Calorimetric study of glassy and liquid toluene and ethylbenzene: Thermodynamic approach to spatial heterogeneity in glass-forming molecular liquids

The heat capacities of glassy and liquid toluene and ethylbenzene were measured with an adiabatic calorimeter. Both samples were doped with about 10% of benzene to suppress crystallization. The effects of the doping were corrected for by assuming the additivity of the heat capacities of toluene (or ethylbenzene) and benzene. The configurational entropies of several glass-forming liquids, including toluene and ethylbenzene, were calculated as functions of temperature from their heat-capacity data. For these calculations, the vibrational heat capacities were determined by the least-squares fitting of the Debye and Einstein functions to the experimental values using auxiliary spectroscopic data from the literature. The size of cooperative rearranging region (CRR), which was first conceived by Adam and Gibbs, was calculated from the configurational entropy in a simplifying approximation that neglects distribution of CRR Size and internal entropy of CRR. For all of the systems examined, the size of CRR increases with decreasing temperature and is frozen-in at four to eight molecules per region at the glass-transition temperature.