Graphene : Strongest Substance Known to Humankind?

Graphene : Strongest Substance Known to Humankind?

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Graphene is a miracle material of the 21st century. Apart from its exceptional flexibility and electrical and thermal conductivities, it is also the strongest material known to humankind. Or is it?

What is the hardest material known to us? You’d probably answer, diamond. And you would be mostly correct. Hardness means that diamond will almost never wear down, and you can’t drill into it using any other material. It is also one of the stiffest materials known. That means that, if a force is applied on it that tries to bend it or twist it out of shape, it resist deformation extremely well indeed. In fact, the only known material that is even close to diamond in “stiffness” is the humble pencil tip.

Well, not quite the pencil tip. More specifically, a certain form of one of the principal ingredients of a pencil tip.

Pencils are wonderful objects. They are both the messiest and the cleanest writing instruments around. They can be the most practical as well as the most hazardous writing instruments in outer space. And they are fun to sharpen. And they are made of lead…

Err…not quite. This is a common misconception that is, hopefully, no longer so common. Pencil cores are a combination of graphite mixed with a clay binder. Graphite is an allotrope of carbon. In graphite, carbon atoms are arranged in hexagonal lattices making up individual layers that are an atom thick. A very large number of such layers stacked on top of each other make up graphite. The layers stick to each other rather loosely, and are prone to slippage. Which is why a graphite pencil leaves marks on paper or other relatively rough surfaces which pull stacks of graphite layers off of each other. So graphite is quite the opposite of diamond when it comes to hardness.

Illustration of the honeycomb structure of graphene

An atomic monolayer of graphite is called graphene. It was the first two-dimensional atomic crystal known to us 1. Graphene has incredible electronic 2,3, optical 4 and thermal 5 properties that makes it ideal for cutting-edge real-world applications such as flexible electronic displays, corrosion resistant coatings, biological devices and a host of others 6–8.

In addition to all this, graphene is also very stiff. Very very stiff. So stiff that “It would take an elephant, balanced on a pencil, to break through a sheet of graphene the thickness of Saran Wrap.

This statement was made nine years ago by James Hone of Columbia University who, in 2008, co-authored a paper 9 where he and his coworkers describe how they used an atomic force microscope (AFM) to measure the so-called “strength” of graphene. Their experiment involves spreading graphene out on a perforated plate. Holes on the plate of diameters 1-1.5 micrometre are separated by distances of 0.5 micrometre. They then use the AFM to indent the graphene just above the central parts of the perforations, and were consequently able to measure its mechanical properties. Their experiments were in agreement with phonon instability studies of graphene done a year earlier 10 which set the value of Young’s modulus of graphene at an incredible 1.05 TPa, or 1050 GPa.

Young’s modulus is a measure of the stiffness of solid material. If a load, that is, a force is applied to a solid body, it will deform, but it will resist that deformation. Once the load is removed, it will try to regain its original shape. This is elasticity, a property of solid materials that can be easily demonstrated with a simple rubber band. One can apply different loads to a solid body and experience different deformations. By measuring the stress (the force per unit area) and the strain (proportional deformation of the body), one can draw a graph with these two quantities. If the load is such that the stress-strain graph is a straight line, then the body is said to be in the Hookean11 or linear regime. In this regime, the slope of the stress-strain graph is the Young’s modulus (E). It is the ratio of the applied stress to the resultant strain, and is measured in units of pressure 12. SI units are the N/m2 or the pascal, while pounds per square inch (psi) is the Imperial measure. More practical units for E are the megapascal (MPa), the gigapascal (GPa) or even the terapascal (TPa).

Young’s modulus is thus a measure of how much load we need to see a certain amount of deformation in the material, provided we are in the linear regime, of course. If we increase the load too much and step out of the linear regime, nonlinear terms enter the force-displacement relation and E no longer remains the only measure of stiffness. In either case, a large value of E implies that a large load is necessary to bend the material and consequently, one can conclude that the material in question is very stiff.

So how stiff is graphene? How high is 1050 GPa?

