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A football is stitched from pentagons and hexagons. Count them on a classic black-and-white ball and you’ll find 12 black pentagons and 20 white hexagons, with 60 corners where the seams meet. Put a carbon atom at every one of those corners, make every seam a covalent bond, and you have C₆₀, buckminsterfullerene: a hollow molecule about a nanometre across and the most famous member of the fullerene family.
Fullerenes were discovered in 1985 by Robert Curl, Harold Kroto and Richard Smalley, with their co-workers, while studying carbon clusters formed when graphite is vaporised by a laser. The three shared the 1996 Nobel Prize in Chemistry. The name honours the architect Buckminster Fuller, whose geodesic domes use a similar pattern of linked polygons; “buckyball” is the popular nickname.
What makes a fullerene
A fullerene is a closed cage made only of carbon atoms, in which:
- every carbon is bonded to three other carbons;
- the faces of the cage are pentagons and hexagons only.
Diamond and graphite are giant covalent structures with no natural end (see giant covalent structures). Fullerenes are different: each cage is a discrete molecule with a definite formula such as C₆₀, C₇₀, C₇₆ or C₈₄. That puts fullerenes in a different class from the network allotropes (see allotropes of carbon).
Why exactly twelve pentagons?
Here’s a result that feels like magic until you see why. Every closed fullerene cage, whatever its size, has exactly 12 pentagons. Only the number of hexagons changes.
Think about a flat sheet of graphene: a honeycomb of hexagons that lies perfectly flat, and can’t close on itself. To curve a surface into a ball, you have to introduce some shape that makes the surface bend. A pentagon does this: five corners around a point instead of six leave a “gap” that pulls the surrounding sheet into a cone. Paper modellers know this trick: cut a wedge from a hexagon of card, tape the edges together, and it pops up into a shallow cone.
Mathematically, Euler’s rule for polyhedra (vertices − edges + faces = 2), combined with the condition that three edges meet at every vertex, forces the number of pentagons to be exactly 12. Hexagons contribute no curvature, so you can add any number of them (except one) without changing the count of pentagons.
That’s also why a fullerene with n carbon atoms has (n/2 − 10) hexagons. For C₆₀: 30 − 10 = 20 hexagons, plus the 12 pentagons.
The isolated pentagon rule
Pentagons that share an edge create a region of high strain and poor electronic structure. The most stable fullerenes have every pentagon completely surrounded by hexagons: the isolated pentagon rule. C₆₀ is the smallest fullerene that can satisfy it, and C₇₀ the next. This helps explain why C₆₀ and C₇₀ are by far the most abundant fullerenes in the soot where they form.
Bonding in C₆₀
Each carbon uses three electrons in σ bonds to its three neighbours. The fourth electron occupies an orbital with mostly p character pointing out from the surface of the ball. These combine into a π system that spreads over the cage (see sigma and pi bonds).
The carbon atoms are often described as roughly sp² hybridised, but the curvature changes things. In flat graphene, the three σ bonds lie in one plane; on a sphere, they bend down slightly, like the legs of a very squat tripod. The atom is pyramidalised, somewhere between sp² (flat) and sp³ (tetrahedral), and this adds strain.
Two kinds of bond
In C₆₀ every atom is in an identical environment, but the bonds are not all the same. There are two types:
| Bond | Where it is | Approximate length | Character |
|---|---|---|---|
| 6:6 bond | Shared by two hexagons | about 140 pm | More double-bond character |
| 6:5 bond | Shared by a hexagon and a pentagon | about 145 pm | More single-bond character |
In a perfectly delocalised system like benzene, every C–C bond would be identical. In C₆₀ they are not, which tells us the π electrons are not fully delocalised. A good working model is that the double bonds sit on the 6:6 edges and avoid the pentagons. For comparison, the C–C distance in graphene is 142 pm, a single bond is about 154 pm, and an isolated C=C double bond is about 134 pm.
