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Polymer nanocomposites refer to a broad range of composite materials with polymer acting as the matrix and any material which has at least one dimension in the order of 1 ~ 100 nanometer acting as the filler. Due to unprecedented improvement observed in properties of the nanocomposites, research interest in this area has grown exponentially in recent years. In designing better nano-composites for advanced technological applications some of the major challenges are: understanding the structure-property relationships, interaction and integrity of the two components at the interface, the role of nanofillers in enhancing the properties of the resulting material. In our work, we have utilized first principle calculations, atomistic simulations, coarse-grained modeling and constitutive equations to develop structureproperty relationships for an amorphous aromatic piezoelectric polyimide substituted with nitrile dipole, carbon nanotubes and resulting nanocomposites. We have studied in detail structure-property relationships for carbon nanotubes and (? ?CN)APB/ODPA polyimide. We have developed chemically sound coarse-grained model based on atomic level simulations of the piezoelectric polyimide to address the larger length and time scale phenomena. The challenge of coarse grain model for these polymers is to reproduce electrical properties in addition to the structure and energetics; our model is the first to successfully achieve this goal. We have compared and analyzed atomistic scale simulation results on the nanocomposite with those predicted from micromechanics analysis. Notably, we have investigated the time dependent response of these highly complex polymers, to our best knowledge this is the first of its kind. In particular we have studied the thermal, mechanical and dielectric properties of the polyimide, nanotube and their nanocomposites through multi-scale modeling technique. We expect the results obtained and understanding gained through modeling and simulations may be used in guiding development of new nanocomposites for various advanced future applications. In conclusion we have developed a computational paradigm to rationally develop next generation nano-materials.