Coupling of Localized Surface Plasmon Resonance in Self-Organized

J. Phys. Chem. C 2009, 113, 21293–21302

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Coupling of Localized Surface Plasmon Resonance in Self-Organized Polystyrene-Capped Gold Nanoparticle Films He´le`ne Yockell-Lelie`vre,†,‡,| Daniel Gingras,§,| Reál Valleé,§,| and Anna M. Ritcey*,†,‡,| De´partement de chimie, Centre de recherche sur les mate´riaux aVance´s (CERMA), De´partement de physique, geńie physique et d’optique, Centre d’optique, photonique et laser (COPL); UniVersite´ LaVal, Que´bec, Que´bec Canada, G1K 7P4 ReceiVed: May 29, 2009; ReVised Manuscript ReceiVed: October 28, 2009

Glass-deposited monolayers of polystyrene-coated gold nanoparticles with controlled interparticle distance have been prepared. Normal incidence extinction spectra show a progressive red shift of the plasmon resonance wavelength as the interparticle gap within the film is reduced. Polarized extinction spectra were measured at in-plane incidence using an optical waveguide lightmode spectroscopy (OWLS) setup. The in-plane (TE)polarized spectra show a red shift with decreasing interparticle gap, whereas the out-of-plane (TM)-polarized component shows no visible change. These observations are typical of dipolar near-field interparticle plasmon coupling. Simulations using the discrete dipole approximation have been conducted to compare the decay rate of the red shift with increasing interparticle gap for different particle arrangements (pair, row of 5 and 2D hexagonal array of 19). The calculations show that the variation of the relative red shift with the relative interparticle spacing follows a first-order exponential decay law in all three structures, with a decay constant similar to results previously reported. A secondary, slower decay rate, occurring at relative interparticle gap values above 1.25, is found for the 2D array. The decay constant of this large-distance regime is close to that of the measured extinction spectra of the polystyrene-coated gold nanoparticles monolayers, which present relative interparticle distances within this range. This second decay constant may be the result of an increased contribution of higher-order modes. Introduction Illuminated metallic nanoparticles with dimensions that are small compared to the incoming wavelength exhibit a specific behavior known as the localized surface plasmon resonance (LSPR).1 This very intense electronic resonance originates from the relatively dense, space-delimitated free electron cloud contained in the metallic nanosized body that collectively responds to the oscillating electric field of the incoming light. Numerous factors affecting the extinction spectrum of a given system, such as the size,2,3 the shape,4,5 and the structural disposition6-8 of the metallic nanoparticles (NPs) as well as the refractive index of the surrounding medium,9 have been extensively studied and the nature of their impact is now well established. For gold particles with a size ranging from 5 to 60 nm, the LSPR takes the shape of a single dipole that absorbs and re-emits light in the near-field. The very intense local electric field emerging in the vicinity of a particle when its LSPR is excited is known to be responsible for the strong signal enhancement observed in the Raman and fluorescence spectra of dyes adsorbed on the particle’s surface. Near-field effects are also known to be mainly responsible for the interparticle coupling of the plasmon modes occurring when two particles are brought close to one another. Consequently, it has been demonstrated by Maier et al.10 that energy can be transmitted through a linear array of gold nanoparticles and that the transmission is conducted almost solely through * To whom correspondence should be addressed. E-mail: Anna.Ritcey@ chm.ulaval.ca, Tel.: 418-656-2368, Fax: 418-656-7916. † De´partement de chimie. ‡ Centre de recherche sur les mate´riaux avance´s (CERMA). | Centre d’optique, photonique et laser (COPL). § De´partement de physique.

