© Copyright 2003 by the American Chemical Society
VOLUME 107, NUMBER 38, SEPTEMBER 25, 2003
LETTERS Optical Absorption Study of the Surface Plasmon Resonance in Gold Nanoparticles Immobilized onto a Gold Substrate by Self-Assembly Technique Takayuki Okamoto* and Ichirou Yamaguchi† RIKEN (The Institute of Physical and Chemical Research), Hirosawa 2-1, Wako, Saitama 351-0198, Japan ReceiVed: March 3, 2003; In Final Form: August 3, 2003
The resonance wavelength of the surface plasmon in gold nanoparticles above a gold substrate has been measured using transmission absorption spectroscopy. Gold nanoparticles with diameters in the range of 20100 nm are immobilized onto a thin gold film deposited onto a glass substrate by a self-assembled monolayer of aminoethanethiol. The resonance wavelength obtained in the experiments shows a large red shift. Its dependence on the particle diameter shows good agreement with theoretical results that are calculated using a static approximation that includes multipole effects.
Introduction The resonance wavelength of the surface plasmon in metallic nanoparticles is highly dependent on the environment around the particles.1 The increase of the refractive index of the ambient medium or the film thickness coated on the particles gives a red shift in the resonance wavelength. These effects have been used for sensor applications.2-5 This class of red shift, i.e., that which is due to the increase of the refractive index of the surrounding dielectric media, is not so eminent. On the other hand, an aggregation of metallic nanoparticles exhibits a larger red shift in the resonance wavelength. It is well-known that an aggregation of gold nanoparticles changes the color from red to violet or blue. Another factor that affects the red shift is the existence of substrates. When a metallic nanoparticle is supported in a uniform medium, a homogeneous external field induces a dipole in the nanoparticle. However, when the nanoparticle is supported on a substrate whose refractive index is different from that of the ambient, the field that acts on the particle is no longer homogeneous, because of the field by the image dipole that is * Author to whom correspondence should be addressed. E-mail:
[email protected]. † Currently at Gunma University.
induced in the substrate. Consequently, multipoles are induced in the nanoparticle, which results in a red shift in the plasmon resonance. This multipole effect has been predicted theoretically.6-8 The theory also predicts that the amount of the red shift will be larger for noble-metal substrates with a very small gap between the particle and the substrate. However, very few experimental results that exhibit such a large red shift have been reported. Kume et al.9 observed such a large red shift in the scattering spectra for silver nanoparticles that had been deposited onto an aluminum substrate with an attenuated total reflectance illumination geometry. In this paper, we present an experimental demonstration of the large red shift in the surface plasmon resonance in gold nanoparticles that have been deposited onto a gold substrate, through the use of simple transmission absorption spectroscopy. Here, the gold nanoparticles are immobilized onto the substrate with a self-assembled monolayer that acts as a coupling agent and a spacer between the particles and the substrate. We then compare the resonance wavelengths obtained in the experiments with those obtained by theoretical calculation, considering multipole effects, and show that a large red shift is caused by the multipole effects. Theoretical calculation suggests that the optical properties of a nanoparticle above a substrate are very similar to those of two-particle aggregates, where the image
10.1021/jp034537l CCC: $25.00 © 2003 American Chemical Society Published on Web 09/04/2003
10322 J. Phys. Chem. B, Vol. 107, No. 38, 2003
Letters Aravind and Metiu6 and Wind et al.8 used a static approximation to solve a scattering problem for a sphere above a substrate; i.e., only the retardation effect is neglected. Aravind and Metiu solved the Laplace equation for the potential in bispherical coordinates, whereas Wind et al. solved it in polar coordinates. Both methods, which give identical results, consider multipoles to be higher than dipole and mirror image effects that are due to the substrate. According to Wind’s method,8 the polarizability of the sphere above the substrate is given by
Figure 1. Schematic configurations of the systems for (a) theoretical calculations and (b) experiments. Legend is as follows: 1, gold nanosphere; 2, ambient; 3, gold substrate or gold film; 4, glass substrate; 5, chromium thin film; and 6, 2-aminoethanethiol.
