Graphene and Fullerenes

To understand its unique properties, we must look at its bonding step by step:

• First, each carbon atom forms strong covalent bonds with exactly three other carbon atoms, creating a continuous hexagonal lattice (interlocking rings of six carbon atoms).
• Then, because carbon atoms typically form four bonds, one electron from each carbon atom is left over and becomes a delocalised electron.
• Finally, these delocalised electrons are free to move across the entire surface of the sheet, allowing graphene to be an excellent conductor of electricity and thermal energy.

Graphene is incredibly strong and has a very high melting point due to its vast network of covalent bonds, but it is much lighter than graphite because it lacks the weak intermolecular forces between layers. It is also nearly transparent, absorbing only about $2.3\%$ of visible light. Because it is highly conductive, transparent, and strong, it is widely used in electronics, touchscreens, and to make composite materials stronger and lighter.

Fullerenes and Buckminsterfullerene ($C_{60}$)

Imagine a structure perfectly shaped to trap a tiny drug molecule and transport it safely through the human bloodstream. A fullerene is a molecule of carbon atoms with a hollow shape, such as a sphere, ellipsoid, or tube. The first one discovered was Buckminsterfullerene, a spherical hollow shape consisting of 60 carbon atoms ($C_{60}$).

To recognise Buckminsterfullerene in diagrams, look for a hollow "soccer ball" shape about $1$ nm in diameter. It is constructed from exactly 20 hexagonal rings and 12 pentagonal rings of carbon atoms. Each carbon atom is bonded to three others via strong covalent bonds.

Unlike diamond or graphene, Buckminsterfullerene is a simple molecular structure—it is NOT a giant covalent structure. While it does contain delocalised electrons, $C_{60}$ is a poor conductor of electricity because its electrons cannot easily move between the separate, individual molecules.

Common Uses of Spherical Fullerenes:

• Drug delivery: The hollow "cage" structure can encapsulate (trap) drugs, protecting them until they reach specific target sites in the body.
• Lubricants: Because they are spherical, fullerene molecules can easily roll over one another, heavily reducing friction.
• Catalysts: They are highly effective catalysts because they possess a massive surface area to volume ratio.

Worked Example: Calculating Covalent Bonds in $C_{60}$

• Formula: Total bonds = $(\text{Number of atoms} \times \text{Bonds per atom}) / 2$

• Step 1: Identify the values. There are 60 carbon atoms, and each forms 3 bonds.

• Step 2: Substitute into the formula. $(60 \times 3) / 2 = 180 / 2$

• Step 3: Final answer. There are $90$ covalent bonds in one $C_{60}$ molecule.

Carbon Nanotubes and Nanotechnology

Why do professional tennis players use rackets that weigh almost nothing but never snap under the immense force of a serve? The answer lies in carbon nanotubes, which are cylindrical fullerenes. You can think of them as a single layer of graphene seamlessly rolled into a microscopic tube.

These tiny cylinders are a key part of nanotechnology, a field dealing with materials that have dimensions less than $100$ nm. Carbon nanotubes have a very high length-to-diameter ratio, meaning they are exceptionally long compared to their microscopic width.

Because they maintain the continuous hexagonal lattice of graphene, nanotubes possess extremely high tensile strength (meaning they are highly resistant to breaking when stretched) and low density, making them incredibly lightweight. Furthermore, their delocalised electrons can move freely along the entire length of the tube, making them excellent conductors of electricity and thermal energy.

Common Uses of Carbon Nanotubes:

• Reinforcing composite materials: They are added to materials like high-end tennis rackets, badminton rackets, and bicycle frames to provide immense strength without adding significant weight.

Worked Example: Calculating Length-to-Diameter Ratio

• Formula: $\text{Ratio} = \text{Length} / \text{Diameter}$

• Step 1: Write down what you know. A nanotube has a length of $2000$ nm and a diameter of $2$ nm.

• Step 2: Substitute into the equation. $\text{Ratio} = 2000 / 2$

• Step 3: Final answer. The length-to-diameter ratio is $1000:1$ (or $10^3$).