plasmon interactions between nearest neighbors. Interparticle plasmon coupling is also responsible for the significant difference between the extinction spectra of metallic NPs in dispersed and aggregated states. Whereas colloidal gold suspensions present a characteristic deep red coloration, slight particle aggregation induces a red shift in the resonance peak giving the suspension a purple tint when viewed in transmitted light. This striking variation in color is currently being exploited for many biotechnological applications, such as assays,11 biosensors,12 in vivo imaging,13 and as a potential scaling tool to study specific DNA interaction mechanisms.14 The coupling process between neighboring metallic NPs has been experimentally observed for systems consisting of pairs,8,15,16 linear chains,17,18 and planar arrays19,20 of nanodiscs. For particle sizes within the range where the dipolar plasmon mode is dominant (i.e., diameters below 50 nm for gold), two in-phase, active coupled modes between neighboring particles are found. The first mode oscillates along the axis joining the particles (the longitudinal mode), whereas the second oscillates in the perpendicular direction (the transverse mode). It is now wellknown that these two modes evolve differently as the particles are brought closer together. Whereas the longitudinal mode shows a significant red shift and a certain gain in intensity, the transverse mode shifts slightly to the blue and loses intensity. The particle arrays on which these observations have been made are usually synthesized by electron beam lithography (EBL). This technique permits a very precise control over the designed structure, thus allowing for the systematic study of the influence of particle geometric parameters on the optical properties of the array. Alternative methods using the bottom-up approach to generate nanostructured arrays of particles at lower costs have been shown to give similar results for a limited range of

10.1021/jp905063m CCC: $40.75  2009 American Chemical Society Published on Web 11/24/2009

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Yockell-Lelie`vre et al.

Figure 1. Experimental OWLS setup used to measure polarized extinction spectra with edge-on incidence. The thin glass slide acts as a planar waveguide, enabling a surface evanescent field to interact with the sample.

Figure 2. Schematic representation of the 19 particle target employed for the DDA calculations. Calculations were carried out for both normal and edge-on incidence. In the case of edge-on incidence, spectra were calculated for TE and TM polarizations and along the two symmetry axes indicated by the dashed arrows.

structures.21-23 Typically, self-assembled structures show a lower level of order but optical measurements show overall trends24-26 similar to those found for EBL generated structures. Recent developments in the self-assembly field make it now possible to produce structures that allow for better control over the dimensional parameters of nanoparticle arrays.27,28 In this article, we present a study of plasmon coupling as a function of interparticle gap dimensions for a bidimensional array of selfordered gold nanospheres capped with polystyrene (PS). These particles self-assemble into hexagonal-packed monolayers upon solvent evaporation and the distance between the gold cores within the array can be modified by varying the length of the PS chains. In the present study, polarized extinction spectra of nanoparticle arrays are recorded using optical waveguide lightmode spectroscopy (OWLS), a method that was first introduced by Qi et al.29 Using this specific setup, we are able to inject polarized light edge-on into the plane of the monolayer, thereby enabling the distinct excitation of in-plane and out-of-plane modes, corresponding respectively to the longitudinal and

transverse coupled modes. Conventional transmission spectroscopic setups offer access to a limited range of angles of incidence and thus do not allow for the complete isolation of contributions from each of the coupled modes. Methods using total internal reflection excitation through a prism have made it possible to observe the light scattered by metallic particles excited by incoming polarized light.30,31 However, the collection of the scattered light, usually with a scanning near-field optical microscope (SNOM), requires considerable experimental effort, and the results may be affected by sample-tip interactions. Collection of the scattered light using a conventional microscope is possible, but limited to metallic particles with sizes exceeding 10 nm, due to the weak contrast between the signal emitted from small particles and the background noise.31 In the present study, OWLS is demonstrated to be a simple and fast way of studying the interaction between an evanescent field and a surface-deposited sample, yielding signals of sufficient intensity to separate the coupled plasmon modes of arrays of gold particles with a diameter of 5 nm. Jain et al.16 recently reported a systematic study of the effect of the distance of separation between two gold particles on the position of maximum extinction for the longitudinal plasmon coupled mode. The goal of this work was to establish a general scaling relationship that would enable the use of metallic nanoparticle pairs as universal molecular-scale rulers. The relation they established proved to be applicable to gold NPs pairs in different environments because the data obtained by Reinhard et al. in the measurements of the length of DNA strands grafted onto the surfaces of gold nanospheres obeyed the same scaling relation.32 Su et al. had previously demonstrated that a single relationship between the measured plasmon shift and interparticle distance can be used for particles of varying sizes if the shift (∆λ) and separation (D) are normalized with respect to the position of the single-particle plasmon maximum (λ0) and the particle size (2r), respectively.33 Jain et al. compiled numerous experimental measurements with theoretical calculations conducted using the discrete dipole approximation (DDA) method and determined that by fitting an exponential decay of the form y ) ae-x/τ to a plot of the relative shift (∆λ/λ0) versus the relative spacing (D/2r), the decay constant τ remained basically unchanged from one system to another. They con-

