Director Distortions Research Articles

Particle-based model of liquid crystal skyrmion dynamics.

Motivated by recent experimental results that reveal rich collective dynamics of thousands-to-millions of active liquid crystal skyrmions, we have developed a coarse-grained, particle-based model of the dynamics of skyrmions in a dilute regime. The basic physical mechanism of skyrmion motion is related to squirming undulations of domains with high director twist within the skyrmion cores when the electric field is turned on and off. The motion is not related to mass flow and is caused only by the reorientation dynamics of the director field. Based on the results of the "fine-grained" Frank-Oseen continuum model, we have mapped these squirming director distortions onto an effective force that acts asymmetrically upon switching the electrical field on or off. The resulting model correctly reproduces the skyrmion dynamics, including velocity reversal as a function of the frequency of a pulse width modulated driving voltage. We have also obtained approximate analytical expressions for the phenomenological model parameters encoding their dependence upon the cholesteric pitch and the strength of the electric field. This has been achieved by fitting coarse-grained skyrmion trajectories to those determined in the framework of the Frank-Oseen model.

Electrophoretic propulsion of matchstick-shaped magnetodielectric particles in the presence of external magnetic fields in a nematic liquid crystal.

Synthesis of micro- and nanoparticles of pre-designed shape and surface properties is an integral part of soft and synthetic active matter. We report synthesis of matchstick-shaped (MS) magnetodielectric particles and demonstrate their potential as active agents with field-controllable trajectories in a nematic liquid crystal (NLC). The MS particles with homeotropic anchoring in NLCs align either parallel or perpendicular to the director depending on the dipolar or quadrupolar director distortions. When subjected to transverse electric and magnetic fields, the particles experience electric and magnetic torques trying to align them in the respective field directions. At equilibrium, the long axis is tilted at an angle with respect to the director. The change in orientation alters the surrounding elastic distortion, which results in unbalanced electroosmotic flows. These flows provide the necessary impetus for propelling the particles in various directions with different velocities depending on their orientations.

Jetting and Droplet Formation Driven by Interfacial Electrohydrodynamic Effects Mediated by Solitons in Liquid Crystals.

Solitons are highly confined, propagating waves that arise from nonlinear feedback in natural (e.g., shallow and confined waters) and engineered systems (e.g., optical wave propagation in fibers). Solitons have recently been observed in thin films of liquid crystals (LCs) in the presence of ac electric fields, where localized LC director distortions arise and propagate due to flexoelectric polarization. Here we report that collisions between LC solitons and interfaces to isotropic fluids can generate a range of interfacial hydrodynamic phenomena. We find that single solitons can either generate single droplets or, alternatively, form jets of LC that subsequently break up into organized assemblies of droplets. We show that the influence of key parameters, such as electric field strength, LC film thickness, and LC-oil interfacial tension, map onto a universal state diagram that characterizes the transduction of soliton flexoelectric energy into droplet interfacial energy. Overall, we reveal that solitons in LCs can be used to focus the energy of nonlocalized electric fields to generate a new class of nonlinear electrohydrodynamic effects at fluid interfaces, including jetting and emulsification.

Thin pyramidal cones in nematic liquid crystals.

The present study investigates the arrangement of hollow pyramidal cone shells and their interactions with degenerate planar anchoring on the inner and outer surfaces of particles within the nematic host. The shell thickness is in order of the nematic coherence length. The numerical behavior of colloids is determined by minimizing the Landau-de Gennes free energy in the presence of the Fournier surface energy and using the finite element method. Colloidal pyramidal cones can orient parallel and perpendicular with the far director orientation. In the parallel alignment, we found the splay director distortion into the pyramid with two boojum defects at the inner and outer tips. The director shows bending distortion without defect patterns when the pyramid is aligned perpendicularly. They induce long-range dipolar interaction and can form nested structures in close contact.

The structure of disintegrating defect clusters in smectic C freely suspended films.

