Читать книгу Encyclopedia of Glass Science, Technology, History, and Culture - Группа авторов - Страница 293
4.2 Non‐bridging Vertices (or Singly Coordinated Atoms)
ОглавлениеThere has been much discussion in the literature [26] about the role of dangling vertices (or non‐bridging nodes) and their influence (if any) on the rigidity characteristics of a network. At least conceptually, it is clear that dangling vertices should not affect the stiffness of the network because they are not network‐forming. In this respect, a confusion in the literature exists primarily because of the way constraints and degrees of freedom are counted. Clearly, if a dangling vertex is counted as being part of the network, then it is necessary to count also the length and angle constraints associated with it. A dangling vertex adds three degrees of freedom but also three constraints (one length and two angles), so that it does not make any net contribution to the degrees of freedom in a network if the counting is done correctly. However, the problem is that extra degrees of freedom often appear when the angular constraints of the dangling vertices are not included in the count [26, 27]. Because these extra degrees of freedom are associated with the floppiness of the dangling vertices themselves, they do not influence the rigidity or the flexibility of the underlying network. Thus, the opinion of this writer is that it is best to disregard the onefold coordinated atoms (i.e. dangling or non‐bridging vertices) as they have no influence on the rigidity characteristics of a network.