Estimation of Dielectric Function of Biotin-Capped Gold Nanoparticles

Jul 20, 2006 - (b) Size distribution of the biotin-capped gold nanoparticles (based on 110 .... The SPR data at the other two wavelengths λ = 1152 an...
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J. Phys. Chem. B 2006, 110, 15755-15762

15755

Estimation of Dielectric Function of Biotin-Capped Gold Nanoparticles via Signal Enhancement on Surface Plasmon Resonance Xinheng Li,† Kaoru Tamada,*,†,‡ Akira Baba,§ Wolfgang Knoll,| and Masahiko Hara† Department of Electronic Chemistry, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, Nagatsuta-cho, Yokohama, Kanagawa 226-8502, Japan, Bio-Photonics Group, Photonics Research Institute, National Institute of AdVanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565, Japan, Department of Chemistry, UniVersity of Houston, Texas 77204, and Max-Planck-Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany ReceiVed: March 31, 2006; In Final Form: May 15, 2006

Biotin-capped gold nanoparticles assembled on flat gold with volume fraction f are studied by surface plasmon resonance (SPR) spectroscopy and atomic force microscopy (AFM) in order to estimate the dielectric function of the gold nanoparticles based on the Maxwell-Garnett (MG) theory. The complex dielectric function (′, ′′) of the spherical nanoparticles at three representative wavelengths in the vis-near-IR region, i.e., λ ) 543, 632.8, and 1152 nm, is estimated for a surface homogeneously covered with nanoparticles in order to discuss the wavelength dependence of the dielectric function. The SPR response of a surface covered with particles in 2D aggregates is also analyzed. The experimental SPR curve of the particle aggregates deviates from the theoretical predictions, suggesting dipole interactions between particles.

Introduction Recent advances in the fabrication of gold nanoparticles have yielded nanostructured materials with distinctive properties, which can be potentially applied to biosensors, nonlinear optics, catalysis, telecommunications, and other fields.1-3 For example, these functionalized gold particles have shown 104 to over 107 times signal enhancements on Raman spectroscopy (surface enhanced Raman scattering, SERS),4-6 more than 1000-fold enhancements on surface plasmon resonance (SPR) spectroscopy compared with nonparticle binding events,7 improvements of colorimetric sensing of DNA,8,9 and other applications.10-13 These enhancements result from the particles’ collective properties, which are dependent on the particle’s dielectric function (optical properties of a single particle), the volume fraction of particles, and their spatial distribution. For metallic nanoparticles that are small compared to the wavelength λ of an incident light, the dielectric function is known to be size-dependent, i.e., different from bulk values.10,12,14,15 However, the exact value of the dielectric function of metallic nanoparticles has not been well-determined yet, and quantitative studies on the effective dielectric function of particle assemblies, especially quantitative discussions of the correlation with the volume fraction of the particles, have not been intensively conducted yet (only a few studies have been reported16-19). Drude’s free-electron model, the Mie theory, and the MaxwellGarnett (MG) theory are developed to describe or to use the dielectric function of small nanoparticles. Drude’s free-electron model describes the dielectric constants of a material as a function of the particle radius R;20 however, this model cannot be applied properly to the visible and near-ultraviolet region * To whom correspondence should be addressed. Tel. and fax: +8145-924-5400. E-mail: [email protected]. † Tokyo Institute of Technology. ‡ AIST. § University of Houston. | Max-Planck-Institute for Polymer Research.

