``Improved'' Free-Volume Theory of Liquids. II

Abstract

The Kirkwood nonlinear integral equation for determining the optimum free volume of a liquid is integrated by an iterative procedure with the approximation that the cell distribution function is spherically symmetrical. The potential of the system is assumed to be pairwise additive and the interaction between two molecules obeys the Lennard-Jones 12–6 potential. To simplify the computations, the contributions to the cell potential by molecules beyond the first shell of nearest neighbors are calculated as though the molecules were located at their lattice points. The method of Levine, Mayer, and Aroeste was used to optimize the lattice dimensions and take into account the existence of holes. Extensive tables are given for the configurational internal energy, compressibility factor, and configurational entropy. Comparison of the configurational internal energy and compressibility factor with the Monte Carlo calculations indicates that our isotherms correspond to extensions of the crystalline phase into a metastable low density region. Comparison of our configurational entropy with experimental data indicates that we are lacking the entropy of fusion. Our values of the configurational internal energy agree rather well and our values of the compressibility factor agree very poorly with the experimental data. Comparisons are also made with the results of other theoretical treatments.