Prigogine-Flory corresponding-states theory

Corresponding-states theory (Prigogine, 1957 Flory, 1970) incorporates features of the pure component properties and liquid structure in the mixture equation-of-state, producing nonzero values of AFm and contributing enthalpic and entropic terms beyond those in Flory-Huggins theory. The theory assumes that all pure components and mixtures obey the same universal equation-of-state, e.g., (Flory, 1970)... 

It is often of industrial interest to be able to predict the equilibrium sorption of a gas in a molten polymer (e.g., for devolatilization of polyolefins). Unfortunately, the Prigogine-Flory corresponding-states theory is limited to applications involving relatively dense fluids 3,8). An empirical rule of thumb for the range of applicability is that the solvent should be at a temperature less than 0.85 Tp, where Tp is the absolute temperature reduced by the pure solvent critical temperature. 

The corresponding-states theory of polymer solution thermodynamics, developed principally by Prigogine and Flory, has provided a reliable predictive tool requiring only minimal information. We have seen here several examples of the use of the corresponding-states theory. We have also seen that the corresponding-states theory is a considerable improvement over the older Flory-Huggins theory. 

Flory (11) improved the notation and form of Prigogine s expressions, and it is essentially the Flory form of Prigogine s free-volume theory that is of most use for design purposes. The Flory work (11) leads to an equation of state which obeys the corresponding-states principle ... 

To recapitulate, the Flory version of the Prigogine free-volume or corresponding-states polymer solution theory requires three pure-component parameters (p, v, T ) for each component of the solution and one binary parameter (p ) for each pair of components. 

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 ... 

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.)... 

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