Van der Waals-like global phase diagrams

Since the first global phase diagram (1970) based upon the van der Waals equation of state for binary mixtures, there have been many newer ones, most recently that obtained by Yelash and Kraska (Ber. Bunsen-Ges. Phys. Chem., 1998, 102 213) by combining the Carnahan and Starling hard-sphere equation of state (J. Chem. Phys., 1969, 51, 635) with the original van der Waals attraction. Of the various such equations the results for the original van der Waals equation seem to be the least satisfactory in comparison with the experimental one-component fluid, and probably also for binary mixtures. However the Carnahan and Starling equation diverges only at a density much higher than close-packed. Sanchez (J. Chem. Phys., 1994, 101, 7003) has developed a new 4,3 Pade′ approximant that fits the virial coefficients of the hard sphere fluid and which diverges almost exactly at the close-packed density. If this expression is used in a van der Waals-like equation of state, it produces the same kind of closed-loop diagrams that Yelash and Kraska found, although over a substantially smaller area of the global phase diagram. Extensions of global phase diagrams to mixtures of molecules of different size (even to polymer systems) seem promising. In particular a simple equation of state with the Flory mixing equation and the Prigogine entropy parameter (TheMolecularTheoryofSolutions, North Holland, Amsterdam, 1957, ch. XVI) has led to a satisfactory account of tricritical points in hydrocarbon systems and should be investigated further.