by Brian Clegg
Yet faced with all these obstacles, and without any precautions to prevent it curling up or disintegrating, separation of graphene flakes using the sticky tape method just worked. It seems that the way graphene is typically produced from a three-dimensional block overcomes some of the issues of attempting to form a two-dimensional layer from scratch. And because its layers are easily removed at room temperature, there is less tendency for them to scroll up, while, once on a substrate, the van der Waals forces tend to keep the graphene pressed flat against the surface and safe from damage. There is some weak reaction with the air – but not enough to destroy graphene’s remarkable capabilities.
Beyond the tape
Although ‘exfoliation’ methods like the original Scotch tape production approach are still used to get hold of small flakes of very pure, single-layer graphene, it isn’t an ideal mechanism for larger-scale requirements. It’s hard to imagine mass production of graphene-based devices if it all had to start with pieces of sticky tape being repeatedly applied to a graphite block and a substrate. ¶ A number of alternative production methods are now in use which, though often tending to produce less consistently perfect samples than the tape and block method, make it possible to manufacture much larger continuous sheets of graphene and, in principle, should be able to produce it to any size required.
Perhaps the simplest method, which is still hand-crafted but can make a larger sample, is effectively to stitch smaller graphene flakes together. A number of flakes that have been produced via the traditional method are first oxidised, which makes it possible to suspend them in water; the water is then passed through a filtering membrane, which has holes in it that are large enough to allow water through but catch some of the graphene flakes. A number of flakes get caught on the membrane, which gradually builds up a graphene layer that can be moved onto the usual silicon or equivalent substrate for support.
Apart from being relatively low-tech, the other advantage of this approach is that the graphene produced is of relatively high quality as it is still the lifted layers from graphite. However, it is very difficult to get a uniform single layer this way, while the graphene oxide needs to be treated to get it back to graphene, a process which itself can introduce irregularities into the graphene. And there is still the original sticky tape step in the process, so while it can be useful to make larger samples in the laboratory, with relatively low expenditure on kit, it is unlikely to became a large-scale production method.
An alternative approach is to produce so-called epitaxial || graphene. This is done by heating a block of silicon carbide to around 1,500°C. This material, also known by the rather magnificent name carborundum, has been produced for over 100 years. It was first used as an abrasive and in cutting discs, but now turns up in more high-tech applications such as ceramic brakes on high-performance cars, in LED manufacture and in steel production. Because of the large market, high-quality silicon carbide is relatively low-cost. When the surface reaches a high temperature the exposed silicon atoms boil off, leaving a single atom carbon layer, which can be stripped away as graphene.
However, a more controlled approach that can produce even larger uniform graphene sheets is to heat up a carbon filament in a very high vacuum. Just as the old incandescent light bulbs with a heated filament would leave a deposit of the material that the filament was made from on the inside of the glass, so the glowing carbon filament sprays carbon atoms into the vacuum to land on a metal substrate and form a layer of graphene. This approach can produce large, high-quality films, but it does require room-sized and expensive equipment to produce an extremely high vacuum encompassing a large enough space to accommodate the sheet of graphene.
A more recent variant, called chemical vapour deposition, involves heating a sheet of copper to around 1,000°C at a low pressure, although not requiring such a high level of vacuum as the carbon filament method. A combination of methane and hydrogen is then passed over the surface of the hot copper. Catalysed by the hydrogen, the methane and the copper react, leaving a layer of carbon on the surface. If the sheet is then quickly cooled, the carbon crystallises into a sheet of graphene.
Because chemical vapour deposition does not need an extreme level of vacuum, this is a cheaper mechanism than the approach with a carbon filament, but the quality of the graphene tends not to be as good, as the film of carbon is more likely to pick up impurities from the gases that pass over it. However, it does seem possible to keep these impurities down enough to make a graphene layer of much greater size, coming close to the quality of the flakes from the Scotch tape method. The other challenge with this method is how to get a smooth sheet, as the graphene tends to wrinkle during the cooling process. This is because the copper shrinks at a different rate to the carbon as it drops in temperature. There is still work to be done on improving this method, but it holds out promise for a graphene mass-production mechanism.
Although none of the approaches is yet perfect, there are now several ways to make graphene sheets large enough to be able to produce solar cells or complex electronic devices at a significantly lower cost than, say, silicon equivalents. Large-scale production tends still to be relatively low-quality – but there is no more of a problem here than faced the silicon industry when producing high-quality silicon wafers. That took several decades to perfect – the chances are, with both the wider range of applications and the experience with silicon, that the same quality improvements could be achieved much faster for graphene.
The scene is set for the potential applications of graphene to take off, many of which revolve around its remarkable electronic properties.
Dancing the light electric
As mentioned previously, one of graphene’s most remarkable abilities is its extremely high conductivity. This occurs because of a peculiar effect of the graphene sheet’s crystal lattice. To get a feeling for this, we need to take a further plunge into the area of physics called band theory. This refers to the workings of the band structure of a substance. As we have seen (see page 56 ), when a solid conducts electricity, it depends on electrons being able to pull free from the atoms in the substance to conduct the electric current. And the band structure defines how well a particular substance will be able to allow those electrons to act freely.
