Linear and Polygonal Assemblies of Plasmonic Nanoparticles

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Linear and Polygonal Assemblies of Plasmonic Nanoparticles: Incident Light Polarization Dictates Hot Spots Reshmi Thomas, and Rotti Srinivasamurthy Swathi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b04589 • Publication Date (Web): 01 Aug 2016 Downloaded from http://pubs.acs.org on August 10, 2016

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The Journal of Physical Chemistry

Linear and Polygonal Assemblies of Plasmonic Nanoparticles: Inci‐ dent Light Polarization Dictates Hot Spots† Reshmi Thomas and R. S. Swathi* School of Chemistry, Indian Institute of Science Education and Research-Thiruvananthapuram (IISER-TVM), Kerala, India, 695016 ABSTRACT: The assemblies of metal nanoparticles, thanks to their intriguing plasmonic properties, have provided numerous opportunities for manipulating light at the nanoscale. Driven by the recent experimental success in using polarization of light as a handle to control plasmonic features, we consider the organization of spherical gold nanoparticles as linear and polygonal assemblies (n = 1-6) and perform a detailed analysis of the optical features as a function of the polarization of the incident light (θ = 0o, 30 o, 60 o and 90 o) using the finite-difference time-domain (FDTD) method. Our investigations reveal that the extinction features in linear chains show a strong dependence on the state of polarization of the source whereas those in the polygonal assemblies are polarization insensitive. However, the hot spot distribution in polygonal assemblies is strongly dependent on the polarization state of the incident light, thereby giving rise to interesting control over hot spot features for surface-enhanced spectroscopy. Finally, we also comment on the role of the wavelength of light, size of the metal particle and the gap size between the particles in governing the plasmonic properties of the assemblies.

INTRODUCTION The unusual properties of nanomaterials arising from the localized surface plasmons associated with them1-2 have been widely applied in the fields of spectroscopy, optics, and nanoelectronics. Plasmons can be construed as the collective oscillations of conduction electrons in the metal structures upon interaction with electromagnetic radiation. When the plasmon modes are excited on nanoparticles they are known as localized surface plasmon resonances (LSPRs).3-4 The LSPRs are responsible for the intriguing properties observed in nanostructures compared to the bulk metals. To explore the advantages of these properties for various applications, nanostructures of various shapes like spheres,5 cubes,6 rods,7 bipyramids,8 flowers,9 wires10 etc. have been synthesized and studied. The LSPRs present in the noble metals like, Ag11 and Au12 fall in the visible region of the electromagnetic spectrum, making them candidates of choice in plasmonics. Tuning the LSPRs to desired wavelengths is a major challenge in plasmonics research as it is a key requirement to intensify the extinction cross-sections and optical fields in the preferred regions of the electromagnetic spectrum. In this aspect, coupling the metal nanoparticles is considered as a major development.13 When the nanoparticles are brought in close proximity, the LSPRs on the individual particles couple with each other, in a phenomenon referred to as plasmon hybridization.14 The hybrid LSPR modes give rise to pronounced shifts in the extinction maxima and enormous enhancement in the plasmonic fields when compared to the corresponding monomeric systems. Thus the coupled nanoparticle systems can efficiently enhance and focus the incident electromagnetic fields to the nanogaps at the junctions of the particles making them materials of interest.15 Recent advances in the synthesis of well-defined nanoparticle assemblies and arrays provide opportunities for the systematic coupling of LSPRs.16-18 Various strategies for the synthesis of nanoparticle assemblies have been

