"Block copolymer materials have been shown to self-assemble into a variety of morphologies, some which exhibit complex and intricate nanometer scale structures. That attribute has led researchers to propose material and device fabrication strategies. The majority of synthetic, characterization, and theoretical work on block copolymers has focused on their bulk behavior. A smaller effort has focused on the study of multiblock copolymers, their mixtures with homopolymers and nanoparticles under confinement. Complex morphologies have been elucidated with the help of theoretical models and theoretically predicted phase diagrams have often provided much needed roadmaps for experimentalists. Available theoretical and computational approaches face considerable challenges when trying to describe large 3-dimensional multiblock copolymer samples, nanoparticle-copolymer composites, confined copolymers and composites and the effects of fluctuations on such systems. The central idea of our proposed work is to direct the assembly of thin copolymer films by creating nanoscale patterns on substrates that the polymer can recognize. Past work has shown that it is possible to achieve perfect, defect-free registration between block-copolymer morphology and a nanoscale surface pattern over macroscopic length scales. The goal is to use directed assembly as a platform on which to improve a molecular-level understanding of block copolymers and copolymer nanocomposites through the systematic application of external, molecular-level constraints that induce well defined responses. The applied, technological goal is to create a multi-scale theoretical and computational formalism that will facilitate study of confined block copolymer-based systems, and guide development of efficient nanofabrication strategies for large-scale production of materials and devices such as those already encountered in the semiconductor industry or those encountered in the photovoltaic and energy storage industries"