Director Field Research Articles

Flowing Liquid Crystal Torons Around Obstacles

Liquid crystal torons, localized topological structures, are known for their stability and dynamic behaviour in response to external stimuli, making them attractive for advanced material applications. In this study, we investigate the flow of torons in chiral nematic liquid crystals around obstacles. We simulate the fluid flow and director field interactions using a hybrid numerical method combining lattice Boltzmann and finite difference techniques. Our results reveal that the toron dynamical behaviour depends strongly on the impact parameter from the obstacle. At impact parameters smaller than half cholesteric pitch, the flowing toron is destabilized by the interaction with the obstacle; otherwise, the flowing toron follows a trajectory with a deflection which decays exponentially with the impact parameter. Additionally, we explore the scattering of torons by multiple obstacles, providing insights into how the dynamics of these structures respond to complex environments.

Chiral, Topological, and Knotted Colloids in Liquid Crystals

The geometric shape, symmetry, and topology of colloidal particles often allow for controlling colloidal phase behavior and physical properties of these soft matter systems. In liquid crystalline dispersions, colloidal particles with low symmetry and nontrivial topology of surface confinement are of particular interest, including surfaces shaped as handlebodies, spirals, knots, multi-component links, and so on. These types of colloidal surfaces induce topologically nontrivial three-dimensional director field configurations and topological defects. Director switching by electric fields, laser tweezing of defects, and local photo-thermal melting of the liquid crystal host medium promote transformations among many stable and metastable particle-induced director configurations that can be revealed by means of direct label-free three-dimensional nonlinear optical imaging. The interplay between topologies of colloidal surfaces, director fields, and defects is found to show a number of unexpected features, such as knotting and linking of line defects, often uniquely arising from the nonpolar nature of the nematic director field. This review article highlights fascinating examples of new physical behavior arising from the interplay of nematic molecular order and both chiral symmetry and topology of colloidal inclusions within the nematic host. Furthermore, the article concludes with a brief discussion of how these findings may lay the groundwork for new types of topology-dictated self-assembly in soft condensed matter leading to novel mesostructured composite materials, as well as for experimental insights into the pure-math aspects of low-dimensional topology.

Edge-on anchored discotic liquid crystals in spherical shells: A computational study of the phases and defects.

The self-assembly of liquid crystal droplets and shells represents a captivating frontier in soft matter physics, promising precision engineering of functional materials. In this study, we delve into the phase behavior and investigate defect formation patterns in spherical shell-confined discotic liquid crystals (DLCs) through NpT Monte Carlo simulations. These shells are created by confining DLCs between two spherical surfaces, promoting the same anchoring. In this study, we focus on the case when both surfaces promote edge-on (planar) anchoring. Our study confirms a general result which states that, when a liquid crystal is under strong confinement, the nature of the isotropic-nematic transition changes from first order into continuous. Furthermore, as expected, topological defects at the spherical surface arise due to the topological constraints on the director field. Notably, our investigation reveals a unique topological defect configuration, characterized by the formation of four disclination lines that bridge the inner and external surfaces. Additionally, we observe a mixed ±1/2 wedge-twist disclination line that forms an arch that terminates at the outer surface. This arch decreases its length with decreasing temperature to eventually disappear.

Topologically frustrated structures in inkjet printed chiral nematic liquid crystal droplets - experiments and simulations.

Director field alignment in inkjet printed droplets of chiral nematic liquid crystalline materials is investigated using both experiments and numerical simulations. Experimental investigations are performed by depositing droplets of varying sizes and pitches on homeotropic alignment layers. The competition between the bulk behaviour of the chiral nematic liquid crystal and the boundary conditions imposed by the droplet surface leads to the formation of a range of possible internal director configurations. Numerical investigations are performed using a free energy minimisation approach, and the resultant simulated polarising optical microscope images are found to agree well with experimental observations.

Many-defect solutions in planar nematics: interactions, spiral textures and boundary conditions.

From incompressible flows to electrostatics, harmonic functions can provide solutions to many two-dimensional problems and, similarly, the director field of a planar nematic can be determined using complex analysis. We derive a closed-form solution for a quasi-steady state director field induced by an arbitrarily large set of point defects and circular inclusions with or without fixed rotational degrees of freedom, and compute the forces and torques acting on each defect or inclusion. We show that a complete solution must include two types of singularities, generating a defect winding number and its spiral texture, which have a direct effect on defect equilibrium textures and their dynamics. The solution accounts for discrete degeneracy of topologically distinct free energy minima which can be obtained by defect braiding. The derived formalism can be readily applied to equilibrium and slowly evolving nematic textures for active or passive fluids with multiple defects present within the orientational order.

Nonsymmetrical thermal conductivity along the director field in ferroelectric nematic liquid crystals.

