Nanoparticle morphology and aspect ratio effects in

TheorChemAcc(2012)131:1078DOI10.1007/s00214-011-1078-6

REGULARARTICLE

NanoparticlemorphologyandaspectratioeffectsinAg/PVDFnanocomposites

ChristopherK.Rowan?IrinaPaci

Received:13June2011/Accepted:1August2011/Publishedonline:11January2012ÓSpringer-Verlag2012

AbstractOpticalresponseinsilver/polyvinylidene?uo-ridenanocompositematerialswithnonsphericalinclusionswasexaminedusingdirectdipolarinterbandtransitions,fromdensityfunctionaltheory.Wediscussherethedependenceoftheopticalresponseofthematerialonthegeometry,crystallographicmakeupandend-capmorphol-ogyofthemetallicinclusions,aswellasontheirorienta-tionrelativetothepolarizationdirectionoftheappliedelectromagnetic?eld.Eachperiodicunitcellcontainedasingleinclusionandapolymermatrix;thus,thecompositebehavedasamonodisperse,perfectlyorientedmaterial.Overall,thespectrallocationofthecompositeexcitationspectrumwastiedtothatofthemetallicinclusionsandcorrelatedwelltoquantumcon?nementmodelsforthedirectionofpolarization:Aslinearsizeoftheinclusionincreasedinagivendirection,theexcitationspectrumoflightpolarizedinthatdirectionwasred-shifted.Theeffectofthepolymermatrixwasalsoexamined.Coulombrepulsionfrommatrixenergystatesledtosplittingofnanoparticle-basedenergylevels,andthematrixconduc-tionbandbecameinvolvedinhigh-energytransitions.Theseeffectsledtoextensionsofthespectraofnano-compositeswithlessstable{100}–http://wendang.chazidian.comparisonswithexperimentaland

Publishedaspartofthespecialcollectionofarticlescelebratingthe50thanniversaryofTheoreticalChemistryAccounts/TheoreticaChimicaActa.

C.K.RowanÁI.Paci(&)

DepartmentofChemistry,UniversityofVictoria,POBox3065,Victoria,BCV8W3V6,Canadae-mail:ipaci@uvic.ca

time-dependentdensityfunctionaltheoryresultssuggestthatestimatingthecomplexdielectricconstantfromin-terbandtransitiondipolemoments,inatime-independentfashion,providesreliablequalitativespectraforthesesystems.

KeywordsMetal/polymernanocompositesÁOpticalresponseÁDensityfunctionaltheoryÁInclusionmorphologyÁBirefrigentmaterials

1Introduction

Inmetal-polymernanocomposites(NCs),theversatilityofpolymerscanbecombinedwiththedistinctive?eld-responsepropertiesofmetalnanoparticles(NPs)toobtaininterestingnewmaterialswithhighlytunablecharacteris-tics.Evenatsmallinclusionloadings,theabsorptionspectraofthematerialcanbeenhancedbymanyordersofmagnitudewhennoblemetalNPsaredispersedinapolymermatrix[1,2].ThisenhancedsignalisduetoNPelectronsthatcollectivelyoscillate,knownaslocalizedsurfaceplasmonresonances[3].Absorptionstrengthsandresonantfrequenciesaredependentonthechoiceofpoly-merandNP,particlesize,shape,distribution,orientationandvolumefraction(loading),andthepolarizationoftheincidentelectric?eld.Thus,engineeringmaterialsforspeci?cfunctionsrequiresinsightintotheindependentandcorrelatedeffectsofallofthesevariables.

AgNPshaveelectronictransitionsinthevisiblerange,andavarietyofshapesandsizeshavebeenfabricatedtotunetheirabsorptionbands.Geometrieshaveincludedvariouspolyhedrals[4–6],spheres[7],disks[8],sheets[9],rods[8]andwires[10].ThedistributionofNPsizescanbenarroweddowntoproducenearlymonodispersesystems

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Page2of11throughbottom-upreaction-drivenapproaches[11]ortop-downlithographicmethods[12].NCstructuresareoftenlimitedtorandomdistributionsofNPs,exceptin2-Dlithographicarrays,butnewapproachesarebeingdevel-oped[13,14].

