The general corresponding states theory of Prigogine and collaborators, applicable to the thermodynamics of mixtures of quasi-spherical molecules and polymer solutions, is compared to the theory of Flory, Abe, Orwoll and Vrij. The mixing functions are divided into two contributions : an interaction term due essentially to the weakness of (1-2) interactions, and a term due to the dissimilarity of the free volumes of the two components. The latter term is small or negligible in mixtures of quasispherical molecules but dominant for polymer solutions. These terms are contrasted with the contact interaction term and the equation of state term of the Flory theory. The mixing functions are calculated by a new approximate procedure, using several liquid models based on the cell partition function (including the model used by Flory and collaborators). The results are similar and the models make certain errors in common.

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The Prigogine corresponding states theory and a cell model are used to predict the main features of the critical line in P,T, composition space for a mixture of chain-molecules. A simple van der Waals dependence of the configurational energy on volume (as used by Flory) is assumed in most of the calculations. For a mixture of homologues of small chain-length difference, a continuous critical line is predicted ; it ends at the critical points of the pure components rising to a high maximum critical pressure at an intermediate concentration. Comparison is made between the predicted and observed lines for normal alkanes. With a large chain-length difference between components, the line is broken at low concentration of the longer molecules by a three-phase line running between a lower critical solution point (L.C.S.P.) and an upper critical end-point (U.C.E.P.). For normal alkane mixtures, methane+C7, ethane+(&, propanefCa2, are predicted to be the system of minimum chain-length difference which show the L.C.S.P., in agreement with experiment. Satisfactory predictions without adjustment of any parameters are made for portions of the critical line found by Ehrlich and Kurpen for polyethylene in the n-alkanes from ethane to pentane. The pressure dependence of the lower critical solution temperature at zero pressure is successfully predicted for polymer+ solvent systems. The free energy of mixing is obtained as a function of pressure and temperature for chain-molecules of different species. The pressure dependences of the upper and lower critical solution temperatures are compared.

The Prigogine principle of corresponding states for chain-molecule liquids is tested using published density, thermal expansion coefficient and isothermal compressibility data for the n-alkane series from methane to polymethylene. The principle is well obeyed allowing reduction parameters P*, V* and T* to be determined. The equation-of-state data for the pure liquids and the corresponding states theory applied to their mixtures permit the accurate prediction of excess volumes and their temperature and pressure dependence. Theoretical equations of state based upon the cell partition function (including the new Flory theory) show systematic errors. Analyses of experimental data using these theories produce, as artefacts, a variation of the reduction parameters with T, and an important decrease of P* with decreasing chain index. The present analysis shows P* to be constant to 3rl % from polymethylene to butane indicating that the terminal methyl groups and the interior methylene groups are similar in intermolecular contact energies. Without end-effects, the cell model theories predict an incorrect negative sign for H E of n-alkane mixtures at ordinary temperatures.

Heats of mixing have been obtained at 25" for the following mixtures of linear methylsiloxanes : hexamethyldisiloxane (dimer)-octamethyltrisiloxane (trimer) ; dimer-tetramer ; dimer-pentamer ; trimer-pentamer and dimer-polymer. The heats are consistent with the Prigogine cell theory for the thermodynamics of chain-molecule mixtures and with Bramsted's principle of congruence. Two assumptions concerning the volume dependence of the configurational energy of a liquid were tested : that of a van der Waals liquid which gave good results and a 6-12 model which gave poor results. Two excess volume results were also in accord with the former model. The relation between the Prigogine cell theory and the recent theory of Flory, Orwoll and Vrij is examined.