Equilibrium Wertheim theory

The extension of these ideas to fluids with multiple attraction sites has been given by Wertheim and used by him to develop a theory of equilibrium polymerization. The difficulty with extension of the single-attraction site theory to multiple attraction sites is in incorporating the increasingly complex steric incompatibility (SI). In particular, the difficulty commonly encountered is SI3, which physically corresponds to the absence of self-hindrance, where the rigidity of an s-mer prevents two of its component molecules from encountering each other. In another paper, Wertheim has considered fluids of dimerizing hard spheres and fluid mixtures of hard spheres and diatomics. 

The perturbed-hard-ehain (PHC) theory developed by Prausnitz and coworkers in the late 1970s was the first successful application of thermodynamic perturbation theory to polymer systems. Sinee Wertheim s perturbation theory of polymerization was formulated about 10 years later, PHC theory combines results fi om hard-sphere equations of simple liquids with the eoneept of density-dependent external degrees of fi eedom in the Prigogine-Flory-Patterson model for taking into account the chain character of real polymeric fluids. For the hard-sphere reference equation the result derived by Carnahan and Starling was applied, as this expression is a good approximation for low-molecular hard-sphere fluids. For the attractive perturbation term, a modified Alder s fourth-order perturbation result for square-well fluids was chosen. Its constants were refitted to the thermodynamic equilibrium data of pure methane. The final equation of state reads ... 

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