Activity in nematics drives interfacial flows that lead to preferential alignment that is tangential or planar for extensile systems (pushers) and perpendicular or homeotropic for contractile ones (pullers). This alignment is known as active anchoring and has been reported for a number of systems and described using active nematic hydrodynamic theories. The latter are based on the one-elastic constant approximation, i.e., they assume elastic isotropy of the underlying passive nematic. Real nematics, however, have different elastic constants, which lead to interfacial anchoring. In this paper, we consider elastic anisotropy in multiphase and multicomponent hydrodynamic models of active nematics and investigate the competition between the interfacial alignment driven by the elastic anisotropy of the passive nematic and the active anchoring. We start by considering systems with translational invariance to analyze the alignment at flat interfaces and, then, consider two-dimensional systems and active nematic droplets. We investigate the competition of the two types of anchoring over a wide range of the other parameters that characterize the system. The results of the simulations reveal that the active anchoring dominates except at very low activities, when the interfaces are static. In addition, we found that the elastic anisotropy does not affect the dynamics but changes the active length that becomes anisotropic.
We propose a simple and reliable method to measure the liquid crystal surface anchoring strength by molecular simulation. The method is based on the measurement of the long-range fluctuation modes of the director in confined geometry. As an example, molecular simulations of a liquid crystal in slab geometry between parallel walls with homeotropic anchoring have been carried out using the Monte Carlo technique. By studying different slab thicknesses, we are able to calculate separately the position of the elastic boundary condition, and the extrapolation length.
We theoretically investigate the threshold for the director reorientation from the homeotropic state to the hybrid homeotropic-planar state and vice versa in a cell filled with a flexoelectric nematic liquid crystal (NLC) subjected to an electric field. The liquid crystal is doped by a CTAB-like substance, a part of molecules of which dissociates into positive and negative ions. The anchoring on one of the cell surfaces is assumed to be strong and homeotropic, while the other surface can adsorb positive ions which play the role of an orienting surfactant for NLC molecules on this surface. At c…
Combining molecular simulation, Onsager theory and the elastic description of nematic liquid crystals, we study the dependence of the nematic liquid crystal elastic constants and the zenithal surface anchoring coefficient on the value of the bulk order parameter.
Experimentally it is possible to manipulate the director in a (chiral) smectic-$A$ elastomer using an electric field. This suggests that the director is not necessarily locked to the layer normal, as described in earlier papers that extended rubber elasticity theory to smectics. Here, we consider the case that the director is weakly anchored to the layer normal assuming that there is a free energy penalty associated with relative tilt between the two. We use a recently developed weak-anchoring generalization of rubber elastic approaches to smectic elastomers and study shearing in the plane of …
Recently Biscari, DiCarlo and Turzi ["Anisotropic wave propagation in nematic liquid crystals", to appear (arXiv:1311.1802)] proposed a theory for nematoacustics which models nematic liquid crystals as nematic elastomers with molecular relaxation. Here, we extend the analysis of this theory to account for the director motion possibly induced by the propagation of a sound wave. We find that the director vibration is related to the - usually small - anisotropy of the molecular distribution, thus providing a justification to the relative high ultrasonic intensities required to observe non-negligi…
McMillan liquid crystal model sandwiched between strong homeotropic anchoring walls is studied. Phase transitions between isotropic, nematic, and smectic A phases are investigated for wide ranges of an interaction parameter and of the system thickness. It is confirmed that the anchoring walls induce an increase in transition temperatures, dissappearance of phase transitions, and an appearance of non-spontaneous nematic phase. The similarity between influence of anchoring walls and that of external fields is discussed.
