Fabrication of new types of nanoscale oscillators with enhanced operating frequency has become the focal centre of interest. The aim of this paper is to explore the mechanical oscillatory behaviour of chloride ion tunnelling through carbon nanotubes (CNTs) decorated with identical functional groups at both ends. To this end, our previously proposed analytical expression for total potential energy between an ion and a functionalized CNT is used to derive a new semi-analytical expression for the accurate evaluation of oscillation frequency. With respect to the proposed frequency formula obtainedfrom the conservation of mechanical energy principle, a comprehensive study is conducted to gain an insight into the effects of different parameters such as, sign and magnitude of functional group charge, nanotube length and initial conditions on the operating frequency of chloride ion-electrically charged CNT oscillators. It is revealed that the presence of functional groups, especially ones with the opposite charges to the chloride ion, leads to enhancement of the maximum achievable frequency. It is further observed that optimal frequency is attained when the ion oscillates near the ends of a positively charged nanotube.

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 ${\rm I}_h$ 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, asemi-analytical expression is also derived to accurately evaluate the oscillation frequency. Numerical results are presentedto examine the influences of size of carbon onion and initial conditions (initial separation distance and initial velocity) onthe operating frequency of carbon onion–SLG sheet oscillators. It is shown that carbon onion executes oscillatory motionabove the graphene sheet with frequencies in the gigahertz (GHz) range. It is further observed that smaller structures ofcarbon onions produce greater frequencies. We comment that the presented results in this study would contribute to thedevelopment of new generation of nano-oscillators.