Gold NanoparticleâPolydimethylsiloxane Thin Films Enhance

Article pubs.acs.org/JPCC

Gold Nanoparticle−Polydimethylsiloxane Thin Films Enhance Thermoplasmonic Dissipation by Internal Reflection Jeremy R. Dunklin,† Gregory T. Forcherio,‡ Keith R. Berry, Jr.,† and D. K. Roper*,†,‡ †

Ralph E. Martin Department of Chemical Engineering, University of Arkansas, Fayetteville, Arkansas 72701, United States MicroElectronics-Photonics Graduate Program, University of Arkansas, Fayetteville, Arkansas 72701, United States

‡

S Supporting Information *

ABSTRACT: Thermal relaxation dynamics of resonantly excited plasmons is important in optoelectronic, medical, and catalytic applications. This work shows introducing gold nanoparticles (AuNPs) into thin polydimethylsiloxane (PDMS) films enhanced thermoplasmonic dissipation coincident with internal reflection of incident resonant irradiation. Measured thermal emission and dynamics of AuNP−PDMS thin films exceeded emission and dynamics attributable by finite element analysis to Mie absorption, Fourier heat conduction, Rayleigh convection, and Stefan− Boltzmann radiation. Refractive-index matching experiments and measured temperature profiles indicated AuNP-containing thin films internally reflected light and dissipated power transverse to the film surface. Enhanced thermoplasmonic dissipation from metal−polymer nanocomposite thin films could affect opto- and bioelectronic implementation of these systems.

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concentrations.21 Recent examination of nanoscale photothermal effects from pulsed laser illumination of various nanostructure dispersions using three-dimensional coupled computational electromagnetics and fluid dynamics provided excellent insight but requires rigorous description of nanoparticle shape and configuration.22,23 A compact finite element description of thermoplasmonics for AuNPs dispersed threedimensionally within a solid matrix could be useful to increase understanding of these these systems and support integration into opto- and bioelectronic devices24−27 but has not yet been reported. Prior work indicates thermal transport properties of bulk polymer−nanoparticle composites are consistent with that of the bulk polymer when inclusions are well-dispersed and at relatively low concentrations. Significant increases in thermal conductivity have been demonstrated only with nanoparticle clustering and/or high filler fractions. Evans et al. analyzed the effects of aggregation, filler concentration, and interfacial thermal resistance on the thermal conductivity of colloidal nanofluids and nanocomposites, 28 while Huang et al. demonstrated notable increases in thermal conductivity for ferroelectric polymer nanocomposites containing 20% filler volume of silver NPs.29 In contrast to previous results, this work examines photothermal effects induced by thermoplasmonic inclusions embedded at low mass fraction (≤0.005 mass %) in a thin dielectric film. Optical trapping from plasmonic metal NPs in thin film absorbers was reviewed by Atwater and Polman.30 Wang et al. demonstrated enhanced light trapping upon introduction of plasmonic AuNPs on fluorine-doped tin dioxide featuring nanostructured photonic patterns.31 However,

INTRODUCTION Resonant irradiation of noble metal nanostructures allows localized control of thermal energy for targeted drug delivery,1,2 cancer ablation,3,4 catalytic reactions,5,6 and membrane separations.7−9 The morphology, size distribution, and arrangement of nanoparticles (NPs) determine their respective optical and thermal properties. Gold nanoparticles (AuNPs) embedded in optically transparent polymer exhibit high optical absorption and thermal response suitable for biomedical and optoelectronic applications.10−12 However, optical and thermal characterization of AuNP-containing polymer thin films has been limited to experimental measurement. A compact description of thermoplasmonic transport in AuNP−PDMS thin films could identify unusual thermoplasmonic features and guide integration of these structures into a variety of devices. Optical and thermal properties of AuNPs suspended in fluids or deposited on solid substrates have been analyzed for one- to three-dimensional dispersion under both continuous and pulsed-laser illumination. Power dissipation from an individual AuNP under pulsed or continuous illumination is modest, but simultaneous resonant irradiation of AuNP ensembles produces macroscopic bulk heating, even melting of surrounding materials.13,14 A one-dimensional analytical description for optoplasmonic heating was validated for NPs suspended in fluid or deposited on substrates and resonantly irradiated.15−17 Computational extension of this approach accurately described thermoplasmonic evaporation from open silica cells and AuNP plated capillaries filled with water, butanol, and air.18,19 Onedimensional theoretical and experimental examination of nanoand millimeter scale thermal effects in AuNPs containing water droplets indicated high light-to-heat conversion efficiencies.20 Photothermal conversion efficiency of variously sized and shaped Au nanocrystals were found to be superior to lead sulfide, carbon black, and organic dyes at comparable © 2014 American Chemical Society

Received: November 15, 2013 Revised: March 19, 2014 Published: March 20, 2014 7523

dx.doi.org/10.1021/jp4112124 | J. Phys. Chem. C 2014, 118, 7523−7531

The Journal of Physical Chemistry C

Article

incidence from the opposite side of the sphere with a 532 nm diode laser (MXL-H-532, CNI, Changchun, China). To measure transmission, the sample was placed with a small gap between it and a lens which focused transmitted light into the detector. This small gap was filled with air for normal transmission measurement (analogous to thermal measurements) and glycerol (n = 1.47) for RI matching with PDMS (n = 1.415). A power meter (PM100D, Thorlabs, Newton, NJ) captured forward scattering (i.e., transmission), and a spectrometer (AvaSpec-2048, Avantes, Broomfield, CO) detected reverse scattering (i.e., external reflection) coupled by the integrating sphere. Transmission and reflection values were obtained as fractional values and then converted to a power by multiplying them by 100 mW, the incident laser power for both measured and simulated thermal experiments. The difference between transmission in the presence and absence of RI matching constituted internally reflected power. Mie absorption was estimated independently based on Beer− Lambert absorption measured for AuNPs dispersed in a glycerol water mixture (61% glycerol/39% water) that matched the RI of PDMS. Spectral absorption was measured using a UV−vis spectrometer (UV-1800, Shimadzu Instruments, Kyoto, Japan). The molar absorptivity (ε) of 0.342 mm−1 mM−1 was calculated from absorption measured at 532 nm, the incident laser wavelength, for the AuNP−PDMS films using the Beer−Lambert law, A = εLc. For the setup, the molar concentration of AuNP was c = 0.293 mM, the optical path length was the cuvette thickness, L = 4 mm, multiplied by solution RI (n = 1.415), and the absorbance was A = 0.567. For the AuNP−PDMS films, Beer−Lambert absorbed power was taken as 100 mW × (1 − 10−A). A for each respective thin films was calculated by multiplying its molar concentration per unit area, converted from nmol/cm2 to mmol/mm2, by the RI of PDMS and the molar absorptivity. Thermal Characterization. Temperatures were measured on surfaces of 5 mm × 5 mm samples of the films suspended vertically with the laser spot (2 mm diameter) centered within the film. Tweezers affixed to the bottom-left corner of the film held it in place. The infrared thermal imaging camera (ICI 7320, Infrared Cameras Inc., Beaumont, TX) was oriented toward the surface of the film opposite incident laser irradiation and focused on the film to collect temperature data. A neutral density filter was used to adjust laser power to approximately 100 mW. The setup was enclosed in a plexiglass environmental chamber to minimize forced convection. The infrared camera recorded the thermal data at 1 Hz during a 3 min heating period with the laser on and a subsequent 2 min cooling period with the laser turned off. Data were recorded as thermal images with temperature values at each image pixel (320 × 240 pixels per image). The images were analyzed using Matlab R2012a (Mathworks, Natick, MA) to produce the temperature distribution throughout the sample during irradiation. Because conduction by the tweezers distorted the temperature distribution, only the right half of the film was considered for power dissipation and dynamic time constant calculations. Measured values of convective and radiated power emanated from the surface were calculated at each individual pixel and added together across the film to obtain the total power emitted. Relationships used to calculate convection and radiation are discussed in detail in the following section. Time constants, τ, measure the thermal equilibration time of a system.15 Time constant values are obtained as the negative

