Mathematical Modelling for a C60 Carbon Nanotube Oscillator

The discovery of fullerenes C₆₀ and carbon nanotubes has created an enormous impact on nanotechnology. Because of their unique mechanical and electronic properties, such as low weight, high strength, flexibility and thermal stability, fullerenes C₆₀ and carbon nanotubes are of considerable interest to researchers from many scientific areas. One problem that has attracted much attention is the creation of gigahertz oscillators. While there are difficulties for micromechanical oscillators, or resonators, to reach a frequency in the gigahertz range, it is possible for nanomechanical systems to achieve this. A number of studies have found that the sliding of the inner-shell inside the outer-shell of a multi-walled carbon nanotube can generate oscillatory frequencies up to several gigahertz. In addition, it has been observed that the shorter the inner tube, the higher the frequency, leading to the introduction of a C₆₀-nanotube oscillator. Thus instead of multi-walled carbon nanotubes, high frequencies can be generated using a fullerene C₆₀ oscillating inside a single-walled carbon nanotube. In this paper, using the Lennard-Jones potential, we determine the potential for an offset C₆₀ molecule inside a single-walled carbon nanotube, so as to determine its position with reference to the cross-section of the carbon nanotube. The condition for the C₆₀ initially at rest outside the carbon nanotube to be sucked in and to start oscillating is also presented together with a mathematical model for the resulting oscillatory motion. This paper summarizes recent results obtained by the present authors.