On the oscillatory frequency of the carbon nanotube-based nanothermometers

Electromechanical nanothermometers are instruments that work on the basis of the van der Waals (vdW) potential energy and interaction force of their constituent carbon nanotubes (CNTs). The CNT-based nanothermometers have two different configurations: telescope and shuttle configurations. In this article, based on the Lennard-Jones potential function together with the continuum approximation, first, the vdW potential energy and interaction force for a telescope configuration with finite CNTs are derived, which have not been obtained in the previous research studies. Thereafter, by employing the interaction force, the equation of motion between constituent CNTs is solved. Subsequently, a new semi-analytical expression is obtained which enables one to precisely evaluate the oscillation frequency. By employing the given formulae, effects of different system parameters on the vdW interactions and oscillation frequency are shown.