reported in the literature, including lithographic techniques,19-20 DNA-based method,21-22 molecularly linked systems,23-24 electrostatic interactions25-27 etc. Attempts to vary the gap between the individual particles in order to tune the coupling between the particles have also been reported.28-30 In this context, a detailed theoretical understanding of the plasmons and their coupling is necessary for the design of efficient plasmonic materials. Computational techniques like finite-difference time-domain (FDTD) method,31-33 discrete dipole approximation (DDA),34-36 finite element method (FEM),34 boundary element method (BEM)37 etc. are widely used for performing the electrodynamics studies of nanostructures. Using these methods, efforts are made to systematically study the factors affecting the plasmons, design protocols to improve the plasmonic features and develop newer areas of applications.38-39 In an earlier report from our group we have investigated the effect of size variation in the plasmonic features of a trimeric nanoparticle assembly.38 There are numerous theoretical and experimental reports in the literature about well-defined nanoassemblies like short linear arrays and aggregates of few particles.40-44 However, studies on larger and controlled assemblies are rare because of the difficulty in controlling the kinetics and thus the lack of reproducibility. Mulvaney and co-workers have reported the light scattering properties of linear chains of gold nanoparticles with up to six nanoparticles.45 Li et al. showed the controlled formation of polygonal metal nanostructure assemblies, including dimer, triangle, tetragon, pentagon, and hexagon arrays on top of predefined flexible polymer pillars with the aid of microcapillary forces and examined the symmetry dependence of the nanoplasmonic structures.20 Distance between the nanoparticles in the arrays,46-49 the dielectric of the medium,50-51 angle between the individual particles,52-53 size of the clusters54-56 etc. are few other factors which have been investigated. The polarization dependence

†

This paper is dedicated to Prof. K. L. Sebastian on the occasion of his superannuation

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RE ESULTS AND DISCUSSION N Our prim mary objective in this work is to investigate aand com mpare the plasm monic propertiees of linear and polygonal nanooassem mblies. The systtems under inveestigation are the assemblies of Au nannoparticles (Auu NPs) and thee number of naanoparticles in tthe asssemblies varies ffrom 1 to 6. Thee radius of the coonstituent Au N NPs is cchosen to be r = 10 nm and thee gap between thhe nanoparticlees is keppt uniform throuughout as, g = 3 nm (Figure 1)). The monomeer is labbeled as M and the t linear structtures are labeledd as L2, L3, L4, L5 andd L6 with the inncreasing numbber of nanopartiicles in the asseemblyy. The polygonal systems are labbeled as trianglee, square, pentaggon andd hexagon. We investigate the vvariation in thee optical propertties of tthe above assem mblies when theyy are excited witth incident lightt of varrying polarizatioon states (θ = 0, 30, 60 and 990). The variatiion of the extinction m maxima with θ is examined. The T regions of enhannced electric fieeld for various aangles of excitaation are identiffied andd the variation in i the field intennsities at the hoot spots for varioous asssemblies is studiied systematicallly.

60 000 30 000 0

COMPUTATIONAL DETAILS The F FDTD simulatiions reported hherein are perfoormed using the program FDTD Soluutions (version 88.9.138), a prodduct of Lumerical Soluutions, Inc., Vanncouver, Canadda. The FDTD technique involves obtaining solutiions to the Maxxwell time-dependent curl equations iin order to desccribe the variatioon of electromaggnetic waves with timee within a finite space. It makes use of the Yee’ss algorithm, in whichh the derivativess involving spacce and time varriables are replaced byy the corresponnding finite diffeerences. Johnson and Christy dielectrric data was ussed for modelinng the frequenccy dependence of thhe dielectric connstant of Au. A total field-scatttered field (TFSF) ssource of light,, consisting of plane waves iin the wavelength range 400−700 nm m, is used as the incident beam in the simulations. Thhe amplitude off the incident fieeld was chosen to be 1.0 V/m, and hhence the field inntensities actuallly represent thee relative intensities. Water, with a refractive r indexx of 1.33, is chossen as the backgroundd medium. Thee electric field iintensity distribbution patterns arounnd all the naanostructures rreported hereinn are calculated at 6333 nm, a typicaal laser excitatioon wavelength tthat is used in experim ments. 0.3 nm m mesh size was em mployed for the simulations. The m mesh size was chosen by prior testing foor the convergence off the numericall results. We usse perfectly maatched layer (PML) and a symmetric as well as antisymmetric bouundary conditions wheerever the symm metry allowed ttheir use to savve the computational ttime.

