Bending instability characteristics of double-walled carbon nanotubes

Abstract

The bending instability characteristics of double-walled carbon nanotubes (DWNTs) of various configurations are studied using a hybrid approach in which the deformation-induced increase of the intratube interaction energy is modeled with the bending deformation energy using the elastic theory of beams. The intertube interaction energy is calculated using the van der Waals interatomic potential. This study shows that the bending instability may take place through the formation of a single kink in the midpoint of a DWNT or two kinks, placed symmetrically about the midpoint, depending on both the tube length and diameter. The double-kink mode is more favorable for longer DWNTs with the same diameter, and there exists a threshold length for a fixed diameter, below which the single-kink mode occurs at the onset of the bending instability and above which the double-kink mode prevails. The onset characteristic of bending instability is determined by the effectiveness of the intertube interaction in transferring the load from the outer tube onto the inner tube, and the load-transfer effectiveness increases with the increasing tube length. For a fixed length/diameter ratio, the load-transfer effectiveness is found to decrease with the increasing diameter for smaller tubes while it increases for larger tubes, and, thus, the double-kink mode can prevail for both small DWNTs and large DWNTs. ©2005 The American Physical Society.