Energetics of plastic bending of carbon nanotubes

Plastic bending of single-wall carbon nanotubes is analyzed using minimum energy path calculation with a bond-order potential. The calculation demonstrates that plastic deformation is only thermodynamically favorable above a threshold “yield curvature” ${\rho }_{\mathrm{yield}}$, and is kinetically feasible above $1500\mathrm{K}$, which agree with our experimental observations. A deformation mechanism map as function of temperature and bending curvature is constructed, and the dependence of ${\rho }_{\mathrm{yield}}$ on the nanotube diameter is analyzed.

Figure 1

(a) The back and belly positions of bent SWNT, (b) plastic deformation accomplished by bond rotation (adapted from Ref. 3), (c) first nucleation event in armchair SWNT and zigzag SWNT, respectively.

Figure 2

(Color online) MEP of 5-7-7-5 defect nucleation and 5-7 pairs migration in (5,5) SWNT (a), (b), (c) and (8,0) SWNT (d), (e), (f) at bending curvature $\rho =0{\mathrm{nm}}^{-1}$ (a), (d); $0.25{\mathrm{nm}}^{-1}$ (b), (e); and $0.34{\mathrm{nm}}^{-1}$ (c), (f). Labels “ND” and “SW” mean the defect-free state and the state with the 5-7-7-5 defect, respectively. $x$ axis is the split step of the two pairs. Snapshots in (g) and (h) are the atomic configurations of each split step starting from (a) and (d), respectively.

Figure 3

Activation energies of 5-7-7-5 defect nucleation as a function of the bending curvature $\rho$, in (a) (5,5) SWNT, (b) (8,0) SWNT, and formation energies of the defective configuration of 4 and 6 split steps in (c) (5,5) SWNT, and (d) (8,0) SWNT, respectively, as a function of $\rho$.

Figure 4

Illustration of the total-energy model for the preference of plastic versus elastic deformation. The elastic energy can be relieved by 5-7-7-5 defect nucleation and 5-7 pairs migration (plastic cut), if that energy relief exceeds the self-energy of the plastic cut.

Figure 5

(a) The yield curvature ${\rho }_{\mathrm{yield}}$ versus the tube diameter $D$. (b) The formation energies versus $D$ at $\rho =0.05{\mathrm{nm}}^{-1}$. The dashed line in (a) and (b) is the approximate scaling ($D^{-1}$ and $a_0+a_{1}D-a_2{D}^2$, respectively). The solid symbols are the actual numerical results.

Figure 6

Deformation mechanism map for bending SWNTs. Horizontal axis is the imposed curvature. Vertical axis is the temperature.