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

TL;DR

This paper models supercooled liquids using a generalized random energy model to explain their thermodynamic and kinetic anomalies, including transitions and fragility, through an energy landscape perspective.

Contribution

It introduces a mean field generalized random energy model that captures multiple transitions and fragility features of supercooled liquids based on energy landscape characteristics.

Findings

Identifies dynamical, ideal glass, and liquid-liquid transitions in the model.

Establishes a relation between diffusion constant and saddle index of the energy landscape.

Links fragility to landscape ruggedness and cooperative motion size.

Abstract

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 the 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 a 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 $D \propto f^{a}$, where a depends on the size of the cooperative motion.