The hard sphere glass transition

Abstract

The thermodynamic properties of hard sphere fluids and their glasses, from molecular dynamics simulations, are described within a unified formalism, by expressing the number of configurations of a fluid as a sum, over all its glasses, of the number of configurations of each glass. For pure hard spheres and a mixture this provides an equation of state that interpolates between the ideal gas low density limit and an ideal glass high density limit, and includes a thermodynamic glass transition. On a finite timescale, a real glass transition pre-empts the ideal one. The real transition occurs when the root-mean-square displacement of the spheres, on the simulation timescale, becomes smaller than a sphere diameter.