Perfect position and oscillation frequency of nanosectors orbiting inside carbon nanotori

This paper aims to develop a new semi-analytical method based on the continuum approximation and Lennard-Jones (LJ) potential function to investigate the potential energy and van der Waals (vdW) interaction force between sectors of nanotorus and carbon nanotori molecule. Following the present method, a semi-analytical formulation is achieved in terms of double integrals which can be readily employed to obtain the interactions. A semi-analytical expression is also presented to determine the oscillation frequency. The sector is assumed to be orbiting inside the carbon nanotori and is free to choose its perfect position inside this nanostructure. The effects of geometrical parameters such as tube and ring radii of nanotori as well as angle of nanosector on the variation of potential energy, vdW interaction force and frequency are examined. As a significant finding, it is shown that the oscillation frequency, which is in the gigahertz (GHz) range, is independent of the sector angle. Results of this study are shown to be consistent with the existing data and can be beneficial for the future studies on the GHz oscillators.