In the mean field approximation, we evaluate the temperature dependence of the anchoring energy strength of a nematic liquid crystal in contact with a solid substrate due to thermal fluctuations. Our study is limited to the weak anchoring case, where the microscopic surface energy is small with respect to the mean field energy due to the nematic phase. We assume furthermore that the physical properties of the substrate can be considered temperature independent in the range of the nematic phase. According to the thermodynamical perturbative approach, the macroscopic surface energy is deduced by…
We present a Monte Carlo study of external surface anchoring in nematic cells with partially disordered solid substrates, as well as of intrinsic anchoring at free nematic interfaces. The simulations are based on the simple hexagonal lattice model with a spatially anisotropic intermolecular potential. We estimate the corresponding extrapolation length $b$ by imposing an elastic deformation in a hybrid cell-like nematic sample. Our estimates for $b$ increase with increasing surface disorder and are essentially temperature--independent. Experimental values of $b$ are approached only when both th…
We propose a theoretical model of the light-induced director slippage effect. In this effect the bulk director reorientation contributes to the surface director reorientation It is found that the director and ellipticity profiles, obtained in the geometric optics approximation, are dependent on the ellipticity of the incident light wave. The director distribution is spatially modulated in linearly polarized light but grows monotonically in circularly polarized light. The surface director deviation has been examined, and comparison made with existing experimental data, which then permits the ma…
The isotropic-to-nematic transition in liquid crystals is studied in d=3 spatial dimensions. A simulation method is proposed to measure the angle dependent interfacial tension g(theta), with theta the anchoring angle of the nematic phase at the interface. In addition, an alternative liquid crystal model is introduced, defined on a lattice. The advantage of the lattice model is that accurate simulations of anchoring effects become possible. For the lattice model, g(theta) depends sensitively on the nearest-neighbor pair interaction, and both stable and metastable anchoring angles can be detecte…
We propose a simple surface potential favoring the planar degenerate anchoring of nematic liquid crystals, i.e., the tendency of the molecules to align parallel to one another along any direction parallel to the surface. We show that, at lowest order in the tensorial Landau-de Gennes order-parameter, fourth-order terms must be included. We analyze the anchoring and wetting properties of this surface potential. In the nematic phase, we find the desired degenerate planar anchoring, with positive scalar order-parameter and some surface biaxiality. In the isotropic phase, we find, in agreement wit…
We investigate the effects of electric double layers and flexoelectricity on the surface anchoring in general nematic fluids. Within a simplified model, we demonstrate for a nematic electrolyte how the surface anchoring strength can be affected by the surface charge, bulk ion concentration and/or flexoelectricity, effectively changing not only the magnitude of the anchoring but also the anchoring type, such as from planar to tilted. In particular, we envisage possible tuning of the anchoring strength by the salt concentration in the regime where sufficiently strong electrostatic anchoring, as …
By means of a molecular model, we examine hybrid nematic films with antagonistic anchoring angles where one of the surfaces is in the strong anchoring regime. If anchoring at the other surface is weak, and in the absence of wetting by the isotropic phase, the anchoring transition may interact with the capillary isotropic-nematic transition in interesting ways. For general anchoring conditions on this surface we confirm the existence of the step-tilt, biaxial phase and the associated transition to the linear, constant-tilt-rotation, configuration. The step-like phase is connected with the bulk …
As recently reported [Turiv T. et al., Science, 2013, Vol. 342, 1351], fluctuations in the orientation of the liquid crystal (LC) director can transfer momentum from the LC to a colloid, such that the diffusion of the colloid becomes anomalous on a short time scale. Using video microscopy and single particle tracking, we investigate random thermal motion of colloidal particles in a nematic liquid crystal for the time scales shorter than the expected time of director fluctuations. At long times, compared to the characteristic time of the nematic director relaxation we observe typical anisotropi…
We analyze the interplay between wetting and anchoring of nematic liquid crystals on disordering, e.g., rough substrates in the framework of the Landau-de Gennes theory, in situations of competing homeotropic and planar easy axes on the substrate and the nematic-isotropic (NI) interface. The phase diagram for azimuthally symmetric substrates is calculated. We identify two regimes - a strongly coupled regime, where the wetting transition coincides with an anchoring transition, and a weakly coupled regime, where the two are separated. The anchoring transition is first order and switches between …