0

L4

0o 30o 60o 90o

450 600 Wavelength (nm))

9000 6000

6000

0

L5

0o 30o 60o 90o

9000 6000

450 600 Wavelength (nm) o

L L6

0 30 o 60 o 90 o

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450 600 Wavelength (nm)

L L3

0o 30o 60o 90o

3000

450 600 Waveelength (nm)

3000 0

9000

Cross-section (nm2)

L2

3000

450 600 Wavelength (nm m)

Cross-section (nm2)

0

6000

0o 30o 60o 90o

2

3000

9000

Cross-section (nm )

6000

90 000

Figure 1: Schem matic representatiion showing the linear and the polygonal assemblies off Au nanoparticlees under investiggation.

M

0o o 30 60o 90o

Cross-section (nm2)

9000

Cross-section (nm2)

of optical prooperties for vvarious monom meric particless like nanocube,57 nannorod,58 nanocrresecent59 etc. hhave been reporrted in literature. It is found that plassmonic propertiies show a stronng dependence on thhe polarization of the incidentt light in the caase of these anisotroppic structures. H However, the vaariation in plasm monic features as a ressult of change inn polarization off exciting light ssource for nanoparticlle aggregates and arrays is reelatively an undderexplored topic.60-661 Keeping aside thhe sporadic reports r of vaarious nanoassembliess, a detailed com mparative and ccomprehensive aanalysis of the plasm monic features in linear and polygonal p assem mblies with varying nuumber of nanopaarticles has not been reported to t our knowledge. Hence, in this papper, we focus onn a comparative study of linear and asssembled structtures of spherical gold nanoparticles and their responnse towards the variation in thee angle of polarizzation of the light souurce by perform ming FDTD simuulations.62-63 Wee look into the linearr chains and the t polygonal nanostructures with number of monnomeric particlees varying from m 1 to 6. The anngle of polarization θ oof the incident rradiation is varieed from 0o to 900o. We investigate the extinction featuures and the eleectric field profifiles at the junctions off nanoparticles iin the assembliees as a function of the angle of polarizzation. A detaileed analysis of this kind is expectted to have significantt implications inn the design of nnovel plasmonicc substrates for surface-enhanced spectroscopy.

Cross-section (nm2)

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Figgure 2: The extinnction spectra of m monomeric and linear assembliess of Au NPs for varying angles of polarizzation of the inciddent light.

The moonomer (M), being an isotropicc spherical particcle, shoowed extinctionn maximum (λmmax) at 530 nm foor all the angless of exccitation. In the linear structurres, interesting features were oobserrved in the extinnction profiles, as shown in Fiigure 2. In L2, tthe exttinction maximuum was observed at 549 nm at θ = 0o and it shoows a hypsochromic h shhift as θ is varied from 0o to 900o. The intensityy of thee peak also reduces as θ is variedd from 0o to 90o. Similar trend w was obsserved for all the other linearr assemblies. Inn the higher ordder chaains, we observee that a second bblue shifted peaak comes up at 660o andd at 90o, the firstt peak completeely disappears annd the blue shift fted peaak is the only siignificant peak observed. The shift in λmax of tthe lineear assemblies ffrom the monom meric λmax increaases from L2 to L L6. Thhe extinction maaxima values aree tabulated in Taable 1. The highhest vallue of λmax was obbserved for the L L6 system as 5773 nm. Tabble 1: λmax valuees (in nm) for thhe various linearr and polygonal assem mblies of Au NP Ps for varying anngles of polarizattion of the inciddent lighht. θ

0o

30o

L2

549 9

L3

558 8

L4

Asssembly

λmax

524

Triiangle

546

524

Squ uare

546

527, 567

524

Pen ntagon

549

527, 573

524

Hex xagon

560

60 0o

90o

546

532

524

557

529, 552

567 7

567

529, 564

L5

570 0

570

L6

573 3

573

Assembly

Polygonnal structures haave distinctly different optical ffeaturres when compaared to the linearr assemblies (Fiigure 3). In eachh of thee structures, thee extinction peakk position remaiins constant forr all thee angles of excitaation. A bathochhromic shift in thhe peak positionn