because contributions of transitions from the filled d bands to the sp conduction bands are neglected.21,22 The Mie theory provides a rigorous solution for light scattering by an isotropic sphere embedded in a homogeneous medium.14 Extensions of the Mie theory include solutions even for core/shell spheres or alloys23 and have been widely used to predict absorption coefficients of nanostructured materials.18,24 However, the Mie theory often uses the bulk dielectric values of a metal also for the nanoparticles for the prediction of the extinction crosssection (efficiency of extinction at the interface).25 Moreover, it fails for colloidal aggregates of small metallic particles.26 Our aim here is to estimate the dielectric function of small metallic nanoparticles from the visible light region to the near-IR region and to quantify the effective dielectric function of not only the dispersed particles on the surface but also those assembled in 2D aggregates. The MG model explains reflection and absorption features as a function of the particles’ volume fraction in a composite material and accurately describes the interaction of the surface plasmon modes at high volume fractions of nanoparticles assembled in a thin film.27-29 Hence, if a monolayer of particles deposited on a surface is treated as the layer with the effective dielectric function, one could extract the dielectric function of the nanoparticles and correlate it with their collective optical properties. In this paper, we report the use of SPR and atomic force microscopy (AFM) data for the estimation of the dielectric function of gold nanoparticles based on the Maxwell-Garnett theory. The synthesized biotin-capped gold nanoparticles with a diameter of ca. 24 nm were self-assembled on substrates via biotin-avidin molecular recognition. The number of particles dispersed on the surface was carefully counted by AFM in order to obtain the volume fraction f in the nanoparticle composite layer. SPR in the Kretschmann geometry was used to accurately obtain the effective dielectric function eff of the composite layer30 at three representative wavelengths in the vis-near-IR region, i.e., at λ ) 543, 632.8, and 1152 nm respectively. The

10.1021/jp062004h CCC: $33.50 © 2006 American Chemical Society Published on Web 07/20/2006

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SPR response of the surface covered with the particles in 2D aggregates were also analyzed. Experimental Section Preparation of Biotin-Functionalized Gold Nanoparticles. Colloidal gold was prepared by citrate reduction of HAuCl4‚ 3H2O (Sigma, 99.9%) using Frens’ method.31 The aqueous citrate solution (10 mL, 1 wt %) was added to 90 mL of 1.4 mM HAuCl4‚3H2O, and the obtained colloidal particles were washed and redispersed in water (0.01 wt %). Mercaptopropionyl PEG-biotin (PEG ) poly(ethylene glycol)) with eight ethyl glycol units (Code, 41151-0895; LCC Engineering and Trading GmbH, Switzerland) was added to 5.0 mL of redispersed nanoparticle solution and stirred at room temperature for 4 h.. The solution was then centrifuged at 6000 rpm for 30 min.. The red precipitates were washed by MilliQ water to remove the excess free biotin completely, and the supernatants were disposed of. Assuming a homogeneous reaction (exchange reaction between the thiols and the acidic groups), approximately 10% of the particle surface is covered with biotin functional groups.32 All the chemical compounds were used without further purification. Formation of gold nanoparticles was confirmed by the local plasmon absorption band recorded in a Shimadzu UV-vis 1601 spectrometer. The size of the biotin-capped gold particles was determined by transmission electron microscopy (TEM), shown in Figure 1 using a Philips FE CM300 microscope at 300 kV. The mean diameter of the particles was determined to be 24 (2 nm with standard deviation σ ) 7.3. The biotin-capped gold nanoparticles were prepared to be ca. 0.1 nM in concentration for use. SPR Surface Preparation. Thin gold films for SPR measurements at λ ) 632.8 nm were deposited on LaSFN9 glass substrates (Schott, n ) 1.85) by thermal evaporation in a vacuum chamber (R-DEC Co. Ltd., Ibaraki, Japan). Prior to evaporation, the substrates were cleaned in 2% Hellmanex solution in an ultrasonic bath and rinsed by MilliQ water and absolute ethanol several times. Gold deposition was performed in a sample rotation system at a pressure of ∼5.0 × 10-5 Pa without temperature control. The deposition rate was 1.0 Å/s, and the thickness was controlled to be ∼47 nm. The substrates were kept in ethanol before use to avoid contamination. For the SPR measurements at λ ) 543 nm, 8 nm of gold was deposited onto a 38 nm silver film. For the SPR measurements at λ ) 1152 nm, a 36 nm gold film was deposited as the optimized thickness for SPR excitation. SPR Instrumentation. The schematic experimental setup for surface plasmon resonance spectroscopy is shown in Figure 2. The SPR measurements were carried out using a Kretschmann geometry with a triangular prism (LaSFN9 glass, Schott), which is index-matched to LaSFN9 substrates with the gold (or silver) films via immersion oil (n25°C ) 1.700, Cargille Lab, NJ). The p-polarized He-Ne laser beams (λ ) 632.8 nm (Unifase, 5 mW), λ ) 543 nm (Unifase, 5 mW), and λ ) 1152 nm (Unifase, 5 mW)) are mechanically chopped in conjugation with a lockin amplifier before entering the prism. The intensity of the beam reflected off the gold interface (“reflectivity”) is monitored by a photodiode detector. The change of reflectivity as a function of the incident angle is recorded as “angular scan” data on a θ-2θ rotation stage, while kinetics scan data are recorded as a function of time at a fixed incident angle. The resolution of measured coupling angle is estimated to be 0.001°. After the substrate was mounted on the SPR setup, an angular scan of the bare gold film was taken in absolute ethanol in order

