In situ measurements of twist and bend elastic constants in the oblique helicoidal cholesteric.

Unique electro-optical properties of the oblique helicoidal cholesteric (Ch_{OH}) stem from its heliconical director structure. An applied electric field preserves the single-harmonic modulation of the director while tuning the Ch_{OH} period and the corresponding Bragg-peak wavelength within a broad spectral range. We use the response of Ch_{OH} to the electric field to measure the elastic constants of twist K_{22} and bend K_{33} directly in the cholesteric phase. The temperature dependencies of K_{22} and K_{33} allow us to determine the range of the electric tunability of the Ch_{OH} pitch and the heliconical angle. The data are important for understanding how molecular composition and chirality influence macroscopic elastic properties of the chiral liquid crystals and for the development of Ch_{OH}-based optical devices.

Combined electric and photocontrol of selective light reflection at an oblique helicoidal cholesteric liquid crystal doped with azoxybenzene derivative.

An oblique helicoidal cholesteric liquid crystal Ch_{OH} represents a unique optical material with a single-harmonic periodic modulation of the refractive index and a pitch that can be tuned by an electric or magnetic field in a broad range from submicrometers to micrometers. In this work, we demonstrate that the oblique helicoidal cholesteric doped with azoxybenzene molecules can be tuned by both the electric field and light irradiation. The tuning mechanism is explained by the kinetics of trans-cis photoisomerization of the azoxybenzene molecules. At a fixed voltage, UV irradiation causes a redshift of the reflection peak by more than 200 nm. The effect is caused by an increase of the bend elastic constant of Ch_{OH} under irradiation. The demonstrated principle has the potential for applications such as smart windows, sensors, tunable lasers, and filters.

Topology control of human fibroblast cells monolayer by liquid crystal elastomer.

Eukaryotic cells in living tissues form dynamic patterns with spatially varying orientational order that affects important physiological processes such as apoptosis and cell migration. The challenge is how to impart a predesigned map of orientational order onto a growing tissue. Here, we demonstrate an approach to produce cell monolayers of human dermal fibroblasts with predesigned orientational patterns and topological defects using a photoaligned liquid crystal elastomer (LCE) that swells anisotropically in an aqueous medium. The patterns inscribed into the LCE are replicated by the tissue monolayer and cause a strong spatial variation of cells phenotype, their surface density, and number density fluctuations. Unbinding dynamics of defect pairs intrinsic to active matter is suppressed by anisotropic surface anchoring allowing the estimation of the elastic characteristics of the tissues. The demonstrated patterned LCE approach has potential to control the collective behavior of cells in living tissues, cell differentiation, and tissue morphogenesis.

Three-dimensional solitary waves with electrically tunable direction of propagation in nematics.

Production of stable multidimensional solitary waves is a grand challenge in modern science. Steering their propagation is an even harder problem. Here we demonstrate three-dimensional solitary waves in a nematic, trajectories of which can be steered by the electric field in a plane perpendicular to the field. The steering does not modify the properties of the background that remains uniform. These localized waves, called director bullets, are topologically unprotected multidimensional solitons of (3 + 2)D type that show fore-aft and right-left asymmetry with respect to the background molecular director; the symmetry is controlled by the field. Besides adding a whole dimension to the propagation direction and enabling controlled steering, the solitons can lead to applications such as targeted delivery of information and micro-cargo.

Dye-doped dual-frequency nematic cells as fast-switching polarization-independent shutters.

We present polarization-independent optical shutters with a sub-millisecond switching time. The approach utilizes dual-frequency nematics doped with a dichroic dye. Two nematic cells with orthogonal alignment are driven simultaneously by a low-frequency or high-frequency electric field to switch the shutter either into a transparent or a light-absorbing state. The switching speed is accelerated via special short pulses of high amplitude voltage. The approach can be used in a variety of electro-optical devices.

Publisher Correction: Electrically driven three-dimensional solitary waves as director bullets in nematic liquid crystals.

The original version of this article contained an error in the description of Supplementary Movie 7, which incorrectly read 'Collision resulting in annihilation of two solitons. U = 45.1 V, f = 600 Hz, T = 50 °C, d = 8.0 µm. The original movie is taken at the frame rate of 91 fps. The playback speed is 7 fps.' The correct version reads 'Death of a soliton at a dust particle. U = 65.6 V, f = 800 Hz, T = 50 °C, d = 7.7 µm. The original movie is taken at the frame rate of 92 fps. The playback speed is 7 fps.' The HTML has been updated to include a corrected version of the 'Description of Additional Supplementary Files' file.

