Interplay of Structure, Elasticity and Dynamics in Actin-Based Nematic Materials

Abstract: Achieving control and tunability of lyotropic materials has been a long-standing goal of liquid crystal research. Here we show that the elasticity of a liquid crystal system consisting of a dense suspension of semiflexible biopolymers can be manipulated over a relatively wide range of elastic moduli. Specifically, thin films of actin filaments are assembled at an oil-water interface. At sufficiently high concentrations, one observes the formation of a nematic phase riddled with $\pm1/2$ topological defects, characteristic of a two-dimensional nematic system. As the average filament length increases, the defect morphology transitions from a U-shape into a V-shape, indicating the relative increase of the material's bend over splay modulus. Furthermore, through the sparse addition of rigid microtubule filaments, one can further control the liquid crystal elasticity. We show how the material's bend constant can be raised linearly as a function of microtubule filament density, and present a simple means to extract absolute values of the elastic moduli from purely optical observations. Finally, we demonstrate that it is possible to predict not only the static structure of the material, including its topological defects, but also the evolution of the system into dynamically arrested states. Despite the non-equilibrium nature of the material, our continuum model, which couples structure and hydrodynamics, is able to capture the annihilation and movement of defects over long time scales. Thus, we have experimentally realized a lyotropic liquid crystal system that can be truly engineered, with tunable mechanical properties, and a theoretical framework to capture its structure, mechanics, and dynamics.