Studies in Molecular Dynamics. III. A Mixture of Hard Spheres

For an equimolar mixture of hard spheres differing in radius by a factor of 3 it is shown that the numerical method gives the thermodynamic properties within 1% accuracy in the fluid region but generates metastable states at solid densities. The Percus—Yevick theory for mixtures is shown to be as accurate as for pure systems, which makes it plausible that no two-fluid phase region exists for mixtures of spheres. The volume of the mixture is found to be always smaller than the volume of the two pure fluid components, however, at high pressures when a solid and fluid must be mixed to give a fluid mixture, the excess volume is positive. The excess properties are small so that the assumption of ideal mixing (no excess volume) leads to an accurate prediction of the properties of hard sphere mixtures. Furthermore, the conclusion can be drawn that the excess properties in mixing ordinary liquids are primarily determined by differences in the attractive potentials rather than solely by the molecular sizes of the pure components.