Polystyrene-Capped Gold Nanoparticle Films

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Figure 3. TEM images of self-assembled monolayers of citrate-reduced (a) and phase-transfer-reduced (b) gold NPs with grafted PS of Mn ) 6500 g/mol. Similar images obtained for NPs coated with PS of higher molecular weights have been published elsewhere.28

Figure 4. Center-to-center particle separation (D) normalized with respect to particle diameter (2r) as determined from TEM images for self-assembled monolayers of gold nanoparticles coated with PS of varying molecular weight.

cluded that, for a pair of metallic nanoparticles, the exponential decay length of the coupling is roughly 0.2 times the particle diameter and that this rate remains constant for particles consisting of either gold or silver, with shapes that were either discs or spheres. The influence of the refractive index of the surrounding medium on the decay behavior was also demonstrated to be rather weak, with the decay constant changing only from 0.23 to 0.27 when the medium dielectric constant was varied from 1.00 to 2.25. According to the authors, the universal nature of this relation is based on the fact that the two factors responsible for the relative frequency shift, the interparticle nearfield dipolar coupling potential, and the intraparticle restoring potential, depend on similar powers of the separation distance and particle radius, respectively.16 If this is indeed the case, it can be anticipated that similar behavior will be observed for bidimensional arrays of metallic nanoparticles with regular interparticle spacing within the same size range. In this article, we test this hypothesis with experimental data obtained for bidimensional arrays of PS-coated gold nanoparticles. We also compare the predicted plasmon shift, as a function of particle separation, calculated from the discrete dipole approximation (DDA) for a variety of arrangements including particle pairs, rows, and hexagonal 2D arrays. Experimental Methods Materials. Starting materials were commercially obtained from Aldrich. Water was purified using a Nanopure II (Barn-

stead) filtering system. The PS-grafted gold NPs were prepared following a 2-step grafting-to procedure that has been previously detailed elsewhere.28 Two different methods were used to synthesize the gold cores. The first used the phase-transfer reduction method developed by Brust et al.34 and yielded particles with an average radius of 2.7 ( 0. 3 nm. The second NP population was synthesized using citrate as the reducing agent,28 and the particles produced had a mean radius of 5.50 ( 0.06 nm. Transmission Electron Microscopy. Transmission electron microscopy (TEM) observations were carried out with a Jeol JEM-1230 microscope operated at an acceleration voltage of 80 kV. A drop of dilute Au-PS NPs suspended in HPLC-grade chloroform was evaporated onto a nickel grid coated with a Formvar-supported carbon film. Optical Spectroscopy. UV-vis extinction spectra were recorded with a Varian Cary 500 Scan spectrometer. A drop of a dilute suspension of Au-PS NPs in HPLC-grade chloroform was evaporated onto a glass slide and transmission spectra were recorded at normal incidence. In-plane polarized extinction spectra were recorded with the spectroscopic setup sketched in Figure 1. Light from a standard incandescent white source was guided through a silica multimode optical fiber (core diameter ) 100 µm), and injected into a 140 µm thick, 10 × 10 mm SF-11 glass slide (V-A Optical Laboratories), acting as a planar slab waveguide. Samples were deposited on the top surface of the waveguide from dilute suspensions in HPLC-grade chloroform. Light exiting the waveguide was passed through a polarizer before being collected and analyzed with a USB2000 spectrometer (Ocean Optics). Because of the relatively high refractive index of PS (near 1.6 in the visible range), the index of the waveguiding material was selected to be about 1.7 over most of the visible range so as to ensure the generation of an adequate evanescent field at the interface coated with Au-PS nanoparticles. It is important to note that, with this optical setup, the extinction maxima observed with TE polarization were red-shifted by about 30 nm with respect to transmission spectra measured with normal incidence. Similar spectral shifts were observed in the waveguide absorption spectra recorded for a number of organic dyes dispersed in polystyrene films. At present, we are unable to identify the cause of this spectral shift and the OWLS presented in this article have thus been corrected to correspond to the position of maximum extinction of the transmission spectra. Theoretical Calculations. Theoretical extinction spectra were calculated using the DDA DDSCAT 6.1 code developed by

