Elastic Wave Propagation in 2D Carbon Nano‐Onion Lattices

This study presents a simple analytical model to investigate wave propagation in 2D carbon nano‐onions (CNOs) and nitrogen‐doped carbon nano‐onions (N‐CNOs) lattices. Furthermore, the dispersion relationships of the waves and bandgaps in these lattices are derived based on Bloch's theorem. The CNOs and N‐CNOs lattices are modeled as infinite 2D mass‐in‐mass structures accurately assembled using linear springs. The Lennard–Jones potential energy is employed to obtain equivalent spring constants. A key finding of this research is the identification of bandgaps within all lattice structures, signifying regions where wave propagation is prohibited. The existence of these bandgaps offers potential for the advancement of adjustable nano‐scale metamaterials.