Modeling of van der Waals force for infinitesimal deformation of multi-walled carbon nanotubes treated as cylindrical shells

Abstract

This paper models van der Waals (vdW) force for axially compressed multi-walled carbon nanotubes (CNTs), whereby each tube is treated as a cylindrical shell continuum. Explicit formulas are derived for predicting the critical axial strain of a triple-walled CNT using a more refined vdW model. The analysis of a cylindrical shell continuum model of multi-walled CNTs using this refined vdW force model is carried out to study the influence of the effect of vdW interaction between different layers of a CNT and the size effect of a CNT on the vdW interaction. It is shown herein that the greatest contribution to the vdW interaction comes from the adjacent layers and the contribution from a remote layer may be neglected. The vdW interaction is found to be strongly dependent on the radius of the tube, especially when the radius is small enough (40 nm), the vdW interaction coefficient cij can be taken as a constant value (i.e. independent of radius). However, these constant values are different for the vdW interaction between two different layers of a multi-walled CNT. The effect of the vdW interaction on the critical axial strain of a triple-walled CNT for the cases of before and after buckling is also examined for various innermost radii. © 2005 Elsevier Ltd. All rights reserved.