1. Introduction

Resonant irradiation of plasmonic gold nanoparticles (AuNPs) within flexible polymer films could support enhanced light trapping in organic photovoltaic [1–3], sensing [4,5], optoelectronic [6–8], biomedical [9–12], and catalytic systems [13,14]. The morphology, polydispersity, and distribution of AuNPs inside polymer films determine the optical and thermal properties of these metal-polymer nanocomposites. To replace expensive lithographic or solution synthesis, AuNPs have been reduced in situ within optically transparent polydimethylsiloxane (PDMS) by infusion with hydrogen tetrachloroaurate (TCA) [15,16]. Polydisperse, reduced AuNPs (rAuNP) concentrated asymmetrically in PDMS films were recently contrasted with uniformly distributed rAuNP [17], for which geometric optics had been modeled using linear algebra [18]. This work compares measured and predicted geometric optics from rAuNP-PDMS films with films containing uniform distributions of monodisperse, organic-coated AuNPs (oAuNPs) for the first time. Single as well as multi-layered films and reflectors are analyzed. The quantitative results for mono-and polydisperse AuNPs distributed uniformly or asymmetrically in single- or multi-layer configurations could guide design and insertion of NP-polymer films into emerging flexible photonic devices [19].

Algebraic calculation of geometric transmission, reflection, and attenuation for polydisperse and non-uniform AuNP-PDMS films [18] provides a compact, workable alternative to expensive computational approaches, effective medium approximations, or simple fits of experimental data. Accurate numerical analysis of physicochemical and electromagnetic interactions in complex NP arrangements requires precise specification of NP features and distribution and is difficult to employ at system boundaries [20,21]. Finite difference [22,23], finite element [24,25], or dipole approximations [26–29] supported by well-defined geometries like particle ensembles, metal-dielectric disks, or nanoellipsoid/film pairing remain impractical for heterogeneous AuNP-PDMS thin films. Effective medium approaches can describe well-characterized size and spatial distributions of nanoparticles (NP), but are ill-suited to asymmetric and/or polydisperse rAuNPs [30–32]. Purely experimental approaches afford general correlations, but extrapolation beyond measured ranges is unreliable. As examples, light trapping in plasmon-enhanced solar cells or plasmon-coupled emission from metal-polymer multi-layers as a function of AuNP size provide useful insight but not a descriptive or quantitative design basis for AuNP-PDMS films [33,34].

This work evaluates trends in transmission, reflection, and resulting attenuation measured from PDMS thin films containing uniformly or asymmetrically distributed polydisperse rAuNPs or uniformly distributed monodisperse oAuNPs and accurately predicts results from films adjacent to optically active polymer or metal elements. Generally, transmission and reflection increased with AuNP isotropy and particle density. Optical attenuation from uniform and asymmetric polydisperse AuNP-PDMS films increased proportional to order-of-magnitude increases in gold content while attenuation from uniform monodisperse AuNP-PDMS film was linearly proportional to gold content. Irregular AuNP morphology and size distribution in rAuNP-PDMS films led to higher reflection and lower attenuation on a per mass basis relative to oAuNP-PDMS films. Reduced AuNPs concentrated into an asymmetric distribution attenuated more light than uniformly distributed AuNPs. Measured optical responses from asymmetric rAuNP-PDMS films with an adjacent back-reflector, as well as pairs of uniformly distributed oAuNP or rAuNP-PDMS films, were within 0.04 units on average of linear algebraic estimates based on geometric optics. Differences were attributable to refractive index changes between adjacent thin film interfaces.

