Ringlike cores of cylindrically confined nematic point defects

Nematic liquid crystals confined in a cylindrical capillary and subjected to strong homeotropic anchoring conditions is a long-studied fundamental problem that uniquely incorporates nonlinearity, topological stability, defects, and texture physics. The observed and predicted textures that continue to be investigated include escape radial, radial with a line defect, planar polar with two line defects, and periodic array of point defects. This paper presents theory and multiscale simulations of global and fine scale textures of nematic point defects, based on the Landau-de Gennes tensor order parameter equations. The aim of this paper is to further investigate the ringlike nature of point defect cores and its importance on texture transformation mechanisms and stability. The paper shows that the ringlike cores can be oriented either along the cylinder axis or along the radial direction. Axial rings can partially expand but are constrained by the capillary sidewalls. Radial rings can deform into elliptical structures whose major axis is along the capillary axis. The transformation between several families of textures under capillary confinement as well as their stability is discussed in terms of defect ring distortions. A unified view of nematic textures found in the cylindrical cavities is provided.     

Nematodynamics and structures in junctions of cylindrical micropores

ABSTRACT

We explore equilibrium structures and flow-driven deformations of nematic liquid crystals confined to 3D junctions of cylindrical micropores with homeotropic surface anchoring. The topological state of the nematic ordering field in such basic unit of porous networks is controlled by nematic orientation profiles in individual pores, anchoring frustration along the edges of joining pores and coupling to the material flow field. We numerically investigate formation of the flow-aligned configurations in single cylindrical pores and pore junctions. Depending on the arrangement of inlet and outlet flows in the junction, we demonstrate existence of numerous stationary nematic configurations, characterised by specific bulk defects and surface disclinations along joining edges. Observed bulk defects are nonsingular escaped structures, disclinations in the form of loops or disclination lines pinned to the joining edges of the pores. Furthermore, we show examples of defect dynamics during the flow-induced topological transformations.     

Point and ring defects in nematics under capillary confinement

The textures exhibited by nematic liquid crystals confined to cylindrical capillaries under homeotropic anchoring have been studied for nearly thirty years. One of the reasons behind this maintained interest is that the processing of many high-performance fibers including carbon fibers and spider silks involves these textures. Three of these textures, the planar radial with line defect, the planar polar with two line defects (PPLD), and the escape radial (ER), are relatively well understood. A third one, the escape radial with point defects presents, however, some unresolved issues and recent studies have questioned the real nature and dimensionality of the defects involved in this texture. It seems that the defects are not in the form of points but rather in the form of closed lines or rings. This paper presents a detailed study on the connection between point and ring defects in a cylindrical cavity using three-dimensional simulations based on the continuum Landau-de Gennes theory. The results show that true point defects cannot exist in cylindrical cavities and that the merging of two ringlike defects may lead to two qualitatively different stable textures, namely, the ER and PPLD textures. The various results are in qualitative agreement with recent molecular dynamic studies and with theoretical predictions based on experimental observations. The predictions provide new insights on the structural connections between synthetic and biological superfibers.     

Role of surface anchoring and geometric confinement on focal conic textures in smectic-A liquid crystals

A high surface area-to-volume ratio in microchannels increases the importance of surface interactions within them. In layered liquids, such as smectic liquid crystals, surface interactions play an important role in the formation of defect textures. We use 8CB liquid crystal, which is in the smectic-A phase at room temperature, as a model layered liquid. PDMS surfaces can be tuned to be hydrophilic or hydrophobic, and due to the nature of liquid crystalline molecules, we show that this results in planar or homeotropic anchoring conditions, respectively. In a confined system, contrary to the bulk, generated defects cannot grow freely. In the present work, we show that the confinement offered by PDMS microchannels along with the capability of creating mixed anchoring conditions within them results in the formation of particular ordered defect textures through increased surface interactions in smectic-A liquid crystals. Our observations imply that microscale confinement is useful for controlling the size, size distribution, and packing structure of microscale defect structures within these materials. In addition, we show that by placing a droplet of smectic-A liquid crystal on a PDMS surface containing microscale parallel cracks, ordered focal conic defects form between two adjacent cracks. The distance between two adjacent cracks dictates the size of the defects. These observations could lead to useful ideas for exploring new technologies for flexible optical devices or displays that utilize smectic-A liquid crystals.     

Second order elasticity in nematics: A new anchoring source

By considering, in the expression of the nematic free energy density, an additional term in the square of the director second derivatives, an unexpected anchoring source results, due only to surface and bulk elastic constants. As an example, the case of a planar homogeneous and of a homeotropic nematic cell, equally anchored on both walls, is discussed. In both situations the new anchoring source has a destabilizing effect.     