dipole induced in the substrate is just replaced with an actual dipole induced in the other particles. Therefore, we can also predict the optical properties of two-particle aggregates from the experimental results obtained in this paper. Theory Figure 1a shows a schematic diagram of the system used for theoretical calculation. A gold nanosphere is placed above a flat gold substrate whose thickness is semi-infinite. The simplest method to calculate the absorption efficiency (Qabs) of the nanosphere is use of the dipole approximation, where the sphere is represented by a single dipole. Considering the image dipole induced in the substrate, the polarizability R of the sphere is given by
(
R ) 4πa3
)[
( )(
)( )]
1 - 2 a 3 1 - 2 3 - 2 1-β 1 + 22 2d 1 + 22 3 + 2
-1
(1)
where 1, 2, and 3 are the dielectric constants of the sphere, the ambient, and the substrate, respectively; a is the radius of the sphere; d is the distance between the center of the sphere and the surface of the substrate; and β is a constant that is equal to 1 for the parallel electric field or 2 for the normal electric field. Using the polarizability R, the absorption efficiency Qabs and the scattering efficiency (Qsca) are given by
Qabs )
k Im(R) πa2
(2a)
and
Rp ) 4π2a3Ap1
Qsca )
k |R|2 2 2 6π a
(2b)
respectively, where k is the wave vector in the ambient. The extinction efficiency of the sphere (Qext) is given by the sum of these two efficiencies: Qext ) Qabs + Qsca. From eqs 1 and 2, the surface plasmon resonance, which represents a peak in the spectrum of extinction efficiency, shows a red shift with decreasing gap distance. The resonance wavelength of a gold nanosphere, which is 511 nm in ambient air, shifts to 528 nm when the sphere contacts a gold substrate and is excited by a electric field normal to the surface of the substrate. Thus, the amount of the red shift is very small when calculated using the dipole approximation. Even in ambient water, the resonance wavelength shifts from 523 nm to 573 nm. The amount of the red shift is much smaller than that obtained in the experiments, as described later in this paper. This discrepancy is caused by the fact that the dipole approximation does not consider multipoles such as quadrupoles and octupoles.
(3)
where Ap1 is one of the solutions of the following infinite series of linear equations. When the incident electric field is perpendicular to the substrate, the linear equations are given by ∞
( {
δkj + ∑ j)1
[
k(1 - 2)(2 - 3)
[k1 + (k + 1)2](2 + 3) 1 - 2 (k + j)! A⊥j ) δk1 1 + 22 k!j!(2d/a)k+j+1
])
}
(for k ) 1, 2, ...) (4)
and when it is parallel to the substrate, they are given by ∞
∑ j)1
( { [ δkj +
k(1 - 2)(2 - 3)
[k1 + (k + 1)2](2 + 3) (k + j)!
(k + 1)!(j - 1)!(2d/a)k+j+1
])
}
A|j )
1 - 2
δk1 1 + 22
(for k ) 1, 2, ...) (5)
where δkj is the Kronecker delta. Using the polarizabilities given by eq 3, the absorption efficiency and the scattering efficiency of a sphere for a p-polarized incident beam with angle of incidence θ are given by
Qabs )
k xIm2[|1 + rp|sin θ R⊥] + Im2[|1 - rp|cos θ R|] πa2 (6)
and
Qsca ) 4
(for p ) ⊥ or |)
k4[||1 + rp|sin θ R⊥|2 + ||1 - rp|cos θ R||2] 6π2a2
(7)
respectively, where rp is the Fresnel reflection coefficient for p-polarized beams. Figure 2 shows the Qext spectrum for a gold sphere above a flat gold substrate, calculated using the static approximation for various ratios of the gap distance between the sphere and substrate to the sphere radius. A p-polarized illumination with an incident angle of θ ) 60° is assumed. The dielectric constants used are deduced from the literature values,10 including the size effect, where the dielectric constant is dependent on the particle diameter.11 In the calculations, we assumed a gold sphere with a diameter of 20 nm. The resonance wavelength shifts toward longer wavelengths remarkably as the gap distance decreases. This shift is caused by the multipoles that are induced by the image dipole in the substrate. For an s-polarized incidence, the calculated red shift was almost negligible. Figure 3 shows the calculated spectrum of a 20-nm gold sphere separated from a gold substrate by a distance of 0.1 nm, for p-polarized incident beams with various angles of incidence θ. When θ ) 0° (i.e.,
Letters
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Figure 2. Calculated extinction efficiency of a gold particle above a gold substrate for various ratios of the gap distance to the particle radius. A p-polarized beam at an incident angle of θ ) 60° is assumed. Figure 4. Scanning electron microscopy (SEM) micrograph of 40nm-diameter gold particles immobilized onto a glass substrate coated with a gold film.