2. Materials and Methods

2.1 AuNP-PDMS thin film fabrication

Asymmetric AuNP-PDMS thin films were fabricated by diffusing TCA into partially-cured PDMS as recently described [17]. Briefly, a PDMS film was cured at ambient conditions for 24 hours, after which aqueous dilutions of 0.005, 0.05, and 0.5 mass-percent TCA, respectively, were allowed to diffuse into the PDMS film for 24 hours. Films containing uniformly dispersed AuNPs were made by mixing diluted TCA or oAuNPs into PDMS, spincoating the resulting solution at 600 rpm for 60 seconds, then fully curing the films. Films containing 5 nm alkanethiol-stabilized oAuNPs from Nanocomposix (San Diego, CA, USA) were fabricated with 0.05 and 0.1 mass-percent AuNP content. TCA from Sigma-Aldrich (St. Louis, MO, USA) was mixed into films fabricated at 0.1, 0.4, and 0.6 mass-percent TCA. The laminar asymmetric film containing reduced AuNPs was created by spincoating a 1.2 mass-percent TCA mixture at 4000 rpm (~25 μm) on top of an Au-free PDMS substrate spincoated on glass at 1500 rpm (40 μm). For the 0.05 and 0.1 mass-percent oAuNP films, the oAuNP mixture was allowed to sit for one hour prior to spincoating to allow evaporation of hexane solvent in which AuNPs were dispersed. This step was added to ensure similar viscosities amongst AuNP-PDMS mixtures and resulting film thicknesses. The relatively dilute organic AuNP solution (1 mg/mL) and the high solubility of PDMS in hexane result in a significantly less viscous solution when compared to aqueous 25% TCA solution with PDMS.

2.2 Transmission and reflection measurements

Transmission and reflection were measured at a resonant wavelength of 532 nm using a integrating sphere (IS200-4, Thorlabs, Newton, NJ, USA) as recently described [18]. Briefly, samples fixed to the sphere exterior were illuminated with a 532 nm diode laser (MXL-H-532, CNI, Changchun, China) at normal incidence from the opposite side of the sphere at about 18 mW. The Au-free PDMS layer was always oriented toward the laser. Forward scattering (i.e. transmission) was measured with a power meter (PM100D, Thorlabs, Newton, NJ, USA). Reverse scattering (i.e. reflection) collected in the sphere was detected by a spectrometer (AvaSpec-2048, Avantes, Broomfield, CO, USA). Reported transmission and reflection for each sample were averaged from three replicates to account for variations in operation, measurement, or sample placement. Reported uncertainty corresponds to the standard deviation from the mean, which is within the size of the plotted points in Fig. 2. Optical evaluation using an integrating sphere has been performed on nanotextured PDMS films [35].

2.3 Geometric optical predictions of two component systems

A linear algebraic model of geometric optics was used to describe transmission, reflection, and attenuation values of each asymmetric AuNP-PDMS thin film paired with a back reflector, as well as pairs of oAuNP and rAuNP-PDMS films [18]. For AuNP-PDMS film pairs, films with the highest gold content were replaced the back-reflector. Each two-component system irradiated at plasmon resonant frequency and normal incidence was treated as homogenous media with isotropic values of fractional transmission ($T_i$) and reflection ($R_i$), where i refers to a particular component. Optical attenuation ($A_i$) arising from plasmonic absorption and non-resonant losses in the media is described by [18]

Inserting a second component at the interface opposite to incident irradiation induced multiple light passes (n) within the system to enhance attenuation in the two-component system. Figure 1 illustrates these multiple light passes for a two-component system as a function of its constituent components’ optical properties. Enhanced attenuation accrues from light reflected by the second component, which was either a metal mesh used to mechanically support thin polymer films under vacuum conditions in membrane separations [36] or a second AuNP-PDMS film layer to be employed in a photovoltaic cell. Linear superposition of geometric optics in each light pass allowed cumulative transmission and reflection to be predicted using infinite sums of linearly compounding fractions representing each component’s optical properties. The sum that defines fractional attenuation of a system is [18]

 

Fig. 1 Geometric optical pathways for AuNP-PDMS film and an adjacent optical element as a function of transmission (_T), reflection (R), and attenuation (A). For oAuNP and rAuNP-PDMS film pairs, the second optical element would be a second film with higher gold content. For estimation of the attenuation of asymmetric AuNP-containing layers, the AuNP-containing portion would be the 2nd component and the Au-free PDMS would be the 1st component.