Figure 1. (a) TEM image of the biotin-capped gold nanoparticles. (b) Size distribution of the biotin-capped gold nanoparticles (based on 110 particles). d ) 24 ( 2 nm, and σ ) 7.3.

to determine the exact gold film thickness and the complex refractive index by curve fitting with Fresnel’s equations. The first biotinylated layer on gold was fabricated in the SPR flow cell by injection of a mixed solution of 10 mol % biotinylated thiol and mercaptoundecanol (short-chain thiol to dilute the biotin functions on the surface). The total concentration of the thiols was 0.25 mM in ethanol. The change in reflectivity by the thiol adsorption was monitored by a SPR kinetics scan. After the reflectivity reached a constant value, the surface was rinsed by ethanol and the thickness of the biotinylated thiol layer was confirmed by a SPR angular scan. Prior to streptavidin adsorption, ethanol was changed to 0.1 M NaCl of phosphate-buffered saline (PBS; pH 7.4), and then the adsorption of streptavidin on the biotinylated thiol layer was recorded in PBS buffer in the same manner. The optical thickness of each layer was determined from SPR angular shift with the fixed refractive index (n ≈ 1.5) and compared with the literature value. Finally, the solvent was changed to MilliQ water for injection of the biotin-capped gold nanoparticles. The volume fraction of the particles was controlled by adsorption time by monitoring the kinetic scan.

Biotin-Capped Au Nanoparticles Dielectric Function

J. Phys. Chem. B, Vol. 110, No. 32, 2006 15757 an applied electromagnetic field is described in terms of a complex dielectric constant of the particles: (ω) ) ′(ω) + i′′(ω), where ′ and ′′ are the real and imaginary components of the dielectric function, respectively, and ω is the angular frequency. If such particles are assembled in a medium, the collective optical response to an applied field is described in terms of an effective dielectric function of the particle assembly: eff(ω) ) eff′(ω) + ieff′′(ω), where eff′, eff′′ are the real and imaginary components of the effective dielectric function of the composite material composed of particles and the surrounding medium, respectively. In our proposed model, the ensemble of the metallic nanoparticles embedded in the medium are depicted as a dielectric layer with an effective dielectric function eff(ω) and a thickness that equals the diameter of the particles; i.e., d ) 24 nm of Figure 3a. The Maxwell-Garnett theory describes the direct relation of the effective dielectric function of composite materials with the dielectric function and volume fraction f of the metallic particles,34

Figure 2. Schematic experimental setup of surface plasmon resonance spectroscopy with λ ) 543, 632.8, and 1152 nm excitation light sources in the Kretschmann configuration.

