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

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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 et al. Nature (London) 355, 333 (1992) 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=4.70TPa, ν=0.34, h=0.75 Å, 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 Å 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 ∞.