Topological ordering during flexible to rigid transitions in disordered networks

This contribution focuses on the structural origin of flexible to rigid transitions and the possible underlying intermediate phase which have been reported to occur in a variety of network glasses such as chalcogenides or modified oxides. Here, using molecular dynamics simulations of densified glass-forming liquids, 2SiO$_2$-Na$_2$O, which are known to display a numerical reversibility window as a signature of an intermediate phase, we focus on structural functions emphasizing topological ordering using the Bhatia–Thornton formalism. Results not only reveal that densified silicates display topological ordering on lengthscales of about 25 Å, but also display obvious threshold behaviors close to the isostatic condition when the network undergoes a flexible to rigid transition. The mechanical constraint count of the atomic network structure reveals that a typical lengthscale characterizing the decay of topological correlations emerges for stressed rigid systems at $\simeq $3.5 Å, whereas small wavevector oscillations are found to be minimal when the isostatic condition is merely satisfied. An additional analysis building on diffusivity and liquid entropy suggests that the locus of flexible to rigid transitions has also connections with water-like anomalies of densified tetrahedral liquids.