Disclinations or disclination clusters in smectic C freely suspended films with topological charges larger than one are unstable. They disintegrate, preferably in a spatially symmetric fashion, into single defects with individual charges of +1, which is the smallest positive topological charge allowed in polar vector fields. While the opposite process of defect annihilation is well-defined by the initial defect positions, disintegration starts from a singular state and the following scenario including the emerging regular defect patterns must be selected by specific mechanisms. We analyze experimental data and compare them with a simple model where the defect clusters adiabatically pass quasi-equilibrium solutions in one-constant approximation. It is found that the defects arrange in geometrical patterns that correspond very closely to superimposed singular defect solutions, without additional director distortions. The patterns expand by affine transformations where all distances between individual defects scale with the same time-dependent scaling factor proportional to the square-root of time.

Director Distortion and Phase Modulation in Deformable Nematic and Smectic Liquid Crystal Spheroids.

The growing interest in integrating liquid crystals (LCs) into flexible and miniaturized technologies brings about the need to understand the interplay between spatially curved geometry, surface anchoring, and the order associated with these materials. Here, we integrate experimental methods and computational simulations to explore the competition between surface-induced orientation and the effects of deformable curved boundaries in uniaxially and biaxially stretched nematic and smectic microdroplets. We find that the director field of the nematic LCs upon uniaxial strain reorients and forms a larger twisted defect ring to adjust to the new deformed geometry of the stretched droplet. Upon biaxial extension, the director field initially twists in the now oblate geometry and subsequently transitions into a uniform vertical orientation at high strains. In smectic microdroplets, on the other hand, LC alignment transforms from a radial smectic layering to a quasi-flat layering in a compromise between interfacial and dilatation forces. Upon removing the mechanical strain, the smectic LC recovers its initial radial configuration; however, the oblate geometry traps the nematic LC in the metastable vertical state. These findings offer a basis for the rational design of LC-based flexible devices, including wearable sensors, flexible displays, and smart windows.

Topological capillarity in a phase separated liquid crystal system

Emulsions of isotropic liquids have spherical phase boundaries. Liquid crystals have elastic forces associated with the director distortions and preferred boundary conditions that can also play a role in defining the phase boundary shape. Here we show a liquid crystal in liquid crystal emulsion where a chemically distinct guest phase resides in the topological disclinations of the host phase. These disclinations act as effective capillaries and various meniscus and droplet phenomena are observed. This “topological capillary emulsion” shows that additional forces associated with anisotropic molecules can play a critical role in determining the shape and properties of a phase boundary.

Particle trapped at the isotropic-nematic liquid crystal interface: Elastocapillary phenomena and drag forces.

We present numerical simulations of a particle trapped at the isotropic-nematic liquid crystal (Iso-N) interface. We use our recent model, based on a phase-field approach [see Qiu et al., Phys. Rev. E 103, 022706 (2021)10.1103/PhysRevE.103.022706], to couple the capillary forces acting on the interface with the elastic stresses in the nematic phase along with topological defects. A range of floating configurations are first investigated as a function of the contact angle and various anchoring conditions at the fluid interface. The results show that the response of the system is driven by the existence of an anchoring conflict at the contact line. Substantial particle displacements and/or interfacial deformations may occur in this case even for moderate anchoring strengths. These findings highlight the coupling between elastic and capillary forces. In a second part, we compute drag forces exerted on a particle that moves along the Iso-N interface for several contact angles and a moderate Ericksen number. Because of the coupling between the velocity and order parameter fields, topological defects are swept downstream of the particle by the flow and sometimes escape from the particle or merge with the interface. We also find linear force-velocity laws, with drag forces at the Iso-N interface being slightly greater than their isotropic counterparts due to director distortions. We discuss these results in light of past studies on the behavior of particles being dragged in the bulk of a liquid crystal matrix.

