Heat transport in model jammed solids

TL;DR

This study numerically investigates vibrational modes and heat transport in 3D jammed soft sphere packings, revealing how the crossover frequency and diffusivity behavior influence thermal conductivity near the rigidity transition.

Contribution

It provides a detailed numerical analysis of vibrational modes and energy diffusivity in jammed solids, linking microscopic properties to macroscopic thermal transport.

Findings

Crossover frequency shifts to zero at the rigidity threshold.

Diffusivity exhibits a power-law divergence below the crossover.

Thermal conductivity near the jamming transition matches experimental glass data.

Abstract

We calculate numerically the normal modes of vibrations in 3D jammed packings of soft spheres as a function of the packing fraction and obtain the energy diffusivity, a spectral measure of transport that controls sound propagation and thermal conductivity. The crossover frequency between weak and strong phonon scattering is controlled by the coordination and shifts to zero as the system is decompressed towards the critical packing fraction at which rigidity is lost. Below the crossover, the diffusivity displays a power-law divergence with inverse frequency, which suggests that the vibrational modes are primarily transverse waves, weakly scattered by disorder. Above it, a large number of modes appear whose diffusivity plateaus at a nearly constant value independent of the inter-particle potential, before dropping to zero above the Anderson localization frequency. The thermal conductivity of a marginally jammed solid just above the rigidity threshold is calculated and related to the one measured experimentally at room temperature for most glasses.