Application of the Cell Method to the Statistical Thermodynamics of Solutions

The cell method for pure liquids in the form used by Lennard-Jones and Devonshire is extended to solutions. It is assumed that (a) the constituents are spherical in shape, with an isotropic field of force, (b) the distance of the maximum interaction for AA, BB, and AB pairs is about the same, and (c) there is random mixing. For the mean field in the ``cage,'' the complete 6–12 law, the harmonic oscillator, and the smoothed potential model have been studied. The smoothed potential model (potential curve with vertical walls and flat bottom, both depth and width depending on concentration) fits the liquid state best. For this model, one obtains important corrections on both the heat of mixing and the excess entropy to the classical, strictly regular solutions. These corrections are related to the volume changes on mixing resulting from the changes of interactions. According to the value of εAB*, the excess properties such as volume, entropy, heat of mixing, and free energy present a large variety of shapes, including dissymmetry and inversions which correspond rather nicely to experimental evidence. This model permits discussion of the severe limitations of Longuet-Higgins's recent theory of conformal solutions.