The thermodynamics of mixtures and the corresponding mixing rules in the SAFT-VR approach for potentials of variable range

Abstract

The statistical associating fluid theory (SAFT) has been extended recently to describe the thermodynamic properties of chain molecules formed from monomeric segments interacting with attractive potentials of variable range (VR) (Gil-Villegas, A., Galindo, A., Whitehead, P. J., Mills, S. J., Jackson, G., and Burgess, A. N., 1997, J. chem. Phys., 106, 4168). The SAFTVR approach is based on an accurate and compact representation of the free energy of chain molecules in terms of the contact value of the radial distribution function of the monomer reference system. This paper takes advantage of the SAFT-VR approach to focus on the nature of the expressions for mixtures of non-conformal molecules. A number of mixing rules are proposed, from the usual van der Waals one-fluid prescription to a complete description in terms of the pair distribution functions of the pair interactions that goes beyond the one-fluid level. As a first test of the adequacy of the theory for mixtures the SAFT-VR prediction is compared with Gibbs ensemble simulation data for the vapour-liquid and liquid-liquid equilibria of two prototype mixtures containing square-well molecules.