Continuum study on the mechanics of ion-based carbon nanocones as gigahertz oscillators

There is a growing interest in the development of nanomechanical oscillators operating in the gigahertz range and beyond. This paper introduces a novel nano-oscillator based on a chloride ion inside an open carbon nanocone decorated by functional groups at both small and wide ends. Assuming that the carbon atoms and the electric charges of functional groups are evenly distributed over the surface and the two ends of nanocone, respectively, a continuum-based model is presented through which potential energy and interaction force are evaluated analytically. The van der Waals interactions between ion and nanocone are modeled by the 6-12 Lennard-Jones potential, while the electrostatic interactions between ion and two functional groups are modeled by the Coulomb potential. With respect to the proposed formulations, potential energy and interaction force distribution are presented by varying sign and magnitude of functional groups charge and geometrical parameters (size of small and wide ends of nanocone and its vertex angle). Using the fourth-order Runge-Kutta numerical integration scheme, the equation of motion is also solved to arrive at the time histories of separation distance and velocity of ion. An extensive study is performed to investigate the effects of sign and magnitude of functional groups charge, geometrical parameters, and initial conditions (initial separation distance and initial velocity) on the oscillatory behavior of ion-electrically charged open carbon nanocone oscillator. Numerical results demonstrate that the oscillation frequency of chloride ion inside an uncharged nanocone is respectively lower and higher than those generated inside a nanocone whose small end is decorated by positively and negatively charged functional groups. It is further shown that oscillation frequency is highly affected by the sign of electric charges distributed at the small end of nanocone.