Topological Constraint Theory of Glass: Counting Constraints by Molecular Dynamics Simulations

Despite many successes, the application of topological constraint theory to engineering novel glasses with tailored properties has been limited by a lack of knowledge of glass structure and topology. To this end, atomistic simulations (e.g. molecular dynamics) can yield valuable information as they offer a full and direct access to the atomic structure of glasses. In turn, these inputs can be used to inform analytical topological models that can be used to guide glass design. In this chapter, we review a series of methods aiming to describe the rigidity of glasses by means of atomistic simulations. We show that atomistic simulations can offer a robust estimation of the density of topological constraints acting in a given glass. By assessing the existence of internal floppy modes of deformation and internal stress in glassy networks, atomistic simulations can also be used to track some signatures of flexible-to-rigid and unstressed-stressed transitions. The topological information offered by atomistic simulations is key to inform predictive, analytical composition-property models and to pinpoint promising glass formulations featuring optimally connected networks.