Graphene and other giant covalent structures — Chemistry

Before this

This leads to

Empirical and molecular formulae

A Nobel Prize from sticky tape

The last lecture ended with a promise: graphene, a single layer of graphite, and other giant covalent structures. Here is how graphene was first made.

At the University of Manchester, Andre Geim and Konstantin Novoselov pressed ordinary adhesive tape onto graphite and peeled it off. Flakes of graphite came away. They pressed new tape onto those flakes and peeled again, and again. Each time the flakes got thinner. In the end, some were just one atom thick. They reported this in 2004, and in 2010 they shared the Nobel Prize in Physics for it.

Now the puzzle. Graphite is soft. It is soft enough to leave marks on paper. Yet one layer of it turned out to be one of the strongest materials ever measured. It also conducts electricity about as well as copper, and you can almost see through it. How can a soft grey material become a strong, transparent one, just by taking one layer?

The bonding model from the last lecture answers this completely. Then we use the same model on silicon dioxide, the substance of sand and quartz.

Graphene: one layer, no weak links

Graphene is a flat sheet of carbon atoms in a honeycomb of hexagons. It is exactly one layer of graphite.

Count the electrons, as you did for graphite. Each carbon atom has four outer electrons. It uses three of them in three covalent bonds to its three neighbours, 120° apart, all in the flat sheet. The fourth electron is not in any one bond. It is delocalised: it can move across the whole sheet, like the electrons in a metal, but only in two dimensions.

Now remember why graphite is soft. The last lecture showed that the layers are 335 pm apart, more than twice the length of a C–C bond. They are held together only by weak London forces. So the layers slide over each other, and that is what happens when you write with a pencil. The softness is between the layers. Inside a layer, every atom is held by strong covalent bonds.

Graphene has no "between". It is a single layer, so every atom is held only by strong covalent bonds. There is no weak direction left in the sheet. That is it. That is the whole idea. Graphite is soft because it is many sheets weakly stacked. Graphene is strong because it is one sheet, and the sheet itself has no weak links.

Stop and think

A student says: "Graphene is 200 times stronger than steel, and graphite is made of graphene. So a block of graphite should be stronger than steel." What is wrong with this?

Show the answer

The strength of graphene is the strength of the bonds within one sheet. A block of graphite breaks in a different place: between the sheets, where only weak London forces hold it together. A material is as strong as its weakest way of coming apart. For graphite, that weak way is sliding or splitting between layers. A single sheet of graphene does not have that weak way.

The measurements are remarkable. In 2008, a team at Columbia University in the United States pressed a diamond-tipped probe into sheets of graphene stretched over tiny holes, until they broke. They reported in the journal Science that graphene was the strongest material ever measured, about 200 times stronger than structural steel. The Nobel committee also described graphene as conducting electricity about as well as copper, and conducting heat better than any other known material.

Each property traces back to the structure:

Property of graphene	Where it comes from
Very strong in the plane	Every atom is held by three strong C–C covalent bonds, with no weak layer to slide
Conducts electricity well	One delocalised electron per carbon atom, free to move across the sheet
Flexible	A single sheet can bend without breaking its bonds
Almost transparent	It is only one atom thick, so there is very little material in the way of the light

From one layer to a pencil line

In 2008, researchers at Manchester measured how much light one layer of graphene absorbs. The answer was 2.3% of white light. The other 97.7% passes straight through. Yet a pencil line, which is made of stacked layers, is dark grey. Use the explorer to see how many layers it takes.

Explore — from graphene to graphite

Add layers one at a time, then faster. Watch how much light gets through and how thick the stack becomes. How many layers block half the light?

Layers: 1

A simple model: each layer absorbs 2.3% of the light that reaches it, so the share that gets through n layers is 0.977ⁿ. Each layer adds 0.335 nm of thickness.

Layers	Thickness	Light that gets through
1	0.335 nm	97.7%
10	3.35 nm	≈ 79%
30	≈ 10 nm	≈ 50%
100	33.5 nm	≈ 10%
300	≈ 100 nm	≈ 0.1%

About 30 layers block half the light, and a few hundred layers block almost all of it. A stack only 100 nm thick, a thousandth of the thickness of this page, already looks black.

