10 Mixtures of dissimilar molecules

Equations (10.14) and (10.15), which are the basis of the present theory, are mathematically exact. The choice of the closure expression, Equation (10.21), relating the cross-direct-correlation integral to the other two integrals in a binary mixture allows us to solve these equations simply and analytically using only the pure-fluid thermodynamic data. It is demonstrated here that simple geometric- and arithmetic-mean closures are needed for simple model fluids. It is also demonstrated that a weighted-arithmetic-mean closure expression is sufficient to represent the relation between the cross-direct-correlation integral to the other two correlation integrals of binary mixtures. Success of this theory in its application to a variety of mixtures comprised of components with polar and associating intermolecular potential energies is indicative of its promise as a strong technique for prediction of properties of complex dissimilar mixtures of practical interest. The present theory has allowed us to perform calculations of properties and phase equilibria of mixtures. There are several points to be noted about the advantages of the present techniques compared with other existing thermodynamic calculation methods for mixtures: (i) The present theory allows us to perform thermodynamic calculations for the whole range of mixture compositions and not just at the infinite-dilution and high-concentration limits as has been the case for most of the fluctuation-theory techniques. (ii) The present theory is applicable for mixtures consisting of dissimilar species with large differences in molecular size, shape, and energetics. It is specifically useful for polar and associating molecular fluids for which, generally, no accurate intermolecular-potential-energy functions are available. (iii) With the application of the weighted-arithmetic-mean closure for the cross-direct-correlation-function integrals, Equation (10.21), it has become possible to derive analytic expressions for activity coefficients in complex mixtures consisting the dissimilar molecules. The resulting activity-coefficient expressions allow us to perform vapor-liquid and liquidliquid equilibria computations for such mixtures. The accuracy of these calculations are is good as the best available phase-equilibria computational techniques for mixtures. (iv) What makes the relations among the direct-correlation-function integrals (or fluctuation integrals) introduced here particularly interesting is the fact that only one closure relation is needed to determine all the binary-mixture properties. Detailed studies are under way in order to develop analytic expressions for total and partial molar properties of multicomponent systems using the present theory.