To get a feel for that, we would need to compare it to everyday items that are also considered strong in everyday parlance, and stiff from a material science perspective. Take A36 standard structural steel, the most common building steel in the USA. Steel is usually considered a strong material. Superman 13 is the Man of Steel. A36 has an E value of 200 GPa . That is a fifth of graphene.

We could start calling him the Man of Graphene. Just a thought, DC.

Some sources argue that graphene is over 200 times as strong as steel. They are talking about tensile strength, which is the resistance to being pulled apart. The intrinsic or tensile strength of graphene is 130 GPa 9 whereas that of A36 steel is a 400-550 MPa 14. That is a factor of nearly 250!

Now hold on here. Steel is strong, but not as strong as tungsten. Tungsten is strong. And robust. It has the highest melting point of all known elements and the second highest boiling point. It is 1.7 times denser than lead, and as dense as gold or uranium. It also has an E value of 400 GPa. That’s two-fifths of graphene. It has a tensile strength of 1510 MPa, which is the highest among metals 15.  That’s a factor of 86.

Ok, scratch tungsten.

What else is left? Diamond. Yes, diamond is stiff enough, isn’t it?

So, we’re back to diamond, are we?

Err…

“It would take an elephant, balanced on a pencil, to break through a sheet of graphene the thickness of Saran Wrap.” — James Hone

Before we move on to diamond, let us try and do a bit of back-of-the-envelope calculations to figure out if Hone’s elephant-pencil analogy has any merit. There are, primarily, three species of elephants on Earth. Asian elephants are smaller, lighter and have smaller ears than their African cousins, who tend to weigh about 6 tons 16. That is 6000 kg. This is the mass. Their weight is thus approximately 60000 N or 6*10^4 N 17. Now, a pencil lead (made of graphene) is about 2 mm in diameter. I shall assume that a well-sharpened tip will be about a tenth in size, or about 1*10^(-4) m in radius. That is equivalent to an area of π*10^(-8) sqm. Thus the pressure is of the order of 10^12 N/sqm or 1 TPa, the same as the Young’s modulus of graphene. So yes, Hone wasn’t quite rambling when he spoke of elephants, pencils and Saran Wraps…

Hold on. Saran Wraps?

Saran is the trade name for polyvinylidene chloride, and has been used for decades to wrap and store food. Sheets of Saran Wrap have thicknesses in the tens and hundreds of micrometers, whereas graphene, being an atomic monolayer, is thousands of times thinner. So I don’t quite understand why Hone spoke of the thickness of Saran Wraps. Perhaps I should ask him. I think I’ll put a pin on that idea.

Anyway, diamond. It has an E value that is about or a little more than 1 TPa, and is comparable to graphene in stiffness. However, diamond and graphene are not the stiffest materials known. Linear acetylenic carbon (LAC) or carbyne is an allotrope of carbon composed of chains of C atoms with alternate single and triple bonds. Carbyne has an E value of 32.7 TPa! 18 Everything stiff is carbon.

So all that is very stiff stuff. But are these materials tough?

Toughness and stiffness are both mechanical properties of solid materials that have to do with strength of some form or the other. Stiffness, as described earlier, is the ability of a material to resist deformation. Toughness, on the other hand, is the ability to resist fracture. It is difficult to beat a stiff material out of shape, just as it is difficult to break a tough material. Unfortunately, in most materials, these two properties are often mutually exclusive 19. For instance, tungsten is very stiff. It is very hard to bend tungsten or beat it out of shape. However, unless it is in a pure single crystalline state, tungsten is brittle and prone to breakage. This is because polycrystalline tungsten has grains, and fractures occur along the grain boundaries separating the grains 20, just like earthquake-prone geological faults. Or magnetic domains, as I explain later.

So what about graphene? Is it tough?

Grain boundaries (GB), being the interface between two grains, and Triple Junctions (TJ), being the intersection point of three GBs, in graphene. The former is a line defect, while the latter is a point defect. Residual stresses concentrate and accumulate at these defects, lowering the inherent toughness of graphene significantly.

Well, if Zhang and his coworkers 21 or Shekhawat and Ritchie 7 are to be believed, no, not quite. At least not in its polycrystalline form anyway.

