What are they?

A fullerene is any series of hollow carbon molecules that form either a closed cage, as in a buckyball, or a cylinder, like a carbon nanotube.  The carbon nanotube is 100 times stronger than steel and is one-sixth the weight.  They can also act as either conductors or superconductors.  The most commonly created fullerene is the C60 molecule.  It is in the shape of a truncated icosaheedron or the shape of a soccer ball.  Each vertex contains one carbon atom and each carbon atoms has a double bond with one other carbon atom and two single bonds with other atoms.  In every fullerene, the hollow cage structure contains twelve pentagons.  The number of hexagons, however can be varied to give you other configurations like C20 and C70 (Frey). 

How are they formed?

Single Walled Carbon Nanotubes are long slender one-dimensional tubes with a thickness of only a few nanometers.  They are composed of a hexagonal honeycomb carbon structure.  To construct these nanotubes, scientists must roll flat sheets of graphite into cylinders on one of three angles (chiral angle).  They can then form three different nanotubes: armchair with a chiral angle of 30 degrees, zig-zag with an angle of 0 degrees, and chiral with a variable angle.  The armchair formation yields nanotubes that behave like metals which are interesting for scientists to study.  Depending on the thickness of the wall and the angle at which the nanotube is folded, the nanotube could be a semi-conductor. 

Carbon Arc Method:  One method to construct carbon nanotubes is the Carbon Arc Method.  This is where carbon nanotubes are formed from graphite on a negative electrode suspended in helium gas while the positive electrode is used to create the arc. 

Vaporization Method:  Another method is using a high powered laser to vaporize graphite and cobalt compounds.  Nanotubes are formed after vaporization and are then moved to a cooler location by a catalyst gas. 

Applications of Fullerenes

Superconductors:  Fullerenes can be inserted, or doped, with certain atoms to form a superconductor.  They can also be elongated to create nanotubes called buckytubes.  These tubes are useful for their strong wall and can be used to build supercomputers (Emory University).

Medical:  Because of their unique hollow structure, fullerenes can trap atoms inside of them and can therefore be used as a biological sponge.  If for example, someone ingests a harmful chemical, fullerenes can be inserted and used to soak up the chemical (Emory University).

HIV Protease Inhibitor:  The Protease active sight on the HIV virus allows it to reproduce.  The active sight is hydrophobic and round, both properties that are exhibited by buckyballs.  If you put positively charged aspartate amino groups on the surface of a buckyball, it will no longer be hydrophobic and it will form a bridge with the negatively charged aspartate groups that are found in the protease active site.  It was discovered that a C60 fullerene fits perfectly inside the active site and could help to inhibit the virus from reproducing (Science Service).