Dynamics and thermodynamics of supercooled liquids and glasses from a model energy landscape

The dynamics and thermodynamics of a model potential-energy surface are analyzed with regard to supercooling and glass formation. Relaxation is assumed to be mediated by pathways that connect groups of local minima. The dynamics between these groups is treated via transition state theory using appropriate densities of states consistent with the thermodynamics of the model, with a general expression for the free energy barrier. Nonergodicity is admitted by successive disconnection of regions that no longer contribute to the partition function as a function of the observation time scale. The model exhibits properties typical of supercooled liquids and glasses spanning the whole range of "fragile" and "strong'' behavior. Non-Arrhenius dynamics, characteristic of ''fragile'' glass formers, are observed when the barriers to relaxation increase as the potential energy decreases, but only if the observation time scale is long enough. For a fixed observation time, fragility generally increases as the free energy barriers decrease and vibrational frequencies increase. We associate higher vibrational frequencies with systems that have more local minima, and hence when the model exhibits dynamic fragility we usually see a large change in the heat capacity at the glass transition. However, in some regions of parameter space the expected correlations between dynamics and thermodynamics are not present.