J. Phys. Chem. B 2001, 105, 3441-3452
3441
Optical Properties of Thin Films of Au@SiO2 Particles Thearith Ung,† Luis M. Liz-Marza´ n,‡ and Paul Mulvaney*,† Nanotechnology Laboratory, Chemistry School, UniVersity of Melbourne, ParkVille, VIC, 3010, Australia, and Departamento de Quı´mica Fı´sica, UniVersidade de Vigo, E-36200, Vigo, Spain ReceiVed: September 27, 2000; In Final Form: December 12, 2000
Homogeneous films of Au@SiO2 particles have been deposited on glass as a prototype 3D “artificial solid” using the LBL method. The film thickness is controlled by the number of dipping cycles and is measured by AFM. Each cycle results in approximately one monolayer of particles being deposited. The particle films are dense, but disordered. The optical properties of the resulting thin films have been analyzed as a function of the particle volume fraction, which is controlled through the silica shell thickness. We find that the surface plasmon peak position in films with volume fractions up to φ > 0.5 is accurately predicted by the MaxwellGarnett model. The films exhibit remarkably uniform, transmitted colors and display metallic reflection at low angles of incidence, even at low volume fractions. The films can be annealed at T > 500 K to provide extremely stable, optical films.
I. Introduction The assembly of nanocrystallites into macrostructures, thin films or 3D “artificial solids” offers an exciting pathway for the construction of materials with designer-specified optical, electrical, and catalytic properties. In the case of macrostructures composed of metal nanoparticles, such materials have potential applications in areas such as X-ray optics,1 nonlinear optics,2 microelectronics,3,4 optical data storage, and surface-enhanced Raman spectroscopy (SERS).5,6 In general, the attraction of such materials arises from two tunable parameters. First, the individual nanoparticles used as elementary building blocks may have size- or shape-dependent properties. Second, the geometry or interparticle spacing can be varied through dilution within the host matrix, so that particle-particle coupling can be utilized as a secondary means to influence the properties of the material. The ultimate, macroscopic properties may be determined by the periodicity of the particle assembly or by the character of the individual nanocrystals. Numerous groups have already reported initial results on the synthesis of nanoparticle composites from small metal particles. Papavassiliou deposited small colloids on glass walls and noted that the surface plasmon band of the nanoparticle films could be dramatically affected by both solvent composition and particle density.7 Efrima has used liquid-liquid interfaces to confine and compact silver particles into a variety of 2D arrays.8 Whetten et al. have synthesized large alkanethiol-capped gold nanocrystals 9 using the colloidal gold synthetic method developed by Brust et al.10 Whetten et al. were able to coax the particles into large, ordered lattices with sizes approaching millimeters, but their cohesion was limited by weak van der Waals forces. More recently, Schiffrin and colleagues have synthesized AB lattices and other mixed nanostructures,11 which are nanoparticle versions of the AB crystals well-known from colloid chemistry.12,13 Other groups have used electrophoresis to induce 2D ordering of metal nanoparticles,14,15 while Heath and colleagues have reported on extensive studies of the optical properties of silver colloid monolayers as a function of the * Corresponding author. E-mail:
[email protected]. † University of Melbourne. ‡ Universidade de Vigo.
interparticle spacing.16,17 The spacers used in their work were comprised of surfactant molecules, and the spacing was varied over a small range from 0.2 to 2 nm. This distance is critical for electrical coupling via tunneling through the metalinsulator-metal junctions between particles, and they observed a metal-to-insulator transition in this spacing regime. Another method for creating more complex structures is through biomolecule directed coupling of particles. Biologically coupled gold nanoparticle clusters have been used as a means to monitor DNA hybridization reactions.18 These organically linked clusters are likely to have a geometrical structure different from those encountered during normal colloid aggregation, and the optical properties of such aggregates have recently been modeled by Lazarides and Schatz.19 Foss and colleagues have looked at the assembly of gold nanoparticles in polyethylene films and have successfully interpreted the optical properties of both gold spheres and rods using effective medium theory, though the angle dependence of the film transmission did not show quantitative agreement. They also had to contend with some aggregation of their particles within the films.20-22 In this article, we examine the creation of macroscopic and homogeneous nanoparticle films synthesized from 15 nm Au particles encapsulated in silica. This inorganic spacer allows a much greater range of interparticle spacings to be created than is possible with conventional molecular capping agents. A number of aspects of silica-coated gold particles have already been described; in particular, a simple wet-chemical synthetic route has been reported23 and the effects of the shell on the optical properties of the core metal and the role of the solvent refractive index have been considered.24 The primary focus in this paper is the potential use of silica coated particles as building blocks for so-called “artificial solids”. It will be shown that by starting the synthesis with Au@SiO2 particles of various shell thicknesses, films can be assembled with tunable optical properties, which are dictated by the variations in the shell thickness. The particles are optically coupled through their dipole interactions, but there is negligible electronic coupling. Since the gold nanoparticles themselves have strongly size dependent optical properties, the resultant optical properties of the composite material may be due both to the intrinsic particle size effects and to the geometrical constraints outlined above.