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2.4 Estimation of attenuation from AuNP-containing layer

This linear algebraic description can be used to decouple the optical response of the asymmetric film AuNP-containing layers from adjacent Au-free PDMS as follows. Measured transmission and reflection were considered to be aggregate values from an assembled pair of thinner Au-free and Au-containing films. Optical values for the ‘Au-free PDMS layer’ were measured from a separate, Au-free PDMS film and substituted into Eq. (2) for the first ( = 1) optical component, i.e.,$A_{1st}$ and $T_{1st}$. Transmitted light from this 1st layer was incident upon the second (i.e.,n = 2 in Eq. (2)), AuNP-containing, ~5-micron layer. Measured attenuation from the complete asymmetric AuNP-PDMS film was substituted into for $A_{total}$ in the LHS of Eq. (2). The geometric optics of the second, AuNP-containing layer could then be distinguished from the adjacent PDMS layer by rearranging Eq. (2):

3. Results & Discussion

3.1 Geometric optics of individual AuNP-PDMS films

Measured fractional values of transmission, reflection, and attenuation from each individual film, film pairs, and film-back reflector pairing are displayed in the modified ternary diagram of Fig. 2. Top, right, and left vertices in this diagram correspond to maximum values (1.0) of transmission, reflection, and attenuation. Each point in the triangle denotes a system with a unique combination of measured or predicted transmission (T) and reflection (R) and resulting attenuation (A). Specific film and film-back reflector pairs are distinguishable by shape, color, and cross-hatch pattern (reflector). The large number of data points with a narrow range of reflection necessitated the addition of the two columns to the left of the main triangle. Values of transmission are equal across each data set, but the attenuation scale is offset. To illustrate the interpretation of Fig. 2: the 0.1 oAuNP-PDMS and the 0.05 mass-percent asymmetric film had,measured attenuation values of 0.36 and 0.52, respectively.

 

Fig. 2 Measured fractional transmission (T), reflection (R), and attenuation (A) for AuNP-PDMS films with and without an adjacent reflector. Measurements for each system are represented by the shape, color, and hatching of filled symbols. Solid colored circles represent single films, while split circles represent pairs of two adjacent films. A hatched triangle identifies the stainless steel reflector. Circles with hatching represent data from the reflector paired with a thin film of the corresponding color. Predictions for coupled systems are indicated by a small filled dot connected to a symbol. Dashed green arrows connect data from a single film with data from that film adjacent to the reflector. Arrow length shows the relative optical effect due to the support mesh.

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Figure 2 shows distributing AuNPs either uniformly (blue/red) or asymmetrically (violet) in PDMS film reduced both its transmission and reflection, thereby raising attenuation. Predictable attenuation increases could yield better optoplasmonic heating in biomedical or microelectromechanical devices or more light trapping in solar photovoltaics [37]. Increasing Au content influenced the size, morphology, distribution, and density of AuNP which changed optical behavior of the films. Asymmetric rAuNP-PDMS films provided the largest range of attenuation, tunable from 0.13 for 0.005 mass-percent gold to 0.85 for 0.5 mass-percent gold. This attenuation increased linearly with order of magnitude increases of Au content in TCA solution. Uniform rAuNP-PDMS films exhibited a similar, but lower, log-linear behavior. More densely packed rAuNPs attenuated light more efficiently. Consider the 0.6 mass-percent film (darkest blue; 130 μm thick) with rAuNPs dispersed uniformly versus the 1.2 mass-percent film (yellow; 130 μm thick overall) with rAuNPs dispersed into a 25 μm layer: the former film has ~2.5x the total Au content of the latter laminar film, but nearly identical attenuation. Concentrating the rAuNP decreases the Wigner-Seitz radius (average NP spacing) which appears to internally reflect and/or absorb more incident light – a useful guide for increasing optoplasmonic heating or light trapping.

Films containing monodisperse oAuNPs attenuated light linearly with respect to mass Au, which was more efficient than for rAuNPs. This suggests oAuNP films might be implemented at less cost than rAuNP films. As an example, doubling oAuNP content from 0.05 (pink) to 0.1 (red) mass-percent doubled attenuation (after accounting for the inherent attenuation of PDMS of about 0.06). The 0.1 mass-percent oAuNP film attenuated 0.36 compared to 0.14 for the 0.1 mass-percent rAuNP-PDMS film. Previous work similarly showed that optical extinction and temperature change of oAuNP-PDMS films were 2-3x higher than rAuNP-PDMS films with comparable gold content [16]. Heterogeneous sizes and irregular shapes observed for rAuNPs [15] translate into lower relative extinction at 532 nm.

