Mechanics of atoms and fullerenes in single-walled carbon nanotubes. II. Oscillatory behaviour

摘要

The discovery of carbon nanotubes and C-60 fullerenes has created an enormous impact on possible new nanomechanical devices. Owing to their unique mechanical and electronic properties, such as low weight, high strength, flexibility and thermal stability, carbon nanotubes and C-60 fullerenes are of considerable interest to researchers from many scientific areas. One aspect that has attracted much attention is the creation of high-frequency nanoscale oscillators, or the so-called gigahertz oscillators, for applications such as ultrafast optical filters and nano-antennae. 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. This study focuses on C-60 single-walled carbon nanotube oscillators, which generate high frequencies owing to the oscillatory motion of the C-60 molecule inside the single-walled carbon nanotube. Using the Lennard-Jones potential, the interaction energy of an offset C-60 molecule inside a carbon nanotube is determined, so as to predict its position with reference to the cross-section of the carbon nanotube. By considering the interaction force between the C-60 fullerene and the carbon nanotube, this paper provides a simple mathematical model, involving two Dirac delta functions, which can be used to capture the essential mechanisms underlying such gigahertz oscillators. As a preliminary to the calculation, the oscillatory behaviour of an isolated atom is examined. The new element of this study is the use of elementary mechanics and applied mathematical modelling in a scientific context previously dominated by molecular dynamical simulation.