New approach to model the buckling and stable length of multi walled carbon nanotube probes near graphite sheets

Modeling the buckling of multi walled carbon nanotube (MWCNT) probes/actuators in the vicinity of thin and thick graphite has been carried out for the first time via two analytical approximation methods as well as a numerical one. A hybrid nano-scale continuum model based on Lennard-Jones potential is applied to simulate the intermolecular force-induced deflection of MWCNT. The critical values of MWCNT tip deflection and MWCNT-graphite attraction at the onset of the instability are computed. In addition, minimum nanotube-graphite initial gap and stable length of freestanding CNT 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.