Kauzmann temperature

Let us now turn to a discussion of the relation of the temperature dependence of the polymer melt s configurational entropy with its glass transition and address the famous paradox of the Kauzmann temperature of glass-forming systems.90 It had been found experimentally that the excess entropy of super-cooled liquids, compared with the crystalline state, seemed... 

An ambiguity of the F metric or the choice of the ratio Tg/Tx, where TK is the Kauzmann temperature, is that experimental data have to be extrapolated to obtain the VTF and the Kauzmann temperatures [37,43],... 

One way to improve the Adam-Gibbs model is to include details of the structure of the interface between the various aperiodic minima [39]. Near the Kauzmann temperature, the interface broadens, and correct scaling laws are obtained by wetting the droplet surface [39]. In this case, the surface tension of the entropic droplet is a function of its radius and can be obtained by renormalization group arguments. Analysis reveals that the activation barrier to configuration rearrangement is [39]... 

Computer simulations have pointed toward the fact that for temperatures below the Kauzmann temperature T%, replica symmetry is broken [157,158, 160], The variable that describes this phenomenon, rarepiica(T), is proportional to temperature [157,158,160] ... 

Here, Cv h(T) and Svlh(T) are the vibrational contributions to the heat capacity and the entropy, respectively. Note that the slope of the replica symmetry-breaking parameter with respect to temperature is not unity as predicted by one-step replica symmetry breaking. Rather, the slope is governed by three factors the Narayanaswamy-Moynihan nonlinearity parameter x, the Kauzmann temperature, and the ratio of the Kauzmann temperature to the glass transition 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). 

Figure 12.2 Variation of the heat capacity for fragile glass formers in crystal (C), supercooled liquid (Lgc), equilibrium liquid (Leq) and glass (G) phases. is the Kauzmann temperature.

The entropy crisis described in the preceding paragraph is the result of an extrapolation. With the exception of He and " He (Wilks, 1967)," there is no known substance for which a Kauzmann temperature is actually reached. Nevertheless, the extrapolation needed to provoke a conflict with the Third Law is indeed modest for many substances (Angell, 1997), and what intervenes to thwart the imminent crisis is a kinetic phenomenon, the laboratory glass transition. This suggests a connection between the kinetics and... 

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.)...

In spite of the remarkable agreement between theoretical predictions, on the one hand, and the logical consequence of the simulations, on the other, we beheve that the generality of behavior such as shown in Fig. 16 cannot be accepted uncritically but should instead be regarded as a fundamental open question on the properties of disordered materials. This caution is warranted by the approximate, mean-held nature of the calculations, as well as by microscopic critiques of the very notion of a Kauzmann temperature (Stillinger, 1988). Perhaps more signihcantly, recent experiments on... 

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. 

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