Perturbation theory for mixtures of simple liquids

Abstract

The perturbation approach developed by Weeks, Chandler, and Andersen (WCA) and by Verlet and Weis (VW) for pure systems is here generalized to the case of mixtures. We study binary mixtures of molecules interacting with the 12–6 Lennard-Jones potential, for which Monte Carlo simulations are available for comparison. The work is divided into two parts: The first part presents results of Monte Carlo calculations on mixtures of hard spheres of 864 and 1000 particles. The radial distribution functions generated are used to test the VW representation for the correlation functions of hard-sphere mixtures. This representation is found to work satisfactorily within the expected error limits. The second part deals with the two-step perturbation procedure for calculating the thermodynamic quantities of the Lennard-Jones system. The Lennard-Jones potential is divided into a reference potential, which is strictly repulsive, and an attractive part. The system of the reference potential is represented by a system of hard-sphere mixture with equivalent diameters determined by the WCA rule. Analytical expressions are given for evaluating these equivalent diameters. The Lennard-Jones system is then recovered to the first order by a λ expansion over the reference system. Comparison with Monte Carlo results for a mixture of Lennard-Jones molecules, obeying the Berthelot rule, shows that the total thermodynamic properties are reproduced by the perturbation theory to 1 per cent, while the agreement in excess properties is only moderately successful, similar to some other analytical theories compared here. To reproduce these excess properties, which are extremely small, a precision of 0·1 per cent in the theory is required. The present theory is estimated to be accurate to 1 per cent in view of the successive approximations made.