresultswillbehigherfromhigherordersduetotheretardationeffect.Inaddition,thanthespectraobtainednumericallyfromDDSCATatRsurfthescatteringcontributiontotheextinctionspectraofasingle5262https://dx.doi.org/10.1021/acs.jpcc.1c01071J.Phys.Chem.C2021,125,5260−5268

3TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure3.Spectra(QabsandQscat)fromAu20nm(A,B)andAu80nm(C,D)dimerswithE-fieldparalleltothedimeraxis(longitudinalmode),sameconditionsasinFigure2.DDSCATcalculationsweredonewithdipoledistancesof0.2nm(for20nmNPs)and0.4nm(for80nmNPs).AuNPbecomessignificantforthetwolargersizes(seemaximumpeakintensityinQextspectrachangesbyafactorof2SupportingInformationFigure3formonomerextinction,whenthereisstrongcoupling,thepeakintensityofQNFscattering,andabsorption,respectively).Allnumericalincreasesbyalmostafactorof50.RecallthattheSERScalculationshaveuseddielectricconstantsofJohnsonandenhancementfactorisproportionaltothe4thpowerofelectricChristy38measuredforametallicAufilm.Nosizecorrection2fieldenhancementorQNF.ThisimpliesthattheSERSwasappliedasitwasknownthatsizecorrectionforNPsisenhancementofRamanreportermoleculesonthesurfaceof39neededonlywhentheparticlesizeislessthan10nm.FortheplasmonicNPscouldexperienceupto1000-foldenhancementnear-fieldcalculation,wehavechosenRsurf=1.0nmandallascomparedwiththatfromasingleparticleattheseDDSCATcalculationswereperformedwithddkeptbelow0.5conditions.Thelongitudinalcouplingmodeleadstoanm.Figure1showstheQextandQNFspectraforasingleAusignificantincreaseintheintensityofthenear-fieldspectra.NPwiththefoursizesandcomparestheresultsfromtheMieManyhavediscussedtheshiftintheplasmonicpeaksduetotheory(1Aand1B)andfromtheDDA(1Cand1D).Thefar-couplinganditisunderstoodthatinthelongitudinalmodefieldproperties,suchastheQext,Qscat,andQabs,areinnear-thiscouplingleadstoalowerenergystatethatissuperperfectagreementwiththeMietheoryresults.TheQNFfromradiative.ThisisconfirmedbyexaminingthecontributionofDDSCATarealsoingoodagreementwiththeMieresultsabsorbanceandscatteringtotheoverallextinction.Thetwoexceptthattheoverallintensityisslightlylower.AverygoodsizesofAuNPsstudiedrepresenttwodistinctregimes:the20linearcorrelationisobtainedbetweenthepeakpositionandnmAuNPhaslittlescatteringcontributiontotheextinctionintensityinQNFfromDDSCATandMieresults(seecoefficientasamonomer,whilethe80nmAuNPhasaSupportingInformationFigure4).Thisshowsthatwecansignificantscatteringcontribution(seeSupportingInformationapplythismethodtoreliablyevaluatethenear-fieldspectraofFigure3).Figure3showsthecontributionofQscatandQabsforthesemetalNPsinmultimersusingDDSCAT.20and80nmAuNPdimersatthreedifferentgapdistancesandcomparesthemwiththemonomer.Thecontributionof■RESULTSANDDISCUSSIONthescatteringcomponentislowforthesmallersize(20nm;ACouplingofDimersintheLongitudinalMode.WeandB)butisverysignificantforthelargerparticlesize(80nm;firstexaminethecouplinginAuNPdimerswhentheincidentCandD).E-fieldisparalleltothedimeraxis(thelongitudinalmode).PaststudiesconsideringthecouplingofdimershavefocusedFigure2presentsQextandQNFatthreedifferentgapdistancesontheshiftinpeakpositionofQextforthelongitudinalmodefortwoAuNPsizes:20nm(AandB)and80nm(CandD).asafunctionofgapoverparticlediameter.WeperformedaTheQNFspectraareobtainedoneachspherefirst,andinthesimilaranalysisonthefractionalshiftasafunctionofgapovercaseofdimercouplinginthelongitudinalmode,thetwoparticlediameterforbothQextandQNFandournumericaldataspectraobtainedfromthetwospheresarethesame(withinsuggestthatthescalinglawdependencecanonlybeappliedtonumericalerrors)andthepresentedspectraareaveragedoveralimitedrange(seeSupportingInformationFigure5)ofthetwospheres.Theobservedfeatureinextinctionspectradueparticlesizes,consistentwithfindingsbyseverallater3,1421,40tocouplingisconsistentwithearlierstudies.Whenstudies.WefurtherexaminedthecorrelationofthepeakcomparedtotheQext,onenotablefeatureinFigure2isthepositioninQNFwithQextanddataarepresentedinFigure4.greaterQNFenhancementduetothecoupling.WhiletheThedataarefittedtoalinearequationy=x+12.2.Thepeak5263https://dx.doi.org/10.1021/acs.jpcc.1c01071J.Phys.Chem.C2021,125,5260−5268

4TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleDimerCouplingintheTransverseMode.Figure5presentstheQextandQNFforthedimercouplingwhenboththeE-field(E)andthelightpropagation(k)areperpendiculartothedimeraxis(thetransverse-Ymode).Inthistransversemode,weobservethatcouplingleadstoadecreaseinbothQextandQNFpeakintensityalongwithaverysmallblueshiftinthepeakposition.Thesmallerthegapdistance,thelowertheintensityinQextandQNF,theoppositetrendofthelongitudinalmode.Forthe20nmAuNPs,thegradualdecreaseinintensityisnoticeableasthegapdistancedeceases.Forthe80nmAuNPs,thedimersystemsallhaveweakerintensitiesthanthemonomer,butthedependenceonthegapdistancebecomeslessnoticeable.Thedecreaseintheextinctionspectrainthetransverse-Ymode(seeFigure6forNPgeometryalignment)couldbeseenFigure4.CorrelationplotbetweenQNFandQextpeakpositionsinthelongitudinalmode.Inthecaseofmorethanonepeakinthespectra,onlythelong-wavelengthpeakisincludedintheanalysis.DDSCATcalculationsweredonewithdipoledistancesof0.2nm(for15and20nmNPs),0.25nm(for50nmNPs),and0.4nm(for80nmNPs).positionofQNFisred-shiftedfromtheQextbyabout12nm.ItFigure6.(a)Illustrationoftheelectricfieldduetotheinduceddipolecanbenoticedthatforthelargeparticle,thedatapointsinasphericalparticlewhenonlythedipolarmodeisconsidered;(b)deviatefromthelinearrelationshipmorethanforthesmallerinthelongitudinalmode,theelectricfieldfromtheneighboringNPparticles.addswiththeincidentelectricfield,causingagreaterinduceddipole;TheredshiftinthepeakpositionofQNFascomparedtothe(c)inthetransverse-Ymode,theelectricfieldfromaneighboringNPpeakpositionofQextisgenerallyobservedineachsystem,addsagainsttheincidentelectricfield,causinganoverallreducedincludingthemonomerAuNPs,basedontheexactMieinduceddipole;and(d)inthetransverse-Xmode,theelectricfieldtheory.Theexactamountofshift,however,maydependonbetweenneighboringNPsmayaddwithoragainstdependingontheparticlesizeandthegapdistance.Amoredetailedstudyofthephaselagbetweenthespheres.relationshipbetweenthesetwowillbethefocusofafuturestudy.Figure5.Qext(A,C)andQNF(B,D)forthedimerinthetransversemode(thelightpropagationandE-fieldarebothperpendiculartothedimeraxis).Thetoptwoplots(A,B)areforthe20nmAuNPdimerandthebottomtwo(C,D)areforthe80nmAuNPdimer.DDSCATcalculationsweredonewithdipoledistancesof0.2nm(for20nmNPs)and0.4nm(for80nmNPs).5264https://dx.doi.org/10.1021/acs.jpcc.1c01071J.Phys.Chem.C2021,125,5260−5268

5TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticle14inanearlierstudy,althoughthisphenomenondidnotreceivemuchattention.Thephysicalreasonbehindtheintensitydecreases,however,iscongruentwithwhathasbeensuggestedwhenconsideringthecouplingofdipolarmodes.WerecallthatwithintheframeworkoftheDDA,thecentralequationtobesolvedistheinduceddipole{Pj}onallsites,whichisgovernedbythefollowingequation:ÄÅÅÉÑÑÅÅÑÑÅÅÑÑPjj=+arÅÅEEinc()j∑kj()rÑÑÅÅÑÑÅÅÇkj≠ÑÑÖ(3)wheretheelectricfieldatsiterjincludestheincidentfieldplusallelectricfieldsproducedbydipolesPklocatedatsitek.Theinduceddipoles{Pj}aresolvedself-consistentlyforeq3.WhentheincidentE-fieldisparalleltothedimeraxis,theresultantelectricfieldfromthedipoleontheneighboringNPaddswiththeincidentE-field,causingagreaterinduceddipole(P).Inthetransversemode,however,theresultantE-fieldfromtheneighboringNPisintheoppositedirectionoftheincidentE-field,whichcausesareducedoveralldipolemoment(seeillustrationinFigure6).Thegreaterinduceddipoleleadstoagreaterabsorptionandscatteringaswellasagreaternear-fieldenhancement.Areduceddipoleleadstoanoveralldecreasedabsorptionandscatteringandanoverallreducednear-fieldintensity.Thissimplephysicalpicturehelpstovisualizeandunderstandthechangeinnear-fieldintensityforNPsystems.CouplingofMultimers.EvidenceofdipolarcouplingbetweenNPsextendsbeyondthenearest-neighborNPandisseenwhenweexaminelargermultimersystems.WefirstconsidertheQNFspectraforalineartetramer.Inthiscase,theFigure7.QNFspectraobtainedfromthelineartetramerof15nmAutwospheresontheedgehavethesamespectra,whilethetwoNPswith2nmgapsforthelongitudinalmode(A)andtransverse-Yinthemiddlehavethesamespectraduetosymmetry.Figure7mode(B),shownseparatelyfromthetwoedgespheresandfromtwopresentstheQNFobtainedfromtheedgespheresversusthemiddlespheres,alongwithQNFfromthecorrespondingdimer.DDSCATcalculationsweredonewithadipoledistanceof0.2nm.middlespheresforthelongitudinalandtransverse-Ymodeconfigurations.Inthelongitudinalmode,theQNFfromthemiddlespheresisstrongerthanthetwoedgespheres.Inthelongitudinalmode,theadditiveeffectleadstoagreatertransversemode,theorderisswitched.Moreover,whetherinduceddipoleoneachsphere,withthecenterspherehavingfromedgespheresorfromthemiddlespheres,QNFfromthethegreatesteffectsinceitexperiencestheadditiveeffectsfromtetramerarebothhigherthantheQNFfromthedimerinthetheneighboringparticles(includingparticlesbeyondthelongitudinalmode,butQNFfromthetetramerarebothlowernearestneighbor)themost.Inthetransversemode,thethantheQNFforthedimerinthetransversemode.Thepeakoppositeistrueforthecentersphere(Figure8).positionintheQNFspectradidnotshiftfordifferentspheresinRetardationEffect.Intheabovediscussion,theaxisofthethelongitudinalmodebuthasasmallblueshiftforthelinearmultimersisperpendiculartothelightpropagation.transversemodeforthemiddlesphere.Moreover,peakWhenthelightpropagationisparalleltotheaxisofthepositionintheQNFforthelongitudinalmodelfromthemultimers,thepossibleE-fieldsareallperpendiculartothistetramerisred-shiftedfromthatofthedimer.axis,whichwouldbesimilartoadifferenttransversemodeInthecaseofapentamer,duetosymmetry,theQNFspectra(showninFigure6).Wewillrefertothisconfigurationassplitintothreesets,withthecenteronebeingdistinctfromthetransverse-X,whereasthepreviousdiscussedtransversemodetwoontheedgesandthetwonexttothemiddleone.QNFistransverse-Y.Inthetransverse-Xmode,thenear-fieldspectraspectrafromthemiddlesphereisthestrongestintheofthetwospheresarenolongerthesame.TheQNFforthefirstlongitudinalmodebutistheweakestinthetransversemode.sphereishigherthanthatforthesecondoneduetotheWehavealsoconfirmedthatthesephenomenaholdtrueforretardationeffect.Apartoftheelectromagneticfieldhasbeendifferentgapdistancesanddifferentparticlesizes.Weattributeabsorbedbythefrontsphere.Theintensitydifferencebetweenthisphenomenontothelong-rangecouplingeffectbetweenthetwospectradecreaseswhenthegapdistancebetweenthetheseparticlesinsteadofnearest-neighborcoupling.Ifthedimerincreases.Figure9presentsthe15nmAuNPdimercouplinghappensonlybetweenneighboringparticles,onearrangedinthetransverse-Xgeometry.ForsmallAuNPwouldnotexpectQNFforthecentersphereinthepentamertosystems,suchasthe15nmNPs,althoughtheQNFforthetwobedifferentfromthetwomiddlespheressincetheyhavethespheresinthetransverse-Xmodearenolongerthesame,thesamenumberofneighboringparticles.IfweconsiderthattheaverageofthesetwospectraisclosetotheQNFspectraforthecouplingextendsbeyondthenearestneighbor,thesetransverse-Ymode.Inaddition,theQextinthetransverse-XphenomenacouldallbeunderstoodusingthesameframeworkmoderemainsthesameastheQextforthetransverse-Ymodeofhowneighboringdipolesaddtothelocalelectricfield.Inthe(datanotshown).5265https://dx.doi.org/10.1021/acs.jpcc.1c01071J.Phys.Chem.C2021,125,5260−5268

6TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure10A.Previously,forthetransverse-Ymode,QextforthedimerislowerthantheQextforthemonomer.ItcanbeseenFigure10.ComparisonoftheQext(A)andQNF(B)forthe80nmAuNPdimerforthetransverse-Xmode,witha2nmor5nmgap,vsthetransverse-Ymode,witha2nmgap.DDSCATcalculationsweredonewithadipoledistanceof0.4nm.thatasthegapdistanceincreases,theQextforthetransverse-Xmodeincreasesfurtherandapproachesthatofthemonomer.Mostsurprisingly,theQNFinthetransverse-XmodebecomesmuchhigherthantheQNFinthetransverse-Ymode,withthetwosphereshavingdifferentintensitiesjustastheydidinthesmallerAuNPdimers.Asthegapdistanceincreases,theQNFforthetwospheresinthetransverse-Xmodedecreasesandapproachesthatofthemonomer.Figure8.QNFspectraobtainedfromthelinearpentamerof15nmAuThedifferencesinthetransverse-Xandtransverse-YmodesNPswith2nmgaps,shownseparatelyforeachsphereforthelongitudinalmode(A)andtransversemode(B).DDSCATcanbeexplainedwhenweconsiderthephasedifferencecalculationsweredonewithadipoledistanceof0.2nm.betweentheE-fieldalongthepropagationdirection.Whenthedimeraxisisparalleltok,thesecondNPexperiencesaphaselagfromthefirstspherebyϕ=kRaccordingtothetermexp(-ikR),whereRisthedistancefromthefirstNPtothesecondNP.ForsmallNPsystems,suchasa20nmAuNPdimerwitha2nmgap,thephasedifferenceissmall(takingλ=500−700nm,kR=0.09π∼0.06π).Therefore,thedipolesonthetwoNPsmaystillbeconsideredinphase.ThecouplingbetweenthetwoNPsinthetransverse-Xmodeissimilartothatinthetransverse-Ymode.TheE-fieldsfromtheneighboringNPaddnegativelytoeachother.However,thefrontNPwillabsorbapartoftheE-fieldsandlesswillpropagatetothesecondNP.Asaresult,thenear-fieldaroundthefrontNPbecomesslightlyhigherthanthenear-fieldaroundthesecondNP.TheFigure9.QNFforthetworespectivespheresofa15nmAuNPdimerextinctionspectraandtheabsorptionandscatteringspectrawitha2nmgaporientedparalleltothelightpropagation(transverse-forthedimerremainthesameforthetransverse-XmodeandXmode)plottedtogetherwiththeQNFofthesamedimerinthetransverse-YmodeforthesmallNPs.Foran80nmAuNPtransverse-Ymode.Theextinctionspectra,scattering,andabsorptiondimerwitha2nmgap,thephasedifferencebecomeslarge(kRbetweentransverse-Xandtransverse-Yareindistinguishable(datanot=0.3π∼0.2π).ThedipolesonthetwoNPswillnotalwaysbeshown).DDSCATcalculationsweredonewithadipoledistanceofinphase,rathertheymayhaveoppositedirections.Whenthis0.2nm.happens,theE-fieldfromtheneighboringNPcouldaddpositively,ratherthannegatively,tothelocalfieldsontheNP.Adifferentphenomenonisobservedforlargerparticles,suchThiscanresultinagreaterinduceddipoleontheNP,justasinas50and80nmAuNPs.First,theQextspectraforthethecaseofthelongitudinalmode,whichleadstostrongertransverse-Xarehigherthaninthetransverse-Yasshowninnear-fieldspectraaroundeachNP.Inthetransverse-Ymode,5266https://dx.doi.org/10.1021/acs.jpcc.1c01071J.Phys.Chem.C2021,125,5260−5268

7TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlethereisnosuchphaselag.ThedipolesontwodifferentNPsthemean-fieldapproachhasbeenappliedtodescribethe42,43arealwaysinphaseandtheyalwaysaddnegativelytoeachdipole−dipoleinteractioninthesehybridsystems.Theother.Thisexplainsthedifferenceobservedinnear-fieldnear-fieldspectraobtainedinthecurrentstudymightprovidespectrabetweentransverse-Xandtransverse-Ymodeforlargeadditionalinsightstothesehybridsystems.NPs.■ASSOCIATEDCONTENT■CONCLUSIONS*sıSupportingInformationWehavedevelopedanumericalproceduretoobtainthenear-TheSupportingInformationisavailablefreeofchargeatfieldspectra(QNF)atadistanceawayfromtheNPsurfacehttps://pubs.acs.org/doi/10.1021/acs.jpcc.1c01071.usingDDSCAT.WefirstestablishedthatthenumericallyNear-fieldspectraQNFobtainedfromtheDDAatobtainedQNFaroundasingleAuNPwithsizesrangingfromdifferentdistancesawayfromthemetalsurface,impact15to80nmprovidingconsistentresultswiththeMietheory.ofthedipoledistanceusedintheDDAcalculationonRelyingonthetooldeveloped,weinvestigatedthecouplingoftheQNFincomparisonwithMieresults,contributionsofAuNPsinlinearchainassemblies.TheQNFspectracalculatedscatteringandabsorptioncomponentsforsinglemetalaroundeachsphereleadtonewinsightsaboutthemechanismNPs,correlationbetweentheDDSCATresultsandMieofcoupling.resultsonthenear-fieldspectra,andscalingdependenceFirst,thewell-knownplasmonicpeakshiftintheofdimercouplinginthelongitudinalmodedeterminedlongitudinalmodeisobserved,buttheQNFshowsmuchviaDDA(PDF)greaterenhancementduetocouplingthanthatoftheQext.WhiletheQextintensitycouldincreasebyafactorof2to3,the■QNFpeakintensityincreasesbyafactorof50ormore.TheAUTHORINFORMATIONpeakoftheQNFisred-shiftedfromthepeakoftheQextbyCorrespondingAuthorabout12nm,otherwisethepeaksofthetwospectraareYongmeiWang−DepartmentofChemistry,TheUniversityofcorrelated.Inthecaseofmultimercouplinginthelinearchain,Memphis,Memphis,