Carbon Nanotubes:  Graphene on a Roll!

View the structures of the two crystalline forms of carbon.  For help with using Chime structures, see the Chime Guide.  What is the hybridization of carbon in each structure?

Diamond                                                    Graphite


spacefill                                                 spacefill

Which structure is more dense?  View in the spacefill mode and look at the packing of the atom carbons from all sides.

The carbon in diamond is tetrahedral (sp3) and trigonal planar in graphite (sp2).


The p orbital on the sp2 carbons in graphite allow for the electrical conductivity.  The sheets, held together by induced dipole interactions, allow for the layer to slip.

Graphene: A Single Layer from Graphite:

Now let's explore a single layer from the graphite structure.  The individual layers are called graphene.

Suppose the graphene sheet was to roll up and have the edges meet?  Here are four possible ways for the graphene to roll.  You may want to right click on each Chime image and deselect rotation to stop them from rotating.

Produced using TubeGen 3.3 (web-interface,

These are carbon nanotubes.  What do you notice about the arrangement of the carbon atoms in the four different nanotubes?

The Rolling Process:

Note the upper edge in these first two movies.  What type of nanotube is forming?  zig-zar or armchair  Click on image to play the movie file.


Depending on how the graphene sheet rolls determines the type of nanotube.

Now view these two movies where the rolling is NOT along one of the edges as above.  Click on image to play the movie file.


These nanotubes are two different chiral types.  Chiral nanotubes will have either a left or right-handed helical spiral and hence have two optical isomers.  The last two Chime structures in the series of four nanotubes above are optical isomers.

Chiral Carbon Nanotubes:

The type of nanotube depends on how the graphene sheet is oriented on rolling.  This is described by the chiral vector, which is determined by two integers (n, m) .  To see how the two integers (n, m) influence the size and properties plus an interactive display of the chiral vector, click here to go to an Excelet (interactive Excel spreadsheet).

Using the (n, m) notation, give an example of the following nanotubes:

Type (n, m)   (n, m)
armchair   -- --
zig-zag   -- --
chiral   the other isomer:  

Band Gap Behavior of Carbon Nanotubes:

Graphite is an excellent metallic conductor.  How does the type of carbon nanotube, armchair, zig-zag, or chiral, influence the conductivity or band gap?  See the Excelet: Conductor, Semiconductor, or Insulator? for a discussion of band gap.  See the Excelet: Band Gap Behavior in Carbon Nanotubes for an examination of how type and size influence the band gap of a carbon nanotube.

Vibrations in Carbon Nanotubes:

Here is a molecular dynamics simulation of vibrations in a (10, 10) carbon nanotube.  You may need to refresh the browser to get the animation to play.



To explore other nanotube structures, see Forms of Carbon at

For further information of chirality, see Visual Material to Understand Chirality at

Nanotube structures were generated by TubeGen Online, see TubeGen 3.3 (web-interface,,  J. T. Frey and D. J. Doren, University of Delaware, Newark DE, 2005.

Wrapping of graphene animations were produced by Nanotube coordinate generator with a viewer for Windows from S. Maruyama, The University of Tokyo, 2004 at


This work is supported by the Howard/Hopkins/PGCC Partnership for Research and Education in Materials (PREM), which is funded by NSF Grant No. DMR-0611595.

Please e-mail any corrections, modifications, suggestions, or questions.

Scott A. Sinex        Prince George’s Community College       11/2008