Scanning of the surface polar angle values in liquid crystal cells using the surface memory effect

An optical polarization method for indication of recorded oriented smectic C textures by the process of surface memorization and their accumulation and storage in the nematic temperature range is presented. The recorded accumulated data are identified with the surface conditions-the polar and azimuthal angles. Using strong boundary conditions the assumption is made that the interval for recorded and accumulated textures increases when the anchoring energy is weak.     

Scanning of the surface polar angle values in liquid crystal cells using the surface memory effect

An optical polarization method for indication of recorded oriented smectic C textures by the process of surface memorization and their accumulation and storage in the nematic temperature range is presented. The recorded accumulated data are identified with the surface conditions-the polar and azimuthal angles. Using strong boundary conditions the assumption is made that the interval for recorded and accumulated textures increases when the anchoring energy is weak.     

Orientational defects near colloidal particles in a nematic liquid crystal

We study the interaction between a surface-anchoring colloidal particle and a liquid-crystalline host, and in particular the formation of orientational defects near the particle. A mean-field theory based on the nonlocal Marrucci-Greco nematic potential is used to represent molecular interactions in an inhomogeneous orientational field. An evolution equation for the molecular configuration tensor is solved numerically whose steady state minimizes the total free energy of the system. With strong homeotropic anchoring on the particle surface, three types of solutions may appear depending on initial conditions and particle size: Saturn rings, satellite point defects, and polar rings. The Saturn ring remains stable on micrometer-sized particles, contrary to previous calculations but consistent with experiments. A phase diagram is constructed for the three regimes. Based on the free energy, the most stable state is the Saturn ring for smaller particles and the satellite defect for larger ones.     

Chiral symmetry-breaking dynamics in the phase transformation of nematic droplets

Dynamic simulations of the isotropic–nematic phase transformation of liquid crystal droplets with homeotropic surface anchoring are found to predict chiral symmetry-breaking dynamics. These observations occur when using material parameters for pentyl-cyanobiphenyl (5CB) but not with the single elastic constant approximation for this material, which is frequently used in simulations. The twisting dynamic process occurs during the relaxation of the domain from an unstable radial texture to a stable uniform texture and involves simultaneous defect loop motion and twisting of the bulk nematic texture.     

Transition levels of defects in ZnO: Total energy and Janak's theorem methods

Transition levels of defects are commonly calculated using either methods based on total energies of defects in relevant charge states or energy band single particle eigenvalues. The former method requires calculation of total energies of charged, perfect bulk supercells, as well as charged defect supercells, to obtain defect formation energies for various charge states. The latter method depends on Janak's theorem to obtain differences in defect formation energies for various charge states. Transition levels of V(Zn), V(O), and V(ZnO) vacancy defects in ZnO are calculated using both methods. The mean absolute deviation in transition level calculated using either method is 0.3 eV. Relative computational costs and accuracies of the methods are discussed.     

Spontaneous size selection in cholesteric and nematic emulsions

We study the spontaneous size selection in lyotropic cholesteric (W/O) and thermotropic nematic (O/W) liquid crystal emulsions. The droplet sizes have been characterized by dynamic light scattering, which indicates a narrow monomodal distribution of droplets achieved spontaneously even without emulsion filtration. Anchoring of the director, provided by the chosen surfactant on the interface, may generate a topological defect inside the droplet. Below the critical radius R = K/W, determined by the ratio of Frank elastic and the surface anchoring constants, the effective anchoring strength is weak and droplets are not topologically charged; this allows them to coalesce freely, depleting the size distribution in this range. Large droplets possess a topological charge of +1 and present a high elastic energy barrier for pair coalescence; the resulting size distribution is skewed, with R > R, and effectively frozen.     

Influence of K24 on the structure of nematic liquid crystal droplets

A phenomenological free energy is used to describe the stable ordering of nematic liquid crystals confined to supramicron spherical cavities. In particular the effects of the saddle splay elastic constant, K₂₄, on the equilibrium structures and phase diagram of droplets with homeotropic surface anchoring are discussed. Some structures are illustrated by the corresponding simulated polarization microscope textures. Possibilities for an experimental determination of the saddle-splay elastic constant and surface anchoring strength by studying the radial-axial structural transition in such droplets are analysed. It is shown that the K₂₄ term in the elastic free energy stabilizes a deformed droplet structure even in the limit of the zero anchoring strength.     

Topologically non-equivalent textures generated by the nematic electrohydrodynamics

Some classes of nematic liquid crystals can be driven through turbulent regimes when forced by an external electric field. In contrast to isotropic fluids, a turbulent nematic exhibits a transition to a stochastic regime that is characterised by a network of topological defects. We study the deformations arising after the electric field has been switched-off. In contrast to the turbulent regime, the relaxation of this topological-defect regime involves the annihilation of an interlacement of defect lines. We show that these defect lines separate regions of the nematic having topologically non-equivalent textures.     

