Theory of Specific Heat in Glass Forming Systems

Experimental measurements of the specific heat in glass-forming systems reveal anomalies in the temperature dependence of the specific heat, including the so called "specific heat peak" in the vicinity of the glass transition. The aim of this paper is to provide theoretical explanations of these anomalies in general and a quantitative theory in the case of a simple model of glass-formation. We first present new simulation results for the specific heat in a classical model of a binary mixture. We show that in addition to the formerly observed specific heat peak there is a second peak at lower temperatures which was not observable in earlier simulations. Second, we present a general relation between the specific heat and the bulk modulus and thus offer a smooth connection between the liquid and amorphous solid states. The central result of this paper is a connection between the micro-melting of clusters in the system and the appearance of specific heat peaks. We relate the two peaks to changes in the bulk and shear moduli. We propose that the phenomenon of glass-formation is accompanied by a fast change in the bulk and the shear moduli, but these fast changes occur in different ranges of the temperature. Lastly, we demonstrate how to construct a theory of the frequency dependent complex specific heat, expected from heterogeneous clustering in the liquid state of glass formers. A specific example is provided in the context of our model for the dynamics of glycerol. The theoretical frequency dependent specific heat agrees well with experimental measurements on glycerol. We conclude the paper by stating that there is nothing universal about the temperature dependence of the specific heat in glass formers - unfortunately one needs to understand each case by itself.