by Brian Clegg
A moment of health and safety
Since we’ve brought up carbon nanotubes and slivers of graphene, it’s worth bringing up a potential health hazard associated with them. While carbon itself is non-toxic and is sometimes prescribed medically to pick up unwanted material in the stomach, the tiny forms of carbon, if allowed to float around in the atmosphere, could give humans a similar problem to asbestosis. If the tiny fibres or ribbons are inhaled, they are small enough to cause damage inside the lungs, reducing the organs’ effectiveness and increasing the risk of cancer.
In practice, in most of the applications of carbon nanotubes and graphene ribbons (a large sheet would be too big to cause a problem) the graphene is either embedded in a composite – as is the case with carbon fibre materials, with the carbon playing a similar role to glass fibres in fibreglass – or attached to a device, as we’ll see in the various applications of graphene in later chapters. However, there is a potential risk when large-scale manufacture of graphene and carbon nanotube products is under way, and appropriate health and safety regulations need to be observed.
In this case, the important factor is the sheer thinness of the tubes or ribbons, which make it easy for them to get into the lungs. But equally important to the usefulness of carbon allotropes is the internal structure of the material.
Shapes rule
What makes the different structures of carbon interesting is that the way the carbon atoms are linked together has a huge influence on the physical properties of the material, such as strength, electrical conductivity and heat conductivity. Although diamond and graphite are made up of exactly the same atoms – carbon with six protons and six neutrons in the nucleus, plus six electrons |||| – by virtue of their different structures, they become radically different substances.
The most immediate difference is that diamond is transparent, while graphite is opaque. A transparent material allows light to pass through it. Some of the light may still
interact with the atoms: an electron can absorb a photon of light and jump up to a higher energy level, but then the electrons will soon re-emit another photon to continue on its journey through the material. Diamond has a good structure to allow this kind of passage. By contrast, the multiple sheets of graphite, which are aligned so that the atoms in one layer sit above the gaps in the next, succeed in blocking the passage of the photons entirely unless we have a very thin slice with only a small number of layers.
Equally, graphite, as we have seen, is very soft due to the ease with which the sheets of graphene pass over each other – but diamond is renowned for its hardness. Electrically, the allotropes are also distinct opposites: graphite is an excellent electrical conductor (and graphene, as we shall see, far more so), while diamond, though rarely employed this way for reasons of expense, is one of the best electrical insulators there is. Again, it is the crystalline structure that makes all the difference. In graphite’s hexagonal structure, each carbon atom is connected to three others, leaving a loosely attached fourth electron from each of the atoms’ outer shells able to float through the material and conduct electricity. Diamond, by contrast, has each carbon atom bonded to four other atoms, leaving no free electrons in the outer shells to conduct.
It’s often the case that good electrical conductors are also good conductors of heat, and vice versa, because the same free electrons that carry electricity can be used to transmit heat energy. But diamond is something of an oddity in this respect, as it is an excellent conductor of heat – five times as good a heat conductor as copper. It can do this because it is also possible for heat to pass through a solid as vibrations, transmitted through the bonds between the atoms. Bear in mind that temperature is just a measure of the energy of the atoms that make up a substance. At a high temperature, the atoms jiggle around far more than they do at a low temperature.
The more rigid the bonds in a substance are, the less heat energy is lost as vibrations move through the material, *** so a very rigid structure like that of diamond can make for a very good heat conductor. In fact, diamond is so good in this role that artificial, high-purity diamonds are the best known thermal conductors of any solid. Boring old carbon really is quite remarkable.
Going small
So far, what we’ve seen is comprehensible in terms of classical physics, the kind of physics that was understood in the 19th century and is still largely what we are taught in school. But to really grasp the significance of ultrathin materials such as graphene, we need now to take a plunge into the quantum world. Here small objects like atoms and electrons behave quite differently from regular objects we can see and touch – and it is these quantum properties that give graphene and other ultrathin substances many of their capabilities as wonder materials.
* There is very little evidence for the life of Leucippus, who preceded Democritus, and some have suggested he was a fictional means to add weight to the theory of atoms.
† The original word is a combination of a meaning ‘not’ and tomos for (roughly) a cut or cutting. It came to us via the Latin atomus .
‡ Brown got the glory, even though the Dutch biologist Jan Ingenhousz had observed something similar with charcoal grains in water a good 50 years earlier.
§ Traditionally given the non-PC description of a ‘drunkard’s walk’.
¶ Strictly speaking, the electrons are not represented by plums, but by raisins. Plum pudding was a distinctly misleading name for what is now called Christmas pudding.
|| The one with the counter.
** Rutherford had already predicted some kind of central small charge in 1911 after less sophisticated experiments, but it was the 1913 version that cemented his theory.
