Size effect and sp$^3$ bond formation in carbon nanotube bending

We report molecular dynamics simulations of bending behaviors of carbon nanotubes (CNTs). Due to the interlayer interaction, single- walled CNTs (SWCNTs) and multi-walled CNT (MWCNTs) show different buckling characters both in deformation pattern and energetic evolution. Simulations in post-buckling region show that large bending strain leads to sp$^{3}$ bond formation in kink areas and that the capability of sp$^{3}$ bond formation is sensitive to tube size. These results suggest a new route for structure engineering of CNTs.