Topological and activity-induced constraints in nematic liquid crystals
Creators: name: Head, Louise Catherine
Publisher: name: The University of Edinburgh
Year: 2024
Subjects: active nematic liquid crystals
dynamical defect behaviours
dynamics of topological defects
structure of topological defects
bio-inspired liquid crystals

description: Active matter encompasses a broad class of out-of-equilibrium materials with internally-driven components. A trademark feature of these materials is that energy injections at microscopic scales develop into complex pattern formation and collective flows on scales many times larger. Further, examples from cytoskeletal biopolymers, bacteria suspensions and biological tissues have additional constraints on their self-organisation, emerging from their elongated components forming orientational order. To study the interplay between orientational order and emergent flow patterns,active nematic liquid crystal theory is often utilised. This hydrodynamic model accounts for instabilities that emerge from nematic deformation, and haselucidated the crucial role of topological defects in establishing the characteristiclengthscales of the steady-state structures. Numerical and analytical work onthis model, has led to a popular viewpoint on active flow states as arisingfrom point-like two-dimensional topological defects. However, this framework isinsufficient for the recent experimental and numerical advancements in three-dimensional active nematics, where defects are points, lines and loops, withdifferent conservation laws and interactions. In addition, colloidal inclusions caninduce stable point defects in the orientation field. To understand the relationship between topological defects and self-organised dynamics in three-dimensional materials requires novel numerical methods and theoretical frameworks.This thesis contributes three advancements towards topological active nematics. The first study adapts a versatile mesoscopic algorithm to include colloids that are responsive to the bulk nematohydrodynamic fields. The elastic interactions between colloids and their passive nematic environment are demonstrated,in addition to the topological properties of three-dimensional defect loops accompanying colloidal particles. This work contributes a useful simulation package that can study inclusions in complex geometries and active settings. The second study explores how topology can be engineered to control active flow patterns. By tuning the number of inclusions inside an active nematic emulsion,the bulk fluid alternates between topologically-charged disclination loops, and defect-free states. Simulations reveal that, in addition to direct topological constraints, the inner emulsions fix particular geometric constraints on the loop,supporting dynamical states resembling a rotor through to a chaotic oscillator.This work contributes to the understanding of three-dimensional active defect dynamics in the presence of colloidal particles. The third study revisits defect dynamics in two-dimensional active films, to discover a mesoscopic bridge between topological structures in the coupled orientation and flow field. Analysing simulation and experimental data shows that +1/2 defects are constrained to specific isosurfaces of the Q criterion, a parameter that indicates the topology of the local streamlines. The relationship between defects and the Q criterion offers a new framework for understanding two- and three-dimensional defect dynamics.These results reveal a previously invisible, yet dominant, class of defects that locally break mirror-symmetry, with regards to the local streamline structure. Overall, we demonstrate that defect dynamics can be understood through the framework of nematic topological, geometric, and activity-induced self-constraints. This work may guide future studies on exploring how biological fluids constrain their own dynamics.