Cells and Boundaries All Around Us

该奖项支持软凝聚态物理领域的理论研究和教育。研究将集中在两个问题上：(1)大分子和纳米晶体自组装理论的关键要素是纯排斥势与面积最小化、空间填充结构或蜂窝状结构之间的联系。这种相互作用与表明密排晶格更受青睐的熵论证并列。在二维空间中，紧密填充和周长最小化都会产生相同的三角形晶格，而在三维空间中，填充熵和面积最小化晶格之间存在根本性的矛盾。PI计划进一步发展这些想法，将它们扩展到非立方晶格，并在分子细节和这种类比之间建立更紧密的联系。分子动力学和蒙特卡罗模拟为这些想法提供了验证。(2) PI计划探索层状体系的非线性弹性。当加上旋转不变性所要求的非线性时，缺陷的能量学就会发生巨大的变化——从指数衰减的相互作用转变为幂律。PI将进一步探索这种效应，并采用最小曲面的新颖线性分解作为变分计算的起点。这项活动也有助于软凝聚态物质理论的研究生教育。该奖项支持软凝聚态物理领域的两个理论研究和教育项目。第一个涉及到分子组合所表现出的各种晶体结构的研究，如二嵌段共聚物、树突聚合物和超星聚合物。PI试图扩展他之前的工作，以理解这些结构作为额外的“界面相互作用”对自由能的贡献的结果，这些自由能来自这些分子组装的刷状涂层之间的相互作用。在这种相互作用和聚合物的微观性质之间将建立更牢固的联系。这项工作对基础科学和发展概念有潜在的影响，以帮助设计技术上重要的自组装材料的结构。二是研究了当弹性层系弹性为非线性时，缺陷在弹性层系中的作用。＊＊＊

This award supports theoretical research and education in the area of soft-condensed matter physics. Research will focus on two problems: (1) The key element in the theory of the self-assembly of macromolecular-and nano-crystals is a connection between purely repulsive potentials and area-minimizing, space-filling structures or honeycombs. This interaction is juxtaposed with entropic arguments that show that close-packed lattices are favored. While in two dimensions both close packing and perimeter minimization result in the same triangular lattice, in three dimensions there is a fundamental frustration between packing entropy and the area-minimizing lattices. The PI plans to further develop these ideas, to extend them to non-cubic lattices, and to make a closer connection between molecular details and this analogy. Molecular dynamics and Monte Carlo simulations provide tests of these ideas. (2) The PI plans to explore the nonlinear elasticity of layered systems. The energetics of defects is dramatically altered when one adds those nonlinearities required by rotational invariance -changing from exponentially decaying interactions to power laws. The PI will further explore this effect and employ novel linear decompositions of minimal surfaces as a starting point for variational calculations. This activity also contributes to postgraduate education in the theory of soft-condensed matter.%%%This award supports theoretical research and education in the area of soft-condensed matter physics on two projects. The first involves the study of the wide variety of crystal structures exhibited by molecular assemblies, such as diblock copolymers, dendritic polymers, and hyperstar polymers. The PI seeks to extend his previous work to understand these structures as a consequence of an additional 'interfacial interaction' contribution to the free energy that arises from the interactions between the brush-like coats of these molecular assemblies. A firmer connection will be developed between this interaction and microscopic properties of polymers. This work has potential impact on fundamental science as well as on developing concepts to aid in designing structures in technologically important self-assembling materials. The second project is concerned with studying the role of defects in elastic layered systems when the elasticity of the layer is nonlinear. ***