†† Shells as opposed to orbits, to emphasise that the solar system model doesn’t work. The nature of shells requires quantum theory, but for now the idea is essentially that each shell is a bit like a track. Electrons can only run on these tracks or jump between them as a result of a quantum leap. The electrons can be configured differently within each shell – these different configurations are confusingly referred to as orbitals, though each possible orbital is a probability distribution – a mathematical description of the chances of finding an electron at a particular location – not in any sense an orbit like that of a satellite.
‡‡ The word ‘ion’ comes from the Greek present participle of ‘to go’ (i.e. going), reflecting its first use to describe whatever it was that went from one electrode to another during the process of electrolysis.
§§ The angle is around 105 degrees.
¶¶ Ice’s ability to float on water has helped shape the biology of fresh-water species. If it didn’t, water would freeze from the bottom up and would not leave an insulated layer of liquid water beneath the ice for life to survive in.
|||| It’s these six electrons that make carbon so versatile and the backbone of the chemicals making up life on Earth. Carbon has four electrons in its outer shell and four vacancies, allowing for a wide range of structures, both when linking to other carbon atoms and in the many and extremely varied organic compounds necessary for life.
*** You can see why a rigid substance has less loss of vibration by thinking of trying to send a pulse through a piece of cloth and something rigid like a pen. Push one end of the cloth and the movement is lost in the floppiness of the material, but push one end of a pen and the movement easily reaches the other end.
3
QUANTUM REALITY
Why quantum makes the difference
Some of the remarkable abilities of graphene that we will explore later are down to its flexibility and strength, which we can understand from its lattice structure using traditional Victorian physics. But to be able to explore its significance for the future of electronics, we need to have a basic grasp of quantum physics. This is one of the most essential aspects of physics, yet remains one that most of us know least about.
The word ‘quantum’ gets bandied around in all sorts of unlikely scenarios from the Quantum Leap TV show
to Quantum dishwasher tablets and websites offering ‘quantum healing’. When scientists use the word, though, they are thinking of something much more precise. A quantum is a separable chunk of something, and quantum physics reflects the aspects of nature that come in separable chunks, rather than having a continuous nature.
To take an everyday example, my local petrol station is currently selling petrol at 116.7 pence per litre. That’s effectively treating price as if it were a continuum. They might equally sell it at 116.682314159 pence per litre if they really wanted to. But when it comes to paying, if I buy the minimum five litres, I can’t pay, say, 583.5 pence, because the British cash system is quantised in units of 1p. There has been no such thing as half a penny since 1984, and there has never been a smaller unit of currency since decimalisation. So, if I bought exactly five litres, I would have to pay either 583p if the company were generous, or, more likely, 584p because they had rounded the value up to the nearest whole penny.
It turns out that a lot of aspects of nature that had once been thought of as a continuum until the early 20th century – a beam of light, for example – are in fact quantised, and so come in minimum-sized chunks or ‘quanta’. In the case of light, these quanta are called photons. The name ‘quanta’ (plural of quantum) dates back to Max Planck, the German physicist who first considered light to be broken up this way. He didn’t like the idea, because everyone at the time thought that light was a wave; looking back in his old age, he said: ‘Briefly summarized, what I did can be described as simply an act of desperation.’
Planck assumed that quanta of light were just a helpful calculation tool, but Einstein would demonstrate that they must actually exist. It’s not that the wave theory of light was entirely wrong – light often does act as if it were a wave, but there are times when it can only be understood if we consider it to be acting as a collection of quanta – photons. By this time, scientists were also already aware of the effective quantisation of matter, into atoms (or subatomic particles to go for the ultimate matter quanta, as far as we know). Even here, our senses can deceive us. It appears that a stream of water, or a piece of rock, is a continuous thing, but we know that in reality it is made up of tiny, separate particles, held together by bonds.
Of itself, the existence of these particles is not such a surprise. What shook the early 20th-century physicists was that the basis of every normal object was revealed to be a collection of particles which refused to behave the way that they were expected to. Quantum particles do not behave like everyday objects. Such was the resistance from Albert Einstein – who had been instrumental to proving the existence of the quantum world – that for years he would regularly come up with thought experiment challenges which he hoped would show that quantum theory was wrong. Every one of his challenges proved ineffective.
What offended such a great mind as Einstein? He famously wrote to his friend Max Born: ‘The theory says a lot, but does not really bring us any closer to the secret of the “old one”. I, at any rate, am convinced that He is not playing at dice.’ The choice of imagery was a reaction to the way that quantum theory has probability at its heart. As we will see, crucially for some electronic applications, quantum particles that haven’t interacted with something else for a while aren’t situated in one place, but rather exist merely as a collection of probabilities for different locations. Such uncertainty made Einstein also write to Born on another occasion: ‘In that case, I would rather be a cobbler, or even an employee in a gaming house, than a physicist.’
