A carbon nanotube is a rolled sheet of graphene; the roll direction (n,m) determines both its diameter and whether it conducts like a metal or a semiconductor.
Metallic if (n - m) mod 3 == 0, otherwise semiconducting
Diameter d = a × sqrt(n² + nm + m²) / π (a = 0.246 nm lattice constant)
- Chirality — armchair (n,n) is always metallic; zigzag (n,0) and chiral (n,m) can be either, depending on the rule above.
- Tube length — number of hexagonal rings rendered along the tube axis.
- Tensile force — pulls the lattice along its axis; past a critical strain the bonds visibly snap.
Real-world relevance: this same metallic/semiconducting split is why CNTs are used both as nanoscale wires and as transistor channels, and their C-C bond strength is what gives them a tensile strength many times that of steel by weight.