Читать книгу Encyclopedia of Glass Science, Technology, History, and Culture - Группа авторов - Страница 36

When viscous liquids escape crystallization, why do they eventually vitrify instead of remaining in the supercooled liquid state? One answer to this question is purely kinetic and relies only on increasingly long relaxation times on cooling. If experiments could last forever, any glass would eventually relax to the equilibrium state. Then, the glass transition would result only from the limited timescale of feasible measurements. A simple thermodynamic argument known as Kauzmann's paradox [45] indicates that this answer is incorrect. At its basis is the existence of a configurational contribution that causes the heat capacity of a supercooled liquid to be generally higher than that of an isochemical crystal and its entropy to decrease faster than that of a crystal when the temperature is lowered (Figure 20). If the entropy is extrapolated to temperatures below the glass transition range, it becomes lower than that of the crystal at a temperature T_K, which is high enough for such an extrapolation to remain reasonable. Although this situation is not thermodynamically forbidden, it seems unlikely that an amorphous phase could have a lower entropy than an isochemical crystal.

Figure 20 Kauzmann catastrophe for amorphous selenium and ortho‐terphenyl (C₈H₁₄). Differences between the glass transition and Kauzmann temperatures indicating the smallness of the C_p extrapolations performed.

Source: Data from [46, 47].

The conclusion is that an amorphous phase cannot exist below T_K. The temperature of such an entropy catastrophe constitutes the lower bound to the metastability limit of the supercooled liquid. As internal equilibrium cannot be reached below T_K, the liquid must undergo a phase transition before reaching it. This is, of course, the glass transition. In its original form, Kauzmann's paradox implicitly neglects possible differences in vibrational entropy between the amorphous and crystalline phases. This simplification is actually incorrect but it does not detract from the gist of the argument, for taking into account such differences would only shift T_K slightly. A more rigorous statement of the paradox is that the catastrophe would occur when the configurational entropy of the supercooled liquid vanishes.