Suction energy and offset configuration for double-walled carbon nanotubes

Nanostructures such as carbon nanotubes and fullerenes offer the means to create new mechanical devices operating at the nanoscale. Such devices include oscillators constructed from an inner carbon nanotube sliding inside another carbon nanotube. The resultant oscillatory frequency is found to be in the gigahertz range and they have applications in the computing industry for signalling devices, such as an ultra-fast optical filter. While most research in the area is dominated by molecular dynamics simulations, our approach here is to use elementary mechanical principles and classical applied mathematical modelling techniques to formulate explicit analytical criteria and ideal model behaviour. In this paper, we first investigate the suction force experienced by a single-walled carbon nanotube located near an open end of a semi-infinite single-walled carbon nanotube, using the Lennard–Jones potential and the continuum approximation. Second the equilibrium position of an offset inner tube with reference to the cross-section of the outer tube is determined.