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Isotherms and isobars for polymer liquids using corresponding states principle to establish function describing dependence of internal pressure on volume or temperature

The phase behavior at high temperatures of non-polar polymer solutions is discussed in a qualitative way in terms of the free volume theory of liquids developed by Prigogine, Patterson and Flory. This theory is necessary to explain the existence of a Lower Critical Solution Temperature (LCST) in non-polar polymer solutions and the related exothermic heats of mixing. The classical theory of polymer solutions and its limits is first reviewed.

A recently elaborated theory of the p‐V‐T properties successfully describes the behavior of amorphous polymers above the glass temperature. The improvement over earlier results arises from the introduction of a vacancy fraction which is obtained as a function of volume and temperature by a maximization of the partition function. We now explore a possible application of this theory to the glassy state by introducing an assumption following a frequently used idea, namely, the freezing of one parameter, (or more), for example, an unoccupied volume ratio. The natural quantity to consider is the vacancy fraction and its effect on the thermal expansion coefficient at the glass temperature. Experimental data at atmospheric pressure on a series of polymers, encompassing a wide range of Tg's, are examined and compared with theoretical predictions. The computed expansivities αg at T=Tg are uniformly smaller than is observed. We suggest as the primary reason for this discrepancy the assumption of a complete freezing of the hole fraction at the glass temperature, which should be replaced by a decreased dependence on volume and temperature as compared with the liquid. Additional factors are discussed.