We introduce a coarse-grained description of the surface energy of a nematic liquid crystal. The thermal fluctuations of the nematic director close to the surface renormalize at macroscopic scales the bare surface potential in a temperature-dependent way. The angular dependence of the renormalized potential is dramatically smoothed, thus explaining the success of the Rapini-Papoular form. Close to the isotropic phase, the anchoring energy is strongly suppressed and the change of its shape allows for anchoring transitions. Our theory describes quantitatively the temperature dependence of the an…
We study theoretically the formation of long-wavelength instability patterns observed at spreading of nematic droplets on liquid substrates. The role of surface-like elastic terms such as saddle-splay and anchoring in nematic films of submicron thickness is (re)examined by extending our previous work [Manyuhina et al EPL, 92, 16005 (2010)] to hybrid aligned nematics. We identify the upper threshold for the formation of stripes and compare our results with experimental observations. We find that the wavelength and the amplitude of the in-plane director undulations can be related to the small bu…
In this paper we revisit the problem of a nematic liquid crystal in contact with patterned substrates. The substrate is modelled as a periodic array of parallel infinite grooves of well-defined cross section sculpted on a chemically homogeneous substrate which favors local homeotropic anchoring of the nematic. We consider three cases: a sawtooth, a crenellated and a sinusoidal substrate. We analyse this problem within the modified Frank-Oseen formalism. We argue that, for substrate periodicities much larger than the extrapolation length, the existence of different nematic textures with distinc…
We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary co…
Various director configurations of a nematic liquid crystal, confined in a toroidal volume and subject to an external magnetic field, were evaluated numerically by performing finite element calculations in three dimensions. The equilibrium director field is found from a minimization of the elasto-magnetic energy of the nematic. The director at the inner surface of the torus is fixed, either along homeotropic or tangential direction. We consider both a homogeneous and an azimuthal magnetic field, with its direction being in conflict with the respective surface anchoring. The relative stability …
The critical field of the Freedericksz transition and switching dynamics are investigated for polymer stabilized nematic liquid crystals as a function of polymer concentration. A simple phenomenological model is proposed to describe the observed critical field and dynamic response time behaviors as a function of concentration. In this model the polymer fibrils form director domains, which are bounded by virtual surfaces with a finite anchoring energy. The Freedericksz transition occurs independently within each of these domains.
The director configuration of disclination lines in nematic liquid crystals in the presence of an external magnetic field is evaluated. Our method is a combination of a polynomial expansion for the director and of further analytical approximations which are tested against a numerical shooting method. The results are particularly simple when the elastic constants are equal, but we discuss the general case of elastic anisotropy. The director field is continuous everywhere apart from a straight line segment whose length depends on the value of the magnetic field. This indicates the possibility of…
Advent of nematic liquid crystals flows have attracted renewed attention in view of microfluidic transport phenomena. Among various transport processes, electroosmosis stands as one of the efficient flow actuation method through narrow confinement. In the present study, we explore the electrically actuated flow of a nematic fluid with ionic inclusions taking into account the influences from surface induced elastic and electrical double layer phenomena. Influence of surface effects on the flow characteristics is known to get augmented in micro-confined environment and must be properly addressed…
We solve the forward and inverse problems associated with the transformation of flat sheets to surfaces of revolution with non-trivial topography, including Gaussian curvature, without a stretch elastic cost. We deal with systems slender enough to have a small bend energy cost. Shape change is induced by light or heat causing contraction along a non-uniform director field in the plane of an initially flat nematic sheet. The forward problem is, given a director distribution, what shape is induced? Along the way, we determine the Gaussian curvature and the evolution with induced mechanical defor…
A dilute suspension of carbon nanotubes (CNTs) in a nematic liquid crystal (LC) does not disturb the LC director. Due to a strong LC-CNT anchoring energy and structural symmetry matching, CNT long axis follows the director field, possessing enhanced dielectric anisotropy. This strong anchoring energy stabilizes local pseudo-nematic domains, resulting in non-zero dielectric anisotropy in the isotropic phase. These anisotropic domains respond to external electric fields and show intrinsic frequency response. The presence of these domains makes the isotropic phase field-responsive, giving rise to…
Elliptic shear applied to a homeotropically oriented nematic above the electric bend Freedericks transition (FT) generates slow precession of the director. The character of the accompanying nonlinear waves changes from diffusive phase waves to dispersive ones exhibiting spirals and spatio-temporal chaos as the FT is approached from above. An exact solution of the flow alignment equations captures the observed precession and predicts its reversal for non-flow aligning materials. The FT transforms into a Hopf bifurcation opening the way to understand the wave phenomena.
