Theory of Liquid Crystals and Soft Materials

该奖项支持软凝聚态领域的理论研究和教育。对层状结构、向列型液晶、扭曲晶界相、向列型弹性体和颗粒状物质的研究表明，层状结构，如独立的近晶C膜、具有溶解蛋白质的溶致近晶在其双层膜内形成2D晶格的溶致近晶，或者DNA与脂质双层之间的DNA-脂质复合体，都可以显示出显著的新的物质滑移相。尽管存在非零层间耦合，但这些相的关联行为仍表现为2D幂定律行为。这些相在二维经典体系堆叠和一维量子线阵列中的许多性质还没有被探索或不完全被理解，将被PI研究。向列相液晶既表现出线错位又表现出点刺激性缺陷。倾斜环可以产生等同于点刺猬的远场指向矢构型，并且可以携带刺猬电荷。这些载荷环的拓扑和同伦群是很好理解的。然而，刺猬电荷沿斜向环的分布在很大程度上是未知的。PI将开发量化刺猬密度的方法，探索其能量后果，并研究其在从各向同性相淬火进入向列相后对缺陷图案粗化的影响。扭曲晶界(TGB)相是超导体Abrikosov涡旋晶格相的液晶类似物。现在，除了最初的TGBA相之外，至少还有三个不同的TGBC相被预测或实验观察到。对这些阶段之间的能量差异和决定其稳定性的参数的调查是拟议计划的重要组成部分，但人们对此知之甚少。由交联型向列型聚合物形成的向列型弹性体结合了橡胶的弹性性能和向列型液晶的取向有序性。它们具有不同寻常的弹性特性，具有许多潜在的应用，最引人注目的是作为人造肌肉。拟议计划的主要部分将致力于向列型弹性体的静态和动态性能的研究，包括向列型弹性体薄膜和溶致向列型弹性体，这些向列型弹性体是通过将胶棒分散在膨胀的凝胶中形成的。当受到足够强的剪应力时，颗粒物质会部分流态化，并表现出与牛顿流体不同的流动特性。PI将使用具有非弹性碰撞的Chapman-Ensgog动力学流体动力学方程的推广来研究不同流动几何中的颗粒材料的流动，其中颗粒关联的影响被模拟为随机紧密堆积附近的粘性，该粘性比其他输送系数更快地随密度发散。该奖项支持软凝聚态领域的研究和教育。“软材料”一词涵盖了广泛的材料，包括复杂的流体和液晶，以及对工业和大多数生物物质都很重要的材料。PI将以这些材料为舞台，探索凝聚态物理中的基本概念，如对称性破缺、拓扑缺陷和低维系统中长程有序的涨落破坏。这项工作有助于提高我们对软材料的基本理解，涉及到新的物质相，即出现在层状“软物质”中的“滑动相”，出现在向列相液晶中的拓扑缺陷，出现在液晶、向列相弹性体和复杂流体中的扭曲晶界相。***

This award supports theoretical research and education the area of soft condensed matter. Research will be carried out on layered structures, nematic liquid crystals, twist grain boundary phases, nematic elastomers, and granular matter.The PI has demonstrated that layered structures, such as free standing smectic-C films, lyotropic smectics with dissolved proteins that form 2D lattices within their bilayer membranes, or DNA-lipid complexes with DNA intercalated between lipid bilayers can exhibit remarkable new "sliding phases" of matter. These phases are characterized by 2D power law behavior of correlations in spite of nonvanishing interlayer couplings. Many properties of these phases both in stacks of 2D classical systems and in arrays of 1D quantum wires are unexplored or incompletely understood and will be investigated by the PI.Nematic liquid crystals exhibit both line disclination and point hedgehog defects. Disclination loops can produce far-field director configurations equivalent to those of point hedgehogs and can carry hedgehog charge. The topology and homotopy group of these charge carrying loops is well understood. The distribution of hedgehog charge along a disclination loop is, however, largely unexplored. The PI will develop ways of quantifying hedgehog density, explore its energetic consequences, and study its effect on coarsening of defect patterns after a quench into the nematic phase from the isotropic phase. Twist-grain boundary (TGB) phases are liquid-crystal analogs of the Abrikosov vortex lattice phase of superconductors. At least three distinct TGBC phases in addition to the original TGBA phase have now been predicted or observed experimentally. Investigations of the energetic differences among these phases and the parameters that determine their stability, which are poorly understood, form an important part of the proposed program. Nematic elastomers, formed by crosslinking nematic polymers, combine the properties of rubber elasticity and orientational order of nematic liquid crystals. They have unusual elastic properties that have a number of potential applications, most notably as artificial muscles. A major part of the proposed program will be devoted to the study of the static and dynamic properties of nematic elastomers, including nematic elastomeric membranes and lyotropic nematic elastomers formed by dispersing colloidial rods in a swollen gel. When subjected to sufficiently strong shear stresses, granular matter becomes partially fluidized and exhibits flow properties that differ from those of a Newtonian fluid. The PI will investigate the flow of granular materials in various flow geometries using a generalization of the Chapman-Ensgog kinetic hydrodynamical equations with inelastic collisions in which effects of particle corrrelations are modeled near random close packing by a viscosity that diverges more rapidly with density than other transport coefficients. %%%This award supports research and education in the area of soft condensed matter. The term "soft materials" encompasses a wide spectrum of materials that includes complex fluids and liquid crystals and that are important to industry, as well as most biological matter. The PI will use these materials as an arena to explore fundamental concepts in condensed matter physics, such as broken symmetry, topological defects, and fluctuation destruction of long-range order in low-dimensional systems. This work helps improve our fundamental understanding of soft materials, and involves novel new phases of matter, "sliding phases," that occur in layered 'soft matter,' topological defects that occur in nematic liquid crystals, twist-grain boundary phases that occur in liquid crystals, nematic elastomers, and complex fluids. ***