Chiral Optical Force Generated by a Superchiral Near-Field of a Plasmonic Triangle Trimer as Origin of Giant Bias in Chiral Nucleation

《Chiral Optical Force Generated by a Superchiral Near-Field of a Plasmonic Triangle Trimer as Origin of Giant Bias in Chiral Nucleation》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/JPCCArticleChiralOpticalForceGeneratedbyaSuperchiralNear-FieldofaPlasmonicTriangleTrimerasOriginofGiantBiasinChiralNucleation:ASimulationStudyHiromasaNiinomi,*TerukiSugiyama,An-ChiehCheng,MihoTagawa,ToruUjihara,HiroshiY.Yoshikawa,RyuzoKawamura,JunNozawa,JunpeiT.Okada,andSatoshiUdaCiteThis:J.Phys.Chem.C2021,125,6209−6221ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Wepreviouslyreportedthatgiantcrystalenantio-mericexcess(CEE)canbeobtainedwhensodiumchlorate(NaClO3)chiralcrystallizationfromasolutionisinducedbytheexcitationoflocalizedsurfaceplasmonresonance(LSPR)ofaAutriangletrimernanostructurebyacircularlypolarizedlaser.However,theroleoftheLSPRexcitationinthegiantCEEremainsunclear.Inthiswork,weshowed,byfinite-differencetime-domainanalysisofplasmonicnear-field,thatthemagnitudeofachiralopticalgradientforceoriginatingfromthestrongsuperchiralnear-fieldattheAutrimernanogaponavirtualNaClO3chiralcrystallineclusteriscomparabletothatoftheelectric-fieldgradientforceinpreviouslaser-trapping-inducedcrystallizationfromunsaturatedsolution.WerevealedthatthegiantCEEresultedfromadifferenceinthefrequencyofattachmentofchiralcrystallineclusterstocrystalnucleiorinthelocalconcentrationduetochirallybiaseddiffusionratherthanenantioselectiveopticaltrapping.1.INTRODUCTIONofthischirallight−matterinteractionisconsideredtobeduetothelargedifferenceinscalebetweenchiralmoleculesandChiralityisafundamentalpropertypresentinvariousthehelicalpitchofCPL,whichisdeterminedbyitshierarchiesinnature.LifeonearthshowsapreferenceforL-11aminoacidsandD-sugars,despitetheequalthermodynamicwavelength.ThischaracteristicintrinsicallylimitstheabilitystabilitiesoftheL-andD-enantiomersinbothcases.Becausetoachievealargechiralbiasinlight-basedchiralitycontrol.eachmemberofapairofenantiomersshowsdifferentRecentprogressinplasmonicshasshownthatthenear-fieldDownloadedviaUNIVOFNEWMEXICOonMay16,2021at06:15:58(UTC).generatedbyexcitationoflocalizedsurfaceplasmonresonanceinteractionsfromtheother,chiralcompoundsshowdistinctbioactivitiesthatdependontheirhandedness;forexample,one(LSPR)ofmetalnanoparticlescanmarkedlyboostthechiral12enantiomermightbetoxicoritmightdestroythefunctionalitylight−matterinteraction.Forinstance,ithasbeenreportedSeehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.ofvariousbiomolecules,leadingtodiseasessuchasAlzheimer’sthattheintrinsiccirculardichroism(CD)peakofachiral1orParkinson’s.Consequently,enantiomercontrolorsepara-moleculeintheultravioletregioncanbeenhancedbyafactortionofchiralmaterialsishighlydesirableinfieldssuchasof102andshiftedtothevisibleregioncorrespondingtothe2pharmacologyandmedicalscience.wavelengthofplasmonresonancewhenthechiralmoleculeSincethe1970s,whenKaganandCalvinfirstdemonstratedresidesinaso-calledplasmonichotspotwherethefieldthattheabsoluteasymmetricphotosynthesisofheliceneinaintensityisstronglyenhancedatananogapofplasmonicliquidphasewithcircularlypolarizedlight(CPL)asachiralnanoparticles.13−15Althoughseveralmechanismshavebeen3,4sourceyieldsanapproximately2%enantiomericexcess(ee),proposedtoexplaintheplasmonicenhancementofchiralchiralitycontrolbasedonasymmetricinteractionsbetweenlight−matterinteraction,16theenhancementoftheopticalchiralmoleculesandcircularlypolarizedlighthasbeenextensivelystudiedfromviewpointssuchastheachievementofcompletechiralitycontrolbylight5orthedevelopmentofReceived:December13,2020hypothesesfortheoriginofbiohomochirality.6,7SuccessiveRevised:March2,2021applicationsofchiralphotosynthesistovariouscompoundsPublished:March17,20218,9generallyproducesmalleevaluesoftheorderof0.5−2%.Thesesmalleevaluesoccurbecausetheinteractionbetweena10chiralmoleculeandCPLisintrinsicallyweak.Theweakness©2021AmericanChemicalSocietyhttps://doi.org/10.1021/acs.jpcc.0c111096209J.Phys.Chem.C2021,125,6209−6221

1TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlechiralitydensityoftheelectromagneticfield(EMfield)isofchiralcrystallineclustersinachiralplasmonicnear-fieldconsideredtocontributetotheenhancementofthechiraluntiltheyreachanobservablesizethroughnucleationas1727light−matterinteraction.Theopticalchiralitydensity,C,isaNiinomietal.pointedout.Thismeansthattheresultingtime-evenparity-oddpseudoscalarconservedquantityderivedenantiomorphmightreflectaneffectofthechiralplasmonicfromMaxwell’sequations,andthequantityinavacuumisnear-field.Therefore,thesephenomenaareintriguingfromthe18−20definedasfollowsviewpointofasymmetricphotoreactionsinasuperchiralfield.Chengetal.alsopointedoutthepossibilityofenantioselectiveε01CEEBB≡·∇×+·∇×opticaltrappingofchiralcrystallineclustersduetoadifference22μintherefractiveindicesofclustersforleft-handedandright-0εωhandedCPL(l-CPLandr-CPL),byanalogytolaser-trapping-0=−Im(EB*·)inducedcrystallization,whereforcedcrystalnucleationcanbe2(1)inducedevenfromanunsaturatedmothersolutionbylocallywhereε0andμ0arethepermittivityandpermeabilityoffreeconcentratingthesolutionvialasertrappingofcrystalline35,36space,respectively;ωistheangularfrequencyoftheEMfield;clustersinthesolutionatthelaser-focus.However,theandEandBdenotethetime-dependentrealpartsofthedetailedmechanismandthefeasibilityofenantioselectiveelectricandmagneticfields(E-andM-field),respectively.opticaltrappingremainedunclear.OpticalchiralitydensityisameasureofthechiralityoftheEMToassesstheveracityofthehypothesisofenantioselectivefield,whichdependsonthemagnitudeandorientationoftheEplasmonicopticaltrappingofcrystallineclusters,weperformedandBfields,whichoscillateπ/2radiansoutofphase.21Inanumericalanalysisofthespatialdistributionofenantiose-particular,thedegreeofchiralityismaximalwhenthelectivechiralopticalpotentialoriginatingfromanopticalorientationbecomesparallelorantiparallel,whichcorrespondchiralitydensityenhancementintheplasmonicnear-fieldneartothenegativeandpositivesignsofopticalchiralitydensity,aAunanotriangletrimer,inaccordancewiththeanalysisnamely,right-handedorleft-handed,respectively.22Therefore,providedbyCaoetal.regardingenantioselectiveoptical37anenhancedopticalchiralitydensitycanbeobservedinatrapping.Wefoundthatthechiralopticalforceoriginatingplasmonicnear-fieldbecausetheplasmonicnear-fieldexhibitsfromthegradientofthechiralopticalpotentialcanbevariousrelationshipsinthephaseandtheorientationofitsEcomparabletotheelectricgradient,whichcorrespondstotheandBfieldscomparedwithpropagatingEMwaves,suchastrappingforce,seeninpreviousexperimentsoflaser-trapping-CPL,inadditiontotheplasmonic-fieldenhancement.Suchainducedcrystallizationfromunsaturatedsolutionlocallyattheplasmonicnear-fieldwithanenhancedopticalchiralitydensitynanogapoftheAunanostructure.Wealso,forthefirsttime,istermedasuperchiralfield.takethecontributionofthechiralopticalpotentialandchiralAnenhancementofchirallight−matterinteractionhasbeengradientforceexertedonNaClO3chiralcrystallineclustersexperimentallydemonstratedinspectroscopicplatformswithintoconsiderationtodiscusschiralnucleationratedifferenceplasmonicmetalnanostructureswheretheopticalchiralitybetweenthetwoenantiomorphs,whichshouldresultinthedensityshowsanenhancementintheplasmonicnear-field.23giantCEE,whereasthepreviousdiscussionsregardinglight-Hendryetal.reportedthattheenhancementfactoroftheinducedcrystallizationhavebeensolelylimitedtothesensitivityincreasesby106-foldcomparedwiththatincontributionof“achiral”opticalpotentialoriginatingfromconventionaltechniquesrelyingonCPL.24ThesereportstheinteractionbetweentheE-fieldandadielectriccrystalline38−44havemotivatedattemptstoapplysuperchiralfieldsincluster.Weassessedthethermodynamiccontributionofasymmetricphotosynthesisbeyondtheframeworksbasedonthechiralopticalpotentialbyextendingtheclassical-far-fieldphotonics.25However,noeeenhancementresultingnucleation-theory-basedformalismofthechangeinGibbsfromasymmetricphotosynthesisinachiralplasmonicnear-free-energydifferencebetweenthesolutionandcrystalphasefieldhasbeenclearlydemonstratedtodate.dependingonthesizeofthecrystallineclustertothecaseWerecentlydiscoveredthatagiantcrystalenantiomericunderthesuperchiralfield.Thisassessmentsuggestedtheexcess(CEE)couldbeobservedinthenucleationrateduringpossibilitythatthegiantCEEresultedfromadifferenceinthethechiralcrystallizationofNaClOinducedbyexcitationoffrequencyofattachmentofchiralcrystallineclusterstocrystal3thelocalizedsurfaceplasmonresonanceofmetalnanoparticlesnucleiorinthelocalconcentrationdueto“chirally”biasedirradiatedbycircularlypolarizedlaserlightinsolution.26−28diffusionratherthanthethermodynamiccontributionoftheChiralcrystallizationistheformationofchiralcrystalsfromanchiralopticalpotentialtothenucleationrate.achiralcompoundandisanalogoustoabsoluteasymmetricsynthesisinthattheproductundergoesanachiral−chiral2.METHODS29−31transition.WehavedemonstratedthataCEEofaboutNumericalEM-fieldanalysisbasedonthefinite-difference25%canbeinducedinchiralcrystallizationofNaClO3time-domain(FDTD)methodwasperformedusingainitiatedbyheterogeneousnucleationonsilver(Ag)nano-commercialthree-dimensionalFDTDsoftwareprogramaggregatesopticallytrappedbyaCPLvisiblelaser(λ=532(PoyntingforOptics;Fujitsu,Japan).Usingavirtualthree-27nm)atanair−solutioninterface.Chengetal.laterreporteddimensionalspaceintheFDTDprogram,wemimickedthethatCEEvaluesexceeding50%couldbeattainedwhen,situationintheNaClO3chiralcrystallizationexperimentofinsteadofAgnanoaggregates,awell-definedgold(Au)Chengetal.,inwhichaAutriangletrimernanostructurewas28triangulartrimernanostructurewith3-foldrotationalsymme-irradiatedbynear-infraredCPLfromalaser(λ=1064nm).tryandananogapatitscenterwasexcitedbyanear-infraredFigure1showsthesetupfortheEM-fieldsimulation.28CPLlaser(λ=1064nm).BecausechiralnucleationisThedimensionsofthesimulationboxweresetto800×800consideredtooccurthroughrepetitiveassociationand×1100nm3onthex-,y-,andz-axes,respectively(from−40032−34dissociationofchiralcrystallineclustersinsolution,to+400nminthex-coordinate,from−400to+400nminthethesephenomenamightbetheconsequenceofrapidgrowthy-coordinate,andfrom−500to+600nminthez-coordinate).6210https://doi.org/10.1021/acs.jpcc.0c11109J.Phys.Chem.C2021,125,6209−6221

2TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticlestateEM-fieldanalysis.Thecalculatedopticalchiralitydensityoftheplasmonicnear-fieldwasnormalizedbytheabsolutevalueoftheopticalchiralitydensityoftheincidentCPLtoshowtheenhancementfactorinaspatialdistributionmapping.TheopticalchiralitydensityofCPL(CCPL)canbeexpressed47asfollowsεω02CCPL=±E02c(3)whereE0istheE-fieldintensityoftheincidentCPLandcisthespeedoflight.Thenegativeandpositivesignscorrespondtoright-handedandleft-handedCPL,respectively.Byassumingthatthecrystallineclusterscanberegardedassphericalnanosphereswithaclearinterfaceandhomogeneousphysicalproperties,weanalyzedthechiralopticalpotentialimposedonthechiralcrystallineclustersinteractingwiththechiralplasmonicnear-fieldwithanenhancedopticalchiralitydensitybyfollowingtheanalysisprovidedbyCanaguier-Figure1.SchematicillustrationshowingthemodelfortheFDTDDurandetal.48−50Theydiscussedanenantioselectivechiralelectromagneticnumericalsimulation.Thefigureontheleftshowsaopticalforcebyconsideringthetime-averagedopticalforceFbird’s-eye-viewschematicofthecalculationdomain.Thepink-coloredexertedonachiralnanospherewithdimensionsthatareregionrepresentstheexcitationsourceofa1064nmCPLplanewavesignificantlysmallerthanthespatialchangeinthesurroundingpropagatinginthez-direction.TheyellowobjectisAu,asrepresented3745harmonicEMfield:thevalueofFcanbederivedfromthebyaLorentz−Drudemodel.Theupper-rightschematicshowstheLorentzforcelaw.TheopticalforceFcanberepresentedasacalculationdomainobservedfromthe+zplane.Thelower-rightschematicshowsthecalculationdomainobservedfromthe+yplane.sumofanonenantioselectivegradientforceFdandanThecoordinatesoftheanalysisplane,indicatedbyareddottedline,enantioselectivegradientforceFc,asfollowsweresettoz=5,15,25,35,45,55,65,and75nmasthecoordinatesofthebottomplaneofthenanostructureissettoz=0.FFF=+dc(4)Here,werefertoFdasthe“dielectric”gradientforceandFcasAperfect-matching-layerboundaryconditionwasadoptedforthe“chiral”gradientforce,inaccordancewiththeterminology51theoutersurfacesoftheboxperpendiculartothez-axis,andaadoptedbyZhaoetal.Thetwogradientforcescaneachbeperiodicboundaryconditionwasadoptedfortheouterdividedintoreactiveanddissipativeconstituents,whichconsistsurfacesperpendiculartothex-andy-axestoavoidreflectionofrealandimaginarypartsoftheelectric,magnetic,andofthenear-fieldfromtheoutersurfaces.Themediumelectromagneticpolarizabilities,α,β,andχ,respectively.ThemimickingtheAutriangletrimernanostructure(Figure1)reactiveanddissipativeconstituentsofthechiralgradientforce37wassetsothatthez-coordinateofthebottomsurfaceofthecanbeexpressedasfollowsnanostructurewas0.DielectricdispersionofAuwasexpressedbytheLorentz−Drudemodel45presetinthesoftware[seethereaccεμ00ωεμmmFc=·ωRe()χ∇{Im(EH·*)}SupportingInformation(SI),S1].ThethicknessoftheAuεμmm2(5)nanostructurewassetto50nm.Alightsource,whichexcitedacircularlypolarizedplanewavepropagatingalongthez-axis(λ2εμi∇×Πy=1064nm),wasalsosetsothatacircularlypolarizedplaneFdiss=·mmIm()χjjΦ−zzcjzwaveirradiatedtheAunanostructurefrom460nmbelowitscεμ00k2{(6)bottomsurface.Weanalyzedthesteady-stateEMfieldintheanalysisx−yplanesetatthez=5,15,25,35,45,55,65,andwhereωistheangularfrequencyoftheEMfield;εmandμm75coordinates(nm).ThediscretizationconditionsofspatialaretheelectricpermittivityandthemagneticpermeabilityofcoordinationandtimedomainweresetasΔx=2nm(×200),thesurroundingmedium,respectively;ΦistheflowofΔy=2nm(×200),Δz=20nm(×55),andΔt=4.61148aschirality;andΠisthePoyntingvector.(6500steps;totaltime:29974.41as).ThespatialdistributionTheelectromagneticpolarizabilityχcanbeexpressedasofthesteady-stateEMfieldwasmappedusingtheintensitiesatfollowsthephasegivingthemaximumfieldintensitiesateach3κcoordinate.Thevalueofopticalchiralitydensitywascalculatedχπ=12r2usingthefollowingequation46(2εμκp++)(2p)−(7)ωε0whereristheradiusofthechiralparticle,κisthechiralityCE={|xx||BE|Δsin(x)+|yy||B|Δsin(y)2parameter(Pasteurparameter)ofthechiralmedium+||||EBzzsin(Δ}z)(2)containingthechiralparticle,andεpandμpare,respectively,therelativeelectricpermittivityandthemagneticpermeabilitywhereΔx,Δy,andΔzarethephasedifferencesbetweenEandwithrespecttothesurroundingmedium.ThechiralityBforeachspatialcomponent,obtainedbysubtractingtheparameterisameasureofthemagnitudeofthehandednessphaseoftheelectricalfieldfromthatoftheM-fieldusingtheofachiralmedium,andithasthefollowingrelationshipwithinformationonE-andM-fieldintensitiesandtheirphasesfortherefractiveindicesforleft-handed(l-)CPL,nL,andright-52eachcomponentineachcoordinateprovidedbythesteady-handed(r-)CPL,nR6211https://doi.org/10.1021/acs.jpcc.0c11109J.Phys.Chem.C2021,125,6209−6221

3TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure2.Spatialdistributionoftheelectric(E),magnetic(M)fieldintensityenhancement,andtheenhancementofopticalchiralitydensitynearaAunanotriangletrimerilluminatedbyCPL.(a)SpatialdistributionoftheE-(upper)andM-field(lower)intensityenhancementsneartheAunanotriangletrimerirradiatedbyCPLwithanE-fieldintensityof561mV/mandanM-fieldofapproximately1.5mA/m.Theintensitiesineachcoordinationweremappedusingthephasethatgavethemaximumfieldintensity.Theleftandrightcolumnsshowthecasesforl-CPLandr-CPLexcitation,respectively.(b)SpatialdistributionofopticalchiralitydensityenhancementrelativetoCPL.Theupperfigureshowsamappinginwhichthecolorgradationvariesintherange−2to+2.Thelowerfigureshowsamappinginwhichthecolorgradationvariesintherange−30to+30.Theleftandrightcolumnsshowthecasesforl-CPLandr-CPLexcitation,respectively.Theupperfiguresuggeststhatl-CPLandr-CPLexcitationsresultindominantdistributionsofaleft-handedsuperchiralfield(positivesign)andaright-handedsuperchiralfield(negativesign),respectively,nearthenanostructure.Thelowerfiguresuggeststhattheopticalchiralityenhancementshowsaremarkablelocalenhancementinthenanogapatthecenterofthetriangulartrimer.1wherenmistherefractiveindexofthesurroundingmedium.κ=−()nnLR2(8)Accordingly,fromtherelationshipbetweentheopticalgradientforceandtheopticalpotential(F=−∇U),thechiralopticalThenegativeandpositivesignsofκindicatelevorotatory(l)potential,Uc,canbeexpressedasfollowsanddextrorotatory(d)enantiomers,respectively.Notethatthecrefractiveindexbetweenl-andr-CPLincludedineq8istheUcm=−nCRe()χ·ω(11)subtractionnRfromnL,whichisoppositetothatdescribedinref52,i.e.,thesubtractionnLfromnR.ThisoppositeThechiralpotentialwasanalyzedbytheformulaegivenrelationshipisnecessarytoestablishconsistencywiththeaboveusingtheradiusofachiralparticlerandthechiralityphysicalpictureofopticaltrapping,inwhichamediumwithaparameterκasvariables.higherrefractiveindexisattractedbythestrongE-fieldregion.Morespecifically,amediumwithahigherrefractiveindexwith3.RESULTSANDDISCUSSIONrespecttor-CPL,whichcorrespondstothel-enantiomer,3.1.StrongLocalEnhancementoftheEMFieldandshouldbeattractedbyther-CPLfieldrelativelytothel-CPL-OpticalChiralityDensityinPlasmonicNear-Fieldatafield.Tojustifythisphysicalpicture,itisnecessarytodefineNanogapoftheAuTriangleTrimerNanostructure.thechiralityparameteraseq8.DetaileddiscussionsarewrittenFigure2ashowsthespatialdistributionofthesteady-stateEM-below.Intheiranalysis,Caoetal.neglectedthedissipativefieldintensityenhancementofaplasmonicnear-fieldneartheconstituentofthechiralforcebecausetheyconsideredthattheAutriangletrimernanostructureirradiatedbyCPLwithanE-37valueofIm(χ)issignificantlysmallerthanthatofRe(χ).Wefieldintensityof561mV/mandanM-fieldofapproximatelyalsoregardedthedissipativeconstituentasnegligiblebecausea1.5mA/m.NaClO3crystalshouldshownosignificantCDpeak,whichisNoapparentdifferencesbetweenthecasesofl-CPLandr-governedbyIm(κ)at1064nm.Namely,weregardthechiralCPLirradiationwereobservedintheenhancementdistribu-reactiveforceasequaltothechiralgradientforce.Notethattions.Astrongenhancement,inexcessof1000-fold,oftheE-thereducedchiralgradientforceisproportionaltothegradientfieldoftheincidentCPLwasobservedinthenanogapattheoftheopticalchiralitydensitybecausethetermincludedin∇centerofthetriangulartrimerstructure.ThismeansthattheE-istheopticalchiralitydensityinthesurroundingmedium,asafieldwasfocusedintensivelyonthenanogapbeyondtheresultofthefollowingdefinitiondiffractionlimit.Iftheconventionaldielectricoptical-trappingforce,namely,theE-fieldgradientforce,isexpressedbytheεω0εμω00followingformulae,53CE=−Im(*·B)=Im(E·*H)22(9)12FEd=∇α⟨⟩Wecanthereforerewritethereactivepartofthechiral2(12)gradientforceasfollowsijjεεpm−yzzreaccα=3VεmjjjjzzzzFc=·nmRe()χ∇Cεεpm+2ω(10)k{(13)6212https://doi.org/10.1021/acs.jpcc.0c11109J.Phys.Chem.C2021,125,6209−6221

4TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure3.Landscapeofthechiralopticalpotentialimposedonachiralnanospherewitha|κ|valueof0.6andaradiusrof20nmnearaAunanotriangletrimerstructureonthebasisofthex−ydistributionofopticalchiralitydensityatz=25forr-CPLexcitation.(a)Landscapeofthechiralopticalpotentialimposedonthed-andl-chiralnanoparticles.Theupperandlowerschematicsshowthechiralopticalpotentiallandscapesforthed-andl-nanospheres,respectively.MAXandMINindicatethemaximumandminimumvaluesofthechiralopticalpotential,respectively.(b)Landscapeofthedifferenceinthechiralopticalpotentialbetweenthel-andd-chiralnanospheres.Namely,thelandscapecanberegardedastherelativechiralopticalpotentialexertedonl-nanoparticlefromthatond-nanoparticle.where⟨E2⟩isthetime-averagedsquareoftheE-fieldoftherotationwasobservedforr-CPLandclockwiserotationforl-incidentlaser,αisthepolarizabilityofthetargetparticle,VCPL(seetheSupportingInformation,FigureS2).(=4πr3/3)isthevolumeoftheparticle,andεandεarethepmFigure2bshowsthespatialdistributionsofopticalchiralitydielectricconstantsoftheparticlesandthesurroundingdensitynormalizedbytheopticalchiralitydensityofthemedium,respectively,itcanbededucedthatcrystallineincidentCPLforthex−yplaneofz=35asanexample(seeclustersinsolutionareopticallytrappedinanefficientmanneralsotheSupportingInformation,S3).Anenhancementin36,54,55atthenanogapinso-calledplasmonicopticaltrapping.opticalchiralitydensitywasobservednearthetriangulartrimerInadditiontothelocalconcentrationincreaseasaresultofnanostructureforthecasesofbothr-andl-CPLincidence.plasmonicopticaltrapping,thesurfacesoftheAunano-Thedominantlyenhancedopticalchiralitydensityshowedtrianglesformingthenanogapshouldlowertheactivationoppositesignsforl-andr-CPLincidence,andleft-andright-56energyforcrystalnucleationbyheterogeneousnucleation.handedsuperchiralfieldswereenhancedbyl-CPLandr-CPLThisshouldcausethenanogaptobeahotspotforcrystalincidence,respectively(Figure2b,upper).Theenhancementnucleation.Althoughtherewerenocleardifferencesbetweenintheabsolutevalueoftheopticalchiralitydensitywasthecasesofl-CPLandr-CPLirradiationinthesteady-stateE-maximizedattheplasmonichotspotinthenanogapofthefieldenhancementdistributionsmappedusingthephasestriangulartrimer,andachiralhotspotoccurredatthegivingthemaximumfieldintensitiesineachcoordinate,theplasmonichotspot.Themaximumenhancementwasapprox-steady-stateE-fielddistributionmappedusingtheidenticalimately40.8-foldforl-CPLincidenceand37.2-foldforr-CPLphaseineachcoordinateshowedcleardifferencesbetweentheincidence.Themagnitudeofopticalchiralitydensityenhance-twocases(seetheSupportingInformation,S2).Forthementdependsonthez-coordinate,andtheenhancementmappingusinganidenticalphaseforeachcoordination,the57factorwasfoundtobebeyond100-folddependingonthez-strongestE-field(i.e.,aplasmonichotspot)wasobservedatcoordinate(seetheSupportingInformation,S3).thenanogapbetweenanarbitrarypairofnanotrianglesamongTheFDTDanalysisshowedthattheE-fieldandopticalthethreenanotriangles.TheplasmonichotspotmovedfromchiralitydensityarestronglyenhancedlocallyatthenanogaptheinitialnanogaptoanothernanogapwiththeadvancementoftheAutriangletrimernanostructurerelativetotheincidentofthephase,resultinginarotationoftheplasmonichotspot.CPL.Especially,theenhancementofopticalchiralitydensityThedirectionofrotationdifferedbetweenthecasesofr-CPLandl-CPLirradiation:acounterclockwiserotationwaslocallyreachesseveraltensoftimesoftheincidentCPL,observedforr-CPLandclockwiserotationwasobservedforsuggestingthatasteepgradientofthechiralopticalpotentiall-CPL.Ontheotherhand,theM-fieldenhancementwasactingonchiralnanoparticlesexistsatthenanogap.moderaterelativetothatoftheE-field.Anapproximately30-Hereinafter,wescaledtheresultingvaluesofoursimulationbymultiplyingthefactorofE2/E2,whereE2istheE-fieldfoldenhancementoftheM-fieldwasobservednearthesidesofexsimexeachnanotriangle,ratherthanattheapex,whereitwasintensityoftheincidentCPLintheexperimentofChenget282observedinthesteady-stateM-fieldenhancementmappingal.andEsimistheE-fieldintensityoftheincidentCPLintheusingthephasesgivingthemaximumintensities;moreover,simulation,toconvertthevaluesinthesimulationtothevaluesthatcouldbereachedintheexperimentofChengetal.TheE2therewasnosignificantdifferencebetweenthetwocasesofexCPLirradiation.LikethecaseoftheE-field,forasteady-statewasobtainedfromtherelationshipbetweenthelaserintensity,I,andE-fieldstrength,namely,I=0.5cεE2.ThevalueofIisM-fieldmappingusingtheidenticalphase,theenhancedM-0fieldrotatedasthephaseadvanced.Acounterclockwise1.0MW/cm2accordingtoChengetal.6213https://doi.org/10.1021/acs.jpcc.0c11109J.Phys.Chem.C2021,125,6209−6221

5TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticle3.2.ChiralOpticalPotentialLandscapeforaChiralisonwithDielectricOpticalPotentialinLaser-Trapping-NanoparticleintheVicinityoftheAuNanostructure.InducedCrystallizationExperiments.BecausethechiralThestrongenhancementintheabsolutevalueoftheopticalopticalpotentialisafunctionofrandκforachiralchiralitydensityatthenanogapsuggeststhatachiralopticalnanoparticle,thedepthofthewellofthechiralopticalpotentialisintensivelygeneratedatthenanogapforchiralpotentialdifference,whichdirectlygovernstheenantioselec-particlesinsolution.Moreover,fromthesteepincreaseofthetivity,variesdependingonthevaluesofrand|κ|fortheabsolutevalueoftheopticalchiralitydensityfromtheregionassumedchiralsphere.Itis,therefore,necessarytoclarifytheawayfromthenanogaptothenanogap,wecandeducethatdependencyofthemaximumchiralopticalpotentialdifferencethereisastrongchiralgradientforcetowardthenanogap.Toonrand|κ|toevaluatetheeffectivenessofthechiralplasmonicinvestigatethefeaturesofthechiralopticalpotentiallandscapenear-fieldneartheAutriangletrimerinenantioselectiveopticalexertedonchiralparticles,wevisualizedthechiralopticaltrapping.potentiallandscapebycalculatingthechiralopticalpotentialFigure4showsthedependencyofthechiralopticalexertedonachiralnanosphereoftheradius(r)of20nmandpotentialdifferenceonrand|κ|foratargetchiralnanoparticle.anabsolutevalueofthechiralityparameter(|κ|)of0.6,usingThedependencywascalculatedfromthepointinthespatialthex−yspatialdistributionofopticalchiralitydensityatz=25distributionofopticalchiralitydensity,whichgivestheforr-CPLirradiation.Thesetvalueofκwasdeterminedbymaximumchiralopticalpotentialdifferencebetweenl-and51referringtothepreviousreportbyZhaoetal.,whichd-nanoparticlesatz=45(seetheSupportingInformation,S5).suggestedthatthevalueofκrangesfrom−1.45to1.45forThevaluesofrand|κ|areshownintherangesfrom0to100chiralspecimensthatincludeachiralassemblyofplasmonicnmandfrom0.05to1.45,respectively.Thedependencyshowsnanostructures.Wechoseavalueof0.6toinvestigatethethatthechiralopticalpotentialdifferenceincreasesnonlinearlychiralopticalpotentiallandscapeforaparticlewithamediumasthevalueofrincreasesbecausethedifferenceisdegreeofchirality.Figure3showsthechiralopticalpotentialproportionaltor3andthatthedifferenceincreaseswithlandscape.Althoughthechiralopticalpotentiallandscapewasincreasing|κ|.Iftheparticlesizeissmall,forexample,10nm,attractivetowardthenanogapforthelevorotatory(l-)thedepthofthechiralopticalpotentialdifferencewillrangenanoparticlewithapositivechiralityparameter,itwasrepulsivefrom0.29to10.68kBTfortheshownrangeof|κ|values,forthedextrorotatory(d-)one.Indeed,thechiralopticalwhereasitwillrangeapproximatelyfrom290to10679kBTforpotentialdepthorheight,whichdependsontheenantiomerofaparticlewitharadiusof100nm.Thisconcretelyshowsthatthenanosphere,wasfoundtobemaximalatthechiralhotspotthepotentialdifferenceincreaseswithr3.intheplasmonichotspotatthenanogap.AlthoughthereseemToevaluatethesignificanceofthechiralopticalpotentialtobetwopeaksinthechiralopticalpotentialatthenanogap,differenceconcerningcrystallization,wecomparedther−|κ|thesepeakshavenophysicalmeaning,suchasEM-fielddependencesofthechiralopticalpotentialdifferenceswiththeresonance,becausetheseareduetotheroughgridmeshrdependencesofdielectricopticalpotentialsfrompreviousgeneration(gridmeshintervalis2nm)andthelimitationtoexperimentalstudiesonlaser-trapping-inducedcrystallization.smooththeinterval.Thedielectricopticalpotentialswerecalculatedusingeq12ThemaximumandminimumvaluesofthechiralopticalandtherelationshipF=−∇U(seetheSupportingpotentialsforthed-nanoparticlewere10.60and−0.92kBT,Information,S6).Therdependencesofthedielectricopticalrespectively,whereasthoseforthel-nanoparticlewere0.92andpotentialswereplottedagainstther−|κ|dependenceofthe−10.60kBT,respectively(Figure3a).Figure3bshowsthechiralopticalpotentialdifferenceinFigure4.Theyellow,landscapeofthechiralopticalpotentialdifferencebetweenthegreen,andpurplesquarescorrespondtothelaser-trapping-l-nanoparticleandthed-nanoparticle,namely,therelativeinducedcrystallizationobservedbyYuyamaetal.(L-phenyl-6061chiralopticalpotentialimposedonthel-nanoparticlefromthealanine),Rungsimanonetal.