A STUDY OF THE PAIR DISTRIBUTION FUNCTIONS OF MIXTURES OF IDEALIZED MOLECULES USING MOLECULAR SIMULATION

The partial pair distribution functions describe the average conformation of groups of molecules in a mixture. The functions are used in the conformal solution theories of Leland et al, who assume that the thermodynamic properties of mixtures can be calculated from the corresponding properties of a pure-fluid reference using the Mean Density Approximation (MDA). The MDA assumes that the partial distribution functions for a pair of components i and j, in a mixture can be approximated by the total distribution functions of a pure-fluid reference. The reference fluid consists of a single molecular type with intermolecular potential parameters that are averages of the potential parameters of components i and j. Although the validity of the MDA is assumed in the solution theories of Leland et al, the value of the mean density has not been rigorously defined before, nor has the MDA been systematically studied. An analysis of the Ornstein-Zernike equation showed that the pure-fluid reference can be chosen only when the component molecules in the mixture have similar intermolecular potential parameters. Under this condition, the best choice for the pure-fluid reference is such that the packing fraction in the reference is the same as that in the original mixture. To test the MDA, the partial pair distribution functions of mixtures and the total distribution functions of pure fluids were generated, using the Metropolis Monte Carlo method. The MDA was found to be accurate for hard-sphere mixtures even when the molecular diameter ratios are as large as two. The approximation is less accurate for Lennard-Jones mixtures, especially when the components have very different intermolecular potentials. In fluids of non-spherical molecules, the MDA is used to approximate the angle-averaged partial pair distribution functions of the spherocylinder fluid by the distribution functions of a pure-fluid of spherical molecules. The structure of a fluid of spherocylinder molecules was found to depend very strongly on the shape of the component molecules indicating that the MDA is inaccurate for such systems