It has been observed that the van der Waals interaction can cause an extruded core of a multiwalled carbon nanotube (MWNT) to retract into the outer shells. In a previous report [Q. Zheng and Q. Jiang, Phys. Rev. Lett. $88,$ 045503 (2002)], the authors pointed out that the restoring force resulted from the excess van der Waals interaction energy due to the core extrusion would drive the core to oscillate with respect to its fully retracted position because of the small intershell sliding resistance force and they predicted that the oscillation frequency could be in the gigahertz range. The present article gives detailed theoretical calculations of the excess van der Waals energy due to the extrusion and the corresponding restoring force. The authors have further derived an explicit expression of the oscillation frequency in terms of the physical and geometrical parameters of the MWNT, with the interatomic locking effect taken into account, and they have shown that the oscillation frequency can be significantly higher than one gigahertz.

• Received 7 January 2002

DOI:https://doi.org/10.1103/PhysRevB.65.245409