Accuracy optimization of combined multiparameter measuring systems with application to polarized light microscopy.

We study the accuracy of combined multiparameter measuring systems (CMPMSs) that determine several unknown quantities from measurements of a single variable at different preprogrammed conditions determined by control parameters. To reduce inaccuracies of determined quantities, we propose a mathematical method for selection of control parameters that are optimal for all possible values of determined quantities. Using the submultiplicativity of the spectral and Frobenius matrix norms, we construct the upper bound of the error function and determine the set of control parameters by minimizing this bound. To demonstrate the capability of our method for CMPMSs, we apply it to the polarized light microscopy technique called LC-PolScope, which is used for determining inhomogeneous two-dimensional fields of optical retardation and orientation of the slow optic axis in thin organic and inorganic samples. We compare the computed set of control parameters with other sets, including the one used in the PolScope, and demonstrate that our choice of control parameters works very well even though it does not take into account any specific features of the PolScope. We expect that our method will be successful in various CMPMSs, as it is applicable to any error distribution of the control parameters and measured values.

Electrically driven three-dimensional solitary waves as director bullets in nematic liquid crystals.

Electric field-induced collective reorientation of nematic molecules is of importance for fundamental science and practical applications. This reorientation is either homogeneous over the area of electrodes, as in displays, or periodically modulated, as in electroconvection. The question is whether spatially localized three-dimensional solitary waves of molecular reorientation could be created. Here we demonstrate that the electric field can produce particle-like propagating solitary waves representing self-trapped "bullets" of oscillating molecular director. These director bullets lack fore-aft symmetry and move with very high speed perpendicularly to the electric field and to the initial alignment direction. The bullets are true solitons that preserve spatially confined shapes and survive collisions. The solitons are topologically equivalent to the uniform state and have no static analogs, thus exhibiting a particle-wave duality. Their shape, speed, and interactions depend strongly on the material parameters, which opens the door for a broad range of future studies.

Tuning selective reflection of light by surface anchoring in cholesteric cells with oblique helicoidal structures.

Selective reflection of light by oblique helicoidal cholesteric (ChOH) can be tuned in a very broad spectral range by an applied electric field. In this Letter, we demonstrate that the peak wavelength of the selective reflection can be controlled by the surface alignment of the director in sandwich cells. The peak wavelength is blue-shifted when the surface alignment is perpendicular to the bounding plates and red-shifted when it is planar. The effect is explained by the electric field redistribution within the cell caused by a spatially varying heliconical ChOH structure. The observed phenomenon can be used in sensing applications.

Fine structure of the topological defect cores studied for disclinations in lyotropic chromonic liquid crystals.

The detailed structure of singularities of ordered field represents a fundamental problem in diverse areas of physics. At the defect cores, the deformations are so strong that the system explores states with symmetry different from that of an undistorted material. These regions are difficult to explore experimentally as their spatial extension is very small, a few molecular lengths in the condensed matter. Here we explore the cores of disclinations in the so-called chromonic nematics that extend over macroscopic length scales accessible for optical characterization. We demonstrate that the amplitude S and the phase (the director) of the order parameter vary along both the radial and azimuthal directions, in contrast to the classic models in which S varies only with the distance from the centre and depends only on the azimuthal coordinate. This unexpected core structure is explained by a strong coupling of the phase and amplitude of the order parameter in the free energy.

Elastic and viscous properties of the nematic dimer CB7CB.

We present a comprehensive set of measurements of optical, dielectric, diamagnetic, elastic, and viscous properties in the nematic (N) phase formed by a liquid crystalline dimer. The studied dimer, 1,7-bis-4-(4'-cyanobiphenyl) heptane (CB7CB), is composed of two rigid rodlike cyanobiphenyl segments connected by a flexible aliphatic link with seven methyl groups. CB7CB and other nematic dimers are of interest due to their tendency to adopt bent configurations and to form two states possessing a modulated nematic director structure, namely, the twist-bend nematic, N_{TB}, and the oblique helicoidal cholesteric, Ch_{OH}, which occurs when the achiral dimer is doped with a chiral additive and exposed to an external electric or magnetic field. We characterize the material parameters as functions of temperature in the entire temperature range of the N phase, including the pretransitional regions near the N-N_{TB} and N-to-isotropic (I) transitions. The splay constant K_{11} is determined by two direct and independent techniques, namely, detection of the Frederiks transition and measurement of director fluctuation amplitudes by dynamic light scattering (DLS). The bend K_{33} and twist K_{22} constants are measured by DLS. K_{33}, being the smallest of the three constants, shows a strong nonmonotonous temperature dependence with a negative slope in both N-I and N-N_{TB} pretransitional regions. The measured ratio K_{11}/K_{22} is larger than 2 in the entire nematic temperature range. The orientational viscosities associated with splay, twist, and bend fluctuations in the N phase are comparable to those of nematics formed by rodlike molecules. All three show strong temperature dependence, increasing sharply near the N-N_{TB} transition.