enhanced thermoplasmonic dissipation and dynamics coincident with internal optical reflection has not been distinguished or evaluated in thin metal−polymer nanocomposite films. This work compared independent spectroscopic, optical, and thermal measures of AuNP−PDMS thin films with corresponding estimates attributable to Beer−Lambert and Mie absorption, geometric optics, and thermoplasmonic heating, respectively. Thermal equilibrium dissipation and dynamics were computed using finite element analysis of thermoplasmonic heating via Mie absorption, Fourier conduction, Rayleigh convection, and Stefan−Boltzmann radiation in nonadiabatic, plasmonic metal−polymer thin films. Measured spectral extinction from the thin films exceeded values attributable to plasmonic absorption alone. Independently measured geometric optics used RI matching to distinguish internal reflection in AuNP−PDMS thin films from external reflection and attenuation due to AuNP and PDMS absorption. Measured thermal dissipation from AuNP−PDMS films exceeded computed estimates that neglected thermoplasmonic contributions from internal reflection. Measured spectroscopic extinctions, equilibrium temperature profiles, and dynamic thermal time constants coincident with internal reflection due to low mass fraction AuNPs embedded in thin PDMS films indicate internal reflection could contribute to thermoplasmonic dissipation. These observations motivate further examination of internal reflection in plasmonic metal−polymer dieletric waveguiding films.

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MATERIALS AND METHODS Sample fabrication. PDMS (Sylgard 184 silicone elastomer kit #4019862) was prepared with a 1:10 cross-linker to monomer ratio and then degassed for AuNP−PDMS film fabrication. AuNPs were suspended in a stock solution of ethanol at a concentration of 1013 NP mL−1. Different volumes of this dilution were mixed with PDMS, yielding concentrations from 0.0020 to 0.0050 mass %. Mass percent was calculated as the mass of AuNPs divided by the entire AuNP−PDMS film mass. The resulting mixture was degassed then poured onto a glass curing surface. The films were then cured at 150 °C for 10 min and cut into 5 mm × 5 mm sections. Thickness of each film (∼620 μm) was measured in triplicate using an intergrated light microscope (Eclipse LV100, Nikon Instruments, Melville, NY) and digital camera (Infinity 2, Lumenera, Ottawa, ON, Canada). Fabrication of these films has been detailed elsewhere.10 Multiplying the Au concentration of each film by its average measured thickness resulted in comparable planar Au densities in units of nanomoles Au per square centimeter (nmol/cm2): 5.31, 6.97, 10.2, and 13.4 nmol/cm2. Optical Characterization. Spectral extinction of each AuNP−PDMS film was measured with an integrated light microscope (Eclipse LV100, Nikon Instruments, Melville, NY) and spectrometer (Shamrock 303, Andor Technology, Belfast, UK). Maximum magnification of the light microscope is 100×. The slit size of the spectrometer is 200 μm. Measured spectral absorbed power was calculated for each film by multiplying 100 mW, the incident laser power, by (1 − 10−A), where A is the measured spectral extinction. Geometric optics (i.e., transmission and reflection) of each films were measured at 532 nm, independently from spectral extinction, using an integrating sphere apparatus recently described by Forcherio et al.32 To measure external reflection, each sample was affixed to the exterior of an integrating sphere (IS200-4, Thorlabs, Newton, NJ) and irradiated at normal 7524



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⎛ ⎞ ⎜ ⎟ ⎜ ⎟ 1/4 0.67RaL k ⎟, h = ⎜0.68 + 9/16 ⎞4/9 ⎟ L⎜ ⎛ ⎛ ⎞ ⎜ ⎜⎜1 + 0.492k ⎟ ⎟⎟ ⎟⎟ ⎜ μCp ⎠ ⎝ ⎝ ⎠ ⎠ ⎝

inverse of the slope of a natural log of dimensionless temperature, Θ, plotted versus time. The dimensionless temperature is defined as Θ = (Tambient − T)/(Tambient − Tmaximum). Measured τ values are an average of 10 random points within the laser spot, while simulation τ values are considered at a single point. Calculated τ values for both measured and simulation results were evaluated from 0 to 30 s, which provided the best linear fit to the ln(Θ) vs time data. Finite Element Heat Transfer Modeling. This work employed the Heat Transfer in Solids module in Version 4.2b of COMSOL Multiphysics (COMSOL, Stockholm, Sweden). COMSOL is a finite element analysis (FEA) simulation and solver software package used for various engineering and physics applications, specializing in coupled phenomena. An initial modeling approach used a 2D conjugate model (Heat Transfer in Solids and Laminar Flow) that solved for the temperature profiles in both the solid film and the surrounding air as well as the velocity profiles in the surrounding air due to buoyancy-driven Rayleigh convection. The results of this model were validated with a similar model available from COMSOL which was shown to be in excellent agreement with experimental data. For a detailed explanation and correspondence between the COMSOL provided heated vertical surface model, the conjugate model, and the proceeding model using heat transfer coefficients, see Supporting Information. Heat Transfer Modeling with Convective Heat Transfer Coefficients. To reduce computational expense, heat transfer from the AuNP−PDMS films were modeled with convective heat transfer coefficients. Fourier’s law for conductive heat transfer in the AuNP−PDMS films with a heat source is given by33 ∂T + ∇·(k∇T ) = Q ρCp ∂t

