Scaling Laws Governing the Elastic Properties of 3D-Graphenes

In this study, we have 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 as functions of honeycomb hole size, denoted by the graphene wall length $L$, were provided. All five independent elastic constants in the large $L$ limit are proportional to $L^{-1}$. The associated coefficients are combinations of two-dimensional graphene's elastic constants. 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 of solid angles between graphene plates, and the bending distortion of graphene plates. Significantly, the chirality becomes essential with the decreasing of $L$, 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.