(glycine),andChengetal.62d-nanoparticle.Themaximumdepthofthewellofthechiral(potassiumchloride),respectively.Thiscomparisonshowedopticalpotentialdifferencewas21.20kBT.Notethatthatthedepthofthedielectricopticalpotentialrequiredtoexperimentallystableopticaltrappingofadielectricparticleinducecrystalnucleationiscomparabletothatofthechiralrequiresthedepthofthedielectricopticalpotentialwelltobeopticalpotentialdifference.Notethatthedielectricoptical58<10kBT.Thismeansthatthechiralopticaldifferenceshouldpotentialsplottedherecorrespondtothecaseinwhichcrystalpermitstableenantioselectiveopticaltrappingofchiralnucleationwassuccessfullyinduced,evenfromanunsaturatedparticleswithr=20nmand|κ|=0.6ifachiraldielectricsolution.Generally,crystalnucleationdoesnottakeplaceopticalpotentialisconsideredasthe“background”,whichspontaneouslyfromanunsaturatedsolution.Moreover,evenifequallyinfluencesthedynamicsofbothenantiomericnano-amothersolutionisinamoderatelysupersaturatedstate,particles(forthelandscapeof“total”opticalpotentialcrystalnucleationisarareeventbecauseofthepresenceofanconsideringdielectricopticalpotential,seealsotheSupportingactivationenergybarriertonucleationarisingfromtheenergyInformation,S4).lossforsurfacecreation.Accordingly,crystalnucleationThelocalandstrongenhancementofopticalchiralitygenerallyrequiresasufficientlyhighdegreeofsupersaturation.densityatthenanogapoftheAunanostructure,shownbytheInlaser-trapping-inducedcrystallizationexperiments,liquid−FDTDanalysis,wasfoundtoimposetheenantioselectiveliquidphaseseparation(LLPS)ofaglycinesolutioncouldbe63chiralopticalpotentialwellsufficienttostablytraponeofthesimultaneouslyinduced,althoughLLPSofglycinesolutiontwoenantiomericnanoparticlesatthenanogapasasuperchiralcannototherwisebeinducedevenifasolutionthatissaturated64hotspotonanassumedchiralnanoparticlewithr=20nmandat40°Cissupercooledto0°C,whichcorrespondstoan65|κ|=0.6.approximately150%supersaturation.Thismeansthata3.3.DependencyoftheChiralOpticalPotentialdielectricopticalpotentialcapableofinducingcrystalDifferencebetweenEnantiomericNanoparticlesonnucleationmightbeabletotrapandsufficientlyconcentrateTheirSizesandChiralityParameters,andItsCompar-solutemoleculestoraisethelocalsupersaturationtomorethan6214https://doi.org/10.1021/acs.jpcc.0c11109J.Phys.Chem.C2021,125,6209−6221

6TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticle150%.Therefore,thesuperchiralplasmonicnear-fieldgeneratedbyCPLirradiationoftheAutriangulartrimercanproduceanenantioselectiveopticalfieldofastrengthcomparabletothelargedielectricopticalpotentialofachiralnanospherewitha|κ|valueintherangeof0.25−1.45.Comparingthedependencyofthemaximumdepthofthechiralopticalpotentialwellintheanalysisplaneonrforchiralnanoparticleswithvarious|κ|valuesintherangeof0.25−1.45andthedependencyofthedepthofdielectricopticalpotentialonrinthepreviousexperimentsoflaser-trapping-inducedcrystallization,wherehighsupersaturationstatesufficienttoexceedmetastabilitylimitofasupersaturatedsolutioncanbeprobablyreached,thesewerefoundtobecomparable.Thisimpliesthatenantioselectivecondensationofchiralcrystallineclusterssufficienttoinduceenantioselectivechiralcrystal-lizationmightoccuratasuperchiralhotspotoftheAunanostructureifthe|κ|valueofthechiralcrystallineclusterismorethan0.25.3.4.ChiralGradientForceExertedonaNaClO3ChiralCrystallineNanoclusterattheSuperchiralHotspotandItsComparisonwiththeDielectricGradientForceintheLaser-Trapping-InducedCrystallizationExperi-ments.Intheabovediscussion,weevaluatedthecharacter-isticsoftheenantioselectiveopticalpotentialgeneratedthroughexcitationbytheplasmonicnear-fieldproducedbyCPLirradiationofaAunanotriangletrimer,assumingthepresenceofachiralnanospherewitha|κ|valueintherangefrom0.05to1.45.TheevaluationshowedthatachiralopticalpotentiallargeenoughtoinducestableseparationofenantiomerscouldforminthenanogapatthecenteroftheAunanotriangletrimerifthedegreeofchiralityissufficientlylarge.However,the|κ|valueofNaClO3crystalsshouldbesmallerthanthatoftheassumedchiralnanosphere.Thisisbecause|κ|ishalfthedifferencebetweenthetworefractiveindicesofachiralmaterialforl-CPLandr-CPL,andthedifferenceshouldbesignificantlysmallerthantheorderoftheintrinsicrefractiveindicesofnaturalchiralmaterialsforlinearlypolarizedlight.Notethatthesmall|κ|valuesofnaturalchiralmaterialsarisefromthemeasurementsoftheopticalactivitybasedoninteractionsbetweenpropagatinglightandthetargetchiralmaterialinwhichchirallight−matterinteractionsareintrinsicallyveryweakbecauseofthelargedifferenceinscaledifferencebetweenlightandthechiralpitchofnaturalchiralmaterials.Althoughweneedtoevaluatehowmuchthe|κ|valueofnaturalchiralmaterialswouldbestrengthenedbyresolvingthespatialmismatch,anddosousingtheinteractionbetweentheplasmonicnear-fieldandthechiralnanosphere,wewillfirstdiscussthechiralopticalpotentialandchiralgradientforcewhenthe|κ|valueofNaClO3isimposedonthechiralnanosphereforthecalculation.The|κ|valueofNaClO3canbecalculatedasbeingoftheorderoffrom10−4to10−3fromexperimentalopticalrotatorydispersion(ORD)measure-Figure4.Dependenceontheradius(r)andtheabsolutevalueofthementsperformedintherangefromtheultraviolettothevisiblechiralityparameter(|κ|)ofthemaximumchiralopticalpotential66region(approximately235−625nm)(seetheSupportingdifferencebetweenthel-andd-chiralnanoparticlesimposedbytheInformation,S7).Althoughwecannotcalculatethe|κ|valueatsuperchiralfieldgeneratedneartheAunanotriangletrimer,andits1064nm(thewavelengthoftheincidentcircularlypolarizedcomparisonwithther−|κ|dependenceofthedielectricopticallaser)becausenoORDmeasurementhasbeenperformedatpotentialsinsomepreviousexperimentalstudiesonlaser-trapping-−4thatwavelength,wecanadopta|κ|valueof600nm(3×10)inducedcrystallization.Forreference,theredhighlightinthemiddleasarepresentativevaluebecausetheasymptoticcharacteristicfigureindicatestheregionwheredielectricopticaltrappingisexperimentallypossible,andtheyellowhighlightindicatestheregionofthefunctionofORDtowardthelongerwavelengthregionwheredielectricopticaltrappingistheoreticallypossible.ThegreensuggeststhatthedifferenceinvaluesoftheORDbetweenhighlightinthelowerfigureindicatesthepotentialdepthreportedin1064and600nmisinsignificant.AsevidentfromFigure4,the59previousstudiesoncolloidalcrystallization,forref59.depthofthechiralopticalpotentialislikelytobeinsufficientto6215https://doi.org/10.1021/acs.jpcc.0c11109J.Phys.Chem.C2021,125,6209−6221

7TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure5.Dependenceofthedifferenceinthechiralgradientforcebetweenthel-andd-chiralnanospheresontheradius(r)andtheabsolutevalueofthechiralityparameter(|κ|)ofthechiralnanoparticle,anditscomparisonwiththedielectricgradientforceinpreviousexperimentalstudieson60−62laser-trapping-inducedcrystallization.Thecircledatapointswithacolorgradationfromredtoblueindicatethedifferenceinthechiralgradientforceexertedonachiralnanoparticlewitha|κ|valuefrom1×10−4to5×10−3,whicharetheorderofthe|κ|valueofNaClOchiralbulk3crystals.Thesquaredatapointsrepresentthedielectricgradientforcefrompreviouslaser-trapping-inducedcrystallizationexperimentsinwhich60−62crystallizationfromanunsaturatedsolutionwasachieved.Theschematicsoutlinedinredandgreenhighlightthescaledifferenceofthechiralanddielectricopticalpotentialwellsbetweenthecalculationsinthisstudyandthosefrompreviousexperimentalstudiesonlaser-trapping-inducedcrystallization,respectively.Theregionhighlightedinyellowindicatestherangeofthedielectricgradientforceinapreviousexperimentof67plasmonicopticaltrapping-inducedcondensationofpolymermolecules.inducestableandenantioselectivetrappingofachiralparticlebesufficienttoinducecrystalnucleation,evenfromanwitha|κ|valueoftheorderof10−4to10−3;moreover,theunsaturatedsolution.Thevaluesofthechiralgradientforcesdepthofthechiralopticalpotentialisnotcomparablewiththecomparabletothedielectricgradientforcesmightbesufficientdielectricopticalpotentialsinpreviouslaser-trapping-inducedtoproduceadifferenceinthenucleationratebetweenthetwocrystallizationexperimentsbecausethedepthofthechiralenantiomorphs,althoughtheymightbeinsufficienttoensureopticalpotentialistoosmallcomparedwiththedepthofthecompleteenantioselectivechiralnucleationfromanunsatu-dielectricopticalpotential.However,thedifferenceintheratedsolution.Moreover,severalpreviousstudiesonopticalspatialwidthoftheseopticalpotentials,whichinfluencesthemanipulationhaveshownthatafemtonewton-scaleopticalmagnitudeofthegradientforceactingoncrystallineclusterforce(ormagneticgradientforce)iscapableofdirectingorparticles,shouldbetakenintoconsiderationbecause,inthelocallyconcentratingdielectric(magnetic)nanoparticleswithpreviouscrystallizationexperiments,theopticalfieldwassizesrangingfromseveraltensofnanometerstoseveral68−70localizedintoamicrometerscalebyfocusingalaserbeamwithhundredsofnanometers.Therefore,itisquitepossibleanopticallens.Incontrast,thesuperchiralfieldwaslocalizedthatthechiralcrystallineclustersofthetwoenantiomorphsintoascaleofafewtensofnanometersduetothecanbelocallyseparatedorcanshowdifferentresidencetimescharacteristicsoftheplasmonicnear-field.inthechiralhotspotandalsothesurfaceofthenanostructure71Figure5comparestherdependenceofthedielectricasaresultofchirallybiaseddiffusion.Thenanogapofthegradientforcefromthepreviousexperimentswiththechiralnanotrimerstructure,wherethechiralhotspotislocated,gradientforcecalculatedbyassumingthatthespotsizeoftheshouldformanexcellentnucleationsite,notonlybecausethefocusedlaserbeamisapproximately1.4μmandthatthespatialsurfaceoftheAunanostructuresurroundingthenanogapspreadingofthesuperchiralfieldisapproximately10nm.Thepromotesnucleationthroughheterogeneousnucleationbutfigureshowsthatthedielectricgradientforcethatactsonalsobecausethenanogapisahotspotofdielectricopticalcrystallineclusternanoparticleswitharadiusfrom0.1to20trappingforcrystallineclusters.Thus,nucleationshouldoccurnminthepreviousstudiesrangesfromapproximately0to450intheregionwheretherearedifferentpopulationsorincomingfN,whereasthechiralgradientforcethatactson20nmchiralprobabilitiesofthetwoenantiomorphiccrystallineclusterstonanoparticleswitha|κ|valueoftheorderof10−4to10−3nuclei.Thispossiblyleadstotheresultinggiantenantiomericrangesfromapproximately1.9to95fN.Thisresultmeansthatexcess.thecalculatedchiralgradientforcesarecomparablewiththeOntheotherhand,weneedtopointoutthattheemployeddielectricgradientforcesinthepreviousexperimentsinsize|κ|valueofNaClO3iscalculatedfromORDmeasurementsrangingfrom0to20nm.Moreover,itshouldbenotedthatthebasedonfar-fieldoptics.Inotherwords,thesizeofthe|κ|dielectricgradientforceinapreviousexperimentinwhichvalueofNaClO3ininteractionswiththenear-fieldisnotpolymermoleculesarelocallyandreversiblycondensedbyknown.Generally,ORDisknowntobeacounterpartofCDin67plasmonicopticaltrappingisalsocomparabletothetheKramers−Kronigrelationship,meaningthatthemagnitudecalculatedchiralgradientforceinthesizerangeofatargetofORDismutuallydependentonthemagnitudeofCD.CDnanoparticle(Figure5,theregionhighlightedinyellow).ofachiralmoleculeisknowntoarisethroughinterferenceAsmentionedabove,itshouldbeemphasizedthatthebetweentheelectricdipoletransitionandeithertheelectricdielectricgradientforcesmeasuredinpreviousstudieswouldquadrupoleormagneticdipoletransitionsatthequantum-6216https://doi.org/10.1021/acs.jpcc.0c11109J.Phys.Chem.C2021,125,6209−6221

8TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticle72mechanicallevel.Becausetheelectricdipolecontributiontothesuperchiralfield.Ontheotherhand,althoughthe|κ|valueCDisinsensitivetothehandednessofchiralmolecules,theoftheNaClO3crystalmeasuredbyfar-fieldoptics,whichweelectricquadrupoleandmagneticdipolecontributions,theemployedinouranalysis,issmall,the|κ|valueresultingfromsignsofwhichdependonthehandednessofchiralmolecules,theinteractionbetweentheNaClO3chiralcrystallineclusterareresponsibleforCD.However,highermultipoletransitionsandthechiralplasmonicnear-fieldmightbeseveralordersofareexcitedmoreweaklythanelectricdipolesbypowersofa/λ,magnitudelargerthanthe|κ|value,whichweemployedwhereaisthemolecularsizeandλisthewavelengthofthefar-consideringtheexperimentalfactthatthedissymmetryfactor11,19fieldlight.ThisisonereasonwhymolecularCDisbasedonrefractiveindexdifferencebetweenchiralbiomole-intrinsicallyweakforfar-fieldradiation.Inparticular,theculesontheleft-andright-handedchiralplasmonicmagnitudeofanelectricquadrupoletransitionisproportionalmetamaterials,whichgeneratechiralplasmonicnear-field,tothemagnitudeoftheelectric-fieldgradientandiscanbeenhancedbyafactorof106relativetothevaluecomparabletothespreadingscaleofthemolecularwaveobtainedbyfar-fieldmeasurement.Ifsuch|κ|valueenhance-function.Therefore,theplasmonicnear-fieldhasbeenmentisvalidalsoforoursystem,thedepthofthechiralopticalsuggestedasacandidatefortheenhancementofCDpotentialwellmightbecomparabletothedepthofthe73responses.ThecontributionofthequadrupoletransitionisdielectricopticalpotentialwellevenforNaClO3chiralusuallyconsideredtobezeroforfreechiralmoleculesincrystallineclusters.solutionbecausethesignofthequadrupolecontribution3.5.OriginoftheGiantCEEfromtheViewpointofdependsontheorientationofthemoleculerelativetotheSteady-StateNucleationRate:ThermodynamicContri-incidentfield,andthecontributionshouldhaveanaveragebutionofChiralOpticalPotentialorKineticContribu-valueofzeroasaresultoftherandommoleculartionofChiralGradientForceExertedonChiral11,19,73orientations.However,inthecaseofchiralcrystallineClusters?Ontheotherhand,theCEEshouldbedeterminedclusters,thechiralunitsareorientedduetocrystalsymmetry.bythedifferenceinthenucleationratesofl-andd-Consequently,acontributionofthequadrupoletransitionenantiomorphs.Therefore,theequationforthenucleationmightappear.ThiscouldcauseCDenhancementrelativetorateshouldprovidephysicalinsightsintothecauseofthegiantthatmeasuredbyfar-fieldmethods.Inpractice,thesignificantCEE.Intheframeworkofclassicalnucleationtheory,thecontributionofquadrupoleexcitationoforientedchiralsteady-statenucleationrateunderthesupersaturatedstate,J,74moleculesthroughtheplasmonicnear-fieldhasbeencanbewrittenasfollowsexperimentallyimpliedbythereportedfactthatthedissymmetryfactorenhancementbyafactorof106observedJJexpijjΔ*Gyzz=−0jzbyHendryetal.cannotbeexplainedsolelyintermsofchiralkkT{(15)24dipolarexcitationandopticalchiralityenhancement.ItJC=*ωΓ(16)shouldbementionedthatthisdissymmetryfactorgisdefined0sonthebasisofthedifferencebetweentherefractiveindicesofsingle-handednessofchiralbiomoleculesadsorbedonleft-4erC*2xpijjΔUyzzωπν*=sλj−zhandedandright-handedchiralmetamaterials,asfollowskkT{(17)nnRH−LH1/2g=ijjΔG*yzznnRH+LH(14)Γ=jj*2zzk3πkTn{(18)wherenRHandnLHaretherefractiveindicesofthebiomoleculeonleft-handedandright-handedchiralplasmonicmetamate-whereΔG*istheactivationenergyfornucleation,kistherials,respectively.BecauseκishalfthedifferenceintheBoltzmannconstant,Tisthetemperature,ω*isthefrequencyrefractiveindicesofachiralmediumforl-CPLandr-CPL,theofattachmentofbuildingunitstothecriticalnucleus,Γisthedissymmetryfactorenhancementby106-foldsuggeststhattheZeldovichfactor,Csisthesteady-stateconcentrationofasingle|κ|valueofNaClO3chiralcrystallineclustersthatinteractwithmoleculeinsolution,r*istheradiusofthecriticalnuclei,νisaachiralplasmonicnear-fieldmightbemuchlargerthanthefrequencyfactor,λisthemeanfreepathofparticlesinthevalueemployedinourcalculation.Wecannot,therefore,liquid(approximatelyequaltotheatomicdiameter),ΔUistheneglectthepossibilitythattheactualdepthofthechiralopticalenergyofdesolvation,andn*isthenumberofmoleculesinpotentialwellandthechiralgradientforcearelargerthanthosethecriticalnucleus.Astheequationshows,thenucleationratesuggestedbyourcalculation.isgovernedbythefrequencyofattachmentofbuildingunitsConsideringthesmall|κ|valueoftheNaClO3crystal(ortheconcentrationofmolecules)andbytheactivationmeasuredbyconventionalORDspectroscopyrelyingonfar-energyfornucleation.Theactivationenergyfornucleationisfieldoptics,althoughthedepthofthechiralopticalpotentialgenerallydeterminedbyconsideringΔG(r),i.e.,thechangeinwellatthesuperchiralhotspotisincomparablysmallerthantheGibbsfreeenergydependingonthesizeofnucleithatofthedielectricopticalpotentialwellinthepreviousassociatedwiththegrowthofnucleibecauseΔG(r)isaconvexexperimentsoflaser-trapping-inducedcrystallization,thechiralupwardfunctionasaresultofcompetitionbetweentheenergygradientforceexertedonNaClO3chiralcrystallineclustersbygainedbyanincreaseinthevolumeofthestablephaseandthethechiralopticalpotentialwellwasfoundtobecomparabletoenergylossresultingfromsurfacecreation.ΔG(r)canbe67thedielectricgradientforceinthepreviousexperiments.Thiswrittenasfollowsindicatesthatenantioselectivechirallybiaseddiffusionis4πμΔ32comparabletothedielectricbiaseddiffusioninthepreviousΔGr()=−rr+4πγ3v(19)experimentsinspiteofthesmall|κ|valueoftheNaClO3crystalinthevicinityofthesuperchiralhotspotbecauseofthesteepwhereΔμisthethermodynamicdrivingforceforcrystal-gradientofthechiralopticalpotentialduetothelocalizationoflizationduetosupersaturation,visthevolumeofthemolecule,6217https://doi.org/10.1021/acs.jpcc.0c11109J.Phys.Chem.C2021,125,6209−6221

9TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleandγistheinterfacialfreeenergy.BecauseΔG(r)isaconvexcausedbyenantioselectivelybiaseddiffusionprovidesamoreupwardfunction,ΔG*canbeobtainedbyinvestigatingtherealisticexplanationoftheoriginofthegiantCEEthandoesradiusofcriticalnucleir*bysolvingthefollowingequationenantioselectiveopticaltrappingofchiralcrystallineclusters.Ontheotherhand,ourcalculationsshowedthatstable∂Gr()=0enantioselectiveopticaltrappingofchiralcrystallineclusters∂r(20)couldbeachievedifthe|κ|valueofNaClO3islargerthanoftheorderof10−1.This|κ|valuemightnotbeunrealisticifweWecanthenestimatethesteady-statenucleationrateifeachconsidertheexperimentalfactthattheg-factorenhancementofthephysicalparametersintheformulaisknown.Alexander6reached10-foldintheinteractionofchiralmoleculeswithaandCampdiscussedtheeffectoftheE-fieldoflaserlightonchiralplasmonicnear-field.Itis,therefore,necessarytoclarifytheactivationenergyfornucleationbasedontheprocedure75theactual|κ|valueofchiralcrystallineclustersinteractingwithdescribedabove.Namely,theyconsideredthattheE-fieldofachiralplasmonicnear-field.Sucha|κ|valuewillneedtobelaserlightcouldmodifytheGibbsfree-energyrelationshipdeterminedbyCDmeasurements,similartothoseofHendrybetweenthecrystallinephaseandthesolutionphase,andtheyetal.,usingaNaClO3thinfilmasachiralthinfilminsteadofintroducedtheelectrostatic(optical)potentialenergyasanbiomoleculesinthefuture.additionaltermtomodifyeq18asfollowsTodiscussthemechanismofthegiantchiralimbalancein4πμΔ3221thenucleationrateofNaClO3chiralcrystallization,theΔGrE(,)=−rrE+−4πγα3v2(21)formulaofsteady-statenucleationbasedonclassicalnucleationtheorywithoutanyexternalfieldconsideredwasextendedtoByfollowingthisprocedure,weshouldbeabletodiscussthethecasewiththepresenceoftheinteractionbetweenthecontributionofthechiralopticalpotentialbyintroducinganNaClO3chiralcrystallineclusterandthesuperchiralfieldbyadditionalchiralopticalpotentialtermintoeq20,asfollowsconsideringthethermodynamiccontributionofthechiral(seeSupportingInformation,S8)opticalpotentialtothechangeintheactivationenergyfornucleation.Asaresult,itwasfoundthatthegiantchiral4πμΔ3221Δ=GrEC(,,)−rrE+−4πγαimbalancecannotbeexplainedbythethermodynamic3v2contribution,implyingthatthecontributiontokineticfactors,c−·nCmRe()χsuchasthefrequencyofattachmentofchiralcrystallineω(22)clustersontocrystalnucleiorthelocalconcentrationofchiralHere,weassumedthatthechiralcrystallineclustercouldbeclustersaroundthenucleiresultingfromthemobilityoftheregardedasabuildingunitofthecrystal,likeasinglemolecule.clusters,mayberesponsibleforthegiantchiralimbalance.TheproceduredevelopedbyAlexanderandCampthenallowsustoformulateanequationforthesteady-statenucleationrate,4.CONCLUSIONSconsideringtheeffectofthechiralopticalpotentialontheTosummarize,wehaveperformedanumericalanalysisofthenucleationrate.Becausethesignofthecontributionoftheopticalchiralitydensityintheplasmonicnear-fieldgeneratedchiralopticalpotentialdependsonthehandednessofthechiralbyCPLirradiationofaAunanotriangletrimerstructuretocrystallinecluster,thedifferenceinnucleationratebetweentheevaluatethecontributionofthechiralopticalforceexertedontwoenantiomorphsappearstobeduetoadifferenceintheNaClO3chiralcrystallineclusterstotheexperimentallyactivationenergyfornucleationofthetwoenantiomorphs.ByreportedgiantCEEvalueinthechiralcrystallizationofassuming,forthesakeofsimplicity,thatthetermfortheNaClO3inducedbyCPLirradiationofthenanostructure.Thethermodynamicdrivingforceiszero(otherwise,thecon-analysisshowedthatastrongenhancementofopticalchiralitytributionsofopticalpotentialswouldbeinsignificantbecausedensity,approximately40-foldthatofCPL,canbeobservedthecontributionofthethermodynamicdrivingforceislocallyinthenanogapatthecenteroftheAunanotrianglesignificantlylargerthanthatoftheopticalpotentials),wetrimerstructureatascaleofafewtensofnanometers.ThecalculatedthevalueofJd/Jl,whereJdandJlarethesteady-state“chiralhotspot”oftheplasmonicnear-fieldwasfoundtobenucleationratesthattakeintoaccounttheeffectsofthechiralcapableofproducingachiralopticalpotentialwellthatisopticalpotentialforthed-andl-enantiomorphs,respectively,significantinrelationtoenantioselectiveopticaltrappinginatoexaminewhetherthevaluebecomesapproximately4whilechiralnanospherewitha|κ|valueofmorethan10−1andasizecancelingoutJ0.However,thevaluewascalculatedtobelargerthanafewtensofnanometers,butnottothatinachiralapproximately1,whichmeansthatnochiralimbalanceoccurs,virtualNaClO3nanosphereinwhichthe|κ|valuefortheevenifthe|κ|valueissetto1.45tomaximizethedifferenceinNaClOchiralcrystalsis10−4to10−3,asmeasuredby3thenucleationratesofthetwoenantiomorphs.Thisresultconventionalfar-fieldORD.Ontheotherhand,calculationsofimpliesthatthegiantCEEiscausedbyafactorthatincludesJ0,thechiralgradientforce,takingintoaccountthescaleofspatialthefrequencyofattachmentofchiralcrystallineclusters,orthespreadingoftheopticalpotentialwell,showedthattheconcentrationofchiralclusters,ratherthantheeffectofthemagnitudeofthedifferenceinthechiralgradientforcechiralopticalpotentialontheactivationenergyfornucleation.betweenthel-andd-chiralvirtualNaClO3nanospheresisThisinsightisreasonablebecausetheunderlyingassumptioncomparabletothatofthedielectricgradientforcepresentinoftheabovediscussionthatachiralopticalpotentialwithapreviousexperimentsonlaser-trapping-inducedcrystallizationconstantvaluespreadsinspacewidelyenoughtoincludethefromunsaturatedsolutions.Theseanalysesindicatethatwholevolumeofthecrystalnucleiisunrealistic,astheenantioselectivechirallybiaseddiffusioncanoccur,althoughmaximumchiralopticalpotentialislimitedtoonepointatthestableenantioselectiveopticaltrappingmightbeimpossible.Innanogap.Also,asmentionedabove,ourcalculationswith|κ|addition,analysisofthedifferenceinthesteady-statevaluesofNaClOof10−4to10−3suggestedthatthedifferencenucleationrate,takingintoconsiderationtheeffectofthe3inthefrequencyofattachmentofchiralcrystallineclusterschiralopticalpotential,showedthatthedifferenceinactivation6218https://doi.org/10.1021/acs.jpcc.0c11109J.Phys.Chem.C2021,125,6209−6221

10TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleenergyfornucleationcausedbythechiralopticalpotentialisHiroshiY.Yoshikawa−DepartmentofChemistryandinsignificantandcannotexplainthegiantCEE.ThisresultDivisionofStrategicResearchandDevelopment,Graduateimpliesthatthemainfactorcausingthenucleation-rateSchoolofEngineering,SaitamaUniversity,Saitama338-differenceisthefrequencyofattachmentofchiralbuilding8570,Japan;orcid.org/0000-0003-0624-6039unitsontocrystalnucleiortheconcentrationofchiralbuildingRyuzoKawamura−DepartmentofChemistryandDivisionofunitsaroundthenuclei,ratherthanthethermodynamicStrategicResearchandDevelopment,GraduateSchoolofcontributionofthechiralopticalpotential.AlthoughitisEngineering,SaitamaUniversity,Saitama338-8570,Japannecessarytoknowthe|κ|valueforaNaClO3chiralcrystallineJunNozawa−InstituteforMaterialsResearch,Tohokuclusterwhentheclusterinteractswithchiralplasmonicnear-University,Sendai,Miyagi980-8577,Japan;orcid.org/field,ouranalysisimpliedthatthegiantCEEmightbecaused0000-0001-7735-3515byadifferenceinthefrequencyofincidenceofcrystalnucleiatJunpeiT.Okada−InstituteforMaterialsResearch,TohokuthenanogapasaheterogeneousnucleationsiteorbythelocalUniversity,Sendai,Miyagi980-8577,JapandifferenceinconcentrationbetweenchiralcrystallineclustersSatoshiUda−InstituteforMaterialsResearch,TohokuduetoenantioselectivelybiaseddiffusionevenifweassumeUniversity,Sendai,Miyagi980-8577,Japanthatthe|κ|valueisthatobtainedbyfar-fieldORDCompletecontactinformationisavailableat:measurements.Ontheotherhand,stableenantioselectivehttps://pubs.acs.org/10.1021/acs.jpcc.0c11109opticaltrappingofchiralcrystallineclustersisnotunrealisticasacauseofthegiantCEE,ifweassumethatthe|κ|valueofNotesNaClO3isstronglyenhancedbyinteractionwiththechiralTheauthorsdeclarenocompetingfinancialinterest.plasmonicnear-field,asimpliedinpreviousstudiesonchiralplasmonics.■ACKNOWLEDGMENTS■ThisworkwassupportedbyJSPSKAKENHIgrant-in-aidforASSOCIATEDCONTENTScientificResearch(B)GrantNumberJP20H02686,JSPS*sıSupportingInformationKAKENHIfundforthePromotionofJointInternationalTheSupportingInformationisavailablefreeofchargeatResearch[FosteringJointInternationalResearch(B)]Granthttps://pubs.acs.org/doi/10.1021/acs.jpcc.0c11109.NumberJP19KK0128,JSPSKAKENHIScientificResearchonPermittivityparametersoftheLorentz−DrudemodelforInnovativeAreas“Nano-MaterialOptical-Manipulation”Au(S1);differenceintheEMfieldoftheplasmonicGrantsJP16H06507(toT.S.),thejointusage/researchnear-fieldofaAunanotriangletrimerbetweenl-andr-programoftheInstituteofMaterialsandSystemsforCPLexcitation(S2);spatialcharacteristicoftheopticalSustainability(IMaSS),NagoyaUniversity,TohokuUniversitychiralitydensitydistributionintheplasmonicnear-fieldNanoFabricationPlatforminNanotechnologyPlatformofaAunanotriangletrimer(S3);estimationofthe|κ|ProjectSponsoredBytheMinistryofEducation,Culture,valueofaNaClO3chiralcrystalfromORDmeasure-Sports,ScienceandTechnology(MEXT),Japanments(S7);andSIreferences(S9)(PDF)[JPMX09F(A)F-20-TU-0012],theSumitomoFoundation,andtheMinistryofScienceandTechnologyinTaiwanundercontractsMOST109-2113-M-009-008-,MOST109-2634-F-■AUTHORINFORMATION009-028,andMOST109-2927-I-009-513(toT.S.).CorrespondingAuthorHiromasaNiinomi−InstituteforMaterialsResearch,Tohoku■REFERENCESUniversity,Sendai,Miyagi980-8577,Japan;orcid.org/(1)Dobson,C.M.ProteinFoldingandMisfolding.Nature2003,0000-0001-7003-5434;Phone:+81-22-215-2103;426,884−890.Email:h.niinomi@imr.tohoku.ac.jp,niinomi37@(2)Smith,S.W.ChiralToxicology:It’stheSameThing...Onlygmail.com;Fax:+81-22-215-2101Different.Toxicol.Sci.2009,110,4−30.(3)Moradpour,A.;Nicoud,J.F.;Balavoine,G.;Kagan,H.;AuthorsTsoucaris,G.PhotochemistrywithCircularlyPolarizedLight:TheTerukiSugiyama−DepartmentofAppliedChemistryandSynthesisofOpticallyActiveHexahelicene.J.Am.Chem.Soc.1971,93,2353−2354.CenterforEmergentFunctionalMatterScience,National(4)Bernstein,W.J.;Calvin,M.;Buchardt,O.AbsoluteAsymmetricChiaoTungUniversity,Hsinchu30010,Taiwan;DivisionofSynthesis.I.OntheMechanismofthePhotochemicalSynthesisofMaterialsScience,GraduateSchoolofScienceandNonracemicHeliceneswithCircularlyPolarizedLight.WavelengthTechnology,NaraInstituteofScienceandTechnology,Ikoma,DependenceoftheOpticalYieldofOctahelicene.J.Am.Chem.Soc.Nara630-0192,Japan;orcid.org/0000-0001-9571-43881972,94,494−498.An-ChiehCheng−DepartmentofAppliedChemistryand(5)Inoue,Y.AsymmetricPhotochemicalReactionsinSolution.CenterforEmergentFunctionalMatterScience,NationalChem.Rev.1992,92,741−770.ChiaoTungUniversity,Hsinchu30010,Taiwan(6)Flores,J.J.;Bonner,W.A.;Massey,G.A.AsymmetricPhotolysisMihoTagawa−DepartmentofMaterialsScienceandof(RS)-LeucinewithCircularlyPolarizedUltravioletLight.J.Am.EngineeringandInstituteofMaterialsandSystemsforChem.Soc.1977,99,3622−3624.(7)Sandford,S.A.;Nuevo,M.;Bera,P.P.;Lee,T.J.PrebioticSustainability(IMaSS),NagoyaUniversity,Nagoya,AichiAstrochemistryandtheFormationofMoleculesofAstrobiological464-8603,JapanInterestinInterstellarCloudsandProtostellarDisks.Chem.Rev.ToruUjihara−DepartmentofMaterialsScienceand2020,1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