Percolation transitions in the hard‐sphere fluid

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 pe σ 3 = 0.0785 ± 0.01 and ρ pa σ 3 = 0.537 ± 0.005. The present value of ρ pe σ 3 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