Thermodynamic Aspects of the Glass-Rubber Transition

In 1933 Ehrenfest defined transitions in which not only the thermodynamic potential but also the specific volume and entropy of the two states are equal. For these transitions he derived three relations, between the differences of the coefficients of dilatation and of compressibility and the specific heat on one hand and the slope of the transition curve in p-T-space on the other hand. Although it is beyond any doubt that the glass-rubber transition in polymers is not a second order transition as defined by Ehrenfest, yet the term “second order transition” is often applied to it. The confusion arising from this abuse of a physically well defined concept is enhanced by the fact that some of Ehrenfest's relations are under certain circumstances valid for the glass-rubber transition, although in those cases the physical background of these relations is quite different from that of a second order transition in Ehrenfest's sense. In fact, the essence of the glass transition was formulated clearly and correctly by Simon in 1931 and consists in the assumption that in a glass one or more internal parameters are not in equilibrium but are frozen in. Conditions required for the validity of each of Ehrenfest's relations are inspected. The equality of two functions of the dilatation and the compressibility coefficients and the specific heats of the two states depends on the condition that there is only one frozen parameter in the glass state. If there is more than one frozen parmeter, then the equality turns into an inequality and the physical meaning of the difference between the two sides is derived. Similar relations as those derived between the quantities mentioned, can be derived between specific heat, modulus of elasticity and temperature coefficient of that modulus. These new relations are more interesting for practical purposes and less subject to experimental errors than the older ones. Finally expressions for the slope of the transition curve are investigated. Validity of any one of the expressions depends on the physical condition required for a material to become a glass. Inversely from the validity of any of the possible expressions insight in the glass transformation can be derived. The scarce available data give the impression that a material turns into a glass whenever its excess entropy decreases below a critical value.