LightabsorptionbynonsphericalNPsisdependentontheirorientationintheincident?eld.MetalNPsplacedinanelectricallyinsulatingenvironmentexperiencequantumcon?nement,andelectronicabsorptionsoccuratlowerenergieswhenpolarized?eldsinduceelectronicreso-nancesalonglongerNPaxes[15].WhenamajorityofNPsareorientedinthesamedirection,thematerialresponsedependsonthe?eldpolarization,resultingindichroicorbirefringentmaterials[16,17].TheabilitytocontroltheorientationandalignmentofNPsinaNCcouldfacilitateapplicationsassensors[18],broadbandwaveguidepolar-izers[19],opticalantennas[20]andoptical?bersthatemploysurfaceenhancedRamanspectroscopy[21,22].AlignedandorientedAg/polymerNCshaverecentlybeenreportedwithnanorods[23]andwires[14,23].

InterfacialareasplayanessentialroleinestablishingthedielectricandopticalpropertiesofaNC.NPsurfacespresentvariouscrystallographicfacets,withdifferentsur-faceenergiesandatomicdensities,whichimpactthenatureofphysisorptionsitesandgenerallytheinteractionsbetweentheinclusionandthematrix.Agandotherface-centeredcubiccrystalsadoptprimarily{111}facets,asthesearethemostenergeticallystable,followedby{100}and{110}facets[24,25].ExperimentshaveshownthatAgnanodisksoftenhave{111}basalplanes[26–28].Nano-rodsfrequentlyhavepentagonalcross-sections,with{100}sidesandpyramidalend-capswith{111}facets[29–32].Opticalpropertiesforthesenanoparticleshavebeenwellstudiedexperimentally[10,33–37]andtheoretically[38–40].However,thedevelopmentofNCmaterialsbuiltwiththeseinclusionsisstillanemergingareaofresearch.

Wepreviouslyapplieddensityfunctionaltheory(DFT)tothestudyofAg/polyvinylidene?uoride(PVDF)toinvestigatetherelationshipsbetweenabsorptionspectra,particlesize,loadinganddispersion[41].Inideal,mono-dispersesystems,wefoundthattheopticalpropertiesoftheNCwerestronglyin?uencedbythoseofthemetallicinclusions.Analysisofdensityofstates(DOS)diagramsshowedthattheinclusionsintroducedmultipleorbitalsandelectronsinthe&7eVpolymerbandgap.ThisledtotheappearanceofopticaltransitionsintheNCwheretherewerenoneinthepolymer.Theelectronicpopulationofthe?lledmetallicorbitalsledtoashiftintheFermienergyofthematerialandtheinvolvementofthepolymericcon-ductionbandinsomeofthehigher-energytransitions.Overall,theNPabsorptionpeaksintheimaginarypartofthedielectricconstant??2absorptionspectrawereshiftedslightlyandbroadenedbythepresenceofthepolymer.

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IncreasedNPloadingresultedinmoreoccupiedandavailableorbitalsintheDOS,andthusinstrongeropticalresponsepeaks.NPanisotropyledtoashiftofabsorptionlinesthroughquantumcon?nement:PolarizationalongthelongerNPaxesresultedinredshiftingoftheNCabsorptionpeaks.Additionally,theabsorptionspectrumofasimplepolydispersesystemcouldbetracedbacktotheindividualmonodispersesystems:SpectralenergiesandintensitiesofthepolydisperseNCwerecorrelateddirectlytointerparti-clespacingofNPs,ratherthanNPloading.

ThesestrongrelationshipsbetweenNPandNCopticalpropertiesledtoourinterestinasystematicstudyoftheopticalbehaviorofNCscontaininganisotropicinclusions.Theintentwastoperformamorein-depthexaminationofhowmaterialpropertiescanbetunedbyusingNPsofdifferentgeometriccharacteristics.Thus,wedescribeheretheopticalbehaviorofarangeofNCs,containingsmallAgdisksandrodsofdifferentaxisratiosandcrystallographicmakeup,withthegoalofelucidatingtheeffectofthesevariableson??2inpolarizedelectromagnetic?elds.Inadditiontopyramidalend-capsonnanorods,nanobarsandnanoricewithbluntorhemispherical-liketermini,respec-tively[42],http://wendang.chazidian.comparisonswithexistingexperimentalandtheoreticalresultsareprovided,whereavailable,toprobethereliabilityofthetime-inde-pendentmethodusedhere,foropticalcalculations.