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Figure 5. Extinction spectra measured at normal incident for glass-deposited monolayers of PS-coated gold nanoparticles prepared by phasetransfer reduction (a) and citrate reduction (b). Corresponding spectra calculated by DDA for a planar array of 19 gold spheres, 5 nm in diameter, in a PS matrix are presented in (c). The wavelength of maximum extinction evaluated from the experimental and theoretical spectra are plotted in (d) as a function of relative interparticle separation.

Figure 6. Sketch illustrating the proposed cross-sectional structure of the monolayers at high interparticle separation leading to a decrease in the effective matrix refractive index relative to an infinite PS matrix.

Draine and Flatau.35,36 A target of 19 spheres, organized in a planar hexagonal array, was constructed (Figure 2) and extinction spectra were simulated for various interparticle distances. The dielectric function for the particles was based on the data of Johnston and Christy,37 with the size-correction factor introduced by Doyle,38 relative to the dielectric function of the coating material (PS).39 The distance between two dipoles inside the target was 0.62 nm for the r ) 5 nm NPs and 0.37 nm for the r ) 3 nm NPs, yielding approximately 2000 dipoles/particle. This density of dipoles has been previously demonstrated to be appropriate for the modeling of gold particles within this size range. Fe´lidj et al.,40 for example, showed that extinction spectra for gold particles calculated using the DDA with similar dipolar densities are comparable to the spectra calculated from Mie theory. As illustrated in Figure 2, calculations for the planar hexagonal array were conducted for two different orientations of the incident oscillating electric field, corresponding to the in-plane (TE) and out-of-plane (TM) polarizations, respectively. The reported calculated spectra are averages of calculations

carried out for irradiation along the two different symmetry axes of a hexagon, represented by the dotted arrows in Figure 2. At separation distances relevant to the experimental measurements (D/2r > 1.5), no significant differences are found between the calculated spectra for the two axes of incidence for a given polarization. Calculations carried out for particles in very close proximity (D/2r ) 1.03) do, however, show a significant difference in the position of maximum extinction for irradiation along the two axes. Results and Discussion Structure of the Nanoparticle Monolayer Arrays. TEM images of arrays formed by the two populations of gold nanoparticles (phase-transfer- and citrate-reduced), both functionalized with PS of Mn ) 6500 g/mol, are shown in Figure 3. The monolayers display a somewhat regular bidimensional hexagonal arrangement, as can be expected from a system in which the ordering process is governed by the lateral capillary force exerted by the evaporating solvent. It is relevant to note that most of the citrate-reduced samples show the presence of


Figure 7. Polarized extinction spectra (TE-, TM---) recorded with OWLS for self-assembled monolayers of PS-coated gold NPs. Spectra obtained for NPs synthesized by phase-transfer reduction are shown at the left (a-d) and for those obtained by citrate reduction at the right (e-h). Particles are coated with PS of varying molecular weight: 4300 (a,e), 8000 (b,f), 23 000 (c,g), and 39 000 g/mol (d,h). No value for the reduced particle separation is provided for the highest molecular weight samples as they do not form ordered arrays.

