Order and Defects in Soft Matter Architecture

技术总结该奖项支持与实验相联系的理论和计算研究，这些研究涉及曲面和界面上软物质系统中有序、缺陷和几何之间的相互作用，重点是结晶、六次、矢量和向列有序。即使在曲面上有序系统的基态中，拓扑缺陷也经常出现。某些拓扑结构(如球体和其他形状)需要一些缺陷来降低系统的总能量。缺陷区是生物活性、化学连接、异常弹性反应和无序聚集的自然场所。该项目将深入了解各种曲面上晶体、六方、向量和向列有序缺陷的首选配置类型。这将为通过自组装或控制制造作为新型介观分子或块体材料的构建块的整个介观组件(中原子)库的第一性原理设计铺平道路。这项研究将使用一套来自几何学、拓扑学、统计力学和计算科学领域的工具，并将与实验小组密切结合。在拟议的研究过程中开发的技术和工具，包括分析方法、模拟小程序和数据库，将免费提供给跨学科的研究人员。PI计划让本科生、研究生和博士后助理参与他的研究计划。将特别努力招募和留住物理学专业的学生，特别是女性，让他们参与软凝聚态研究项目。PI还计划通过一个新的软物质本科生将他的研究带入课堂，并通过在周六早上物理项目和Cafe Science fique的锡拉丘兹分会的公开讲座以及访问当地的K-12学校，将他的研究带到更广泛的社区。作为研究项目开发的曲面上肥皂泡阵列的演示可以在课堂和公共讲座中使用。非技术性总结该奖项支持理论和计算研究以及与凝聚态物理、数学和生物学交叉的实验相联系的教育。PI将研究粒子如何在曲面上以及在两种材料或介质之间的界面上组织起来。例如，实验已经能够将带有静电的小颗粒放置在悬浮在油中的水滴的球面上。这些粒子试图以规则的几何图案进行自我组织。但因为它们是在球体上而不是平面上，伤疤？一边的有序数组与另一边的有序数组不匹配的形式。如PI所示，理论至少能够对自组织系统的特征做出有用的预测。PI将研究更多种类的系统，目的是了解伤疤？或者出现的有序缺陷，以及如何使用几何图形来控制粒子如何自组装成所需的结构。病毒表面蛋白质外壳的结构是PI感兴趣的另一个例子。在这种情况下，分子可能优先结合到病毒蛋白外壳曲面上有缺陷的区域，这表明了药物开发的策略。相互作用的粒子如何在曲面上排列这一普遍的挑战性问题一直是数学领域的普遍兴趣。在拟议的研究过程中开发的技术和工具，包括分析方法、模拟小程序和数据库，将免费提供给跨学科的研究人员。PI计划让本科生、研究生和博士后助理参与他的研究计划。将特别努力招募和留住物理学专业的学生，特别是女性，让他们参与软凝聚态研究项目。PI还计划通过一个新的软物质本科生将他的研究带入课堂，并通过在周六早上物理项目和Cafe Science fique的锡拉丘兹分会的公开讲座以及访问当地的K-12学校，将他的研究带到更广泛的社区。作为研究项目开发的曲面上肥皂泡阵列的演示可用于课堂和公开讲座。

TECHNICAL SUMMARYThis award supports theoretical and computational research in contact with experiment on the interplay among order, defects and geometry in soft matter systems on curved surfaces and interfaces with a focus on crystalline, hexatic, vector and nematic order.Topological defects frequently appear even in the ground state of ordered systems on curved surfaces. Some defects are required by certain topologies such as the sphere and others form to lower the total energy of the system. Defect regions are natural places for biological activity, chemical linking, unusual elastic response and aggregation of disorder. This project will develop a thorough understanding of the preferred types of defect configurations for crystalline, hexatic, vector and nematic order on a variety of curved surfaces. This will pave the way for the first-principles design of entire libraries of mesoscale components (mesoatoms) that could serve as the building blocks of novel mesomolecules or bulk materials via self-assembly or controlled fabrication.A suite of tools from the fields of geometry, topology, statistical mechanics and computational science will be employed in this investigation which will be closely coupled with experimental groups. The techniques and tools developed in the course of the proposed research, including methods of analysis, simulation applets, and databases, would be made freely available to researchers across disciplines.The PI plans to involve undergraduates, graduate students and postdoctoral associates in his research program. A particular effort will be made to recruit and retain Physics majors, particularly women, by involving them in soft condensed matter research projects. The PI also plans to bring his research into the classroom through a new Soft Matter undergraduate and to the wider community through public lectures in the Saturday Morning Physics program and the Syracuse chapter of Cafe Scientifique as well as visits to local K-12 schools. Demonstrations of soap bubble arrays on curved surfaces developed as research projects can be used in both the classroom and public lectures.NON-TECHNICAL SUMMARYThis award supports theoretical and computational research and education in contact with experiments that lies at the intersection of condensed matter physics, mathematics, and biology. The PI will study how particles organize themselves on curved surfaces and at the interfaces between two materials or media. For example, experiment has been able to place small particles with an electrostatic charge on the spherical surface of a water droplet suspended in oil. The particles attempt to organize themselves in a regular geometric pattern. But because they are on a sphere rather than a flat surface, ?scars? form where the ordered array on one side does not match up with that on the other. As shown by the PI, theory is at least able to make useful predictions about features of the self-organized system. The PI will study a wider variety of systems with an aim to understand the ?scars? or defects in ordering that emerge and how geometry might be used to control how particles self-assemble into desired structures. The structure of the protein coat on a virus is another example of interest to the PI. In this case, molecules might preferentially bind to areas where there are defects on curved surface of the virus protein coat suggesting strategies for drug development. The general challenging problem of how interacting particles arrange themselves on curved surfaces has been of general interest in the field of mathematics. The techniques and tools developed in the course of the proposed research, including methods of analysis, simulation applets, and databases, would be made freely available to researchers across disciplines.The PI plans to involve undergraduates, graduate students and postdoctoral associates in his research program. A particular effort will be made to recruit and retain Physics majors, particularly women, by involving them in soft condensed matter research projects. The PI also plans to bring his research into the classroom through a new Soft Matter undergraduate and to the wider community through public lectures in the Saturday Morning Physics program and the Syracuse chapter of Cafe Scientifique as well as visits to local K-12 schools. Demonstrations of soap bubble arrays on curved surfaces developed as research projects can be used in both the classroom and public lectures.