Phonon transport properties of particulate physical gels

TL;DR

This study investigates how the unique multiscale structure of particulate physical gels influences phonon transport, revealing multiple crossover behaviors and strong scattering effects that lead to phonon localization.

Contribution

It demonstrates the extension of multiscale vibrational characteristics to phonon transport properties, identifying specific crossover frequencies and the localization of phonons in physical gels.

Findings

Phonon transport shows two distinct crossovers at characteristic frequencies.

Both transverse and longitudinal phonons transition from Rayleigh scattering to diffusive damping.

The Ioffe--Regel limit occurs at a low frequency, indicating phonon localization.

Abstract

Particulate physical gels are sparse, low-density amorphous materials in which clusters of glasses are connected to form a heterogeneous network structure. This structure is characterized by two length scales, $\xi_s$ and $\xi_G$: $\xi_s$ measures the length of heterogeneities in the network structure, and $\xi_G$ is the size of glassy clusters. Accordingly, the vibrational states of such a material also exhibit a multiscale nature with two characteristic frequencies, $\omega_\ast$ and $\omega_G$, which are associated with $\xi_s$ and $\xi_G$, respectively: (i) phonon-like vibrations in the homogeneous medium at $\omega < \omega_\ast$, (ii) phonon-like vibrations in the heterogeneous medium at $\omega_\ast < \omega < \omega_G$, and (iii) disordered vibrations in the glassy clusters at $\omega > \omega_G$. Here, we demonstrate that the multiscale characteristics seen in the static structures and vibrational states also extend to the phonon transport properties. Phonon transport exhibits two distinct crossovers at the frequencies $\omega_\ast$ and $\omega_G$~(or at wavenumbers of $\sim \xi_s^{-1}$ and $\sim \xi_G^{-1}$). In particular, both transverse and longitudinal phonons cross over between Rayleigh scattering at $\omega < \omega_\ast$ and diffusive damping at $\omega>\omega_\ast$. Remarkably, the Ioffe--Regel limit is located at the very low frequency of $\omega_\ast$. Thus, phonon transport is localized above $\omega_\ast$, even where phonon-like vibrational states persist. This markedly strong scattering behavior is caused by the sparse, porous structure of the gel.