Theoretical analysis of the achievement of random close packing of hard spheres and a conjecture on spinodal decomposition

Abstract

We report the results of an analysis of bifurcation points of the nonlinear equation for the density distribution in an inhomogeneous system. The theory used predicts the freezing transition. In addition, if the unstable fluid branch of the solution beyond the freezing point is followed to higher density, another bifurcation point is found. This latter bifurcation point is identical with the limit of compression of the system, i.e., achievement of random close packing in the fluid. The density of random close packing of hard spheres is predicted to be 1.202, in very good agreement with computer simulation data. We show that the second bifurcation point is a limit of the first bifurcation point and that no freezing transition is possible beyond this point. Comparison of the behavior of the hard-sphere and Lennard-Jones fluids leads to the conjecture that spinodal decomposition of the Lennard-Jones fluid occurs when the density, computed with a temperature- and density-dependent effective hard-sphere diameter, reaches the value corresponding to random close packing of hard spheres.