Percolation transitions in the hard-sphere fluid

Abstract

The number densities (ν/V) above or below which “pockets” of additional-sphere excluded volume (ρ_pe) and available volume (ρ_pa) begin to percolate the whole volume of the system, sometimes referred to as percolation thresholds, have been determined for the equilibrium hard-sphere fluid of diameter σ using a Monte Carlo (MC) approach. Values obtained are ρ_peσ³ = 0.0785 ± 0.01 and ρ_paσ³ = 0.537 ± 0.005. The present value of ρ_peσ³ agrees with an interpolation of previous data for the percolation diameter (σ_p) for various densities from Heyes et al. The available volume (V_a) can be resolved as a “radial acceptance function” (u(r)), which is easily obtained from MC acceptance ratio statistics providing a direct route to the chemical potential up to liquid-like densities. The closed-virial equation-of-state of the hard-sphere fluid is found to deviate slightly, but significantly from thermodynamic pressures at densities exceeding ρ_pa. Knowledge of the hard-sphere fluid percolation transitions could lead to a more formal description of the critical point and origins of the liquid state, in the spirit of van der Waals. © 2011 American Institute of Chemical Engineers AIChE J, 2012