What did you see? One layer let through almost all the light. Each new layer took 2.3% of what was left, so the losses multiplied. About 30 layers blocked half the light. By 300 layers, about 100 nm thick, almost nothing got through. This is a simple model, but it explains the puzzle. Graphene and graphite are the same material, made of the same layers. A pencil line is dark only because it contains thousands of them. One millimetre of graphite contains about three million layers.

Rolled sheets and closed cages

A graphene sheet can also be imagined rolled into a tube, a few nanometres across. This is a carbon nanotube. Like graphene, it is held together by strong C–C bonds along its whole length, so it is extremely strong along the tube.

Carbon can also close up into a ball. In 1985, Robert Curl, Harold Kroto and Richard Smalley discovered a molecule of 60 carbon atoms, $C_{60}$ , shaped like a football, made of hexagons and pentagons. They shared the Nobel Prize in Chemistry in 1996. Molecules like this are called fullerenes.

Here is the important difference. $C_{60}$ is not a giant structure. Each ball is a separate molecule, with exactly 60 atoms. The bonds inside each ball are strong covalent bonds, but neighbouring balls are held to each other only by London forces. So solid $C_{60}$ behaves like a simple molecular substance. It is soft, and much less heat is needed to separate its molecules than to break a network. The word "giant" means the bonding never stops: it runs through the whole piece of material.

Silicon dioxide: a network of two elements

Giant covalent structures are not only made of carbon. Silicon dioxide, $SiO_{2}$ , is the main substance in sand and quartz. It is a giant structure built from two elements.

Silicon is in Group 14, like carbon. It has four outer electrons and forms four covalent bonds. In silicon dioxide, each silicon atom is bonded to four oxygen atoms, arranged in a tetrahedron, as the carbon atoms are in diamond. Each oxygen atom is bonded to two silicon atoms. So every oxygen atom is a bridge between two silicon atoms, and the bridges continue in all three directions.

A flattened picture of the silicon dioxide network. In the real crystal, the four oxygen atoms around each silicon atom form a tetrahedron. The highlighted silicon atom has four oxygen atoms, but each of those is shared with another silicon atom, so it "owns" half of each: 4 × ½ = 2. That is why the formula is SiO₂.

Look at the formula carefully. In a molecule such as $CO_{2}$ , the formula counts the atoms in one molecule. In silicon dioxide, there are no molecules. The formula $SiO_{2}$ tells you only the ratio of atoms in the network: one silicon atom for every two oxygen atoms. The figure shows where the ratio comes from. Each silicon atom has four oxygen neighbours, but each oxygen is shared between two silicon atoms. So each silicon atom has $4 \times \frac{1}{2} = 2$ oxygen atoms of its own.

Reading any giant covalent structure

1. Which atoms, and how many bonds? Strong covalent bonds throughout mean a very high melting point and no solubility in water.

2. What shape is the network? Bonds in all three directions make a hard material. Layers with weak forces between them make a soft one.

3. Are any electrons delocalised? If yes, it conducts electricity. If every outer electron is in a bond or a lone pair, it does not.

Apply it to silicon dioxide. Every atom is held by strong Si–O covalent bonds in all three directions, so it is hard and has a very high melting point, about 1713 °C. All its outer electrons are held in bonds or lone pairs on the oxygen atoms. None is free to move, so it does not conduct electricity. Water cannot break covalent bonds, so it does not dissolve. It is also unreactive with most chemicals. One well-known exception is hydrofluoric acid, HF, which attacks it and is used to etch patterns into glass.

The same three questions explain the most common exam mistake about it. Find it below.

Spot the error — why silicon dioxide melts so high

A student explains the properties of silicon dioxide. Exactly one line contains the mistake. Tap it.

A student's answer about silicon dioxide. Line 3 is wrong.

Line 1. Silicon dioxide has a giant covalent structure. Correct.
Line 2. Each silicon atom is bonded to four oxygen atoms, and each oxygen atom to two silicon atoms. Correct.
Line 3. To melt it, the strong intermolecular forces between SiO₂ molecules must be overcome. Wrong: there are no SiO₂ molecules, so there are no intermolecular forces. Melting breaks strong covalent bonds.
Line 4. This needs a lot of energy, so the melting point is very high. Correct.
Line 5. All its outer electrons are held in bonds or lone pairs, so it does not conduct electricity. Correct.

