Prigogine-Flory-Patterson theory

Three adjustable parameters are specific for each substance eg, r, and c. The parameters are fitted to pVT and vapor pressure data. The PHCT is applicable to a very wide domain for simple molecules where c —> 1, it reduces to the perturbed Camahan-Starling eos at low density, it gives a reasonable second virial coefficient and approaches ideal gas at very low density for high densities, PHCT is essentially equal to the Prigogine-Flory-Patterson theory of polymer liquids. 

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 ... 

There are many papers in the literature that applied the Prigogine-Flory-Patterson theory to polymer solutions as well as to low-molecular mixtures. Various modifications and improvements were suggested by many authors. Sugamiya introduced polar terms by adding dipole-dipole interactions. Brandani discussed effects of non-random mixing on the calculation of solvent activities. Kammer et al. added a parameter reflecting differences in segment size. Shiomi et assumed non-additivity of the number of external... 

The Flory-Huggins theory can be improved to incorporate new terms. For example, the Prigogine-Flory-Patterson theory introduces an entropic contribution due to free volume effects in order to obtain more realistic results [70]. This contribution does not modify the solubility criterion as stated above. When the Flory interaction parameter (/) is considered to have both an enthalpic component and... 

Letcher, T. M. Baxter, R. C. Application of the Prigogine-Flory-Patterson theory. Part I. Mixtures of n-alkanes with bicycUc compounds, benzene, cyclohexane and n-hexane J. Solution Chem. 1989,18,65-80... 

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. 

The quantitative description of the above results may be made from the Flory EOS, or Prigogine-Flory theory, which originated from Prigogine s concepts and was developed by Flory (Patterson, 1982). It was based on the generalized van der Waals partition function ... 

Theoretical g° The theoretical expression for the g° parameter, using the theory of polymer solutions developed by Flory and by Patterson based on the ideas of Prigogine and his school, has been given by Horta [8],... 

To explain the existence of the LC. ST of such a type, a theory of corresponding states (called the theory of liquid state as well) ha.s received a large d< velopment effort by Prigogine et al. (1953), Prigogine (1957), Flory el al. (196dab), Flory (1965, 1970), Patterson and Delmas (1970),, Siow et al. (1972). This approach is baseil on the theory of r-dimcnsional liquids developed by the Brussels school (Ilia Prigogine el al.)... 

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 ... 

In most cases, in order to estimate the miscibility of two polymers, the approximations of the theories of regular solutions are used. New statistical theories developed by Prigogine, Patterson, Sanchez, and Flory are also widely used. 

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