Three quantum essentials
Perhaps the best known of the probabilistic aspects of quantum theory, at least by name, is Heisenberg’s uncertainty principle. This does not mean that ‘everything is uncertain’ as the term is sometimes loosely used to imply. It’s quite the reverse, in that the uncertainty principle describes a series of precise relationships. It tells us that any quantum particle has pairs of properties associated with it where, the more accurately we know one value, the less accurately we can pin down the other. So, for instance, the more accurately we know the location of a quantum particle, the less accurately we can know its momentum. We can never know both perfectly at the same time. If we exactly know the momentum, say, the particle could literally be anywhere in the universe. Similarly, the more accurately we can pin down the energy of a quantum particle, * the less accurate we can be about the timeframe in which we make the measurement.
Even more fundamental to quantum behaviour is the Schrödinger equation. This describes the way that a quantum system – in its most useful simple application a single quantum particle – changes over time. When the equation was first developed it caused considerable confusion, as it was assumed that it dealt with the location of a particle. And if this were the case, it seemed to say that, over time, a quantum particle would spread out, occupying more and more space. This doesn’t happen (thankfully). But the same Max Born to whom Einstein wrote about his quantum concerns realised that the equation † did not describe the location of a particle, but rather the probability of finding a particle in a particular location. Over time, the range of possible locations where the particle could be spread out through space.
This provided a radically different view to the then conventional conception of quantum particles such as electrons and atoms being like tiny balls which were able to move around but which were in a single, specific location at any one time, just like the kind of ball that we play with in a game. Instead, once a quantum particle has been created, its potential locations spread further and further out. It’s not that it has equal probability of being in all those places. It is typically more likely to be where we would expect it to be if it were a conventional ball – but it also has a possibility of being in totally unexpected places, and in some cases even the most likely location is totally different from what we’d expect from experience. All that exists at this point, when the quantum particle is not interacting with anything, is a smear of probabilities across space. The particle is not, as is sometimes described, in two places at once. It does not have any location at all. It’s only when the particle interacts with something else at one of its possible locations that its settles down on a specific place to be. We can calculate the exact probability of any particular location being the one where we will find the particle, but until it interacts with its surroundings we have no idea which one of the possible locations will prove correct.
This ‘smeared out’ nature of quantum particles enables a third quantum oddity which turns up regularly in electronics and will be crucial to using graphene: quantum tunnelling. In the conventional world, if I send an object towards a barrier, and the object hasn’t enough energy to get over or through the barrier, it can’t go any further. It stops. But by the time a quantum particle is most likely to be in the vicinity of a barrier, because the possible locations have spread out, there is a probability (usually small) that it is already the other side of the barrier. In the event that this turns out to be the case, it’s as if the particle has tunnelled through the barrier and out the other side – taking no time in the process. It’s already there. That is quantum tunnelling.
It’s a bit like someone throwing a tennis ball repeatedly at a wall and finding out that every now and then the ball doesn’t bounce off it and fall to the ground, but is already heading away from the other side of the wall. This sounds ridiculous – yet quantum tunnelling has been observed many times and is both frequently used and occasionally a problem to avoid in electronics. It’s common, too, in nature. We wouldn’t even exist without quantum tunnelling, as it is needed to make the Sun work.
The Sun produces the energy that has enabled life to thrive on Earth using a process known as nuclear fusion, where the nuclei of hydrogen atoms are joined together to produce the heavier element helium, giving off energy in the process. Inside a star like the Sun, hydrogen nuclei are squashed together under immense temperature and pressure – but it’s not enough to get them to fuse. Because they are positively charged, th
e electrical repulsion between the nuclei prevents them from getting close enough for the fusion process to occur. It’s only because the hydrogen nuclei are quantum particles and can tunnel through the barrier formed by the electromagnetic repulsion that the Sun can function.
In electronics, tunnelling is something that circuit designers have to be aware of. If they make parts of the circuit on a chip too close together, electrons can tunnel through the barrier between two parts of a circuit, resulting in a glitch in the system. On the positive side, though, tunnelling has proved a boon for constructing certain types of transistor and for keeping information when the power is turned off.
We now take it for granted that we have memory chips that function without power. This so-called flash memory is used in phones, memory sticks and the solid-state drives that are fitted in many modern computers instead of the old hard discs. Conventional computer memory simply loses the electrical charges that make up the 0s and 1s of the data held in it when the device is turned off. But flash memory hangs onto those charges despite a lack of electrical power. This is because each bit of the flash memory is stored in a tiny insulated island. It is only by intentionally getting electrons to tunnel through the barrier that the value in the memory can be changed.
When we think specifically of graphene and its curious properties, we need to get a quantum view of what’s happening to the electrons that are part of the atom, for which we will have to go back to Manchester at the start of 1912, when the young Niels Bohr had just arrived at a new laboratory.
Bohr’s atom
