Continuum modeling of breathing-like modes of spherical carbon onions

In this letter, an analytical formulation is developed for predicting the breathing-like modes of spherical carbon onions consisting of an arbitrary number of layers. The spherical layers of the carbon onions are concentrically nested, and are coupled through van der Waals (vdW) forces between two adjacent layers. Lennard-Jones potential and continuum models are utilized to estimate the vdW interaction coefficients and the breathing-like modes of the carbon onions. The formulation is justified by a good agreement between the results given by the present model and available experimental and numerical data. Finally, numerical results are obtained for various carbon onions.