Perturbation theory and the thermodynamic properties of fluids. II. The CRIS model

This paper is the second of three articles describing a hard sphere perturbation theory of liquids and dense gases. The general theory presented in the preceding paper is used to derive a model for calculating thermodynamic properties. Three approximations are made. First, we assume that each molecule is located at the center of a spherical shell formed by its neighbors. The radius of this shell varies throughout the fluid according to a distribution function which is known for hard spheres. Second, the coordination number varies along with the nearest neighbor distance in such a way that the volume per molecule is constant and equal to the macroscopic value. Third, the potential energy of a molecule in the field of its neighbors depends only on the nearest neighbor distance and coordination number. Using this approximation, the energy of a liquid molecule can be calculated from the zero-temperature isotherm of the solid at the same nearest neighbor distance. There are no adjustable parameters in the theory. All that is needed to apply the model is the cold curve of the solid, which can be obtained from either theory or experiment