Topics in the Theories of Elasticity and of Liquid Crystals

技术概述：该提案支持三个不同领域的理论研究和教育：等静力和近等静力材料，印迹液晶弹性体，以及向列液晶中线（斜向）和点（刺猬）缺陷之间的相互作用。这项研究的一个主要部分是研究周期性等静力格的许多奇特而迷人的特性，比如简单的方形和立方格，以及通过增加刚度——包括额外的弹簧，比如桥上的横梁——而形成的近乎等静力格。这些系统提供了对一般均衡系统的深入了解，而不受更多研究中固有的非点阵随机性的影响。卡”系统。利用现代合成化学和光化学，现在可以在聚合物或相关向列相中创建以指导者为特征的空间变化的各向异性模式，并通过化学交联过程在这些模式中冻结。例如，人们可以制造出一种薄膜弹性体，它的导流器被限制在薄膜的平面上，在薄膜的上下表面之间旋转90度。这种印迹使上下表面不同，并使它们对温度、pH值或光强的变化作出不同的反应，从而在薄膜中产生形状变化。因此，这些薄膜是各种机械传感器的理想候选材料。一个主要的研究工作集中在计算弹性体薄膜和窄管的弹性和其他性能与不同的定向图案。胶体粒子现在可以以一种可控的方式分散到液晶中，形成与被称为斜位的拓扑缺陷线阵列纠缠在一起的粒子晶格。这些线的闭合回路产生的指向图案相当于那些被称为刺猬的点缺陷。在第三项研究中，PI的目标是制定方法来表征每单位长度的线缺陷所携带的刺猬电荷量。我们的目标是提供这种电荷密度的数学表征，并用它来帮助理解像胶体分散体那样的偏斜网络。该提案的广泛影响是扩大软物质物理跨学科领域的学生和博士后的经验、教育和培训。为了将这些新的跨学科研究带到更大的社区，PI计划写一篇关于非线性弹性的主要评论文章，并开始更新他的流行教科书“凝聚态物理原理”。PI是他所在部门的主席，并鼓励部门外展项目，其中一个项目每年吸引数百名当地高中生观看迷人的物理演示。非技术摘要：本提案支持软凝聚态物理领域的理论研究和教育。该程序建立在PI以前在液晶，弹性和相变方面的经验之上。液晶是由于液晶显示（LCD）的应用而广为人知的一类材料，它是具有丰富多样的内部结构的材料，分子在空间上的排列不如固体晶体有组织，但组成分子的方向形成了定向图案。由于分子取向是空间组织的一个额外变量，研究人员发现，液晶、聚合物和其他软物质系统的内部结构可以非常复杂，但非常符合逻辑。图案和结构与强度和稳定性有关。众所周知，工程师们不会用方形或长方形的水平和垂直支柱来建造桥梁；相反，他们采用对角横梁来增加结构的稳定性。事实上，一个正方形或立方体晶格，其最近邻的顶点由弹簧无摩擦连接，只能支持沿其轴方向的载荷，这本身就是不稳定的。这些格代表了所谓均衡系统的一般类别，这些系统几乎有足够的约束，但还不够稳定。自然界中有许多系统，包括成堆的沙子、被压得很紧直至卡住的球形珠子，甚至是玻璃，它们几乎都是等静力的。这项研究的一个主要部分是研究周期性等静力格的许多奇特而迷人的性质，比如简单的方形和立方格，以及它们通过增加刚度的弹簧（如桥上的横梁）而形成的近乎等静力格。这些系统提供了对一般均衡系统的洞察，以一种摆脱传统研究系统中出现的许多复杂性的方式。液晶弹性体是一种迷人的材料，它结合了液晶的定向性能和橡胶的显著拉伸性能。液晶弹性体是通过化学结合（交联）长链分子（聚合物）与液晶形成的分子亚基，形成一个可以承受拉伸的液晶网络。利用现代合成化学和光化学，现在可以创造和？冻结吗?定向秩序的空间变化模式。例如，人们可以制造一种薄膜弹性体，其中长链分子的方向从顶部表面的一个方向平滑地扭曲到底部的另一个方向。这种印迹使上下表面不同，并使它们对温度、pH值或光强的变化作出不同的反应，从而在薄膜中产生形状变化。这些印迹薄膜和其他印迹几何形状，如管状弹性体，是各种机械传感器的理想候选者。PI旨在计算印迹薄膜和管的性能。该提案的广泛影响主要是软物质物理跨学科领域的学生和博士后的教育和培训。为了将这些新的跨学科研究带到更大的社区，PI计划写一篇关于非线性弹性的主要评论文章，并开始更新他的流行教科书“凝聚态物理原理”。PI是他所在部门的主席，他鼓励部门拓展项目，其中一个项目每年吸引数百名当地高中生观看简单物理的迷人演示。

TECHNICAL SUMMARY:This proposal supports theoretical research and education in three distinct areas: isoststatic and nearly isostatic materials, imprinted liquid crystal elastomers, and the interplay between line (disclination) and point (hedgehog) defects in nematic liquid crystals. A major part of this research studies the many peculiar and fascinating properties of periodic isostatic lattices, like the simple square and cubic lattices, and their nearly isostatic forms created by adding rigidity-by including additional springs like the cross beams on a bridge. These systems offer insight into general isostatic systems in a context that is not complicated by the off-lattice randomness inherent in more studied ?jammed" systems.Using modern synthetic and photo chemistry, it is now possible to create spatially varying patterns of anisotropy characterized by the director in polymer or related nematics and to freeze in those patterns via a chemical cross linking process. For example, one might create a thin-film elastomer whose director, restricted to the plane of the film, rotates by 90 degrees between the film's top and bottom surfaces. This imprinting makes the top and bottom surfaces different and causes them to respond differently to changes in temperature, pH, or light intensity and, thereby, to produce shape changes in the film. These films are thus ideal candidates for mechano sensors of various sorts. A major research effort focuses on calculating the elastic and other properties of elastomer films and narrow tubes imprinted with various director patterns.Colloidal particles can now be dispersed in a controlled way into liquid crystals to create particle lattices entangled with arrays of topological defect lines called disclinations. Closed loops of these lines produce director patterns equivalent to those of point defects called hedgehogs. In a third research thrust, the PI aims to formulate ways of characterizing the amount of hedgehog charge a line defect carries for each unit of its length. The goal will be to provide a mathematical characterization of this charge density and to use it to help understand networks of disclinations like those in colloidal dispersions.The broader impact of the proposal is expanding the experience, education and training of students and post-docs in the interdisciplinary field of soft-matter physics. Bringing these new interdisciplinary