(3a)

h=

k 0.54RaL1/4 , L

RaL ≤ 107

(3b)

where L is the height of the plate, μ and k are viscosity and thermal conductivity of the fluid, respectively, and Cp is its specific heat capacity. RaL, the Rayleigh number, is a dimensionless ratio of buoyancy driven heat flux relative to conductive heat flux commonly defined as RaL =

gρCp(T − Tinf )L3 kμ

(4)

where g is the acceleration due to gravity, T is the surface temperature, Tinf is ambient temperature well away from the wall, and L is the plate height. For horizontal plates, L is commonly given as plate area divided by plate perimeter. Surface-to-ambient radiation was considered as a boundary condition in addition to convective cooling. Mathematically, this is given as −n·( −k∇T ) = εσ(Tinf 4 − T 4)

(5)

where ε is emissivity and σ is the Stefan−Boltzmann constant. There is no established value for the emissivity of PDMS, so a value of 0.85 was used as an approximation. This value is a reasonable approximation for a transparent polymer. Incorporation of Plasmonic Heating in AuNP−PDMS Films. The AuNP−PDMS films were assigned constant dimensions of 5 mm × 5 mm × 0.62 mm. Values of density and specific heat capacity for each AuNP−PDMS film were estimated as weighted averages of respective values for gold and PDMS based on mass fraction of gold in the film. The thermal conductivity of AuNP−PDMS was assumed to be that of Aufree PDMS as low mass fraction metallic dispersions in polymer typically have a negligible effect on bulk thermal conductivity.34 Density, specific heat capacity, and thermal conductivity values for PDMS used were 970 kg/m3, 1460 kJ/(kg K), and 0.16 W/ (m K), respectively.35 For gold, values are 19320 kg/m3, 128 J/ (kg K), and 317.9 W/(m K).36 Plasmonic heating from laser irradiation was approximated by using a heat source within the AuNP−PDMS films. A Gaussian laser power distribution was approximated in the model by evenly distributing the power between a center cylinder with a radius of 0.25 mm and seven concentric rings each with a thickness of 0.25 mm radiating outward. This distribution is consistent with manufacturer data and independent characterization of the laser spot using an adjustable aperture and power meter. Simulation heat source power was estimated as the product of incident laser power (100 mW) and the measured spectral extinguished power corrected for internal reflection. To match measured dynamic heating values, dynamic heating and cooling simulation results were evaluated once per second for 300 s, with the heat source removed after 180 s.

(1)

where ρ is the material density, Cp is the heat capacity, T is temperature, t is time, ∇ is the Del operator, k is the thermal conductivity, and Q is the sum of external heat sources (or sinks). Convective heat transfer is a common boundary condition in determining heat transfer in solids (e.g., fins). Convective heat transfer can be described by finite element analysis of flow and heat transfer both in the bulk and in the surrounding fluid (see Finite Element Heat Transfer Modeling section and Supporting Information) or by using heat transfer coefficients at the solid surfaces. In the second approach, the heat flux at the solid−fluid interface is specified as being proportional to the temperature difference across an imaginary thermal boundary layer. Mathematically, this is described as33 −n·( −k∇T ) = h(Tinf − T )

RaL ≤ 109

(2)

where n is the vector normal to the solid surface, h is a heat transfer coefficient, and Tinf is the external fluid temperature far from the boundary. Results using convective heat transfer were within a maximum deviation of 2.3% compared to finite element analysis of both bulk and surrounding air using heat sources across 3 orders of magnitude, which resulted in film temperatures ranging from 27 to 185 °C. Commonly used, empirically derived heat transfer coefficients for natural convection from vertical and horizontal plates were employed in this work. Correlations for a vertical (a) and horizontal (b) wall respectively are33 7525



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RESULTS AND DISCUSSION

PDMS as a Model Polymer. Gold nanoparticles (AuNP) were distributed in polydimethylsiloxane (PDMS) due to unique chemical, physical, and optical properties that support its use in a variety of biochemical and optoelectronic applications.37 In particular, its optical transparency in the visible spectrum allows facile measurement of spectroscopic and geometric optical features of embedded plasmonic NPs.38 Low metal content in the films studied in this work (5.31−13.4 nmol/cm2) yields bulk density and specific heat values for AuNP−PDMS within 0.1% of bulk PDMS. While local inhomogeneity of the polymer matrix and/or metal inclusions may lead to microscopic differences in these values, macroscopic thermal responses remain unaffected. Thermoelastic effects in AuNP−PDMS are not expected to contribute significantly to system behavior at the modest temperature increases in this work, as the thermal expansion coefficient of PDMS is 3 × 10−4 °C−1.35 PDMS cross-links as it cures, making silicon hydroxide groups available to reduce hydrogen tetrachloroaurate into AuNPs within the polymer matrix.12,39 Refinement of AuNP− PDMS thin films that result from in situ reduction has yielded films with superior optical and thermal properties relative to uniform dispersion of homogeneous as-synthesized NPs. However, uncertainty about the size, shape, and concentration of reduced AuNP (rAuNP) inhibits complete characterization of rAuNP−PDMS thin films. Investigation of internal reflection in these systems is not considered in this article but remains the subject of ongoing work. Spectroscopic Characterization of AuNP−PDMS Thin Films. Transmission UV−vis (T-UV) microspectroscopy40 can distinguish aggregate optical extinction features41 specific to plasmonic NPs suspended in fluid15,42 or locally assembled in condensed17,19 substrates. Customized optical beamlines,43,44 that integrate collimation, lenses for focusing and polarizing, beamsplitting, or flow paths can elicit specific transmission features that arise from interparticle coupling45,46 or interfacial reaction47 due to unique nanoparticle orientations, arrangements, and/or composition. Largely transparent PDMS thin films containing plasmonic AuNP support comprehensive TUV characterization.10,11,48 This study advances adaptability and fidelity of customized beamlines by integrating an Andor spectrometer with a Nikon light microscope to conduct the first TU-V microspectroscopy of AuNP−PDMS thin films. Absorbed power of AuNPs embedded in PDMS was distinguished from extinguished power based on measured spectral extinction in AuNP−PDMS films using independently obtained estimates of Mie absorption based on the Beer− Lambert law. Internal reflectance has likewise been distinguished from absorption and external reflection in measures of geometric optics. Figure 1 compares absorbed power of AuNP−PDMS calculated from measured spectral extinction of thin films (filled squares), maximum absorbable power of the same AuNPs estimated from measured Mie absorption using Beer−Lambert’s law (dotted line), and absorbed power after correcting for internal reflection (open squares). Transmission UV−vis extinction spectra for each thin film are shown in the inset. Spectral extinction values were measured for each AuNP−PDMS thin film at the resonant irradiation of 532 nm, shown by the vertical dashed line in the inset. Measured absorption spectra and corresponding Mie predictions for

Figure 1. Measured spectral extinguished power of AuNPs in PDMS (filled squares) calculated as 100 mW × (1 − 10−A), where A is the measured spectral absorbance of the AuNP-PDMS film at 532 nm normalized relative to control PDMS. Spectral absorbed power (hollow squares) is given as measured spectral extinguished power minus internal reflection. Inset shows the absorbance spectra of each AuNP−PDMS film and PDMS control sample.

