Percolation transitions in the hard-sphere fluid



The number densities (ν/V) above or below which “pockets” of additional-sphere excluded volume (ρpe) and available volume (ρpa) 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 ρpeσ3 = 0.0785 ± 0.01 and ρpaσ3 = 0.537 ± 0.005. The present value of ρpeσ3 agrees with an interpolation of previous data for the percolation diameter (σp) for various densities from Heyes et al. The available volume (Va) 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 ρpa. 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