We analyse the homogeneous instabilities in a nematic liquid crystal subjected to plane steady Couette or Poiseuille flow in the case when the director is pre-aligned perpendicular to the flow plane taking into account weak anchoring at the confining surfaces. The critical shear rate decreases for decreasing anchoring strength and goes to zero in the limit of torque-free boundary conditions. For Poiseuille flow one has two types of instability depending on the values of the azimuthal ($W_a$) and polar ($W_p$) surface anchoring strengths. The critical line in $(W_a,W_p)$ space which separates t…
Using laser tweezers and fluorescence confocal polarizing microscopy, we study colloidal interactions of solid microspheres in the nematic bulk caused by elastic distortions around the particles with strong tangential surface anchoring. The particles aggregate into chains directed at about 30 degrees to the far field director and, at higher concentrations, form complex kinetically trapped structures. We characterize the distance and angular dependencies of the colloidal interaction forces.
The surface alignment of lyotropic chromonic liquid crystals (LCLCs) can be not only planar (tangential) but also homeotropic, with self-assembled aggregates perpendicular to the substrate, as demonstrated by mapping optical retardation and by three-dimensional imaging of the director field. With time, the homeotropic nematic undergoes a transition into a tangential state. The anchoring transition is discontinuous and can be described by a double-well anchoring potential with two minima corresponding to tangential and homeotropic orientation.
Understanding the flow of liquid crystals in microfluidic environments plays an important role in many fields, including device design and microbiology. We perform hybrid lattice-Boltzmann simulations of a nematic liquid crystal flowing under an applied pressure gradient in two-dimensional channels with various anchoring boundary conditions at the substrate walls. We investigate the relation between flow rate and pressure gradient and the corresponding profile of the nematic director, and find significant departures from the linear Poiseuille relation. We also identify a morphological transiti…
The McMillan liquid crystalline models under the influence of homeotropic anchoring walls and of external fields are investigated. For thin systems, the existence of the critical thickness, below which the system does not undergo a discrete phase transition, is confirmed. Apparent differences between the influence of the anchoring walls and of external fields are elucidated by investigating the order parameters and a temperature vs external field phase diagram for the bulk systems.
Nematic phase is the most fundamental mesophase exhibited by most of the rod shaped anisotropic liquid crystalline molecules. Nematics are orientationally ordered fluids whose average orientation direction can be manipulated on application of electric and magnetic fields. Carbon nanotube (CNT), a highly shape anisotropic object can find numerous industrial application because of its interesting electronic and mechanical properties. The self-organizing properties of nematics can be used to align CNTs dispersed in them. We have dispersed functionalized CNTs in nematic liquid crystal and carried …
To model a nematic emulsion consisting of a surfactant-coated water droplet dispersed in a nematic host, we performed a molecular dynamics simulation of a droplet immersed in a system of 2048 Gay-Berne ellipsoids in a nematic phase. Strong radial anchoring at the surface of the droplet induced a Saturn ring defect configuration, consistent with theoretical predictions for very small droplets. A surface ring configuration was observed for lower radial anchoring strengths, and a pair of point defects was found near the poles of the droplet for tangential anchoring. We also simulated the falling …
We studied in-plane bistable alignments of nematic liquid crystals confined by two frustrated surfaces by means of Monte Carlo simulations of the Lebwohl-Lasher spin model. The surfaces are prepared with orientational checkerboard patterns, on which the director field is locally anchored to be planar yet orthogonal between the neighboring blocks. We found the director field in the bulk tends to be aligned along the diagonal axes of the checkerboard pattern, as reported experimentally [J.-H. Kim et al., Appl. Phys. Lett. 78, 3055 (2001)]. The energy barrier between the two stable orientations i…
We perform optical, surface anchoring, and textural studies of an organo-siloxane tetrapode material in the broad temperature range of the nematic phase. The optical, structural, and topological features are compatible with the uniaxial nematic order rather than with the biaxial nematic order, in the entire nematic temperature range -25C < T < 46C studied. For homeotropic alignment, the material experiences surface anchoring transition, but the director can be realigned into an optically uniaxial texture by applying a sufficiently strong electric field. The topological features of textures in …
We present a study of the hydrodynamics of an active particle, a model squirmer, in an envi- ronment with a broken rotational symmetry: a nematic liquid crystal. By combining simulations with analytic calculations, we show that the hydrodynamic coupling between the squirmer flow field and liquid crystalline director can lead to re-orientation of the swimmers. The preferred orientation depends on the exact details of the squirmer flow field. In a steady state, pushers are shown to swim parallel with the nematic director while pullers swim perpendicular to the nematic director. This behaviour ar…