Figure 3. Calculated extinction efficiency of a 20-nm gold particle above a gold substrate with a gap distance of 0.1 nm. A p-polarized incident beam is assumed.
normal incidence), no peak appears at ∼700 nm, because no electric-field component exists normal to the substrate surface. Deposition of Colloidal Gold Particles Figure 1b shows a schematic diagram of the system used in the experiments. We used a thin gold film as the substrate, instead of a semi-infinite gold substrate, for the transmission absorption measurements. We deposited a chromium film that was a few nanometers thick, followed by a 25-nm-thick gold film, onto a microscope glass slide (used as the substrate) with thermal vacuum evaporation. Gold nanoparticles were immobilized onto the substrate using a self-assembly technique that is explained later in this paper. Various coupling agents have been used to immobilize gold nanoparticles onto various types of substrates.12-16 Here, we used aminoethanethiol (AET) as the coupling agent for gold substrates.15 Six types of gold colloid suspensions were purchased from British BioCell. The mean diameters of the particles are 20.2, 30.4, 41.3, 60.8, 80.8, and 99.8 nm. The substrates were immersed in a 10 mM ethanol solution of AET for 1 h. In this process, the mercapto base of AET forms attachments to the gold surfaces and forms its monolayer on the gold surfaces. After the AET immersion, the substrates were rinsed with distilled water and dried with a nitrogen gun. The substrates coated by AET were then immersed in a colloidal gold suspension for 8-20 h. After immersion, the samples were rinsed with distilled water and dried with a nitrogen gun. In these processes, the colloidal gold particles were strongly immobilized onto the gold substrates, because of the affinity of the amino group to the gold. Figure 4 shows a scanning electron microscopy (SEM) micrograph of 41.3-nm-diameter gold particles that have been immobilized onto a glass substrate coated with a gold film. The particles were immobilized uniformly and separated from each other. The mean interparticle
Figure 5. Measured extinction spectra for various incident angles.
distance is a few times larger than the particle diameter, so that we can neglect the interaction between particles. The particle density can be controlled by the immersion time in the colloidal gold suspension. Experimental Results and Discussion We measured the extinction spectra of the deposited colloidal nanoparticles with a UV-visible double-beam spectrophotometer (model UV2500, Shimadzu). The same glass slides that were coated with a gold/chromium film, but without gold particles, were used as the references. To induce an electric field normal to the substrate, we tilted the sample and reference substrates against the incident beams and used a couple of polarizers to obtain p-polarized incidence. Figure 5 shows the measured extinction spectra of 41.3-nm-diameter gold nanoparticles that were deposited onto a gold film substrate for various incident angles. For the normal incidence, a single peak appears at ∼510 nm. Because the normal incident wave has only an electric-field component that is parallel to the substrate surface, the resonance wavelength is located at almost the same position as that of isolated gold nanoparticles. The second peak at ∼680 nm appears when the incident angle θ is >30°. This peak results from the image dipole that is induced in the substrate. The height of the second peak increases as the incident angle increases, because of the increase of the electric-field component normal to the substrate surface. Figure 6 summarizes the resonance wavelength of the gold particles on the gold substrate, as a function of the particle diameter that is measured with p-polarized light at θ ) 60°. Two theoretical curves are also plotted. One curve is for the ambient air with a gap distance of 0.25 nm (solid curve), and the other curve is calculated for the ambient whose dielectric constant is the same as that for the AET monolayer film and
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Letters three or more particles. The extinction spectra of two nanoparticles can be also calculated with the static approximation, including multipole effects. Wind et al.8 showed that the calculation algorithm for two particles is very similar for a particle above a substrate. From both similarities in the experiments and the theory, we consider the large red shift in the extinction spectra of aggregated gold nanoparticles to be explained not by the interaction between three or more particles but by that between two adjacent particles. Conclusion
Figure 6. Peak wavelength of the extinction spectra versus particle diameter.