We have conveniently skipped an aspect of the whole graphene story that, for almost a hundred and fifty years 22,23 before 2004, no one knew the solution to. The question was simple : how does one actually synthesise graphene? Getting graphite is easy. It occurs as a mineral in rocks and can be mined. World production of graphite was 1.2 million tonnes in 2016 24. We can go to a stationary store, buy a few pencils, extract the cores and we’ll have all the graphite we’ll need.

But how does one go about extracting graphene? It has to be an atom thick, since it is, by definition, a monolayer of graphite. Extracting a  monolayer of graphite is no mean task, and it took researchers a century and a half and exotic, complicated and expensive methods 23 to finally hit upon the solution. In 2004, Andre Geim and his colleague Konstantin Novoselov realised they could extract graphene using the humble Scotch tape 25.

Yes. Scotch tape. Also called Sellotape, transparent tape, and really-that-was-all-it-took-to-extract-graphene? Costs virtually nothing.

This method of extracting graphene is called, rather logically, exfoliation. It is excellent for lab work, and can be tweaked to produce nearly perfect pure monocrystalline graphene. However, it is extremely ineffective for industrial production since (a) it is not scalable and (b) it is rather expensive. Although Scotch tape itself is rather cheap, the process of synthesis of graphene using exfoliation is decidedly not. In fact, as of April 2008, a square centimetre of exfoliated graphene would cost $100 million! 26

Thus, a second technique 27, that of chemical vapour deposition (CVD), is now used to produce nearly 300,000 sqm of graphene annually 7. However, graphene synthesized using CVD is decidedly polycrystalline, and this brings in imperfections such as grain boundaries (GB) and triple junctions (TJ). A GB is the interface between crystalline regions of different lattice orientations, while a TJ is an intersection of three such interfaces. Crystalline grains are a bit like magnetic domains, where all the small molecular magnetic dipoles point towards a particular direction on average, but different magnetic domains can have different magnetic orientations. In polycrystalline graphene, GBs and TJs are defects where residual stresses concentrate and accumulate, and, ultimately lead to fracture. In fact, it was found, both numerically and experimentally, that the toughness of polycrystalline graphene is only about 20-50% of polycrystalline diamond 7,21.

Does that mean that graphene is no longer the undisputed strongmaterial champion of the world?

Illustration of graphene deforming on being struck by a high-energy projectile

Well, not quite. It is still possible to produce low quantities of very high-grade graphene that is free of GB and TJ faults. In fact, layers of such graphene have been stacked to successfully test out bulletproof armour 28. However, unless we develop scalable fabrication techniques that enable large-scale production of fault-free graphene, mass production cannot happen. Nevertheless, graphene is a miracle material, and has the potential to be the next disruptive technology 1, becoming a mascot of the scientific and technological progress of early twenty-first century physics and science. Who knows, perhaps the real-life artificially intelligent android Lt Cmdr Data will be mostly graphene.

References

Some of the links marked “PubMed” are quite wrong. The references are correct, however. This is an issue with the otherwise wonderful Academic Blogger’s Toolkit (Derek Sifford) that I am using. I hope to be able to correct it soon.

