Molecular based modeling of associating fluids via calculation of Wertheim cluster integrals

We examine a virial-like treatment for the equation of state of associating fluids defined in terms of a detailed molecular model. The approach implements Wertheim's formulation of statistical thermodynamics of a classical fluid of molecules having strong directionally dependent association interactions. We employ the theory in its fundamental form, which expresses the pressure as an expansion in two or more aggregation densities, which themselves are related to each other by other series expansions. We employ Mayer-sampling Monte Carlo simulations to evaluate the cluster integrals defining the coefficients appearing in these series, yielding a multidensity virial-like equation of state, appropriate for the molecular system for which the cluster integrals were computed. We demonstrate this approach with a well-studied Lennard-Jones + association model, considering cases of atoms having one and two binding sites, respectively, and including all clusters involving up to four atoms. It is shown for this application that the Wertheim treatment is vastly superior to the standard (single-density) virial formulation, which fails in its description of the associating-fluid equation of state at very low densities. The Wertheim formulation for associating fluids is seen to be effective up to densities where the standard virial treatment to the same order begins to fail when applied to nonassociating fluids.