The relationship between fragility, configurational entropy and the potential energy landscape of glass-forming liquids

Glass is a microscopically disordered, solid form of matter that results when a fluid is cooled or compressed in such a manner that it does not crystallize. Almost all types of materials are capable of glass formation, including polymers, metal alloys and molten salts. Given such diversity, general principles by which different glass-forming materials can be systematically classified are invaluable. One such principle is the classification of glass-formers according to their fragility(1). Fragility measures the rapidity with which a liquid's properties (such as viscosity) change as the glassy state is approached. Although the relationship between the fragility, configurational entropy and features of the energy landscape (the complicated dependence of energy on configuration) of a glass-former have been analysed previously(2), a detailed understanding of the origins of fragility is lacking. Here I use simulations to analyse the relationship between fragility and quantitative measures of the energy landscape for a model liquid whose fragility depends on its bulk density. The results reveal that fragility depends on changes in the vibrational properties of individual energy minima in addition to their total number and spread in energy. A thermodynamic expression for fragility is derived, which is in quantitative agreement with kinetic fragilities obtained from the liquid's diffusivity.