Scaling laws governing the elastic properties of 3D graphenes

In this study, we comprehensively investigated the scaling law for elastic properties of three-dimensional honeycomb-like graphenes (3D graphenes) using hybrid neural network potential-based molecular dynamics simulations and theoretical analyses. The elastic constants were obtained as functions of honeycomb hole size, denoted by the graphene wall length L. All five independent elastic constants in the large-L limit are proportional to L⁻¹. The associated coefficients are combinations of elastic constants of two-dimensional graphene. High-order terms including L⁻² and L⁻³ emerge for finite L values. They have three origins, the distorted areas close to the joint lines of 3D graphenes, the variation in solid angles between graphene plates, and the bending distortion of graphene plates. Significantly, the chirality becomes essential with decreasing L because the joint line structures are different between the armchair and zigzag-type 3D graphenes. Our findings provide insights into the elastic properties of graphene-based superstructures and can be used for further studies on graphene-based materials.