Carbon Nanotube Chirality Simulator

Chirality (n, m)

n 10

m 5

Bending strain 0%

Diameter

–

Chiral angle

–

Conduction type

–

How it works

A single-walled carbon nanotube is a sheet of graphene — a hexagonal lattice of carbon atoms — rolled into a seamless cylinder. Exactly how it is rolled is fixed by a pair of integers (n, m) called the chiral indices: they define the "chiral vector" that becomes the tube's circumference once the sheet closes on itself. Those two integers alone determine the tube's diameter, the tilt of its hexagon rows (the chiral angle) and, remarkably, whether it conducts electricity like a metal or behaves like a semiconductor.

C = a·√(n² + nm + m²)   (circumference)
d = C / π                (diameter)
θ = atan[ √3·m / (2n + m) ]   (chiral angle, 0°–30°)
metallic  ⇔  (n − m) mod 3 = 0
a = √3·a_C-C ≈ 0.246 nm

n, m — the chiral indices. m = 0 gives a "zigzag" tube (θ = 0°); n = m gives an "armchair" tube (θ = 30°); anything else is a general chiral tube.
Diameter grows with √(n² + nm + m²) — bigger indices roll a wider cylinder from the same graphene lattice.
Conduction type — roughly one tube in three is metallic (ballistic electron transport along the axis, no band gap); the rest are semiconducting, with a gap that grows as the tube gets thinner.
Bending strain — curves the tube like a real one under mechanical load; carbon nanotubes can bend to very large curvatures without breaking bonds, thanks to sp² carbon's exceptional stiffness (Young's modulus ≈ 1 TPa).
Electron flow — toggles a visualization of charge carriers: they stream smoothly along a metallic tube (ballistic transport, near-zero scattering) but sit trapped near one end on a semiconducting tube, illustrating the band gap.

Carbon atom C–C bond Electron (metallic)

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