Statistical physics of confined and self-assembling wormlike polymers

高分子物理学是一个涉及物理学、化学、生物学和材料科学的交叉学科研究领域。它研究由线性或线性分支分子组成的物理系统，这些分子包括我们的生物系统和塑料材料。由诺贝尔奖获得者Pierre-Gilles de Gennes等先驱创立的聚合物理论是一个在过去半个世纪在基础和应用研究方面都有巨大新发展的领域。 该提案提出了一个集中的理论研究限制和自组装半柔性聚合物。聚合物的主要理论模型是一个蠕虫状链的数学描述，它在自由空间中波动其形状。这项研究符合一个更广泛的研究主题，即在各种物理条件下（溶液，界面，限制，熔体，液晶态的形成，熔体中的介观自组装，缺陷态等）构建蠕虫状聚合物的完整物理图像，涵盖了软凝聚态的一些主题领域。在我们的理论处理中，一个共同点是使用统计物理学和场论来研究这些系统。一些亮点包括：解开被限制的DNA分子的包装结构，理解链柔性在液晶型有序结构中的作用，并在材料设计中预测由半柔性聚合物组成的自组装结构的形态。基于这一提议的令人兴奋的发现将大大推进对软物质的基本理解-构建明天新材料的操场。 在过去的10年里，我的研究小组已经开发出了尖端的理论工具，可以很容易地利用这些工具来研究这些问题。它们包括：蠕虫状聚合物链的自洽场理论和在高性能计算环境中解决该理论所需的数值算法。通过其明确的设计，这个多方面的研究计划非常适合培养硕士和博士研究生，以及博士后研究员。研究问题将在智力上挑战这些学员的道路，使学术和工业研究产生重大影响。

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.