Addition of AuNPs decreased reflection in all AuNP-PDMS films, but the magnitude of reflection reduction was different for each film type. Decreased reflection could benefit solar efficiency or raise thermoplasmonic temperatures. While PDMS film alone reflected 0.057 units, average reflection was 0.042 for asymmetric rAuNP-PDMS films, 0.028 for uniform rAuNP-PDMS films, and 0.033 for uniform oAuNP-PDMS films. In related work, adding 2-4 nm silver NPs onto silicon reduced average reflectance by about 7% [22]. Fresnel calculations suggest a small refractive index change between alkanethiol-stabilized oAuNPs and PDMS may contribute to reflection reduction. Lower reflection reduction of oAuNPs relative to rAuNPs could also be attributed to the differences in AuNP size and morphology. Asymmetric rAuNP-PDMS films contained micron-size, irregularly shaped particles as well as spherical AuNP as shown in the transmission electron microscope (TEM) image inset in Fig. 2. Extinction spectra from these were broader than uniform oAuNP or rAuNP-PDMS films, but the plasmon extinction peak was not measurably red-shifted. Observed optics of non-spherical AuNPs in similar films could be explained by hyper Rayleigh scattering [38], causing angular scattering in 3D dispersions [18].

3.2 Geometric optics of asymmetric films with adjacent back-reflector

Figure 2 illustrates measured values of transmission, reflection, and attenuation for asymmetric films with (hatched circles) and without (unhatched) an adjacent optical element (i.e., back-reflective mesh or AuNP-PDMS film). Linear algebraic estimates (small colored dots) for each pair are linked to corresponding measured values. Close proximity of measurements and predictions obscures appearance of small colored dots for the 0.05 mass-percent and 1.2 mass-percent laminar samples. Progressively shorter lengths of green arrows between measurements of singular AuNP-PDMS thin films vs. back-reflector pairings indicated that attenuation from respective components did not sum linearly. Attenuation enhancement due to the support mesh decreased with increasing Au content in the asymmetric thin films. This was because progressively less light was transmitted to the mesh.

Measured and estimated values of T, R, and A for asymmetric film-back reflector pairs were within 0.04 absolute units on average. Differences between measured and predicted values in film-back reflector pairs could be attributed to cumulative effects of angular scattering, trapped light, and/or reradiation. Results in Fig. 2 suggest influences of AuNP morphology, polydispersity, concentration, and distribution on anomalies. All measured reflection values were within 0.02 of predictions. Measured attenuation was higher than predictions for asymmetric film-back reflector pairs. This was consistent with previous results for rAuNP dispersions for a range of reflective mesh supports [18]. Superimposability of geometric optics in adjacent plasmonic and standard components was also report for silver NP deposited on silicon nano-pillar arrays [39]. Such data is useful to guide design of asymmetric AuNP films for use in pervaporative recovery of sustainable biofuels [17,36].

Lower measured transmission compared to predictions in asymmetric film-back reflector pairs can be explained in part by the asymmetric distribution of AuNPs not accounted for by the linear algebraic sum. The description regarded the film as a homogenous element with uniform optical properties, while the asymmetric film was composed of two optically distinct parts. On the secondary light passes, reflection was incident on the AuNP-containing layer, as opposed to Au-free PDMS. Since reflection of each thin film was measured with irradiation incident on the Au-free PDMS layer, inserting these values into the sum would yield a higher cumulative reflection. This would result in a lower estimated transmission relative to the measured value. Higher metal content would exacerbate this effect as the difference in reflection between the Au-free and AuNP-containing layer increased. Such differences may also be attributed to cumulative non-linear effects such as re-radiation and saturation.