2



2000

0

450 6000 Wavelength (n nm)

4000

0o 30 o 60 o 90 o

Hexagon

2000

0

450 600 Wavelength h (nm)

Figure 3: The exxtinction spectra of polygonal asssemblies of Au NPs N for varying angles off polarization of tthe incident lightt.

is however obseerved from trianngle to hexagonn. The λmax valuues are 546 nm for triaangle, 546 nm fo for square, 549 nm n for pentagoon and 560 nm for hexxagon. The extiinction peak inttensity also incrreases with the increasse in the number of nanoparticlles in the assembbly. In the linear chainns, for θ = 0o poolarization the pplasmon peak waas observed to be reed shifted in com mparison with the monomericc peak evidencing stroong longitudinall plasmon couppling between thhe nanoparticles. As we change the θ in steps of 300o, the extent of coupling decreases leading to a dam mpening of the peak intensity and a at 90o the monom meric plasmon peak p is almost reecovered due too very weak transversee coupling betw ween the particlees in the assembbly. In contrast, in thee case of polygoonal assemblies,, the overall couupling between the naanoparticles in thhe entire assem mbly is similar for various angles of exxcitations and hhence λmax is inseensitive to the sttate of polarization of the t incident lighht. Argum ments based onn symmetry can be invoked tto describe the origin of the opticall features of meetal NP assembllies in terms of the pllasmonic modees on individuall particles. Usinng the dipolar modes on o the individuaal particles as a basis b and using group theoretical arguuments, it is possible to arrive at a reducible rrepresentation for eaach assembly. O On obtaining thee correspondingg irreducible represenntations that coomprise it and chhecking for thosse that transform as thhe dipole components in the ccharacter table oof the point group too which the asssembly belongss, the optical acctivity (bright or dark)) of the LSPR m modes can be asccertained. An annalysis of this kind in conjunction witth the plasmon hybridization m model can unravel thee origin of the ooptical modes inn complex plasm monic architectures annd has been reeported for the triangle, squarre and hexagon configuurations.52, 64-65 Furthher, the electricc field intensityy distribution at a the junctions of thee nanoparticles in each assemblly for different angles a of polarization θ was studied. The electric com mponent of thee electromagnetic radiation excites a dipolar plasm mon resonancee on a metal particle, which in turn creates an enhaanced electric ffield.66 This resultant eelectric field is inn the direction of polarization of the incident radiation, as can be cleearly seen in thee electric field prrofiles of the monomeeric Au NP for various θ valuees (Figure S1 inn Supporting Inform mation). At the jjunctions of nanoparticles in hhigher order assembliees, the electric fields on the surfa face of each of thhe 633 nm  = 0o

633 nm  = 0o

10 nm

10 nm 633 nm o  = 60

100 50 0

10 nm

0o 30o 60o 90o

M

20 10

400 200

0 -10

6 600

0 X (nm)

0

1 10 0o 30o 60o 90o

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0 X (nm)

40

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0 X (nm)

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0 X (nm)

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400 200

o

0 o 30 o 60 o 90

o

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600

-20

0 X (nm)

20

40 o

L L6

0 o 3 30 o 6 60 o 9 90

400 200 0

-60

-30

0 30 X (nm)

600

Figgure 5: The electtric field intensityy profiles in the vvicinity of the linnear assemblies of Au N NPs at 633 nm ffor varying anglees of polarizationn of v X show the ccuts thee incident light. The plots of E Field Intensity vs takken through the ccenters of the naanoparticles from m the correspondding conntours. (Note: T The scale on the E Field Intensityy axis for M is diff fferentt from the other linear l assembliess.)