AuNPs dispersed in RI-matched glycerol−water solution are illustrated in Figure S1 of the Supporting Information. Absorbed power of each AuNP−PDMS thin film (filled squares) calculated from corresponding measured spectral extinction (shown in inset) increases with gold content in the thin film from 8.74 mW at 5.31 nmol/cm2 to 20.27 mW at 13.4 nmol/cm2. Absorbed power calculated from spectral extinction exceeded the maximum absorbable power for each film based on its AuNP content (dotted line) in every case. Maximum power absorbable was computed using a Beer−Lambert absorption coefficient measured from AuNPs in a RI-matched glycerol water solution. Measured spectra compared well with Mie predictions for similarly sized particles (Figure S1, Supporting Information). Prior results have shown good agreement between measured thermoplasmonic power absorption and dissipation and estimates based on spectral extinction values for ca. 20 nm AuNPs formed on silica surfaces in liquid,17 gas,19 and mixed18 environments. Thermoplasmonic absorption and dissipation for ca. 20 nm AuNPs suspended in water was lower than calculated from spectral extinction values, but the decrease was attributable to light-induced AuNP aggregation.15 Scattering amplitude at 532 nm for 20 nm AuNPs is 1% of extinction according to Mie theory. Aggregation of AuNPs in PDMS during metal−polymer film formation would reduce absorption and broaden spectral extinction from increased scattering. This would decrease power absorption and dissipation relative to values predicted by Mie theory but could possibly increase overall extinction magnitude. Distinguishing dissipative absorption by AuNPs embedded in PDMS from nondissipative effects (e.g., scattering, diffraction) is therefore key to predicting AuNP− PDMS thermoplasmonic behavior. Red- or blue-shift of a plasmon absorption peak as a function of interparticle separation, d, between AuNPs in a PDMS 7526



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matrix could also influence absorbed power calculated from a spectral extinction profile. Previous comparison of theoretical and experimental dispersions of AuNPs has shown that as relative separation distance, d/2r (r is AuNP radius), decreases from >10 to approximately 1.1, the plasmon peak first blueshifts and then red-shifts.26 These shifts were observed for AuNPs with r ≥ 20 nm. Inspection of the plasmon absorption peak for 20 nm AuNPs suspended in PDMS in Figure S1 shows absorption is near maximum at 532 nm. Measurable red- or blue-shifts would likely decrease extinction and corresponding power absorption. Possible heterogeneity in the environment local to AuNPs embedded in PDMS is expected to broaden the plasmon absorption peak and reduce its intensity. Peak broadening is evident comparing the full width at halfmaximum of the absorption profile in Figure S1 with the spectra inset in Figure 1. Characterization of separation distance between AuNPs embedded in PDMS is also important to predicting and understanding thermoplasmonic behavior. The imperviousness of PDMS to chemical or thermal dissolution impedes facile characterization of aggregation or separation distance of embedded AuNP.10 Time and expense remain barriers to comprehensive high-resolution transmission or scanning electron microscopy of AuNP−PDMS sections,40,49 especially when taking into account potential polydispersity in AuNP distribution within the matrix. Discrepancy between power absorption calculated from spectral extinction in AuNP−PDMS films and maximum power obtainable from Mie absorption is confounded by the intransience of physical characterization methods for AuNPs in PDMS. This can be clarified in part by distinguishing aggregate correlates of absorption and nondissipative effecs from dispersed AuNPs using geometric optic measurements. Geometric Optic Measurements of AuNP−PDMS Thin Films. A linear algebraic model and corresponding integrating sphere system were recently introduced to distinguish far field transmission, reflection, and attenuation (losses) for distributions of heterogeneous AuNPs embedded in polymer matrix in which particle distribution and local optical environment of individual particles vary.32 Advancing beyond classical interference optics, this system accounts for radiative and absorptive (i.e., thermal) losses due to plasmonic interactions in nanocomposite media. Using this system, measured transmission, reflection, and attenuation of AuNP−PDMS thin films coupled with other optical media were within 0.04 units on average of linear algebra estimates.48 Figure 2 shows power transmitted from PDMS thin films containing 0, 5.31, 6.97, 10.2, and 13.4 nmol/cm2 Au in the absence of RI-matching (downward-pointing triangles). Transmitted power decreased with increasing Au content, from 94.3 mW at 0 nmol/cm2 to 68.3 mW at 13.4 nmol/cm2 Au. Also shown is power transmitted from each PDMS film when RImatching fluid was placed on the AuNP−PDMS thin film surface, in contact with an adjacent lens that focused light to the detector (upward-pointing triangles). Au-free PDMS transmitted 1.4 mW more power when RI-matching fluid was added. Transmitted power increased upon addition of RImatching fluid by an average of 6.2 mW. This transmitted power increase grew larger with AuNP content up to 10.2 nmol/cm2, where the maximum increase was 9.1 mW. Snell’s law predicts oblique light incident on a lower RI medium will be bent away from the normal, thus decreasing detected transmission.50 This attribute of Snell’s law remains valid in effective media containing subwavelength inclusions.51

Figure 2. Measured transmitted power of AuNP−PDMS films both with (up triangles) and without (down triangles) refractive index (RI) matching fluid adjacent to back film surface. Inset shows Weigner− Seitz estimates of nominal AuNP particle separation distances.