Three-dimensional soliton-like distortions in flexoelectric nematic liquid crystals: modelling and linear analysis

ABSTRACT This article models experimentally observed three-dimensional particle-like waves that develop in nematic liquid crystals, with negative dielectric and conductive anisotropy, when subject to an applied alternating electric field. The liquid crystal is confined in a thin region between two plates, perpendicular to the applied field. The horizontal, uniformly aligned director field is at equilibrium due to the negative anisotropy of the media. However, such a state is unstable to perturbations that manifest themselves as confined, bullet-like, director distortions travelling up and down the sample at a speed of several hundred microns per second. It is experimentally predicted that flexoelectricity plays a key role in generating the soliton-like behaviour. We develop a variational model that accounts for ansiostropic dielectric, conductive, flexolectric, elastic and viscous forces. We perform a stability analysis of the uniformly aligned equilibrium state to determine the threshold wave numbers, size, phase-shift and speed of the soliton-like disturbance. We show that the model predictions are in very good agreement with the experimentally measured values. The work models and analyzes a three-dimensional soliton-like instability reported, for the first time in flexoelectric liquid crystals, pointing towards a potential application as a new type of nanotransport device.

Electrically Powered Locomotion of Dual-Nature Colloid-Hedgehog and Colloid-Umbilic Topological and Elastic Dipoles in Liquid Crystals.

Colloidal particles in liquid crystals tend to induce topological defects and distortions of the molecular alignment within the surrounding anisotropic host medium, which results in elasticity-mediated interactions not accessible to their counterparts within isotropic fluid hosts. Such particle-induced coronae of perturbed nematic order are highly responsive to external electric fields, even when the uniformly aligned host medium away from particles exhibits no response to fields below the realignment threshold. Here we harness the nonreciprocal nature of these facile electric responses to demonstrate colloidal locomotion. Oscillations of the electric field prompt repetitive deformations of the corona of dipolar elastic distortions around the colloidal inclusions, which upon appropriately designed electric driving synchronize the displacement directions. We observe the colloid-hedgehog dipole accompanied by an umbilical defect in the tilt directionality field (c-field), along with the texture of elastic distortions that evolves with a change in the applied voltage. The temporal out-of-equilibrium evolution of the director and c-field distortions around particles when the voltage is turned on and off is not invariant upon reversal of time, prompting lateral translations and interactions that markedly differ from those accessible to these colloids under equilibrium conditions. Our findings may lead to both technological and fundamental science applications of nematic colloids as both model reconfigurable colloidal systems and as mesostructured materials with predesigned temporal evolution of structure and composition.

Anchoring-induced nonmonotonic velocity versus temperature dependence of motile bacteria in a lyotropic nematic liquid crystal.

The elastic and viscous properties of lyotropic chromonic liquid crystals have a very sharp, often exponential temperature dependence. Self-propelled bacteria swimming in this viscoelastic medium induce director deformations which can strongly influence their velocity, and we study the temperature behavior of their motility in the whole range of the nematic phase. We observe experimentally that, with increasing temperature, while the viscosity drops exponentially and the frequency of the flagellum rotation grows linearly, the swimmers' speed first conventionally increases but then, above some crossover temperature, slows down and at the same time bacteria-induced director distortions become visible. It is shown that the physics behind this temperature-driven effect is in a sharp rise in the ability of the bacterium's flagellum to induce director deformations. As temperature increases, the splay and bend elastic constants sharply decrease and the anchoring extrapolation length of the flagellum surface gets shorter and shorter. At the crossover temperature the resulting effective anchoring effect dominates the fast dropping viscosity and the distortion strengthens. As a result, a fraction of the torque the flagellum applies for the propulsion is spent for the elastic degrees of freedom, which results in a bacterium slowdown. To find the director distortions, the flagellum is presented as a collection of anchoring-induced elastic monopoles, and the bacterium velocity is found from the balance of the energy spent for the propulsion and the viscous drag and nematodynamic dissipation.

Interplay of Particle Morphology and Director Distortions in Nematic Fluids.

