A carbon atom orbiting around the outside of a carbon nanotube

In this paper, we examine a carbon atom orbiting around the outside of a (6,6) carbon nanotube, where the orbiting phenomena is assumed to arise only from the van der Waals interactions between the carbon atom and the atoms on the surface of the carbon nanotube. We model the van der Waals forces utilizing the Lennard-Jones potential and assume that the carbon atoms are uniformly distributed over the surface of the carbon nanotube, so that a discrete sum of the atomic potential energy between the carbon atom and the molecule can be approximated by a line integral. The circular orbiting frequency of the system can be estimated by investigating the minimum energy configuration of the effective potential energy. An instability calculation is performed to ensure that the circular orbit remains stable, and the classification of the atompsilas possible loci is determined numerically. We find that the circular orbiting frequency of the proposed system reaches the gigahertz regime, which suggests that such a system has potential to be utilized as an ideal device in future technological development. We also briefly show that the results obtained from the above system can be extended to a fullerene orbiting around the outside of a carbon nanotube without conceptual difficulties, but with increased mathematical complexity.