When I was a lad, we were taught that carbon had two allotropes, graphite and diamond.  Although they’re both covalently connected, in neither of these is there anything that one would regard as a ‘molecule’. 

Carbon molecules were known, however, particularly the C₂ molecule, but it was only found in hot places like carbon arc lamps and carbon-rich stars like La Superba.  But in cooler places, such molecules will readily combine with each other to form soot.  Red giant stars, in their second giant phase (known as the Asymptotic Giant Branch) tend to puff and pulsate, and the carbon that has been cooked up in their nuclear furnaces is scattered into space to form soot.  Space is a dusty place!

In space, however, molecules are few and far apart, which allows many reactive molecules to survive a long time without bumping into another molecule or atom [1], so that not all the carbon ends up as soot.  Nitrogen and oxygen are formed along with the carbon, and cyanopolyynes such as HC₉N and other exotic molecules are found in the interstellar medium, where they can be detected by infrared spectroscopy. 

Suddenly, out of the void, so to speak, there appeared in 1985 a paper:

C60: Buckminsterfullerene:  H. W. Kroto, J. R. Heath, S. C. O'Brien, R. F. Curl&R. E. Smalley

During experiments aimed at understanding the mechanisms by which long-chain carbon molecules are formed in interstellar space and circumstellar shells, graphite has been vaporized by laser irradiation, producing a remarkably stable cluster consisting of 60 carbon atoms. Concerning the question of what kind of 60-carbon atom structure might give rise to a superstable species, we suggest a truncated icosahedron, a polygon with 60 vertices and 32 faces, 12 of which are pentagonal and 20 hexagonal. This object is commonly encountered as the football shown in Fig. 1. The C₆₀ molecule which results when a carbon atom is placed at each vertex of this structure has all valences satisfied by two single bonds and one double bond, has many resonance structures, and appears to be aromatic.

Nature 318, 162 - 163 (14 November 1985); doi:10.1038/318162a0

Now most of these folks were at Rice University, in Houston, Texas, but Harry Kroto (now SIR Harold: Hank – a verse of Land of Hope and Glory, please!) was visiting them from Sussex University, and his interest was molecules in outer space.  The folks at Rice had developed a technique for blasting carbon into molecular fragments and analysing the products.  So here was an opportunity to simulate what sort of stuff might be exhaled by a carbon-rich star.

As expected, they found lots of fragments with an even number of carbon atoms, but the distribution was a bit enhanced at number 60 and a tiny little bit at 70.  The clever bit comes next.  They added what they called an “integration chamber” to allow the carbon clusters to ‘stew in their own juice’ for a little time before being spewed into the mass spectrometer where they were counted.  This allowed them to react with each other and so enhance the proportion of the more stable clusters formed.  Et voilà, a large amount of C₆₀ and a smaller but sizable fraction of C₇₀ was produced.

Notice that I said fraction, not amount.  The quantities were tiny, and not sufficient to do anything with, if you were into chemistry or materials science.

However, in the next few years, a cooperation developed between the *Max-Planck-Institut für Kernphysik[2], Heidelberg, Germany and the †Department of Physics, University of Arizona in Tucson, AZ, USA.  Then, five years after the discovery, there appeared:

Solid C60: a new form of carbon:  W. Krätschmer*, Lowell D. Lamb†, K. Fostiropoulos*&Donald R. Huffman†

A new form of pure, solid carbon has been synthesized consisting of a somewhat disordered hexagonal close packing of soccer-ball-shaped C₆₀ molecules. Infrared spectra and X-ray diffraction studies of the molecular packing confirm that the molecules have the anticipated 'fullerene' structure. Mass spectroscopy shows that the C₇₀ molecule is present at levels of a few per cent. The solid-state and molecular properties of C₆₀ and its possible role in interstellar space can now be studied in detail.

Nature 347, 354 - 358 (27 September 1990); doi:10.1038/347354a0

The upshot of which was, that a day’s work could produce a tenth of a gram of buckyballs, which is enough to do a lot of interesting chemistry or physics.

I’m hoping shortly to tell you more about this, but I’m waiting for some figure permissions.

Meanwhile, what has Archimedes to do with this?  He is the one who gave us (in the West at least) our formulae for the surface area and volume of a sphere.  But that’s only for starters.  Watch this space …..

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[1] That is why OH molecules, which are highly reactive free radicals, can be observed spectroscopically in space.

Similarly, a long period without contact allows excited doubly ionized oxygen atoms to survive until ‘forbidden’ transitions to occur, which led to the proposal of an undiscovered element ‘Nebulium’.  These oxygen atoms are ionized by hard UV from very hot stars, leaving electrons above the ground state.  However, in these particular states the quantum-mechanical probability of dropping to a lower state by emission of a photon is very small, so the atom can stay in the higher state typically for several minutes.  In conditions attainable on Earth, the atom would transfer its excess energy by bumping into another atom or molecule.

[2] Kern is the German cognate of our English word kernel, the centre of a nut, which is nucleus in Latin.