Constructing bilayers with tuneable ring statistics and topologies

Abstract

A computationally tractable method is developed and described to generate two-dimensional networks with the aim of producing configurations for thin films (bilayers) of SiO2 and related materials. The method developed allows ideal (defect-free) networks of any given shape to be grown from seeds with both tuneable ring statistics (ring distributions) and topologies, the latter characterised by the Aboav–Weaire parameter, α. The method developed is demonstrated by growing networks which differ in their ring distributions and topologies as controlled by a combination of the choice of the ‘allowed’ rings and the effective growth ‘temperature’. Configurations are generated with Aboav–Weaire parameters commensurate with those obtained from an analysis of experimental configurations, improving significantly on previous methods for generating these networks (which systematically underestimate this parameter). The ability to efficiently grow configurations allows us to explore the structural basis of Lemaitre's law (which couples the underlying network ring distribution second moment with the fraction of six-membered rings, p6) in terms of maximum entropy. A rationale for the commonly observed value of p6 ∼ 0.4 is presented as a balance between entropic and enthalpic contributions to the free energy. The deviations of the respective ring areas from the ideal are discussed and the relative insensitivity of the ring area (in systems of this type) to relatively strong distortions is highlighted.