small 2 or 3 particles aggregates (Figure 3 of ref 29). The reason for this is unclear but the presence of such aggregates does not seem to affect the overall interparticle distance throughout the sample. The distance between neighboring gold cores is relatively constant within a given sample and increases from one sample to another with increasing molecular weight of the grafted PS chains. TEM images of the arrays obtained for other molecular weights of polystyrene have been published elsewhere.28 The mean center-to-center distance (D) between the gold cores for each sample, normalized with respect to particle diameter (2r), is plotted in Figure 4 as a function of the molecular weight of the grafted PS chains. Because the range of the interparticle steric repulsion is a function of the size of the grafted species,41 a certain degree of control over the interparticle distance can be achieved by modifying the length of the grafted polymer chains. This tendency has been previously observed for similar systems.26,27

J. Phys. Chem. C, Vol. 113, No. 51, 2009 21297 Optical Properties. Extinction Spectra at Normal Incidence. Extinction spectra recorded at normal incidence for nanoparticle monolayers assembled on glass are shown in Figure 5. Spectra obtained for the smaller phase-transfer particles are presented in part a of Figure 5, whereas those of the citrate-reduced particles are plotted in part b of Figure 5. In both cases, samples were grafted with PS of various molecular weights, giving rise to arrays with differing average reduced interparticle separations (D/2r), as indicated. For comparison purposes, simulated optical extinction spectra, generated with Draine and Flatau’s code,36 are also shown. Calculations were performed for systems composed of 19 spheres, laid out in a flat hexagonal array. The radii of the spheres were set to 3 and 5 nm, corresponding to the experimental phase-transfer-reduced and citrate-reduced gold nanoparticles, respectively. For the spectra shown in part c of Figure 5, the oscillating electric field was oriented parallel to the surface of the array, thus corresponding to the configuration of experimental measurements made with the Varian spectrometer. Calculated spectra are shown only for the array of 5 nm particles because near-identical results are obtained from calculations performed for 3 nm spheres, as expected from the universal nature of the relationship between the normalized plasmon shift and reduced particle separation. In considering Figure 5, the first observation to note is that both populations of nanoparticles show the same expected tendency, that is a red shift of the plasmon wavelength as interparticle separation diminishes. The same trend is found in the calculated spectra. The evolution of the position of maximum extinction as a function of reduced separation is plotted in part d of Figure 5. Several monolayer samples were prepared for each particle population and the position of the plasmon absorption was found to vary from one sample to another by about 15 nm for the citrate-reduced particles and by about 5 nm for the phase-transfer-reduced particles. The experimental points are found to deviate from the calculated predictions at both high and low reduced separations. Most notable is the deviation at low D/2r where citrate-reduced nanoparticles grafted with PS of lower molecular weight show a more pronounced red shift than that calculated for a model system of similar interparticle spacing. This deviation can possibly be attributed to the presence of small aggregates of 2 or 3 particles. As mentioned above, such aggregates are indeed observed in the TEM images of citrate-reduced samples grafted with the lower molecular weights of PS. The presence of these clusters, within which the particles are essentially in contact, would contribute to an increased shift of the resonance wavelength toward higher values. Furthermore, the sporadic presence of these aggregates in the citrate-reduced samples could be responsible for the higher experimental variability of the peak position from one sample to another, as compared to the phase-transfer-reduced samples. A second important observation from part d of Figure 5 is the difference between calculated and experimental values at higher particle separations. According to the theoretical calculations, at D/2r equal to 3 coupling vanishes and above this separation distance the particles can be considered as individual entities. The calculations predict a plasmon peak maximum at 547 nm for isolated particles of both sizes. Although the number of experimental points is somewhat limited, the plasmon of both the phase-transfer- and citrate-reduced particles appears to continue to move to shorter wavelengths at reduced separations above 3. Furthermore, the experimental plasmon at high separation distances appears at shorter wavelengths than that predicted by DDA. In the case of the smaller phase-transferreduced particles, the plasmon peak at the highest separation

