The theory of regular solutions

Abstract

The usual theory of regular solutions, which is based on the assumption that all molecules are on the sites of a lattice, is modified. Each molecule is supposed to move near its site in a potential determined by the field of its nearest neighbours. The number of neighbours of each component is fixed by the quasi-chemical approximation. Four modifications are considered, which differ only in the way in which the free-volume of any molecule is supposed to depend on the nature of its neighbours. The first of these modifications gives the usual theory. The second and third are cases which have been considered by Ono and by Prigogine & Garikian respectively. The fourth is new, and is probably the most exact. It is shown that, for all modifications, the usual theory is unchanged, to a first approximation, if ∆=1, where ∆ 2 = E 2 AB / E AA E BB , and E is the energy of interaction of an isolated pair of molecules. If ∆≠1, then an important correction term is needed. The application of the most exact of these modified theories to the critical solution temperature is discussed. It is shown that, for molecules with similar energies of interaction, this theory gives the same relations between the properties of the solution and those of the components, as does the theory of conformal solutions, derived by Longuet-Higgins.