Polyisobutylene is a hydrophobic polymer. It has uniform structure and is amorphous. Due to above attributes the polymer chains make compact structure which does not allow water and even any gas to pass through it.
Sorry, but I guess you are mixing two different concepts. Pure Poly(isobutylene) best known in market as OPPANOL is an homopolymer fully saturated and can not be vulcanized by sulphur.
Butyl rubber which is produced by co-polymerization of about 98% of isobutylene with about 2% of isoprene. Butyl rubber can be and is vulcanized by sulphur and by peroxydes.
Butyl rubber and Poly(isobutylene) are different products with similar structure.