Article pubs.acs.org/Langmuir
Tailoring the Refractive Indices of Thin Film Polymer Metallic Nanoparticle Nanocomposites Jenny Kim,† Hengxi Yang,‡ and Peter F. Green*,†,§,∥ †
Department of Materials Science and Engineering, ‡Department of Physics, §Applied Physics, ∥Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States S Supporting Information *
ABSTRACT: We demonstrate how to tailor the spatial distribution of gold nanoparticles (Au-NPs) of different sizes within polystyrene (PS) thin, supported, film hosts, thereby enabling the connection between the spatial distribution of Au-NPs within the polymer film and the optical properties to be determined. The real, n, and imaginary parts, k, of the complex refractive indices N = n(λ)+ik(λ) of the nanocomposite films were measured as a function of wavelength, λ, using multivariable angle spectroscopic ellipsometry. The surface plasmon response of films containing nearly homogeneous Au-NP distributions were well described by predictions based on classical Mie theory and the Drude model. The optical spectra of samples containing inhomogeneous nanoparticle distributions manifest features associated with differences in the size and interparticle spacings as well as the proximity and organization of nanoparticles at the substrate and free surface.
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INTRODUCTION For the past two decades, metallic nanoparticles (MNPs), including gold, silver, and copper, have been widely used in biological sensors, surface-enhanced spectroscopies, and photovoltaics for their intrinsic ability to absorb and/or scatter light.1−5 Unique optical properties of MNPs originate from surface plasmon resonance (SPR) phenomena arising from the collective oscillation of conduction electrons in response to an electromagnetic field. The absorption of light is evident from color changes exhibited by solutions and from multiple supported layers of films containing nanoparticles.6 Numerous studies reveal that the magnitude of the SPR effect is influenced by the interparticle distances, the size and shapes of particles, and the relative permittivities of the environment, substrate, or solution.6−12 Whereas surface plasmon resonance studies have generally been devoted to understanding and controlling the character© 2012 American Chemical Society
istics of NPs (e.g., size, shape, and surface treatment) or their surrounding media, systematic studies devoted to controlling the organization of NPs within a polymer thin film host, to understand the connection between optical properties and structure, are rare. Potential opportunities for applications involving such polymer/nanoparticle systems would enhance, or complement, the use of polymers in applications where their optical properties are essential. Such applications include: antireflection coatings, organic/inorganic photovoltaics, and biological sensors.1,3,5,13 In this study, we demonstrate how systematic control of the spatial distribution of metallic nanoparticles throughout a polymeric thin film host enables understanding the structureReceived: January 25, 2012 Revised: May 22, 2012 Published: May 29, 2012 9735
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grafting densities, σ, of the nanoparticles. The TGA measurements were performed in air at a heating rate of 5 °C/min. Further details of our synthetic procedures and analyses are described in earlier publications.15,24 The diameters of the NP cores, Dcore, and the grafted brush thicknesses, hbrush, were determined from scanning transmission electron microscopy (STEM, JEOL 2010F), high angle annular dark field (HAADF) operated at 200 kV, images of the samples. The average particle sizes and the interparticle spacings (2*hbrush + Dcore) were determined by measuring the diameters of groups more than 300 NPs in each image. Three sets of brush-coated nanoparticles were prepared: (1) Au(5)-PS is a nanoparticle of Dcore = 4.7 ± 1.2 nm, N = 50, σ = 1.0 chains/nm2; (2) Au(2)-PS is a nanoparticle of Dcore = 2.2 ± 0.45 nm, N = 10 and σ = 1.9 chains/nm2; (3) Au(7)-PS is a nanoparticle of Dcore = 7.1 ± 1.9 nm, N = 30, and σ = 1.9 chains/nm2. Polystyrenes (PS) of number-average molecular weight Mn = 7500 g/mol and Mn = 170 kg/mol and polydispersity, Mw/Mn ≤ 1.06 were purchased from Pressure Chemical Inc. Homogeneous solutions containing well-defined concentrations of the PS and the nanoparticles were prepared using toluene as a solvent. The solutions of PS/ Au(dNP)PSN (N = 10, 30, 50) mixtures were spin-casted on to cleaned silicon substrates with native oxide layer (∼14 Å) then dried in vacuum oven at 65 °C for 16−24 h to remove excess solvent in the film.
