Topological Defects, Curved Geometries, and Shape Evolution in Soft Matter

技术总结该奖项由材料研究部资助，支持软物质物理的理论和计算研究与教育。这个跨学科的项目还汇集了微分几何、应用力学和计算材料科学等领域的研究思路和工具。该项目的主要目标是解释定向有序软物质的性质和行为，如脂泡、液晶和液晶弹性体。当弯曲的几何形状使统一的方向顺序变得不可能时，这种材料表现出几何上的挫折感。在这样的材料系统中，缺陷微观结构的时间演化与整体样品形状是紧密耦合的。缺陷迁移和样品形状演变的竞争动力学允许形成简单的几何形状或复杂的无序结构，这些结构是深度亚稳的。PI将使用一套模拟技术和理论工具来探索各种软物质和生物系统中的这种现象：(1)类脂薄膜：倾斜凝胶相或向列相中小泡的形状演变，小泡中倾斜结构域的相分离，以及带有不同小叶的双层中的孔洞和片层相的形成；(2)液晶弹性体：具有缺陷的向列型弹性体，并且具有挠曲电子效应，弯曲和静电极化之间的耦合；(3)受限几何形状的液晶：弯曲固体衬底上的薄膜，向列相或胆甾相中的液滴或壳层，以及弯曲环境中的层状液晶相。在所有这些情况下，PI将与实验科学家合作，将预测与物理和生物系统的实验进行比较。这种拓扑缺陷和曲率之间的复杂相互作用是驱动具有取向有序的软物质中图案形成和形状演化的基本机制。同时模拟缺陷织构和样品变形的共同演化将揭示现有分析理论尚未解决的动力学效应，但这对于理解实验是重要的。这项工作将有助于从根本上理解软物质的性质和行为。该奖项还支持对学生的教育和新模拟技术的开发。对凝胶相脂质中缺陷结构和形状演化的深入了解将影响膜力学领域，在自组装、包埋方法和细胞生物学方面具有潜在的应用。了解液晶中的缺陷织构动力学将有助于低功耗显示技术的发展，而对液晶弹性体的预测建模可能会导致新的形状随温度变化的器件。PI还将协调一项针对高中生的志愿者研究实习计划，该计划将促进STEM大学专业的招生，并建立对未来科学职业的抱负。非技术概述：该奖项支持软物质的理论和计算机模拟研究，重点是由倾向于平行排列自发排列的拉长分子组成的材料，如液晶、液晶橡胶和类脂膜。由于材料的弹性行为取决于其基本的分子结构，这些材料有时会在加热或冷却时形成不寻常的图案和形状，在相变中，它们的分子排列会发生变化。当材料呈中空球或其他弯曲几何形状时，这种行为尤其明显，在这些形状中，分子不可能完全有序地平行排列，缺陷--分子取向的不规则性--是不可避免的。项目团队将使用各种理论和模拟工具来探索这些缺陷如何导致复杂的样品形状和图案的形成。这项工作旨在探索和解释这种驱动取向有序软物质中图案形成和形状演化的基本机制。这项工作的广泛影响包括未来科学家的教育和新模拟技术的发展。薄膜研究的潜在技术应用包括封装方法和细胞生物学，液晶研究的潜在应用包括低功率显示技术和致动器。该项目非常适合在化学物理和计算材料建模方法方面培训下一代研究人员。PIS还将协调一项针对高中生的志愿者研究实习计划，该计划将促进STEM大学专业的入学，并建立对未来科学职业的抱负。

TECHNICAL SUMMARYThis award is funded by the Division of Materials Research and supports theoretical and computational research and education in soft matter physics. This interdisciplinary project also brings together research ideas and tools from the fields of differential geometry, applied mechanics, and computational materials science. The primary goal of the project is to explain properties and behavior of orientationally ordered soft matter such as lipid vesicles, liquid crystals, and liquid crystal elastomers. Such materials display geometric frustration when curved geometries make uniform orientational order impossible. In such material systems, time evolution of defect microstructure and overall sample shape is closely coupled. Competing kinetics of defect migration and sample shape evolution allow the formation of either simple geometric shapes or complex, disordered structures that are deeply metastable. The PIs will use a suite of simulation techniques and theoretical tools to explore such phenomena in a variety of soft matter and biological systems: (1) Lipid membranes: shape evolution of vesicles in a tilted gel phase or a nematic phase, phase separation of tilted domains in vesicles, and pore formation and lamellar phases in bilayers with distinct leaflets; (2) Liquid-crystal elastomers: nematic elastomers with defects, and with the flexoelectric effect, the coupling between bend and electrostatic polarization; (3) Liquid crystals in confined geometries: thin films on curved solid substrates, droplets or shells in the nematic or cholesteric phase, and lamellar liquid-crystal phases in curved environments. In all these cases, the PIs will collaborate with experimental scientists to compare predictions with experiments on physical and biological systems. This complex interaction between topological defects and curvature is a fundamental mechanism driving pattern formation and shape evolution in soft matter with orientational order. Modeling simultaneous co-evolution of defect textures and sample deformation will reveal kinetic effects not yet addressed in existing analytical theories, but which are important to understand experiments. This work will thus contribute to fundamental understanding of the properties and behavior of soft matter. This award also supports education of students and the development of novel simulation techniques. Deeper understanding of defect textures and shape evolution in gel phase lipids will impact the field of membrane mechanics with potential applications in self-assembly, encapsulation methods, and cell biology. Understanding defect texture dynamics in liquid crystals will contribute to development of low-power display technologies, and predictive modeling of liquid crystal elastomers may lead to new devices that change shape with temperature. The PI's will also coordinate a volunteer research internship program for high school students that will promote enrollment in STEM college majors and build aspirations for future science careers.NON-TECHNICAL SUMMARY:This award supports theoretical and computer simulation studies of soft matter, with a focus on materials composed of elongated molecules that tend to order spontaneously in parallel alignment, such as liquid crystals, liquid crystalline rubber, and lipid membranes. Because a material's elastic behavior depends on its underlying molecular structure, these materials sometimes form unusual patterns and shapes when heated or cooled through a phase transition in which their molecular alignment is altered. This kind of behavior is seen particularly when the material is in the shape of a hollow sphere or other curved geometry where fully ordered parallel alignment of molecules is not possible, and defects - irregularities in molecular orientation - are inevitable. The project team will employ a variety of theoretical and simulation tools to explore the way these defects give rise to the formation of complex sample shapes and patterns. This work aims to explore and to explain this fundamental mechanism driving pattern formation and shape evolution in soft matter with orientational order.Broader impacts of the work include education of future scientists and the development of novel simulation techniques. Potential technological applications of the membrane research include encapsulation methods and cell biology, and potential applications of the liquid-crystal research include low-power display technologies and actuators. This project is well-suited to train the next generation researchers in the methods of both chemical physics and computational materials modeling. The PIs will also coordinate a volunteer research internship program for high school students that will promote enrollment in STEM college majors and build aspirations for future science careers.