Rigidity of glasses and jamming systems at low temperatures

TL;DR

This paper presents a microscopic scheme to compute the rigidity of glasses and jamming systems at low temperatures, revealing entropic rigidity behavior that diverges near the jamming transition.

Contribution

It extends existing methods to include repulsive contact systems, providing a unified approach to rigidity in glasses and jamming systems at low temperatures.

Findings

Rigidity proportional to temperature in repulsive contact systems.

Rigidity diverges approaching the jamming density.

Method applicable to both harmonic glasses and contact systems.

Abstract

We discuss a microscopic scheme to compute the rigidity of glasses or the plateau modulus of supercooled liquids by twisting replicated liquids. We first summarize the method in the case of harmonic glasses with analytic potentials. Then we discuss how it can be extended to the case of repulsive contact systems : the hard sphere glass and related systems with repulsive contact potentials which enable the jamming transition at zero temperature. For the repulsive contact systems we find entropic rigidity which behaves similarly as the pressure in the low temperature limit: it is proportional to the temperature and tends to diverge approaching the jamming density with increasing volume fraction, which may account for experimental observations of rigidities of repulsive colloids and emulsions.