Prigogine’s parameter

Although originally developed to model thermodynamic properties of volatile fluids, cubic equations of state have also been applied to polymer mixtures. Sako, Wu and Prausnitz proposed a cubic equation of state for polymers based on the Soave-Redlich-Kwong equation of state with the Prigogine s parameter c to account for the non-sphericity of chain molecules. The Sako-Wu-Prausnitz... 

Donahue and Prausnitz [23] developed the perturbed-hard chain theory (PHCT) based on perturbed hard-sphere theory for small molecules and Prigogine s theory for chain molecules. In order to account for attractive and repulsive forces among molecules, empirical parameters such as the c parameter were introduced by subsequent investigators. More accurate expressions for the repulsive and attractive forces were... 

The invariant hole size and energy of hole formation in the Lacombe-Sanchez model implies a dependance of the internal energy on the density that is strictly of the van der Waals form, as in Flory s theory. Another, somewhat more complicated, model developed by Simha and his collaborators is similar to that of Sanchez and Lacombe in its use of a liquid lattice with vacant sites, but it also retains features of Prigogine s earlier cell model in the c parameter for external degrees of freedom and a lattice energy with a density dependence based on an effective (6-12) pair potential. Like the other theories, this one has been successful in correlating equation of state data both for neat polymer liquids and for nondilute solutions. 

Their derivation consisted in expanding the pressure in a power series of the parameter A, and was valid only for small values of A. The procedure which will now be adopted in this paper is not so refined as de Boer and Blaisse s theory, but it will not be required that A is small. The procedure is the same as that adopted by Prigogine and Philippot27 in their theory of energies of liquid helium, and it will be applied to other liquids than liquid helium. These substances are, of course, solid at 0° K except for helium. However, it will be assumed that the same method can be applied to these substances in the following treatment, considering the comparative crudeness of our theory which does not discriminate between liquid and solid states. 

Construct the phase diagram for the MMA-S and SAN blend. Use the binary interaction parameter values tabulated in Chapter 3, and use the Prigogine square-well cell theory as the equation of state. 

The local equilibrium assumption was the basis on which the Brussels school developed a global thermodynamic theory. Use of this assumption makes possible the macroscopic evaluation of entropy production and entropy flow terms with macroscopic thermodynamic methods. The assumption states that "there exists within each small mass element of the medium a state of local equilibrium for which the local entropy, s, is the same function of the local macroscopic variables as at equilibrium state" (Glansdorff and Prigogine, 1971, p. 14). In other words, each small element of a system may be treated as a state near equilibrium but need not necessarily be at equilibrium. This does not mean that the system as a whole need be near equilibrium thus, neighboring local elements may differ in parameters (temperatures, chemical affinities, etc.) which are reflected in the function describing their local entropy. The additional assumption is made that the sum of the criteria of local stability for each element corresponds to the global stability criterion for the whole system. 

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