Allotropes of Carbon

Carbon exists in many distinct allotropic forms, the two most familiar being graphite and diamond; the more recently characterised graphene, fullerenes and carbon nanotubes round out the list.

Graphite (Figure 2.4) is the most thermodynamically stable form of carbon at ordinary temperature and pressure. It is soft and conducts electricity. Structurally, it is built from flat, two-dimensional sheets in which each carbon atom is sp² hybridised and forms three σ bonds to its three nearest neighbours (C-C bond length 1.41 Å, essentially the same as benzene's 1.40 Å), arranging the whole sheet into a hexagonal net. The fourth electron of every carbon, sitting in an unhybridised p orbital, is not localised into any single bond but instead delocalised across the entire sheet as a π system -- it is this mobile electron cloud that gives graphite its electrical conductivity. Successive sheets are held to each other only by weak van der Waals forces (3.40 Å apart), which is why graphite cleaves and slides so easily and is used as a solid lubricant, either on its own or as 'graphited oil'.

Diamond (Figure 2.5), by contrast, is extremely hard. Every carbon atom is sp³ hybridised and σ-bonded to four neighbouring carbon atoms (C-C bond length 1.54 Å), building a tetrahedral arrangement that repeats through the entire three-dimensional lattice. Because all four valence electrons of every carbon atom are tied up in these localised σ bonds, there are no free/delocalised electrons left for conduction, so diamond does not conduct electricity. Being the hardest known natural material, it is used for sharpening hard tools, cutting glass, and in bores and rock-drilling equipment.

Fullerenes (Figure 2.6) are a more recently synthesised class of carbon allotrope, existing as discrete cage molecules (e.g. C₃₂, C₅₀, C₆₀, C₇₀, C₇₆) rather than as an extended lattice or sheet like graphite and diamond. The best known, C₆₀ ('buckminsterfullerene' or buckyball), has a hollow, soccer-ball-shaped cage built from 20 six-membered and 12 five-membered carbon rings fused together. Every carbon in this cage is sp² hybridised, forming three σ bonds plus a delocalised π system that gives the whole cage an aromatic character; the C-C bond distance is 1.44 Å and the C=C distance 1.38 Å. …