Entropy and fragility in supercooling liquids

We review the Kauzmann paradox and what it implies about the configuration space energy hypersurface for "structural glassformers." With this background, we then show how the relaxation expression of Adam and Gibbs qualitatively accounts for most of the phenomenology of liquid and polymeric glassformers including the strong/fragile liquid pattern, and the behavior of nonergodic systems. Extended temperature range relaxation studies are consistent with a relaxation time pre-exponent on the quasilattice vibration time scale. When this boundary condition is imposed on Vogel-Fulcher-Tammann fittings, correspondence of T-0 with T-K is found for liquids with T-g ranging over 1000 K. When it is imposed on the WLF equation C-1 is obliged to become similar to 16, and the corresponding force-fitted C-2 provides a measure of the polymer fragility which is generally not available from thermodynamic studies. Systems which exhibit discontinuous changes in configurational entropy on temperature increase, which include unfolding proteins, are briefly reviewed.