The statistical thermodynamics of mixtures of Lennard-Jones molecules II. Deviations from random mixing

Abstract This paper describes a new statistical treatment of ordering effects in mixtures of spherical molecules, based on a general expansion of the Helmholtz free-energy function about the condition of random mixing. This expansion is similar to that introduced by Kirkwood (1938) for lattice theories, but unlike the latter is based only on the canonical distribution of petit ensemble theory. It is shown that for mixtures of Lennard-Jones molecules the moments in the expansion can be reduced to non-thermodynamic statistical functions of a single reference substance; and by using the assumptions of the cell model, these functions are related to thermodynamic properties. The first approximations for the thermodynamic functions of ordering are discussed for a certain class of mixtures, and it is shown that although ordering effects are small in mixtures of molecules of equal size, they can be large when the molecules differ in size. The equations are used to calculate the ordering effects in liquid mixtures of carbon monoxide and methane.