10.1021/jp003500n CCC: $20.00 © 2001 American Chemical Society Published on Web 04/10/2001
3442 J. Phys. Chem. B, Vol. 105, No. 17, 2001 The resultant films have optical properties that may be completely tuned between those of the uncoupled, isolated nanoparticles, through to those with colors and reflectivity close to those of bulk, gold metal films. II. Analysis A. Layer-by-Layer Self-Assembly. Spontaneous layer-bylayer self-assembly (LBL) is used in this work to prepare films of bare and silica-coated gold particles. It is used frequently for particle assembly, and the technique has been modified and improved dramatically since its inception. It involves sequentially dipping a substrate alternately into solutions containing species to be adsorbed and a solution of polymer. The technique owes its widespread usage to its simplicity and versatility. It allows the preparation of composite films containing a very diverse range of materials, including proteins25,26 and other biological molecules,27,28 polyelectrolytes,29 clay platelets,25,30,31 semiconductor particles,32,33 metal particles,34,35 silica particles,36,37 and exfoliated layered compounds,38-40 all of which have been deposited onto numerous types of substrates, such as glass, quartz,6,41 Teflon6,41 Formvar,6,41 ITO glass,6,41 and metals.42 The LBL method was initially developed as an alternative to the classical Langmuir-Blodgett film technique (LB)43 and underwent a series of modifications to become simpler and more versatile. For about 60 years, the molecularly controlled fabrication of nanostructured films had been dominated by the LB technique, which required specialized, expensive equipment, and it had severe limitations with respect to substrate size and topology. In addition, such materials evinced limited film quality and durability. In 1966, Iler44 introduced the LBL technique as a greatly simplified alternative to the LB technique, employing it to prepare films of micron-sized particles. Since the early 1980s, as a further alternative to the classical technique, LBL methods based on chemisorption were devised.45 However, the technique was restricted to certain classes of organics, and highquality multilayer films could not be obtained reproducibly. Such limitations were later removed when Decher and Hong extended their previous method (which involved consecutive physisorption of anionic and cationic bipolar amphiphiles onto charged surfaces adsorbed from aqueous solutions46) to multipolar compounds such as polyelectrolytes.47 Subsequently, in 1995,32 Kotov et al. successfully pioneered the application of LBL to the preparation of stable, ultrathin films containing alternate layers of the cationic polyelectrolyte (polydiallymethylammonium chloride), PDDA, and semiconductor nanoparticles. This also solved the problem of achieving a high degree of monodispersity in particle films, which had long been a problem for vapor deposited films (see below). While both LBL and LB methods can be used for particle film formation, multilayers in LB films are mechanically unstable, as they are held together simply by dispersion forces.48,49 An important advantage of the LBL technique over the Langmuir-Blodgett technique is that the coating process is independent of the substrate size and topology.47 However a common difficulty with both the LB and LBL techniques is controlling the particle-particle interactions within the film during assembly. In contrast to much of the previous work outlined above, in this study silica coated particles are used, so the interparticle spacing within the film is already predetermined, which improves the quality and homogeneity of the films. B. Optical Model for Particle Composites. Fascination with the optical properties of metal particle films dates back at least as far back as the last century, and theoretical models to interpret
