Normal modes of carbon nanotubes: similarities and differences with their continuum counterpart

Carbon nanotabes (CNTs) possess a range of unusually interesting and useful physicochemical properties. In this paper, the mechanical properties of single wall CNTs are investigated via free vibration normal modes using molecular mechanics models. The force field used is empirical and the usual assumptions of potential energy contributions coming from bond-stretching, bond angle bending, and bond twisting for two, three, and four atom interactions respectively, are made. The validity of continuum behaviour is examined by comparing the modal spacing obtained from the molecular mechanics models and that obtained from classical continuum elastodynamics. The breakdown of continuum behaviour is systematically characterised for various combinations of length to diameter ratio as well as for the number of atoms per circumference.