The Kauzmann Paradox Revisited

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.