Perspective on the glass transition

Some of the reasons for the current interest in the phenomenology of vitrification are reviewed and progress due to, as well as limitations of, mode coupling theories (MCT) for viscosity divergence are examined. Liquids which fit the MCT predictions best are also those with the most imminent Kauzmann entropy crises near the glass transition temperature, T_g. Mode coupling predictions break down far above T_g at the point, T_x, where Goldstein long ago argued that activated processes controlled by the (3N + 1)-dimensional potential energy surface for the N- particle system should become dominant. Examining behavior in the energy topology-controlled regime, we note that ergodicity-breaking is not simply a consequence of viscosity divergence. In the liquids best fitting MCT, which are at the fragile extreme of liquid behavior, shear and structural relaxation processes slowly decouple below T_x, leading to breakdown of the Adam-Gibbs equation for viscosity. The latter in its original and derived Vogel-Fulcher forms remains valid for enthalpy (and presumably volume) relaxation processes. The distinction between strong and fragile behavior in liquids is related to the density of configurational states (minima) characterizing the potential energy surface.