Modeling the instability of CNT tweezers using a continuum model

Carbon nanotube (CNT) tweezers are composed of two parallel cantilever CNTs with a distance in between. In this paper, the static response and instability of CNT-made nano-tweezers is theoretically investigated considering the effects of Coulomb electrostatic force and van der Waals molecular attraction. For this purpose, a nano-scale continuum model is employed to obtain the nonlinear constitutive equation of the nano-tweezers. The Euler-Bernoulli beam theory is applied to model the elastic response of the CNT. The van der Waals attraction is computed from the simplified Lennard-Jones potential. In order to solve the nonlinear constitutive equation of the system, three approaches, e.g. the hemotopy perturbation method (HPM), the Adomian decomposition (AD) and the finite difference method (FDM) are employed. The obtained results are in good agreement with the experimental measurements. As a case study, freestanding CNT tweezers has been investigated and the detachment length and minimum initial gap of the tweezers are determined. Moreover, the effective operation range of the van der Waals attraction that affects the instability behavior of the CNT tweezers is discussed.