We report on the alignment transition of a nematic liquid crystal from initially homeotropic to quasi-planar due to field-induced anchoring breaking. The initial homeotropic alignment is achieved by Langmuir-Blodgett monolayers. In this geometry the anchoring strength can be evaluated by the Frederiks transition technique. Applying an electric field above a certain threshold provokes turbulent states denoted DSM1 and DSM2. While DSM1 does not affect the anchoring, DSM2 breaks the coupling between the surface and the liquid crystal: switching off the field from a DSM2 state does not immediately…
Successful realization of ferromagnetic nematic liquid crystals has opened up the possibility to experimentally study a completely new set of fundamental physical phenomena. In this contribution we present a detailed investigation of some aspects of the static response and the complex dynamics of ferromagnetic liquid crystals under the application of an external magnetic field. Experimental results are then compared with a macroscopic model. Dynamics of the director were measured by optical methods and analyzed in terms of a theoretical macroscopic model. A dissipative cross-coupling coefficie…
We study electrophoretic mobility of metal-dielectric Janus particles with dipolar director profile in two nematic liquid crystals (LCs) having same (positive) conductivity anisotropy and opposite dielectric anisotropy. The applied ac electric field is parallel and perpendicular to the director for the positive and negative dielectric anisotropy LCs, respectively. The velocity of the Janus particles in both LCs is significantly higher than that of the non-Janus particles. We map the electroosmotic flow fields surrounding the particles using microparticle image velocimetry ($μ$-PIV) and show th…
We present numerical and analytic results for uniaxial and biaxial order at the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory. We study the case where an oblique anchoring condition is imposed asymptotically on the nematic side of the interface, reproducing results of previous work when this condition reduces to planar or homoeotropic anchoring. We construct physically motivated and computationally flexible variational profiles for uniaxial and biaxial order, comparing our variational results to numerical results obtained from a minimization of the Ginzburg-Landau-de Genn…
We study the phase diagram of director structures in cholesteric liquid crystals of negative dielectric anisotropy in homeotropic cells of thickness d which is smaller than the cholesteric pitch p. The basic control parameters are the frustration ratio d/p and the applied voltage U. Fluorescence Confocal Polarising Microscopy allows us to directly and unambiguously determine the 3-D director structures. The results are of importance for potential applications of the cholesteric structures, such as switchable gratings and eyewear with tunable transparency based.
We examine fluctuation-induced (pseudo-Casimir) interactions in nematic liquid-crystalline films confined between two surfaces, where one of the surfaces imposes a strong homeotropic anchoring (ensuring a uniform mean director profile), while the other one is assumed to be a chemically disordered substrate exhibiting an annealed, random distribution of anchoring energies. We employ a saddle-point approximation to evaluate the free energy of interaction mediated between the two surfaces and investigate how the interaction force is influenced by the presence of disordered surface anchoring energ…
We provide a minimal model for an active nematic film in contact with both a solid substrate and a passive isotropic fluid, and explore its dynamics in one and two dimensions using a combination of hybrid Lattice Boltzmann simulations and analytical calculations. By imposing nematic anchoring at the substrate while active flows induce a preferred alignment at the interface ("active anchoring"), we demonstrate that directed fluid flow spontaneously emerges in cases where the two anchoring types are opposing. In one dimension, our model reduces to an analogue of a loaded elastic column. Here, th…
We study two-dimensional equilibrium configurations of nematic liquid crystal (NLC) director in a cell confined between two parallel surfaces: a planar surface and a spatially modulated one. The relief of the modulated surface is described by a smooth periodic sine-like function. The director easy axis orientation is homeotropic at one of the bounding surfaces and is planar at the other one. Strong NLC anchoring with both surfaces is assumed. We consider the case where disclination lines occur in the bulk of NLC strictly above local extrema of the modulated surface. These disclination lines ru…
Active flows drive anchoring of nematics at rigid walls
Princeton University（普林斯顿大学）；Rudolf Peierls Centre for Theoretical Physics, University of Oxford（牛津大学鲁道夫·派尔斯理论物理中心）；Department of Chemical Engineering, Indian Institute of Technology, Madras（印度马德拉斯理工学院化学工程系）；Jožef Stefan Institute（约热普史特凡研究所）；University of Ljubljana, Faculty of Mathematics and Physics（卢布尔雅那大学数学与物理学院）
The dielectric dispersion in the uniaxial nematic liquid crystals affects the switching dynamics of the director, as the dielectric torque is determined by not only the present values of the electric field and director but also by their past values. We demonstrate that this dielectric memory leads to an unusual contribution to the dielectric torque that is linear in the present field and thus polarity-sensitive. This torque can be used to accelerate the switch-off phase of director dynamics.
