Modeling the Oscillatory Behavior of Carbon Nano-onions Inside Single-walled Carbon Nanotubes Based on the Continuum Approximation Method

In this paper, oscillatory behavior of carbon nano-onions inside single-walled carbon nanotubes is investigated. To this end, using the continuum approximation along with the Lennard-Jones potential function, analytical expressions are derived for the evaluation of van der Waals interaction force and potential energy of system. Based on the Newton’s second law and ignoring the frictional forces, the motion equation is solved numerically and the time histories of displacement and velocity of oscillator are obtained. Moreover, in order to determine the oscillation frequencies of system, a semi-analytical expression is derived based on the conservation of mechanical energy principle. The proposed expression of frequency is dependent on both geometrical parameters and initial conditions. Using this expression, a comprehensive study is performed on the oscillatory behavior of carbon nano-onions inside single-walled carbon nanotubes by varying system parameters. Numerical results indicate that the generated frequency of this type of nano-oscillators is in the gigahertz range. It is further observed that the escape velocity as well as the maximum oscillation frequency decrease as the number of layers of carbon nano-onion increases.