whose gap distance is 0.95 nm (dashed curve). The dielectric constant of the AET monolayer film is 2 ≈ 2.0,17 which we used in the calculation. Note that, in the theoretical calculations, the dielectric constant of the gap between the sphere and the substrate is assumed to be equal to that of the ambient, as described previously. The greater the dielectric constant of the gap medium and the ambient, the longer the resonance wavelength becomes for a given gap distance. In Figure 6, the resonance wavelengths for particles with diameters of 20.2, 30.4, and 41.3 nm almost lie on both theoretical curves. Therefore, we consider that the actual gap distance between the particles and the substrate takes a value in the range of 0.25-0.95 nm. For particles with diameters of 60.8, 80.8, and 99.8 nm, however, the experimentally obtained resonance wavelengths are longer than the corresponding theoretical values. Two reasons can be considered for this discrepancy. First, the theoretical curves were calculated under the static approximation, where the retardation effect was ignored; the retardation effect becomes more pronounced for larger particles. The resonance wavelength of isolated particles, which can be calculated with the Mie formula exactly, shifts toward longer wavelength as the particle size increases. We consider that the resonance wavelength of the particles on the substrate has the same property. Second, the calculation model assumes that the thickness of the substrate is semi-infinite. In the experiments, however, the thickness of the gold substrate is only 25 nm for the transmission measurements. This may cause the discrepancy. The extinction spectra of gold nanoparticles on a gold substrate are very similar to those of aggregated gold nanoparticles. Many papers have explained this large red shift in aggregated particles as being caused by the interaction between
In this paper, transmission absorption spectroscopy has been used to measure the wavelength of the surface plasmon resonance in gold nanoparticles above a gold substrate. The measured resonance wavelength increases as the particle size increases. This dependence cannot be explained using the dipole approximation but can be explained by the theory using the static approximation with the multipole effects. According to the theoretical calculations, the dipole approximation can be applied only for gap distances that are larger than a few tenths of the particle radius. References and Notes (1) Okamoto, T. In Near-Field Optics and Surface Plasmon Polaritons; Kawata, S., Ed.; Springer: Berlin, 2001. (2) Meriaudeau, F.; Downey, T. R.; Passian, A.; Wig, A.; Ferrell, T. L. Appl. Opt. 1998, 37, 8030. (3) Meriaudeau, F.; Downey, T.; Wig, A.; Passian, A.; Buncick, M.; Ferrel, T. L. Sens. Actuators, B 1999, 54, 106. (4) Meriaudeau, F.; Wig, A.; Passian, A.; Downey, T.; Buncick, M.; Ferrel, T. L. Sens. Actuators, B 2000, 69, 51. (5) Okamoto, T.; Yamaguchi, I.; Kobayashi, T. Opt. Lett. 2000, 25, 372. (6) Aravind, P. K.; Metiu, H. Surf. Sci. 1983, 124, 506. (7) Ruppin, R. Surf. Sci. 1983, 127, 108. (8) Wind, M. M.; Vlieger, J.; Bedeaux, D. Physica A 1987, 141, 33. (9) Kume, K.; Hayashi, S.; Yamamoto, K. Phys. ReV. B 1996, 55, 4774. (10) Johnson, P. B.; Christy, R. W. Phys. ReV. B 1972, 6, 4370. (11) Bohren C. F.; Huffman, D. R. Absorption and Scattering of Light by Small Particles; Wiley: New York, 1983. (12) Giersig, M.; Mulvaney, P. Langmuir 1993, 9, 3408. (13) Doron, A.; Katz, E.; Willner, I. Langmuir 1995, 11, 1313. (14) Freeman, R. G.; Grabar, K. C.; Allison, K. J.; Bright, R. M.; Davis, J. A.; Guthrie, A. P.; Hommer, M. B.; Jackson, M. A.; Smith, P. C.; Walter, D. G.; Natan, M. J. Science 1995, 267, 1629. (15) Wang, J.; Zhu, T.; Tang, M.; Cai, S. M.; Liu, Z. F. Jpn. J. Appl. Phys. 1996, 35, L1381. (16) Grabar, K. C.; Smith, P. C.; Musick, M. D.; Davis, J. A.; Walter, D. G.; Jackson, M. A.; Guthrie, A. P.; Natan, M. J. J. Am. Chem. Soc. 1996, 118, 1148. (17) Hutter, E.; Fendler, J. H.; Roy, D. J. Appl. Phys. 2001, 90, 1977.