optical property behavior of this nanocomposites. Thin film polystyrene (PS)/Au-NP nanocomposites were designed and prepared to understand how the nanoparticle size, proximity, and environment would influence the complex permittivity, N = n(λ) + ik(λ), where λ is the wavelength and n and k are the index of refraction and the extinction coefficient respectively of the film. Two types of samples were prepared; in one case the gold nanoparticle distribution was nearly homogeneous throughout the film. In the second, the NPs formed two thin layers localized exclusively at the external interfaces (i.e., free surface and substrate). Changing the film thickness enabled the distance between these two layers, lz, to be controlled. NPs of three different core diameters, Dcore = 2, 5, and 7 nm, were used to prepare a range of nanocomposite films of thickness h, where 70 nm < h < 120 nm. The design, and preparation, of thin film polymer nanocomposites in which the depth distribution of metallic nanoparticles of various sizes is tailored was accomplished by exploiting a strategy that involves grafting polymer chains of degree of polymerization N onto gold nanoparticles of core diameter Dcore, with grafting density σ (chains/nm2). The NP distribution within a polymer host of degree of polymerization, P, is determined by the following parameters: h, σ, Dcore, N, P, the energetic interaction parameter between the grafted and host chains, and the Kuhn lengths of the grafted and the host polymer chains.18 Judicious choices of these parameters enable control of the entropic and enthalpic forces, including van der Waals forces between the nanoparticles and between the nanoparticles and a substrate, and therefore the morphology of the system.18 On the basis of the film thicknesses and the grafting densities σ∼1−2 chains/nm2 used in this study, the nanoparticle distribution (i.e., nearly homogeneous distributed or interfacially segregated within the films) is determined primarily through changes in N, P, and Dcore. The optical spectra, n(λ) and k(λ), measured using multivariable angle spectroscopic ellipsometry (SE), manifested differences in nanoparticle sizes, separation distances, and proximity to interfaces in the nanocomposite thin films. Mie theory and the Drude model provided a good description of the optical response of films containing nearly homogeneously distributed nanoparticles throughout.10,21,22 The spectra of the inhomogeneous, phase-separated, systems exhibited significant changes associated with the particle-rich and particle-poor layers, separated by lz. Samples containing only ∼1−2 volume percent nanoparticles exhibited local variations in n by nearly 20%, in the wavelength range of 500 to 700 nm. Our experiments also reveal that when the distance lz between the nanoparticle-rich layers at the interfaces is on the order of a few particle radii the response of the film is similar that of a film containing a homogeneous distribution of nanoparticles.
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STRUCTURAL CHARACTERIZATION The morphologies of the thin film polymer nanocomposites (PNCs) and the Au NP distributions were determined using a combination of STEM and dynamic secondary ion mass spectrometry (DSIMS); the surface topographies were determined using atomic force microscope (AFM). The samples examined using STEM were prepared first by spincasting solutions onto glass slides and then floating the films from the slides onto distilled water. These films were then transferred onto Si3N4 grids and subsequently dried by annealing them in vacuum at 65 °C for 16 h. DSIMS measurements, performed at University of California Santa Barbara by Tom Mates, using a Physical Electronics 6650 Quadropole instrument, were used to determine the depth profile of Au within the PS films. AFM studies of the films were performed in our laboratory using the MFP-3D (Asylum Research, Inc.) microscope, in tapping (AC) mode with silicon cantilevers (Nano and More Inc., spring constant 20 N/m and resonant frequency of 130 kHz) to determine the roughness of each film. The rms roughness of each film was less than 1.0 nm.
