Topological Constraints and Rigidity of Network Glasses from Molecular Dynamics Simulations<\/i><\/p>\n

Topological constraint theory provides an interesting means to understand the important microscopic physics governing the thermal, mechanical and rheological properties of glasses with changing compositions, while filtering out unnecessary details that ultimately do not affect its macroscopic properties. It has been successful in predicting compositional trends in covalent network-forming glasses such as chalcogenides. Its application appears however more challenging in iono-covalent glasses such as silicates where neighbors\/bonds and angles need to be properly defined. Here we derive such constraints for different alkali silicates using an atomic scale approach (Molecular Dynamics, MD) combined with partial bond angle distributions (PBAD). The latter allows having access to the second moments (standard deviations) of the distributions. Large (small) standard deviations correspond to large (small) angular excursions around a mean value, and are identified as broken (intact) bond-bending constraints. A similar procedure is used for bond-stretching constraints. Systems examined include glassy and liquid disilicate 2SiO2-M2O (LS2, NS2, KS2). In the glass, MD constraint counting closely matches Maxwell enumeration of constraints using the octet binding (8-N) rule. Results show that the standard deviations of the partial bond angle distributions increase with temperature and suggest a softening of bond-bending constraints. A bimodal bonding oxygen distribution is obtained for T>Tg, and the fraction of thermally activated broken bond-bending constraints computed as a function of temperature. As a preliminary work, pressure effects are also presented. Overall, these results provide a microscopic rationale for extending constraint counting from chalcogenides to complex oxides, and also a numerical basis for recent functional forms of temperature-dependent constraints proposed from energy landscape approaches.<\/p>\n