Prigogine-Defay ratio and its change with fictive temperature approaching the ideal glass transition

Abstract

According to equilibrium thermodynamic theory, a liquid of zero configurational entropy would undergo an Ehrenfest type second order transition to another disordered structure at a temperature T2 known as the ideal glass transition temperature, but glass formation prevents one from observing it. The heat capacityCp, isothermal compressibility, κT, and isobaric thermal expansion coefficient, αp, change by an amount Δ at the Ehrenfest temperature, TEH=T2, and also at the glass transition temperature Tg. The Ehrenfest ratio RE at TEHorT2, ΔCp,EHΔκT,EHTEHVEH(Δαp,EH)2≡1. In contrast, experimentally determined Prigogine-Defay ratio, ∏P−D at Tg, ΔCpΔκTTV(Δαp)2>1, where V is the volume at the respective temperatures. Angell and Sichina [Ann. N. Y. Acad. Sci. 279 (1976) 53-67] discussed how ∏P−D would change to RE if a liquid could be cooled slowly enough to reach T2. After critically reviewing the basic aspects of RE and of experimental and theoretical values of ∏P−D, we use generic variations of ΔCp, ΔκT, ΔαP and V with the fictive temperature, Tf, and the extrapolated values of these quantities for o-terphenyl at T=T2, and calculate RE and ∏P−D. We find that RE<∏P−D, thus contributing to Angell-Sichina's discussion of the unique structure of the low temperature disordered phase. We then consider how ∏P−D would change if the entropy of a liquid were extrapolated such that it did not violate the third law of thermodynamics and there was no need for the conjecture of an Ehrenfest transition.