  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. 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. Of course, 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 packings with different particle radii distributions,
varying polydispersity and skewness independently of one another. We find two
significant results. First, the skewness can have a significant effect on the
packing density and in some cases can have a larger effect than polydispersity.
Second, the packing fraction is relatively insensitive to the 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.
