Carbon Nanotubes, Fullerenes, Graphene and Carbon Quantum Dots

Why carbon, and why the bonding matters

Carbon has four valence electrons and forms three distinct hybrid states, and almost everything in this topic follows from which one is present.

• sp³ — four single bonds in a tetrahedron. Diamond: every electron locked in a bond, so it is an insulator, and the rigid three-dimensional network makes it the hardest known material.
• sp² — three bonds in a plane at 120°, leaving one p electron per atom delocalised above and below. Graphite, graphene, nanotubes and fullerenes are all sp².

That delocalised electron is the whole story. It makes sp² carbon electrically conducting, chemically reactive at the surface, and optically active — none of which diamond is.

The nanoforms below are all the same sp² sheet, arranged differently: rolled into a tube, closed into a ball, left flat, or cut into fragments.

Graphene

Structure. A single layer of sp² carbon in a hexagonal honeycomb, one atom thick. Two-dimensional in the strict sense.

Properties, and why:

• Electrical conductivity exceeding copper. Electrons behave as massless particles and travel micrometres without scattering.
• Thermal conductivity the highest known, above 5000 W m⁻¹K⁻¹.
• Mechanical strength about 130 GPa — roughly 200 times steel by weight — from the in-plane sigma bonds.
• Transparent, absorbing only 2.3% of visible light, yet conducting.
• Surface area about 2630 m² per gram, since every atom is a surface atom.
• Impermeable even to helium.

The combination that matters: transparent and conducting and flexible. Indium tin oxide, the incumbent transparent conductor, is brittle and made from a scarce element. Graphene is neither.

Applications: transparent flexible electrodes for displays and touch screens; supercapacitor and battery electrodes; composite reinforcement; sensors, where a single adsorbed molecule measurably changes the conductance; and desalination membranes.

Its problem: graphene has no band gap. It conducts superbly and cannot be switched off, so it cannot replace silicon in a transistor without engineering a gap into it — an unsolved problem, and the reason graphene has not displaced silicon despite twenty years of trying.

Carbon nanotubes

Structure. A graphene sheet rolled into a seamless cylinder, one to a few nanometres in diameter and up to millimetres long. Enormous aspect ratio.

• SWCNT — single-walled, one cylinder.
• MWCNT — multi-walled, concentric cylinders about 0.34 nm apart.

The chirality result, which is the striking one. The direction in which the sheet is rolled — the chiral vector — determines whether the tube is a metal or a semiconductor. Armchair tubes are metallic; zigzag and chiral tubes are usually semiconducting, with a band gap inversely proportional to diameter.

The same element, the same bonding, the same structure — rolled at a different angle — gives a wire or a transistor. No other material does this, and it is also the practical obstacle: synthesis produces a mixture of chiralities, and separating them is difficult and expensive.

Properties: tensile strength around 100 GPa, the strongest measured; current density a thousand times copper's; excellent thermal conductivity along the axis; chemically inert but functionalisable at the ends and defects.

Applications: composite reinforcement in sports equipment and aerospace; field emission displays; transistors and interconnects; conductive additives in battery electrodes; sensors; and drug delivery after functionalisation.

Fullerenes

Structure. A closed cage of sp² carbon. C₆₀ — buckminsterfullerene — is the familiar one: 60 atoms in 20 hexagons and 12 pentagons, exactly a football, about 0.7 nm across.

The 12 pentagons are not decorative. Euler's theorem requires exactly twelve pentagons to close any hexagonal sheet into a sphere, no matter how large the cage. Hexagons alone tile only a flat plane; the pentagons supply the curvature.

Properties: soluble in organic solvents, unlike graphite and diamond; a good electron acceptor, taking up to six electrons; forms superconducting compounds when doped with alkali metals; and the cage can trap an atom inside.

Applications: the electron acceptor in organic solar cells, its main commercial use; lubricants, since the molecules act as tiny ball bearings; antioxidants and drug carriers in cosmetics and medicine; superconductors.

Carbon quantum dots

Structure. Quasi-spherical carbon nanoparticles below about 10 nm, part sp² and part sp³, with oxygen-containing groups on the surface.

The property that defines them: strong, tunable photoluminescence — they absorb ultraviolet and emit visible light, with the colour shifting with size and with surface chemistry.

Why they matter against conventional quantum dots. CdSe and PbS quantum dots have excellent optical properties and contain cadmium and lead. Carbon dots are made of carbon, are essentially non-toxic and biocompatible, and can be made cheaply from citric acid or even food waste. For anything going into a living organism, that difference decides it.

Applications: bio-imaging and cell labelling; sensing of metal ions, where the fluorescence is quenched by the target; LEDs; photocatalysis; and anti-counterfeiting inks.

Summary