Optomechanic Coupling in Ag Polymer Nanocomposite Films

Abstract

Particle vibrational spectroscopy has emerged as a new tool for the measurement of elasticity, glass transition, and interactions at a nanoscale. For colloid-based materials, however, the weakly localized particle resonances in a fluid or solid medium renders their detection difficult. The strong amplification of the inelastic light scattering near surface plasmon resonance of metallic nanoparticles (NPs) allowed not only the detection of single NP eigenvibrations but also the interparticle interaction effects on the acoustic vibrations of NPs mediated by strong optomechanical coupling. The "rattling" and quadrupolar modes of Ag/polymer and polymer-grafted Ag NPs with different diameters in their assemblies are probed by Brillouin light spectroscopy (BLS). We present thorough theoretical 3D calculations for anisotropic Ag elasticity to quantify the frequency and intensity of the "rattling" mode and hence its BLS activity for different interparticle separations and matrix rigidity. Theoretically, a liquidlike environment, e.g., poly(isobutylene) (PIB) does not support rattling vibration of Ag dimers but unexpectedly hardening of the extremely confined graft melt renders both activation of the former and a frequency blue shift of the fundamental quadrupolar mode in the grafted nanoparticle Ag@PIB film.

Figure 1

(a) HRTEM image of Ag (14) NP films. (b) Fourier-filtered and magnified image of the rectangular area (b) in (a). (c) Fourier-filtered and magnified image of the rectangular area (c) in (a).

Figure 2

BLS (anti-Stokes) spectra of polymer nanocomposites (a) Ag (14)/PVP, (b) Ag (14)/PVA, (c) Ag (29)/PVP, and Ag (22)/PVP on glass (main panels) and the SiN substrate (insets to (a) and (b)) with Ag diameter D = 14.1 nm (a,b), D = 29.4 nm (c), and D = 21.6 nm (d). The inset to (d) is the reduced spectrum, intensity × frequency square, of the spectrum in the main figure. The representation of the spectra by Lorentzian lines (green lines) is indicated by the solid red lines (see text).

Figure 3

(a) Computed displacement spectrum for single Ag (14) in PVP in the case of anisotropic elasticity (black curve with black dots) and isotropic elasticity (red symbols). Inset: The displacement map norm within the Ag NP associated with modes referred to as (1), (2), and (3) at ≈ 20, 76.6, and 113 GHz, respectively. (b) Simulated extinction cross-section of Ag (14)/PVP. Inset: The scattered E-field norm map depicted over a cross-section of the NP in the ozx-cut plane at λ₀ = 532 nm. (c) Simulated unpolarized OM coefficients versus the frequency for a Ag (14) NP placed in the PVP matrix (Figure S1a) convoluted with a Lorentzian curve having a full width at half maximum set to Δf = 1.5 GHz, and then divided by the square of frequency so to mimic the BLS spectrum of thermally excited phonons. Inset: The displacement map norm within NPs associated with the E_g mode (2) and higher frequency modes (4) to (7). (d) Frequency of the fundamental E_g (red line) computed for single Ag NP in the PVP matrix (red line slope 1069 m/s) as a function of the Ag diameter D.

Figure 4

(a) Computed displacement spectrum corresponding to the dimer geometry (Figure S1b) of 14.1 nm diameter Ag in the PVP matrix for a separation, d_dmr= 1 nm. Inset: The absolute displacement field map norm within Ag NPs associated with split modes referred to as (1), (2), (3), and (4). (b) Normalized extinction cross-section of the dimer and the x–component of the scattered E⃗–field with resonance wavelengths λ_r1 ≈ 432 nm and λ_r2 ≈ 525 nm.The vertical green line at 532 nm denotes the wavelength of the excitation laser light. (c) Frequency of the rattling mode (out-of-phase red, in-phase black symbols) and the E_g mode (out-of-phase blue, in-phase pink symbols) for a Ag dimer in the PVP matrix as a function of the Ag–Ag separation d_dmr. (d) Frequency of the out-of-phase rattling (black line) and in-phase E_g (red line) computed for the Ag dimer in the PVP matrix as a function of the Ag diameter D for a separation, d_dmr = 3 nm. The dashed blue line denotes the prediction of the fundamental E_g for a single Ag in the PVP matrix. The experimental frequency of the rattling and E_g modes for Ag with three different Ag diameters in PVP is denoted by black and red squares, respectively.

Figure 5

Anti-Stokes side of the BLS vibrational spectra of three polymer-grafted Ag films: (a) Ag@PS3k, (b) Ag@PIB3k with 20% metal, and (c) Ag@PIB3k with 65% metal (see Table 3). The insets show the reduced spectra of the main figures and the sharp peaks relate to the glass phonons at 90° (∼16 GHz) and artificial back scattering (∼32 GHz).