Structure of single-wall carbon nanotubes: a graphene helix

Evidence is presented in this paper that certain single-wall carbon nanotubes are not seamless tubes, but rather adopt a graphene helix resulting from the spiral growth of a nano-graphene ribbon. The residual traces of the helices are confirmed by high-resolution transmission electron microscopy and atomic force microscopy. The analysis also shows that the tubular graphene material may exhibit a unique armchair structure and the chirality is not a necessary condition for the growth of carbon nanotubes. The description of the structure of the helical carbon nanomaterials is generalized using the plane indices of hexagonal space groups instead of using chiral vectors. It is also proposed that the growth model, via a graphene helix, results in a ubiquitous structure of single-wall carbon nanotubes.