Exact and approximate geometric parameters for carbon nanotubes incorporating curvature

A new model for the geometric structure of carbon nanotubes is described. The existing model of rolled plane graphene sheet ignores discrepancies due to curvature. The new model adopts all bond angles and all bond lengths to be equal in the cylindrical state, and all atoms to be equidistant from a common axis of symmetry, which means that all atoms are truly equal. Exact formulae are presented for the major geometric parameters, such as nanotube radius. An asymptotic series expansion leads to the conventional formulae as the leading order term, but in addition simple analytical formulae are given for correction terms. Although the correction terms are typically small, knowledge of the precise subtleties of the fine structure might be critical in terms of comprehending many new nanoscale phenomena. The new model also gives rise to a natural expression for the nanotube wall thickness for which to date no reliable information is available.