Molecular excess free energy mixture

Conformal (second-order) solution theory has been applied to a mixture of almost equal-sized hard spheres of diameters 1 and 1 + p, p< l, by Buchowski and Bellemans. Denoting by n and x the number density and mole fraction of hard spheres of diameter 1 at temperature T and pressure p they find the exact low density result to terms of order p for the molecular excess free energy g of the mixture... 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

The potential of mean force between two particles of a liquid mixture of ionic and molecular species breaks up into their direct interaction and the solvent contribution which can be presented as a difference in the excess free energy of their solvation in a given relative arrangement and at infinite separation,... 

An interesting point to note is that the excess free energy depends only on the value of 6 which is a molecular parameter of the mixture, and on the properties of the pure components, i.e. on the curvature of r) (T) and on the difference between the reduced temperature Taa and Tbb- All other excess properties may be discussed similarly. The important point is to know the sign of the first two derivatives of the universal function Tq (T). 

Chialvo, A. A. 1990b. Determination of excess Gibbs free-energy from computer-simulation via the single charging-integral approach. I. Theory. Journal of Chemical Physics. 92, 673. Chialvo, A. A. 1991. Excess properties of liquid-mixtures from computer-simulation—A coupling-parameter approach to the determination of their dependence on molecular asymmetry. Molecular Physics. 73, 127. 

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