Non-equilibrium configurational Prigogine–Defay ratio

Abstract

Classically, the Prigogine-Defay (PD) ratio involves differences in isobaric heat capacity, 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 exactly take into account the non-equilibrium character of the glass transition. In this paper, we assess this question by taking into account the time dependence of configurational contributions to the three thermodynamic coefficients in the glass transition range upon varying temperature and/or pressure. Macroscopic non-equilibrium thermodynamics is applied to obtain a generalised form of the PD ratio. The classical PD ratio can then be taken as a particular case of this generalisation. Under some assumptions, the configurational PD ratio (CPD ratio) can be expressed in terms of fictive temperature and fictive pressure which, hence, provides another possibility to experimentally verify this formalism.

Affinity and its derivatives in the glass transition process

“…The possibility to calculate jumps in C p , α p , or κ T at T g or p g following different simulated experimental protocols have practical applications and allows one to define and compute classical Prigogine-Defay ratio as well as linear PrigogineDefay ratio 44 or non-equilibrium Prigogine-Defay ratio. 15 While the model is able to reveal most of the principal characteristics of the glass transition, it describes also qualitatively some experimental behavior. For example, the predicted glass transition temperature of o-terphenyl is quantitatively consistent with experiments.…”

“…This corresponds to the linearity assumption such as discussed in the Appendix A of the Ref. 15. To further illustrate our point, the computations of the configurational specific heat are plotted on the Fig.…”

“…This may prove to be useful in the general case when the expression of the Gibbs free energy is not known and when the out of equilibrium thermodynamic formalism is pushed to its limits. 15 Since the affinity is a state function, its total differential is dA = ∂A ∂T p,ξ dT + ∂A ∂P T ,ξ dp + ∂A ∂ξ p,T dξ. (12) Maxwell relations 32 are used to transform the partial derivatives, and the equation above may be expressed in a practical way making explicitly apparent the infinitesimal time evolution…”

“…3 Non-equilibrium thermodynamics has been used all along the last century by different groups of researchers, and has seen renewed interest in the last few years. [4][5][6][7][8][9][10][11][12][13][14][15] As an example, Bouchbinder equilibrium thermodynamics based on internal variables to investigate one of the most striking aspect of the glass transition, i.e., the Kovacs effect. 16 They provided fits of the numerical simulation curves obtained by Mossa and Sciortino on the Kovacs effect.…”

Comment on “On the theoretical determination of the Prigogine-Defay ratio in glass transition” [J. Chem. Phys. 136, 124502 (2012)]

“…Such as originally demonstrated by Garden et al, 7 and published recently, 8 a general expression can be derived when the configurational contributions of the three thermodynamic coefficients C p , α p , and κ T , are used in order to define a nonequilibrium configurational PD ratio:…”