Hydrodynamic instabilities in active cholesteric liquid crystals

Symmetry Breaking of Self-Propelled Topological Defects in Thin-Film Active Chiral Nematics

Active nematics represent a range of dense active matter systems which can engender spontaneous flows and self-propelled topological defects. Two-dimensional (2D) active nematic theory and simulation have been successful in explaining many quasi-2D experiments in which self-propelled +1/2 defects are observed to move along their symmetry axis. However, many active liquid crystals are essentially chiral nematic, but their twist mode becomes irrelevant under the 2D assumption. Here, we use theory and simulation to examine a three-dimensional active chiral nematic confined to a thin film, thus forming a quasi-2D system. We predict that the self-propelled +1/2 disclination in a curved thin film can break its mirror symmetry by moving circularly. Our prediction is confirmed by hydrodynamic simulations of thin spherical-shell and thin cylindrical-shell systems. In the spherical-shell confinement, the four emerged +1/2 disclinations exhibit rich dynamics as a function of activity and chirality. As such, we have proposed a new symmetry-breaking scenario in which self-propelled defects in quasi-2D active nematics can acquire an active angular velocity, greatly enriching their dynamics for finer control and emerging applications.

Rectification of polymer translocation through nanopores by nonchiral and chiral active particles

We study translocation of a flexible polymer chain through a membrane pore under the influence of active forces and steric exclusion using Langevin dynamics simulations within a minimal two-dimensional model. The active forces on the polymer are imparted by nonchiral and chiral active particles that are introduced on one side or both sides of a rigid membrane positioned across the midline of a confining box. We show that the polymer can translocate through the pore to either side of the dividing membrane in the absence of external forcing. Translocation of the polymer to a given side of the membrane is driven (hindered) by an effective pulling (pushing) exerted by the active particles that are present on that side. The effective pulling results from accumulation of active particles around the polymer. This crowding effect signifies persistent motion of active particles causing prolonged detention times for them close to the confining walls and the polymer. The effective pushing that hinders the translocation, on the other hand, results from steric collisions that occur between the polymer and active particles. As a result of the competition between these effective forces, we find a transition between two rectified cis-to-trans and trans-to-cis translocation regimes. This transition is identified by a sharp peak in the average translocation time. The effects of active particles on the transition is studied by analyzing how the translocation peak is regulated by the activity (self-propulsion) strength of these particles, their area fraction, and chirality strength.

Dynamics of coreless defects during winding up transitions in confined chiral nematic liquid crystals

Twist-coupled elastic deformations are ubiquitous and in the limelight of interest for next-generation self-shaping materials. Here, we describe how twist dynamics under fixed anchoring lead to bend deformation and defect dynamics in a field-unwound chiral liquid crystal material. We use the Q-tensor dynamics under the Landau-de Gennes formalism in a finite-element mesh to explore the texture pathways from the unwound (homeotropic) to the helical planar structure. Our simulations describe well previously reported experiments and confirm that the process occurs by forming pairs of coreless defects that interact with each other and create quadrupolar structures called Lehmann clusters. The dynamics and coarsening of dipoles and quadrupoles of defects are described. This numerical study describes the full dynamics, which has been sought for several years.

Dispersing swimming microalgae in self-assembled nanocellulose suspension: Unveiling living colloid dynamics in cholesteric liquid crystals

Active matter comprises individual energy-consuming components that convert locally stored energy into mechanical motion. Among these, liquid crystal dispersed self-propelled colloids have displayed fascinating dynamic effects and nonequilibrium behaviors. In this work, we introduce a new type of active soft matter based on swimming microalgae and lyotropic nanocellulose liquid crystal. Cellulose is a kind of biocompatible polysaccharide that nontoxic to living biological colloids. In contrast to microalgae locomotion in isotropic and low viscosity media, we demonstrate that the propulsion force of swimming microalgae can overcome the stabilizing elastic force in cholesteric nanocellulose liquid crystal, with the displacement dynamics (gait, direction, frequency, and speed) be altered by the surrounding medium. Simultaneously, the active stress and shear flow exerted by swimming microalgae can introduce local perturbation in surrounding liquid crystal orientation order. The latter effect yields hydrodynamic fluctuations in bulk phase as well as layer undulations, helicoidal axis splay deformation and director bending in the cholesteric assembly, which finally followed by a recovery according to the inherent viscoelasticity of liquid crystal matrix. Our results point to an unorthodox design concept to generate a new type of hybrid soft matter that combines nontoxic cholesteric liquid crystal and active particles, which are expected to open opportunities in biosensing and biomechanical applications.

