Statistical thermodynamics of mixtures. A new version for the theory of conformal solution

Abstract

A new method for the calculation of thermodynamic properties of simple fluid mixtures constitutes an extension of the approach defined earlier as the “van der Waals” conformal solution theory. This extension is made possible by advances in the analytical representation of the thermodynamic properties of a mixture of hard spheres which permit the properties to be calculated directly, without the use of a reference fluid. A new hard-sphere excess function, defined as a property of the mixture less the value of this property for the hard-sphere mixture, is obtained by a new conformal solution theory using a single pure fluid as a reference substance. Although the reference substance properties could be experimentally measured values, this work obtains them from an analytical form of the Barker-Henderson perturbation theory.This new method improves prediction of the effects of large molecular size differences on the excess properties of the mixture. It uses the reference fluid to account for most of the temperature dependence of the cut-off parameter needed to define the molecular diameters in the direct hard-sphere mixture calculations and the calculations need only the high temperature limit of the cut-off parameters, even far below the critical temperature. The new method extends the original vdW conformal solution method to lower temperatures and provides an opening for inclusion of three-body interactions.Conventional excess mixing functions for several binary liquid mixtures calculated by the new method are compared with the predictions of other theories and with both experimental and Monte Carlo data.