Theory of hierarchically structured soft matter

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This proposed research program focuses on the development of new concepts, theoretical frameworks, and methodologies for the study of hierarchically structured soft matter self-assembled from macromolecular systems. The study will be carried out using block copolymers as a primary model system. Block copolymers are macromolecules composed of two or more chemically distinct sub-chains or blocks. The competition between the repulsion between the different blocks and the chain connectivity drives these macromolecules to form ordered structures or morphologies with nanometer-sized domains of different sizes and shapes. For example, recent experiment and theory have demonstrated that block copolymers can self-assemble into an extremely complex spherical packing phase (the so-called Frank-Casper σ-phase) with five types of domains of different shapes. The ability of block copolymers to form well-ordered nanostructures with domains of very different physical properties provides a powerful platform to engineer and control materials with desirable morphologies. These hierarchically nanostructured polymeric materials could have many useful applications, including periodically ordered soft materials for photonic crystals, nanosized vesicles for drug delivery, and sub-nanometer patterns for next-generation lithography. The objective of this proposed research program is to develop molecule-based theories to understand and predict the emergence, stability, and physical properties of hierarchically structured soft matter. ******The formation of hierarchically structured polymeric materials involves a number of components with diverse physical attributes such as chain topology, molecular size, rigidity, and chirality. Furthermore, the interactions between these monomers could be more complicated than the usual non-specific van der Waals interactions. Examples of these complicated interactions are hydrogen bonding and electrostatic interactions. To study systems with these diverse properties, I will develop theoretical frameworks for polymeric systems composed of complex architectures and rigid and/or chiral components. Specifically, my proposed research program includes three inter-related topics: (1) The structure and phase transition of multiblock copolymers, focusing on the emergence, mechanism of formation, and properties of hierarchically structured polymeric materials; (2) The phase behavior of polymeric systems containing semiflexible, chiral and associative components, focusing on the effects of molecular size, shape, rigidity and association on the self-assembled phases; (3) The structure and morphology of amphiphilic block copolymer solutions, focusing on the formation and property of nanosized aggregates including bilayer membranes.