The synthesis of ferroelectric nematic liquid crystals (FNLCs) concludes the long wait for their existence and potential usage in multiple liquid crystal based applications. In FNLCs, electric polarization in the nematic phase significantly decreases the switching time of in-on display pixels. In this article, we report the occurrence of translation symmetry breaking for heat propagation along the director field n[over ̂] in the ferroelectric nematic phase. Due to the C_{∞V} symmetry of such a phase and close similarity to the bent-core polar liquid crystal phase, a rank-3 tensor describes its scalar order parameter and algebraic deductions. The finite element simulations show the occurrence of the nonsymmetrical thermal conductivity along n[over ̂]. The preferential heat transport in FNLCs can allow them to work as an all-thermal monophase non-nanostructured single-material thermal rectifier. We expect that this study will contribute towards the FNLCs application as functional layers and inks.

Surface-directed dynamics in living liquid crystals.

We study living liquid crystals (LLCs), which are an amalgam of nematic liquid crystals (LCs) and active matter (AM). These LLCs are placed in contact with surfaces which impose planar/homeotropic boundary conditions on the director field of the LC and the polarization field of the AM. The interplay of LC-AM interactions and the surface-directed conditions yield controlled pattern dynamics in the LLC, which has important technological implications. We discuss two representative examples of this pattern dynamics.

Hele-Shaw flow of a nematic liquid crystal.

Motivated by the variety of applications in which nematic Hele-Shaw flow occurs, a theoretical model for Hele-Shaw flow of a nematic liquid crystal is formulated and analyzed. We derive the thin-film Ericksen-Leslie equationsthat govern nematic Hele-Shaw flow, and consider two important limiting cases in which we can make significant analytical progress. First, we consider the leading-order problem in the limiting case in which elasticity effects dominate viscous effects, and find that the nematic liquid crystal anchoring on the plates leads to a fixed director field and an anisotropic patterned viscosity that can be used to guide the flow of the nematic. Second, we consider the leading-order problem in the opposite limiting case in which viscous effects dominate elasticity effects, and find that the flow is identical to that of an isotropic fluid and the behavior of the director is determined by the flow. As an example of the insight which can be gained by using the present approach, we then consider the flow of nematic according to a simple model for the squeezing stage of the one-drop-filling method, an important method for the manufacture of liquid crystal displays, in these two limiting cases.

Achiral hard bananas assemble double-twist skyrmions and blue phases.

Skyrmions are topologically protected, vortex-like structures found in various condensed-matter systems including helical ferromagnets and liquid crystals, typically arising from chiral interactions. Using extensive particle-based simulations, we demonstrate that non-chiral hard banana-shaped particles, governed solely by excluded-volume interactions, spontaneously stabilize skyrmion structures through the bend-flexoelectric effect. Under thin confinement, we observe the formation of quasi-2D layers of isolated skyrmions or dense skyrmion lattices. These structures, comprising a racemic mixture of left- and right-handed skyrmions, show resilience against thermal fluctuations while remaining responsive to external fields, offering intriguing possibilities for manipulation. We also find that the size of these skyrmions can be adjusted by the dimensions and curvature of the banana-shaped particles. In the absence of geometric frustration due to confinement, a blue phase III may emerge, characterized by a 3D network of chiral skyrmion filaments of the nematic director field within an isotropic background. Our findings provide valuable insights into stabilizing skyrmion lattices and blue phases, showcasing non-Gaussian fluid-like dynamics in systems of achiral hard particles. Furthermore, they highlight the remarkable capacity of these complex fluids in designing advanced functional materials with diverse applications in photonics and memory devices.

Orientational order and topological defects in a dilute solutions of rodlike polymers at low Reynolds number.

The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align with the velocity field in order to minimize the friction with the solvent fluid, while regions of rotational disorder are related to strong vorticity gradients, and therefore to the chaotic flow. The "turbulent-like" behavior of the system is therefore associated with the emergence and interaction of topological defects of the mean director field, similarly to active nematic turbulence. The analysis has been carried out in both two and three spatial dimensions.

Dynamic control of active droplets using light-responsive chiral liquid crystal environment

Microscopic active droplets are of interest since they can be used to transport matter from one point to another. In this work, we demonstrate an approach to control the direction of active droplet propulsion by a photoresponsive cholesteric liquid crystal environment. The active droplet represents a water dispersion of bacterial Bacillus subtilis microswimmers. When placed in a cholesteric, a surfactant-stabilized active droplet distorts the local director field, producing a point defect-hedgehog, with fore-aft asymmetry, and allows for the chaotic motion of the bacteria inside the droplet to be rectified into directional motion. When the pitch of the cholesteric confined in a sandwich-like cell is altered by light irradiation, the droplet trajectory realigns along a new direction. The strategy allows for a non-contact dynamic control of active droplets trajectories and demonstrates the advantage of orientationally ordered media in control of active matter over their isotropic counterparts.