Compare carbon dioxide. Carbon is in the same group as silicon, and the formulas look alike. But $CO_{2}$ is made of small separate molecules, held to each other only by weak London forces, and it is a gas at room temperature. Silicon dioxide is one enormous network. The two formulas look alike, but they describe completely different things: a molecule in one case and a ratio in the other.

Worked examples

Worked Example 1 — Graphene conducts, silicon dioxide does not

Both graphene and silicon dioxide are giant covalent structures, and both have very high melting points. Explain why only one conducts electricity.

Use question 3. In graphene, each carbon atom uses three of its four outer electrons in bonds. The fourth is delocalised across the sheet, so electrons can move when a potential difference is applied. In silicon dioxide, each silicon atom uses all four outer electrons in bonds to oxygen, and every oxygen electron is in a bond or a lone pair. No electron is free to move.

So the type of structure decides the melting point, but the delocalised electrons decide the conductivity. Being "giant covalent" does not, on its own, tell you whether a substance conducts.

Worked Example 2 — Silicon or silicon dioxide?

A student writes: "Silicon is used to make windows because it is transparent." Correct the sentence.

Silicon, the element, is a shiny grey solid. Its structure is like diamond: each silicon atom is bonded to four other silicon atoms. It is a semiconductor, which conducts electricity weakly, and that is why it is used to make computer chips. Windows are made of glass, which is mostly silicon dioxide. Adding oxygen changes the network to Si–O–Si bridges, and changes the material from a grey semiconductor into a clear insulator.

A correct sentence: "Glass, which is mostly silicon dioxide, is used for windows because it is transparent, hard and unreactive."

Worked Example 3 — Why glass suits windows and oven dishes

Explain, using structure and bonding, two reasons why glass made mainly of silicon dioxide is used for oven dishes.

First, it must not soften in a hot oven. Silicon dioxide is held by strong covalent bonds throughout, so a lot of energy is needed to disrupt it, and an oven is far below its melting temperature. Second, it must not react with food. The strong Si–O network is unreactive towards almost everything in a kitchen.

One honest detail: ordinary glass is not pure silicon dioxide. Glass makers add other oxides to make it melt at a lower temperature, so it is easier to shape. Unlike quartz, glass is also not a crystal. Its network is irregular, which is why it softens gradually over a range of temperatures instead of melting at one sharp temperature.

Three classic mistakes

Trap 1 — Intermolecular forces in a giant structure

Diamond, graphite, graphene and silicon dioxide contain no separate molecules. Their melting points are about breaking covalent bonds. Write "strong covalent bonds must be broken", never "strong intermolecular forces". The one place weak forces appear is between the layers of graphite.

Trap 2 — Thinking every carbon structure is giant

Diamond, graphite, graphene and nanotubes are giant: the bonding never stops. A fullerene such as $C_{60}$ is a molecule with a fixed number of atoms, and its molecules are held together only by weak forces. Ask: does the bonding end at a fixed number of atoms?

Trap 3 — Mixing up silicon and silicon dioxide

Silicon is a grey semiconductor with Si–Si bonds. Silicon dioxide is a clear insulator with Si–O–Si bridges. They share a name, not their properties. Read the formula before you write the explanation.

Try it yourself

Work each one on paper first. Open a hint only when you are stuck.

Four solids, A to D, are tested. A melts at about 1713 °C and does not conduct. B does not melt, even far above 3000 °C, and conducts. C turns to vapour at a few hundred degrees and does not conduct. D does not melt, even far above 3000 °C, and does not conduct. Which could be graphite, diamond, silicon dioxide and $C_{60}$ ? Explain each.

Hint 1
A low temperature means separate molecules. A very high one means a giant structure.

Hint 2
Among the giant structures, ask which one has delocalised electrons.

Full answer
A is silicon dioxide: giant, so high-melting, with all electrons in bonds or lone pairs, so it does not conduct. B is graphite: giant, and the delocalised electrons let it conduct. C is $C_{60}$ : separate molecules held by weak forces, so little energy is needed, and no electrons move between molecules. D is diamond: giant, with every outer electron in a bond, so it does not conduct. Check: only one substance, B, conducts, and only graphite has delocalised electrons among the four ✓.
In hexagonal boron nitride, each boron atom is bonded to three nitrogen atoms, and each nitrogen atom to three boron atoms, in flat hexagonal layers like graphite. (a) What is its formula? (b) Boron has three outer electrons and nitrogen has five. Do you expect delocalised electrons, as in graphite?

