During the past few years, studies involving the synthesis, characterization, and structure-property relations of especially well-defined or "model" block and graft copolymers have received increasing interest among academic and industrial communities. The well-defined nature of such polymers makes them ideal subjects for both fundamental studies and specialty polymer applications. This study addresses the synthesis and characterization of well-defined block and graft copolymers through the use of reactor systems and permeability instrumentation designed specifically for this purpose. The engineering design, construction, operation, and in some cases automation of the above instrumentation is discussed in detail. Examples of the synthesis and permeability characterization of several especially interesting multiphase graft and star block copolymers are provided to demonstrate the utility of the instrumentation described. The primary focus of this work has been to address the effects of varying degrees of microphase separation and morphological development on the physical properties of well-defined block and graft copolymers and their hydrogenated derivatives. The application of gas permeability as an especially sensitive probe of morphology in well-defined poly(methylmethacrylate) -poly(dimethylsiloxane) graft copolymers has been given special emphasis. The synthesis these graft copolymers has been accomplished by the copolymerization of model, methacrylate-functional, poly(dimethylsiloxane) CPDMS) "macromonomers" with methylmethacrylate, using conventional free-radical and novel anionic and group transfer techniques. These techniques are described and referenced with chemical characterization provided. The resulting graft copolymers have PDMS-modified surface and bulk morphologies that dominate particular physical property responses and provide for interesting structure-permeability studies. The characterization of these copolymers to demonstrate their well-defined nature has been performed with a focus on the application of gas permeability as an especially sensitive morphological probe. A review of the relevant literature is followed by detailed experimental procedures, a summary and discussion of results, and descriptive appendices. The appendices include details concerning the design, fabrication, and automation of instrumentation to perform volumetric, equilibrium sorption experiments and computer programs for the acquisition and analysis of permeability data. / Ph. D.