Relation of Wertheim association constants to concentration-based equilibrium constants for mixtures with chain-forming components

Several association modeling approaches have been developed to accurately describe the properties of polar solutions. Chemical theory and Wertheim's perturbation theory are among the most popular of these and they have been shown to yield similar functional forms for the contributions of association to Helmholtz energy and activity coefficients. In this paper, we study Flory polymerization theory through the work of Campbell and elucidate its correlation to Wertheim's theory. A simple key relationship between the concentration-based equilibrium constant and Wertheim's association constant is developed for systems in which all associating components have one acceptor and one donor site. Algebraic and numerical proofs are given for the equivalence of Flory's polymerization theory and Wertheim's perturbation theory for pure fluids and mixtures. Additionally, a new generalized activity expression is developed for Wertheim's theory.