Frequency dependent heat capacity within a kinetic model of glassy dynamics

There has been renewed interest in the frequency dependent specific heat of supercooled liquids in recent years with computer simulation studies exploring the whole frequency range of relaxation. The simulation studies can thus supplement the existing experimental results to provide an insight into the energy landscape dynamics. We here investigate a kinetic model of cooperative dynamics within the landscape paradigm for the dynamic heat capacity C(omega,T) behavior. In this picture, the beta-process is modeled as a thermally activated event in a two-level system and the alpha-process is described as a beta-relaxation mediated cooperative transition in a double well. The model resembles a landscape picture, apparently first conceived by Stillinger [Science 267, 1935 (1995)], where an alpha-process is assumed to involve a concerted series of beta-processes. The model provides a description of the activated hopping in the energy landscape in close relation with the cooperative nature of the hopping event. For suitable choice of parameters, the model predicts a frequency dependent heat capacity that reflects the two-step relaxation behavior. The separation between the two peaks grows as the temperature drops, indicating the stringent constraint on the alpha-process due to the cooperativity requirement. The temperature dependence of the position of the low-frequency peak, due to the alpha-relaxation, shows a non-Arrhenius behavior as observed experimentally. The shape of the alpha-peak is, however, found to be temperature independent. The high-frequency peak appears with considerably larger amplitude than the alpha-peak. We attempt a plausible reason for this observation that is in contrast with the general feature revealed by the dielectric spectroscopy. The relative amplitudes of the beta- and alpha-peaks in the present framework are found to depend on several characteristic features of the energy landscape, including the extent of cooperativity requirement for the alpha-relaxation and the asymmetry of the double well.