Transient Deformation Regime in Bending of Single-Walled Carbon Nanotubes

Pure bending of single-walled carbon nanotubes between $(5,5)$ and $(50,50)$ is studied using molecular dynamics based on the reactive bond order potential. Unlike smaller nanotubes, bending of $(15,15)$ and larger ones exhibits an intermediate deformation in the transition between the buckled and fully kinked configurations. This transient bending regime is characterized by a gradual and controllable flattening of the nanotube cross section at the buckling site. Unbending of a kinked nanotube bypasses the transient bending regime, exhibiting a hysteresis due to van der Waals attraction between the tube walls at the kinked site.

Figure 1

Predicted shape of single-walled carbon nanotubes just after buckling, based on MD simulations. (a) 15.7-nm-long $(10,10)$ SWNT at $\theta =43°$ and (b) 23.6-nm-long $(30,30)$ SWNT at $\theta =23°$. Note the difference in scale.

Figure 2

Strain energy $U$ and bending moment $M=dU/d\theta$ for a 23.6-nm-long $(30,30)$ SWNT as a function of the bending angle $\theta$. The letters a–e indicate the points for which the tube shape and cross section at the buckling point are shown in Fig. 3. TBR denotes the transient bending regime.

Figure 3

Side views and buckling point cross sections of a 23.6-nm-long $(30,30)$ SWNT at various bending angles corresponding to the points a–e marked on the strain energy curve in Fig. 2. Only the portion near the buckling region [darkened region in Fig. 1b] is shown for the longitudinal views. Bending occurs in the plane of the journal page.

Figure 4

Strain energy of various segments of a 23.6-nm-long $(30,30)$ SWNT as a function of the bending angle $\theta$. (1) Tube segment ($\sim 1/3$ of SWNT length) away from buckling region, (2) thin ring at the buckling point, and (3) thin ring away from buckling point. The van der Waals energy is excluded. The TBR region is observed between 12° and 32°.

Figure 5

(a) Strain energy $U$ for a 23.6-nm-long $(30,30)$ SWNT during bending and unbending operations. While all three bending regimes are present during bending, unbending proceeds by a direct switch from the kinking to the linear elastic regime. (b) Strain energy of bending and unbending of a $(15,15)$ SWNT. The energy does not depend on the direction of bending. TBR denotes the transient bending regime.