Structural relaxation and frequency-dependent specific heat in a supercooled liquid

Frequency-dependent specific heat in quantum supercooled liquids: A mode-coupling study

Frequency-dependence of specific heat in supercooled hard sphere liquid is computed using quantum mode-coupling theory (QMCT). Mode-coupling equations are solved using a recently proposed perturbative method that allows us to study relaxation in the moderate quantum regime where quantum effects assist liquid to glass transition. Zwanzig's formulation is used to compute the frequency-dependent specific heat in the supercooled state using dynamical information from QMCT. Specific heat shows strong variation as the quantumness of the liquid is changed, which becomes more significant as density is increased. It is found that, near the transition point, different dynamical modes contribute to specific heat in classical and quantum liquids.

Conventional methods fail to measure cp (omega) of glass-forming liquids

The specific heat is frequency dependent in highly viscous liquids. By solving the full one-dimensional thermoviscoelastic problem analytically it is shown that, because of thermal expansion and the fact that mechanical stresses relax on the same time scale as the enthalpy relaxes, the plane thermal-wave method does not measure the isobaric frequency-dependent specific heat c{p}(omega) . This method rather measures a "longitudinal" frequency-dependent specific heat, a quantity defined and detailed here that is in between c{p}(omega) and c{V}(omega) . This result means that no reliable wide-frequency measurements of c{p}(omega) on liquids approaching the calorimetric glass transition exist. We briefly discuss consequences for experiment.

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.