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

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 [Nature (London) 355, 333 (1992)] and is shown to be consistent with the classic shell theory by which Young's modulus, the Poisson ratio, and the effective wall thickness of SWNT's are obtained as Y=4.70 TPa, nu=0.34, and h=0.75 Angstrom, respectively. The elasticity of a multiwalled carbon nanotube (MWNT) is investigated as the combination of the above SWNT's of layer distance d=3.4 Angstrom and the effective Young's modulus of the MWNT is found to be an apparent function of the number of layers, N, varying from 4.70 to 1.04 TPa for N=1 to infinity.