Effect of Nonrandom Mixing of Molecules and Holes on Phase Diagram in Mixture

Abstract

ABSTRACT:The effect of nonrandom mixing of molecules and holes on phase diagrams of liquid mixtures has been investigated by comparing the numerical results calculated from the first and zeroth approximations of the hole theory. To study the effect of nonrandom mixing of molecules, calculations have also been made for the case in which the hole is not considered. In general, the nonrandom distribution of holes has a larger effect on phase diagrams than that of molecules. Nonrandomness increases or decreases compatibility depending on the system considered. The pressure dependence of compatibility has been also calculated using the first and zeroth approximations.KEY WORDS Nonrandomness I Phase Diagram I Hole Theory I Polymer Solution I Pressure IThe lower critical solution temperature (LCST) is known to be general for nonpolar polymer solutions rather than the exception. 1 The LCST is caused by a sort of condensation of a more volatile component. 2 The free volume theories, presented by Prigogine, 3.4 Flory, 5 -? and their coworkers, can predict the LCST and can explain other thermodynamic behavior qualitatively. Therefore, it is apparent that free volume plays an important role in the thermodynamics of polymer solutions. In these theories, the same free volume is assigned to each molecule. In a real fluid mixture, however, the average size of vacant space around a molecule as well as the distribution of molecules of different species around it, should depend on the cohesive energy of the molecule considered. Renuncio and Prausnitz 8 have suggested that one limitation of the Flory theory might be the random-mixing assumption for component molecules. The nonrandom distribution of vacant space might also have appreciable influence on solution properties.Recently, Sanchez and Lacombe 9 -11 presented a simple type of hole theory called the lattice fluid theory, which allows for the volume change of a system and predicts the LCST. In this theory, the cell volume is fixed and the hole plays the same role as the free volume. It is reasonable to assume that the nonrandom distribution of vacant space can be represented by the nonrandom mixing of holes and molecules in the hole theory with fixed cell volume. In previous papers, 12 • 13 we applied the quasichemical treatment to the lattice fluid theory from this viewpoint and investigated the effects of nonrandom mixing of holes and molecules on various thermodynamic quantities. The present paper investigates the effect of nonrandom mixing on phase diagrams which are very sensitive to the parameters characterizing the system. Another purpose of this paper is to study various features of phase diagrams predicted by the hole theory. This theory can be applied to gas-liquid equilibrium, but here we limit ourselves to investigating liquid-liquid phase diagrams. THEORETICALAs regards the calculation method, the lattice fluid theory is very similar to the Flory-Huggins theory. The main difference lies only in the fact that an additional component, i.e., the hole, is created or ...