Trapping of isotropic droplets by disclinations in nematic liquid crystals controlled by surface anchoring and elastic constant disparity.

Linear defects such as dislocations and disclinations in ordered materials attract foreign particles since they replace strong elastic distortions at the defect cores. In this work, we explore the behavior of isotropic droplets nucleating at singular disclinations in a nematic liquid crystal, predesigned by surface photopatterning. Experiments show that in the biphasic nematic-isotropic region, although the droplets are attracted to the disclination cores, their centers of mass shift away from the core centers as the temperature increases. The shift is not random, being deterministically defined by the surrounding director field. The effect is explained by the balance of interfacial anchoring and bulk elasticity. An agreement with the experiment can be achieved only if the model accounts for the disparity of the nematic elastic constants; the so-called one-constant approximation, often used in the theoretical analysis of liquid crystals, produces qualitatively wrong predictions. In particular, the experimentally observed shift towards the bend region around a +1/2 disclination core can be explained only when the bend constant is larger than the splay constant. The described dependence of the precise location of a foreign inclusion at defect cores on the elastic and surface anchoring properties can be used in rational design of microscale architectures.

Microfluidic flow tuning via asymmetric flow of nematic liquid crystal under temperature gradient

In this work, efficient microfluidic flow rate tuning based on the asymmetric flow of nematic liquid crystal 5CB under a horizontal temperature gradient is studied. Rectangular microchannels with the width of 100 μm are fabricated through soft lithography and treated with homeotropic surface anchoring conditions. Polarized optical microscopy is applied to explore the unique optical anisotropic characteristics of the nematic liquid crystal. The asymmetric velocity profiles in the microchannel are obtained by particle tracking velocimetry. The effects of temperature, flow rate, and aspect ratio on the velocity profile and split ratio of the asymmetric flow are quantitatively studied for the first time, while the mechanism of the flow asymmetry of the nematic liquid crystal is discussed. The results show that the asymmetric flow of the nematic liquid crystal occurs after the horizontal temperature gradient is applied, with the velocity in the heated region markedly higher than its counterpart. The split ratio of the asymmetric flow increases with the increase in the temperature gradient and the decrease in the flow rate. The aspect ratio influences the asymmetric flow through approaches of average velocity and surface anchoring strength, while the former is more distinct. The impacts of temperature gradient, flow rate, and aspect ratio on the flow asymmetry of nematic liquid crystals are caused by the coupling between physical properties, velocity field, and director field. Microchannels based on the asymmetric flow characteristics of nematic liquid crystals can act as a novel kind of temperature-controlled microvalve to achieve efficient microfluidic flow tuning.

Molecular shape, elastic constants and spontaneous twist in chiral and achiral nematics: insights from a generalised Maier–Saupe framework

ABSTRACT Ordinary nematic liquid crystals have a uniform director field as ground state. However, there are relevant examples of spontaneously twisted nematic states, not only in chiral, but also in achiral materials. Different twist configurations can be found, with the director modulation along the twist axis, as in the cholesteric and in the twist-bend nematic phase, or perpendicular to it, as in blue phases and in skyrmion structures. Here, we develop a generalised Maier–Saupe theory to calculate the thermodynamic and elastic properties, included saddle-splay, of nematics made of particles whose shape can be described as a distorted rod. This turns out to be a powerful approach for screening the relation between the molecular shape and the formation of modulated nematic phases. Application to the paradigmatic models of banana-shaped and helical particles allows us to identify the role of distinct shape features, such as curvature and chirality, and the distinct mechanisms by which these promote twisted configurations.

On the Existence and Partial Stability of Standing Waves for a Nematic Liquid Crystal Director Field Equations

AbstractIn this paper, following the studies in Amorim et al. (Partial Differ Equ Appl 4, 36, 2023), we consider some new aspects of the motion of the director field of a nematic liquid crystal submitted to a magnetic field and to a laser beam. In particular, we study the existence and partial orbital stability of special standing waves, in the spirit of Cazenave and Lions (Commun Math Phys 85:549–561, 1982) and Hadj Selem et al. (Milan J Math 82:273–295, 2014) and we present some numerical simulations.

Layer topology of smectic grain boundaries

ABSTRACT Grain boundaries in extremely confined colloidal smectics possess a topological fine structure with coexisting nematic and tetratic symmetry of the director field. An alternative way to approach the problem of smectic topology is via the layer structure, which is typically more accessible in experiments on molecular liquid crystals. Here, we consider exemplary density functional theory results for two-dimensional hard rods to illustrate how the concept of endpoint defects, which appear as tetratic disclinations of quarter charge in director topology, translates to smectic layer topology built around the networks formed by density maxima and minima. By doing so, we elaborate on further advantages of a topological concept evolving around the layer structure rather than the director field, such as providing insight in the structure of edge dislocations or virtual defects at the confining walls.

