Analytical solutions of the proper integral equations for interaction site fluids: Molecules composed of hard-sphere interaction sites

Abstract

Interaction site models are used quite extensively to describe molecular fluids. However, theories for these fluids are not as well developed or tested as compared to those for simple fluids. With this in mind, it appears useful to develop analytical expressions for the thermodynamic properties of fluids whose molecules are composed of hard-sphere interactions sites, since these systems can serve as a convenient reference state for perturbation theories for molecular fluids. In an effort to achieve this goal and advance our understanding of molecular fluids, in this paper, we present an analysis of the Chandler–Silbey–Ladanyi (CSL) equations, a diagrammatically proper set of integral equations for interaction site fluids, with the specific aim of solving them analytically. First, we rewrite the CSL equations to explicitly account for the presence of equivalent sites. We find that the mathematical structure of the resulting CSL equations remains the same as that of the original CSL equations, subject to slight modifications in some of the matrices which appear in these equations. Subsequently, we apply the Wiener–Hopf factorization technique to the CSL equations with the Percus–Yevick (PY) closure for a general fluid composed of hard-sphere interaction sites. We then analytically solve these equations for symmetric n-atomic tangent hard-sphere molecules (n≤4: spheres, diatomics, triangles, and tetrahedrals), which results in analytical expressions for the equation of state and other thermodynamic properties of the fluid. Finally, we compare the predictions of the analytical equation of state with those of other theories as well as with those of Monte Carlo simulations of these systems. The CSL equations with the PY closure are found to provide fair predictions for the equation of state of the fluids under investigation. More specifically, the CSL–PY equations tend to perform better for smaller molecules and at lower densities.