Equations of state and gas–gas separation in soft-sphere mixtures

The Monte Carlo method is used to compute equations of state for mixtures having intermolecular pair potentials of the form u(r)=ε(σ/r)n, where n=12 and n=6. Calculations are given for binary equimolar mixtures with additive diameters having the ratio σ1/σ2=3. In contrast to hard sphere mixtures, it is found that soft-sphere mixtures have a positive volume of mixing at high pressures. For the mixture with n=6, this effect leads to the separation of two fluid phases at a pressure that is below the freezing point of the larger component. These results show that, under certain conditions, large differences in molecular size are sufficient to cause this type of phase separation. The ideal mixing and van der Waals one-fluid (vdW1) theories are also discussed, and the predictions of these two models are compared with the Monte Carlo data. The vdW1 approximation gives satisfactory results at low pressures but is poorer than ideal mixing at high pressures.