Properties of fullerenes
| Property | Explanation |
|---|---|
| Molecular solid; sublimes on strong heating | Individual C₆₀ molecules are held together in the crystal only by London forces |
| Soft compared with diamond | Breaking the solid only means separating molecules, not breaking covalent bonds |
| Dissolves in some organic solvents (e.g. methylbenzene), giving coloured solutions | Non-polar molecules dissolve in non-polar solvents; C₆₀ solutions are purple |
| Insoluble in water | Non-polar cage cannot form hydrogen bonds with water |
| Pure solid is a poor electrical conductor | Electrons are delocalised within each ball but can’t hop easily between balls |
| Readily accepts electrons | Low-lying empty orbitals; C₆₀ can be reduced step by step to anions carrying several negative charges |
The weak forces between fullerene molecules are the same kind of London forces that act between any non-polar molecules (see London dispersion forces). The large surface area of the ball makes them strong enough for C₆₀ to be a solid at room temperature.
How fullerenes react
Because the π electrons are concentrated on the 6:6 bonds, C₆₀ behaves more like a large, electron-poor alkene than like benzene. It reacts with nucleophiles, undergoes addition reactions across 6:6 bonds, and can be built up with many groups attached. Every addition relieves a little strain, because it converts pyramidalised, curved-surface carbons into sp³ carbons, which are comfortable with a non-planar shape.
Fullerenes can also be modified in two other ways:
- Endohedral fullerenes trap an atom or small molecule inside the cage. They’re written with an @ sign: La@C₈₂ means a lanthanum atom inside a C₈₂ cage.
- Fullerides are salts formed when metals transfer electrons to the cage. Some alkali-metal fullerides, such as K₃C₆₀ (see potassium), become superconductors when cooled to low temperatures.
Research uses include electron acceptors in some types of organic solar cell, and as building blocks for new materials. Many proposed medical applications remain at the research stage.
Relatives: C₇₀ and beyond
C₇₀ is the next most common fullerene. It has the same 12 pentagons plus 25 hexagons, and the extra atoms stretch it into an elongated, rugby-ball shape. Larger fullerenes have many possible isomers, because there are many ways to place 12 isolated pentagons among a larger number of hexagons. Open or very long versions of the same idea lead to carbon nanotubes, whose ends are often capped by half-fullerenes (see graphene and carbon nanotubes).
Common mistakes
- “C₆₀ is a giant covalent structure like diamond.” It is a simple molecular substance. Strong covalent bonds exist within each cage, but only weak forces between cages.
- “C₆₀ is aromatic like benzene, with identical bonds.” It has two bond lengths (6:6 and 6:5), and its reactions are more like those of an alkene.
- “Fullerenes are made of hexagons, like graphite.” Hexagons alone can’t close a cage; there are always exactly 12 pentagons.
- “Solid C₆₀ conducts like graphite.” The π electrons are confined to each molecule; the pure solid is not a good conductor.
- “Each carbon in C₆₀ has one double bond and two single bonds, so there are 60 double bonds.” Each double bond is shared between two atoms, so a C₆₀ Kekulé structure has 30 C=C bonds and 60 single bonds, 90 bonds in total.
- “Fullerenes are hollow, so they must be fragile.” The cage is held by strong covalent bonds; C₆₀ molecules survive high temperatures in an inert atmosphere.
Key takeaways
- Fullerenes are closed, hollow cages of carbon with every atom bonded to three others; C₆₀ (12 pentagons + 20 hexagons) is the best-known.
- Every closed fullerene has exactly 12 pentagons; pentagons provide the curvature, hexagons fill in.
- Carbon atoms are roughly sp² but pyramidalised by curvature; C₆₀ has two bond types, 6:6 (shorter) and 6:5 (longer).
- Fullerenes form molecular solids held by London forces: soluble in some organic solvents, poor conductors, and reactive like electron-poor alkenes.
- Discovered in 1985 by Curl, Kroto and Smalley, who shared the 1996 Nobel Prize in Chemistry.
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