Are defect models consistent with the entropy and specific heat of glass formers?

Abstract

We show that point-like defect model of glasses cannot explain thermodynamic properties of glassformers, as for example the excess specific heat close to the glass transition, contrary to the claim of J.P. Garrahan, D. Chandler [Proc. Natl. Acad. Sci. 100, 9710 (2003)]. More general models and approaches in terms of extended defects are also discussed.Kinetically constrained models (kcm) display trivial thermodynamics but non trivial dynamics [1,2,3]. They encapsulate in a specific way the 'free volume' idea according to which the slow dynamics of glasses is due to rare, localized mobility defects [4,5]. For most kcms, slow dynamics is indeed due to defect motions [3]. A remarkable aspect of these models is that although the dynamical rules are very simple and local, the emergent defect dynamics lead to highly non trivial physical behaviour. As a consequence kcms provide a theoretical framework for understanding many of the remarkable dynamical properties of fragile glass-formers, such as superArrhenius relaxation time [3,6,7], dynamical heterogeneities [8,9,10,11] and viscosity/diffusion decoupling [12]. That these models may in fact describe quantitatively the physical properties of glasses has been strongly advocated in a series of papers by J.P. Garrahan and D. Chandler (gc) [9,10], and investigated further in [13].One of the major tenet of kcms is the complete decoupling between dynamics and thermodynamics, at variance with the traditional view of Adam and Gibbs [14], and others [15,16], in which the decrease of configurational entropy with temperature is the fundamental underlying mechanism for the viscous slowing down. It is therefore a priori surprising that kcms could have anything sensible to say about the entropy and specific heat of real materials -even if these turn out to be acceptable models of their dynamics. Nevertheless, the claim made in [10] is that these models are also in quantitative agreement with the specific heat of these materials. More precisely, assuming a perfect gas of free defects, gc give a formula for the specific heat at fixed pressure per particle of the liquid (in excess of that of the solid), which we reproduce from ref.[10] to be:where N is the number of physical molecules contributing to enthalpy fluctuations in a coarse-graining cell, J is the enthalpy cost, in kelvins, for creating a mobile cell (remember that liquids are considered here at constant pressure, hence the importance of distinguishing between enthalpy and energy). The concentration of mobile cells c is assumed to be given by c(T )/(1 − c(T )) = A exp(−J/T ), where the numerical prefactor A is argued by gc to be rather large: ln A is akin to an entropy gain ∆s 0 /k B associated with the creation of a mobile cell. Note that there is a small difference between the specific heat in excess to that of the glass (considered in [10]) and that in excess of the crystal; this difference is however irrelevant for the present discussion.In the following we first adress the results of [10] showing that even if the value o...

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