Mechanics of fullerenes oscillating in carbon nanotube bundles

In this paper, we examine the mechanics of a nano-scaled gigahertz oscillator comprising a fullerene that is moving within the center of a bundle of carbon nanotubes. Although numerical results specifically for a C60 fullerene are presented, the method is equally valid for any fullerene which can be modeled as a spherical molecule. A general definition of a nanotube bundle is employed which can comprise any number of parallel carbon nanotubes encircling the oscillating fullerene. Results are presented which prescribe the dimension of the bundle for any nanotube radius and the optimal configurations which give rise to the maximum suction energy for the fullerene. Prior results for fullerene single-walled nanotube oscillators are employed, and new results are also derived. These include a calculation of optimum nanotube bundle size to be employed for a C60-nanotube bundle oscillator, as well as new analytical expressions for the force and energy for a semi-infinite nanotube and a fullerene not located on the axis of the cylinder