The existing microscopic theories for elasticity of nematics are challenged by recent findings on systems, whether bent molecules or semiflexible polymers, which do not comply with the model of rigid rodlike particles. Here, we propose an extension of Onsager-Straley second-virial theory, based on a model for the orientational distribution function that, through explicit account of the director profile along a particle, changes in the presence of deformations. The elastic constants reveal specific effects of particle morphology, which are not captured by the existing theories. This paves the way to microscopic modeling of the elastic properties of semiflexible liquid crystal polymers, which is a longstanding issue.

Influence of the saddle-splay term on nematic liquid crystals confined between two coaxial cylinders

A theoretical study of saddle-splay term on nematic liquid crystal confined between two coaxial cylinders elucidates director configurations. By solving the numerical solution of Euler–Lagrange equation based on Frank elastic theory and finite-difference iterative method, the effect of saddle-splay term on cylindrical system have been discussed explicitly. We investigate the spontaneous deformation by saddle-splay term K24 in the weak axial anchoring conditions. And we compare the effect of the twist elastic constant K22 on director distortion to the influence of saddle-splay term K24 in the twist anchoring conditions. Finally, we calculate the critical radius ratio and the critical twist elastic constant in the planar anchoring conditions, in which the spontaneous deformation occurs.

Controlled Placement of Microparticles at the Water-Liquid Crystal Elastomer Interface.

Controlled placement of microparticles is of prime importance in production of microscale superstructures. In this work, we demonstrate the remote control of microparticle placement using a photoactivated surface profile of a liquid crystal elastomer (LCE) coating. We employ light-responsive LCEs with preimposed patterns of molecular orientation (director) in the plane of coating. Upon UV illumination, these in-plane director distortions translate into deterministic topographic change of the LCE coating. Microparticles placed at the interface between the LCE coating and water, guided by gravity, gather at the bottom of photoinduced troughs. The effect is reversible: when the substrates are irradiated with visible light, the coatings become flat and the microparticle arrays disorganize again. The proposed noncontact manipulation of particles by photoactivated LCEs may be useful in development of drug delivery or tissue engineering applications.

Interaction of supramolecular aggregates and the enhanced optical torque on the director in a dye doped nematic liquid crystal.

There has been strong experimental evidence that molecules of some dyes in an anisotropic solvent, nematic liquid crystal, form aggregates. We present a detailed experimental analysis of the light-induced director reorientation (DR) in a dye-doped nematic liquid crystal (known as the Jánossy effect) and a theoretical model of its strong enhancement based on the aggregates' interaction. The DR transition is found to be very different from the Frederiks effect. If the light polarization is normal to the director, the transition is jump-like first order. Moreover, light polarization along the director also induces a DR which is a smooth second order transition with a very low threshold intensity. The theoretical model which explains these effects is based on the idea that dye molecules form rodlike supramolecular aggregates. The aggregates interact via the director distortions and their effective diameter gets certain field-dependence. As a result, the related entropy depletion depends on the light intensity and polarization and can be decreased by a certain DR along with the aggregate subsystem. This entropy gain is proportional to the square of light intensity which is a two-photon effect: the first resonance photon excites the dye molecule and the second photon polarizes the aggregate. This is in line with the experimental dependence of the critical intensity on the sample thickness. A special experiment shows that the effect is not connected with a possible heat-induced isotropic phase and hydrodynamic motion.

Electrokinetic effects in nematic suspensions: Single-particle electro-osmosis and interparticle interactions.

Electrokinetic phenomena in a nematic suspension are considered when one or more dielectric particles are suspended in a liquid crystal matrix in its nematic phase. The long-range orientational order of the nematic constitutes a fluid with anisotropic properties. This anisotropy enables charge separation in the bulk under an applied electric field, and leads to streaming flows even when the applied field is oscillatory. In the cases considered, charge separation is seen to result from director field distortions in the matrix that are created by the suspended particles. We use a recently introduced electrokinetic model to study the motion of a single-particle hyperbolic hedgehog pair. We find this motion to be parallel to the defect-particle center axis, independent of field orientation. For a two-particle configuration, we find that the relative force of electrokinetic origin is attractive in the case of particles with perpendicular director anchoring, and repulsive for particles with tangential director anchoring. The study reveals large scale flow properties that are respectively derived from the topology of the configuration alone and from short scale hydrodynamics phenomena in the vicinity of the particle and defect.

