Universal Jamming Phase Diagram in the Hard-Sphere Limit

TL;DR

This paper introduces a universal jamming phase diagram for sphere-based glass-forming fluids, revealing that at low pressure, system behavior is independent of interaction details when scaled appropriately, unifying various prior results.

Contribution

The authors propose a new universal formulation of the jamming phase diagram using dimensionless variables, demonstrating its applicability across different interaction potentials at low pressure.

Findings

Phase diagram is universal at low pressure when scaled properly.

Observables like relaxation time collapse onto hard sphere values.

The shape of the jamming surface is determined and related to previous results.

Abstract

We present a new formulation of the jamming phase diagram for a class of glass-forming fluids consisting of spheres interacting via finite-ranged repulsions at temperature $T$, packing fraction $\phi$ or pressure $p$, and applied shear stress $\Sigma$. We argue that the natural choice of axes for the phase diagram are the dimensionless quantities $T/p\sigma^3$, $p\sigma^3/\epsilon$, and $\Sigma/p$, where $T$ is the temperature, $p$ is the pressure, $\Sigma$ is the stress, $\sigma$ is the sphere diameter, $\epsilon$ is the interaction energy scale, and $m$ is the sphere mass. We demonstrate that the phase diagram is universal at low $p\sigma^3/\epsilon$; at low pressure, observables such as the relaxation time are insensitive to details of the interaction potential and collapse onto the values for hard spheres, provided the observables are non-dimensionalized by the pressure. We determine the shape of the jamming surface in the jamming phase diagram, organize previous results in relation to the jamming phase diagram, and discuss the significance of various limits.