Oscillation of nested fullerenes (carbon onions) in carbon nanotubes

Nested spherical fullerenes, which are sometimes referred to as carbon onions, of I _h symmetries which have N(n) carbon atoms in the nth shell given by N(n) = 60n ² are studied in this paper. The continuum approximation together with the Lennard-Jones potential is utilized to determine the resultant potential energy. High frequency nanoscale oscillators or gigahertz oscillators created from fullerenes and both single- and multi-walled carbon nanotubes have attracted much attention for a number of proposed applications, such as ultra-fast optical filters and ultra-sensitive nano-antennae that might impact on the development of computing and signalling nano-devices. Further, it is only at the nanoscale where such gigahertz frequencies can be achieved. This paper focuses on the interaction of nested fullerenes and the mechanics of such molecules oscillating in carbon nanotubes. Here we investigate such issues as the acceptance condition for nested fullerenes into carbon nanotubes, the total force and energy of the nested fullerenes, and the velocity and gigahertz frequency of the oscillating molecule. In particular, optimum nanotube radii are determined for which nested fullerenes oscillate at maximum velocity and frequency, which will be of considerable benefit for the design of future nano-oscillating devices.