PDMS without AuNPs obliquely scatters little of normal incident irradiation. Embedding AuNPs in the PDMS thin film appears to result in light with a trajectory oblique from normal incident irradiation. Without RI-matching fluid, this oblique light is internally reflected within the film in a net direction transverse to normally transmitted light. Internal reflection reduces transmitted power and increases measured spectral extinction of AuNP−PDMS thin films. With RI-matching fluid, light with an oblique trajectory escapes the film, to be detected as transmitted power. The difference between transmitted power in the presence and absence of RI-matching fluid corresponds to the power with a net transverse trajectory (i.e., internally reflected) due to the presence of AuNPs in PDMS thin films. Subtracting internally reflected power for each respective AuNP−PDMS thin film shown in Figure 2 from the measured spectral power in Figure 1 estimates the maximum power absorbed. The resulting power absorbed by AuNP−PDMS thin films, corrected for internal reflection, is shown in Figure 1 (hollow squares). The corrected maximum power absorbed is much less than the maximum power predicted for ideal 20 nm AuNPs with negligible scattering using Mie absorption and the measured Beer−Lambert coefficient in all but the 13.4 nmol/ cm2 film. Transmitted power in the presence of RI-matching fluid from the 13.4 nmol/cm2 Au thin film was artificially decreased due to surface damage during sample handing. The damage was evident as discoloration which was insoluble to aqueous and mild organic solvents. This inflated the maximum power absorbed in Figure 1 to a level comparable to Mie theory prediction. The magnitude of internally reflected power was 64%, 109%, and 118% respectively of the maximum spectral absorbed power corrected for internal reflection for the 5.31, 6.97, and 10.2 nmol/cm2 films. Figure 2 inset shows nominal separation distance, rs, between AuNPs in PDMS films estimated using the Weigner−Seitz rule.52 Separation decreased from 2.1 μm for 5.31 nmol/cm2 Au to 1.5 μm for 13.4 nmol/cm2. The decrease in rs is proportional to (mass percent)−1/3. Observed increases in 7527



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spectroscopic extinction as PDMS film thickness decreases at similar AuNP densities (data not shown) indicate internal reflection and obliquely oriented light in these systems increases as rs decreases. Larger separation distances near the resonant plasmon wavelength increase the likelihood that obliquely oriented light remains unabsorbed by neighboring particles and effects internally reflecting surfaces of the thin film. Work is underway to distinguish the origin and magnitude of power transmitted parallel to thin film surfaces. This power is anticipated to be relatively small fraction of obliquely oriented light. This may further decrease the maximum absorbed power in Figure 1. Having distinguished dissipative absorption via AuNP from nondissipative activity (e.g., scattering, diffraction) using RI-matching, the measured absorbed power for each AuNP−PDMS thin film corrected for internal reflection in Figure 1 provides a basis for estimating power emitted from the film surfaces. Emission away from the film surface, power dissipation within the film, and dynamically changing dissipation can now be considered. Power Dissipated from AuNP−PDMS Thin Films Surface. A model based on a microscopic continuum energy balance that accounts for power absorbed optoplasmonically into an isolated system as well as conduction, convection, and radiation away from the system has been introduced15 and experimentally validated16 for macroscopic systems. The model has been successfully extended to describe equilibrium and dynamic thermoplasmonics in conductive metal−ceramic,17 solid−fluid,19 and thermodynamically open systems with phase change.18 Predicted equilibrium and dynamic temperature profiles and energy fluxes have shown excellent agreement with measured values. In this work, this energy balance approach is further extended to characterize power dissipated in insulating metal−polymer nanocomposite thin films open to an ambient environment. The macroscopic scale and slow thermal dynamics anticipated for this system required accurately distinguishing absorbed power from incident energy lost due to transmission, external reflection, and scattering and internal reflection. High spatial and temporal resolution of temperature data and accurate accounting of conductive, radiative, and convective losses were also important. See Thermal Characterization section for a detailed description. Modeling of thermoplasmonic dissipation in this work used COMSOL, a finite element analysis (FEA) simulation and solver software package. Relations for thermoplasmonic Mie absorption, Fourier heat conduction, Rayleigh convection, and Stefan−Boltzmann radiation were included in the model. Attention was focused on accurately estimating effective parameters supporting composite bulk thermal diffusivity, edge effects corrections, and representation of the spatial power density of incident radiation. For example, thermal conductivity was not measured previously in metal nanoparticle−PDMS nanocomposites, but copper (Cu) particles added to polypropylene and silver NPs added to polyethylene changed thermal conductivity less than 0.01 W/(m K) for metal inclusions lower than 5 mass %.53,54 This indicated thermal conductivities for 0.0020−0.0050 mass % Au (5.31− 13.4 nmol/cm2) in PDMS would be indistinguishable from Aufree PDMS. See Finite Element Heat Transfer Modeling section for a detailed description. Power emitted from one film surface based on observed equilibrium surface temperatures was 0.64−1.23 W (37−42%) greater than power emitted based on maximum power absorbed by AuNPs for the 5.31−10.2 nmol/cm2 films. Figure

3 shows key illustrative results of the COMSOL model for thermoplasmonic dissipation from an insulating PDMS thin

Figure 3. Total convected and radiated power from AuNP−PDMS film surface calculated from measured (red diamonds) temperatures and simulated (blue squares) via finite element using measured spectral absorbed power corrected for internal reflection as the heat source power. Inset shows measured (red diamonds) and simulated (blue line) temperature distribution across axial slice of the 6.97 nmol/ cm2 AuNP film.

film. Power dissipated from one face of each AuNP−PDMS thin film via radiation and conduction based on measured twodimensional temperature distributions at thermal equilibrium are indicated by filled (red) diamonds. Power emitted from one surface of the 5.31, 6.97, 10.2, and 13.4 nmol/cm2 films was calculated to be 2.50, 2.83, 4.03, and 4.27 mW, respectively. Over two-thirds of emitted power is from natural convection. As an example, the 6.97 nmol/cm2 mass percent film had emitted powers of 1.96 mW due to convection and 0.87 mW due to radiation. Corresponding estimates of dissipated power based on measured values of maximum absorbed power that were corrected for internal reflection are indicated by filled (blue) squares. These emitted powers were 1.83, 2.19, 2.80, and 5.18 mW respectively for the 5.31, 6.97, 10.2, and 13.4 nmol/ cm2 films. Reconciling these two sets of emitted power data requires identifying a source of power beyond thermoplasmonic absorption by AuNP of normal, incident irradiation. Figure 3 inset compares a measured radial temperature distribution through an axial slice of the 6.97 nmol/cm2 film (filled red diamonds) with the corresponding distribution computed based on maximum power absorbed by AuNPs (solid blue line) and the experimentally verified power distribution of the incident laser. Enhanced radial heat dissipation appears evident in the actual, thermally equilibrated AuNP−PDMS film from its broader, flattened profile with higher edge temperatures. Enhancement of PDMS thermal conductivity from inclusion of dispersed AuNPs would not account for this broadened temperature profile. Inserting massaveraged thermal conductivities of AuNP−PDMS into the COMSOL model, considered a conservative upper limit, still 7528