Controlling placement of nonspherical (boomerang) colloids in nematic cells with photopatterned director.

Placing colloidal particles in predesigned sites represents a major challenge of the current state-of-the-art colloidal science. Nematic liquid crystals with spatially varying director patterns represent a promising approach to achieve a well-controlled placement of colloidal particles thanks to the elastic forces between the particles and the surrounding landscape of molecular orientation. Here we demonstrate how the spatially varying director field can be used to control placement of non-spherical particles of boomerang shape. The boomerang colloids create director distortions of a dipolar symmetry. When a boomerang particle is placed in a periodic splay-bend director pattern, it migrates towards the region of a maximum bend. The behavior is contrasted to that one of spherical particles with normal surface anchoring, which also produce dipolar director distortions, but prefer to compartmentalize into the regions with a maximum splay. The splay-bend periodic landscape thus allows one to spatially separate these two types of particles. By exploring overdamped dynamics of the colloids, we determine elastic driving forces responsible for the preferential placement. Control of colloidal locations through patterned molecular orientation can be explored for future applications in microfluidic, lab on a chip, sensing and sorting devices.

Control of colloidal placement by modulated molecular orientation in nematic cells.

Colloids self-assemble into various organized superstructures determined by particle interactions. There is tremendous progress in both the scientific understanding and the applications of self-assemblies of single-type identical particles. Forming superstructures in which the colloidal particles occupy predesigned sites and remain in these sites despite thermal fluctuations represents a major challenge of the current state of the art. We propose a versatile approach to directing placement of colloids using nematic liquid crystals with spatially varying molecular orientation preimposed by substrate photoalignment. Colloidal particles in a nematic environment are subject to the long-range elastic forces originating in the orientational order of the nematic. Gradients of the orientational order create an elastic energy landscape that drives the colloids into locations with preferred type of deformations. As an example, we demonstrate that colloidal spheres with perpendicular surface anchoring are driven into the regions of maximum splay, whereas spheres with tangential surface anchoring settle into the regions of bend. Elastic forces responsible for preferential placement are measured by exploring overdamped dynamics of the colloids. Control of colloidal self-assembly through patterned molecular orientation opens new opportunities for designing materials and devices in which particles should be placed in predesigned locations.

Nanosecond switching of micrometer optical retardance by an electrically controlled nematic liquid crystal cell.

Electro-optic response of liquid crystals in mainstream display applications exhibits a millisecond switching of optical retardance on the order of one micrometer. We demonstrate that a similarly large optical retardance can be switched much faster, within 10-100 nanoseconds, by using multiple passes of light through a cell filled with the nematic liquid crystal. The fast response is based on the so-called nanosecond electric modification of order parameters (NEMOP) effect. The described approach can be used to develop ultrafast optical shutters and modulators.

Kerr effect at high electric field in the isotropic phase of mesogenic materials.

The well-known Kerr effect in isotropic fluids consists in the appearance of uniaxial orientational order and birefringence that grows as the square of the applied electric field. We predict and observe that at a high electric field, the Kerr effect displays features caused by the nonlinear dependence of dielectric permittivity on the field-induced orientational order parameter. Namely, the field-induced birefringence grows faster than the square of the electric field and the dynamics of birefringence growth slows down as the field increases. As a function of temperature, the field-induced birefringence is inversely proportional to the departure from an asymptotic critical temperature, but this temperature is no longer a constant (corresponding to the lower limit of the supercooled isotropic phase) and increases proportionally to the square of the electric field.

Liquid crystals with patterned molecular orientation as an electrolytic active medium.

Transport of fluids and particles at the microscale is an important theme in both fundamental and applied science. One of the most successful approaches is to use an electric field, which requires the system to carry or induce electric charges. We describe a versatile approach to generate electrokinetic flows by using a liquid crystal (LC) with surface-patterned molecular orientation as an electrolyte. The surface patterning is produced by photoalignment. In the presence of an electric field, the spatially varying orientation induces space charges that trigger flows of the LC. The active patterned LC electrolyte converts the electric energy into the LC flows and transport of embedded particles of any type (fluid, solid, gaseous) along a predesigned trajectory, posing no limitation on the electric nature (charge, polarizability) of these particles and interfaces. The patterned LC electrolyte exhibits a quadratic field dependence of the flow velocities; it induces persistent vortices of controllable rotation speed and direction that are quintessential for micro- and nanoscale mixing applications.

