Carbon nanotubes: III. Toroidal structures and limits of a model for the construction of helical and S-shaped nanotubes Original Research Article

Formulae are derived for the calculation of geometrical characteristics of polygonal toroidal frameworks used to model helicoidal nanotubes, and some structural defects associated with these models are explained. Although the construction of both single-shell and multi-shell toroidal structures seems possible, that a of series of coaxial helical or pseudo-helical shells separated by the same distance is, in general, impossible.