By definition, a fullerene is 'a closed graphitic form of carbon with exactly twelve pentagons'. Should this seem a little confusing, remember that graphite (planar sheets of hexagons) cannot form spheres. Therefore, pentagons are necessary to allow proper curvature - exactly twelve in the case of buckminsterfullerene.

Since this was the form found first, other fullerenes are defined by this benchmark - so some carbon tubes are fullerenes (those with the appropriate number (ratio?) of 5 to 6 membered rings, and capped at the ends with hemispheres) while others are rolled up graphite sheets - like a rolled up newspaper.

The smallest fullerene is, therefore, C20+ (this ion has recently been made) - not to be confused with dodecahedrane or C20H20 which has no double bonds and is much more stable. An example of a fullerene larger than a buckyball is C70, which has an extra 'belt' of hexagons round the middle (five times two extra atoms - work it out :).

If you were wondering "what size is a bucky ball?", you should know that it is 7 Ångstrom or 7 ten-billionths of a meter. This is smaller than most proteins, and almost a third the diameter of (B)-DNA. Fullerene tubes can be larger in diameter (large enough even to fit bucky balls inside - or DNA!) and could potentially extend indefinately. Since they are defined to be closed, there should be a cap on the end of tubes, but these could be quite long.

Actually, fullerenes aren't "new". A fairly significant amount of soot (I believe the figure I read was 5%) contains fullerenes. Candle soot contains fullerenes.

Anytime carbon atoms sublime and remain unoxidized, they cluster to form fullerenes. They like it, energetically speaking.

Since fullerenes are aromatic, they should be transition-metal coordinatible. If one coordinates two transition metal atoms at the fullerene's "poles", and can manage to coordinate these atoms to a stationary matrix (a polyethylene derivative with cyclopentadienyl sidegroups comes to mind), the freaking fullerene could spin in place. If one then successfully coordinated additional ferromagnetic transition metals at the spinning equator of this trapped fullerene, and transmitted mechanical energy into the system (think windvane), and interact these moving transition metal species with additional magnetically-active species, one begins to see the technology to create nanogenerators. Hopefully this will lead to technology like a Brownian Motion Collector. That would rock.

Just a note: I don't think buckyballs are named after their researcher. I've heard that the full name is Buckminsterfullerene, the architect who popularized geodesic domes and spheres, which fullerenes bear a resemblance to. Thus, Buckminsterfullerene was shortened (considerably) to fullerene and the more catchy buckyball.

One of the most interesting attributes of the fullerenes (or whatever of the many names this allotrope of carbon goes by that you happen to prefer), is the strange way in which they become superconductors when extremely cold, whereas graphite does not.

As The Alchemist noted above, buckyball is very similar to graphite, in that its bonding is primarily sp2 hybridized, with each carbon atom forming 3 bonds, and sharing a fourth bond aromatically with its neighbors through pi bonding. The really glaring major difference between graphite and C60 is that graphite is flat, with "even" pi bonds among p orbitals of the atoms, whereas in buckyball you see a "bent" effect. Largely this has caused a great deal of speculation among organic chemists as to whether this "bending" of these orbitals is what causes the superconducting effect, and has led to some research into conical shaped carbon structures as a result.

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