Configurational Prigogine-Defay ratio

TL;DR

This paper generalizes the Prigogine-Defay ratio by incorporating configurational contributions and non-equilibrium effects during the glass transition, offering a new framework to analyze thermodynamic changes.

Contribution

It introduces a configurational PD ratio based on macroscopic non-equilibrium thermodynamics, considering non-isoaffine glass transition and linking it to fictive temperature and pressure.

Findings

Generalized PD ratio accounts for non-equilibrium effects.

Classical PD ratio is a special case of the new formalism.

Experimental verification is possible through fictive variables.

Abstract

Classically, the Prigogine-Defay (PD) ratio involves differences in isobaric volumic specific heat, isothermal compressibility and isobaric thermal expansion coefficient between a super-cooled liquid and the corresponding glass at the glass transition. However, determining such differences by extrapolation of coefficients that have been measured for super-cooled liquid and glassy state, respectively, poses the problem that it does not take into account the non-equilibrium character of the glass transition. In this paper, we asses this old question by taking into account the gradual change of configurational contributions to the three thermodynamic coefficients upon varying temperature and pressure. Macroscopic non-equilibrium thermodynamics is applied to obtain a generalized form of the PD ratio. The classical PD ratio can then be taken as a particular case of this generalization. Under some assumptions, a configurational PD ratio (CPD ratio) can be expressed in terms of fictive temperature and fictive pressure what, hence, provides the possibility to experimentally verify this formalism. Noteworthy and differing from previous approaches towards the PD ratio, here, the glass transition is considered as non-isoaffine.