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and simulated time constants were mirrored in the 5.31, 10.2, and 13.4 nmol/cm2 films. Internal reflection concentrates radially transmitted power inside the film at the interface of the dielectric film and adjacent medium with lower RI (air). In combination with the radially decaying incident irradiation, the high fraction of internal reflection relative to absorbed power would increase the resonant power density within the film at the edges relative to its center. This could result in a net increase in axial power flux within the film toward its surface, relative to flux in the absence of internal reflection. Because internal reflection at the speed of light would be faster than thermal conduction via phonon transport, it is conceivable that power transported via internal reflection could occur faster than axially oriented thermal conduction driven by surface emission of thermoplasmonically absorbed power throughout the medium. This process would support enhanced dynamic dissipation of absorbed power, consistent with the observed dynamic enhancement. Future Direction. Dissipation of thermoplasmonically absorbed energy away from the film surface and radially outward from its center at equilibrium, as well as dynamic changes, were observed to increase relative to predictions based on optoplasmonic power absorption corrected for internal reflection. These increases appear qualitatively self-consistent. They are within measured quantitative limits of possible contributions from internally reflected power to optoplasmonic absorption. Further understanding, quantitative measurement, and fundamental description of contributions to internal reflection and enhanced overall dissipation are the subjects of ongoing work in our lab.

resulted in a substantially more narrow temperature profile than was measured. Conductivity values ∼5× the mass-average were needed to approach the measured temperature profile. Mass averages are considered an upper limit thermal conductivity estimate as they implicitly assume perfect contact between adjacent doped metals throughout the material.34 Literature reports anticipate lower emitted power from the actual film (diamonds) due to underprediction of heat transfer from the film’s narrow vertical surfaces (5 mm × 0.62 mm) at relatively low Rayleigh numbers because eq 5a ignores inward fluid flow induced near the edge of the plate.55 In this reference, an empirical relation for narrow plates was introduced and a Rayleigh number (Ra) of 1000−10 000, which yielded empirical heat transfer coefficients 1.5−2-fold higher than those given by eq 3a. Rayleigh numbers (∼70−200) and surface height-to-width ratio (0.14) used in the present work were not within the validated range of this empirical relation, which yielded erroneous results at Ra < 1000. However, reported trends with decreasing Rayleigh number and heightto-width ratio indicated edge effects become more prominent as Rayleigh number and plate height to width ratio is decreased. Heat dissipated from thermplasmonic absorption of resonant irradiation in AuNP−PDMS thin films was measured to be enhanced relative to comprehensive predictions based on independent optical measurements and validated modeling approaches. Dissipation was increased both radially outward and away from the thin film surface. Coincident with these increases in heat dissipation, from 70 to 114% of the maximum amount of power absorbable according to Mie and Beer− Lambert analysis, was measured to be internally reflected in a direction lateral to the film surface by RI matching. The power incident on the sample from resonant irradiation was measured to have a Gaussian, radially decaying profile. This suggests internal reflection would result in an outward radial flux of power scattered by the AuNPs. Taken together, these observations indicate that the obliquely oriented light in the film was internally reflected with a net direction that was radially outward. Because of the nonuniform laser profile, this contributed to the quantitatively broadened temperature profile and its higher power emission from the film surface. The increase in measured surface power emitted (from two surfaces) for three samples with increasing AuNP content was equivalent to 40%, 20%, and 27% of this internally reflected power. AuNP in PDMS Increased Dynamic Thermal Equilibration. Internal reflection in AuNP−PDMS films coincided with enhanced equilibrium thermal dissipation radially outward and normal to the film surface. Comparing measured and estimated time-dependent changes in temperature in AuNP−PDMS thin films showed that resonantly irradiated film equilibrated faster than predictions based on the absorbed thermoplasmonic power, whether corrected for internal reflection or not. For example, the measured thermal time constant was 14.9 s for the 6.97 nmol/cm2 film, averaged over 10 different points within the laser spot. The values at each point varied by less than 0.5 s of the average. Simulated dynamic time constants for thermal equilibration were longer than measured values, and the difference became larger as it was evaluated away from the center of the laser spot. For example, the 6.97 nmol/cm2 time constant calculated at the film center (2.5 mm in Figure 3 inset) was 17.7 s. This constant increased to 20.8 and 26.2 s at points 0.5 (3 mm in Figure 3 inset) and 1 mm (3.5 mm in Figure 3 inset) from the film center. These trends in measured

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CONCLUSIONS This work integrated spectroscopic measures of power absorbed in AuNP−PDMS thin films and refractive-index matched suspensions of AuNPs with independent measures of geometric optical transmission, external reflection, and attenuation of incident power to quantitatively distinguish internally reflected power from transmission, external reflection, and attenuation. Emitted power, temperature profiles, and relaxation dynamics measured separately from irradiated thin film compared with finite element estimates based on maximum absorbed power revealed enhanced thermoplasmonic dissipation occurred in AuNP−PDMS thin films at increasing Au content. Enhancements occurred radially outward, away from the film surface, and in increased dynamic thermal relaxation, consistent with possible contribution of internally reflected power to thermoplasmonic absorption by AuNP in thin PDMS films. These results motivate further quantitation and modeling of internally reflected power in AuNP−PDMS thin films to describe observed enhancements in thermoplasmonic dissipation and to improve design of dissipative optoelectronic and medical devices based on plasmon absorption in thin metal−dielectric waveguides.

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ASSOCIATED CONTENT

S Supporting Information *

Beer−Lambert AuNP measured absorption compared with Mie theory and further information about COMSOL modeling approach. This material is available free of charge via the Internet at http://pubs.acs.org. 7529



