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Topological Constraint Theory and Rigidity of Glasses

Topological constraint theory has become an increasingly popular tool to predict the compositional dependence of glass properties or pinpoint promising compositions with tailored functionalities. This approach reduces complex disordered networks into simpler mechanical trusses. Thereby, topological constraint theory captures the important atomic topology that controls macroscopic properties while filtering out less relevant second-order structural details. As such, topological constraint theory can be used to decode the genome of glass, that is, to identify and decipher how the basic structural building blocks of glasses control their engineering properties---in the same way as the human genome offers information that serves as a blueprint for an individual's growth and development. Thanks to its elegance and simplicity, topological constraint theory has enabled the development of various physics-based models that can analytically predict various properties of glass. In this Chapter, I introduce some general background in glass science, concepts of atomic rigidity, and topological constraint theory. The topological constraints enumeration scheme is presented for various archetypical glasses and is used to understand the origin of their glass-forming ability. Finally, various topological models enabling the prediction of glass properties are reviewed, with a focus on hardness, fracture toughness, viscosity, fragility, glass transition temperature, and dissolution kinetics.