Tennessee38152,UnitedStates;theQNFaroundeachsphereisnotthesame.ThemiddleNPorcid.org/0000-0002-7418-9489;Email:ywang@experiencesthestrongestnear-fieldenhancementinthememphis.edulongitudinalmodethandotheedgeNPs.ForthetransverseAuthorsmode,oneneedstodifferentiatetwotypes:atransverse-YJamesW.Barr−DepartmentofChemistry,TheUniversityofmode,wherethelightpropagation(k)andE-field(E)arebothMemphis,Memphis,Tennessee38152,UnitedStates;Freed-perpendiculartothemultimerlinearaxis,andatransverse-XHardemanUniversity,Henderson,Tennessee38340,Unitedmode,wherekisalongthemultimeraxisandEisStatesperpendiculartothelinearaxis.Inthecaseofthetransverse-SagharGomrok−DepartmentofChemistry,TheUniversityYmode,weobservedreducedQextandreducedQNFduetoofMemphis,Memphis,Tennessee38152,UnitedStatescoupling.ThemiddleNPinamultimerwillhavetheweakestEliseChaffin−Freed-HardemanUniversity,Henderson,QNFwhencomparedtotheedgeNPs.Thetransverse-XmodeTennessee38340,UnitedStatesrevealsamorecomplexscenario.ForthesmallAuNPs,theXiaohuaHuang−DepartmentofChemistry,TheUniversityofQextandQNFfromthetransverse-XmodearesimilartothatinMemphis,Memphis,Tennessee38152,UnitedStates;thetransverse-YmodeexceptthattheQNFofthefrontNPisorcid.org/0000-0001-6265-3400higherthanthatofthebackNPduetoaretardationeffect.InthecaseofthelargerAuNPs,withasizegreaterthan50nm,aCompletecontactinformationisavailableat:differentresultisobserved.Forthissystem,theQNFinthehttps://pubs.acs.org/10.1021/acs.jpcc.1c01071transverse-Xmodecouldbemoreenhancedthanthetransverse-Ymode.WerationalizethesedatabyconsideringNoteshowtheE-fieldoftheneighboringparticlesaddsto,orTheauthorsdeclarenocompetingfinancialinterest.subtractsfrom,thelocalE-fieldsaccordingtodipolecoupling.■ThiscouldexplaintheenhancedQNFspectrafortheACKNOWLEDGMENTSlongitudinalmodeandthereducedQNFspectrafortheWethankProf.BruceDrainewhosuggestedwaystoimprovetransverse-Ymode.Itcouldalsoexplainthedifferenceinthetheaccuracyofnear-fieldspectra.ThisresearchwaspartiallyQNFspectraonthemiddleNPversustheedgeNPsandtheenabledbythefinancialsupportfromtheNationalInstitutesofdifferencebetweentransverse-Xandtransverse-Y.TheseHealthundergrantnumber1R15CA238890-01A1.resultsprovideanewinsighttounderstandthecouplingofAuNPs.■REFERENCESFinally,itshouldalsobenotedthatthenear-fieldspectra(1)Maier,S.A.;Kik,P.G.;Atwater,H.A.ObservationofCoupledobtainedinthisstudyarelimitedbythevalidityoftheclassicalPlasmon-PolaritonModesinAuNanoparticleChainWaveguidesofelectrodynamictheorytoaccuratelydescribetheplasmonicDifferentLengths:EstimationofWaveguideLoss.Appl.Phys.Lett.responsebymakinguseofthelocal,frequency-dependent2002,81,1714−1716.dielectricfunction.Althoughmanystudieshaveshownthat(2)Rechberger,W.;Hohenau,A.;Leitner,A.;Krenn,J.R.;Lamprecht,B.;Aussenegg,F.R.OpticalPropertiesofTwoInteractingsuchanapproachisvalid,oneshouldbeawareofpossibleGoldNanoparticles.Opt.Commun.2003,220,137−141.quantumeffectsinNPcouplingwhenparticlesizesaresmall(3)Encina,E.R.;Coronado,E.A.PlasmonCouplinginSilver(lessthan10nm)orthegapdistancebetweentheNPsisinNanospherePairs.J.Phys.Chem.C2010,114,3918−3923.41thesubnanometerrange.Additionally,interactionsof(4)Sh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