Jamming in hard sphere and disk packings

Abstract

Hard-particle packings have provided a rich source of outstanding theoretical problems and served as useful starting points to model the structure of granular media, liquids, living cells, glasses, and random media. The nature of “jammed” hard-particle packings is a current subject of keen interest. Elsewhere, we introduced rigorous and efficient linear-programming algorithms to assess whether a hard-sphere packing is locally, collectively, or strictly jammed, as defined by Torquato and Stillinger [J. Phys. Chem. B 105, 11849 (2001)]. One algorithm applies to ideal packings in which particles form perfect contacts. Another algorithm treats the case of jamming in packings with significant interparticle gaps. We have applied these algorithms to test jamming categories of ordered lattices as well as random packings of circular disks and spheres under periodic boundary conditions. The random packings were produced computationally with a variety of packing generation algorithms, all of which should, in principle, produce at least collectively jammed packings. Our results highlight the importance of jamming categories in characterizing particle packings. One important and interesting conclusion is that the amorphous monodisperse sphere packings with density φ≈0.64 were for practical purposes strictly jammed in three dimensions, but in two dimensions the monodisperse disk packings at previously reported “random close packed” densities of φ≈0.83 were not even collectively jammed. On the other hand, amorphous bidisperse disk packings with density of φ≈0.84 were virtually strictly jammed. This clearly demonstrates one cannot judge “stability” in packings based solely on local criteria. Numerous interactive visualization models are provided on the authors’ webpage.