On the jamming phase diagram for frictionless hard-sphere packings

Abstract

We computer-generated monodisperse and polydisperse frictionless hard-sphere packings of 10⁴ particles with log-normal particle diameter distributions in a wide range of packing densities φ (for monodisperse packings φ = 0.46–0.72). We equilibrated these packings and searched for their inherent structures, which for hard spheres we refer to as closest jammed configurations. We found that the closest jamming densities φ_J for equilibrated packings with initial densities φ ≤ 0.52 are located near the random close packing limit φ_RCP; the available phase space is dominated by basins of attraction that we associate with liquid. φ_RCP depends on the polydispersity and is ∼0.64 for monodisperse packings. For φ > 0.52, φ_J increases with φ; the available phase space is dominated by basins of attraction that we associate with glass. When φ reaches the ideal glass transition density φ_g, φ_J reaches the ideal glass density (the glass close packing limit) φ_GCP, so that the available phase space is dominated at φ_g by the basin of attraction of the ideal glass. For packings with sphere diameter standard deviation σ = 0.1, φ_GCP ≈ 0.655 and φ_g ≈ 0.59. For monodisperse and slightly polydisperse packings, crystallization is superimposed on these processes: it starts at the melting transition density φ_m and ends at the crystallization offset density φ_off. For monodisperse packings, φ_m ≈ 0.54 and φ_off ≈ 0.61. We verified that the results for polydisperse packings are independent of the generation protocol for φ ≤ φ_g.