Effects of Molecular Size and Shape in Solution Thermodynamics

Abstract

The one-fluid corresponding states theory is used to predict excess thermodynamic quantities of a mixture of spherical molecules of different e and σ. Two prescriptions of ‘van der Waals type’, and a third used by Flory, give the parameters e m and σ m of the solution. Comparison of the results is made with Monte Carlo calculations of Singer and Singer and the Snider–Herrington theory, and also with experimental features of simple and polyatomic spherical molecule mixtures. For each prescription an intuitive discussion is given of contributions to the excess quantities arising from (a) the energetic weakness of (1–2) contacts relative to (1–1) and (2–2) and (b) dissimilarity of free volume between the components. Two free volume contributions are distinguished. One depends on the second derivative with respect to T of the energy, volume, etc. of the reference liquid. The other occurs only in V E where it is of major importance and depends on d V /d T and a dissimilarity of molecular energy/volume parameters of the components. Recent experiments indicate two effects outside current theory. For systems containing anisotropic molecules, there is a third contribution to excess quantities (c), due to short-range orientational order or correlations of molecular orientations in one or both components. Mixing liquids of differing degrees of order usually brings about a net decrease of order, and hence positive contributions in Δ H M and Δ S M . The effect is illustrated by Δ H M values of branched and normal alkane mixtures at 25°, the temperature dependence of Δ H M for such systems, and the widely different. Δ H M of cis and trans dimethylcyclohexanes mixed with the orientationally ordered n -C 16 . The properties of systems containing a nematic liquid crystal (MBBA) and an alkane are sensitive to the alkane shape and indicate that MBBA molecules correlate their orientations with normal, but not with highly branched alkanes. The fourth contribution (d) is seen in systems involving alkanes of the same molecular shape but different degrees of steric hindrance of torsional oscillations. Heats of mixing point to a thermodynamic effect associated with a coupling of the molecular motions of the components.