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Take a sheet of chicken wire. Flat, it is a honeycomb of hexagons. Roll it into a tube and join the edges, and you have a pipe made of the same hexagons. Now shrink the wire until each joint is a single carbon atom and each strand is a covalent bond. The flat sheet is graphene; the pipe is a carbon nanotube. Everything interesting about these two materials follows from that honeycomb and from the way its electrons are shared.
Starting from graphite
Graphite is a stack of flat carbon layers held together by weak London forces (see giant covalent structures). Within each layer the bonding is strong and covalent; between layers it is feeble, which is why graphite is soft and flaky.
Graphene is one of those layers on its own. It was first isolated and studied in 2004 by Andre Geim and Konstantin Novoselov, who peeled thinner and thinner flakes from graphite with adhesive tape. Their work on it earned the 2010 Nobel Prize in Physics. The technique sounds almost comically simple, but the hard part was finding and proving that a single-atom layer was there at all.
Bonding in graphene
Each carbon atom in graphene uses three of its four outer electrons to form σ bonds to three neighbours in the same plane. The carbon is sp² hybridised, so those three bonds point 120° apart, giving the hexagonal honeycomb (see hybridisation explained). The C–C distance is 142 pm, between a typical C–C single bond (154 pm) and a C=C double bond (about 134 pm).
The fourth electron sits in a 2p orbital pointing straight up and down, perpendicular to the sheet. Every carbon has one of these, and they overlap sideways with their neighbours’ p orbitals across the whole sheet. The result is a single, vast delocalised π system above and below the plane (see sigma and pi bonds).
A helpful picture: the σ bonds are the steel frame of a building, fixing every atom in place, while the π electrons are like a shared corridor that runs the full length of every floor. Electrons in the corridor aren’t assigned to any particular room; they can move anywhere along it.
Why graphene behaves the way it does
| Property | Explanation from the bonding |
|---|---|
| Extremely strong in the plane | Pulling the sheet means stretching strong σ bonds that run in all directions within it, with no weak points |
| Flexible | It is only one atom thick, so it bends easily out of plane, like paper that is strong to pull but easy to fold |
| Excellent electrical conductor | The delocalised π electrons move freely across the sheet |
| Excellent thermal conductor | The stiff, light lattice carries vibrations efficiently |
| Almost transparent | A single layer absorbs only a few per cent of visible light passing through it |
| Impermeable to most gases | The electron clouds of the tight hexagons block even small atoms from passing through a perfect sheet |
In band-theory terms, graphene is unusual: it has no band gap, but the density of available states falls to zero at one energy. It is often called a semimetal. That makes it an excellent conductor, but it also means it can’t easily be switched off like the silicon in a transistor (see semiconductors explained). Much research is about opening a band gap in graphene without destroying its other properties.
From sheet to tube
A carbon nanotube is, in effect, a strip of graphene rolled into a seamless cylinder. The bonding is still mostly sp²: each carbon has three σ bonds and contributes one electron to a delocalised π system. Two main kinds exist:
- Single-walled nanotubes (SWNTs): one rolled sheet, typically around a nanometre across.
- Multi-walled nanotubes (MWNTs): several tubes nested inside one another, like the rings in a cross-section of a tree trunk, separated by roughly the same spacing as the layers in graphite.
Tubes can be thousands of times longer than they are wide. Their ends are often closed by caps that look like half a fullerene, which need a few five-membered rings to curve the surface shut (see fullerenes).
Curvature and strain
In flat graphene, every p orbital points neatly perpendicular to the sheet and overlaps perfectly with its neighbours. Curving the sheet into a tube tilts the p orbitals slightly away from one another and forces the σ bonds out of their ideal flat 120° arrangement. This adds some strain. Narrow tubes are more strained than wide ones, and strained carbon atoms are more reactive, which is one reason chemists can attach groups to nanotube walls and ends.
Chirality: how the sheet is rolled
Here’s where nanotubes get surprising. You can roll the honeycomb straight, or at an angle, like rolling a sheet of patterned wrapping paper so the stripes run around the tube, along it, or in a spiral. Chemists describe the rolling direction with a pair of whole numbers (n, m):
| Type | Indices | Hexagon pattern around the circumference |
|---|---|---|
| Armchair | (n, n) | Edge looks like a row of armchairs |
| Zigzag | (n, 0) | Edge looks like a zigzag line |
| Chiral | any other (n, m) | Hexagons spiral along the tube |
The rolling angle changes which electron states fit around the circumference, and so it changes the electrical behaviour. In the simple theory, a tube is metallic if (n − m) is a multiple of 3, and a semiconductor otherwise. All armchair tubes are metallic; about one-third of all possible tubes are metallic and two-thirds semiconducting. The same atoms and the same bonds give a wire or a semiconductor depending only on geometry, which is one of the most elegant results in materials chemistry.
Nanotubes and graphene compared
| Feature | Graphene | Carbon nanotube |
|---|---|---|
| Dimensions | Flat sheet, one atom thick | Hollow cylinder, about 1 nm to tens of nm wide |
| Hybridisation | sp² | Mostly sp², slightly distorted by curvature |
| Electrical behaviour | Semimetal (zero band gap) | Metallic or semiconducting, set by (n, m) |
| Reactivity | Fairly unreactive on a perfect basal plane; edges more reactive | Walls react more as the tube narrows; caps and ends most reactive |
| Main uses and research areas | Conductive coatings, composites, sensors, membranes | Composites, conductive additives in batteries, fibres, electronics research |
Real-world uses and cautions
Both materials are already used as additives: small amounts in polymers make composites stiffer, lighter or electrically conductive, and nanotubes are added to some lithium-ion battery electrodes to improve conductivity. Graphene-based coatings, inks and sensors are in development and some products are on sale. Making large, defect-free sheets or tubes of a single chirality cheaply remains a major challenge, which is why many of the headline applications are still in the laboratory.
There is also a safety question. Some long, thin, rigid nanotubes resemble asbestos fibres in shape, and researchers study whether inhaled fibres could cause similar harm. Manufacturers handle powders of these materials with dust controls for that reason.
Common mistakes
- “Graphene is a new element.” It is pure carbon: an allotrope, or more precisely a single layer of the allotrope graphite (see allotropes of carbon).
- “Graphene conducts because of free ions.” There are no ions. Conduction is by delocalised π electrons, one contributed by each carbon atom.
- “Nanotubes are sp³ carbon like diamond.” They are sp² carbon; the curvature distorts the geometry a little but does not make four σ bonds per atom.
- “All nanotubes conduct like metals.” Only certain rolling directions give metallic tubes; many are semiconductors.
- “Strong means stiff in every direction.” Graphene is strong when stretched in its plane but bends easily out of plane, because it is so thin.
- “Graphene layers are held by covalent bonds.” Within a layer, yes; between stacked layers, only weak London forces act, which is exactly why a single layer can be peeled off.
Key takeaways
- Graphene is a single, one-atom-thick layer of graphite: a honeycomb of sp² carbon atoms, C–C 142 pm.
- Three σ bonds per carbon give in-plane strength; the fourth electron joins a delocalised π system that makes graphene an excellent conductor.
- A carbon nanotube is a rolled-up sheet of graphene; nanotubes can be single-walled or multi-walled.
- The rolling direction (n, m) decides whether a nanotube is metallic or semiconducting.
- Geim and Novoselov isolated graphene and received the 2010 Nobel Prize in Physics; practical uses are growing, but large-scale, defect-free production is still difficult.
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