Anisotropic Hypersonic Phonon Propagation in Films of Aligned Ellipsoids

A material with anisotropic elastic mechanical properties and a direction-dependent hypersonic band gap is fabricated using ac electric field-directed convective self-assembly of colloidal ellipsoids. The frequency of the gap, which is detected in the direction perpendicular to particle alignment and entirely absent parallel to alignment, and the effective sound velocities can be tuned by the particle aspect ratio. We hypothesize that the band gap originates from the primary eigenmode peak, the $m$-splitted ($s$,1,2) mode, of the particle resonating with the effective medium. These results reveal the potential for powerful control of the hypersonic phononic band diagram by combining anisotropic particles and self-assembly.

Figure 1

(a) Schematic of the directed assembly process (not to scale). (b) SEM images of the top, side, and end view of the resulting aligned film for $a/b=3.99$.

Figure 2

(a) Selected BLS spectra of the infiltrated aligned films with aspect ratio $a/b=2.12$ and 3.52 at scattering wave vector $q$ values below ($0.0081{\mathrm{nm}}^{-1}$), near ($0.0106{\mathrm{nm}}^{-1}$ for 2.12, $0.0118{\mathrm{nm}}^{-1}$ for 3.52) and above ($0.0160{\mathrm{nm}}^{-1}$ for 2.12, $0.0167{\mathrm{nm}}^{-1}$ for 3.52) the value $q_{\mathrm{HG}}$ where the anisotropic hybridization gap (HG) opens. The anti-Stokes BLS spectra for propagation along ($q_{\parallel }$, blue) and normal ($q_{\perp }$, red) to the long axis are represented by either one or the sum of two Lorentzian curves (dotted lines). (b) Phononic band diagram for the $a/b=3.52$ aligned film in both propagation directions. A band gap (shaded region) is only observed in the $q_{\perp }$ direction (indicated by the horizontal red lines). (c) Phononic band diagram in the $q_{\parallel }$ propagation direction for $a/b=2.12$ (blue squares) and 3.99 (green diamonds) with seed spheres (black circles) as a reference. The lines fit the effective longitudinal sound velocity. (d) Same as (c) but for the $q_{\perp }$ propagation direction. The shaded regions indicate the frequency and scattering wave vector of the HG. The assembled spheres exhibit a Bragg-type band gap at high frequencies in addition to the HG irrespective of the direction.

Figure 3

Top: the effective sound velocity as a function of particle aspect ratio and thermal phonon propagation direction. Bottom: $q$-independent eigenmode spectra of seed spheres and ellipsoids (left panel) and frequency dependence of the $m$-splitted ($s$,1,2) peak and the hybridization gap in the $q_{\perp }$ direction. Inset images are FEM calculations for the vibrational deformation of the primary eigenmode peak.