Curvature Effect of Interlayer Van Der Waals Forces on Axial Buckling of A Double-walled Carbon Nanotube

The curvature effect of interlayer van der Waals (vdW) forces on an axially compressed double-walled carbon nanotube is studied. Unlike existing models which assume that the interlayer vdW pressure at any point between the inner and outer tubes depends merely on the difference of their deflections at that point, the present model considers the dependence of the interlayer vdW pressure on the curvature of the difference of deflections at that point. A simple formula is derived for the critical axial strain, which clearly indicates the role of the interlayer vdW forces affected by the curvature of deflection. In particular, the critical axial strain predicted by the present model is higher than or equal to that given by the existing models without the curvature effect provided that the coefficient for the curvature dependence of the interlayer vdW pressure is negative. Furthermore, the curvature effect on the critical axial strain is more significant for buckling modes of smaller wavelengths. These results indicate that the curvature effect, which has been neglected in all existing models, could play a significant role in various buckling problems especially for multi-walled carbon nanotubes of smaller radii.