Validity of the Ehrenfest equation for a system with more than one ordering parameter: Critique of a paper by DiMarzio

Abstract

Davies and Jones have shown that if the configurational state of a liquid is determined by two or more order parameters that freeze in at the glass transition temperature T_g(P), the Ehrenfest relation, r=ΔβΔC_p/TV (Δα)²=1, valid if there is one such parameter, is converted to an inequality r?1. DiMarzio has shown correctly that if the conditions ΔS=0 and ΔV=0 are satisfied at T_g(P), r=1 regardless of the number of order parameters. He has, therefore, concluded that if experimentally r≳1, the order‐parameter concept is inapplicable to the glass transition. It is shown here that r≳1 implies that ΔS and ΔV cannot both be zero at T_g(P), and that there is extensive experimental evidence that the volumes of glasses depend on the pressure under which they were formed, implying ΔV≠0. It is concluded that the experimental observation r≳1 does not render the order‐parameter concept inapplicable.