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OPTICAL CHARACTERIZATION The absorption spectra of the samples were measured using a Varian Cary 50 Bio. The complex refractive indices were measured using multivariable angle spectroscopic ellipsometry (M-2000D with the NIR extension, J.A.Woollam Inc., Co.) and analyzed using the CompleteEASE software (J.A.Woollam Inc., Co.). Ellipsometry measures the reflectance ratio, ρ, of incident p- and s-polarized light, which is parametrized by ψ and Δ: rρ ρ= = tan(ψ )e iΔ rs (1)
EXPERIMENTAL SECTION
Gold nanoparticles (Au NPs) were synthesized using the two-phase arrested precipitation method reported by Brust et al.23 Thiolterminated polystyrene molecules (PS-SH) of number-average molecular weight Mn = 1100 g/mol (Mw/Mn = 1.12), 3000 g/mol (Mw/Mn = 1.07), and 5300 g/mol (Mw/Mn = 1.1), purchased from Polymer Source, Inc., were then grafted onto the surfaces of the nanoparticles. We will refer to the surfaces grafted chains as a brushlayer, throughout this article. The newly synthesized particles were cleaned at least 10 times using methanol and toluene to remove excess ligands and salts in the solution. Information from thermogravimetric analyses (TA 2960) of the samples, together with the weight fractions and densities of the gold and the ligands, was used to estimate the
The spectroscopic ellipsometry (SE) data, determined from the change in polarization of light reflected by the film in the wavelength range of 193−1690 nm, were acquired using incident angles between 45 and 80°. To determine the film thicknesses, h, of the nanocomposite samples, the transparent wavelength range 900−1690 nm was initially selected and the data fitted using the Cauchy model. Subsequently, the spectral range was expanded to 300−1690 9736
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nm to fit the optical spectra of the nanocomposites using an iterative effective medium approximation (EMA) model. The merit function used to assess the quality of fitting of the experimental data was the mean-squared error (MSE) between the measured data and calculated data, using the established model: MSE =
1 2N − M
N 2 − Δexp ∑ [(ψjmod − ψjexp)2 + (Δmod j j ) ] j=1
(2)
where N is the number of ψ and Δ data parameters and M is the total number of model parameters. We proceeded with caution when constructing the models and fitting the raw ellipsometric data because a low MSE would not necessarily imply that the result is representative of actual physical property.25 This complication would arise from fitting too many unknown parameters at the same time. However, using this experimental information about the sample from DSIMS, AFM, and STEM enabled us to reduce the number of unknown fitting parameters that we used in the models. Specifically, to analyze the samples containing the inhomogeneous distribution of nanoparticles, the film was divided into three layers, each with a homogeneous distribution of nanoparticles. This approach was not unreasonable because the DSIMS and STEM data showed this to be the case for the samples we designed and prepared. Therefore the information about the compositions and layer thicknesses in our models, used to determine ψ and Δ, were based on actual experimental data. See the section containing Supporting Information for additional information about the analysis.
Figure 1. Au nanoparticle distributions in polystyrene (PS) thin films measured using STEM (left) and DSIMS (right) are shown here. (a) STEM image of Au-NPs of average core radius Dcore = 4.7 ± 1.6 nm, volume fraction φAu = ∼0.013, in a film of thickness h = 80 nm, is shown. This sample is identified as: Au(5)PS50/PS70 ; (b) the same information for NPs of D = 2.2 ± 0.45 nm, φAu∼ 0.013, in a h = 100 nm film, is shown. This sample is identified as Au(2)PS10/PS70.
