Nonuniversality of the Specific Heat in Glass Forming Systems

We present new simulation results for the specific heat in a classical model of a binary mixture glass former in two dimensions. 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. This is a surprise, as most texts on the glass transition expect a single specific heat peak. We explain the physics of the two specific heat peaks by the micromelting of two types of clusters. While this physics is easily accessible, the consequences are that one should not expect any universality in the temperature dependence of the specific heat in glass formers.

Figure 1

In dots: the temperature dependence of the specific heat in the binary mixture model, computed at constant volume, such that the volume agrees with the pressure $P=13.5$ [7] at each temperature. The data indicate the existence of two specific heat peaks, one prominent at about $T=0.5$ and a smaller on at about $T=0.1$, and see the inset for finer detail. The data at lower temperature represent two years of computing time and are believed to be trustable. The error bars are smaller than the points used in the graph. Note that the specific heat is smaller than 2 at $T=0.3$ and $T=0.2$, but larger than 2 for $T=0.1$. It must go to the limit $C_V=2$ for $T\to 0$, making a secondary peak around $T=0.1$.

Figure 2

A snapshot of the system at $T=0.44$. In colors, we highlight the clusters of large particles in local hexagonal order. The colors have no meaning.

Figure 3

Specific heat at constant volume as predicted by the simple theory which is based on the mechanical equation of state supplied by Eqs. (5, 6, 7). Note that the theory predicts the two peaks which are associated with the micromelting or microfreezing of the clusters of large and small particles, respectively. The magnitude of the peaks is too high, reflecting terms missing in the simple approach, like the effect of anharmonicity at the lowest temperatures which are negative, tending to decrease the height of the low-temperature peak.