moonomeric nanopparticles couplee with each otheer to form regioons of intense electricc field termed ass hot spots. In our present stuudy, wee analyze the inteensities at variouus hot spots in tthe linear as well as thee polygonal asseemblies as a funnction of the poolarization statee of thee incident light. All the field prrofiles are compputed at 633 nm m, a typpical laser excitaation wavelengthh that is used in experiments. This T anaalysis is particularly important iin the context off surface-enhancced speectroscopy, wherein field inteensities at hot spots dictate tthe streength of measurrable optical signnals from analyttes. The fieldd intensity profifiles of the L2 assembly for varioous θ are a shown in Figgure 4 and the actual a values cann be seen in Figuure 5. In I L2 we observve an enhanced field at the juncction comparedd to thee field on the monomer. m Maxim mum field intennsity was observved forr θ = 0o, which decreased withh increase in θ aand at θ = 90o tthe fielld at the junctioon is nominal (siimilar to the moonomeric field).. In L3,, the number oof junctions is two and thus ttwo hot spots are creeated of equal inntensity. As in the case of L2, the intensity I,, of eleectric field at thhe hot spots deccreases with θ. A similar trendd in whhich the I valuees fall off and reach a minim mum at θ = 90o is obsserved for all thhe linear chains. The increase inn the intensity I at thee junctions as thhe number of m monomers in the chain increasee is anoother interestingg feature observved, as is evident from Figure 5.. In eacch of the chainns, the maximum m intensity is ffound at the junction/junctions in the t centre of the chain which gradually g decreaases to either sides of tthe chain. The ffield profiles of L3, L4 and L5 are preesented in Figurres S2 and S3 inn Supporting Innformation and tthe proofiles of L6 are shown s in Figuree 4. Note that thhe scale bars in tthe conntours have beeen kept uniform to the value 1000 for a better coomparrison across the images. Howevver, the actual vvalues of I couldd be seeen from the plotts of E Field Inttensity vs X in F Figure 5. The ellectricc field intensity values at the hoot spots for variious θ are givenn in Figgures S8 – S12 inn Supporting Innformation.

633 nm  = 30o 10 nm

633 nm  = 60o

50

10 nm

633 nm o  = 90

633 nm  = 90o

10 nm

100

10 nm 633 nm  = 30o

30

E Field Intensity

P Pentagon

E Field Intensity

0


0o 30o o 60 90o

E Field Intensity

2000

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E Field Intensity

quare Sq

E Field Intensity

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0o 30 o 60 o 90 o

E Field Intensity

o

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4000

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Triangle

2

0o 30o 60o 90

4000

Cross-section (nm )


Cross-section (nm2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Cross-section (nm2)

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0

10 nm

Figure 4: Electriic field intensityy distribution proofiles in the vicinnity of the Au NPs in thhe L2 and L6 asseemblies at 633 nm m for varying anggles of polarization of thhe incident light..

Figgure 6: Schematiic representationn of the polygonaal assemblies under stuudy. In each connfiguration, varioous angles of poolarization, θ of the inccident light are labbeled.

3


The electric e field proofiles in the pollygonal assembllies of nanoparticles exhibit e far moree interesting feaatures than the linear chains. Figure 6 shows a scheematic represenntation of the assema blies, wherein tthe individual nnanoparticles aand the junctionns are labeled for connvenience in diiscussion. In thhe triangle, therre are three junctions,, A, B and C and the electric fieeld intensities att each of these junctioons depend on the polarizationn of the sourcee. The electric field coontours of the trriangle assemblyy are shown in F Figure 7. The value of I at the juncttion A shows a maximum at θ = 0o which subsequeently decreases with increase iin θ. For junctiion B, the value of I is maximum for θ = 90o which corrresponds to ann angle 0f 30o betweenn the junction aand the polarizaation angle θ. HenceH forth we denotee the angle betw ween the junctioons and the pollarization angle θ as θ’. Therefore, foor the junction B in the trianglee configuration show wn in Figure 6, θ = 0o, 30o, 600o and 90o essenntially correspond to θθ’ values of 120o, 90o, 60o and 330o respectivelyy. As is clear from Figuure 7, field intennsity at junction B shows a minimum for θ = 30o and θ’ = 90o. The nuumerical values of electric field intensity at the hot sppots for variouss θ are given in F Figure S9 in Suppporting Informationn. A sim milar trend was observed for tthe square conffiguration. In the squuare configuratiion, there are foour junctions, aamong which A and C behave alike toowards various states s of polarizzation, while the response at B and D is similar. For A and C, θ = 0o corresponds to θ’ = 0o whereas for B and D, θ = 0o corresponds tto θ’ = 90o. Thus the ju unctions A and C have the maxximum field intensity and B and D haave the minimuum intensity for θ = 0o. Howeveer this trend is reverseed for θ = 90o ass it corresponds to θ’ = 90o for A and C and θ’ = 0o ffor B and D. Thhus the maximuum intensities arre observed for the ssquare configurration at 0o andd 90o but in alteernate junctions as can be seen from m Figure 7. Modderate values off field intensities are oobtained for θ = 30o and θ = 600o (see Figure SS10 in Supporting Infoormation for acttual values).

