DMREF: Collaborative Research: Materials Engineering of Columnar and Living Liquid Crystals via Experimental Characterization, Mathematical Modeling, and Simulation

对软物质的科学探索带来了许多技术进步，如超强聚合物凯夫拉尔的合成、液晶显示器（lcd）、药物输送新方法的开发、电解质、纳米模板材料等。该项目的目标是探索软物质形成大量复杂、组织良好的功能结构的非凡能力，并了解在平衡和非平衡条件下设计、生产和控制复杂软物质结构的基本原理。重点是一类广泛的生物相容性取向有序材料，即所谓的溶致变色液晶（LCLCs）及其与游动细菌的复合材料，称为活液晶（LLCs）。lclc和LLCs的复杂结构跨越了广泛的长度尺度，从大约1纳米（典型的分子大小）到10微米（游动细菌的大小），再到宏观尺度，在宏观尺度上，结构可以执行有用的功能，如微流体混合或微观货物（如药物）的输送。该项目结合了与几个新兴应用程序相关的建模和实验工作。特别是，这些研究将概述利用细菌的游泳能力来构建用于混合和定向递送微观货物的微型系统的潜力。该项目还将阐明LCLC与病毒衣壳DNA包装之间的联系。本项目的主要研究目标是探索lclc平衡双相状态的形态发生复杂性，这些状态需要界面能量和体积能量之间的隐式平衡，并了解活的lclc的非平衡行为与组分之间的各向异性相互作用之间的耦合机制，包括细菌活性、细菌浓度、速度矢量场和取向顺序的相互作用。这些目标将通过控制实验和理论建模来实现。在平衡行为的情况下，一个挑战是在受限的几何形状中找到定向和平移有序结构的形状，例如各向同性环境中的慢六角形柱状相的核。实验中观察到的复杂形状需要通过最小化内部弹性体能和各向异性表面锚固能来描述。在llc的动力学研究中，挑战在于同时跟踪多个标量场、矢量场和张量场。该项目旨在提高我们使用数学算法快速获取具有复杂结构的动态系统特征的大数据的能力。它还将通过开发和分析相关的数学模型来增强预测能力。

Scientific exploration of soft matter resulted in numerous technological advances, such as synthesis of a super-strong polymer Kevlar, liquid crystal displays (LCDs), development of new approaches to drug delivery, electrolytes, nano-templated materials, etc. The goal of this project is to explore the remarkable ability of soft matter to form a plethora of complex, well-organized functional structures and to understand the underlying principles by which the complex soft matter structures can be designed, produced, and controlled under both equilibrium and out-of-equilibrium conditions. The focus is on a broad class of biologically-compatible orientationally-ordered materials, the so-called lyotropic chromonic liquid crystals (LCLCs) and their composites with swimming bacteria, called living liquid crystals (LLCs). Complex structures of LCLCs and LLCs span a broad range of length scales, ranging from about 1 nm (the typical molecular size), to 10 microns (the size of a swimming bacterium), and further to the macroscopic scale, at which the structure can perform a useful function, such as microfluidic mixing or delivery of microscopic cargo (such as drugs). The project is a combination of modeling and experimental efforts connected to several emerging applications. In particular, the investigations will outline the potential of using the swimming ability of bacteria in constructing microscale systems for mixing and targeted delivery of microscopic cargo. The project will also elucidate the connections between LCLC and packing of DNA in viral capsids.The principal research objectives of this project are to explore morphogenetic complexity of the equilibrium biphasic states of LCLCs that require an implicit balance between the interfacial and bulk energy and to understand the mechanisms of coupling between the out-of-equilibrium behavior of living LCs and anisotropic interactions between the constituents, including the interplay of bacterial activity, bacterial concentration, vector field of velocities, and orientational order. These goals will be achieved through controlled experiments and theoretical modeling. In the case of an equilibrium behavior, a challenge is in finding the shapes of orientationally- and translationally-ordered structures in confined geometries, exemplified by the nuclei of the chromonic hexagonal columnar phase in the isotropic environment. The complex shapes observed in experiments need to be described through minimization of both the internal elastic bulk energy and the anisotropic surface anchoring energy. In the studies of dynamics of LLCs the challenge is in simultaneous tracking of a number of scalar, vector, and tensor fields. The project aims to advance our ability to use mathematical algorithms for fast acquisition of big data characterizing dynamic systems with complex structure. It will also enhance predictive capabilities via the development and analysis of associated mathematical models.