Ung et al. the interactions in composites are well advanced. One of the most enduring models is also one of the earliest. In 1904, Maxwell-Garnett50,51 developed a theoretical model for the interpretation of the observed optical properties of evaporated, gold-metal, thin films. His model was subsequently verified by various researchers, particularly through the work of Doremus.52 Later, Granqvist and Hunderi53,54 carried out a systematic investigation of the effects of particle size and particle volume fraction and the role of oxide layers on the overall properties of the metal particle films. Unfortunately, the particles were also quite polydisperse and of variable shape, especially for thicker films. Much of the earlier work on metal particle films was hampered by the fact that the particles themselves were polydisperse and often nonspherical and were usually in a partially aggregated form on the substrate. Many of the disadvantages of the sort of films used by Granqvist and Hunderi and by Doremus have been overcome in this study by using the self-assembly of Au@SiO2 particles. The silica spacer allows large well-defined particle separations to be created. Gold particles have been specifically chosen for this work because they can be easily prepared as fairly monodisperse colloids, which are extremely stable against aerial oxidation. However, the combined processes of LBL nanoparticle assembly and silica shell spacing can clearly be extended to any type of core material, e.g., to magnetic, catalytic, and luminescent particles. Such size control over two disparate length scales is essential for the preparation of numerous nanostructured materials such as photonic crystals, which require interparticle spacings of several hundred nanometers between quantum dots or fluorophores, which themselves are only 1-10 nm in diameter. For noninteracting spheres, Mie theory describes quantitatively the absorption and scattering of light by spherical particles in a nonabsorbing medium. This theory has been extended to ellipsoids, coated spheres, multilayer spheres, and even to absorbing media.55,56 Numerous approximations are available, especially for particles small compared to the wavelength of the incident radiation. If one considers only dipole absorption processes, this leads to the well-known equation for the spectrum of nanoparticles:
(M-1 cm-1) )
[
]
18π10-3Vmm3/2 ′′ 2.303λ (′ + 2m)2 + ′′2
(1)
Here m is the dielectric constant of the matrix or solvent, and (ω) ) ′ + i′′ is the dielectric function of the particles. Vm is the molar volume of the material constituting the particles (cm3 mol-1). Equation 1 is inapplicable to films with high volume fractions where a particle embedded in a host matrix is subjected to an average polarization field due to both the matrix and the surrounding nanoparticles. Such additional effects, which alter the optical properties of high-volume-fraction nanoparticle materials, can be accounted for by numerous effective medium theories. We employ the Maxwell-Garnett approximation,50,51 as will be justified a posteriori. Maxwell-Garnett applied the Clausius-Mossotti57,58 or the Lorentz-Lorenz relations59-61 to calculate the effective dielectric constant of a composite consisting of colloidal metals, and for particles isotropically dispersed in a nonabsorbing medium, the effective dielectric constant av of the composite is62 given by the expression
(
av ) m 1 + where
3φβ 1 - φβ
)
(2)
Optical Properties of Thin Films of Au@SiO2
β)
J. Phys. Chem. B, Vol. 105, No. 17, 2001 3443
- m + 2m
(3)
and φ is the volume fraction of the embedded particles. MG theory is most appropriate for small spheres isotropically distributed within a continuous matrix, as is extremely well fulfilled for core-shell nanocomposites. The net effect is the creation of a dense 3D matrix of silica containing monodisperse gold particles with known dielectric properties, embedded at a fixed, uniform distance from each other. Hence the effective electric field experienced by each particle should be identical. This uniformity of preparation distinguishes these films from previous work carried out on nanoparticle films. The absorption coefficient R of the composite film can be written within the dipole approximation as
R)
ω Im(av) 4πkav ) c nav λ
(4)
where c is the speed of light and naV is the real part of the effective complex index of refraction of the composite material, which is related to av by
(nav + ikav)2 ) av
(5)
and kav is the imaginary part of the average complex index of refraction of the composite. Equation 4 is appropriate for dense nanoparticle solutions, but for thin films, reflection losses and interference effects may also contribute to the colors of films, particularly for multilayer films. It is easier to work with the film transmittance. The transmittance of the film can be expressed in terms of nav and kav.