aspects of research to the larger community, the PI plans to write a major review article on nonlinear elasticity and to begin the process of updating his popular text book, "Principles of Condensed Matter Physics." The PI is Chair of his department and encourages Department outreach programs, one of which brings in several hundred local high school students each year to see captivating demonstrations of physics.NON-TECHNICAL SUMMARY:This proposal supports theoretical research and education in areas of soft condensed-matter physics. The program builds on the PI's previous experience in liquid crystals, elasticity, and phase transitions. Liquid crystals, a class of materials widely known because of liquid crystal display (LCD) application, are materials that have a rich variety of internal structures with molecules in spatial arrangements less organized than solid crystals but with directional patterns formed the orientation of the constituent molecules. With molecular orientation an added variable to the spatial organization, researchers have found that the internal structure of liquid crystals, polymers and other soft matter systems can be extraordinarily complex, but very logically patterned. Patters and structure are connected with strength and stability. It is well known that engineers do not build bridges with a motif of only horizontal and vertical struts in a square or rectangular pattern; rather they put in diagonal cross beams to increase structural stability. In fact, a square or cubic lattice with nearest neighbor vertices frictionlessly connected by springs that can only support loads directed along their axes are inherently unstable. These lattices represent a general category of what are called isostatic systems that have almost, but not quite, enough constraints to make them stable. There are many systems in nature, including piles of sand, spherical beads compacted until they become jammed, and even glasses, that are nearly isostatic. A major part of this research is to study the many peculiar and fascinating properties of periodic isostatic lattices, like the simple square and cubic lattices, and their nearly isostatic forms created by adding rigidity-increasing springs like the cross beams on a bridge. These systems offer insight into general isostatic systems in a fashion that is free from many complications that appear in systems that are traditionally studied. Liquid crystal elastomers are fascinating materials that combine the orientational properties of liquid crystals with the remarkable stretching properties of rubber. Liquid crystalline elastomers are formed by chemically binding together (cross linking) long-chain molecules (polymers) with liquid-crystal forming molecular subunits to create a liquid crystalline network that can withstand stretching. Using modern synthetic and photo chemistry, it is now possible to create and ?freeze in? spatially varying patterns of orientational order. For example, one might create a thin-film elastomer in which the orientation of the long-chain molecules twists smoothly from one orientation at the top surface to another at the bottom. This imprinting makes the top and bottom surfaces different and causes them to respond differently to changes in temperature, pH, or light intensity and, thereby, to produce shape changes in the film. These imprinted films and other imprinted geometries such as tubular elastomers are ideal candidates for mechano sensors of various sorts. The PI aims to calculate the properties of imprinted films and tubes.The broader impact of the proposal is primarily the education and training of students and post-docs in the interdisciplinary field of soft-matter physics. Bringing these new interdisciplinary aspects of research to the larger community, the PI plans to write a major review article on nonlinear elasticity and to begin the process of updating his popular text book, "Principles of Condensed Matter Physics." The PI is Chair of his department and encourages Department outreach programs one which brings in several hundred local high school students each year to see captivating demonstrations of simple physics.