On the effects of association in fluids with spherically symmetric interactions

Abstract

The multidensity formalism proposed recently by Wertheim is reformulated in order to describe the effects of association in fluids with spherically symmetric interactions. The basic idea is to separate the total potential into nonassociative and associative parts and make different approximations for each part of the potential. The idea is realized by assuming that the maximum number of particles which can be associated simultaneously with a particular particle is limited and equal to n s. This property of steric saturation is introduced explicitly into the theory via the resummation of diagrams in the activity expansion of the logarithm of the grand partition function. The diagrams appearing in the activity expansion of the one-point density are classified in terms of the number of associative bonds incident upon the labelled white circle. The topological reduction of the diagrams carried out on the basis of this classification leads to an expansion in terms of n s + 1 densities. A generalized version of the Ornstein-Zernike (OZ) equation is derived and closures are discussed. It is pointed out that the OZ equation yields, in the complete association limit, a new integral equation that is “proper” in the sense of Chandler and coworkers. The equation is appropriate to an important class of interaction site models, including a one parameter family of models that range from simple interaction site diatoms to highly cross-linked polymers. Off the complete association limit, our OZ equation provides a “proper” equation for partially associated systems of particles, including the central-force models introduced by Stillinger and his colleagues.