Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2020 / Paper 2 / Section B / 19 / i

A zero-dimensional example is buckminsterfullerene, ${\mathrm{C}}_{60}$: a closed cage with 60 vertices, 90 edges, 12 pentagons and 20 hexagons. Euler's relation is $60-90+32=2$. Each carbon has three neighbors in a curved, approximately $s{p}^2$-bonded network; bonds are not all equivalent. Its cage diameter is of order $0.7\mathrm{nm}$.

Confinement in all directions gives discrete molecular orbitals, unlike the extended dispersion of graphene. It is an electron acceptor with characteristic electronic and vibrational spectra. Its pentagons supply the positive curvature needed to close the carbon network. A molecular solid of cages is held together predominantly by intermolecular forces, so its mechanical and electrical properties differ from those of an individual strongly bonded cage. Undoped fullerene is not a high-conductivity graphene sheet; doping, packing and charge transfer can strongly change transport.