Vibrational entropy, configurational entropy, and the fragility of glassforming liquids

Abstract

A thermodynamic measure of the fragility of liquids has recently (Ito et al ref.1) been defined in terms of the temperature dependence of the excess entropy of liquid over crystal, scaled by the excess entropy at the glass transition temperature, and it has been correlated with kinetic fragility. The correlation has been vigorously contested [2] using dielectric relaxation data on some molecular liquids. We put this conflict in perspective using an extensive data set covering all classes of liquids while retaining the cases of ref 2. The excess entropy of the liquid, used in the thermodynamic quantity being correlated, has both configurational and vibrational components. This is the source of a second conflict which concerns the relative importance of these two components. Experimental tests supporting the Adam-Gibbs "entropy" theory of the temperature dependence of transport in viscous liquids have mostly been made using the excess entropy, but recent simulation studies on the hard sphere fluid [3] SPC-E water [4] and mixed LJ [5,6] have shown, as in the A-G theory, a correlation with the configurational component. We show why, in laboratory studies, the correlation should be with both, inextricably. In the course of this demonstration we identify a key role for excess vibrational entropy in causing fragile behavior in ambient pressure liquids.