Atomic Force Microscopy. The volume fraction of the gold nanoparticles adsorbed on the SPR substrate was determined from the images taken by an atomic force microscope (TMAFM, Digital Instruments Nanoscope IIIA) in the tapping mode with an acquisition rate of 1.0-2.0 Hz and a line density of 512. Standard silicon probes (MPP-11100, Digital Instruments; length of cantilever, 125 µm; tip radius, 15 nm) were used for imaging. The size of the nanoparticles appears to be overestimated in the AFM images due to the convolution with the tip radius.33 Here we only counted the number of particles and then calculated the volume fractions of particles by use of the TEM diameter (24 nm), unless otherwise described. For the determination of the volume fraction f, at least three images (5 µm × 5 µm) were taken from two distinct SPR-measured regions of each sample surface. Representative images are shown in the paper. Results and Discussion Method for Estimating the Dielectric Function Based on the MG Theory. The optical response of colloidal particles to

eff ) m

(

)

(1 + 2f) + 2m(1 - f) (1 - f) + m(2 + f)

(1)

This theory predicts the plasmon absorption peak positions accurately but fails for the shapes of the absorption bands. Garcia et al. modified the Maxwell-Garnett model by introducing geometry and homogeneity factors and reported good agreements with experimental results.35 Here, we applied their modified Maxwell-Garnett equations to derive dielectric function of gold nanoparticles. The simplified equations are given by

eff′ ) m′ +

AC + BD , C2 + D2

eff′′ )

BC - AD C2 + D2

(2)

where A ≡ f(′ - m′), B ≡ f′′, C ≡ m + β(′ - m′) - fγ(′ - m′), D ≡ β′′ - fγ′′, and γ can be described as follows,

γ≡

K 1 + 3m′ 4πm′

(3)

Here ′ and ′′ are the real and imaginary parts of the dielectric function of gold nanoparticles, respectively. m′ is the

Figure 3. (a) Schematic model of an effective dielectric function of a particle layer and the thickness equal to the particle diameter 24 nm. (b) Particle layer embedded in a matrix (water) in a Kretschmann configuration.

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Figure 4. Schematic diagram of the adsorption of the biotin-capped gold nanoparticles on the surface via biotin-streptavidin molecular recognition.

dielectric function of the used matrix, i.e., water in our experiments. Since water is transparent against the laser utilized in our experiments (λ ) 543, 633, and 1152 nm), m′′ becomes zero. K represents the dielectric field at a particle position created by the adjacent particles and/or by the surrounding materials. K is considered to be nearly zero if the particles are separated far enough so that dipolar interactions are negligible, or if particle arrangement is spatially cubic. If K ) 0, γ becomes 1/(3m′). β is a geometric factor of the particles, which is 1/3 if the particles are spherical. In this study, we measure the effective dielectric functions (eff′, eff′′) of the composite layer by the SPR scans at each wavelength and determine the volume fractions f from the corresponding AFM images on the same surfaces. By substituting these values into eq 2 and eq 3, the dielectric constants of gold nanoparticles can be obtained accordingly. Estimation of Dielectric Functions at Three Wavelengths in Vis-Near-IR Region. The schematic diagram of the adsorption of biotin-capped gold nanoparticles to the surface is shown in Figure 4. The biotin-streptavidin interaction is a biomolecular recognition with Ka ≈ 1015 M-1, which is stable over a wide range of pH and temperature, and thus, surface architectures of biotin and streptavidin have a very good reproducibility. The adsorption kinetics and the respective thickness of each layer were carefully monitored by SPR. Both the biotin SAM and the streptavidin layer thicknesses obtained by curve fitting with Fresnel equations (see Figure 1S in the Supporting Information) show good agreement with their chain lengths/dimensions given in previous reports,36,37 i.e., biotin SAM, lbiotin ) 1.9 ( 0.1 nm (n ) 1.50), and streptavidin layer, lSA ) 3.5 ( 0.2 nm (n ) 1.45), indicating the formation of densely packed monolayers. Angular SPR curves at λ ) 632.8 nm before and after particle adsorption of Figure 5a show that the adsorbed particles induce a minimum angle shift larger than biotin or streptavidin, a direct consequence of the large dielectric function of the particles. By fitting the SPR curves with Fresnel’s equations, the effective dielectric constants of the particle layer, i.e., eff′ and eff′′, are obtained as eff′ ) 1.91 and eff′′ ) 0.04, with the dielectric constant of the medium (water) as m′ ) 1.78. The error in determination of the effective dielectric function of the interfacial layer is about 0.01. Figure 5b, the AFM image taken on the SPR measured area, shows that the biotin-capped particles were well-distributed on the surface as a single adsorbed layer, with no multilayer formation due to particle aggregates. We can confirm the narrow size distribution of the particles in the image, although the size of particles is overestimated (averaged diameter of particles is 32 ( 4 nm). The averaged f value of the surface layer is estimated to be 0.027 ( 0.002 using the diameter of the particles determined from the TEM image. The SPR data at the other two wavelengths λ ) 1152 and 543 nm, respectively, are shown in Figure 6a,b, with the number density of the particles on the surface about the same (i.e. f )

