Application of the Cell Method to the Statistical Thermodynamics of Solutions

Abstract

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.

Analysis of broadband dielectric spectra in a Na+ mordenite

“…These oscillations are considered as harmonic, as far as the cation remains in its site. Because of the thermal fluctuations, a non negligeable part of cations can hop over a potential barrier AE [13] between two neighbouring positions represented by a double potential well [14] (Fig. 3).…”

Equations of State and Free‐Volume Content

“…For polymers, Prigogine et al used the mean-field equation (6.16b) to describe interactions between statistical segments of s-unit molecules, with the radius, r, replaced by the cell volume, v [Prigogine and Mathot, 1952;Prigogine et al, 1953aPrigogine et al, ,b, 1957a.…”

“…Prigogine et al extended the cell model equation of state to solutions [Prigogine and Mathot, 1952] and then to s-mer mixtures [Prigogine et al, 1953a[Prigogine et al, ,b, 1957aBellemans et al, 1957a,b]. Assuming that in multicomponent fluids there is only one type of vacancy, and one cell size for all components, Simha [1980, 1984] developed a set of relations for homogeneous binary mixtures.…”

The System Carbon-Tetrachloride+Neopentane: A Complete Thermodynamic Analysis

“…In addition, three experimental values of the liquidus curve and the excess Gibbs energy of the liquid state are known, Eq. [1]. The EGC method via the WINIFIT program provides the excess Gibbs energy of the C $ -ODIC state.…”