Topology of alkali phosphate glass networks

The glass transition temperature of alkali phosphate glasses shows anomalous extremum points that are evidence of an unusual physical trend with chemical composition. In this paper, we develop a topological model for the glass transition temperature of binary alkali phosphate systems that helps elucidate the underlying structural and topological origins of this phenomenon. The topological model is analytically derived accounting for a hierarchy of temperature-dependent constraints and is shown to give an accurate prediction of the scaling of glass transition temperature with composition. We also discuss the general implications of the model, including the relationship between network rigidity and the distinguishability of particles at the glass transition.