Axial-Strain-Induced Torsion in Single-Walled Carbon Nanotubes

Using classical molecular dynamics and empirical potentials, we show that the axial deformation of single-walled carbon nanotubes is coupled to their torsion. The axial-strain-induced torsion is limited to chiral nanotubes—graphite sheets rolled around an axis that breaks its symmetry. Small strain behavior is consistent with chirality and curvature-induced elastic anisotropy (CCIEA)—carbon nanotube rotation is equal and opposite in tension and compression, and decreases with curvature and chirality. The large-strain compressive response is remarkably different. The coupling progressively decreases, in contrast to the tensile case, and changes its sign at a critical compressive strain. Thereafter, it untwists with increasing axial strain and then rotates in the opposite direction, i.e., the same sense as under tension. This suggests that the response is now dictated by a combination of nonlinear elasticity and CCIEA.

Figure 1

Chirality dependence of the a-SIT response for $(8,m)$ SWCNTs. (inset, top left) Atomic-plot of the simulation cell depicting a chiral $(8,4)$ SWCNT subject to an axial strain (in this case, compression). Color indicates the atomic distribution of the twist $\varphi$ about the CNT axis with respect to the unstrained case. (inset, top right) Chirality dependence of zero-strain coupling, $d\varphi /dϵ{|}_{ϵ=0}$.

Figure 2

Curvature dependence of the (a) a-SIT response for $n,n/2$ chiral SWCNTs, and (b) the zero-strain coupling, $d\varphi /dϵ{|}_{ϵ=0}$. The curve fit in (b) is of the form $(a\kappa +b{\kappa }^3+\cdots )$. (c) Chirality-curvature contour map of the coupling in $(n,m)$ SWCNTs, $6\ge n$, $m\ge 12$. The scale bar is in units of $°/\mathrm{nm}$. Dashed lines correspond to constant curvature, while $\theta =\pi /12$ chirality is shown as solid lines.

Figure 3

(a) Strain dependence of the carbon-carbon bond angles ($\alpha$, $\beta$, and $\gamma$) for the $(8,4)$ SWCNT. (b)–(d) Spatial distribution of the change bond lengths, for $ϵ=-2\%$ (b), $ϵ=0\%$ (c), and $ϵ=2\%$ (d). The color scale is $\Delta a_{\mathrm{C}\mathrm{\text{−}}\mathrm{C}}\times {10}^3$ [red (light shading) $>0$ and blue (dark shading) $<0$], where $\Delta a_{\mathrm{C}\mathrm{\text{−}}\mathrm{C}}$ is the change in bond length relative to the average value, i.e., $\Delta a_{\mathrm{C}\mathrm{\text{−}}\mathrm{C}}=a_{\mathrm{C}\mathrm{\text{−}}\mathrm{C}}-{\overline{a}}_{\mathrm{C}\mathrm{\text{−}}\mathrm{C}}$. The average bond lengths are ${\overline{a}}_{\mathrm{C}\mathrm{\text{−}}\mathrm{C}}=1.4262\AA$, ${\overline{a}}_{\mathrm{C}\mathrm{\text{−}}\mathrm{C}}(2\%)=1.4381\AA$, and ${\overline{a}}_{\mathrm{C}\mathrm{\text{−}}\mathrm{C}}(-2\%)=1.4149\AA$.