Allotropes are different forms of the same element in the same physical state
Diamond has a giant covalent structure, made up of carbon atoms that each form 4 covalent bonds. This makes diamond really hard
The strong covalent bonds take a lot of energy to break and give diamond a very high melting point. It doesn't conduct electricity because it has no delocalised electrons or ions
In graphite, each carbon atom forms 3 covalent bonds, creating sheets of carbon atoms arranged in hexagons
There aren't any covalent bonds between the layers - they're only held together weakly, so they're free to move over each other. This makes graphite soft and slippery, so it's ideal as a lubricating material
Graphite's got a high melting point - the covalent bonds in the layers need loads of energy to break
Only 3 out of each carbon's 4 outer electrons are used in bonds, so each atom has 1 electron that is delocalised and can move. Graphite conducts electricity and thermal energy due to its delocalised electrons
Graphene is a sheet of carbon atoms joined together in hexagons. The sheet is just one atom thick, making it a two-dimensional substance
The network of covalent bonds makes it very strong. It's also incredibly light, so can be added to composite materials to improve their strength without adding much weight
Like graphite, it contains delocalised electrons so can conduct electricity through the whole structure. This means it has the potential to be used in electronics
Fullerenes form spheres and tubes
Fullerenes are mainly made up of carbon atoms arranged in hexagons, but also contain pentagons or heptagons
Fullerenes can be used to 'cage' other molecules. The fullerene structure forms around another atom or molecule, which is then trapped inside. This could be used to deliver a drug into the body
Fullerenes have a huge surface area, so they could help make great industrial catalysts - individual catalyst molecules could be attached to the fullerenes. Fullerenes also make great lubricants
Buckminsterfullerene was the first fullerene to be discovered. It's got the molecular formula C60 and forms a hollow sphere arranged in hexagons, but also contain pentagons or heptagons
Fullerenes can form nanotubes - tiny carbon cylinders. The ratio between the length and the diameter of nanotubes is very high
Nanotubes can conduct both electricity and thermal energy. They also have a high tensile strength (they don't break when they're stretched)
Technology that uses very small particles such as nanotubes is called nanotechnology. Nanotubes can be used in electronics or to strengthen materials without adding much weight, such as in tennis racket frames