The Viscous-Liquid-Glassy-Solid Problem

The different aspects of liquid state behavior currently in focus are classified in terms of their place in the range of ralaxation times separating the microscopic (phonon) time from the structural relaxation time at the normal glass transition T_g. The place within this scheme of each of the contributions to this symposium is identified. Special attention is given to the crossover between "free diffusion" and "landscape-dominated" regimes. Thermodynamic estimates of the "height of the landscape" are given for strong and fragile liquids and a correspondence is found between the thermodynamic estimate and characteristic temperatures T_c of mode coupling theory and T_x of Rössler scaling obtained from different analyses of the dynamic properties. Fragile liquids have all their configurational microstates (configurons) packed into a small energy band between kT_K and the upper limit at kT_u i.e. T_u is relatively close to T_K. In the landscape-dominated regime, clustering occurs. We outline a cooperative cluster model which can generate high fragility and which in extreme cases can provoke a first-order phase transition to the fully clustered state.