particles are sufficiently small (radii ∼1 nm, and less than the size of the host chains), and the grafting densities are high and N≪P, the translational entropy of the nanoparticles plays a significant role toward mixing within the host.18 The brush/ host chain interactions are negligible under these conditions, so the NPs gain translational entropy by distributing throughout the sample.18,24 This is the situation for the sample whose NP distribution is shown in part b of Figure 1. However, as Dcore increases, whereas N≪P and σ remain high, there is a strong tendency for the nanoparticles to aggregate and/or segregate toward the interfaces. This aggregation/segregation of the nanoparticles is promoted by the following: long host chains suffer a significant conformational entropy cost if confined between the nanoparticles, so they exhibit a tendency to migrate from between nanoparticles; second, the host chains at the interfaces gain conformational entropy when they are displaced by nanoparticles; additionally van der Waals forces between the nanoparticle cores and substrate tend to favor segregation to the substrate.15,18,19,26 This effect, associated with van der Waals interactions, is mediated by grafting long chains to the nanoparticle surfaces. However, for the same grafting densities, the miscibility of larger nanoparticles with the host may be enhanced if the longer chains, more specifically increasing N/P, are grafted onto the surfaces of the nanoparticles. This is because intermixing between host chains and the brush layer favors nanoparticle miscibility and, second, the particle/substrate interactions are mediated by the longer chains grafted to the particle surfaces.15,18,19 The foregoing ideas were exploited to design and to fabricate the samples used in this study. The optical properties of these samples, the indices of refraction, n(λ), and the extinction coefficients, k(λ), of both samples, are described in Figure 2. It is evident from the data in part a of Figure 2 that the amplitude of SPR peak is smaller and blue-shifted for the sample containing the Dcore = 2.2 nm NPs compared to the other sample containing the Dcore = 4.7 nm nanoparticles.21,27 The peaks are located at 511 and 533 nm for
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RESULTS AND DISCUSSION We begin by discussing the structure and optical properties of samples in which the nanoparticles are distributed nearly homogeneously throughout. The STEM image of a PS sample of thickness h = 80 nm, in which nanoparticles of core diameter Dcore = 4.7 ± 1.6 nm with surfaces onto which PS chains of degree of polymerization N = 50, are grafted, with grafting density σ = 1.0 chains/nm2, is shown in part a of Figure 1. The nanoparticles are laterally distributed homogeneously throughout the host of this polymer whose of degree of polymerization P = 70. We will identify this sample as: Au(5)PS50−PS70. The two peaks in the DSIMS profile indicate preferential segregation of NPs at both interfaces. In the case of the second sample, where the same host of polymer (P = 70) contains NPs of Dcore = 2.2 ± 0.45 nm (N = 10, σ ≈ 1.0 chains/ nm2, and h = 100 nm), the NP distribution is qualitatively similar, though the interfacial segregation is notably smaller (part b of Figure 1). This sample will be identified as Au(2)PS10-PS70. The two samples described above were designed and prepared based on the following principles. The grafting of chains onto the surfaces of the nanoparticles was necessary because bare Au nanoparticles would aggregate due largely to van der Waals interactions. Such interactions are mediated by grafted chains onto the nanoparticle surfaces.18 To control the nanoparticle distribution within a polymer host, entropic effects that include the host chain/grafted chain interactions and NP size effects need to be considered. Because the surfaces of the NPs are shielded from the host chains and because the host chains and grafted chains are of identical chemical structure, enthalpic considerations may be ignored. When the nano9737
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identified as Au(7)PS30-PS1630. For reasons discussed earlier, the free energy is minimized when the nanoparticles are located at the external interfaces.18 We note further that these particles form close packed structures, local two-dimensional crystalline ordering, at the interfaces, a consequence of the segregation.15,18 This ordering is obtained regardless of the film thickness h or Au volume fraction. The distance of separation is determined by the brush layer thickness hbrush. On the basis of the structural characteristics of these samples (Figure 3), optical models were developed in order to interpret Figure 2. (a) Extinction spectra for 1.3 vol % Au NPs of D = 2 and D = 5 nm in dielectric media (εm = 2.5) were calculated using eq 3 (solid lines). The extinction coefficients, k, of the two types of samples (Au(2)PS10/PS70, Au(5)PS50/PS70) are plotted for comparison. (b) the experimental n and k are plotted for both samples.
the Dcore = 2.2 nm and Dcore = 4.7 nm NP samples, respectively. The weaker response of the 2.2 nm diameter sample is due to the short plasmon lifetime, typical for sufficiently small NPs (i.e., the small mean free path of the electrons in the highly confined 2.2 nm diameter nanoparticles).21,27 It is worthwhile to calculate the extinction coefficient, k(λ), spectrum for a monodisperse collection of spherical nanoparticles and compare it with to our data. Contributions to the dielectric function for a metal may be considered to arise from the bound electrons, associated with the interband transitions, and from the free electrons. The dynamics of the free electrons are generally well described by the Drude, Lorenz, and Sommerfield model.10,21,22The dielectric function for a particle of radius R, can be written as ε(ω , R ) = εbulk (ω) +
ωp2 ω 2 + iωγ0
−
Figure 3. STEM, part (a), and DSIMS, part (b), data of phaseseparated Au(7)PS30/PS1630 nanocomposites (ΦAu = ∼0.013, h = ∼97 nm) are shown here. (c) A schematic describing the trilayer structure of a phase-separated film is drawn. On the basis of the Au profile, film is divided into three layers: top (in vicinity of the free surface, (t), middle (m), bottom (b, in the vicinity of the substrate).
