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

Abstract

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 = Δβ/Δα and dT/dP = TVΔα(1 - Λ)/ΔCP - ΔCV with Λ = (αgβl - αlβg)2/βlβ g)Δα2; dV/dP = V αgβl - αlβg/Δα, dV/dP = βlβg(ΔCP - ΔCV)(αgβl - αlβg)/TΔα(αl2 - βg2-βl); dV/dT = V (αgβl - αlβg)/Δβ and dV/dT = βlβg(ΔCP - ΔCV)(αgβl - αlβg)/TΔβ(αl2βg - αg2βl) The Prigogine-Defay ratio is ∏ = 1/1 - (ΔCV - Γ)/ΔCP with Γ = TV(αlβg - αgβl)2/βlβ gΔβ, instead of unity as predicted by the Ehrenfest relations. Dependent on the relative value of ΔCV and F, 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. © 1999 John Wiley & Sons, Inc.