Mean Field Lattice Equations Of State

Abstract

Following the work of Schottky, many have used a lattice of filled and vacant sites to model compressible fluids. The lattice models of Kanig, Kilian, Sanchez & Lacombe, Okada & Nose, Kleintjens et al. (KK), Vera & Panayioutou and similar treatments, can all be summarized by a single equation of state, the various versions representing special cases. Liquid/vapor coexistence data and p(V) isotherms on small molecules, as well as p(V) data on polystyrene, were used to test the variations of the general model. The descriptions of the experimental data Improve in the sequence Kanig-Kilian-Sanchez-Vera-KK. The KK model contains two empirical parameters, the molecular origin of which can be explained with Staverman’s contact number statistics. Differences in molecular size and, hence, in number of nearest neighbors come to the fore as important factors that should not be ignored in molecular modelling. Thus, combinatorial entropy contributions are probably more complex than is usually assumed, and may, for instance, by themselves cause lower and upper critical miscibility to occur in the same polymer blend.