A series of linear and three-arm star poly(styrene-b-isobutylene-b-styrene) (PS-PIB-PS) block copolymers with varying block compositions was synthesized via living carbocationic polymerization using the initiation system 1,3-di(2-chloro-2-propyl)-5-tert-butylbenzene (or 1,3,5-tris-(2-chloro-2-propyl)benzene)/ TiCl4/pyridine/2,6-di-tert-butylpyridine in a 60/40 (v/v) hexane/MeCl solvent mixture at -80 degrees C. High resolution gel permeation chromatography showed that the compositions of the copolymers were complex, consisting of higher molecular weight coupled products, and products of lower molecular weight including, probably, homo-PS. Morphology and physical properties were characteristic of microphase-separated block copolymers, and were affected strongly by the PIB span molecular weight and volume fraction of PS. When the latter was in the range 0.20-0.42 vol%, the morphology was characterized by cylinders of PS in a continuous phase of PIB; however, at least two samples exhibited mixed morphologies in which regions of PS cylinders coexisted with regions of PS spheres and lamellae, respectively. Linear samples showed much better long-range morphological order than star-branched samples. The dynamic mechanical response of block copolymers consisted of separate PIB and PS relaxations whose relative intensities scaled well with copolymer composition. The low-temperature relaxation was broad, which is an inherent characteristic of PIB; the high-temperature PS relaxation was narrow, suggesting well defined phase separation and a sharp PIB-PS interface. Melt rheological studies of representative samples showed that microphase separation persisted up to 265 degrees C. Tensile properties varied with PIB span molecular weight and PS content. An abrupt change occurred from 15-22 vol% PS, indicating a minimum PS content needed for strong network formation. Properties changed from elastomeric within the range 20-37 vol% PS, to ductile in the range 37-45 vol%, to brittle in the range 45-55 vol%. Samples with PS vol% greater than or equal to 35 yielded improved elastomeric properties as a result of annealing above the glass transition temperature of PS. Within the elastomeric range, the PIB span molecular weight was che dominant factor effecting elongation at break. A high tensile strength of 24 MPa was obtained, and most samples displayed strengths greater than or equal to 15 MPa.