Figure 7: Electriic field intensityy distribution proofiles in the vicinnity of the Au NPs in tthe triangle andd the square asseemblies at 633 nm n for varying angles off polarization of tthe incident lightt. 633 nm o =0

633 nm o  = 30

10 nm

10 nm

633 nm  = 90o

633 nm  = 60o

633 nm  = 0o

1 100

5 50

10 nm

633 nm  = 30o

10 0 nm

633 nm  = 90o

0

0 10 nm

10 0 nm

50

10 nm

633 nm  = 60o

100

10 nm

10 nm

Figure 8: Electriic field intensityy distribution proofiles in the vicinnity of the Au NPs in thhe pentagon andd the hexagon asssemblies at 633 nnm for varying angles off polarization of tthe incident lightt.

400 E Field Intensity

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L2 L3 L4 L5 L6

200

0 0

30 60 90 Angle,  (in degrees)

E Field Intensity


Hexag gon Pentag gon Square Triang gle

100

75

50

0

30 60 9 90 Anggle,  (in degrees)

Figgure 9: Variation of average electrric field intensityy at the junctionss of thee linear chains and a the polygonnal assemblies foor various angless of pollarization of the incident i light, θ.

Further,, we look into the plasmonic properties of tthe penntagonal arranggement. At θ = 0o the junction A lying parallell to thee angle of incideence of the light (θ’ = 0o) has maaximum plasmonic fielld (Figure 6 andd Figure 8). Wheereas the junctioon B has θ’ = 72o ressulting in a low w electric field. A similar field iintensity featuree is obsserved at junction E for which θ’ = 108o, whilee at C and D (θθ’ = 1444o and 36o respeectively), the inntensities are higgher than at B aand E. At θ = 30o of ppolarization, the junction D corresponds to tthe low west value of θ’ and hence the field is maximuum at D while tthe junnctions A and B have moderatee field and the other two junctioons (C C and E) experieence negligible ffield. On similaar lines, in the case of θ = 60o the maxi ximum field is obbserved at B. Att θ = 90o the souurce is pperpendicular too the junction A (θ’ = 90o) andd the field intenssity is negligible n whilee larger values oof field are obseerved at the othher fouur junctions (Figure S11). In thhe case of hexaggon configuration, sim milar features weere observed foor θ = 0o and 600o. At θ = 0o, junctions A and D havve θ’ = 30o and juunctions C and F correspond too θ’ = 150o whereas B and E are perpendicular to the angle of pollarisation makinng θ’ = 90o. Hence H significannt electric field of equual intensity is oobserved at thee junctions A, C, C D and F whilee B andd E have negligiible field (Figuree 8). At θ = 60o, junctions C andd F havve negligible fieeld since θ’ = 900o while the othher four junctioons shoow significant fieeld intensities (θ’ = 30o and θ’ = 150o). For θ = 330o andd 90o, junctions A, D and B, E reespectively havee θ’ = 0o, giving rise r to maximum electtric field intensiity while the othher junctions haave neggligible field inteensity (Figure SS12). The inteeresting featuress observed in thee electric field pprofilees of the linear chains c and the polygonal assembblies are a resultt of thee plasmonic couupling between the constituentt nanoparticles.. In thee linear chains, ttwo significant pproperties are obbserved. Firstly, y, as thee angle of polariization is varied from θ = 0o to θ = 90o the electtric fielld intensity at thhe junctions deccreases. θ = 0o exxcitation inducees a stroong longitudinaal plasmon couppling among thee constituent paarticlees and therefore the field intenssity is maximum m. However as θ is inccreased to 90o tthe strength of plasmon couplling decreases aand eveentually correspponds to weak transverse couppling between tthe parrticles thereby lowering the fielld intensity. The other promineent feaature is the increease in field inteensity as the num mber of particless in thee chain increasees. As we movve from L2 to llonger chains, tthe streength of the lonngitudinal dipolle created in thee presence of ellectroomagnetic radiaation increases. Also, as the leength of the chhain inccreases, the extinction maximuum shows a reed shift eventuaally com ming closer to tthe laser wavelenngth 633 nm at which the electtric fielld is monitored.. Apparently, in the linear chainns the field intennsitiess at all the juncttions diminishess from θ = 0o to 90o. Therefore tthe aveerage of I over all a the junctions also diminishess from θ = 0o to 990o (Fiigure 9). This has h interesting implications in surface-enhancced speectroscopy. Whhen the linear cchains of metal nanoparticles are useed for detecting analytes in surfa face-enhanced sppectroscopy