Figure 5. (a) SPR angle shift at λ ) 632.8 nm before and after adsorption of the biotin-capped gold nanoparticles on streptavidin layer. (b) AFM image of the SPR measured area (5.0 µm × 5.0 µm) captured after the SPR measurements. The obtained volume fraction f is 2.7% from this image.

3%). As the incident wavelength becomes longer, the SPR curves sharpen due to the decrease of damping at the gold/ sample interface related to the decay length of plasmons. The SPR curve at λ ) 543 nm shows an interesting phenomenon as compared to those at the other two wavelengths; i.e., the minimum reflectivity is increasing. According to the UV-visnear-IR spectrum of the biotin-capped gold nanoparticles (Figure 7), there is nearly no absorption of local plasmons of the gold nanoparticles at λ ) 633 nm and at λ ) 1152 nm, in good agreement with the deep minimum in the SPR curves at those two wavelengths. In contrast, the particles have a strong plasmon absorption at λ ) 543 nm and a pronounced increase of the minimum reflectivity appears at the corresponding wavelength. Thus, we can conclude that the SPR minimum reflectivity increase at λ ) 543 nm results from the local plasmon absorption of the gold nanoparticles. In an earlier report, Natan et al. pointed out perturbations of SPR curves by the gold particle adsorption. The minimum intensity increase and/or the widened were attributed to the nature of the colloidal particles, i.e., to absorptive damping, defects, and/or roughness sites on the metal surfaces.12,38 From an optimization of SPR sensitivity enhancement point of view, SPR minimum reflectivity associated with scattering and absorption of light can be tuned and minimized to be negligible by either choosing the appropriate excitation source and/or avoiding multilayer aggregates of metallic particles through the proper design of molecular conjugation on the surface.

Biotin-Capped Au Nanoparticles Dielectric Function

J. Phys. Chem. B, Vol. 110, No. 32, 2006 15759 TABLE 1: the Estimated Dielectric Constants of the Biotin-Capped Gold Nanoparticles with Diameter ca. 24 nm at Various Wavelengths laser wavelength/nm

′

′′

543 632.8 1152

-4.51 ( 0.05 -8.03 ( 0.40 -17.4 ( 2.20

1.45 ( 0.10 3.33 ( 0.50 8.50 ( 2.71

obtained values of the gold nanoparticles are very different from their bulk values; e.g., that dielectric function of the gold nanoparticles at λ ) 632.8 nm is  ) -8.03 + i3.33, while that of bulk gold is bulk ) -12 + i1 by Johnson and Christy.21 Garcia et al. reported that the thiol monolayer affects significantly the dielectric function of the small particles, but only for those with a diameter ca. less than 2 nm.39 By contrast, our particle size is relatively large (d ) 24 nm) and the shell biotin is only 10% of the surface coverage; thus, the effect of the biotin capping agent on the obtained dielectric function must be relatively small compared with their case. Our UV-vis-nearIR spectra in Figure 7, exhibiting the small red shift (∼1 nm) after biotin adsorption, support our assumption. It should be added that the influence of refractive index of the citrate/biotin shell (n ∼ 1.50) upon that of the water matrix phase (n ∼ 1.33) is negligibly small compared with the influence of metal core in MG calculations. In addition, the effect of wavelength on the dielectric properties of organic materials is negligibly small compared with that of metals, as confirmed by our own experiments with biotin/streptavidin monolayers (the latter thicknesses estimated with constant refractive indices show quite similar values independent of wavelength; see the Supporting Information). Figure 6. (a) SPR angle shift at λ ) 1152 nm before and after adsorption of the biotin-capped gold nanoparticles on streptavidin layer. (b) SPR angle shift at λ ) 543 nm before and after adsorption of the biotin-capped gold nanoparticles on streptavidin layer.

