Carbon (C), the sixth element on the periodic table is 4-valent, that is, a C-atom can share 4 electrons with neighbouring atoms. Pure C exists in diverse forms. The most familiar are the robust precious diamond (an insulator) and the humble slippery graphite (a conductor), the latter found in pencils. Their significantly diverse crystalline structure leads to different chemical and electrical properties. Carbon, the key component of most known life on earth, has surprised us again and again. 

The 1996 Chemistry Nobel Prize was awarded to H. Kroto, R. Smalley and R. Curl for their discovery of the mathematically predicted BuckminsterFullerene, C60. When C vapour was cooled to only a few degrees above absolute zero, the atoms formed these buckyballs. The C60 molecule has the shape of a truncated icosahedron, the same as that of a football (Figure 1). The hollow structure of fullerenes allows them to hold other atoms inside them. Applications are abound.

The flurry of C-research did not abate. In 2010, the Nobel Prize for Physics went to A. Geim and K. Novoselov from the University of Manchester, “for groundbreaking experiments regarding the two-dimensional material graphene”, at a time when it was thought that such thin crystalline materials were unstable.

Graphene is a one-atom thick flake of carbon atoms, bonded together in a perfect hexagonal lattice. Its exceptional properties stemming from quantum physics are remarkable. A completely new material, it is not only the thinnest ever but also the strongest, six times stronger than steel. This fragile-looking transparent sheet inherits the strength of diamond and the electrical conducting properties of graphite with higher performance for each property. An excellent electrical conductor, it outperforms all other known materials as a conductor of heat. Surprisingly, graphene is so dense that not even helium can pass through it.

In graphene, only 3 of the 4 available valence electrons of C are bonded (Figure 2). Each C-atom offers a delocalised electron. These behave as if they have no mass, as predicted by the theory of relativity for particles travelling at the speed of light. Graphene has semiconducting properties, making experiments possible that give new twists to the phenomena in quantum physics.

Researched for innovative electronics, graphene transistors in computers are predicted to be substantially faster than today’s silicon transistors. Being transparent and a good conductor, graphene is suitable for light and solar cells and touchscreens. When mixed with plastics, graphene can turn them into electric conductors while making them more heat resistant and mechanically robust.

This resilience can be utilised in new thin, elastic, lightweight and super-strong materials. Will satellites, airplanes and cars be manufactured out of these new composite materials?

Irene Sciriha is a professor at the Department of Mathematics within the Faculty of Science of the University of Malta (http://staff.um.edu.mt/isci1).

https://en.wikipedia.org/wiki/GraphenE

Did you know?

• There are special fullerenes, called nuts, predicted to have all C atoms involved in a reaction, formed by adding bonds to six-atom C-motifs. The smallest fullerene is constructed from six motifs [I. Sciriha and P. W. Fowler, On nut and core singular fullerenes, Discrete Mathematics 308 (2008), 267–276].  

• The C framework is a polyhedron whose faces are pentagons and hexagons. From the famous Euler formula for polyhedra that can be embedded on a sphere, a fullerene has precisely 12 pentagons, whatever the number of C-atoms in the molecule.

• Adjacent pentagons tend to produce strain on the molecular bonds. So the smallest isolated pentagon fullerene is C60.

• The seeds of the discovery of fullerenes were sowed by Kroto’s desire to understand the behaviour of carbon in red giant stars and interstellar gas clouds.

For more trivia, see: www.um.edu.mt/think

Sound bites

• From the international scene: Irene Sciriha, Mark Debono, Martha Borg together with Sheffield University professors Patrick Fowler FRS and Barry Pickup classified all C-molecular devices with two terminals in electrical circuits into three varieties according to the types of atomic connecting terminals (I. Sciriha, M. Debono, M. Borg, P. W. Fowler, and B. T. Pickup, Interlacing-extremal graphs, Ars Mathematica Contemporanea 6(2) (2013), 261-278). This theory fitted like a glove to explain the conducting and insulating properties of C-molecules when ballistic electrons with no energy transfer to or from the target molecule enter at an atom terminal, according to the quantum mechanical tight-binding approximation and the source and sink potential model. (American Institute of Physics (AIP), Journal of Chemical Physics, volumes 140, 143 and 145).

• From the local scene: In graphene, C-atoms bond to form hexagons. Graphene is referred to as a 6,6,6 net, so called because at each C-centre, three hexagons meet. The conduction and valence bands meet each other in graphene, which behaves like a zero band gap semiconductor. The points in the reciprocal space (Brillouin zone) where the bands meet are called Dirac points, so called since the electrons (and holes) behave as zero-mass charge carriers satisfying the relativistic Dirac Equation. Through mathematical modelling of the C-atom 4,8,8 net, Noeleen Buttigieg, under the supervision of Irene Sciriha and Joseph Grima, discovered that like graphene, the 4,8,8 net has Dirac points. 

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