Ideal torsional strengths and stiffnesses of carbon nanotubes

The ideal torsional strengths of a class of carbon nanotubes, and the torsional stiffnesses of all carbon nanotubes are computed using a novel combination of an ab initio electronic structure total energy technique and a physically motivated scaling form. The specific torsional strengths of multi-walled tubes are predicted to exceed those of steel by approximately a factor of 20. Closed-form expressions that bound the torsional stiffnesses are also presented. The predictions of the theory give excellent agreement with available experimental data.

Figure 1

The studied SWNTs. (a) Untwisted (10,0) CN viewed both along its axis and perpendicularly. (b) The same nanotube, but twisted uniformly. (c) The twisting distorts the carbon hexagons as shown.

Figure 2

(a) Torque $T_s$ as a function of twist rate $\theta ∕d$ computed using the total energy technique described in the text for different zig-zag nanotubes. (b) $T_s∕r^2$ vs $r\theta ∕d$ plotted, as suggested by Eq. (2). The collapse of the curves suggests that Eq. (2) is a good description of the torsional strength of zig-zag nanotubes. The solid line is a sixth-order polynomial fit to the scaled data used to represent $f\left(x\right).$

Figure 3

The ITS of a MWNT compared with a Fe rod of the same dimensions. The MWNTs are roughly 20 times stronger than an iron rod of the same size.

Figure 4

A comparison of experimentally measured intrinsic torsional stiffness and the theoretical predictions for zig-zag MWNTs. The solid and dashed lines give, respectively, the maximum and minimum stiffnesses predicted by the theory. The fact that some of the measured stiffnesses exceed those predicted by the theory can be attributed to uncertainty in the measured nanotube radii and possibly to enhanced interwall interactions that may enhance the stiffness.