Composition dependence of glass transition temperature and fragility. II. A topological model of alkali borate liquids

Glass transition temperature and fragility are two important properties derived from the temperature dependence of the shear viscosity of glass-forming melts. While direct calculation of these properties from atomistic simulations is currently infeasible, we have developed a new topological modeling approach that enables accurate prediction of the scaling of both glass transition temperature and fragility with composition. A key feature of our approach is the incorporation of temperature-dependent constraints that become rigid as a liquid is cooled. Using this approach, we derive analytical expressions for the composition (x) dependence of glass transition temperature, T_g (x), and fragility, m (x), in binary alkali borate systems. Results for sodium borate and lithium borate systems are in agreement with published values of T _g (x) and m (x). Our modeling approach reveals a natural explanation for the presence of the constant T_g regime observed in alkali borate systems.