Polyisobutylene is a
synthetic rubber, or
elastomer. It's special because it's the only rubber that's gas impermeable, that is, it's the only rubber that can hold air for long periods of time. You may have noticed that balloons will go flat after a few days. This is because they are made of polyisoprene, which is not gas impermeable. Because polyisobutylene will hold air, it is used to make things like the inner liner of tires, and the inner liners of basketballs.
Polyisobutylene, sometimes called butyl rubber, and other times PIB, is a vinyl polymer. It's very similar to polyethylene and polypropylene in structure, except that every other carbon is substituted with two methyl groups. It is made from the monomer isobutylene, by cationic vinyl polymerization.
http://pslc.ws/macrog/pib.htm
http://dictionary.reference.com/browse/polyisobutylene