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Figure 8. Extinction spectra calculated by DDA for a planar hexagonal array of 19 gold spheres embedded in a PS matrix for various particle separations as indicated. Calculated spectra are shown for particles with a radius of 3 nm, with TE (a) and TM (b) incident polarization, as well as for 5 nm particles, also with TE (c) and TM (d) polarizations.

distance (achieved by coating with PS of Mn ) 43 000 g/mol) appears at 528 nm. This value is essentially identical to that observed for dilute suspensions of the same particles in chloroform, thus confirming that interparticle coupling vanishes at this separation distance (D/2r ) 4.2). In the case of the larger citrate-reduced particles, the plasmon peak at the highest separation distance (achieved by coating with PS of Mn ) 66 000 g/mol) appears at 542 nm. The same particles in chloroform suspension exhibit an extinction maximum at 533 nm. Whereas these values may indicate that interparticle coupling persists in the monolayers of these particles at reduced separations as large as 3.5, they could also reflect the influence of the medium refractive index on the plasmon peak position. In the case of the larger particles, DDA calculations carried out with a matrix refractive index of 1.6 (corresponding to PS) yield plasmon frequencies that are red-shifted by about 7 nm relative to calculations carried out in chloroform, with a refractive index of 1.45. The difference between the calculated and experimental values at higher particle separations illustrated part d of Figure 5 could therefore be a consequence of the difference between the refractive index of PS and the actual refractive index of the matrix surrounding the NPs. Previous SEM observations28 of a sample coated with 43 000 g/mol PS chains reveal a topological profile that suggests that the interparticle space may not be completely filled with PS but rather contain a significant volume fraction of air, as illustrated by the sketch in Figure 6. This would lead to a lower value of the effective dielectric environment, thus causing a blue shift of the plasmon resonance from the value of gold NPs in the infinite PS matrix as considered in

the simulation. This effect would be more pronounced for samples with larger interparticle distances and may be totally absent when the particles become sufficiently close that the grafted PS is sufficient to fill the interparticle gap and approach the infinite matrix approximation. Extinction Spectra from Polarized Optical WaWeguide Spectroscopy. Extinction spectra of the nanoparticle arrays recorded by polarized optical waveguide spectroscopy are presented in Figure 7. Unlike simple transmission spectroscopy, this technique allows for the observation of the two orthogonally oriented coupled modes. Experimental spectra are shown for the two populations of particles (phase-transfer-reduced on the left and citrate-reduced on the right) and as a function of the molecular weight of the grafted PS. The spectra of Figure 7 exhibit two significant differences between the two polarization modes, particularly at smaller separation distances. First, the TE mode is typically more intense than the TM mode, and second, the resonance in the TE mode is red-shifted with respect to the TM mode. These features are also exhibited in the calculated spectra presented in Figure 8. DDA calculations were conducted on the same 19-sphere target that has been previously described, but with the incoming oscillating electric field polarized in- and out-of-plane with respect to the target, to best isolate the contribution of each of the two coupled modes. The comparison between the experimental and calculated results can be better visualized in Figure 9, where the extinction maximum is plotted against the reduced interparticle gap, for both particle sizes. The model predictions agree with the experimental observation that the TM mode appears at shorter


Figure 9. Measured and calculated plasmon resonance peak position for the (a) citrate-reduced samples and the (b) two-phase-reduced samples, for both polarization modes. Dashed lines are included solely to aid the eye.

