Calorimetric glass transition explained by hierarchical dynamic facilitation

Abstract

The glass transition refers to the nonequilibrium process by which an equilibrium liquid is transformed to a nonequilibrium disordered solid, or vice versa. Associated response functions, such as heat capacities, are markedly different on cooling than on heating, and the response to melting a glass depends markedly on the cooling protocol by which the glass was formed. This paper shows how this irreversible behavior can be interpreted quantitatively in terms of an East-model picture of localized excitations (or soft spots) in which molecules can move with a specific direction, and from which excitations with the same directionality of motion can appear or disappear in adjacent regions. As a result of these facilitated dynamics, excitations become correlated in a hierarchical fashion. These correlations are manifested in the dynamic heterogeneity of the supercooled liquid phase. Although equilibrium thermodynamics is virtually featureless, a nonequilibrium glass phase emerges when the model is driven out of equilibrium with a finite cooling rate. The correlation length of this emergent phase is large and increases with decreasing cooling rate. A spatially and temporally resolved fictive temperature encodes memory of its preparation. Parameters characterizing the model can be determined from reversible transport data, and with these parameters, predictions of the model agree well with irreversible differential scanning calorimetry.