Three-dimensional spontaneous flow transition in a homeotropic active nematic

Active nematics are driven, non-equilibrium systems relevant to biological processes including tissue mechanics and morphogenesis, and to active metamaterials in general. We study the three-dimensional spontaneous flow transition of an active nematic in an infinite slab geometry using a combination of numerics and analytics. We show that it is determined by the interplay of two eigenmodes – called S- and D-mode – that are unstable at the same activity threshold and spontaneously breaks both rotational symmetry and chiral symmetry. The onset of the unstable modes is described by a non-Hermitian integro-differential operator, which we determine their exponential growth rates from using perturbation theory. The S-mode is the fastest growing. After it reaches a finite amplitude, the growth of the D-mode is anisotropic, being promoted perpendicular to the S-mode and suppressed parallel to it, forming a steady state with a full three-dimensional director field and a well-defined chirality. Lastly, we derive a model of the leading-order time evolution of the system close to the activity threshold.

Energy dissipation mechanism of annihilating reverse tilt domains for various applied voltages.

When a voltage is applied to a uniformly aligned nematic liquid crystal, a characteristic texture designated as reverse tilt domain (RTD) appears. The RTD, surrounded by a domain wall, gradually shrinks and finally disappears. The domain wall splits into a pair of disclination lines by increase of the voltage. This work examines the energy dissipation mechanism of annihilation dynamics by ascertaining the phenomenological viscosity Γ based on experimentation. To evaluate Γ, the time dependence of curvature radius R is analyzed using an equationR=Asqrt[t_{0}-t], where A is a fitting parameter. Parameter A decreased linearly with increasing applied voltage and suddenly became constant. Also, Γ was evaluated from A as a function of voltage. When the voltage reaches a critical value, Γ increased sharply to be one order of magnitude greater than that under low voltages. The critical voltage is consistent with the theoretically expected value at which the splitting of domain wall occurs. The transition of Γ is described clearly by localized deformation of the director field.

Reconfigurable Liquid Crystal Elastomer Director Patterns for Multi-Mode Shape Morphing

Liquid crystal elastomers (LCEs) are a monolithic material with programmable three-dimensional (3D) morphing modes stemming from their designable non-uniform molecular orientations (or director). However, the shape morphing mode is generally fixed when director patterns of LCEs are determined. Multi-mode shape morphing is difficult to achieve since director patterns cannot be reconfigured. Herein, we demonstrate the ability to reconfigure LCE director patterns and initial shapes—and thus shape morphing modes—by the manual assembly and de-assembly of LCE pixels. We measured the mechanical properties of LCEs with and without UV glue and found their Young’s moduli were 9.6 MPa and 11.6 MPa. We firstly fabricate LCE pixels with designed director fields and then assemble 24 pixels with required director fields into an LCE film with a designed director pattern, which corresponds to a programmed shape morphing mode. We further exhibit that we can de-assemble the LCE film back into original pixels or new pixels with different shapes and then re-assemble them into a new film with a different initial shape and director pattern, which corresponds to a second programmed shape morphing mode. Principally, we can have a large amount of shape morphing modes if we have enough pixels. The demonstrated capability of multi-mode shape morphing enhances functions of LCEs, which broadens their applications in soft robotics, programmable origami/kirigami, responsive surfaces, and so on.

Dynamically reconfigurable complex liquid crystal emulsions

ABSTRACT Complex emulsions, containing liquid crystals (LCs) and immiscible oils such as fluorocarbon or silicone oils, present innovative functionalities in soft materials. These emulsions exhibit dynamic reconfiguration in droplet morphology and internal LC organisation, expanding applications in optics, sensing, and active matter. This review highlights the evolution and potential of LC-containing complex emulsions. Emphasis is placed on emulsions featuring dynamic and reversible morphological transformations and LC reorganisation, underpinning their suitability for tunable micro-lenses, chemical sensing, and biosensing. Nematic LCs within complex emulsions allow for topological defect-driven functionalization, attaching antibodies to induce substantial changes in the LC director field upon interfacial recognition events. This feature may facilitate the development of ultrasensitive chemical and biological sensors. Moreover, cholesteric LCs, through their selective reflection, enable the rapid and sensitive detection of foodborne pathogens. The controlled assembly of magnetic nanoparticles at interfaces illustrates advancements towards magnetic field-responsive and active colloids. Future perspectives include exploiting these properties for intelligent colloidal systems capable of autonomous behaviour, and furthering applications in dynamic photonic devices, high-security identification tags, and responsive lens systems.