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0o (57 73) 30o (5 573) 60o (5 573) 60o (5 527) 90o (5 524)

L6

2000 1000 0



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0o (560) 30 0 o (560) 60 0 o (560) 90 0 o (560)

Hexaggon

2000 1000

-60

-30 0

0 30 X (nm)

600

0

-30 -15 0 15 X (nm)

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Figure 10: The electric field inteensity profiles inn the vicinity of tthe Au a at theiir respective extinnction NPs in the L6 annd the hexagon assemblies maxima for varyiing angles of polaarization of the inncident light.

experiments, thhe polarization oof the incident light has to be along the axis of the chhain to get betteer optical signals. Unlikke the linear chaains, the junctioons in each of thhe polygonal assembllies respond diff fferently for diffeerent angles of ppolarization of the source. When a juunction is paralleel to the axis of ppolarization of the ssource (θ’ = 0o), the electric fieeld intensity is maximum and as θ’ varies the fieldd at this junctioon slowly diminnishes. However otherr junctions can now become pparallel to the aaxis of polarization annd exhibit highher intensities.. It is evidentt that regardless of thhe angle of polaarization of the source, hot spoots are created in the ppolygonal assem mblies, even thouugh at differentt junctions. Thus thee average of I oover the junctioons is roughly aall the same from θ = 0o to 90o (Figuure 9). Therefore, in contrast tto the case of linear chains, c the polaarization state of the incidentt light becomes irrelevvant when polyggonal assembliees are used in suurfaceenhanced specttroscopy experiments. Howeveer, the observedd field profiles in polyygonal assemblies imply that itt is possible to selectively excite parrticular hot spotts using the pollarization of lighht as a handle. Such seelectivity in hot spot features inn a single metal particle assembly cann be useful in suurface-enhancedd spectroscopy. The eelectric field proofiles reported thhus far are com mputed at 633 nm. Thee reasons for choosing this wavvelength are twoo-fold. One, it is a tyypical laser wavvelength used inn experiments. Two, computing the pplasmonic propperties of the lineear and the polyygonal assemblies at a single wavelenngth (633 nm) w was done for ease of comparison acrross all the nannostructures. Hoowever, the hott spot intensities are expected e to be m much higher at ttheir resonance wavelengths. To dem monstrate this asspect, we have ccomputed the ellectric fields in the viciinity of the L6 annd the hexagon assemblies at thheir

