Phonon transport properties of particulate physical gels

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.

15 pages, 12 figures

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