nav )
kav )
(x (x
) )
Re[av]2 + Im[av]2 + Re[aV] 2
0.5
Re[av] + Im[av] - Re[av] 2
0.5
2
2
(6)
(7)
The transmittance of light by a thin film is given in the general case by
Tfilm )
(1 - R)2 + 4R sin2ψ R exp(-Rh) + exp(Rh) - 2R cos(ζ + 2ψ) 2
(8)
where R is the reflectance at normal incidence and h is the film thickness
R)
(nav - 1)2 + kav2 (nav + 1)2 + kav2 ζ)
ψ ) tan-1
(
4πnavh λ
2kav
)
nav + kav2 - 1 2
(9)
(10)
0eψeπ
(11)
Importantly, eq 8 applies to a thin film in air. For a thin film on a thick, nonabsorbing substrate further reflections should be taken into account. However, since the film matrix has virtually the same refractive index as the glass substrate, we will assume that direct reflections from the film-substrate interface do not
directly affect the measured film absorbance. Equations 4-11 can be solved to give the absorption spectrum of Au@SiO2 films for various volume fractions and film thicknesses. The primary parameter of interest will be the new peak position of the coupled surface plasmon band as a function of the interparticle spacing. While numerous improvements and modifications to the original MG model have been proposed,63 Gaponenko has asserted that it works well for QDs impregnated in glass.64 Abeles and Gittleman have concluded that the MG dielectric function provides a much more accurate description of the properties of nanoparticles in films than the Bruggeman dielectric function.65 C. Optical Properties of the Isolated Gold Particles. An important distinction between LBL assembly of gold particles and vapor deposition onto a substrate is that we can synthesize “monodisperse” particles initially and readily measure their size, shape, and distribution by TEM or DLS. We can also calculate from Mie’s equations the dielectric properties of the isolated particles. Subsequent effects during film or crystal manufacture are then attributed to particle coupling. The dielectric function of gold particles in the visible part of the spectrum is well predicted using Drude theory, provided the mean free path (MFP) effect on electron scattering is included. We will use the surface scattering length or electron mean free path as a free parameter to model the optical properties of the isolated particles. The mean free path effect has been discussed in great detail by Kreibig and co-workers,66 and we simply note that for gold the real and imaginary parts of the dielectric function are given by
′ ) ∞ -
′′ )
ωp2 ω2 + ωd2
ωd ωp2 ω(ω2 + ωd2)
(12)
(13)
Surface scattering is accounted for classically by adjusting the collision frequency of conduction electrons to be
ωd(R) ) ωd(bulk) + V/R
(14)
Here ωd(bulk) is 3.7 × 1013 s-1, V is the Fermi velocity of 1.4 × 106 m s-1, and R is the particle radius. III. Experimental Section The following chemicals were of analytical grade and used without further purification: (3-aminopropyl)triethoxysilane (APS), tetraethoxysilane (TES), sodium silicate solution (Na2O(SiO2)3-5, 27 wt % SiO2), 3-mercaptopropionic acid, and a 20% aqueous solution of medium molecular weight poly(diallydimethylammonium chloride) (PDDA, 200 000-350 000) were purchased from Aldrich; HAuCl4‚3H2O was purchased from Sigma; trisodium citrate dihydrate was purchased from Normapur; and NH4OH (28%), NaOH, methanol, H2O2 (28%v/ v), ethanol, and cation-exchange resin (Dualite C225-Na 1452 mesh, in the acid form) were purchased from BDH Chemicals. Milli-Q water and absolute ethanol were used in all preparations. Transmission electron microscopy (TEM) was carried out with a Philips CM10 microscope, and particle size and SiO2 shell thickness distributions were measured from several TEM negatives for each sample. UV-visible spectra were measured
3444 J. Phys. Chem. B, Vol. 105, No. 17, 2001
Ung et al.
with a Hitachi U-2000 spectrophotometer. Films were imaged with a Dimension 3100 AFM operating in tapping mode. A. Synthesis of Gold Particles. Citrate-stabilized gold particles were prepared using the Turkevich method.67 The method produced a deep-red dispersion of gold particles with a diameter of 13.2 ( 0.3 nm. The citrate ion acts as both a reductant and stabilizer. Gold particles were derivatized with mercaptan capping agents by adding dropwise 5 mL of 0.02 M 3-mercaptopropionic acid (HSCH2CH2CO2H) solution neutralized with equimolar NaOH to 100 mL of 0.5 mM citratestabilized gold particles. The preparation of Au@SiO2 particles was based on the method of Liz-Marza´n et al.23,24 The desired silica shell thickness was obtained by allowing solutions to stand over different periods of time prior to centrifugation to remove free silicates, so that further growth could be prevented. Particles with shell thickness 1.5 nm were centrifuged 12 h after the silicate addition, colloids with 2.9 ( 0.1 nm shells after 24 h, and those with 4.6 ( 0.1 nm silica shell layers 10 days after deposition was initiated. Particles with shell thicknesses above 4.6 nm were prepared by the Sto¨ber method,68 using a Au@SiO2 sol with the 4.6 nm silica shell thickness as seeds. To grow the shell further, a solution of 500 mL of 0.5 mM Au@SiO2 sol was centrifuged down to 30 mL. A 170 mL aliquot of ethanol was added slowly with stirring to avoid coagulation. Then 0.60 mL of NH4OH (28%) was added dropwise, followed by addition of 80 µL of TES. The final solution was stirred slowly for 24 h after each addition of TES. Successive amounts of TES were added until the required shell thickness was attained. The approximate volume of TES (V2) required to increase the radius (R1) of the seed particle to a final R2 can be estimated from57
