the structures and properties of allotropes of carbon (diamond, graphite, graphene, fullerenes and carbon nanotubes) and other covalent network lattices including silicon dioxide, explaining their physical properties (including hardness, electrical conductivity, melting point and solubility) in terms of bonding

What this dot point is asking

VCAA wants you to describe the structures of the carbon allotropes (diamond, graphite, graphene, fullerenes, carbon nanotubes) and of silicon dioxide, and to use the bonding and structure of each to explain its physical properties: hardness, melting point, electrical conductivity, solubility.

The answer

What an allotrope is

Allotropes are different structural forms of the same element in the same physical state. Carbon is the textbook example: the atoms are identical, but the way they bond to one another produces wildly different materials.

Diamond

Each carbon atom forms 4 single covalent bonds to 4 neighbours, arranged tetrahedrally ($109.5^{\circ}$ bond angle). The result is a 3D covalent network lattice with no discrete molecules. Every one of the 4 valence electrons sits in a localised bond.

• Hardness: extreme. The 3D network gives no slip plane.
• Melting point: very high (sublimes near 3550 deg C). Many strong C-C bonds must break to melt.
• Conductivity: zero. No delocalised electrons.
• Solubility: insoluble in everything (no IMFs to disrupt; the lattice would need to be dismantled).
• Optical: transparent, high refractive index.

Graphite (and graphene)

Each carbon atom forms 3 single covalent bonds to 3 neighbours in a flat hexagonal sheet. The 4th valence electron is delocalised within the sheet. Sheets stack on top of one another, held by weak dispersion forces.

• Hardness: soft and slippery. Layers slide.
• Melting point: very high (sublimes near 3650 deg C). The in-plane bonds are very strong.
• Conductivity: conducts along the sheets (delocalised electrons), much less between sheets.
• Solubility: insoluble.
• Density: less dense than diamond (more empty space between layers).

Graphene is a single isolated layer of graphite. It is the strongest material known by tensile strength, an excellent in-plane electrical and thermal conductor, transparent and flexible.

Fullerenes

Fullerenes are closed-cage molecules of carbon, the most famous being $C_{60}$ (buckminsterfullerene), a 60-atom sphere of pentagons and hexagons. Each C still forms 3 covalent bonds, but the molecule is a discrete, finite object.

• They are a covalent molecular substance, not a covalent network: solid $C_{60}$ is held together by dispersion forces between molecules.
• Lower melting point than diamond or graphite.
• Soluble in some non-polar solvents (e.g. toluene), unlike diamond or graphite.
• Used in drug delivery research and as electron acceptors in some solar cells.

Carbon nanotubes

A carbon nanotube is a graphene sheet rolled into a cylinder, capped at the ends. Very high tensile strength along the axis, conducts along the tube, used in nanoelectronics and composite materials.

Silicon dioxide ($SiO_2$)

The other key network solid for VCE. Every silicon atom is covalently bonded to 4 oxygen atoms and every oxygen to 2 silicons, building a 3D network of $SiO_4$ tetrahedra. It is the structure of quartz and the basis of glass, sand and many minerals.

• Very hard, very high melting point (about 1710 deg C).
• Does not conduct (no delocalised electrons).
• Insoluble in water.

Property summary

Worked example

Explain in one paragraph why diamond is harder than graphite even though both contain only carbon-carbon covalent bonds.

In diamond every C-C bond is part of a 3D tetrahedral network, so a force in any direction tries to break many strong covalent bonds at once. In graphite the bonds are strong within each layer, but the layers themselves are held by weak dispersion forces; a sideways force just slides one layer over another without breaking any covalent bond. Same element, same bond type, very different macroscopic property, all from the geometry of the lattice.

Common traps

Calling graphite "weakly bonded"

The in-plane covalent bonds are very strong. Only the layer-to-layer forces are weak.

Calling fullerene a network solid

$C_{60}$ is a molecular solid. The covalent bonds end at each cage.

Saying diamond is metallic because it is hard

Diamond is a covalent network. No delocalised electrons. No conductivity.

Mixing up graphene and graphite

Graphene is one isolated sheet. Graphite is many sheets stacked.

Claiming silicon dioxide is ionic because Si and O have different electronegativities. The bonding is polar covalent, and the structure is a network of covalent bonds, not an ionic lattice.

In one sentence

The allotropes of carbon and silicon dioxide are all covalent network or layered solids whose macroscopic properties (very high melting points always, plus hardness or softness, conductivity or insulating behaviour, solubility) follow directly from how the covalent bonds are arranged in three dimensions.

Examples in context

Example 1. Graphite anodes from Hexagon Resources at Halls Creek. Hexagon Resources holds a vein-graphite deposit at McIntosh, Western Australia, that ships flake graphite to Victorian battery-pack assemblers. Each lithium-ion cell uses about $100 \text{ g}$ of graphite shaped into the anode. Graphite works because each carbon atom is $sp^{2}$ hybridised with three covalent bonds in a planar sheet, leaving one delocalised electron per atom in the $p$ orbital perpendicular to the sheet. Those electrons conduct charge along the layers, and the weak dispersion forces between layers let lithium ions slide in between sheets during charging. Diamond, where every carbon is $sp^{3}$ with all four electrons locked into tetrahedral bonds, cannot do this.

Example 2. Silica fibre optics at the Geelong Refinery decommissioning site. When Viva Energy converted the Geelong Refinery into a fuels-import terminal, the site still relied on silica-based fibre-optic data lines threaded through the plant. Fibre cores are pure $\text{SiO}_{2}$ in an amorphous network of $\text{Si}\text{-}\text{O}\text{-}\text{Si}$ tetrahedra with bond energies near $460 \text{ kJ mol}^{-1}$. Every silicon shares four oxygens, every oxygen bridges two silicons, and the rigid three-dimensional lattice gives a melting point of about $1710\text{ }^{\circ}\text{C}$. No delocalised electrons means no conduction, ideal for an optical, not electrical, signal. Hardness near $7$ on the Mohs scale also resists abrasion in industrial settings.

Try this

Q1. Explain in terms of bonding and structure why diamond is an electrical insulator but graphite conducts electricity along its layers. [3 marks]

• Cue. Diamond: every C is $sp^{3}$, four single bonds, no delocalised electrons. Graphite: $sp^{2}$ with one delocalised electron per C in the $\pi$ system, free to move along the sheet.

Q2. A diamond crystal has a density of $3.51 \text{ g cm}^{-3}$. Calculate the number of carbon atoms in a $1.00 \text{ cm}^{3}$ cube of diamond. [3 marks]

• Cue. $n = m/M = 3.51 / 12.01 = 0.2923 \text{ mol}$. Atoms $= n \times N_{A} = 0.2923 \times 6.02 \times 10^{23} = 1.76 \times 10^{23}$.

Q3. Compare graphene and silicon dioxide as covalent network materials. (a) Describe each structure. (b) Predict relative electrical conductivity. (c) Outline one Australian industrial application of each. [2+2+2 marks]

• Cue. (a) Graphene: single $sp^{2}$ carbon sheet. $\text{SiO}_{2}$: 3D tetrahedral network of Si and O. (b) Graphene conducts via delocalised $\pi$ electrons; $\text{SiO}_{2}$ insulates. (c) Graphene: CSIRO sensors. $\text{SiO}_{2}$: fibre optics, silicon-wafer substrates.