A parameterised equation of state, glass transition and jamming of the hard sphere system

TL;DR

This paper develops a parameterised equation of state for hard sphere systems using a Gamma-distribution based potential energy landscape theory, accurately modeling pressure and thermodynamics across glassy and jammed states, and analyzing transport properties near the glass transition.

Contribution

It introduces a novel parameterised EoS incorporating a singularity term for glassy and jammed states, and provides the first analytical EoS for the ideal glass transition in hard spheres.

Findings

Accurately models pressure across metastable and glassy regions.

Identifies a singularity at random close packing, matching simulation data.

Shows both Arrhenius and entropy scaling laws fail at specific packing fractions.

Abstract

A Gamma-distribution based potential energy landscape (PEL) theory has recently been proposed for supercooled liquids and glasses. This new PEL theory introduces a singularity term in the equation of state (EoS) suitable for representing the pressure of a glassy or jammed system. Using this framework, a parameterised EoS, Z(eta J), is developed with the random-jammed-packing fraction, eta J, as an input. This EoS is capable of accurately calculating the compressibility (pressure) across the entire metastable and glassy region from eta J=0.62 to 0.66, while seamlessly passing through the stable fluid region. Two special cases (paths) are examined in detail. The first path exhibits a singularity at the random close packing eta J=eta rcp=0.64, traversing the metastable region explored by most simulations. Various thermodynamic properties calculated are compared to simulation data, showing excellent agreements. The second case addresses the first analytical EoS for the ideal glass transition in the hard sphere system. Finally, the transport properties of the hard sphere fluid are modeled using the Arrhenius law and the excess entropy scaling law. It is found that both laws fail (with slope changing) at eta=0.555, where the heat capacity peaks and the contributions of inherent structures and jamming effects begin to emerge.