V2 ) V1
(( ) ) R2 3 -1 R1
(15)
where V1 is the volume of a seed particle. The 4.6 nm silica shell was increased to 12.2 ( 0.1 nm and 17.5 ( 0.3 nm. For consistency, all citrate-stabilized gold particles to be thiol capped or silica coated were taken from the same batch. B. Particle Film Preparation. Microscope glass slides were cleaned by boiling in methanol for 20 min. The surface was then hydroxylated by boiling in a mixture containing ∼50 mL of H2O2 (28%v/v) and 2-3 drops of NH4OH (28%), for 20 min. The slides were stored in water until used. Films containing bare and silica-coated gold particles deposited on glass slides were prepared by the LBL method. Glass slides were dipped in a PDDA (1% w/w) solution for 5 min, thoroughly washed with water, gently blown dry with N2, and then immersed into a gold sol for a suitable period of time, which depended on the SiO2 shell thickness, as will be described later. The slides were then washed again with water and gently blown dry with N2. The process was repeated to achieve the desired number of layers. Gold sputter-coated film was prepared using an Emitech K575 sputter-coater, with Au(99%) and Al(99%) targets (supplier: ProSciTech). IV. Results A. Isolated Particles. In Figure 1, we show both the experimental and calculated absorption spectra for the gold particles in water. For the 13.2 nm diameter particles used in this study, ωd was adjusted upward to a value of 1.2 × 1014 to account for the MFP effect outlined above. This corresponds to a value of R ) 8 nm, rather than the TEM-determined particle
Figure 1. Calculated (full line) and experimental (dashed line) absorption spectra of dilute 13.2 nm diameter colloidal gold particles in water. The calculated fit is based on eq 1 and utilizing the dielectric data from Johnson and Christy with ωd ) 1.2 × 1014 s-1.76 The calculated peak is at 521 nm; the experimental one is at 518 nm.
radius of 6.6 nm. The fit to aqueous sols has been discussed in detail before.69 If the dielectric data of Johnson and Christy are used for bulk gold, the plasmon band is predicted to lie at 521 nm, which is within 3-4 nm of where it is normally observed experimentally. Quantum size effects begin to play a role in this size regime, and for the 13.2 nm particles employed here, the band was located at 518 nm. However, while the data of Johnson and Christy yield band positions within 0.6% of the observed positions, they predict plasmon absorption bands much weaker than are observed experimentally. By using a larger mean free path of 8 nm, we get a better fit to the spectrum. Overall, this results in a band about 3 nm to the red of the experimental band, and with a peak whose intensity, determined from the ratio of the peak absorbance to the absorbance at 440 nm, is in good agreement with experiment. By further arbitrary manipulation of the dielectric data around the interband transitions, further improvement could be gleaned if necessary. The critical point here is that the dielectric properties of the isolated gold particles are well-defined prior to formation of the 3D solids, and changes in the absorption characteristics of the film can be attributed solely to interactions between particles. Shown in Figure 2 are electron micrographs of a series of bare and silica-coated, monodisperse gold particles. It can be seen that the gold particles, with a diameter of 13.2 nm, are completely and homogeneously coated with silica shells with thicknesses ranging from 1.5 to 17.5 nm. It is important to note that for shell thicknesses 12.2 and 17.5 nm, it was observed that over each entire TEM grid there were no composite particles with more than one core. This puts the upper limit on the percentage of dimer particles at 0.65. The calculated spectra have been normalized with respect to the particle volume fraction, to facilitate comparison of all the films. The film thickness has been set to 100 nm in these calculations. This method of comparison is valid as long as the
3450 J. Phys. Chem. B, Vol. 105, No. 17, 2001
Ung et al.
Figure 13. Calculated spectra of Au@SiO2 films for different film thicknesses. φ ) 0.60, corresponding to strongly coupled particles. Data as per Figure 11.
