Influence of electrostatic force and the van der Waals attraction on the pull-in instability of the CNT-based probe–actuator

Abstract

In recent years, carbon nanotubes (CNTs) have attracted great attention in the fabrication of probe tips and actuators for scanning microscopes. Herein, the pull-in instability of CNT-based probe is investigated using a nanoscale continuum model. 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. Two analytical methods (i.e., Homotopy perturbation method and Adomian decomposition method) are applied to solve the nonlinear governing equation of the system. Furthermore, the obtained results are validated by comparing with experimental results in the literature as well as numerical solutions of the finite difference method. The pull-in parameters are determined and effect of van der Waals force and a geometrical parameter effect on the instability behavior of the CNT is discussed. Moreover, the detachment length and minimum initial gap of the freestanding CNT probe are determined.