Gigahertz oscillators constructed from carbon nanocones inside carbon nanotubes

In the production of carbon nanotubes usually only a small amount of carbon nanocones are produced, and for this reason, carbon nanocones seem to have received much less attention than other carbon nanostructures. Most of the research on carbon nanocones deals with their electronic structure since they are the ideal candidate for the probes of scanning tunneling microscopes. Here, we examine their oscillatory properties inside carbon nanotubes. Such calculations are necessary as a preliminary to creating such future nano-devices. We adopt the Lennard-Jones potential function together with the usual continuum approximation to determine the suction energy for a carbon nanocone entering a single-walled carbon nanotube. We show that a carbon nanocone located co-axially will be sucked into a carbon nanotube when the difference between the cone base radius and the tube radius exceeds 2.5 angstrom and this is irrespective of the direction of the vertex. We also show that the maximum suction energy occurs when these radii differ by 3.0 angstrom. We then examine the oscillatory behaviour of a nanocone once it is inside a nanotube and we obtain pulse-like forces at both ends of the tube which maintain the oscillatory motion along the tube length. On neglecting frictional effects and approximating the pulse-like forces by Dirac delta functions, Newton's second law is employed to determine the oscillation frequency. This is shown to be in the order of 15 to 90 gigahertz, which is the same order of magnitude which has been obtained for oscillating co-axial carbon nanotubes.