The chemical potential in non-ideal liquid mixtures

Abstract

We report Monte Carlo calculations for two non-ideal binary mixtures of Lennard-Jones fluids A and B. In the first the molecules have the same diameter but different well depths, ε_AA = 2ε_BB . In the second the well depths are the same but the diameters differ, (σ _AA /σ _BB )³=2·144. The chemical potentials of both components are obtained over the entire range of compositions, using a modified test particle method called f-g sampling. The simulation data are used to test a variety of mixture theories based on both the n-fluid idea and on a perturbation expansion about a mixture of hard spheres. Of the n-fluid theories the van der Waals 1- and 2-fluid theories are best in general. However, none of the n-fluid theories give good results when the molecular size ratio parameter (σ _AB /σ _BB )³ differs from unity by more than about 30 or 40 per cent. When the molecules are appreciably different in size the Leonard-Henderson-Barker (LHB) and Lee-Levesque (LL) forms of hard sphere perturbation theory are both much better than the n-fluid theories, with the LL theory in closest agreement with the simulation results.