Effective bending stiffness of carbon nanotubes

Owing to their single atom-layer structure, actual bending stiffness of sin gle-walled carbon nanotubes is much lower than that given by the elastic sh ell model if the commonly defined representative thickness is used. In this paper, it is proposed that the effective bending stiffness of single-walle d nanotubes should be regarded as an independent material parameter not rel ated to the representative thickness by the classic bending stiffness formu la. Based on this concept, the modified formulas for the critical axial str ain and the wavelength of axially compressed buckling are found to agree we ll with known data of molecular-dynamic simulations. On the other hand, in contrast to single-walled nanotubes, bending stiffness of multiwalled nanot ubes is found to be well estimated by the classic bending stiffness formula when adjacent nanotubes are squeezed severely so that the induced high fri ction barrier prevents interlayer slips. In particular, these results offer a plausible interpretation for the wavelength of large-strain local buckli ng of multiwalled carbon nanotubes under bending observed by Falvo et al. [ Nature (London) 389, 582 (1997)].