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(10) Berry, K. R.; Russell, A. G.; Blake, P. A.; Roper, D. K. Gold Nanoparticles Reduced in Situ and Dispersed in Polymer Thin Films: Optical and Thermal Properties. Nanotechnology 2012, 23, 375703 (11pp). (11) Dunklin, J. R.; Forcherio, G. T.; Berry, K. R.; Roper, D. K. Asymmetric Reduction of Gold Nanoparticles Into Thermoplasmonic Polydimethylsiloxane Thin Films. ACS Appl. Mater. Interfaces 2013, 5, 8457−8466. (12) Zhang, Q.; Xu, J.-J.; Liu, Y.; Chen, H.-Y. In-Situ Synthesis of Poly(dimethylsiloxane)-Gold Nanoparticles Composite Films and Its Application in Microfluidic Systems. Lab Chip 2008, 8, 352−357. (13) Keblinski, P.; Cahill, D. G.; Bodapati, A.; Sullivan, C. R.; Taton, T. A. Limits of Localized Heating by Electromagnetically Excited Nanoparticles. J. Appl. Phys. 2006, 100, 054305. (14) Govorov, A. O.; Richardson, H. H. Generating Heat with Metal Nanoparticles. Nano Today 2007, 2, 30−38. (15) Roper, D. K.; Ahn, W.; Hoepfner, M. Microscale Heat Transfer Transduced by Surface Plasmon Resonant Gold Nanoparticles. J. Phys. Chem. C 2007, 111, 3636−3641. (16) Hoepfner, M. P.; Roper, D. K. Describing Temperature Increases in Plasmon-Resonant Nanoparticle Systems. J. Therm. Anal. Calorim. 2009, 98, 197−202. (17) Ahn, W.; Roper, D. K. Transformed Gold Island Film Improves Light-to-Heat Transduction of Nanoparticles on Silica Capillaries. J. Phys. Chem. C 2008, 112, 12214−12218. (18) Russell, A. G.; McKnight, M. D.; Sharp, A. C.; Hestekin, J. A.; Roper, D. K. Gold Nanoparticles Allow Optoplasmonic Evaporation from Open Silica Cells with a Logarithmic Approach to Steady-State Thermal Profiles. J. Phys. Chem. C 2010, 114, 10132−10139. (19) Russell, A. G.; McKnight, M. D.; Hestekin, J. A.; Roper, D. K. Thermodynamics of Optoplasmonic Heating in Fluid-Filled GoldNanoparticle-Plated Capillaries. Langmuir 2011, 27, 7799−7805. (20) Richardson, H. H.; Carlson, M. T.; Tandler, P. J.; Hernandez, P.; Govorov, A. O. Experimental and Theoretical Studies of Light-toHeat Conversion and Collective Heating Effects in Metal Nanoparticle Solutions. Nano Lett. 2009, 9, 1139−1146. (21) Jiang, R.; Cheng, S.; Shao, L.; Ruan, Q.; Wang, J. Mass-Based Photothermal Comparison Among Gold Nanocrystals, PbS Nanocrystals, Organic Dyes, and Carbon Black. J. Phys. Chem. C 2013, 117, 8909−8915. (22) Furlani, E. P.; Karampelas, I. H.; Xie, Q. Analysis of Pulsed Laser Plasmon-Assisted Photothermal Heating and Bubble Generation at the Nanoscale. Lab Chip 2012, 12, 3707−3719. (23) Alali, F.; Karampelas, I. H.; Kim, Y. H.; Furlani, E. P. Photonic and Thermofluidic Analysis of Colloidal Plasmonic Nanorings and Nanotori for Pulsed-Laser Photothermal Applications. J. Phys. Chem. C 2013, 117, 20178−20185. (24) Roper, D. K. Enhancing Lateral Mass Transport to Improve the Dynamic Range of Adsorption Rates Measured by Surface Plasmon Resonance. Chem. Eng. Sci. 2006, 61, 2557−2564. (25) Roper, D. K. Determining Surface Plasmon Resonance Response Factors for Deposition Onto Three-Dimensional Surfaces. Chem. Eng. Sci. 2007, 62, 1988−1996. (26) Roper, D.; Ahn, W. Enhanced Spectral Sensing by Electromagnetic Coupling with Localized Surface Plasmons on Subwavelength Structures. IEEE Sens. J. 2010, 10, 531−540. (27) Roper, D. K.; Nakra, S. Adenovirus Type 5 Intrinsic Adsorption Rates Measured by Surface Plasmon Resonance. Anal. Biochem. 2006, 348, 75−83. (28) Evans, W.; Prasher, R.; Fish, J.; Meakin, P.; Phelan, P.; Keblinski, P. Effect of Aggregation and Interfacial Thermal Resistance on Thermal Conductivity of Nanocomposites and Colloidal Nanofluids. Int. J. Heat Mass Transfer 2008, 51, 1431−1438. (29) Huang, X.; Jiang, P.; Xie, L. Ferroelectric Polymer/silver Nanocomposites with High Dielectric Constant and High Thermal Conductivity. Appl. Phys. Lett. 2009, 95, 242901. (30) Atwater, H. A.; Polman, A. Plasmonics for Improved Photovoltaic Devices. Nat. Mater. 2010, 9, 205−213.

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], phone (801) 891-8921, fax (703) 292-9051 (D.K.R.). Author Contributions

J. R. Dunklin performed thermal modeling, measured optical responses, and prepared text and figures for the manuscript. G. T. Forcherio measured optical responses. K. R. Berry fabricated samples and measured thermal responses. D. K. Roper directed the work and refined compilation and finalization of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by NSF CBET-1134222, NSF ECCS-1006927, the University of Arkansas Foundation, and the Walton Family Charitable Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors thank Ken Vickers for helpful discussions regarding construction of the manuscript.

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ABBREVIATIONS PDMS, polydimethylsiloxane; AuNP, gold nanoparticle; NPs, nanoparticles; AuNP−PDMS, gold nanoparticle−polydimethylsiloxane; RI, refractive index.

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REFERENCES

(1) Park, J.-H.; von Maltzahn, G.; Ong, L. L.; Centrone, A.; Hatton, T. A.; Ruoslahti, E.; Bhatia, S. N.; Sailor, M. J. Cooperative Nanoparticles for Tumor Detection and Photothermally Triggered Drug Delivery. Adv. Mater. 2010, 22, 880−885. (2) Kang, B.; Afifi, M. M.; Austin, L. A.; El-Sayed, M. A. Exploiting the Nanoparticle Plasmon Effect: Observing Drug Delivery Dynamics in Single Cells via Raman/fluorescence Imaging Spectroscopy. ACS Nano 2013, 7, 7420−7427. (3) Zhang, J. Z. Biomedical Applications of Shape-Controlled Plasmonic Nanostructures: A Case Study of Hollow Gold Nanospheres for Photothermal Ablation Therapy of Cancer. J. Phys. Chem. Lett. 2010, 1, 686−695. (4) Xu, Y.; Heberlein, W. E.; Mahmood, M.; Orza, A. I.; Karmakar, A.; Mustafa, T.; Biris, A. R.; Casciano, D.; Biris, A. S. Progress in Materials for Thermal Ablation of Cancer Cells. J. Mater. Chem. 2012, 22, 20128−20142. (5) Wang, C.; Ranasingha, O.; Natesakhawat, S.; Ohodnicki, P. R.; Andio, M.; Lewis, J. P.; Matranga, C. Visible Light Plasmonic Heating of Au-ZnO for the Catalytic Reduction of CO2. Nanoscale 2013, 5, 6968−6974. (6) Hallett-Tapley, G. L.; Silvero, M. J.; Bueno-Alejo, C. J.; GonzálezBéjar, M.; McTiernan, C. D.; Grenier, M.; Netto-Ferreira, J. C.; Scaiano, J. C. Supported Gold Nanoparticles as Efficient Catalysts in the Solventless Plasmon Mediated Oxidation of Sec-Phenethyl and Benzyl Alcohol. J. Phys. Chem. C 2013, 117, 12279−12288. (7) Vanherck, K.; Hermans, S.; Verbiest, T.; Vankelecom, I. Using the Photothermal Effect to Improve Membrane Separations via Localized Heating. J. Mater. Chem. 2011, 21, 6079−6087. (8) Russell, A. Plasmonic Pervaporation via Gold NanoparticleFunctionalized Nanocomposite Membranes. Ph.D Disseration, University of Arkansas, 2012. (9) Li, Y.; Verbiest, T.; Vankelecom, I. Improving the Flux of PDMS Membranes via Localized Heating through Incorporation of Gold Nanoparticles. J. Membr. Sci. 2012, 428, 63−69. 7530



