Mechanics of nanoscale orbiting systems

Abstract

At the nanoscale a number of very high frequency oscillating systems involving relative motion with respect to a carbon nanotube have been identified. In this paper, we study the two-body systems of an atom and a fullerene C60 orbiting around a single infinitely long carbon nanotube and a fullerene C60 orbiting around a fullerene C1500. The van der Waals interaction forces are modeled using the Lennard–Jones potential together with the continuum approach for which carbon atoms are assumed to be uniformly distributed over the surfaces of both the fullerenes and the carbon nanotube. Some analytical and perturbation solutions are obtained for the regime where the attractive term of the potential energy dominates. Certain circular orbiting radii of these nanoscale systems are estimated using a stability argument and the corresponding circular orbiting frequencies can then be calculated by investigating the minimum energy configuration of their effective potential energies. We find that the circular orbiting frequencies of the various proposed nano-systems are in the gigahertz range. Finally, the classification of their orbiting paths is determined numerically.