All liquids are topologically disordered materials; however, the degree of disorder can vary as a result of internal fluctuations in structure and topology. These fluctuations depend on both the composition and temperature of the system. Most prior work has considered the mean values of liquid or glass properties, such as the average number of topological degrees of freedom per atom; however, the localized fluctuations in properties also play a key role in governing the macroscopic characteristics of any glass-forming system. This paper proposes a generalized approach for modeling topological fluctuations in glass-forming liquids by linking the statistical mechanics of the disordered structure to topological constraint theory. In doing so we introduce the contributions of localized fluctuations into the calculation of the topological degrees of freedoms in the network. With this approach the full distribution of properties in the disordered network can be calculated as an arbitrary function of composition, temperature, and thermal history (for the nonequilibrium glassy state). The scope of this current investigation focuses on describing topological fluctuations in liquids, concentrating on composition and temperature effects.

Glasses are topologically disordered materials with varying degrees of fluctuations in structure and topology. This study links statistical mechanics and topological constraint theory to quantify the degree of topological fluctuations in binary phosphate glasses. Because fluctuations are a potential mechanism enabling self-organization, we investigated the ability of phosphate glasses to adapt their topology to mitigate localized stresses, e.g., in the formation of a stress-free intermediate phase. Results revealed the dependency of both glass composition and temperature in governing the ability of a glass network to relax localized stresses and achieve an ideal, isostatic state; also, the possibility of a second intermediate phase at higher modifier content was found.

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