film spectra are independent of film thickness, which we have shown to be the case for both dilute and concentrated particle films, according to eq 8. In Figure 15, we compare the SP position observed experimentally with the predictions of MG theory. The only variable is φ, which is given by eq 16. As is clear, the MG model gives excellent agreement with experiment, even at high volume fractions, where it is strictly speaking no longer valid. Note that for large shifts, the peak positions are accurate to within 1 nm experimentally, but the shell thicknesses are so small that the determination of the exact volume fractions becomes prone to error. Nevertheless, we see that for volume fractions as high as 0.5, MG theory does remarkably well to predict the peak positions of the coupled plasmon modes to within about 10-20 nm. This fit is achieved with no free parameters, since φ is determined from TEM. The poorest fits are for the mercaptan- and citrate-stabilized films, where determination of the interparticle spacing is most prone to error. TEM images of coalesced citrate-stabilized particles show almost negligible spacing. In addition, the cationic polymers used for film preparation may cause desorption of the citrate ions, leading to bare particles. The absorption spectra of the gold-silica composites presented in this paper strongly support the contention that “artificial solids” composed of dense nanoparticle assemblies will have dielectric properties well described by MG theory. A more interesting test will be possible once ordered 3D crystals of Au@SiO2 are synthesized, in which the particle volume fraction, and particle spacing, can be measured more accurately. Such a study is underway. In this work, reflection was only examined qualitatively. The reflectance (Figure 10) of the films exhibits similar behavior to the transmittance below a certain shell thickness. As the shell thickens, the reflectance becomes less metallic and less lustrous for thicknesses ranging from 0 to 4.6 nm as the dipole-dipole coupling between the metal particles is diminished, though the variation in the reflected color is not as noticeable as that for the transmittance. However, unlike the plasmon absorption band and film transmittance, for shell thicknesses greater than 12.2 nm, reflectance is now governed by both the shell thickness and the number of deposition cycles. This effect for thicker films is probably due to interference effects and greatly increases the complexity of the optical behavior. The cos term in eq 8 is very
Figure 14. (a) Experimental spectra as a function of the particle spacing, as indicated. (b) Calculated absorbance spectra of the 13.2 nm particles as a function of the volume fraction using eq 10. (m ) n2 ) 1.4562 ) 2.12, and other data as per Figure 11.) Film thickness is 100 nm.
Figure 15. Comparison of the experimental and calculated peak positions of the coupled plasmon bands in the films. The MG theory lines are found using eqs 2 and 3, while the volume fractions are based on the TEM shell thicknesses and eq 16.
sensitive to both the exact film thickness and the average medium refractive index. However, it is only important if the
Optical Properties of Thin Films of Au@SiO2 absolute absorbance is very low. Hence, interference effects are likely only for thick silica shells because of the lower optical density of the corresponding film. High volume fraction films become opaque by the time the film becomes thick enough to create interference effects, and such films remain a glossy gold in reflectance, independent of the number of film layers. However, this interference is a novel property of such artificial solids, where carefully synthesized metal-insulator composites may possess propagation modes, which are determined by coupling of diffraction and surface