title: Mean-field theory of random close packings of axisymmetric particles.
abstract: Finding the optimal random packing of non-spherical particles is an open problem with great significance in a broad range of scientific and engineering fields. So far, this search has been performed only empirically on a case-by-case basis, in particular, for shapes like dimers, spherocylinders and ellipsoids of revolution. Here we present a mean-field formalism to estimate the packing density of axisymmetric non-spherical particles. We derive an analytic continuation from the sphere that provides a phase diagram predicting that, for the same coordination number, the density of monodisperse random packings follows the sequence of increasing packing fractions: spheres <oblate ellipsoids <prolate ellipsoids <dimers <spherocylinders. We find the maximal packing densities of 73.1% for spherocylinders and 70.7% for dimers, in good agreement with the largest densities found in simulations. Moreover, we find a packing density of 73.6% for lens-shaped particles, representing the densest random packing of the axisymmetric objects studied so far.
authors.affiliation: Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA.
authors.forename: Adrian
authors.initials: A
authors.lastname: Baule
authors.forename: Romain
authors.initials: R
authors.lastname: Mari
authors.forename: Lin
authors.initials: L
authors.lastname: Bo
authors.forename: Louis
authors.initials: L
authors.lastname: Portal
authors.forename: Hernán A
authors.initials: HA
authors.lastname: Makse