Statistical physics of confined and self-assembling wormlike polymers

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Polymer physics is a crossdisciplinary research field involving physics, chemistry, biology, and materials science. It studies physical systems that are composed of linear or linearly branched molecules, which comprise our biological systems and plastic materials. Founded by pioneers such as Nobel Prize Laureate Pierre-Gilles de Gennes, polymer theory is a field that has seen vast new developments in the last half century, in both fundamental and applied research.     This proposal presents a focused theoretical study of confined and self-assembling semiflexible polymers. The main theoretical model for a polymer is a mathematical description of a wormlike chain, which fluctuates its shape in a free space. The study fits into a much broader research theme of building a complete physical picture of wormlike polymers in a variety of physical conditions (solution, interface, confinement, melt, formation of liquid crystal states, mesoscopic self-assembly in melts, defect states, etc.), covering a few topic areas in soft condensed matter. In our theoretical treatment, a common ground is the use of statistical physics and field theory to study these systems. Some highlights include: unravelling the packing structure of confined DNA molecules, understanding the role of chain flexibility in liquid-crystal type ordered structures, and predicting the morphologies of self-assembled structures composed of semiflexible polymers in materials design. The exciting discoveries based on this proposal will significantly advance the fundamental understanding of soft matter --- a playground for constructing the new materials of tomorrow.     Over the last 10 years, my research group has developed cutting edge theoretical tools that can be readily exploited to study these problems. They include: the self-consistent field theory of wormlike polymer chains and numerical algorithms needed to solve this theory in a high-performance computing environment. By its explicit design, this multifaceted research program is ideally suited for training Master's and Doctoral graduate students, as well as Postdoctoral Fellows. The research problems will intellectually challenge these trainees in their pathways to make substantial impact in academic and industrial research.