Influence of particle size distribution on random close packing of spheres

The densest amorphous packing of rigid particles is known as random close packing. It has long been appreciated that higher densities are achieved by using collections of particles with a variety of sizes. For spheres, the variety of sizes is often quantified by the polydispersity of the particle size distribution: the standard deviation of the radius divided by the mean radius. Several prior studies quantified the increase of the packing density as a function of polydispersity. A particle size distribution is also characterized by its skewness, kurtosis, and higher moments, but the influence of these parameters has not been carefully quantified before. In this work, we numerically generate many sphere packings with different particle radii distributions, varying polydispersity and skewness independently of one another. We find that the packing density can increase significantly with increasing skewness and in some cases skewness can have a larger effect than polydispersity. However, the packing fraction is relatively insensitive to the higher moment value of the kurtosis. We present a simple empirical formula for the value of the random close packing density as a function of polydispersity and skewness.