plasmon modes. VI. Conclusions In this article we have discussed a model “artificial solid”gold colloid impregnated glass, synthesized with monodisperse interparticle-spacings using core-shell colloids as a starting point, and the LBL method as a protocol for constructing dense films thereof. Similar materials have been prepared by direct reduction of gold salts in heated glass melts before, and also by metal vapor deposition. However, these new materials allow vast improvements in material designscontrolled, reproducible dipole coupling, the use of monodisperse particles of chosen size, and other previously discussed advantages of the LBL method. Further, through use of a well-defined nanoparticle system, we have found that within the experimental constraints, the Maxwell-Garnett model accurately and satisfactorily explains the dipole coupling of the surface plasmon modes within a dense, nanoparticle, designer solid, where the spacing between particles is fixed, and no aggregation is present. In future work, we will describe the changing dielectric behavior of crystallized nanoparticle lattices in comparison to the dense, disordered solids discussed here and the reflectivity of the composite materials, which to date has been a neglected aspect of the MG theory. Acknowledgment. P.M. thanks the Particulate Fluids Processing Centre for support and the ARC for research funding through Grant A29930217 References and Notes (1) Barbee, T. W. Proc. Soc. Photo-Opt. Instrum. Eng. 1985, 563, 2. (2) Katz, H. E. Science 1991, 254, 1485. (3) Kepley, L. J.; Sackett, D. D.; Bell, C. M.; Mallouk, T. E. Thin Solid Films 1992, 208, 132. (4) Katz, H. E.; Schilling, M. L. Chem. Mater. 1993, 5, 1162. (5) Chumanov, G.; Sokolov, K.; Gregory, B. W.; Cotton, T. M. J. Phys. Chem. 1995, 99, 9466-9471. (6) Freeman, G. R.; 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, 1629-1632. (7) Papavassiliou, G. C. Z. Phys. Chem. (Leipzig) Pt.2 1976, 257, 241248. (8) Efrima, S. Heterogeneous Chem. ReV. 1994, 1, 339-353. (9) Whetten, R. L.; Khoury, J. T.; Alvarez, M. M.; Murthy, S.; Vezmar, I.; Wang, Z. L.; Stephens, P. W.; Cleveland, C. L.; Luedtke, W. D.; Landman, U. AdV. Mater. 1996, 8, 428. (10) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman, R. Chem. Commun. 1994, 801-802. (11) Fink, J.; Kiely, C. J.; Bethell, D.; Schiffrin, D. J. Chem. Mater. 1998, 10, 922-926. (12) Sanders, J. V.; Murray, M. J. Nature 1978, 275, 201-202. (13) Hachisu, S.; Yoshimura. Nature 1980, 283, 188-189. (14) Giersig, M.; Mulvaney, P. J. Phys. Chem. 1993, 97, 6334-6336. (15) Trau, M.; Saville, D. A.; Aksay, I. A. Science 1996, 272, 706709. (16) Henrichs, S.; Collier, C. P.; Saykally, R. J.; Shen, Y. R.; Heath, J. R. J. Am. Chem. Soc. 2000, 122, 4077-4083. (17) Collier, C. P.; Saykally, R. J.; Shiang, J. J.; Henrichs, S. E.; Heath, J. R. Science 1997, 277, 1978-1981. (18) Mirkin, C. A.; Letsinger, R. L.; Mucic, R. C.; Storhoff, J. J. Nature 1996, 382, 607.
J. Phys. Chem. B, Vol. 105, No. 17, 2001 3451 (19) Lazarides, A. A.; Schatz, G. C. J. Phys. Chem. 2000, 104, 460467. (20) Alrawashdeh, N.; Foss, C. Nanostruct. Mater. 1997, 9, 383-386. (21) Alrawashdeh, N.; Sandrock, M.; Seugling, C.; Foss, C. J. Phys. Chem. B 1998, 102, 361-371. (22) Lu, A.; Lu, G.; Kessinger, A.; Foss, C. J. Phys. Chem. B 1997, 101, 9139-9142. (23) Liz-Marza´n, L. M.; Giersig, M.; Mulvaney, P. Chem. Commun., 1996, 731-732. (24) Liz-Marza´n, L. M.; Giersig, M.; Mulvaney, P. Langmuir 1996, 12, 4329-4335. (25) Keller, S. W.; Kim, H.-N.; Mallouk, T. E. J. Am. Chem. Soc. 1994, 116, 8817. (26) Lvov, Y.; Ariga, K.; Kunitake, T. J. Am. Chem. Soc. 1995, 117, 6117. (27) Hong, J.