The glassy state, ideal glass transition, and second-order phase transition

According to Ehrenfest classification, the glass transition is a second-order phase transition. Controversy, however, remains due to the discrepancy between experiment and the Ehrenfest relations and thereby their prediction of unity of the Prigogine-Defay ratio in particular. In this article, we consider the case of ideal (equilibrium) glass and show that the glass transition may be described thermodynamically. At the transition, we obtain the following relations: dT/dP = Delta beta/Delta alpha and dT/dP = TV Delta alpha(1-Lambda)/Delta C-p-Delta C-v with Lambda = (alpha(g)beta(l)-alpha(l)beta(g))(2)/beta(l)beta(g)Delta alpha(2); dV/dP = V alpha(g)beta(l)-alpha(l)beta(g)/Delta alpha, dV/dP = beta(l)beta(g)(Delta C-p-Delta C-v)(alpha(g)beta(l)-alpha(l)beta(g))/T Delta alpha(alpha(l)(2)beta(g)-alpha(g)(2)beta(l)); dV/dT = V(alpha(g)beta(l)-alpha(l)beta(g))/Delta beta and dV/dT = beta(l)beta(g)(Delta C-p-Delta C-v)(alpha(g)beta(l)-alpha(l)beta(g))/T Delta beta(alpha(l)(2)beta(g)-alpha(g)(2)beta(l)). The Prigogine-Defay ratio is Pi = 1/1-(Delta C-v-Gamma)/Delta C-p with Gamma = TV(alpha(l)beta(g) - alpha(g)beta(l))(2)/beta(l)beta(g)Delta beta, instead of unity as predicted by the Ehrenfest relations. Dependent on the relative value of Delta C-V, and Gamma, the ratio may take a number equal to, larger or smaller than unity. The incorrect assumption of perfect differentiability of entropy at the transition, leading to the second Ehrenfest relation, is rectified to resolve the long-standing dilemma perplexing the nature of the glass transition. The relationships obtained in this work are in agreement with experimental findings. (C) 1999 John Wiley & Sons, Inc.