Simultaneous Occurrence of Structure-Directed and Particle-Resonance-Induced Phononic Gaps in Colloidal Films

We report on the observation of two hypersonic phononic gaps of different nature in three-dimensional colloidal films of nanospheres using Brillouin light scattering. One is a Bragg gap occurring at the edge of the first Brillouin zone along a high-symmetry crystal direction. The other is a hybridization gap in crystalline and amorphous films, originating from the interaction of the band of quadrupole particle eigenmodes with the acoustic effective-medium band, and its frequency position compares well with the computed lowest eigenfrequency. Structural disorder eliminates the Bragg gap, while the hybridization gap is robust.

Figure 1

SEM top-view images of the PS-307 crystal (left) and the PS-hybrid (right)—both “dry” before infiltration (scale bar is $1\mu \mathrm{m}$). The insets display the Fourier-transform images computed from the SEM pictures over an area of about $4\mu \mathrm{m}$ by $4\mu \mathrm{m}$.

Figure 2

BLS spectra of the wet opal of PS spheres with diameter 307 nm in a PDMS matrix at different wave vectors in the (111) plane of the fcc crystalline colloidal film. The edge of the BZ along the probed direction corresponds to $q_{\mathrm{BZ}}\approx 0.013{\mathrm{nm}}^{-1}$. The deconvolution in different spectral components is indicated for the Stokes side of the spectrum, and the representation of the experimental spectra by the superposition of these Lorentzian lines is shown for the anti-Stokes side. Each spectrum is normalized to the total integrated intensity, for comparison of the relative contributions.

Figure 3

Phononic band diagrams for the different PS wet opals under consideration, along the $\Gamma –M$ direction (see text). The hatched bands mark the phononic gaps, and the vertical arrows indicate the $q$ values in the corresponding spectra of Fig. 2, 4 below. The vertical lines denote the first BZ limit (for $d=307\mathrm{nm}$ and $d=360\mathrm{nm}$, respectively). The change in the DOS induced by the corresponding single PS particle in PDMS is shown in the right-hand panel.

Figure 4

Exemplary BLS spectra of the PS $(d=360\mathrm{nm})/\mathrm{PDMS}$ wet opal (bottom) and the wet PS-hybrid colloidal film (top) at two $q$ values indicated by the arrows in the corresponding diagram of Fig. 3. The deconvolution into different spectral components is shown below each spectrum (note the absence of the BG-induced spectral features in the hybrid).