# Carbon Nanomaterials

There are four types of carbon nanomaterial, graphene (a two dimensional sheet of benzene rings), carbon nanotube (a nanosize tube that can be imagined as a rolled-up graphene sheet), fullerenes (a zero dimensional ball), and dimondoid.

The properties of these materials are summarized in the table below.

## Graphene sheet

The figure shown below is a graphene sheet. It is made up by perfectly align benzene rings. The carbon to carbon bond length is approximately 1.41 angstrom, which is really small. There are rarely any impurities present in graphene sheet.

Graphene sheet is a perfect conductor. As can be seen from the figure below, graphene sheet has an idealized density of state. There is no gap between HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) such that electrons can be promoted easily from HOMO to LUMO, thus, making it a perfect conductor. The unit hexagonal cell of graphene contains two carbon atoms and has an area of 0.052 nm^2. We can therefore calculate its density as being 0.77 mg/m^2. The strength of a 1 m^2 graphene sheet is incredibly high. 1 m^2 graphene sheet, weight less than 1 mg, can hold an object that is up to about 4 kg before it would break.

## Carbon nanotube

Carbon nanotube can be imagined as a “rolled-up” graphene sheet. Different orientation of rolling, or different chirality, determines the conductivity of the carbon nanotube. There are three types of carbon nanotubes, depending on the chirality, armchair tube, zigzag tube, and chiral tube.

(n,m) represent the unit vector of a graphene structure. The zigzag tube has unit vector of (n,0), the armchair tube has unit vector of (n,n), and the chiral tube has unit vector of (n,m)

The figure above illustrated how the chirality affects the conducting property of the carbon nanotube. If n – m = 3q, where q is an integer, then the tube is conducting Otherwise, the tube is semiconducting.

As can be seen from the figure above, Figure a represents the DOE of conducting, and Figure b represents the DOE of semiconducting carbon nanotube. In Figure a, there is clearly no gap in DOE, making it very easy to promote electrons from lower molecular orbital to higher molecular orbital, hence conducting electricity. However, in the case of semiconducting nanotube in Figure b, there is clearly a gap from approximately -1 to 1 unit energy, making it hard to promote electrons.