Energy landscape picture of supercooled liquids: Application of a generalized random energy model

The thermodynamic and kinetic anomalies of supercooled liquids are analyzed from the perspective of energy landscapes. A mean-field model, a generalized random energy model of liquids, is developed which exhibits a dynamical transition of the onset of slow dynamics at T-0, alteration of the nature of motion from saddle-to-saddle to minimum-to-minimum motion at T-c, and an ideal glass transition at T-k. If the energy spectrum of the configurations has a low energy tail, the model also allows a thermodynamic liquid-liquid transition at T-l. The liquid-liquid transition of the model is correlated to the kinetic fragile-strong transition accompanied by the anomalous slowing down of motion. Fragility of the system is classified in terms of features of the energy landscape such as ruggedness of the potential energy surface, size of the cooperative motion invoked in transition from one configuration to another, and energy needed to deform the local structure in the cooperative motion. A simple relation is found between diffusion constant, D and the saddle index of the potential energy surface, f as D-proportional tofa, where a depends on the size of the cooperative motion. (C) 2003 American Institute of Physics.