10 - The thermodynamic transition scenario

Summary

In Chapter 4 we introduced the Kauzmann temperature T_K as a possible limiting temperature for the existence of the supercooled liquid phase. The original hypothesis due to Kauzmann proposes eventual crystallization in the supercooled liquid at very low temperatures as a possible way out of the paradoxical situation in which the entropy of the disordered state becomes less than that of the crystal. Another possible explanation of the Kauzmann paradox could be that the simple extrapolation of the high-temperature result to very low temperature is not correct and the entropy difference between supercooled liquid and crystal remains finite down to very low temperature (Donev et al., 2006; Langer, 2006a, 2006b, 2007), finally going to zero only near T = 0. Either of these resolutions, however, leaves us with no understanding of the dramatic slowing down and associated phenomenology of the supercooled region above T_g. The difference of the entropy of the supercooled liquid from that of the solid having only vibrational motion around a frozen structure represents the entropy due to large-scale motion and is identified with the configurational entropy S_c of the liquid. The rapid disappearance of the configurational entropy of the disordered liquid or the so-called “entropy crisis” poses an important question that is essential for our understanding of the physics of the glass-transition phenomena and the divergence of the relaxation time at T_g. Apart from having a characteristic large viscosity, the supercooled liquid shows a discontinuity in specific heat c_p at T_g due to freezing of the translational degrees of freedom in the liquid.