Topology Driven Flows in Chromonic Liquid Crystals and Active Matter

有色液晶和活性物质中的拓扑驱动流动

• 批准号: 2223707
• 负责人: Jorge Vinals
• 金额: $ 32.5万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-12-01 至 2026-11-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2223707&HistoricalAwards=false
• 关键词: Topology; Driven; Flows; Chromonic; Liquid

NONTECHNICAL SUMMARY This projects aims to describe the properties of so-called nematic phases in a variety of materials. The defining feature of nematic phases is orientational order in that the individual molecules are generally aligned along the same direction, yet their location is disordered. As a consequence, these materials flow like a normal fluid, yet they display solid like features when forces affect their orientational order. Such a hybrid nature is key to recent applications in flow control, material shape design and engineering, even actuation and soft robotics induced by light. More widely, a number of biological tissues exhibit the same properties in that oriented individual cells respond as a nematic phase, and such a response is involved in biological function. Theories to be developed in this project will describe the properties and response of those nematic materials that are comprised of complex molecular units, such a long organic molecules, stacks of individual disks in solution, or aggregates of living cells. The theory will pay special attention to defects in nematic phases. These are small regions in which the orientational order is broken, and that are known to determine the characteristic properties of the material. Such an observation lies at the center of recent efforts in the so-called defect engineering field, which seeks not to eliminate defects, but rather to produce them and to control their location and motion in order to produce material properties that would be unachievable in ideal materials without defects. A theoretical understanding of defects, their interactions, and their motion is central to enable further advances in defect engineering and the many applications that are currently being explored involving nematic phases.On the educational side, the project will involve both graduate and undergraduate students, the latter through Summer internships and Honors Thesis projects. In addition, the PI has created and is teaching a new senior undergraduate course PHYS 4041, “Computational Methods in the Physical Sciences'' which is taken by students in Physics, Computer Science, and Engineering. The course involves semester long computational projects, many of which are drawn from examples of the research in this project. As the research proposed overlaps with Physics, Applied Mathematics, Engineering, and Computational Science, there are many opportunities to engage undergraduate students in interdisciplinary research, including Honors projects.TECHNICAL SUMMARY This project addresses morphology, topological defects, and nonequilibrium transport in lyotropic chromonic liquid crystals, both theoretically and through large scale computation. This material is studied in its nematic phase which displays long range orientational order with characteristic elastic response and defected textures. The research is motivated by recent developments in experimental diagnostics that give, for the first time, access to quantitative detail in the sub-micron range near topological singularities of the nematic director field, as well as related determinations of the material's elastic constants and rheology. These developments open the door to quantitative theories of liquid crystals with complex molecular architectures, extension to many realistic natural systems of the well-known small molecule and isotropic limits. This is necessary as nematic response is under active scrutiny in applications of active and biological matter that display nematic order.A self-consistent field theory is proposed to determine free energies of elastically anisotropic nematics. Phenomenological gradient expansions as in, for example, the Landau-de Gennes theory, lead to unbounded energies to the lowest order necessary to incorporate anisotropy. The functional space to the next order that is necessary to restore boundedness is too large to make the theory viable or useful. A computational implementation of a singular potential method has been introduced as an alternative. It has been validated with experimental determinations of singularity profiles in lyotropic chromonics, as well as with equilibrium morphologies of two phase tactoids. This method will be extended into a field theory that can accommodate two distinct features of chromonics: the microscopic units are charged aggregates, and of length that can change depending on distortion. Novel behavior is expected because the complexity of the interactions in lyotropics manifests itself in very small twist elastic constants, leading to novel modes of disclination interactions in three dimensions, to the appearance of configurations with spontaneous chiral symmetry breaking, and even to propagating localized structures. The analysis will be fully three-dimensional and framed within a newly introduced topological invariant for uniaxial phases and an exact kinematic law for the motion of disclinations.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

非技术性摘要该项目旨在描述各种材料中所谓的nematic阶段的特性。列阶段的定义特征是定向顺序，因为单个分子通常沿着相同的方向对齐，但它们的位置是无序的。结果，这些材料像普通流体一样流动，但是当力影响其定向顺序时，它们表现出坚固的特征。这种混合性质是最新应用，在流量控制，材料形状设计和工程中，甚至是由光引起的软机器人的关键。更广泛地说，许多生物组织在该定向的单个细胞中表现出相同的特性，作为列前相，这种反应参与了生物学功能。该项目中要开发的理论将描述复杂分子单元的那些列非材料的特性和响应，例如长的有机分子，溶液中的单个磁盘堆栈或活细胞的聚集体。该理论将特别关注列在列阶段的缺陷。这些是损坏方向顺序的小区域，并且已知这些区域可以确定材料的特征性能。这样的观察是所谓的缺陷工程领域最近努力的中心，该领域旨在不消除缺陷，而是要产生它们并控制其位置和运动，以便产生在没有缺陷的理想材料中无法实现的材料特性。对缺陷，它们的相互作用和动议的理论理解是使缺陷工程的进一步进步以及目前正在探索的许多应用程序涉及nematic阶段的应用。此外，PI还创建并正在教授新的高级本科课程物理4041，“物理科学中的计算方法”是由学生在物理，计算机科学和工程学领域所采用的。该课程涉及学期的长期计算项目，其中许多是从该项目中的研究中吸引了许多研究的范围，这些研究的学生与该研究的范围进行了许多机构。在跨学科的研究中，包括荣誉项目。该项目摘要解决了理论上和大规模计算中的材料，并在其夜间阶段中研究了较长的范围，从而在较长的范围内研究了特征性的弹性和诊断。在列表主管领域的拓扑奇异性附近，在亚微米范围内获取定量细节，以及对材料弹性常数和流变学的相关确定。这些发展为具有复杂分子体系结构的液晶定量理论打开了大门，扩展到许多众所周知的小分子和各向同性限制的许多逼真的天然系统。这是必不可少的，因为在活跃和生物学物质的应用中，列表反应在表现出列表的应用中受到主动审查。提出了一种自洽的场理论来确定弹性各向异性夜间列明学的自由能。现象形态学梯度的扩展如在例如Landau-de Gennes理论中，导致无限能量达到了融合各向异性所需的最低顺序。恢复界限所需的下一个顺序的功能空间太大，无法使理论可行或有用。已经引入了奇异潜在方法的计算实现。它已通过实验性测定在溶作偶曲染色体中的奇异性谱以及两个相触觉的平衡形态进行了验证。该方法将扩展到可以容纳染色体的两个不同特征的场理论中：微观单元是充电的聚集体，并且长度可以根据失真而改变。预期的是，新型行为是因为溶裂性相互作用的复杂性以很小的扭曲弹性常数表现出来，从而导致了三个维度的新型披露相互作用模式，以表现出具有赞助性手性对称性破坏的构型的外观，甚至导致繁殖局部结构。该分析将是完全三维的，并在新引入的单轴阶段拓扑中构建，并为脱节运动而进行了确切的运动学法律。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和更广泛影响的审查标准来通过评估而被视为珍贵的支持。