Random-close packing limits for monodisperse and polydisperse hard spheres

We investigate how the densities of inherent structures, which we refer to as the closest jammed configurations, are distributed for packings of 10000 frictionless hard spheres. A computational algorithm is introduced to generate closest jammed configurations and determine corresponding densities. Closest jamming densities for monodisperse packings generated with high compression rates using Lubachevsky–Stillinger and force-biased algorithms are distributed in a narrow density range from φ = 0.634-0.636 to φ ≈ 0.64; closest jamming densities for monodisperse packings generated with low compression rates converge to φ ≈ 0.65 and grow rapidly when crystallization starts with very low compression rates. We interpret φ ≈ 0.64 as the random-close packing (RCP) limit and φ ≈ 0.65 as a lower bound of the glass close packing (GCP) limit, whereas φ = 0.634-0.636 is attributed to another characteristic (lowest typical, LT) density φLT. The three characteristic densities φLT, φRCP and φGCP are determined for polydisperse packings with log-normal sphere radii distributions.