Equilibrium glassy phase in a polydisperse hard sphere system

TL;DR

This study maps the phase diagram of a polydisperse hard sphere system, revealing a transition from crystalline to glassy phases and identifying a terminal polydispersity beyond which the glass is the equilibrium state.

Contribution

It introduces a numerical minimization approach of the Ramakrishnan-Yussouff free energy to analyze phase behavior in polydisperse hard spheres, highlighting the glass as the equilibrium phase at high polydispersity.

Findings

Glass becomes the equilibrium phase beyond a critical polydispersity.

Crystalline phase disappears at the terminal polydispersity.

A crystal-glass transition occurs with increasing density at high polydispersity.

Abstract

The phase diagram of a polydisperse hard sphere system is examined by numerical minimization of a discretized form of the Ramakrishnan-Yussouff free energy functional. Crystalline and glassy local minima of the free energy are located and the phase diagram in the density-polydispersity plane is mapped out by comparing the free energies of different local minima. The crystalline phase disappears and the glass becomes the equilibrium phase beyond a "terminal" value of the polydispersity. A crystal to glass transition is also observed as the density is increased at high polydispersity. The phase diagram obtained in our study is qualitatively similar to that of hard spheres in a quenched random potential.