Article

(31) Wang, F.; Wang, Q.; Xu, G.; Hui, R.; Wu, J. Light Trapping on Plasmonic-Photonic Nanostructured Fluorine-Doped Tin Oxide. J. Phys. Chem. C 2013, 117, 11725−11730. (32) Forcherio, G. T.; Roper, D. K. Optical Attenuation of Plasmonic Nanocomposites within Photonic Devices. Appl. Opt. 2013, 52, 6417− 6427. (33) Incropera, F. P.; DeWitt, D. P.; Bergman, T. L.; Lavine, A. S. Fundamentals of Heat and Mass Transfer, 6th ed.; John Wiley & Sons: New York, 2006. (34) Ebadi-Dehaghani, H.; Nazempour, M. Thermal Conductivity of Nanoparticles Filled Polymers. In Smart Nanoparticles Technology; Hashim, A., Ed.; In-Tech: Rijeka, 2012; pp 519−534. (35) Polymer Data Handbook, 2nd ed.; Mark, J., Ed.; Oxford University Press: Oxford, 2009. (36) Buschow, K., Ed.; Encyclopedia of Materials - Science and Technology; Pergamon: Oxford, 2001. (37) McDonald, J. C.; Whitesides, G. M. Poly(dimethylsiloxane) as a Material for Fabricating Microfluidic Devices. Acc. Chem. Res. 2002, 35, 491−499. (38) Massaro, A.; Spano, F.; Cingolani, R.; Athanassiou, A. Experimental Optical Characterization and Polymeric Layouts of Gold PDMS Nanocomposite Sensor for Liquid Detection. IEEE Sens. J. 2011, 11, 1780−1786. (39) Roper, D. K. Self-Assembly of Nanodroplets in Nanocomposite Materials in Nanodroplets Science and Technology. In Nanodroplets; Wang, Z. M., Ed.; Springer: New York, 2013; Vol. 18, pp 73−97. (40) Roper, D. K.; Blake, P.; DeJarnette, D.; Harbin, B. Plasmon Coupling Enhanced in Nanostructured Chem/bio Sensors. In NanoPlasmonics: Advanced Device Applications; Chon, J. W., Iniewski, K., Eds.; CRC Press: Boca Raton, FL, 2013. (41) Ahn, W.; Taylor, B.; Dall’ Asén, A. G.; Roper, D. K. Electroless Gold Island Thin Films: Photoluminescence and Thermal Transformation to Nanoparticle Ensembles. Langmuir 2008, 24, 4174− 4184. (42) Lisunova, M.; Norman, J.; Xingfei, W.; Jenkins, S.; Chen, J.; Roper, D. K. Aqueous Dispersion of Plasmonic Hollow Metal Nanoparticles. Mater. Lett. 2014, 117, 241−243. (43) Blake, P.; Obermann, J.; Harbin, B.; Roper, D. K. Enhanced Nanoparticle Response From Coupled Dipole Excitation for Plasmon Sensors. IEEE Sens. J. 2011, 11, 3332−3340. (44) Jang, G.-G.; Roper, D. K. Continuous Flow Electroless Plating Enhances Optical Features of Au Films and Nanoparticles. J. Phys. Chem. C 2009, 113, 19228−19236. (45) DeJarnette, D.; Roper, D. K.; Harbin, B. Geometric Effects on Far-Field Coupling Between Multipoles of Nanoparticles in Square Arrays. J. Opt. Soc. Am. B 2011, 29, 88. (46) Lisunova, M.; Norman, J.; Blake, P.; Forcherio, G. T.; DeJarnette, D. F.; Roper, D. K. Modulation of Plasmonic Fano Resonance by the Shape of the Nanoparticles in Ordered Arrays. J. Phys. D: Appl. Phys. 2013, 46, 485103. (47) Jang, G. G.; Hawkridge, M. E.; Roper, D. K. Silver Disposition and Dynamics during Electroless Metal Thin Film Synthesis. J. Mater. Chem. 2012, 22, 21942−21953. (48) Dunklin, J. R.; Forcherio, G. T.; Roper, D. K. Geometric Optics of Gold Nanoparticle-Polydimethylsiloxane Thin Film Systems. Opt. Mater. Express 2014, 4, 375−383. (49) Ahn, W.; Blake, P.; Shultz, J.; Ware, M. E.; Roper, D. K. Fabrication of Regular Arrays of Gold Nanospheres by Thermal Transformation of Electroless-Plated Films. J. Vac. Sci. Technol., B 2010, 28, 638−642. (50) Hecht, E. Optics, 4th ed.; Addison-Wesley Longman, Inc.: Boston, 2002. (51) Mie, G. Beiträge Zur Optik Trüber Medien, Speziell Kolloidaler Metallösungen. Ann. Phys. 1908, 330, 377−445. (52) Girifalco, L. A. Statistical Mechanics of Solids; Oxford University Press: New York, 2000. (53) Boudenne, A.; Ibos, L.; Fois, M.; Majesté, J. C.; Géhin, E. Electrical and Thermal Behavior of Polypropylene Filled with Copper Particles. Composites, Part A 2005, 36, 1545−1554.

(54) Jouni, M.; Boudenne, A.; Garnier, B.; Serghei, A. Electrical and Thermal Properties of Polyethylene/Silver Nanoparticle Composites. Polym. Compos. 2013, 34, 11−14. (55) Oosthuizen, P. H.; Kalendar, A. Y. Natural Convective Heat Transfer from Narrow Plates; Springer: Berlin, 2013; pp 15−29.

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