Supercooled Liquids. In: Prigogine I, Rice SA, editors. Advances in Chemical Physics. Hoboken: John Wiley & Sons, Inc.; 1994. pp. 89-158. [DOI: 10.1002/9780470141489.ch2]

Fluctuation Effects in the Adam-Gibbs Model of Cooperative Relaxation

A generalization of the Adam-Gibbs model of relaxation in glass-forming liquids is formulated that takes into account fluctuation in the number of molecules inside the cooperative region. The configurational fraction links the excess entropy with kinetic properties described in the Adam-Gibbs model. We express the configurational fraction at the glass-transition temperature in terms of the width of the distribution of relaxation times, the nonlinearity parameter that demarcates the variations of the relaxation time with structure and temperature, the steepness index that is proportional to the slope of the logarithm of the relaxation time with respect to temperature, the excess heat capacity under constant pressure, and the number of correlated molecules or structural units. The configurational fraction in the absence of fluctuation effects is also determined for several glass-forming liquids at the glass-transition temperature.

Evaluation of activation parameters of molecular mobility of parylene C using differential scanning calorimetry, dielectric spectroscopy, and thermally stimulated depolarization currents

The molecular kinetics of α-relaxation were studied by dielectric spectroscopy (DS) and thermally stimulated depolarization currents (TSDC) for the thermoplastic semicrystalline parylene C (-H2C-C6H3Cl-CH2-)n thin film. Activation energy of the α-relaxation process brings very close values with both methods (155 ± 2 kJ mol(-1)). Dielectric spectroscopy carried out in a wide temperature range allowed one to determine the α-relaxation time against the temperature and then to estimate the Kauzmann and Angell temperatures for parylene C. From these temperatures and the determination of kinetics and thermodynamics parameters from DSC analysis, it was possible to investigate the cooperative rearranging region (CRR) in parylene C. CRR is quantified in terms of characteristic length (ζCRR), volume (VCRR), number z of rearranging units, and height barrier Δμ of the rearranging unit. Moreover, the fragility index m, calculated from these three methods, is discussed. A value of m = 94 is obtained by DSC confirming a "strong" character of parylene C. A lowest value of 35 ± 4 obtained from electric analyses (DS and TSDC) must be considered with caution because these methods of characterizations bring into play only dipolar relaxations. Last, the kinetic and thermodynamic parameters for parylene C highlighted in this work are positioned in comparison with other organic and inorganic materials.

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.

Nonmonotonic temperature dependence of heat capacity through the glass transition within a kinetic model

The heat capacity of a supercooled liquid subjected to a temperature cycle through its glass transition is studied within a kinetic model. In this model, the beta process is assumed to be thermally activated and described by a two-level system. The alpha process is described as a beta relaxation mediated cooperative transition in a double well. The overshoot of the heat capacity during the heating scan is well reproduced and is shown to be directly related to delayed energy relaxation in the double well. In addition, the calculated scan rate dependencies of the glass transition temperature T(g) and the limiting fictive temperature T(f) (L) show qualitative agreement with the known results. Heterogeneity is found to significantly reduce the overshoot of heat capacity. Furthermore, the frequency dependent heat capacity has been calculated within the present framework and found to be rather similar to the experimentally observed behavior of supercooled liquids.