Wave propagation and structural dynamics in graphene nanoribbons

Graphene naoribbons (GNRs) are novel interesting nanostructures for the electronics industry, whereas their state as metallic or semiconductor material depends on the chirality of the graphene. We model the natural frequencies and the wave propagation characteristics of GNRs using an equivalent atomistic-continuum FE model previously developed by some of the Authors, where the C-C bonds thickness and average equilibrium lengths during the dynamic loading are identified through the minimisation of the system Hamiltonian. A molecular mechanics model based on the UFF potential is used to benchmark the hybrid FE model developed. The wave dispersion characteristics of the GNRs are simulated using a Floquet-based wave technique used to predict the pass-stop bands of periodic structures. We demonstrate that the thickness and equilibrium lengths for the different dynamic cases are different from the classical constant values used in open literature (0.34 nm for thickness and 0.142 for equilibrium length), in particular when considering out-of-plane flexural deformations. These parameters have to be taken into account when nanoribbons are designed as nano-oscillators.