What is the chemical composition,
a carbon nanotube is made out of carbon (and a very small amount of unwanted impurities, > .01%)
is it tradenamed,
there are numerous suppliers, i don't know if any have become that well known.
don't know if you would count buckyball as a trade name.
patented,
it consists of 100% carbon, it would be like trying to patent graphite or diamonds
although the manufacturing process probably is.
although, they are usually produced via chemical vapor deposition which has been in use since the 1950's (that patent has expired). but wasn't used to make carbon nanotubes till 1990's.
with the large number of suppliers i doubt if there are patents
organic,
it is totally made of carbon, of course is.
or inorganic.
metallic nanotubes have been produced, but then we are talking about carbon nanotubes, which have no metal.
at $150/gram, I'll take the can of flat black spray paint.