Mechanics of nested spherical fullerenes inside multi-walled carbon nanotubes

•Mechanics of carbon onions inside MWCNTs is studied using continuum approach.•VdW interactions and oscillation frequency depend on the number of shells.•Maximum frequency decreases as carbon onion gets larger.•Oscillation frequency does not increase considerably beyond an optimal number of nanotube shells.

Based on the continuum approximation and Lennard-Jones (LJ) potential, mechanics of nested spherical fullerenes, known as carbon onions, inside multi-walled carbon nanotubes (MWCNTs) is investigated in this study. To this end, direct method is first utilized to determine van der Waals (vdW) interaction force and potential energy between a carbon onion molecule and a semi-infinite MWCNT. According to this method, the interactions between each pair of shells from carbon onion and CNT are summed up over all of the pairs. Thereafter, the suction and acceptance energies for carbon onions entering semi-infinite MWCNTs are evaluated. On the basis of Newton's second law, an analytical expression is then presented to predict the oscillation frequency of a carbon onion molecule inside a MWCNT of finite length. The effect of geometrical parameters on the nature of suction and acceptance energies, vdW interactions and oscillatory characteristics of carbon onion-MWCNT oscillators is thoroughly examined. For a given carbon onion structure, it is found that there exists an optimal value for the number of nanotube shells beyond which the maximum oscillation frequency does not increase considerably. Furthermore, the maximum oscillation frequency decreases as the carbon onion gets larger.