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）高分子和纳米晶体自组装理论的关键要素是纯粹的排斥势和面积最小化，空间填充结构或蜂窝之间的联系。这种相互作用与熵参数并列，表明密排晶格是有利的。虽然在二维中紧密堆积和周长最小化都导致相同的三角形晶格，但在三维中，堆积熵和面积最小化晶格之间存在根本性的挫折。PI计划进一步发展这些想法，将其扩展到非立方晶格，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测试。(2)PI计划探索分层系统的非线性弹性。当我们加上旋转不变性所需的非线性时，缺陷的能量会发生戏剧性的变化--从指数衰减的相互作用变成幂律。PI将进一步探索这种效应，并采用最小曲面的新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理论的研究生教育。%该奖项支持软凝聚态物理领域的两个项目的理论研究和教育。第一个是研究分子组装体所表现出的各种晶体结构，如二嵌段共聚物、树枝状聚合物和超星形聚合物。PI试图扩展他以前的工作，以了解这些结构作为一个额外的“界面相互作用”的自由能的贡献，从这些分子组件的刷状涂层之间的相互作用产生的结果。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以及开发概念以帮助设计具有重要技术意义的自组装材料结构具有潜在影响。 第二个项目是研究当层的弹性为非线性时，缺陷在弹性层状系统中的作用。***

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. ***