wavelengths than the TE mode, suggesting that direct near-field coupling of the oscillating dipolar plasmon modes of neighboring particles is responsible for the optical properties of the monolayer films.42 When the light is TM-polarized, the charge distribution of the neighboring dipoles has an increasing effect on the restoring force of the oscillator, which causes a slight blue shift in the plasmon frequency. When the light is TEpolarized, the restoring force is decreased by the presence of the surrounding in-phase dipoles, therefore a red shift is observed. The longitudinal coupled mode being energetically favored, it is the most intense and usually dominates the absorption spectrum of closely packed arrays of small metallic NPs. The difference between the two polarized spectra becomes less important as the distance between the particles in the film becomes larger, eventually tending toward the spectrum of a single particle when they become sufficiently separated so that no coupling occurs. Unfortunately, the experimental points are limited to the larger separation regime, and the observed plasmon shifts as a function of interparticle separation are close to the uncertainty in peak position associated with the measurement, particularly in the case of the weaker TM mode. The relative distance at which the two modes merge to a single frequency is lower for the simulation, occurring at D/2r ) 3, than for the measured spectra, where a value of about 3.5 is

J. Phys. Chem. C, Vol. 113, No. 51, 2009 21299 observed. Both particle populations seem to demonstrate more plasmon coupling, at a given interparticle distance, than that predicted by the DDA simulations. Aggregation within the samples may again be the cause for the supplementary red shift. Calculated Spectra for Different Particle Arrangements. It is interesting to compare plasmon coupling between nearest neighbors in a planar hexagonal array with the observations of Jain et al. for particle pairs.16 For this reason, a series of calculations using DDA were carried out for a single particle pair as well as a 1D row, both as a function of interparticle spacing. The resulting spectra, presented in Figure 10, were calculated for 10 nm diameter gold spheres embedded in PS. Interestingly, the series of spectra obtained for the pair simulation present a shape transition as the relative spacing is decreased beyond 1.10. At this separation, a second resonant contribution appears and gains in importance as the spheres are brought still closer together. This implies that the excitation of the singleplasmon and the coupled-plasmon modes are very distinct in the case of a particle pair. For simulations carried out on a larger number of spheres, the transition from single-plasmon excitation to the coupled-plasmon is much smoother. The distancedependent red shift is stronger for a straight row of 5 spheres than for a pair for a given relative spacing (for example, 145 and 63 nm, respectively, for D/2r ) 1.03). This is in accordance with observations previously made on linear arrays of NPs, predicting a red shift of the peak wavelength as the number of particles varies from 2 to 5.17,18 The red shift of the hexagonal array is reduced compared to that of the 5-sphere row, and the shape of the resonance is broadened, meaning that the effective plasmonic longitudinal oscillaton of a 5-sphere row is somehow damped by the presence of lateral adjacent neighbors. By plotting the relative red shift (∆λ/λ0) against the varying relative spacing between the spheres, we can see that the trend described by Jain et al.16 is once again observed here, to a certain degree, for all three arrangements. The exact range of reduced distances over which coupling is observed is, of course, different because of the different dielectric constant of the medium. The variation of ∆λ/λ0 obeys a first-order exponential decay function with a decay constant (τ) in the range of what was previously measured on gold NP pairs by other groups.15,16 The decay constant found for the 5-row system (0.19) is very close to that of the pair (0.18), suggesting that the universal scaling behavior also applies for linear arrays of more than 2 particles, as it would be expected for particle systems in the size range where the plasmon coupling is dominated by near-field interactions. In the case of the 2D hexagonal array, the overall shape of the decay is significantly different and cannot be described with a single decay rate. Two regimes are observed. In the first regime, when the particles are sufficiently close (D/2r e 1.25), the decay rate is the same as that found for 1D systems. In the second regime, which appears when the particles are farther apart (D/2r g 1.25), a much slower decay rate, characterized with a larger decay constant (0.60), is found. Figure 11 shows the relative red-shift variation as a function of relative interparticle gap obtained experimentally from the spectra measured on the PS-coated gold NP monolayers. The decay constant of the curve-fit (0.63) is quite close to that found for the second regime of the simulated data. This indicates good agreement between the theoretical predictions and the experimental data since all of the measured values correspond to interparticle gaps in that fall within the large separation regime. The observation of a second component in the decay of the plasmon coupling for the 2D array may be the result of symmetry effects. Through the elaboration of a novel hybridiza-