1.
Novoselov, K. S. et al. A roadmap for graphene. Nature 490, 192–200 (2012). [PubMed]
2.
Novoselov, K. S. et al. Two-Dimensional Gas of Massless Dirac Fermions in Graphene. Nature 438, 197–200 (2005). [PubMed]
3.
Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Reviews of Modern Physics 81, 109–162 (2009). [PubMed]
4.
Bonaccorso, F., Sun, Z., Hasan, T. & Ferrari, A. C. Graphene photonics and optoelectronics. Nature Photonics 4, 611–622 (2010). [PubMed]
5.
Balandin, A. a. et al. Superior Thermal Conductivity of Single-Layer Graphene. Nano Letters 8, 902–907 (2008). [PubMed]
6.
Geim, A. K. & Novoselov, K. S. The Rise of Graphene. Nature Materials 6, 183–191 (2007). [Source]
7.
Shekhawat, A. & Ritchie, R. O. Toughness and strength of nanocrystalline graphene. Nature Communications 7, 10546 (2016). [PubMed]
8.
Potential applications of graphene. Wikipedia Available at: https://en.wikipedia.org/wiki/Potential_applications_of_graphene. (Accessed: 30th August 2017)
9.
Lee, C., Wei, X., Kysar, J. W. & Hone, J. Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science Magazine 321, 385–388 (2008). [PubMed]
10.
Liu, F., Ming, P. & Li, J. Ab initio calculation of ideal strength and phonon instability of graphene under tension. Physical Review B – Condensed Matter and Materials Physics 76, 1–7 (2007). [Source]
11.
That is, it obeys Hooke’s Law, F = k x, where F is the force required to deform the body by a distance x. The constant k is the stiffness.
12.
Strain is a ratio of two displacements and is thus dimensionless.
13.
Played absolutely atrociously by Henry Cavill in the recent Zak Snyder disasters.
14.
Steel Construction Manual. 1–5 (American Institute of Steel Construction, 1986).
15.
Lide, D., R. Handbook of Chemistry and Physics. (CRC-Press, 2000).
16.
Well, there are actually three major extant species of elephants today. The African bush elephant is the largest and weighs 6 tons. The Asian elephants weigh about 5.5 tons, while the African forest elephants weigh in at a mere 2.7 tons. In my calculation I have considered the largest of these.
17.
W = mg, where W is the weight, m the mass and g the acceleration due to gravity, the latter having an approximate value of 10 m s^(-2) on the surface of the Earth. Weight is measure in units of newton, with 1 newton being the weight of 1 kg of mass. That is approximately equal to an exceptionally large apple. Or an exceptionally small turnip.
18.
Liu, M., Artyukhov, V. I., Lee, H., Xu, F. & Yakobson, B. I. Carbyne from First Principles: Chain of a Nanorod or a Nanorope. ACS Nano 7, 10075–10082 (2013). [Source]
19.
Ritchie, R. O. The conflicts between strength and toughness. Nature Materials 10, 817–822 (2011). [PubMed]
20.
Lassner, E. & Schubert, W. D. Tungsten: Properties, Chemistry, Technology of the Element, Alloys, and Chemical Compounds. (Springer US, 2012). [Source]
21.
Zhang, P. et al. Fracture toughness of graphene. Nature communications 5, 3782 (2014). [PubMed]
22.
Brodie, B. C. On the Atomic Weight of Graphite. Philosophical Transactions of the Royal Society of London 149, 249–259 (1859). [PubMed]
23.
Geim, A. K. Graphene prehistory. Physica Scripta T146, 014003 (2012). [Source]
24.
Mineral Commodity Summaries. 75 (US Geological Survey, 2017).
25.
Novoselov, K. S. Electric Field Effect in Atomically Thin Carbon Films. Science 306, 666–669 (2004). [Source]
26.
Geim, A. K. & Kim, P. Carbon Wonderland. Scientific American 298, 90–97 (2008). [Source]
27.
Li, X. et al. Large-Area Synthesis of High-Quality and Uniform Graphene Films on Copper Foils. Science Magazine 2009, 1–12 (2009). [Source]
28.
Lee, J.-H., Loya, P. E., Lou, J. & Thomas, E. L. Dynamic mechanical behavior of multilayer graphene via supersonic projectile penetration. Science 346, 1092–1096 (2014). [PubMed]
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3 Replies to “Graphene : Strongest Substance Known to Humankind?”

  1. A smart lucid comparison of toughest metals. The sillicon valley made blue diamonds precious metal. Can we have a story if graphene should have the same future? Which geography will turn into a colony for that?

    1. Thank you for your comment Paramita. Yes, indeed, graphene does seem to have a vibe similar to that of blue diamonds in the late seventies and early eighties, something that Michael Crichton spoke of in Congo and Satyajit Ray did so in Shonkur Congo Obhijaan. Fiction aside, graphene indeed seems to have a very interesting roadmap ahead, and could well be the future material. In fact, #1 on the references list is a five year old paper that attempts to do exactly that. This article will, hopefully, be the first in a series on graphene. In my second graphene article, I’ll try and talk about the possible and exciting application graphene might have as we enter the third decade of this century.

      Somdeb

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