Thermodynamics of coarse-grained models of supercooled liquids
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Fitting of thermodynamic data near using the facilitated models of Ref. 12 and compared to the formula used by Biroli, Bouchaud, and Tarjus (indicated as BBT) (Ref. 13). Top panel: Excess specific heat of supercooled OTP (left-hand scale) and 3BP (right-hand scale). Symbols indicate experimental data (Ref. 16). The full curves are fits using the formulas for the heat capacity per molecule discussed in the text (where ): , where and . Here , where the first (approximate) equality neglects terms of order and the second introduces the notation used in our Ref. 12: is a degeneracy that we imagine measures the possible directions of mobility, and bounds from above the temperatures we consider. The values of and 16.7 for OTP and 3BP were determined in Ref. 12 from kinetic data. On physical grounds we expect and to increase with temperature. The fitting of gives , , , 0.03, 0.7 and 4.5, 0.04, 0.5 for OTP and 3BP, respectively. at as argued in Ref. 12. Clearly, it is possible to describe the size and modest change with of the specific heat in the vicinity of , in contrast with the observation of BBT. Bottom panel: Excess entropy of OTP (left-hand scale) and 3BP (right-hand scale). Symbols correspond to experimental data Ref. 16. The full curves are fits using the formula for the entropy per molecule which follows from Eq. (28): . The fits shown correspond to the same parameters as before: , , 1.2 and 2.4, 1.8 for OTP and 3BP, respectively.
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