Critical state in chain-molecule mixtures

Abstract

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 + C₂₀, propane + C₃₂, 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.