Phonon transport properties of particulate physical gels.

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, ξ and ξ: ξ measures the length of heterogeneities in the network structure and ξ is the size of glassy clusters. Accordingly, the vibrational states (eigenmodes) of such a material also exhibit a multiscale nature with two characteristic frequencies, ω and ω, which are associated with ξ and ξ, respectively: (i) phonon-like vibrations in the homogeneous medium at ω<ω, (ii) phonon-like vibrations in the heterogeneous medium at ω<ω<ω, and (iii) disordered vibrations in the glassy clusters at ω > ω. 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 frequencies ω and ω (or at wavenumbers of ∼ξ and ∼ξ ). In particular, both transverse and longitudinal phonons cross over between Rayleigh scattering at ω<ω and diffusive damping at ω>ω. Remarkably, the Ioffe-Regel limit is located at the very low frequency of ω. Thus, phonon transport is localized above ω, even where phonon-like vibrational states persist. This markedly strong scattering behavior is caused by the sparse, porous structure of the gel.