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

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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.