Figure 7. UV-vis-near-IR spectra of the gold nanoparticles in water before (dashed line) and after (solid line) adsorption of mercaptopropionyl PEG-biotin. λmax ) 526 nm for biotin-capped gold nanoparticles.

According to the above-described method, the dielectric functions of the biotin-capped gold nanoparticles at each wavelength were calculated by substituting eff and f into eq 2 and eq 3. The obtained dielectric functions are summarized in Table 1. The errors of the estimated dielectric constants of the particles are mainly attributed to the distribution of particle diameter (d ) 24 ( 2 nm). We can see a reasonable trend of the dielectric function changing with the laser wavelength. The

Figure 8. Effective dielectric constants (eff′, eff′′) of the biotin-capped gold nanoparticles at λ ) 632.8 nm as a function of volume fraction, calculated by using the dielectric function of the gold nanoparticles (-8.03, 3.33) obtained in this paper.

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Figure 9. Simulated SPR curves at λ ) 632.8 nm as a function of volume fraction (0 e f e 0.5), using the effective dielectric constants shown in Figure 8.

We corrected the dielectric function of bulk gold using modified Drude’s free electron model with particle radius R in order to make more exact comparisons; however, it results in the critical discrepancy between the theory and experiments: the imaginary part of the dielectric constant ′′ gets saturated in Drude’s model in the wavelength above 800 nm region when R is smaller than the mean free distance of the free electron (∼50 nm), while SPR experiments give reasonable dielectric constants even in the near-IR region. This result points out the invalidity of Drude’s model for the analysis of wavelength dependence. To confirm the reliability of the dielectric functions determined by SPR/MG theory, a direct comparison with other approaches such as Kramers-Kronig (K-K) transformation from extinction spectra is effective. In practice, we have demonstrated this comparison in our previous study using polymer thin films, which exhibited a good agreement between two methods except for the deviation in absolute imaginary values.40 Through the experiments, we are confident that our

Li et al. SPR/MG method is reliable enough to discuss quantitative details of dielectric constants beyond conventional optical techniques. Predicted Effective Dielectric Function against f and SPR Curves. By using the obtained dielectric function of the gold nanoparticles at λ ) 632.8 nm, the effective dielectric functions from minimal volume fraction (i.e., no particles) to the maximal volume fraction (i.e., closely packed assembly, f ) 0.5 41 ) can be quantitatively predicted. As shown in Figure 8, both real and imaginary components of the effective dielectric functions (eff′, eff′′) increase with the volume fraction up to f ) 0.5. Figure 9 shows simulated SPR curves as a function of the volume fraction using the effective dielectric functions shown in Figure 8. We can see drastic changes of the SPR curves with the volume fraction increase of the assembled particles (f ) 0-0.5), which suggests a great potential of metallic nanoparticles for highly sensitive SPR detection. Concerning the effective dielectric function of composite films, Kooij et al. reported eff ) 1.3 + i0.03 at f ≈ 0.09 18 for gold nanoparticles with a diameter of 12.8 nm by ellipsometric spectroscopy. Schiffrin et al.42 and Evans et al.43 reported the values of eff ) 3.86 + i6.62 and  ) 5.32 + i5.68 for densely packed gold particles, respectively (exact volume fractions were not reported in both papers). The inconsistency between our calculated values and their results may originate from the different morphologies of the adsorbed particles on the surfaces, e.g., being dispersed or aggregated. It should be noted again that the dipole interaction between particles is not taken into account in our model (K ) 0 in eq 3), although it cannot be neglected particularly at high volume fractions. We will discuss this in more details in the following section. Experimental Results on Surfaces Covered with Particles in 2D Aggregates. In Figure 10, we present SPR curves and the corresponding AFM images on the surfaces covered with particles of different surface concentration and morphologies. Parts a and b of Figure 10 are the data for dispersed particles,

Figure 10. SPR data at λ ) 632.8 nm and the AFM images with different volume fractions of particles: (a, b) dispersed particles; (c) 2D particle aggregates.