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Figure 10. DDA-calculated extinction spectra for 10 nm gold spheres arranged as a pair (a), as a straight row of 5 units (b), and as a planar hexagonal array of 19 units (c) with varying relative spacing between spheres. All simulations were carried out with incident light polarized along the axis of the aligned spheres. The corresponding relative red shift (∆λ/λ) is plotted as a function of relative interparticle spacing in graphs (d) to (f). Data were fitted to a first-order exponential decay law (y ) A exp (x/τ)) with τ values of 0.18 ( 0.01 and 0.19 ( 0.01 for plots (d) and (e), respectively. The data obtained for the hexagonal array (f) were fitted with two distinct decay curves, with decay constants of 0.19 ( 0.01 and 0.60 ( 0.01, respectively. The dotted curve illustrates the best fit that can be obtained with a single exponential.

tion model, Brandl et al.43 demonstrated that additional coupled modes appear in the case of structures where the particles are not aligned along a single axis. Within this theoretical approach, collective modes are obtained from linear combinations of the plasmons of the individual particles. To be active, the overall structure of a collective mode must be consistent with the symmetry of the system In the case of 2D geometries, higherorder modes can thus contribute in a non-negligible way to the

extinction spectrum. A further difference between the particle pairs and rows and the 2D array is the overall dimension of the system. Retardation effects can be anticipated to become more important for larger systems and can make higher-order plasmon modes more visible.43 The presence of higher-order modes may therefore be responsible for the additional component of the exponential distance decay of plasmon coupling in the case of the more complex 2D array. This is because the higher-order


Figure 11. Relative red shift (∆λ/λ) as a function of relative interparticle spacing, measured on PS-coated gold NPs monolayers. Data were taken from the experimental spectra presented in Figure 5 and the TE-polarized spectra from Figure 7 and for particles with both sizes. The fitted curve is a first-order exponential decay with a τ value of 0.63 ( 0.05.

modes will not necessarily demonstrate the same distance dependence as does the dipolar coupling. Conclusions A bottom-up self-assembly method is used to prepare bidimensional arrays of ordered gold NPs in a transparent media. This approach leads to structures that are regular enough to enable the facile systematic control of the interparticle gap. This parameter has an important effect on the LSPR of the NPs as near-field coupling becomes possible as neighboring NPs are brought close together. Plasmon coupling is reflected in characteristic changes in the optical extinction spectra of the monolayer. In particular, polarized spectra measured parallel and perpendicular to the monolayer plane become increasingly different as the distance between the particles is reduced, with the in-plane component exhibiting a significant red-shifted. This behavior is characteristic of increasing dipolar coupling of the LSPR of neighboring NPs and agrees well with simulations conducted using the discrete dipole approximation. Minor differences between the experimental and calculated results are attributed to the presence of small particle aggregates and a reduction in the matrix refractive index. By comparing the calculated spectra for gold spheres laid out as a pair, a straight row and a 2D hexagonal array, the influence of the array geometry on the red shift of the LSPR was investigated. The variation of the relative red shift as a function of the relative interparticle spacing obeys a first-order exponential decay law in all three structures, with a decay constant similar to results previously reported. In the case of the 2D array, two distinct decay rates are observed. The second rate is less steep and corresponds to the decay rate obtained from the experimental extinction spectra recorded for the PScoated gold nanoparticle monolayers. This second decay constant may result from higher-order modes that become significant in the case of 2D arrays because of symmetry considerations. Acknowledgment. The authors acknowledge the Centre que´bećois sur les mate´riaux fonctionnels (CQMF) and NanoQue´bec, le Fonds Que´bećois de la recherche sur la nature et les technologies (FQRNT) and the National Sciences and Engineering Research Council of Canada (NSERC) for financial support. References and Notes (1) Kreibig, U.; Vollmer, M. Optical Properties of Metal Clusters; Springer: Berlin, 1995..

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