Basics of structure
A carbon nanotube is based on a two-dimensional graphene sheet. (a) The chiral vector is defined on the hexagonal lattice as Ch = nâ1 + mâ2, where â1 and â2 are unit vectors, and n and m are integers. The chiral angle, q, is measured relative to the direction defined by â1. This diagram has been constructed for (n, m) = (4, 2), and the unit cell of this nanotube is bounded by OAB'B. To form the nanotube, imagine that this cell is rolled up so that O meets A and B meets B', and the two ends are capped with half of a fullerene molecule. Different types of carbon nanotubes have different values of n and m.
(b) Zigzag nanotubes correspond to (n, 0) or (0, m) and have a chiral angle of 0°, armchair nanotubes have (n, n) and a chiral angle of 30°, while chiral nanotubes have general (n, m) values and a chiral angle of between 0° and 30°. According the theory, nanotubes can either be metallic (green circles) or semiconducting (blue circles).