Computer Generation of Disordered Networks with Targeted Structural Properties

Abstract: Disordered spatial networks are model systems that describe structures and interactions across multiple length scales. Scattering and interference of waves in these networks can give rise to structural phase transitions, localization, diffusion, and band gaps. The study of these complex phenomena requires efficient numerical methods to computer-generate disordered networks with targeted structural properties. In the established Wooten-Weaire-Winer algorithm, a series of bond switch moves introduces disorder into an initial network. Conventional strain energies that govern this evolution are limited to 3D networks with coordination numbers of no more than four. We extend the algorithm to arbitrary coordination number statistics by introducing bond repulsion in the Keating strain energy. We tune the degree and type of disorder introduced into initially crystalline networks by varying the bond-bending force constant in the strain energy and the temperature profile. The effects of these variables are analyzed using a list of order metrics that capture both direct and reciprocal space. A feedforward neural network is trained to predict the structural characteristics from the algorithm inputs, enabling targeted network generation. As a case study, we statistically reproduce four disordered biophotonic networks exhibiting structural color. This work presents a versatile method for generating disordered networks with tailored structural properties. It will enable new insights into structure-property relations, such as photonic band gaps in disordered networks.