the optical spectra, which are shown in Figure 4. The complex refractive index was obtained by fitting the measured spectra of the sample containing 2.3 vol % Au nanoparticles of diameter Dcore = 7 nm: Au(7)PS30/PS1630. Initially, we ignored the complexity of the structure of the sample developed a model
ωp2 ω 2 + iω(γ0 +Avf /R ) (3)
where ωp is the bulk plasma frequency (9.03 eV), γ0 is the damping frequency (1.64 × 1014 s−1), A is proportionality factor (A ≈ 1.4), and vf is the electron velocity at the Fermi surface (vf = 14.1 × 1014 nm s−1). The values for the bulk permittivity and other parameters were taken from several references.10,21,22 The extinction coefficients were calculated using equation 3, which correctly predict the locations of the maxima and the relative breadths and amplitudes of the response of these samples. The experimental peaks are somewhat broader than the theory predicts and this we believe is due to the polydispersity (Figure 1) of the nanoparticle sizes.9 The real part of the refractive index, n, of the Au(5)PS50PS70 sample manifests the existence of a distinctive anomalous dispersion with a peak location at ∼600 nm; the difference between maximum and minimum values of n was approximately 0.3. In contrast, the Au(2)PS10-PS70 sample exhibited a broad shoulder, between 510−650 nm, without a distinctive peak. This is to be expected based on Kramers−Kronig considerations, which connect n and k.28,29 These results clearly illustrate that for reasonably well distributed nanoparticles, sufficiently separated, throughout a film the classical theory provides an appropriate description of the optical behavior. We will address the effects of interparticle separation later. The other type of sample considered in this study is such that the nanoparticles are located exclusively at the free surface and at the substrate. The values of N and P were chosen such that P≫N and that Dcore was sufficiently large: Dcore = 7 nm, N = 30, P = 1630, and volume fraction ΦAu∼0.013; this sample will be
Figure 4. The ellipsometric data, n and k, for the Au(7)PS30/PS1630 (φAu∼0.023) sample, are plotted. (a) n (left) and k (right), represent the response of a hypothetical homogeneous film of Au volume fraction 0.023. The MSE in this case was unreasonably large. (b) The sample was modeled more realistically by considering it to be composed of three layers, each containing a well-defined nanoparticle concentration. 9738
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based on the assumption that the nanoparticles were distributed homogeneously throughout the film. The average optical spectra calculated for the film are plotted in part a of Figure 4. However, the mean square error associated with this fit was unacceptably large. Therefore, a more appropriate calculation should reflect the NP inhomogeneities within the film. In light of the known nanoparticle distributions within the film, based on the DSIMS and STEM measurements, the actual phase-separated (i.e., nanoparticles reside primarily at the free surface and the substrate) nanocomposite samples were analyzed by dividing the sample into three layers, described here as the top (nanoparticle layer at the free surface), middle, and bottom (layer adjacent to the substrate) layers. The fits were excellent. Detail fitting procedures are provided in the section containing Supporting Information. If we assume that the NPs and the host chains are homogeneously mixed within each individual layer, we may appropriately describe each layer in terms of its average interparticle separations. In part b of Figure 4, the obvious contrast between the refractive indices of the layers is evident for this 2.3 vol % Au/PS mixture. Specifically, the SPR peak locations (part b of Figure 4) are at 535 and 568 nm, for middle and bottom layers respectively. In addition, to being red-shifted, the SPR band due to the particle rich layer in contact with the substrate was larger than that due to the top layer, at the free surface. These data are consistent with the notion of an interparticle coupling effect, associated with the proximity of the nanoparticles, which has been reported to be responsible for the significant red shift and broadening of the SPR band; this is reported to be significant when l < 5R where l is center-tocenter distance of the particles and R (R = Dcore) is the nanoparticle core radius.6,12 In addition, the degree of change that we observe in the SPR band is consistent with the findings of Yockell-Lelièvre et al.’s who measured absorption spectra of monolayers of PS-coated Au NPs on glass substrate with different interparticle distances by changing the ligand size.30 The effect of this 2D particle surface ordering at the interfaces in phase-separated films on the SPR response, compared to that of films in which the nanoparticles are homogeneously distributed is now further examined. In Figure 5 differences between the peak locations determined from experiment λmax,SE and predictions using Mie theory λmax,calcd, Δλmax = λmax,SE − λmax,calcd, are