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 φJ for equilibrated packings with initial densities φ ≤ 0.52 are located near the random close packing limit φRCP; the available phase space is dominated by basins of attraction that we associate with liquid. φRCP depends on the polydispersity and is ∼0.64 for monodisperse packings. For φ > 0.52, φJ 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 φg, φJ reaches the ideal glass density (the glass close packing limit) φGCP, so that the available phase space is dominated at φg by the basin of attraction of the ideal glass. For packings with sphere diameter standard deviation σ = 0.1, φGCP ≈ 0.655 and φg ≈ 0.59. For monodisperse and slightly polydisperse packings, crystallization is superimposed on these processes: it starts at the melting transition density φm and ends at the crystallization offset density φoff. For monodisperse packings, φm ≈ 0.54 and φoff ≈ 0.61. We verified that the results for polydisperse packings are independent of the generation protocol for φ ≤ φg.