Colloid-induced structure in liquid crystal media

The structural perturbations induced by colloidal particles immersed in a model nematic subjected to an external field are calculated employing integral equation methods. Maps of the density-orientational distribution about a colloidal particle are obtained, and these provide a microscopic picture of the colloid's nematic coat. We focus on colloidal particles that favor homeotropic anchoring, but planar anchoring cases are also considered. The range and structure of the nematic coat is shown to be significantly influenced by the nature of the anchoring, the size of the colloidal particle, the range and strength of the colloid-nematogen interaction, and the external field strength. All of these factors are discussed.     

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.     

Computer simulations of nematic droplets

Abstract

Nematic droplets are intimately connected with disclinations, because in nematic droplets, point and line-shaped defects, as well as surface defects, are not generated at random, but inevitably by topological constraints. Thus, droplets provide a good means for investigating nematic defects. There is a growing interest in both topics due to the applications in polymer dispersed liquid crystal devices [1–3], but also in classical display modelling, where nematic defects are to be avoided. Various types of droplets are investigated theoretically with the aid of a previously developed numerical algorithm [4,5], which is based on a dynamic equation for the alignment tensor a _μv. The rotational diffusion, the influence of an orienting external field, and the Frank elasticity (in the one-coefficient approximation) are taken into account, but flow processes are neglected. For the application to nematic droplets, a new type of boundary conditions had to be used, which I have called ‘true planar anchoring’. I simulate the relaxation of the director field of nematic droplets from the isotropic state and vice versa for various types of anchoring and cavity shapes. Contrast pictures, as if viewed under crossed Nicols, are computed and compared to experiment. The results obtained elucidate the nature of the surface disclinations of strength one (boojums). In particular, it is found that their occurrence can be understood as a consequence of the planar anchoring, without any further assumptions. Moreover, a phase transition-like transformation of the director configuration is predicted which is temperature controlled and occurs, as the blue phases do, close to the nematic-isotropic transition temperature T_c.     

Nematic liquid crystal in contact with periodically patterned surfaces

Nematic liquid crystals confined between two different substrates, possessing alternating stripe patterns of planar and homeotropic anchoring, are studied within the Frank–Oseen theory, in which the anchoring energy function is given by the Rapini–Papoular expression. By numerical minimization of the free energy we determine phase transitions between uniform and distorted nematic textures. The calculations reveal that these phase transitions can be triggered by changing the shift of the stripe patterns with respect to each other. A hybrid nematic cell model together with an effective anchoring strength can be used to describe the phase behaviour for sample thicknesses larger than the periodicity of the stripe pattern. Rich phase behaviour is predicted for the case of a generalized expression for the surface free energy.     

Nematic liquid crystal in contact with periodically patterned surfaces

Nematic liquid crystals confined between two different substrates, possessing alternating stripe patterns of planar and homeotropic anchoring, are studied within the Frank-Oseen theory, in which the anchoring energy function is given by the Rapini-Papoular expression. By numerical minimization of the free energy we determine phase transitions between uniform and distorted nematic textures. The calculations reveal that these phase transitions can be triggered by changing the shift of the stripe patterns with respect to each other. A hybrid nematic cell model together with an effective anchoring strength can be used to describe the phase behaviour for sample thicknesses larger than the periodicity of the stripe pattern. Rich phase behaviour is predicted for the case of a generalized expression for the surface free energy.     

Dynamics of nematic point defects in a capillary with tilted boundary conditions

The motion of a single point defect in a cylindrical cavity filled with a nematic liquid crystal is described by solving numerically the simplified equations of nematodynamics. Perfect homeotropic anchoring for the director on the lateral boundary would result in the creation of domains with equal elastic energy, escaped upwards or downwards along the cavity axis and separated by point defects of strength ± 1. Defects do not move as long as they are sufficiently far apart. However, small deviations from homeotropic anchoring remove this degeneracy and the energetically favourable domains start to expand at the expense of the others, thus setting the defects in motion along the tube. We present a new numerical approach, which neglects the backflow, for studying the influence of both the pretilt and the elastic anisotropy (K ₃₃ ≠ K ₁₁) on the motion of a defect. We show how even very small pretilt angles (≈1°) result in speeds observed in experiments. For a moderate elastic anisotropy, the velocity of a +1 defect equals the velocity of a -1 defect, whereas for K ₃₃?K ₁₁ a + 1 defect moves faster than a -1 defect. For small pretilts we confirm a good qualitative agreement with an existing analytical approach, which proves inaccurate for large pretilts.