A potential distribution approach to fused heterochain molecules. I. Mixtures of hard dumbbells and spheres

Abstract

We apply the potential distribution theorems for the cavity distribution functions to the development of thermodynamic formulas for fused-sphere chain molecules. Alternative forms of the potential distribution theorems are derived: in terms of the cavity functions, and in terms of the singlet direct correlation functions. We point out the connections to integral equation theories. To determine the behavior of fused dispheres, we examine the successful Wertheim thermodynamic perturbation theory (TPT) at different bond lengths l in light of the cavity functions. For ternary mixtures of spheres S and B, and fused dispheres (SB), we discover a confluence point where all cavity functions at different mixture compositions converge. This takes place at the tangent disphere limit l=d (l being the bond length, and d, the hard sphere diameter). This point is also in common with the excess Helmholtz free energy from the TPT theory for tangent dumbbells. The cavity functions are obtained from the accurate equation of state of Boublík. To verify the chemical potentials calculated, we compare with new Monte Carlo simulations for mixtures of hard spheres and dumbbells. TPT does not hold for l<d. In order to have a quantitative expression for fused disphere properties, we propose an interpolation formula that performs well for both symmetric dispheres and asymmetric dispheres. This formula, though empirical, performs better than similar interpolative schemes proposed by Phan–Kierlik–Rosinberg. We have also derived purely thermodynamic formulas based on the TPT theory. These formulas can be exploited if one uses many of the existing thermodynamic properties correlations for mixtures.