-D.; Lowack, K.; Schmitt, J.; Decher, G. Prog. Colloid Polym. Sci. 1993, 93, 98. (28) Decher, G.; Lehr, B.; Lowack, K.; Lvov, Y.; Schmitt, J. Biosensors Bioelectronics 1994, 9, 677. (29) Mao, G.; Tsao, Y.; Tirell, M.; Davis, H. T.; Hessel, V.; Ringsdorf, H. Langmuir 1993, 9, 3461. (30) Kleinfeld, E. R.; Ferguson, G. S. Science 1994, 265, 370-373. (31) Lvov, Y.; Ariga, K.; Ichinose, I.; Kunitake, T. Langmuir 1996, 12, 3038. (32) Kotov, A. N.; Dekany, I.; Fendler, H. J. J. Phys. Chem. 1995, 99, 13065-13069. (33) Cassagneau, T.; Mallouk, T. E.; Fendler, J. H. J. Am. Chem. Soc. 1998, 120, 7848. (34) Feldheim, D. L.; Grabar, K. C.; Natan, M. J.; Mallouk, T. E. J. Am. Chem. Soc. 1996, 118, 7640. (35) Schmitt, J.; Decher, G.; Helm, C.; Mo¨hwald, H.; Eck, D.; Machtle, P. Abstr. Pap. Am. Chem. Soc. 1998, 216. (36) Lvov, Y.; Ariga, K.; Onda, M.; Ichinose, I.; Kunitake, T. Langmuir 1997, 13, 6195. (37) Caruso, F.; Lichtenfeld, H.; Giersig, M.; Mo¨hwald, H. J. Am. Chem. Soc. 1998, 120, 8523. (38) Kotov, N. A.; Dekany, I.; Fendler, J. H. AdV. Mater. 1996, 8, 637. (39) Kotov, N. A.; Haraszti, T.; Turi, L.; Zavala, G.; Geer, R. E.; Dekany, I.; Fendler, J. H. J. Am. Chem. Soc. 1997, 119, 6821. (40) Kotov, N. A.; Magonov, S.; Tropsha, E. Chem. Mater. 1998, 10, 886. (41) Grabar, K. C.; Freeman, R. G.; Hommer, M. B.; Natan, M. J. Anal. Chem. 1995, 67, 735-743. (42) Fendler, J. H.; Meldrum, F. C. AdV. Mater. 1995, 7, 607-632. (43) Blodgett, K. B. J. Am. Chem. Soc. 1934, 56, 495. (44) Iler, R. K. J. Colloid Interface Sci. 1966, 21, 569. (45) Lee, H.; Kepley, L. J.; Hong, H.-G.; Akhter, S.; Mallouk, T. E. J. Phys. Chem. 1988, 92, 2597-2601. (46) Decher, G.; Hong, J. D. Makromol. Chem. Macromol. Symp. 1991, 46, 321. (47) Decher, G.; Hong, J. D. Ber. Bunsen-Ges. Phys. Chem. 1991, 95, 1430-1434. (48) Gaines, G. L. Insoluble Monolayers at Liquid Gas Interfaces; Interscience: New York, 1966. (49) Ulman, A. An Introduction to Ultrathin Organic Films: From Langmuir-Blodgett to Self-Assembly; Academic Press: Boston MA, 1991. (50) Maxwell Garnett, J. C. Philos. Trans. R. Soc. 1904, 203, 385. (51) Maxwell Garnett, J. C. Philos. Trans. R. Soc. 1906, 205, 237. (52) Doremus, R. H. J. Appl. Phys. 1966, 37, 2775-2781. (53) Granqvist, C. G.; Hunderi, O. Phys. ReV. B 1977, 16, 3513-3534. (54) Granqvist, C. G.; Hunderi, O. Z. Physik B 1978, 30, 47-51. (55) Kreibig, U.; Vollmer, M. Optical Properties of Metal Clusters; Springer: Berlin, 1995; Vol. 25. (56) Bohren, C. F.; Huffman, D. R. Absorption and Scattering of Light by Small Particles; Wiley: New York, 1983. (57) Clausius, R. Die mechanistische Wa¨ rmelehre II; Vieweg: Brauschweig, 1879. (58) Mossotti, O. F. Mem. della Soc. Scient. Modena 1850, 14, 49. (59) Lorenz, L. Vidensk. Selsk. Skrifter 1869, 8, 205. (60) Lorenz, H. A. Wieden. Ann. 1880, 9, 641. (61) Lorenz, L. Wiedem. Ann. 1881, 11, 70. (62) Kittel, C. Introduction to Solid State Physics, 2nd ed.; Wiley: New York, 1956. (63) Garcı´a, M. A.; Llopis, J.; Paje, S. E. Chem. Phys. Lett. 1999, 315, 313-320. (64) Gaponenko Optical Properties of Semiconductor Nanocrystals; Cambridge University Press: 1998. (65) Abeles, B.; Gittleman, J. I. Appl. Opt. 1976, 15, 2328-2332. (66) Kreibig, U.; Fragstein, C. v. Z. Phys. 1969, 224, 307-323. (67) Enu¨stu¨n, B. V.; Turkevich, J. J. Am. Chem. Soc. 1963, 85, 33173328. (68) Sto¨ber, W.; Fink, A. J. Colloid Interface Sci. 1968, 26, 62-69. (69) Underwood, S.; Mulvaney, P. Langmuir 1994, 10, 3427-3430.
3452 J. Phys. Chem. B, Vol. 105, No. 17, 2001 (70) Giersig, M.; Mulvaney, P. Langmuir 1993, 9, 3408-3413. (71) Mulvaney, P. Langmuir 1996, 12, 788-801. (72) Brust, M.; Bethell, D.; Kiely, C. J.; Schiffrin, D. J. Langmuir 1998, 14, 5425-5429. (73) Mayya, K. S.; Patil, V.; Sastry, M. Langmuir 1997, 13, 25752577.
Ung et al. (74) Lee, M. H.; Dobson, P. J.; Cantor, B. Thin Solid Films 1992, 219, 199-205. (75) Sokolov, K.; Chumanov, G.; Cotton, T. M. Anal. Chem. 1998, 70, 3898-3905. (76) Johnson, P. B.; Christy, R. W. Phys. ReV. B 1972, 6, 43704379.