3.3 Geometric optics of uniformly dispersed AuNP-PDMS film pairs

Cumulative attenuation measured from two adjacent AuNP-PDMS films was higher than linear algebraic estimates, but within 0.04 units on average. This suggests the film-film interface increased refractive light trapping. Note that reflection and transmission values inserted into the linear algebraic description for individual components were obtained relative to an air environment. Eliminating air at the film-film interface would lower linear algebra estimates as more reflection increased attenuation. This occurs, but to a modest degree, suggesting either air or refractive anomalies persist to some extent at the film-film interface.

Comparison of measured and predicted values for film pairs indicated potential nonlinear effects arising from rAuNP morphology and size heterogeneity not seen in oAuNP-PDMS films. Differences in measured and predicted attenuation values can be largely attributed to aforementioned small refractive index change between films. Both measured and predicted transmission values for the 0.1/0.05 and 0.1/0.0 mass-percent oAuNP-PDMS pairs are within 0.01 units. In contrast, measured transmission is noticeably lower than predictions for rAuNP-PDMS film pairs. Effective medium approximations which underlie geometric optics presume a low volume fraction of inclusions with well-described size and distribution, yielding a uniform dielectric function and polarizability [40,41]. Increasing heterogeneity at higher concentration rAuNP films induces optophysical interactions that diverge from accurate geometric optical description. However, the linear algebra sum remains a reasonable first approximation for estimates of cumulative optical interactions in systems containing rAuNPs.

3.4 Geometric optical prediction of second layer attenuation

Attenuation of asymmetric AuNP-containing layer alone was predicted using Eq. (3) as described in section 2.4. Attenuation estimates of ~5 μm thick AuNP-containing layers in the 0.5, 0.05 and 0.005 mass-percent diffusive samples were 0.90, 0.53, and 0.089, respectively. Similarly, attenuation of the 1.2 mass-percent laminar film was predicted to be 0.52. These predictions are within 0.04 attenuation units of the overall measured attenuation, since the Au-free PDMS film attenuated only 0.049 units. The information is useful since asymmetric rAuNP-PDMS films have value in thermoplasmonic applications [17,42–46]. An analogous approach could be used to predict geometric optical response of individual components in multi-layer optical filters, lenses or polarizers which cannot be easily decoupled.

The single light pass assumption used to estimate AuNP-containing layer attenuation was justified by the small degree of reflection in AuNP-PDMS films. This minimizes effects of successive light passes. A trial and error method could be used to obtain results using multiple light passes. However, reflection values for the asymmetric films were less than 0.06 units relative to an air environment. Furthermore, these values would be less for the AuNP-containing layer because of the small refractive index change between layers, and the diminishing effect of AuNP interfaces on reflectance. Incorporation of refractive index and optical path lengths into this description is underway to improve the rigor of this approach. The 2nd element in the paired system need not be physically detached or macroscopically distinct from the component on which irradiation is incident. This allows analysis of summative optical responses of a sequence of 2D elements comprising a 3D assembly to be analyzed. These features are applicable to develop plasmon-functionalized metamaterials for use in nano-electronics, photovoltaics, memory storage, catalysis, and sensing [47].

4. Conclusion

This work examined geometric transmission and reflection from three distinct AuNP-PDMS film configurations with different AuNP type, size, and distribution. Transmission and reflection from PDMS films containing monodisperse AuNPs were lower than films infused with polydisperse reduced AuNPs at comparable metal content. Optical attenuation increased in proportion to linear and order-of-magnitude increases in metal content, respectively, in monodisperse and polydisperse AuNP-PDMS thin films. Concentrating reduced AuNPs at a single interface of the film increased attenuation per metal content. Measured optical properties of AuNP-PDMS thin films paired with another film or a macroscopic back-reflector were within 0.04 units on average of estimates from linear algebra based on geometric optics of individual components. Estimates based on geometric optics diverged from measurements as AuNP size and shape became more heterogeneous and at higher AuNP concentrations. These properties and quantitative estimation of their cumulative effect in multicomponent systems improves understanding to guide design and development of metal-dielectric thin films and their integration with macroscopic optical elements.