This paper presents an analytical method for Young's modulus determination of an individual carbon nanotube under electrostatic loading. Using the pull-in force and large deflection solution of the trajectory of a carbon nanotube, the Young's modulus has been determined analytically. To this end the governing equation for carbon nanotube as a cantilever beam under uniform distributed load was derived. The Direct Nonlinear Solution (DNS) by means of the Homotopy-Perturbation Method (HPM) was implemented to derive the large deflection solution of the trajectory of any point along the beam length. The Young's modulus has been calculated through the proposed method and compared to those obtained experimentally. For the verification the deflections were calculated and compared to those of finite element method (FEM) which was taken as a reference. It was found that the proposed solution overcame the shortcomings of conventional methods; such as experimental difficulties in the determination of Young's modulus or the inaccuracy of linear methods and the dependency on the elliptic integrals. It has been shown that the method is very accurate, efficient, and convenient for the problem discussed and can be applied to similar practical problems related to nano-scale devices.
Polycrystalline carbon tubes were generated by CVD inside electrochemically prepared nano-porous anodic aluminium oxide membranes. This method produced nano-tubes without catalyst, featuring polycrystalline and a few layer thick walls. Individual tubes could be isolated and suspended on microfabricated substrates such that they formed single-side clamped beams. These beams were then used to investigate their mechanical properties employing electrostatic forces for bending the tubes beyond their mechanical stability where pull-in occurs, which could be detected by monitoring the current flowing from the tube to the substrat
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