When atoms come together to form a structure, such as the carbon atoms in graphene’s hexagonal grid, the atoms get close enough to each other for their orbitals to overlap and interact. As we have seen, the particular crystal structure of graphene results in an unusual band structure where there are places where the conduction and valence bands exactly touch. This results in the ability of the electrons to interact with vibrations in the lattice in a way that enables the combination of the two to produce charge-carrying ‘quasiparticles’ which effectively have no mass. Usually, when electrons are the charge-carrier, they travel quite slowly through a conductor, floating along at a walking pace. (The reason electricity doesn’t take a long time to get from one end of the wire to the other is that an electromagnetic wave travels down the conductor at the speed of light, setting all the electrons in motion as it reaches them.)
The slow pace of electrons in a normal conductor is due to their frequent interactions with the electrical charges in the atoms of the material. But in graphene, the charge-carriers, acting almost as if they were photons of light, can get up to speeds of around a million metres per second (for comparison, light in a vacuum travels at around 300 times this speed). This seems almost impossible, but the combination of the electrons and the crystal lattice acts as if the charge is being carried by massless particles that are travelling through it at high speed. **
Where electrons usually find that the atoms in a lattice act like a set of barriers that slows them down, the quasiparticle tunnels through the barriers as if they aren’t there – this is quantum tunnelling, as described in Chapter 3. It’s a bit like the difference between two people trying to move forward in a set of jumps, one on a concrete floor, the other on a very long trampoline.
It’s the interaction between the gymnast’s muscles and the spring structure of the trampoline that generates what would otherwise be impossibly long jumps and fast speed – similarly, the interaction between the electrons and the two-dimensional structure of graphene generates the otherwise impossibly fast charge-carriers.
Because the charge-carriers are moving so quickly, physicists have to switch the equation used to describe their behaviour. As we have seen, when anything is moving as quickly as these particles, the impact of special relativity has to be brought in, which is why in the previous chapter we were introduced to the Dirac equation – this rules the roost in graphene. And it is these relativistic charge-carriers that result in graphene being a far better conductor than copper, silver or gold.
However, with graphene, the surprises keep coming. It has recently been discovered that this isn’t the end of the story. Electrons themselves in the graphene behave in a way that is quite unlike the way they travel in a metal. Individual electrons interact with each other. This happens normally, but the usual result is bouncing off each other and randomly scattering, reducing the ability to carry current. In graphene, the electrons form a kind of gooey electron fluid, which has a viscosity (resistance to movement) that is as much as 100 times that of honey at room temperature. This remarkable and previously unknown behaviour means that the electrons can form whirlpools and eddies inside the graphite like water in a river. Sometimes they have even been observed moving in the opposite direction to the electrical current.
Such perverse behaviour of going against the flow in a systematic way has never been seen in electrons before. This so-called ‘electron hydrodynamics’ is fascinating in its own right and is proving a new avenue of exploration for theoretical physicists who hope to understand better the mechanisms of electrical conduction in solids. However, it also has a surprising side-effect, which is that it can make the graphene even better as a conductor than it would be without it.
This is counter-intuitive, as you would expect that electrons moving backwards against the flow of electrical current would reduce the material’s ability to conduct. What seems to be happening is that the electrons that form the slow-moving, eddying fluid flow stay near the edges of the material. These rivers of electrons provide a pair of repulsive barriers that prevent the faster moving electron/lattice charge-carriers from being held up by collisions with the other electrons, making it possible for the graphene to exceed the theoretical limit for the amount of current that it could carry.
This property was only reported in late 2017 – graphene continues to amaze long past its original discovery. Just as Richard Feynman hoped, opening up the world of the very small has not just made a new scientific discovery possible, but makes so many new areas of exploration available.
In the Hall of the quantum king
There is one extra peculiarity about the electronic behaviour of graphene, for which we need to introduce a little more quantum physics to get a picture of what’s going on. The effect in question has the impressive name ‘the quantum Hall effect’, while also of relevance is ‘the anomalous quantum Hall effect’ – the latter displayed not by graphene but by other ultrathin materials. Let’s deconstruct the names. The Hall effect, which predates quantum physics, was discovered by US physicist Edwin Hall in 1879.
If you put an electrical current through a conductor and add a magnetic field from one side, the flow of electrons through the conductor will not be in a straight line, but will curve as a result of the magnetic field. This means that there will be more negative charge on one side of the conductor than the other, which in turn means that there is an electrical field set up between that relatively negative side and the other side which will be relatively positive.
The next step is the quantum Hall effect, which, as the name suggests, introduces quantum behaviour. This happens in two-dimensional conductors or semiconductors when the temperature is very low (within a few degrees of absolute zero, which is –273.15°C) and the magnetic field is strong. Under these conditions, the resistance of the object at right angles to the electron flow becomes quantised – it can only take on very specific values. To be precise, the only options are limited by two constants of nature – Planck’s constant h, which gives the relationship between a photon’s energy and its wavelength and e, the charge on an electron. The values observed are specified by a variable named ν, which can take a range of integer or fractional values, giving the object a resistance of h/νe2 .
