No Thaw Flaw in the Third LawAt the melting point of a substance, the liquid has a higher entropy than the solid. If the liquid is supercooled below the melting temperature, this entropy difference decreases because the liquid has a larger heat capacity than the solid. Usually kinetics takes over and the liquid freezes, but what if the liquid could be taken to absolute zero? As pointed out by Kauzmann, extrapolations of heat capacities have suggest that the molar entropies of the supercooled liquid and the crystal could become equal at a temperature above absolute zero (a positive Kauzmann temperature TK). In that case, the supercooled, disordered liquid would have negative entropy at absolute zero, in contradiction of the third law of thermodynamics.
Stillinger et al. have analyzed both data for real substances (such as liquid helium and some polymers) as a function of temperature and pressure and results from simulations. They pronounce the third law to be in good shape and also find no support for arguments proposing an “ideal glass transition” based on positive TK values.-PDS
The citation and abstract are:
“The Kauzmann Paradox Revisited”
Frank H. Stillinger, Pablo G. Debenedetti, and Thomas M. TruskettThe Journal of Physical Chemistry B; 2001; ASAP Article;
[J. Phys. Chem. B, ASAP Article 10.1021/jp011840i]Abstract:
Many glass-forming substances display heat capacities for their supercooled liquids that substantially exceed those of the corresponding crystals. Reasonable extrapolation below the kinetic glass transition temperature indicates that the molar entropies of the supercooled liquid and crystal phases would become equal at a "Kauzmann temperature" TK > 0. Furthermore, continuing such extrapolation below TK to absolute zero suggests that the disordered liquid attains lower entropy than the crystal, in conflict with the third law of thermodynamics (hence the "Kauzmann paradox"). The present study cites data for real substances and results from numerical simulation and theoretical modeling in the temperature-pressure plane to demonstrate that a Kauzmann locus TK(p) can indeed occur, though not necessarily for all materials. No third-law conflict arises. Also, the analysis provides no support for the concept of an "ideal glass transition" at positive temperature, often mentioned in connection with glass formers. In the event that classical statistical mechanics is applicable to a substance of interest, the low-temperature endpoint of the Kauzmann locus involves the maximum isotropic tension sustainable by spatially uniform amorphous deposits, a state which coincides in pressure and density with the minimum of the T = 0 liquid spinodal.