Van der Waals interactions and oscillatory behaviour of carbon onions interacting with a fully constrained graphene sheet

This study focuses on the van der Waals (vdW) interactions and oscillatory behaviour of nested spherical fullerenes (carbon onions) in the vicinity of a single-layer graphene (SLG) sheet. The carbon onions are of Ih symmetries and the graphene sheet is modelled as a fully constrained flat surface. Employing the continuum approximation along with the 6–12 Lennard-Jones (LJ) potential function, explicit analytical expressions are determined to calculate the vdW potential energy and interaction force. The equation of motion is solved numerically based on the actual force distribution to attain the displacement and velocity of the carbon onion. Using the conservation of mechanical energy principle, a semi-analytical expression is also derived to accurately evaluate the oscillation frequency. Numerical results are presented to examine the influences of size of carbon onion and initial conditions (initial separation distance and initial velocity) on the operating frequency of carbon onion–SLG sheet oscillators. It is shown that carbon onion executes oscillatory motion above the graphene sheet with frequencies in the gigahertz (GHz) range. It is further observed that smaller structures of carbon onions produce greater frequencies. We comment that the presented results in this study would contribute to the development of new generation of nano-oscillators.