Thermalized connectivity networks of jammed packings

TL;DR

This study investigates how finite temperature affects the elastic properties of jammed sphere packings, revealing counterintuitive softening and stiffening behaviors linked to soft mode spectra, with implications for marginal solids.

Contribution

It introduces an analysis of thermal effects on connectivity networks in jammed packings, highlighting behaviors at finite temperature ignoring bond breaking, and connects these to soft mode spectra near isostaticity.

Findings

Bulk modulus softens rapidly with temperature.

Shear modulus stiffens in fixed volume ensemble.

Soft mode spectrum resembles buckling instability spectrum.

Abstract

Jammed packings of repulsive elastic spheres have emerged as a rich model system within which elastic properties of disordered glassy materials may be elucidated. Most of the work on these packings have focused on the case of vanishing temperature. Here, we explore the elastic properties of the associated connectivity network for finite temperatures, ignoring the breaking of bonds and the formation of new ones. Using extensive Monte Carlo simulations, we find that, as the temperature is increased, the resulting spring network shrinks and exhibits a rapidly softening bulk modulus via a cusp. Moreover, the shear modulus stiffens in a fixed volume ensemble but not in a fixed pressure ensemble. These counter-intuitive behaviors may be understood from the characteristic spectrum of soft modes near isostaticity, which resembles the spectrum of a rod near its buckling instability. Our results suggest a generic mechanism for negative thermal expansion coefficients in marginal solids. We discuss the consequences of bond breaking and an apparent analogy between thermalization and shear.