plotted as a function of effective volume fraction. Since Mie’s theory assumes that particles are isolated and their surrounding medium is homogeneous, Δλmax would illustrate the interparticle coupling effect on the SPR due to 2D packing of NPs.6,12 These data show evidence of a shift in Δλmax for Au fractions larger than ∼0.02; Δλmax increased linearly with increasing Au fraction. These results clearly illustrate the role of the interfaces on the materials response. They, moreover, suggest a wide range of tunability of the SPR band and thus the refractive index of polymer thin films through tailoring the NP distribution. On the basis of the foregoing, it is reasonable to conclude that the differences in the spectra would be associated with two effects. First, interparticle coupling interactions associated with the organization and proximity of the nanoparticles within each layer at the interfaces would be partly responsible. Second, nanoparticle/interface interactions associated with the large change in permittivity, εm = 2.5 for PS and εm = 3.9 for silicon oxide, across the interfaces may also be, in part, responsible.
Figure 5. Differences in maximum peak locations between the measured ellipsometric data and the calculated data (Δλmax = λmax, SE − λmax,calcd) are plotted as a function of effective volume fraction of Au.
The interparticle distances in our phase-separated samples are such that they would, in part, be responsible for the red shifts and broadening. The nanoparticles aggregate into 2D hexagonal close-packed structures at the interfaces; the distance of separation is determined by the brush thickness, hbrush.15,18 Hence, the interparticle spacing between the nanoparticle surfaces, in a close packed structure, would be l0 = 2hbrush + 2R, which is less than 5R. We note that this degree of 2D interfacial aggregation does not occur at the free surfaces of the samples in which the nanoparticles are homogeneously dispersed throughout the interior. This is the reason this effect, Δλmax, is observed only in the phase-separated systems. We note that because the interface is not covered entirely by nanoparticles and that the close-packed structures appear in localized regions throughout the interfaces, it is worthwhile to also calculate an average interparticle spacing based on the fraction of nanoparticles in each layer. On the basis of DSIMS data, the effective volume fractions in each layer were calculated to be 0.064 (top, free surface), 0.005 (middle), and 0.0068 (bottom); the average (nominal) volume fraction of the entire film is 0.023. The average interparticle spacings, l, were then calculated to be l = ltop = 15 nm, l = lmiddle = 52 nm, and l = lbottom = 14 nm, for the top, middle, and bottom layers, respectively. The following equation, 1/D∼ (φm/φ)1/3 − 1 where φm = 0.638 is the maximum random packing fraction, was used to perform these calculations. In all cases l is within the length scale where interparticle coupling effects would be important. Therefore we conclude that in our inhomogeneous samples, an interparticle coupling effect is partly responsible for the spectral changes. The role of the nanoparticle/substrate interaction is now discussed. We can get some insight into this issue by considering experiments in which the angle of incidence is changed; this would increase the effective path length between layers and the effective number of particles along the path of the beam. These data are shown in Figure 6. The response of each layer of the sample, AuPS30-PS1630, containing 2.3 vol % nanoparticles, is shown for the top (part a of Figure 6), middle (part b of Figure 6), and bottom (part c of Figure 6) layers, for different angles. The response, n and k, of the layer of the sample in contact with the substrate exhibited the largest dependence on the incident angle. This is, in part, because the 9739
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particle mixtures by controlling the experimentally accessible molecular characteristics of the system. The Au nanoparticle distributions throughout the films were tailored by controlling the nanoparticle core diameter, Dcore, the grafted brush layer degree of polymerization, N, grafting density, σ, and host chain degree of polymerization, P. Spectroscopic ellipsometry was used to determine the real and imaginary (surface plasmon response) parts of the refractive indices of these PS/Au nanocomposite films. Whereas the surface plasmon peaks arising from homogeneous films were well described using classical Mie theory, the SPR peaks arising from phaseseparated films in which the nanoparticles formed 2D aggregates at the substrate and at the free surface, exhibited large red shifts, and broadening, beyond that expected based on the calculations. The results of this study clearly reveal that systematic control of Au nanoparticles throughout polymer hosts offers unique opportunities to tailor the refractive indiees of thin film polymers for a range of applications from optoelectonic and/or bio- to chemical- sensor devices.
