Thermodynamic status of random close packing

Abstract

An amorphous ground state reminiscent of random close packing (RCP) of spheres terminates a liquid phase that spans all temperatures. On the Gibbs density surface, the liquid phase has bounded by a supercritical percolation line, two-phase liquid–gas coexistence line, and below the triple point, the metastable liquid branch terminating at T = 0 K with the RCP state. There is no “continuity of gas and liquid phases”; they are separated by a supercritical mesophase bounded by percolation transitions. As a consequence, the gas phase cannot be a starting point for liquid-state theory. RCP has a thermodynamic status. For square-well model fluids, evidence from computer simulations shows that the amorphous ground state is the same RCP state of the hard-sphere model. The RCP limiting density state of the hard-sphere fluid, with its reproducible and well-characterized structure, can be obtained by well-defined irreversible and reversible processes which establish a thermodynamic status. Empirical results, within margins of numerical uncertainty, are that the amorphous ground state density corresponds to a packing fraction = 0.6366 ± 0.0005 (Buffon’s constant 2/π) and a residual entropy per sphere ΔS(0) ∼ kB (Boltzmann constant). We conclude that RCP of spheres is a well-defined state with a thermodynamic status, and a central role in the description of liquid phase equilibria, as originally suggested, 50 years ago, by J.D. Bernal. We postulate that the metastable RCP state is the starting point for a modern theory of the liquid state.