Topological Defects in Solids with Odd Elasticity

Crystallography typically studies collections of point particles whose interaction forces are the gradient of a potential. Lifting this assumption generically gives rise in the continuum limit to a form of elasticity with additional moduli known as odd elasticity. We show that such odd elastic moduli modify the strain induced by topological defects and their interactions, even reversing the stability of, otherwise, bound dislocation pairs. Beyond continuum theory, isolated dislocations can self propel via microscopic work cycles active at their cores that compete with conventional Peach-Koehler forces caused, for example, by an ambient torque density. We perform molecular dynamics simulations isolating active plastic processes and discuss their experimental relevance to solids composed of spinning particles, vortexlike objects, and robotic metamaterials.

Propagating wave in a fluid by coherent motion of 2D colloids

Just like in living organisms, if precise coherent operation of tiny movable components is possible, one may generate a macroscopic mechanical motion. Here we report that ~10¹⁰ pieces of colloidally dispersed nanosheets in aqueous media can be made to operate coherently to generate a propagating macroscopic wave under a non-equilibrium state. The nanosheets are initially forced to adopt a monodomain cofacial geometry with a large and uniform plane-to-plane distance of ~420 nm, where they are strongly correlated by competitive electrostatic repulsion and van der Waals attraction. When the electrostatic repulsion is progressively attenuated by the addition of ionic species, the nanosheets sequentially undergo coherent motions, generating a propagating wave. This elaborate wave in time and space can transport microparticles over a long distance in uniform direction and velocity. The present discovery may provide a general principle for the design of macroscopically movable devices from huge numbers of tiny components.

Tiny movable components could generate macroscopic mechanical motion if precise coherent operation can be exerted simultaneously. Here, the authors demonstrate this by using 10^10 pieces of colloidally dispersed nanosheets to generate wave under non-equilibrium state.

Layered Chiral Active Matter: Beyond Odd Elasticity

In equilibrium liquid crystals, chirality leads to a variety of spectacular three-dimensional structures, but chiral and achiral phases with the same broken continuous symmetries have identical long-time, large-scale dynamics. In this Letter, starting from active model H^{*}, the general hydrodynamics of a pseudoscalar in a momentum-conserving fluid, we demonstrate that chirality qualitatively modifies the dynamics of layered liquid crystals in active systems in both two and three dimensions due to an active "odder" elasticity. In three dimensions, we demonstrate that the hydrodynamics of active cholesterics differs fundamentally from smectic-A liquid crystals, unlike their equilibrium counterpart. This distinction can be used to engineer a columnar array of vortices, with an antiferromagnetic vorticity alignment, that can be switched on and off by external strain. A two-dimensional chiral layered state-an array of lines on an incompressible, freestanding film of chiral active fluid with a preferred normal direction-is generically unstable. However, this instability can be tuned in easily realizable experimental settings when the film is either on a substrate or in an ambient fluid.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Geometry of Bend: Singular Lines and Defects in Twist-Bend Nematics

We describe the geometry of bend distortions in liquid crystals and their fundamental degeneracies, which we call β lines; these represent a new class of linelike topological defect in twist-bend nematics. We present constructions for smecticlike textures containing screw and edge dislocations and also for vortexlike structures of double twist and Skyrmions. We analyze their local geometry and global structure, showing that their intersection with any surface is twice the Skyrmion number. Finally, we demonstrate how arbitrary knots and links can be created and describe them in terms of merons, giving a geometric perspective on the fractionalization of Skyrmions.

Three-Dimensional Active Defect Loops

We describe the flows and morphological dynamics of topological defect lines and loops in three-dimensional active nematics and show, using theory and numerical modeling, that they are governed by the local profile of the orientational order surrounding the defects. Analyzing a continuous span of defect loop profiles, ranging from radial and tangential twist to wedge ±1/2 profiles, we show that the distinct geometries can drive material flow perpendicular or along the local defect loop segment, whose variation around a closed loop can lead to net loop motion, elongation, or compression of shape, or buckling of the loops. We demonstrate a correlation between local curvature and the local orientational profile of the defect loop, indicating dynamic coupling between geometry and topology. To address the general formation of defect loops in three dimensions, we show their creation via bend instability from different initial elastic distortions.

