Q.How does graphite function as a lubricant?

Carbon's strong catenation and unique $\pi$-bonding ability let it exist in several structurally distinct allotropes. Diamond is a rigid, three-dimensional covalent network in which every carbon is $sp^3$ hybridised and tetrahedrally bonded to four neighbours (C–C = 154 pm); this extended, strongly-directional bonding with no weak points anywhere makes diamond the hardest known natural substance with an extremely high melting point, but also an electrical insulator, since all four valence electrons of every carbon are locked into localised $\sigma$ bonds. Graphite, by contrast, is built from flat hexagonal sheets of $sp^2$-hybridised carbon (in-layer C–C = 141.5 pm), each carbon using three electrons for in-plane $\sigma$ bonds and delocalising its fourth electron into a mobile $\pi$ system spanning the whole sheet — this delocalisation makes graphite an electrical conductor along the layers, while the weak van der Waals forces between the widely-separated layers (340 pm apart) let the sheets slide past each other, making graphite soft and useful as a solid lubricant. This single structural contrast — rigid 3-D $sp^3$ network versus slippery layered $sp^2$ sheets — explains essentially all the differing physical properties of the two allotropes. Fullerenes are a third, molecular form: closed, cage-like spheres (the famous $C_ …