Biotin-Capped Au Nanoparticles Dielectric Function

Figure 11. Volume fraction obtained by SPR data (fSPR) plotted against those by AFM images fAFM.

while Figure 10c gives the results for particles in 2D aggregates. Since we cannot count the exact number of particles from aggregates, we instead determined the area fractions from the binary images processed by the ImageJ software (NIH) and converted them to volume fractions fAFM. The area fractions obtained by the above method were (a) 0.27 ( 0.2, (b) 0.34 ( 0.1, and (c) 0.62 ( 0.1. The area fractions obtained from AFM images include unavoidable errors resulting from the AFM tip radius, which is estimated to be a factor of 3-4 since the averaged diameter of the particles in Figure 10a,b is 1.7-2 times larger in the AFM images than that obtained by TEM. Thus, the volume fractions fAFM are determined as (a) 0.053 ( 0.007, (b) fAFM ) 0.067 ( 0.010, and (c) fAFM ) 0.121 ( 0.018. At the same time, the volume fractions fSPR were calculated from the SPR angle shifts with dielectric constant of the particles  ) -8.03 + i3.33 and given as (a) 0.04, (b) 0.08, and (c) 0.20. The obtained fSPR is plotted against fAFM, as shown in Figure 11. It is found that fAFM and fSPR agree very well for dispersed particles, while fSPR is much larger than fAFM in aggregates; i.e., the experimental SPR angle shift is much larger than the prediction from the model. Moreover, unlike for dispersed particles, the aggregates’ experimental SPR curve cannot be fit well with Fresnel’s equations (see Figure 2S in the Supporting Information). We assume that these phenomena can be interpreted by dipole interactions between neighboring particles. In aggregates, the dielectric function of particles varies by the dipole interaction closely related with the interparticle distance l,44 which can result in a red shift of the plasmon absorption band.45 Additional light scattering on those domainlike phases also can be considered but would be a very weak contribution because the surface of Figure 10c is so homogeneous (the height of domains is less than 30 nm) as compared to the used wavelength of light. To obtain the full picture of how local plasmons couple to the propagating surface plasmon fields, more systematic studies of particle aggregates are necessary, e.g., in combination with reflection absorption spectroscopy. Nevertheless, we believe we have demonstrated an empirical evidence of the local field effect of nanoparticles on a metallic surface in this study. Conclusions We have studied biotin-capped gold nanoparticles assembled on solid substrates via biotin-streptavidin molecular recognition. The particles well-dispersed on the surface with low volume fraction f have been studied by SPR with three laser wavelengths

