Single- and multi-walled carbon nanotubes viewed as elastic tubes with Young's moduli dependent on layer number

Abstract

The complete energy expression of a deformed single-walled carbon nanotube (SWNT) is derived in the continuum limit from the local density approximation model proposed by Lenosky {\it et al.} \lbrack Nature (London) {\bf 355}, 333 (1992)\rbrack and shows to be content with the classic shell theory by which the Young's modulus, the Poisson ratio and the effective wall thickness of SWNTs are obtained as $Y=4.70$TPa, $\nu =0.34$, $h=0.75\mathring{\mathrm{A}}$, respectively. The elasticity of a multi-walled carbon nanotube (MWNT) is investigated as the combination of the above SWNTs of layer distance $d=3.4\mathring{\mathrm{A}}$ and the Young's modulus of the MWNT is found to be an apparent function of the number of layers, $N$, varying from 4.70TPa to 1.04TPa for N=1 to $\infty$.

4 pages, 1 figure

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• Elastic Properties of C and BxCyNz Composite Nanotubes
• Ab-initio structural, elastic, and vibrational properties of carbon nanotubes
• Coil Formation in Multishell Carbon Nanotubes: Competition between Curvature Elasticity and Interlayer Adhesion
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