Prigogine-Flory-Patterson equation

The first successful theoretical approach of an equation of state model for polymer solutions was the Prigogine-Flory-Patterson theory. It became popular in the version by Flory, Orwoll and Vrij and is a van-der-Waals-like theory based on the corresponding-states principle. Details of its derivation can be found in numerous papers and books and need not be repeated here. The equation of state is usually expressed in reduced form and reads ... 

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 ... 

Today, there are two principal ways to develop an equation of state for polymer solutions first, to start with an expression for the canonical partition function utilizing concepts similar to those used by van der Waals (e.g., Prigogine, Flory et al., Patterson, Simha and Somcynsky, Sanchez and Lacombe, Dee and Walsh,Donohue and Prausnitz, Chien et al. ), and second, which is more sophisticated, to use statistical thermodynamics perturbation theory for freely-jointed tangent-sphere chain-like fluids (e.g., Hall and coworkers,Chapman et al., Song et al. ). A comprehensive review about equations of state for molten polymers and polymer solutions was given by Lambert et al. Here, only some resulting equations will be summarized under the aspect of calculating solvent activities in polymer solutions. 

Flory-Prigogine-Patterson Equation-of-State Theory... 

Dar (Dar, 1999 Dar and Caneba, 2002) calculated Flory-Huggins interaction parameters from the Flory-Prigogine equation-of-state theory (Eq. 1.1.7), which adequately represented the experimental system. From the work of Patterson and coworkers, the following expression for the Flory-Huggins interaction parameter, X, was obtained ... 

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