Study of axial strain-induced torsion of single-wall carbon nanotubes using the 2D continuum anharmonic anisotropic elastic model

Recent molecular dynamic simulations have found that chiral single-walled carbon nanotubes (SWCNTs) twist during stretching, resembling the motion of a screw. Obviously this phenomenon, as a type of curvature-chirality effect, cannot be explained by the usual isotropic elastic theory of SWCNTs. More interestingly, with larger axial strains (before buckling), the axial strain-induced torsion (a-SIT) shows asymmetric behaviors for axial tensile and compressing strains, which suggests the anharmonic elasticity of SWCNTs plays an important role in real a-SIT responses. In order to study the a-SIT of chiral SWCNTs with actual sizes, and to avoid possible deviation of computer simulation results due to the finite-size effect, we propose a two-dimensional (2D) analytical continuum model which can be used to describe SWCNTs of arbitrary chirality, curvature, and length, and which is concerned with their anisotropic and anharmonic elasticity. The elastic energy of the present model comes from the continuum limit of lattice energy based on second generation reactive empirical bond order potential (REBO-II), a well-established empirical potential for solid carbons. Our model has no adjustable parameters, except for those presented in REBO-II, and all the coefficients in the model can be calculated analytically. Using our method, we obtain the a-SIT responses of chiral SWCNTs with arbitrary radii, chiralities and lengths. Our results are in reasonable agreement with recent molecular dynamic simulations (Liang et al 2006 Phys. Rev. Lett. 96 165501). Our approach can also be used to calculate other curvature-chirality-dependent anharmonic mechanical responses of SWCNTs.