Symmetry of chiral nanotubes: Natural torsion and diffraction evidence



Optimizations performed with geometrical, molecular mechanics, and density functional models show that chiral carbon nanotube configuration is slightly twisted with respect to the rolled-up geometry. The torsion angle is small, <1° Å−1 for ultrathin tubes, and decreases with tube diameter. The effect can be explained through breaking of local symmetry of the equally distant neighbors in graphene, which is diminished by the torsion. Although, the twist is small, still, we single out features in diffraction patterns which can distinguish between twisted and non-twisted configurations, at least for narrow single-walled carbon nanotubes.