These narrowly prescribed values of resistance, which are extremely precise, make the quantum Hall effect very useful for devices requiring an exact resistance to make electrical measurements, so it is valuable in various kinds of detector. More interesting still, the resistance of the material in the direction of the current flow disappears. Electrons flow along the edges of the material without any losses to resistance. This means that, in principle, there would be none of the energy loss to heat we get in an ordinary wire conducting electricity.
Interesting though the conventional quantum Hall effect is, it is of little practical value because it’s not realistic to have wires that are kept in a powerful magnetic field at ultra-low temperatures – a fraction of a degree away from absolute zero – for everyday applications. It’s fine for the lab, but it’s not going to be used in a commercial device or in wiring. However, graphene’s weird conductivity means that it can produce the quantum Hall effect at room temperature, though it still requires the strong magnetic field.
Going a final step, we get to the anomalous quantum Hall effect – which is the trick performed by some other ultrathin materials, but not by graphene. The particular type of ultrathin substance is called a magnetic topological insulator, which acts as an insulator in its interior, but conducts on the surface. Bearing in mind the quantum Hall effect influences the edges of the thin material, these seem an ideal constituent with which to use the quantum Hall effect – and they are so good at it that the result is the so-called quantum anomalous Hall effect where the quantum effect occurs without a magnetic field.
In tests with an ultrathin film of a material made from bismuth, antimony and tellurium, doped with chromium, experimenters at Stanford and MIT in the US and the Tsinghua University in China have produced a near-perfect anomalous quantum Hall effect across the material with a low resistance of about 1 ohm lengthways. As yet this only works at ultra-low temperatures. However, the two different approaches with graphene and these special compounds individually overcome one of the limitations of the quantum Hall effect each – in the future, it’s entirely possible that some combination of ultrathin materials could make it useable without a magnetic field and at room temperature.
Superstrength
One of the most remarkable claims for graphene is that it is far stronger than steel. In fact, it’s currently the strongest substance that has ever been tested. We need to give a little clarity to that remark – the invisibly thin sheets of graphene can’t compare with the strength of a centimetre-thick sheet of steel. You can’t lift an elephant using a single two-dimensional sheet of graphene. The problem is that the term ‘strength’ is rather loose in this context.
The claim that graphene is the strongest material ever tested refers to tensile strength, which is the material’s ability to resist being pulled apart lengthways. †† And the standard measure of tensile strength (in which graphene stands out way above its possible competitors) requires an equal cross-section of material for like-for-like comparison. This means that to make a fair comparison we need to put layers of graphene into a composite with some kind of binding material to make it up to the required thickness.
Tensile strength is measured in pascals (equivalent to newtons per square metre), which is more commonly the unit of pressure. (Because the numbers are large, it’s more common to measure it in megapascals, where 1 megapascal = 1 million pascals.) To get a feel for scale, the typical tyre pressure of a car is around 0.2 megapascals. The table opposite shows how graphene stands u
p to the competition.
Substance Tensile strength (megapascals)
Graphene 130,000
Boron nitride nanotubes 33,000
Silicon (monocrystalline) 7,000
Limpet ‡‡ 5,000
Kevlar 4,000
Diamond 2,800
Strong steel 2,500
Brass 500
Human hair 225
Pine 40
Iron 3
Various tube-shaped variants of graphene (carbon nanotubes) also have extremely high tensile strength, though in the context of putting large numbers of them in a composite, these are effectively just alternative ways of structuring the graphene.
The reason that graphene is ridiculously strong is primarily down to its bonds. Looking at the lattice structure of graphene (see page 16 ), it has vast numbers of carbon– carbon covalent bonds all arranged in the same direction. A square metre of graphene, weighing in at an impressively light 0.77 milligrams, contains around 10 20 atoms, §§ each with three bonds attached to each atom.
The covalent bonds between carbon atoms are strong bonds, and combine ideally here to resist being pulled apart, just as in the different crystalline structure of diamond the lattice of covalent carbon–carbon bonds gives the material its hardness. A good piece of graphene is also unusually low in faults in the lattice structure. Anywhere the neat repeating pattern of the bonds is broken is an opportunity for a split to start forming in the material – but compared with a metal like steel, good quality graphene has far fewer such faults.
This remarkable tensile strength makes graphene an ideal choice for the reinforcement in future composites, with the graphene embedded in another material, usually a plastic polymer, to give it extra strength. Like carbon fibre or carbon nanotubes, graphene isn’t great at sticking to the composite material, but it could be treated chemically (for example by converting it to fluorographene – see page 111 ) to make the interface more effective. Graphene is not only stronger than carbon fibres, but because it is a single atom thick, it can’t split in the dimension at right angles to the two-dimensional sheet, increasing its effective strength and making it excellent at stopping crack propagation.