Here we deplete F-actin onto an oil–water interface, thereby forming a quasi-two-dimensional (2D) nematic system ( 23). F-actin suspensions exhibit a nematic phase when the concentration rises above the Onsager limit ( 21, 22). More specifically, we use filamentous actin (F-actin), with a width of ∼7 nm and persistence length of 10 μm to 17 μm ( 19, 20). Here we rely on suspensions of biopolymers to form lyotropic LCs, where long and semiflexible mesogens lead to the formation of nematic phases at sufficiently high concentrations. In addition, certain lyotropic LCs are not toxic to many microbial species ( 16) and neutral to antibody–antigen binding ( 17), providing a possibility for biological applications ( 18). Lyotropic materials in which LC phases emerge at certain solute concentrations circumvent some of these shortcomings. Furthermore, in thermotropic systems, there is a limited range of accessible microstructures that are only achieved with significant changes in temperature ( 12).
In such LCs, the defect size is small ( ∼ 10 nm) ( 15), thereby placing severe constraints on applications that might rely on defects to perform certain functions. The most widely used low-molecular-weight LCs are thermotropic (LC phases emerge at a certain temperature), and exhibit a nematic phase within a certain, relatively narrow temperature range.
Thus, the ability to control and optimize the LC elasticity is essential for emerging applications. That microstructure dictates optical and mechanical response of the LC to external cues.
The microstructure of an LC, the so-called “director field,” is determined by a delicate interplay between elastic forces, geometrical constraints, and the influence of applied external fields ( 13, 14). Defects exhibit unique optical and other physicochemical characteristics, and serve as the basis for many of the applications of these materials. In LCs, topological defects correspond to locally disordered regions where the orientation of the mesogens ( 12) (the units that form an LC mesophase) changes abruptly. Recent advances have extended applications of nematic liquid crystals (LCs) onto realms that go beyond display technologies ( 1) and elastomers ( 2, 3) to colloidal/molecular self-assembly ( 4– 6), pathogen sensing ( 7, 8), photonic devices ( 9), drug delivery ( 10), and microfluidics ( 11). 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. Despite the nonequilibrium nature of the system, our continuum model, which couples structure and hydrodynamics, is able to capture the annihilation and movement of defects over long time scales. 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. 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. Furthermore, through the sparse addition of rigid microtubule filaments, one can gain additional control over the liquid crystal’s elasticity.
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. At sufficiently high concentrations, one observes the formation of a nematic phase riddled with ± 1 / 2 topological defects, characteristic of a two-dimensional nematic system. Specifically, thin films of actin filaments are assembled at an oil–water interface. 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. Achieving control and tunability of lyotropic materials has been a long-standing goal of liquid crystal research.