Topology Driven Flows in Chromonic Liquid Crystals and Active Matter

非技术性概述本项目旨在描述各种材料中所谓的非晶相的性质。双相的定义特征是取向有序，其中单个分子通常沿沿着相同方向排列，但它们的位置是无序的。因此，这些材料像正常流体一样流动，但当力影响它们的取向顺序时，它们显示出固体般的特征。这种混合性质是最近在流动控制、材料形状设计和工程、甚至由光引起的致动和软机器人技术中的应用的关键。更广泛地说，许多生物组织表现出相同的性质，即定向的单个细胞作为一个周期性反应，这种反应涉及生物功能。在这个项目中开发的理论将描述那些由复杂分子单元组成的生物材料的特性和响应，例如长有机分子，溶液中单个圆盘的堆叠，或活细胞的聚集体。该理论将特别注意到缺陷的可调阶段。这些是取向顺序被打破的小区域，并且已知其决定材料的特征性质。这种观察是所谓的缺陷工程领域最近努力的中心，该领域不寻求消除缺陷，而是产生缺陷并控制它们的位置和运动，以便产生在没有缺陷的理想材料中无法实现的材料特性。对缺陷及其相互作用和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到缺陷阶段的许多应用至关重要。在教育方面，该项目将涉及研究生和本科生，后者将通过暑期实习和荣誉论文项目。此外，PI已经创建并正在教授一门新的高级本科课程PHYS 4041，“物理科学中的计算方法”，该课程由物理，计算机科学和工程专业的学生参加。本课程涉及学期长的计算项目，其中许多是从这个项目中的研究的例子。由于本研究课题与物理学、应用数学、工程学、计算科学等学科交叉，因此有很多机会让本科生参与到包括荣誉项目在内的跨学科研究中来。技术概要本项目从理论和大规模计算两方面研究溶致变色液晶的形态、拓扑缺陷和非平衡输运。该材料在其取向相进行了研究，该取向相显示出具有特征弹性响应和缺陷织构的长程取向有序。这项研究的动机是实验诊断的最新发展，第一次获得了在亚微米范围内的定量细节，接近拓扑奇点的指向矢场，以及材料的弹性常数和流变学的相关测定。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，扩展到许多现实的自然系统的众所周知的小分子和各向同性限制。这是必要的，因为弹性各向异性响应在显示有序的活性和生物物质的应用中受到积极的审查。现象学的梯度展开，例如，朗道-德热内理论，导致无限的能量，以最低的顺序，必须纳入各向异性。恢复有界性所需的下一阶函数空间太大，以至于理论不可行或有用。作为一种替代方法，引入了奇异位方法的计算实现。它已被验证与实验测定的奇异性配置文件溶致变色，以及与两相tactoids的平衡形态。这种方法将被扩展到一个场论，可以容纳两个不同的特征的色：微观单位是带电的聚集体，长度可以改变取决于失真。新的行为是预期的，因为在溶致物的相互作用的复杂性表现在非常小的扭曲弹性常数，导致在三维的向错相互作用的新模式，与自发的手征对称性破缺的配置的外观，甚至传播本地化的结构。该分析将是完全三维的，并在一个新引入的单轴相位拓扑不变量和一个精确的向错运动的运动学定律框架内进行。该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.