An estimate of random close packing density in monodisperse hard spheres

Using a simple model for local packing of hard spheres in random close packing state and statistical argument, we have shown that the corresponding packing density on average is 0.64. We assume that a central sphere forms a local cluster with three other spheres. Two of the neighboring ones are in direct contact with the central sphere that in turn support the third one that may or may not be in contact with the central sphere. Based on this cluster configuration the maximum and minimum limits of solid angles between the central sphere and its neighbors are determined. On the other hand, we use the fact that the average nearest neighbors per sphere in hard sphere glass is 12.5 when the close packed (crystal) assembly with 12 nearest-neighbors collapses. Some of these nearest neighbors are in direct contact with the central sphere, forming “touching” neighbors; and the rest may not be in direct contact with the central one but are in contact with other nearest neighbors, forming the “supported” neighbors. The topological model and the statistical data allow us to derive the random close packing density for the monodisperse sphere packing.