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.

本项目旨在描述各种材料中所谓的向列相的性质。向列相的定义特征是取向顺序，即单个分子通常沿同一方向排列，但它们的位置是无序的。因此，这些材料像普通流体一样流动，但当力影响它们的取向顺序时，它们表现出固体的特征。这种混合性质是最近在流动控制、材料形状设计和工程、甚至由光诱导的驱动和软机器人等应用中的关键。更广泛地说，许多生物组织在定向的单个细胞反应为向列相时表现出相同的特性，这种反应涉及生物功能。在这个项目中发展的理论将描述那些由复杂分子单元组成的向列材料的特性和响应，如长有机分子，溶液中单个磁盘的堆叠或活细胞的聚集。该理论将特别注意向列相中的缺陷。这些是取向顺序被破坏的小区域，已知它们决定了材料的特征性质。这种观察是最近在所谓的缺陷工程领域努力的中心，它寻求的不是消除缺陷，而是产生缺陷，并控制它们的位置和运动，以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、它们之间的相互作用以及它们的运动的理论理解，对于缺陷工程的进一步发展以及目前正在探索的涉及向列相的许多应用是至关重要的。在教育方面，该项目将涉及研究生和本科生，后者通过暑期实习和荣誉论文项目。此外，学院还开设了物理学、计算机科学和工程专业学生选修的新课程PHYS 4041“物理科学中的计算方法”。本课程包含了一学期的计算项目，其中许多都来自于本项目中的研究实例。由于所提出的研究与物理、应用数学、工程和计算科学重叠，因此有许多机会让本科生参与跨学科研究，包括荣誉项目。本项目从理论上和大规模计算两方面解决了溶致变色液晶的形态、拓扑缺陷和非平衡输运问题。研究了该材料的向列相，该向列相表现出长程取向有序，具有典型的弹性响应和缺陷织构。这项研究的动机是实验诊断的最新发展，首次获得了亚微米范围内向列指向场拓扑奇点附近的定量细节，以及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结构的液晶的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极限的现实自然系统。这是必要的，因为在显示向列顺序的活性和生物物质的应用中，向列响应受到积极的审查。提出了一种确定弹性各向异性向列线自由能的自洽场论。例如，朗多-德-热纳理论中的现象梯度展开，将无界能量引入到包含各向异性所必需的最低阶。恢复有界性所必需的下一阶的功能空间太大，使理论不可行或有用。作为一种替代方法，引入了奇异势法的计算实现。这一理论已经通过实验确定的溶致变色的奇异分布以及两相的平衡形态得到了验证。这种方法将被扩展为一种能够容纳两种不同特征的场理论：微观单位是带电聚集体，并且长度可以根据畸变而变化。新颖的行为是预期的，因为在冷热带中相互作用的复杂性表现在非常小的扭转弹性常数中，导致三维中新的偏旋相互作用模式，出现自发手性对称破断的构型，甚至传播局域结构。分析将是完全三维和框架内的一个新引入的拓扑不变量的单轴相位和精确的运动学规律的运动的偏斜。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。