Structural effects of the insertion of large rings in two-dimensional networks

The structural effect of inserting large central rings into a two-dimensional network of three-coordinate nodes is investigated using a ring-growth Monte Carlo procedure. The size of the central ring is systematically varied, as is the inherent level of disorder in the surrounding network (as controlled by the Monte Carlo "temperature" and characterized by the fraction of six-membered rings). The effect of the central ring on the overall network topology is analyzed in terms of both topological and geometric distances. For larger central rings, the first topological shell becomes exclusively populated by four- and five-membered rings, which leads to an effective upper limit on the size of the central ring that can effectively be accommodated. The topological shells are found to show ordering at significant distances away from the central ring. The effective correlation lengths are determined as a function of both central ring size and level of network disorder, which allows for an understanding of the potential density of large rings that may be accommodated.