Nanotubes are back in the news! Nanotubes are sheets of carbon atoms, one atom thick, that roll up to form strong cables for tennis rackets and baseball bats. Very strong cables, in turns out, as in a possible material for a space elevator.
But even if the space elevator doesn’t work out, it turns out that carbon nanotubes can be used to make near-ideal black objects: things which absorb light completely, not refracting any of it. ‘Darkest Ever’ Material Created on BBC News in January explains that this is useful for creating solar cells and solar panels.
So what does does this have to do with mathematics? Quite a bit, if you look on wikipedia or if you actually build anything physical with it. But even at a simpler level, one neat property is that the carbon atoms bind in hexagons. You can see that in the picture below of a hexa-tert-butyl-hexa-peri-hexabenzocoronene. (How’s THAT for a word?)
The hexagons in the picture above are regular hexagons, meaning that all the sides and all the angles are equal. You can completely tile a plane with regular hexagons, without leaving any gaps. And this means that the hexagons in the carbon nanotubes must not be exactly perfectly regular, or else there would be no way for them to roll up. Either the angles or the sides must be a little off.
This irregularity doesn’t actually harm the carbon nanotubes. Unfortunately, they have bigger problems right now: BBC news reported Tuesday that when some fibers got into the lungs of mice, they caused inflammation and legions, like asbestos. Poor nanotubes. That doesn’t sound the death knell, however; it’s only one study, and so more research, more money, etc. etc. have to be dedicated to the topic. But it might be a while before we see that solar-powered space elevator.
Pictures used under GNU Free Documentation License.