Topology Driven Flows in Chromonic Liquid Crystals and Active Matter

University Of Minnesota-Twin Cities, Minneapolis MN

Investigators

Abstract

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.