A new solution on the buckling and stable length of multi wall carbon nanotube probes near graphite sheets

Abstract

In this paper, a power series solution is used to study effect of intermolecular forces on the instability of multi walled carbon nanotube (MWCNT) probes/actuators in the vicinity of thin and thick graphite. A hybrid nano-scale continuum model based on Lennard-Jones potential is applied to simulate the intermolecular force-induced deflection of MWCNT. A power series method basis on symbolic computation is introduced to obtain an analytical solution for the distributed parameter model. The critical values of MWCNT tip deflection and MWCNT-graphite attraction at the onset of the instability are computed. Minimum nanotube-graphite initial gap and stable length of freestanding carbon nanotube are determined as basic parameters for engineering applications and nano-devices design. The stable length of MWCNT is determined as a function of its geometrical and material characteristics, initial gap and number of graphene layers. The obtained results are compared with the Adomian decomposition and Green's function as well as numerical results. The obtained results in compare with numerical results represent remarkable accuracy rather than the Adomian decomposition method and Green's function.