The carbon nanotubes are another carbon allotropic form, they have many interesting properties and promise many applications.

## What are carbon nanotubes?

They are cylindrical molecules made of carbon atoms with a diameter on nanometric scale and length on micrometric or millimetric scale. They consist of a rolled graphene sheet, linking opposite extremities.

## Properties

The carbon nanotube’s properties depend on if it has single or multiple walls and how it’s rolled.

### Graphene winding

The two numbers in parentheses (n,m) form the chiral vector (\vec{C}_{h}).

\vec{C}_{h}=n\vec{a}_{1}+m\vec{a}_{2}=(n,m)

Where \vec{a}_{1} and \vec{a}_{2} are unitary vectors, whose modules are equal to 1.

Obtaining the chiral vector \phi formula.

\vec{C}_{h}\cdot \vec{a}_{1}=\left| \vec{C}_{h}\right|\cdot \left| \vec{a}_{1}\right|\cdot cos\phi

\phi=cos^{-1}\left ( \frac{2n+m}{2\sqrt{\left ( m^{2}+n^{2}+mn\right )}} \right )

The tube’s diameter (d).

d=\frac{a\sqrt{3(n^{2}+mn+m^{2})}}{\pi }

Where a is the length of covalent bond between two carbon atoms, which is 1.42 Å (angstrom).

1 Å = 1\times 10^{-10}m

The integral numbers m and n determine if a nanotube is a conductor or a semiconductor.

### Other properties of carbon nanotubes (CNT)

- All nanotubes have great tensile strength, they are 100 times stronger than steel with only 1/6 of density.
- Are excellent heat conductors. Thermal conductivity can reach 6000 W/m\cdot K (watt per meter times Kelvin).
- Since they are made of graphene, Young module (measures resistance to elastic deformation) is close to 1000 GPa, it read gigapascals.
- Carbon nanotubes kill the living cells when they come into contact with the latter.

## Some application examples

- Composite materials with nanotubes of multiple walls can have higher resistance to weariness and break, with less weight.
- The conductors CNT have better conductivity than copper. They can one day be used in electric energy transmission.
- It’s possible to put semiconductor nanotubes in field effect transistors, to make the connection between drain and source terminals. Creating high-performance smaller circuits.

- Can be used in electrochemical and biological sensors.

Carbon nanotubes still are very expensive to mass manufacture.