Induced-charge electro-osmosis around metal and Janus spheres in water: Patterns of flow and breaking symmetries.

We establish experimentally the flow patterns of induced-charge electro-osmosis around immobilized metallic spheres in aqueous electrolyte. The ac field modifies local electrolyte concentration and causes quadrupolar flows with inward velocities being smaller than the outward ones. At high fields, the flow becomes irregular, with vortices smaller than the size of the sphere. Janus metallodielectric spheres create dipolar flows and pump the fluid from the dielectric toward the metallic part. The experimentally determined far-field flows decay with distance as r^{-3}.

Liquid crystal-enabled electro-osmosis through spatial charge separation in distorted regions as a novel mechanism of electrokinetics.

Electrically controlled dynamics of fluids and particles at microscales is a fascinating area of research with applications ranging from microfluidics and sensing to sorting of biomolecules. The driving mechanisms are electric forces acting on spatially separated charges in an isotropic medium such as water. Here, we demonstrate that anisotropic conductivity of liquid crystals enables new mechanism of highly efficient electro-osmosis rooted in space charging of regions with distorted orientation. The electric field acts on these distortion-separated charges to induce liquid crystal-enabled electro-osmosis. Their velocities grow with the square of the field, which allows one to use an alternating current field to drive steady flows and to avoid electrode damage. Ionic currents in liquid crystals that have been traditionally considered as an undesirable feature in displays, offer a broad platform for versatile applications such as liquid crystal-enabled electrokinetics, micropumping and mixing.

Elasticity, viscosity, and orientational fluctuations of a lyotropic chromonic nematic liquid crystal disodium cromoglycate.

Using dynamic light scattering, we study orientational fluctuation modes in the nematic phase of a self-assembled lyotropic chromonic liquid crystal (LCLC) disodium cromoglycate and measure the Frank elastic moduli and viscosity coefficients. The elastic moduli of splay (K1) and bend (K3) are in the order of 10 pN while the twist modulus (K2) is an order of magnitude smaller. The splay constant K1 and the ratio K1/K3 both increase substantially as the temperature T decreases, which we attribute to the elongation of the chromonic aggregates at lower temperatures. The bend viscosity is comparable to that of thermotropic liquid crystals, while the splay and twist viscosities are several orders of magnitude larger. The temperature dependence of bend viscosity is weak. The splay and twist viscosities change exponentially with the temperature. In addition to the director modes, the fluctuation spectrum reveals an additional mode that is attributed to diffusion of structural defects in the column-like aggregates.

Nanosecond electro-optics of a nematic liquid crystal with negative dielectric anisotropy.

We study a nanosecond electro-optic response of a nematic liquid crystal in a geometry where an applied electric field E modifies the tensor order parameter but does not change the orientation of the optic axis (director N ̂). We use a nematic with negative dielectric anisotropy with the electric field applied perpendicularly to N ̂. The field changes the dielectric tensor at optical frequencies (optic tensor) due to the following mechanisms: (a) nanosecond creation of the biaxial orientational order, (b) uniaxial modification of the orientational order that occurs over time scales of tens of nanoseconds, and (c) the quenching of director fluctuations with a wide range of characteristic times up to milliseconds. We develop a model to describe the dynamics of all three mechanisms. We design the experimental conditions to selectively suppress the contributions from the quenching of director fluctuations (c) and from the biaxial order effect (a) and thus, separate the contributions of the three mechanisms in the electro-optic response. As a result, the experimental data can be well fitted with the model parameters. The analysis provides a rather detailed physical picture of how the liquid crystal responds to a strong electric field on a time scale of nanoseconds. The paper provides a useful guidance in the current search for the biaxial nematic phase. Namely, the temperature dependence of the biaxial susceptibility allows one to estimate the temperature of the potential uniaxial-to-biaxial phase transition. An analysis of the quenching of director fluctuations indicates that on a time scale of nanoseconds, the classic model with constant viscoelastic material parameters might reach its limit of validity. The effect of nanosecond electric modification of the order parameter can be used in applications in which one needs to achieve ultrafast (nanosecond) changes in optical characteristics, such as birefringence.