J. Phys. Chem. B, Vol. 110, No. 32, 2006 15761 in the vis-near-IR region; i.e., λ ) 543, 632.8, and 1152 nm, respectively. The SPR curve at λ ) 543 shows a substantial increase of the minimum intensity, while those at the other two wavelengths do not, in agreement with the absorption caused by local plasmon excitation. The dielectric function of the gold nanoparticles was estimated on the basis of a modified MG model and shown in wavelength-dependent values, different from bulk gold. By using the obtained dielectric constants of the gold nanoparticles at λ ) 632.8 nm, the effective dielectric constants eff of composite layers at higher volume fraction f and the corresponding SPR curves have been predicted. The experimental SPR curves of 2D particle aggregates show large deviations from the prediction, not only in the minimum angle position but also in the peak width, while those of the layers with well-dispersed particles can be perfectly fitted by the applied model. We assume that these phenomena can be interpreted by taking into account dipole-dipole interactions of neighboring particles, i.e., local plasmon coupling on surface plasmon field. We will extend systematic studies of particle aggregates on surface in our future work. Supporting Information Available: SPR experimental curves fitting at λ ) 543, 632.8, and 1152 nm (Figure 1S) as well as those of particle aggregates and dispersed particles at λ ) 632.8 nm (Figure 2S). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Niemeyer, C. M. Angew. Chem., Int. Ed. 2001, 40, 4128. (2) Mirkin, C. A. Inorg. Chem. 2000, 39, 2258. (3) Mertens, H.; Verhoeven, J.; Polman, A.; Tichelaar, F. D. Appl. Phys. Lett. 2004, 85, 1317. (4) Wei, A.; Kim, B.; Sadtler, B.; Tripp, S. L. ChemPhysChem 2001, 2, 743. (5) Zhu, Z.-H.; Zhu, T.; and Liu, Z.-F. Nanotechnology 2004, 15, 357. (6) Grabar, K. C.; Smith, P. C.; Musick, M. D.; Davis, J. A.; Walter, D. D.; Jackson, M. A.; Guthrie, A. P.; Natan, M. J. J. Am. Chem. Soc. 1996, 118, 1148. (7) He, L.; Musick, M. D.; Nicewarner, S. R.; Salinas, F. G.; Benkovic, S. J.; Natan, M. J.; Keating, C. D. J. Am. Chem. Soc. 2000, 122, 9071. (8) Storhoff, J. J.; Elghanian, R.; Mucic, R. C.; Mirkin, C. A.; Letsinger, R. L. J. Am. Chem. Soc. 1998, 120, 1959. (9) Storhoff, J. J.; Elghanian, R.; Mirkin, C. A.; Letsinger, R. L. Langmuir 2002, 18, 6666. (10) Link,S.; El-Sayed, M. A. J. Phys. Chem. B 1999, 103, 8410. (11) Chah, S.; Hutter, E.; Roy, D.; Fendler, J. H.; Yi, J. Chem. Phys. 2001, 272, 127. (12) Lyon, L. A.; Pena, D. J.; Natan, M. J. J. Phys. Chem. B 1999, 103, 5826. (13) Patskovsky, S.; Kabashin, A. V.; Meunier, M. Opt. Mater. 2005, 27, 1093. (14) Kreibig, U.; Vollmer, M. Optical Properties of Metal Clusters; Springer: Berlin, 1995. (15) Galletto, P.; Brevet, P. F.; Girault, H. H.; Antonine, R.; Broyer, M. Chem. Commun. 1999, 7, 581. (16) Pipino, A. C. R.; Woodward, J. T.; Meuse, C. W.; Silin, V. J. Chem. Phys. 2004, 120, 1585. (17) See, K. C.; Spicer, J. B.; Brupbacher, J.; Zhang, D.; Vargo, T. G. J. Phys. Chem. B 2005, 109, 2693. (18) Kooij, E. S.; Wormeester, H.; Brouwer, E. A. M.; Vroonhoven, E.; Silfhout, A.; Poelsema, B. Langmuir 2002, 18, 4401. (19) Bruzzone, S.; Malvaldi, M.; Arrighini, G. P.; Guidotti, C. J. Phys. Chem. B 2004, 108, 10853. (20) Grady, N. K.; Halas, N. J.; Nordlander, P. Chem. Phys. Lett. 2004, 399, 167. (21) Johnson, P. B.; Christy, R. W. Phys. ReV. B 1972, 6, 4370. (22) Link, S.; El-Sayed, M. A. J. Phys. Chem. B 1999, 103, 4212. (23) (a) Bruzzone, S.; Arrighini, G. P.; Guidotti, C. Mater. Sci. Eng., C 2003, 23, 191. (b) Belotelov, V. I.; Carotenuto, G.; Nicolais, L.; Pepe, G. P.; Zvezdin, A. K. Eur. Phys. J. B 2005, 45, 317. (c) Moskovits, M.; SrnovaSloufova, I.; Vlckova, B. J. Chem. Phys. 2002, 116, 10435. (24) Templeton, A. C.; Pietron, J. J.; Murray, R. W.; Mulvaney, P. J. Phys. Chem. B 2000, 104, 564. (25) Alvarez, M. M.; Khoury, J. T.; Schaaff, T. G.; Shafigullin, M. N.; Vezmar, I.; Whetten, R. L. J. Phys. Chem. B 1997, 101, 3706.

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