Natural torsion in chiral single-wall carbon nanotubes

Optimizations performed with two geometrical, molecular mechanical and density functional models show that the configuration of single-wall carbon nanotubes is slightly twisted with respect to that predicted by conventional techniques. Geometrical models are used to explain the effect by breaking of local symmetry of the equally distant neighbors in graphene in the course of rolling, which is minimized by torsion. The torsion angle is small, and decreases with nanotube diameter, being less than 1° Å-1 for ultrathin tubes. Therefore this effect can be hard to observe in experiments. Still, we single out features in diffraction patterns which can distinguish between twisted and non-twisted configurations. In addition, torsion makes a blue shift in the radial breathing mode, which for thin tubes can be seen by Raman measurement. The effect is slightly strengthened at room temperature.