Oriented Active Solids

We present a complete analysis of the linearized dynamics of active solids with uniaxial orientational order, taking into account a hitherto overlooked consequence of rotation invariance. Our predictions include a purely active response of two-dimensional orientationally ordered solids to shear, the possibility of stable active solids with quasi-long-range order in two dimensions and long-range order in three dimensions, generic instability of the solid for one sign of active forcing, and the instability of the uniaxially ordered phase in momentum-conserved systems for large active forcing irrespective of its sign.

Visual Appearance of Chiral Nematic Cellulose-Based Photonic Films: Angular and Polarization Independent Color Response with a Twist

Hydroxypropyl cellulose (HPC) is a biocompatible cellulose derivative capable of self-assembling into a lyotropic chiral nematic phase in aqueous solution. This liquid crystalline phase reflects right-handed circular polarized light of a specific color as a function of the HPC weight fraction. Here, it is demonstrated that, by introducing a crosslinking agent, it is possible to drastically alter the visual appearance of the HPC mesophase in terms of the reflected color, the scattering distribution, and the polarization response, resulting in an exceptional matte appearance in solid-state films. By exploiting the interplay between order and disorder, a robust and simple methodology toward the preparation of polarization and angular independent color is developed, which constitutes an important step toward the development of real-world photonic colorants.

Rotation and propulsion in 3D active chiral droplets

Chirality is a recurrent theme in the study of biological systems, in which active processes are driven by the internal conversion of chemical energy into work. Bacterial flagella, actomyosin filaments, and microtubule bundles are active systems that are also intrinsically chiral. Despite some exploratory attempt to capture the relations between chirality and motility, many features of intrinsically chiral systems still need to be explored and explained. To address this gap in knowledge, here we study the effects of internal active forces and torques on a 3-dimensional (3D) droplet of cholesteric liquid crystal (CLC) embedded in an isotropic liquid. We consider tangential anchoring of the liquid crystal director at the droplet surface. Contrary to what happens in nematics, where moderate extensile activity leads to droplet rotation, cholesteric active droplets exhibit more complex and variegated behaviors. We find that extensile force dipole activity stabilizes complex defect configurations, in which orbiting dynamics couples to thermodynamic chirality to propel screw-like droplet motion. Instead, dipolar torque activity may either tighten or unwind the cholesteric helix and if tuned, can power rotations with an oscillatory angular velocity of 0 mean.

Mechanically induced Helfrich-Hurault effect in a confined lamellar system with finite surface anchoring

Soft lamellar phases confined between two parallel plates and subject to a dilatative strain can become unstable exhibiting periodic deformations patterns of the layers. By a variational energy approach, a critical threshold for the imposed finite strain is derived in the case of weak anchoring conditions. The potential, associated to the system, includes a two-terms energy which accounts for the bending of the layers and the dilatation of the bulk as well as an anchoring potential. Classical results for strong anchoring at the walls are recovered. It is shown that weak anchoring conditions can lead to a lower critical threshold of the field, similarly as happens for the instability induced by a magnetic or an electric field normal to the layers. Nevertheless, in the limit of weak anchoring, the model reveals that this instability does not occur. Analytical formulas are provided which certainly encourage further experimental investigations.

Structure Evolution and Drying Dynamics in Sliding Cholesteric Cellulose Nanocrystals

The study of colloidal liquid crystals (LCs) reveals fundamental insights into the nature of ordered materials, giving rise to emergent properties with fascinating applications in soft matter nanotechnology. Here we investigate the shape instabilities, layer undulations, dynamic assembly, and collective behaviors in evaporating a cellulose nanocrystal-based cholesteric LC drop. During the drying process, the drop edges are pinned to the substrate with spontaneous convective flow occurring along the drop, which leads to nonequilibrium sliding of the individual cholesteric fragment with active ordering as well as hydrodynamic fluctuations and flow transitions in the bulk cholesteric phase.