Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium

An elastic double-shell model is presented for infinitesimal buckling of a double-walled carbon nanotube embedded in an elastic matrix under axial com pression. The analysis is based on a Winker model for the surrounding elast ic medium and a simplified model for the van der Waals interaction between the inner and outer nanotubes. An explicit formula is derived for the criti cal axial strain, which indicates the effects of the surrounding elastic ma trix combined with the intertube van der Waals forces. In particular, the p resent model predicts that the critical axial strain of the embedded double -walled nanotube is lower than that of an embedded single-walled nanotube u nder otherwise identical conditions. This implies that inserting an inner t ube lowers the critical axial strain of an embedded single-walled carbon na notube, although the total critical compressive force could be increased du e to the increase in the cross-sectional area of the nanotube. The reduced critical axial strain is attributed to the intertube slips between the inne r and outer tubes. This result indicates that embedded multi-walled carbon nanotubes could be even more susceptible to infinitesimal axial buckling th an embedded single-walled carbon nanotubes. (C) 2001 Elsevier Science Ltd. All rights reserved.