Some novel plane trajectories for carbon atoms and fullerenes captured by two fixed parallel carbon nanotubes

The movement of atoms and molecules at the nanoscale constitutes a fundamental problem in physics, especially following the motion of atoms in many-body systems condensing together to form molecular structures. A number of simplified nanoscale dynamical problems have been analyzed and here we investigate the classical orbiting problem around two centers of attraction at the nanoscale. An example of such a system would be a carbon atom or a fullerene orbiting in a plane which is perpendicular to two fixed parallel carbon nanotubes. We model the van der Waals forces between the molecules by the Lennard-Jones potential. In particular, the total pairwise potential energies between carbon atoms on the fullerene and the carbon nanotubes are approximated by the continuous approach, so that the total molecular energy can be determined analytically. Since we assume that such interactions occur at a sufficiently large distance, the classical two center problem analysis is legitimate to determine various novel trajectories of the atom and fullerene numerically. It is clear that the oscillatory period of the atom for some bounded trajectories reaches terahertz frequencies. We comment that the continuous approach adopted here has the merit of a very fast computational time and can be extended to more complicated structures, in contrast to quantum mechanical calculations and molecular dynamics simulations.Y. Chan and J.M. Hil