The model of elastic multipole

The idea of elastic multipole is based on a number of drastic simplifications. On the one hand, the theories of point-like multipoles are phenomenological as a point-like source cannot produce director distortions. On the other hand, only a spherical particle allows for analytical theory. I present a mathematically consistent analytical model of spherical elastic multipoles of a finite radius a. The core idea is to consider the general problem of a particle in an ambient distorted director field whose actual source is replaced by an equivalent source in the form of a large concentric sphere of radius ã. The solution obtained up to small terms ∼a/ã gives a simple universal tool to derive all particle's interactions. For an example, the interactions of elastic dipoles, quadrupoles, and monopoles with the ambient director, as well as their pair potentials are calculated by the straightforward differentiation. The assumptions underlying the model are discussed in detail. The main ideas of elastic multipoles and their tensorial structure, which are general and do not depend on the particular particle shape, are briefly presented.

Elastocapillary Driven Assembly of Particles at Free-Standing Smectic-A Films.

Colloidal particles at complex fluid interfaces and within films assemble to form ordered structures with high degrees of symmetry via interactions that include capillarity, elasticity, and other fields like electrostatic charge. Here we study microparticle interactions within free-standing smectic-A films, in which the elasticity arising from the director field distortion and capillary interactions arising from interface deformation compete to direct the assembly of motile particles. New colloidal assemblies and patterns, ranging from 1D chains to 2D aggregates, sensitive to the initial wetting conditions of particles at the smectic film, are reported. This work paves the way to exploiting LC interfaces as a means to direct spontaneously formed, reconfigurable, and optically active materials.

Bulk chirality effect for symmetric bistable switching of liquid crystals on topologically self-patterned degenerate anchoring surface.

We demonstrate a bistable switching liquid crystal (LC) mode utilizing a topologically self-structured dual-groove surface for degenerated easy axes of LC anchoring. In our study, the effect of the bulk elastic distortion of the LC directors on the bistable anchoring surface is theoretically analyzed for balanced bistable states based on a free energy diagram. By adjusting bulk LC chirality, we developed ideally symmetric and stable bistable anchoring and switching properties, which can be driven by a low in-plane pulsed field of about 0.7 V/µm. The fabricated device has a contrast ratio of 196:1.

Dynamic states of swimming bacteria in a nematic liquid crystal cell with homeotropic alignment

Flagellated bacteria such as Escherichia coli and Bacillus subtilis exhibit effective mechanisms for swimming in fluids and exploring the surrounding environment. In isotropic fluids such as water, the bacteria change swimming direction through the run-and-tumble process. Lyotropic chromonic liquid crystals (LCLCs) have been introduced recently as an anisotropic environment in which the direction of preferred orientation, the director, guides the bacterial trajectories. In this work, we describe the behavior of bacteria B. subtilis in a homeotropic LCLC geometry, in which the director is perpendicular to the bounding plates of a shallow cell. We demonstrate that the bacteria are capable of overcoming the stabilizing elastic forces of the LCLC and swim perpendicularly to the imposed director (and parallel to the bounding plates). The effect is explained by a finite surface anchoring of the director at the bacterial body; the role of surface anchoring is analyzed by numerical simulations of a rod realigning in an otherwise uniform director field. Shear flows produced by a swimming bacterium cause director distortions around its body, as evidenced both by experiments and numerical simulations. These distortions contribute to a repulsive force that keeps the swimming bacterium at a distance of a few micrometers away from the bounding plates. The homeotropic alignment of the director imposes two different scenarios of bacterial tumbling: one with an 180° reversal of the horizontal velocity and the other with the realignment of the bacterium by two consecutive 90° turns. In the second case, the angle between the bacterial body and the imposed director changes from 90° to 0° and then back to 90°; the new direction of swimming does not correlate with the previous swimming direction.