Cluster perturbation theory for the self-assembly of associating fluids into complex structures

Wertheim's two-density thermodynamic perturbation theory (TPT) has proven to be an indispensable statistical mechanical tool in the description of associating fluids with a single association site. TPT was developed to enforce the monovalence of the hydrogen bond and only recently has been extended to account for divalent association sites. It has been shown through experiment and molecular simulation that certain one-site associating fluids can self-assemble into complex extended supramolecular structures as a result of multiple bonding of association sites. In this paper we reorganize TPT into a form that is more easily applied to complex associated structures. The derived theory is general to all possible self-assemble structures. We obtain the free energy and bonding fractions in a general way in terms of single-cluster partition functions and averages. The new formalism removes any reference to graph theory allowing for the conceptually straightforward application of the two-density formalism to complex self-assembled structures.