ressonance wavelenngths (Table 1)) and the resultss are shown in FigF uree 10 and Figure S4 of Supportinng Information. The field intennsitiess now are muchh higher than thhose computed for 633 nm (note thee scales in Figurre 5 and Figure 10). The trendds in field variatiion witth respect to poolarization of inncident light hoowever remain uunchaanged. Two othher parameters tthat govern the plasmonic proppertiess of the nanosttructures and thhe resultant enhhancement facttors aree the size of the nanoparticle annd the gap size bbetween the meetal parrticles in the asssemblies.67 In order o to shed ssome light on tthis asppect, we went oon to investigatee the effect of siize of the particcles on the plasmonic features by connsidering the L L3 and the trianngle connfigurations formed from metaal particles of sizze r = 20 nm. F Figuree 11 and Figure S7 of Supportinng Information ppresent a compaarisonn of the field inttensities in the vvicinity of the particles of sizes r = 10 nm and 20 nm iin the trimeric aassemblies. An oorder of magnituude enhhancement in thhe intensities foor assemblies w with larger particcles cann be clearly seen. Next, the efffect of gap size on the plasmonic prooperties was proobed by perform ming calculatioons for the L3 aand thee triangle configgurations in whicch the gap size was w chosen to bbe g = 5 nm. The electrric field intensitties at the junctiions as reportedd in Figgure S5 and S6 iin Supporting Innformation are llower comparedd to thee correspondingg g = 3 nm systeems. The polarizzation dependennce of the plasmonic properties of thhe assemblies foormed from meetal parrticles of varyingg sizes and gap ssizes however reemains unchanged. The lastt few years havve witnessed soome theoreticall as weell as experimenntal studies onn understandingg the polarizatiion deppendence of pllasmonic featurres in metal naanoparticle asseembliees. While studiees on linear chaiins were predom minantly on undder45, 49 standing the opticcal extinction features, fe stuudies on polygoonal asssemblies with thhe exception off a few20, 54, 56 weere focused on tthe plaasmonic propertties of nanopartiicle trimers.52, 54, 60 Assemblies w with hexxagonal symmettry (a central paarticle surroundeed by six particles) weere also investiggated, particularrly in the conttext of Fano reesonannces.47-48, 55 How wever a thorouggh analysis of thhe optical featuures andd hot spot distrribution of lineear and polygonnal assemblies aand impplications for surface-enhanced spectroscopyy has not been reporrted. We hope thhat this study brridges the gap inn this area.

CO ONCLUSIONS S In concllusion, we have found that, in assemblies a of meetal nannoparticles, thee number of connstituent particcles and their geomeetrical arrangem ment plays a cruucial role in deteermining the pllasmoonic properties. The influence of the number of particles dim minishhes with increasee in the size of tthe assembly whhich could be seeen froom the convergeence of extinctioon maxima and electric e field intensitiies in higher ordder assemblies. The polarizatioon state of incident eleectromagnetic raadiation can stroongly influence tthe optical proppertiess of the assembbly. The opticall extinction feattures of the linnear chaains exhibit stroong polarization dependence whhereas those of tthe pollygonal assembblies are indepeendent of the polarization p of tthe inccident light. How wever the electrric field profiles in linear as welll as pollygonal assembllies reveal the roole of incident liight polarizationn in conntrolling the hoot spot distribuution. Althoughh, in polygonal assem mblies, the averaage electric fieldd intensity is alm most insensitivee to thee polarization staate.

AS SSOCIATED C CONTENT Figure 11: A coomparison of thee electric field inntensity profiles in the vicinity of the A Au NPs in the L33 and the trianglle assemblies of r = 10 nm and r = 20 nnm at 633 nm foor varying angless of polarization of the incident light.

Eleectric field intenssity profiles and numerical valu ues of electric fiield

intensity at the hot spots in variouus linear and pollygonal assembllies forr varying angles of polarization of the incident light. This mateerial is aavailable free of charge c via the Internet at http://ppubs.acs.org.”

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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

ACKNOWLEDGMENT The authors thank Prof. K. George Thomas for his valuable suggestions. The authors also acknowledge IISER-TVM for computational facilities. RT thanks CSIR, India for financial support.

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TOC Graphic 633 nm o =0 10 nm

633 nm o  = 30 10 nm

633 nm θ = 30o

633 nm θ = 0o

10 nm

weak

θ = 0o

10 nm

electric field

strong

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Linear and Polygonal Assemblies of Plasmonic Nanoparticles

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