Hint 1
Count neighbours both ways, as for silicon dioxide.

Hint 2
(b) Count the electrons each atom needs for three bonds. Does any atom have one left over that is not in a lone pair?

Full answer
(a) Each boron has three nitrogen neighbours, and each nitrogen has three boron neighbours, so the two elements are present in equal numbers: the formula is BN. (b) Boron uses all three of its electrons in its three bonds. Nitrogen uses three of its five, and its remaining two form a lone pair that stays on the nitrogen. So no electron is left over to spread across the sheet, unlike carbon's fourth electron in graphite. Boron nitride is in fact an electrical insulator, even though it looks like graphite and is slippery in the same way.
A pencil line on paper is about 1 µm thick (0.000 001 m). Each graphene layer is 0.335 nm thick. (a) About how many layers are in the line? (b) Use the explorer's model to explain why the line looks dark.

Hint 1
1 nm = 10⁻⁹ m, so divide $1 \times 1 0^{- 6}$ by $0.335 \times 1 0^{- 9}$ .

Hint 2
In the model, 300 layers already let through only about 0.1% of the light.

Full answer
(a) $1 \times 1 0^{- 6} \div (0.335 \times 1 0^{- 9}) \approx 3000$ layers. (b) Each layer lets through 97.7% of the light that reaches it, so 3000 layers let through $0.97 7^{3000}$ , which is far less than a billionth. Almost no light passes through the line, so it looks dark. In fact a pencil line on white paper is seen mostly by the light it fails to reflect, but the conclusion is the same: thousands of layers absorb nearly everything.
Silicon chips once used a layer of silicon dioxide, only a few nanometres thick, as an insulator between the "gate" and the silicon in each transistor. (a) Which property of silicon dioxide made it suitable, and why does it have that property? (b) In 2007, Intel began making chips that used a hafnium-based material instead, because electrons leaked through the very thin silicon dioxide. Suggest why making an insulator thinner makes it worse at insulating.

Hint 1
(a) Use question 3 of the theorem box.

Hint 2
(b) Think about how many atoms thick a few nanometres is, compared with the 0.335 nm of a graphene layer.

Full answer
(a) It is an electrical insulator, because every outer electron is held in a bond or a lone pair, and none is free to move. It is also a strong, unreactive network that forms easily on silicon. (b) A few nanometres is only around ten atoms thick. Our bonding model says no electrons are free to move through the network. But at this thinness, electrons can cross the layer by a quantum effect, even though the material itself does not conduct. The thinner the layer, the more leaks through. The hafnium-based material does the same job when it is thicker, so it leaks less. This is a real limit of the simple model: an insulator only insulates if there is enough of it.

The bigger idea

Graphene began a new field. If one layer can be peeled from graphite, other layered solids can be peeled too. Boron nitride, from Try it yourself, is one of them. Each new sheet has its own properties, and the same three questions explain them: which atoms, what shape, and whether any electrons are free.

Look at how much one bonding model has explained in this unit. Ionic, covalent and metallic bonding, intermolecular forces, and now giant structures. A pencil, a diamond ring, a grain of sand, a window and a computer chip are all explained by where the electrons are and how far the bonds reach.

This lecture also closes the unit on chemical bonding. The next unit turns chemistry into numbers, starting with the mole. You will meet the formula $SiO_{2}$ again there. The idea that a formula can be a ratio, not a molecule, is the idea of an empirical formula.

Key concepts in this lesson

Graphene is a single layer of graphite, in which each carbon atom forms three covalent bonds and has one delocalised electron.
Graphite is soft because its layers are held together by weak London forces, while graphene is extremely strong because a single sheet has only strong covalent bonds.
One layer of graphene absorbs only 2.3% of white light, so it is almost transparent, while thousands of stacked layers in a pencil line look dark.
In silicon dioxide, each silicon atom is bonded to four oxygen atoms and each oxygen atom to two silicon atoms, so the formula SiO₂ is a ratio, not a molecule.
Giant covalent structures have high melting points because strong covalent bonds must be broken, but they conduct only if some electrons are delocalised.
A fullerene such as C₆₀ is a molecule, not a giant structure, because its bonding stops at a fixed number of atoms.