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Percolation transitions in the hard‐sphere fluid
Author(s) -
Woodcock Leslie V.
Publication year - 2012
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.12666
Subject(s) - percolation (cognitive psychology) , volume (thermodynamics) , van der waals force , thermodynamics , monte carlo method , excluded volume , percolation threshold , virial coefficient , equation of state , hard spheres , statistical physics , physics , chemistry , mathematics , statistics , quantum mechanics , polymer , nuclear magnetic resonance , neuroscience , molecule , biology , electrical resistivity and conductivity
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