Relaxation Kauzmann temperature

The Kauzmann temperature plays an important role in the most widely applied phenomenological theories, namely the configurational entropy [100] and the free-volume theories [101,102]. In the entropy theory, the excess entropy ASex obtained from thermodynamic studies is related to the temperature dependence of the structural relaxation time xa. A similar relation is derived in the free-volume theory, connecting xa with the excess free volume AVex. In both cases, the excess quantity becomes zero at a distinguished temperature where, as a consequence, xa(T) diverges. Although consistent data analyses are sometimes possible, the predictive power of these phenomenological theories is limited. In particular, no predictions about the evolution of relaxation spectra are made. Essentially, they are theories for the temperature dependence of x.-jT) and r (T). 

Fig. 12. Adam-Gibbs plots of the dielectric relaxation time of 2-methyltetrahydrofuran (2-MTHF) and 3-bromopentane (3-BP) versus (Tsconi) . The lines are VTF fits, 7 fus is the fusion temperature, and Tb is the temperature below which the VTF equation applies. /I ag and Avf are prefactors in the Adam-Gibbs and VTF equations, respectively. Tk is the calorimetri-cally determined Kauzmann temperature, and To is the VTF singular temperature, which were set equal in the VTF (line) fits. (Reprinted with permission from R. Richer and C. A. Angell. Dynamics of glass-forming liquids. V. On the link between molecular dynamics and configurational entropy. J. Chem. Phys. (1998) 108 9016. Copyright 1998, American Institute of Physics.)...

KWW function with a / of 0.65 0.03 was found to fit well the imaginary parts of CpK ([Q,/r] ) at all temperatures. The peak relaxation frequencies were found to follow VTF law with a To of (128 5) K, very close to the Kauzmann temperature of 134 K. Such specific heat spectroscopy measurements, as described above have great potential for use, where other relaxation spectroscopic methods are either difficult or inconceivable. 

Finally, it is worth noting that the values of Tq or needed to fit the viscosity data are close to the temperature at which the Kauzmann temperature, Tkau is estimated from extrapolations of other properties such as those shown in Fig. 9.8, lending credence to the model. This model also provides a natural way out of the Kauzmann paradox, since not only do the relaxation times go to infinity as T approaches 7)., but also the configuration entropy vanishes since in glass at T = T only one configuration is possible. 

Kauzmann did not accept this implication, however. He argued instead that in the temperature interval between 7 and Tk, the probability of crystallization was increasing so that before the isoentropic point could be reached, the time scale for crystallization would become the same as that for configurational relaxation in the amorphous phase, as discussed in Section II above. This would precipitate a first-order phase transition by the spontaneous growth of fluctuations in the appropriate direction. Such an event would necessarily terminate the liquid-state metastable free-energy surface and make the apparent entropy-crossing problem metaphysical and, Kauzmann therefore reasoned, of no consequence. 

In Fig. 22, the two dashed curves have a similar significance. Curve a, as in Fig. 21, requires the existence of a thermodynamic transition associated with a divergence of the relaxation time at some temperature T> the most natural choice being the temperature (marked TJ, "), which corresponds to the Batchinski-Hildebrand Fq " for the system (see Fig. 4). Curve b represents an alternative resolution of the Kauzmann paradox for this system and implies that the heat capacity must have a maximum, under... 

---