Buckling behavior of single-walled carbon nanotubes and a targeted molecular mechanics approach

During the general (conventional) molecular mechanics (GMM) simulation of the buckling of single-walled carbon nanotubes (SWCNTs), the load is displacement controlled and the calculated critical buckling strain is very sensitive to the specific displacement increment and convergence threshold chosen in molecular dynamics (MD) simulations, which may have led to the contradictory and diverged results in the previous studies. In this paper, a targeted-molecular mechanics (TMM) simulation method is proposed to study the buckling behavior of SWCNTs under axial compression, bending, and torsion. Comparing with the GMM method, the TMM technique is independent of the displacement increment and thus the solution is converged. The critical buckling strain computed from the TMM is higher than that from the GMM under axial compression and torsion, and the TMM results are similar to the GMM results upon bending. The TMM result approaches to the intrinsic critical buckling strain of a perfect tube; in addition, the TMM significantly reduces the computational cost and thus may be more efficient to study larger systems with atomistic simulations.

Figure 1

(Color online) The effect of the compressive displacement increment on the critical buckling strain in the GMM simulations; the tubes with (a) smaller diameters and (b) larger diameters are under the axial compression.

Figure 2

(Color online) The effect of the MM convergence threshold $\left(\xi \right)$ on the critical buckling strain under the axial compression in both the TMM and GMM methods, for (5,5) tubes with different tube lengths.

Figure 3

(Color online) The effect of the bending displacement increment on the critical buckling strain under the bending deformation in the GMM method, for tubes with varying diameter and length.

Figure 4

(Color online) The effect of $\xi$ on the critical buckling strain under the bending deformation in both the TMM and GMM methods, for (5,5) tubes with different tube lengths.

Figure 5

(Color online) The effect of the bending displacement increment on the critical buckling strain under the torsion deformation in the GMM method, for tubes with varying diameter and length.

Figure 6

(Color online) The effect of $\xi$ on the critical buckling strain under the torsion deformation in both the TMM and GMM methods, for (5,5) tubes with different tube lengths.

Figure 7

(Color online) The critical buckling strain under the axial compression computed by the TMM method, for tubes with varying diameter and length. The theoretical results from Eq. (2) are also shown.

Figure 8

(Color online) The critical buckling strain under the bending deformation computed by the TMM method, for tubes with varying diameter and length.

Figure 9

(Color online) The critical buckling strain under the torsion deformation computed by the TMM method, for tubes with varying diameter and length.

Figure 10

(Color online) The schematic of a tube under the torsion deformation in the GMM method.