2Method

Weconsideredthetwentycrystallinedisk-androd-shapedAginclusionsshowninFig.1.Nanodisksconsistedoftwoatomiclayerswithvaryingnumbersofatoms,andnanorodswerecomposedofmultiplestackedlayers(betweenthreeandsevenlayersofuptosevenatomsperlayerwereconsidered).Forbothshapes,{111}and{100}facetswereinvestigated.Bilayerdiskswithlargerdiametersthanthoseconsideredherehaverecentlybeenreportedexperimentally[43].Theinclusionsweconsideredwerecutfromthefcccrystalstructure,ratherthanminimum-energystructures:Suchstructuralminimizationsleadtomaximum-binding,near-sphericalstructuresthatwouldinvalidatethegeometricalanalysiswhichconstitutesthepurposeofthepresentstudy.Toestimatetherelativestabilityofthedifferentgeom-etriesconsideredhere,thebindingenergiesoftheNPswerecalculatedastheenergydifferencebetweenboundandfreeAgatoms:EbðAgnÞ¼

EðAgnÞ

n

ÀEðAgÞ;ð1Þ

whereEbisthebindingenergyperatom,E(Agn)istheenergyofAgn,http://wendang.chazidian.comrgerbindingenergiescorrespondtoincreasedparticle

TheorChemAcc(2012)131:1078Page3of11

A(12)B(13)C(15)

D(16)E (17)

F(19)

G(20)H(22)I(24)J(31)

K(19)L(21)M(25)N(29)

O(13)

P(22)Q(31)R(27)S(25)T(31)

Fig.1Disk-androd-shapedAgninclusions.ParticlesA–Jarebilayerdiskswith{111}basalplanes.K–Narebilayerdiskswith{100}basalplanes.O–Qarerodswithlayered{100}basalplanes.R–Tarerodswithlayered{111}basalplanesandmorphologicallytailoredend-

caps.ThenumberofatomsnisindicatedforeachNPinbrackets.NPz-axesrunverticallyandx-axesrunhorizontally,intheplaneofthepage.PicturesareslightlytiltedtorevealtheNP3-Dstructure

stability.Nanoparticledimensions,aspectratiosandbind-ingenergiesaregiveninTable1.

Throughout,axisoraspectratiosaregivenastheratiobetweentheNPdimensioninthedirectionoftheapplied?eld(normalfordisk-shapedNPsandlongitudinalforrod-shapedNPs)andtheNPdimensioninthexdirection,whichwasalsothealternatepolarizationdirectioncon-sideredinthestudy.NPsmayormaynothaverotationalsymmetryandmayoftenhavedifferentdiametersintheydirection.However,polarizationalongthisaxisdoesnotaddanyfurtherinformationtothepresentdiscussionandwasthusnotconsidered.

Fromthetable,andascon?rmedbypreviousexperi-mentalobservations[44],largerclustersweremorestable.Thepresenceof{111}basalplanesalsoledtotighterbindinginbothdisk-androd-shapedNPs,atrendthatwasexpectedfromcrystalplanesurfaceenergies.Notunex-pectedly,giventheirsmallsizes,alloftheNPsconsideredhereexhibitedstrong?nitesizeeffects:Forcomparison,thePBE/DZP-calculatedbindingenergyforbulkAgwas-5.03eV.TheelectronicstructureofNPs(speci?cally,HOMO-LUMOgaps)haspreviouslybeencorrelatedwiththestabilityoftheclusters,evenawayfromultra-stablemagicnumberclusterswithcompleteelectronicshells[45–49].However,thedependenceisnotmono-tonic,andgenerallyapplicablerelationshipscannotbeestablished.

