Origin of the Acoustic Bandgaps in Hypersonic Colloidal Phononics: The Role of the Elastic Impedance

Abstract

How phonons propagate in nanostructures determines the flow of elastic and thermal energy in dielectric materials. However, a reliable theoretical prediction of the phonon dispersion relation requires experimental verification both near to and far from the Brillouin zone of the nanostructure. We report on the experimental hypersonic phonon dispersion of hard (SiO 2 ) and soft (polymer) fcc colloidal crystals infiltrated in liquid polydimethylsiloxane with different elastic impedance contrast using Brillouin light spectroscopy. We discuss the distinct differences with first-principles full elastodynamic calculations involving a multiple-scattering theory. Interparticle contacts strongly impact the long-wavelength speed of sound and the nature of the particle vibration resonance-induced hybridization hypersonic bandgap. The absence of the order-induced Bragg bandgap in SiO 2 and its presence in soft opals cannot be fully accounted for by the theory, limiting its predictive power. Bridging the elasticity of the two colloidal crystals with suitable SiO 2 core–shell (polymer) particles reveals an unprecedented crossover behavior in the dispersion relation. In view of many conversational parameters, the control tuning of phonon propagation in soft matter-based hypersonic phononics remains challenging.

Tunable Hypersonic Bandgap Formation in Anisotropic Crystals of Dumbbell Nanoparticles

“…Therefore, mechanical interactions (i.e., overlapping nanoparticles) are necessary to achieve a theoretical effective sound velocity comparable to that of the experimental one. We have found similar theoretical trends in the case of fcc crystals of PS spheres, where the jump from the liquid-like acoustic branch to the longitudinal branch results in an abrupt increase in the effective sound velocity as particles begin to overlap even less than 1% …”

“…It appears that the interfacial contact changes the origin of the HG from the quadrupolar (l = 2) to dipole (l = 1) particle resonance in both SiO 2 (hard) and poly(methyl methacrylate) (soft) colloidal crystals. 14 This type of HG was reported in polymer-tethered colloids which, in contrast to the previous resonant units, exhibit an inhomogeneous density profile. 23 Although the realization of hypersonic phononic bandgaps in assembled submicron colloids is well-established, 10,11,14,[17][18][19]23,24 each phononic material is limited to a single bandgap position, requiring a different material in order to target a wider range of frequencies.…”

“…We have found similar theoretical trends in the case of fcc crystals of PS spheres, where the jump from the liquid-like acoustic branch to the longitudinal branch results in an abrupt increase in the effective sound velocity as particles begin to overlap even less than 1%. 14 Returning to the hybridization bandgap, the HG width, Δf/ f HG ∼ 12% resolves due to the strong resonance of the dumbbell particles in the PDMS matrix. HG in disordered spherical colloid films is caused by an anticrossing of two bands with the same symmetry and occurs at q HG d ∼ 3.2 and f HG d/ c eff ∼ 0.5 with d being the NP diameter.…”

“…The BG position may be varied by changing particle size, which changes the lattice parameter of the crystal. In addition to the observations of phononic bandgaps by BLS, − thermally simulated phonon techniques, such as time-resolved picosecond ultrasonics, laser-induced transient grating, and a recently reported frequency-domain hybrid technique have been employed. Pump–probe picosecond ultrasonics provides indirect evidence of a bandgap in silica opals through a surface localized vibration with a frequency located inside the calculated phononic bandgap. , …”

Simultaneous occurrence and compensating effects of multi‐type disorder in two‐dimensional photonic structures

“…Most recently, the topic of transport in disordered structures has also reached the field of acoustics. [23,24] In spite of these manifold applications, fundamental investigations of the functionality limits of real photonic systems have so far looked at individual geometric types disorder, [25][26][27] yet mostly neglected correlations between several types of disorder and the respective influence on device performance. [28] However, these can play a decisive role: deviations from ideal crystallinity occur both in natural and artificial systems.…”