Hole Theory of Liquids and Glass Transition

Abstract

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.