InitialNCstructureswerecompressedusingclassicalmoleculardynamicswithintheGromacs[50]softwarepackageusingperiodicboundaryconditions(PBC).Lennard–JonesparametersforstructureoptimizationsweretakenfromtheUniversalForceField[51].PartialatomicchargeswerebasedonthoseofChenandShew[52];silveratomshadzerocharge.Inordertoprovideconsistencythroughout,NPloadingwasheldconstantat4.2vol%.OneimplicationofthiswasavariationoftheinterparticleseparationbetweenNPimagesinthedifferentsystems,whichinturnaffectedabsorptionintensityandresonance

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Table1NPandNCgeometricpropertiesandbindingenergies

NCA/470B/512C/590D/626E/668F/740G/782

?),axisratios,NPdimensions(A

bindingenergies(eV)andedge-to-edgeinclusion–inclusiondistancesacrossPBCimages?)areincluded.Inclusion(A

diameters(X,YandZ)hadanadditionalatomicdiameter(2.9?)addedtothelargestA

internucleardistances.Thesameatomicdiameterwassubtractedfrominterparticledistances,suchthat,forexample,

X?Xsep=Xlattice,the

simulationcellsizealongX.Theaspectratio(A)inthexzplaneisgivenasz/x

H/860I/938J/1214K/740L/818M/980N/1130O/512P/860Q/1214R/1052S/980T/1214

X8.78.78.711.28.711.611.111.211.214.511.111.015.215.28.78.78.78.78.78.7

Y9.68.78.78.711.610.48.511.611.612.911.111.015.215.28.78.78.79.69.69.6

Z5.35.35.35.35.35.35.35.35.35.34.94.94.94.97.011.115.217.012.312.3

A1/1.651/1.651/1.651/2.141/1.661/2.201/2.101/2.141/2.141/2.751/2.241/2.241/3.071/3.071/1.241.282.171.971.421.42

Eb-3.16-3.29-3.34-3.34-3.45-3.50-3.46-3.50-3.65-3.68-3.26-3.42-3.46-3.47-3.25-3.52-3.63-3.71-3.69-3.67

TheorChemAcc(2012)131:1078

Xsep6.36.87.55.38.29.86.78.710.07.96.47.06.56.68.711.213.712.612.113.7

Ysep8.09.310.210.68.27.112.210.111.511.39.310.18.38.58.712.915.614.413.014.7

Zsep13.413.914.815.215.716.416.915.616.418.216.717.517.017.97.09.88.35.39.511.2

energies.Figure2showsexamplesofGromacs-optimizedunitcellsforadisk-(panela)andarod-shapedinclusion(panelb).Theconstructionofsuitablesimulationcellsandcomputationaldetailshavebeendescribedingreaterdetailelsewhere[41].

TheNPaxesspeci?edinFig.1wereorientedinlinewiththerespectiveaxesofthesimulationcells.Speci?cNPswillbereferredtohereafterasNPX,whereX¼A,B,...;T,asshowninthe?gure.NCmixtureswillbereferredtoas,forexample,A/470,wheretheletterindicatestheinclusionsizeandgeometryandthenumberindicatesthesizeofthepolymerchain.

DFTcalculationswereperformedusingSIESTAversion2.0.2[53].APBE/DZPformalism[54]wasused,withcoreelectronsmodeledusingnorm-conservingTroullier–Mar-tinspseudopotentials[55]fromtheSIESTAwebsite.TheopticalfeatureinSIESTAcalculates??2fromdirectinter-bandtransitions[56,57].Forperiodicmaterials,allowedmomentum–spacetransitiondipolematrixelementsarecalculatedbetweendifferenteigenfunctionsoftheentiresystemHamiltonian.Themodel,basedonthedamped,harmonicLorentzoscillator,assumesthelocal?eldtobeequaltothemacroscopic?eldandisgivenbyasumofthesetransitions:

2

e2"h2XXjli;jðkÞjf0ðEjðkÞÞÀf0ðEiðkÞÞ

??2ðxÞ¼1À:E??0m2Vh"xÀihCEijeiji;jk

ð2Þ

whereeistheelectroniccharge,"h¼h=2p;hisPlanck’s

constant,??0isthepermittivityofavacuum,meisthemassoftheelectron,andVisthevolumeofthecell.Thesumrangesoverallk-pointsinreciprocalspacewithadoublesumoverallelectronicenergyvaluesiandj.li;jðkÞaretransitiondipolematrixelements,f0istheFermidistribu-tionfunction,Eij=Ei(k)-Ej(k),xistheangularfre-quency,andCisapeakbroadeningterm.Allreported??2spectrauseabroadeningfactorof0.05eV.

