Polyisobutylene (PIB) functionalized with terminal reactive unsaturation is disclosed. Carbocationically polymerized monohalogen-terminated PIB is dehydrohalogenated in a hydrocarbon solvent using an alkoxide of the formula RO-M wherein R is alkyl of at least 5 carbon atoms and M is alkali metal. The PIB obtained has terminal unsaturation which is 100% in the reactive ‘exo’ form which can be converted to succinic anhydride groups (PIB-SA) by the ene reaction with maleic anhydride. The PIB-SA is reactive with amine functional dendrimers to obtain a star-branched polymer having a dendrimer core and PIB branches joined by succinimide linkages. Blends of the star-branched polymer with polypropylene have improved energy absorption properties and controllable moisture/oxygen permeabilities useful in films.