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ASSOCIATED CONTENT
* Supporting Information S
The procedures used for the obtaining refractive indices from thin, supported, film nanocomposites are discussed. Measurements using UV−vis and spectroscopic ellipsometry, of identical films are also provided. The samples were prepared on glass substrates to compare the UV−vis and spectroscopic ellipsometric data. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
Figure 6. Angular dependencies on refractive indices of the phaseseparated film (AuPS30-PS1630, (φAu ∼0.023), h ∼ 100 nm) are shown for (a) top (particle-rich), (b) middle (particle-poor), and (c) bottom (particle-rich) layers. Three different sets of angles were measured for each layer; 55° (dash and dot), 65° (dash), and 75° (solid).
*E-mail:
[email protected] Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge in depth discussions with J.A.Woollam’s Dr. James Hilfiker and Dr. Tom Tiwald for interpreting spectroscopic ellipsometry data. Support from the Department of Energy, Office of Science, Basic Energy Sciences, Synthesis and Processing program, DOE no. DE-FG02-07ER46412 is gratefully acknowledged.
scattering is maximized parallel to the thin particle-rich layers. Additionally, the bottom layer is adjacent to the substrate, where there is an abrupt shift in the dielectric properties. Incidentally, this type of analysis is useful for optimizing material performance at angles of incidence different from 0° for optical coatings.25,31 Finally, we note that in the foregoing the film thicknesses were such that h = ∼100 ± 20 nm, and the particle distributions were determined entirely by N, P, and Dcore.18 We note further that the distances, lz, between the nanoparticle layers at the interfaces in the phase-separated samples were sufficiently large that the particles at the interfaces responded independently of the other. In light of this, a natural question would be the following: what determines the threshold film thickness below which the material’s response exhibited no evidence of a trilayer structure (i.e., loss of anisotropy)? This is expected when average particle separations are such that in the x−y plane lxy ∼ 5R and normal to the substrate lz ∼ 5R, as one would conclude from the discussions in this manuscript. The actual film thickness would be determined by the nanoparticle volume fraction, Dcore, N, and P.
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REFERENCES
(1) Atwater, H. A.; Polman, A. Plasmonics for improved photovoltaic devices. Nat. Mater. 2010, 9 (3), 205−213. (2) Barnes, W. L.; Dereux, A.; Ebbesen, T. W. Surface plasmon subwavelength optics. Nature 2003, 424 (6950), 824−830. (3) Homola, J..; Yee, S. S.; Gauglitz, G. Surface plasmon resonance sensors: review. Sens. Actuators, B 1999, 54 (1−2), 3−15. (4) Lim, D.-K.; Jeon, K.-S.; Hwang, J.-H.; Kim, H.; Kwon, S.; Suh, Y. D.; Nam, J.-M. Highly uniform and reproducible surface-enhanced Raman scattering from DNA-tailorable nanoparticles with 1-nm interior gap. Nat. Nano. 2011, 6 (7), 452−460. (5) Rand, B. P.; Peumans, P.; Forrest, S. R. Long-range absorption enhancement in organic tandem thin-film solar cells containing silver nanoclusters. J. Appl. Phys. 2004, 96 (12), 7519−7526. (6) Ghosh, S. K.; Pal, T. Interparticle coupling effect on the surface plasmon resonance of gold nanoparticles: From theory to applications. Chem. Rev. 2007, 107 (11), 4797−4862. (7) Hore, M. J. A.; Frischknecht, A. L.; Composto, R. J. Nanorod assemblies in polymer films and their dispersion-dependent optical properties. ACS Macro Lett. 2012, 1 (1), 115−121.
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FINAL REMARKS In summary, we established a facile method to tailor and to characterize the refractive indices of polymer/metallic nano9740
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dx.doi.org/10.1021/la300374w | Langmuir 2012, 28, 9735−9741