FurtherdetailsoftheopticalSIESTA/DFTcalculations,theiradvantagesandlimitationsaregiveninRef.[41]andreferencestherein.SpinpolarizationwasconsideredforseveralNCscontainingNPO.Theresultingspectrawerevirtuallyindistinguishablefromspin-unpolarizedresults.Thefaster,spin-unpolarizedcalculationsarereportedhere.DFT-basedgeometryoptimizations,beyondtheforce?eldoptimizedstructures,alsohadaminoreffectontheresulting??2spectra.AsmoststandardDFTmethods,thePBEHamiltonianunderestimatesbandgaps[58–60].Empiricalscissoroperatorsareoftenapplied[61,62]tocompensateforthistendency.Theywerenotusedinthiswork,becauseofalackofcomparableexperimentaldata.Ontheotherhand,higherlevelsoftheorywerecomputa-tionallyintractablefortheselargesystems.Therefore,spectraandrelevantexcitationswillbediscussedrelativetooneanother,ratherthanasabsolutevalues.

Polarizedelectric?eldsweredirectedalongtwosym-metryaxesoftheNPs,asshowninFig.3.Fornanorods,

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Fig.2SimulationcellsforNCswithdisk-androd-shapedinclu-sions:SystemN/1130isshownin(a),andR/1052in(http://wendang.chazidian.comrgegrayatomsareAg,Cisdarkgray,Hiswhite,andFatomsarecoloredinlightgreen

longitudinal?eldsweredirectedalongtheprincipal(z)axis,andtransverse?eldswerealongaperpendicular(x)axis.Normalmodepolarizationfornanodiskswasalongthenormalvectorofthedisk,andthetransversemodewasincidentalongtheside,inthexdirections.Page5of113ResultsanddiscussionTheopticalpropertiesoftheNCswerestronglydeterminedbythoseoftheinclusions.Duetotheirsmallsize,NPsgenerallyexhibiteddiscreteelectronicenergylevelswithinafeweVoftheFermienergy,whichledtostrong,discretepeaksintheir‘‘interband’’transitionspectra(notethatduetotheirsmallsizes,theNPsexhibitdiscreteenergylevelsratherthanbands).TheselevelspopulatedthelargebandgapofthepolymermatrixintheNC.Initspureform,bulkPVDFexhibitednoopticalresponseintheUV–visspectralregion.However,intheNCs,polymerbandsinteractedslightlywithNPorbitals,leadingtosomebroadeningofDOSpeaks.Matrixelectronicbandswerealsoinvolvedinthelarger-energytransitionsoftheNC,astheFermienergyofthematerialwasrepositionedduetoNPelectrons.Inthefollowingpages,thediscussionofNCopticalpropertieswilloftenreferbacktotherespectiveNPspectra,duetotheircentralroleindeterminingtheresponseofthematerial.3.1NanodiskaspectratioeffectsChangesinthehorizontal(xy)sizeofthenanodisklayersledsimultaneouslytochangesinclustersize,axis(aspect)ratioandhorizontalinterparticledistanceinthecorre-spondingNCs.Spectrafornormal(z)andtransversal(x)excitationsforNCsofthree{111}-facetdisksarepre-sentedinFig.4,alongwithDOSplotsfortherelevantNPsandNCs.Asexpectedfromcon?nementmodels,absorp-tionforboththeNPsandtheirNCsoccurredathigherenergiesforexcitationsalongtheshorternormaldirection(panela),thanalongthetransversaldirection(panelb).Apervasivefeatureindisk-basedNCspectrawasthatthehigh-energyabsorptionpeaksoftheinclusionswereshiftedtolowerenergiesandbroadenedintheNCs.

This123