Mean-field approach for random close packings of non-spherical particles

Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations involved. Here, a mean field theory based on a statistical treatment of the Voronoi volume is discussed, which allows for the calculation of the random close packing fractions of spherical as well as non-spherical particles [1]. This approach captures in particular the density peaks observed in simulations of different classes of non-spherical shapes. A phase diagram is presented that describes packings of elongated shapes such as spherocylinders and dimers in terms of an analytic continuation from the spherical random close packing [2].

[1] A. Baule, R. Mari, L. Bo, L. Portal, and H. A. Makse, Nature Commun. 4, 2194 (2013)
[2] A. Baule and H. A. Makse, Soft Matter 10, 4423 (2014)