Study of electrokinetics of nematic liquid crystals (LCs) with dissolved impurities hold utmost importance in understanding director distribution characteristics and modified flow rheology. However, no concrete theory for the non-uniform potential and ionic species distribution, due to an induced electrical double layer (EDL) at the LC-substrate interface, derived from fundamental principles have been put forward in this regard. In this work, we have developed coupled governing equations from fundamental free energy considerations for the potential distribution and the director configuration o…
The interaction between two spherical colloidal particles with degenerate planar anchoring in a nematic media is studied by numerically minimizing the bulk Landau-de Gennes and surface energy using a finite element method. We find that the energy achieves its global minimum when the particles are in close contact and making an angle $θ= 28^\circ \pm 2$ with respect to the bulk nematic director, in agreement with the experiments. Although the quadrupolar structure of the director field is preserved in the majority of configurations, we show that for smaller orientation angles and at smaller int…
Capillary microflows of liquid crystal phases are central to material, biological and bio-inspired systems. Despite their fundamental and applied significance, a detailed understanding of the stationary behaviour of nematic liquid crystals (NLC-s) in cylindrical capillaries is still lacking. Here, using numerical simulations based on the continuum theory of Leslie, Ericksen and Parodi, we investigate stationary NLC flows within cylindrical capillaries possessing homeotropic (normal) and uniform planar anchoring conditions. By considering the material parameters of the flow-aligning NLC, 5CB, w…
We report the results of Monte Carlo simulations of the Lebwohl--Lasher model of nematic liquid crystals confined to cylindrical cavities with homeotropic anchoring. We show that the ratio of the bulk to surface couplings is not in general equal to the corresponding parameter K/W used in elastic theory (where K is the Frank elastic constant in the one constant approximation and W is the surface anchoring strength). By measuring the temperature dependence of K/W (which is equivalent to the surface extrapolation length) we are able to reconcile the results of our simulations as well as others wi…
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 s…
We study translational and rotational diffusion of anisotropic gold nanoparticles (NPs) dispersed in the bulk of a nematic liquid crystal fluid host. Experimental data reveal strong anisotropy of translational diffusion with respect to the uniform far-field director, which is dependent on shape and surface functionalization of colloids as well as on their ground-state alignment. For example, elongated NPs aligned parallel to the far-field director translationally diffuse more rapidly along the director whereas diffusion of NPs oriented normal to the director is faster in the direction perpendi…
Tactoids are spindle shaped-droplets of a uniaxial nematic phase suspended in the co-existing isotropic phase. They are found in dispersions of a wide variety of elongated colloidal particles, including actin, fd virus, carbon nanotubes, vanadium peroxide and chitin nanocrystals. Recent experiments on tactoids of chitin nanocrystals in water show that electric fields can very strongly elongate tactoids even though the dielectric properties of the co-existing isotropic and nematic phases differ only subtly. We develop a model for partially bipolar tactoids, where the degree of bipolarness of th…
A nematic liquid crystal in contact with a grating surface possessing an alternating stripe pattern of locally homeotropic and planar anchoring is studied within the Frank--Oseen model. The combination of both chemical and geometrical surface pattern leads to rich phase diagrams, involving a homeotropic, a planar, and a tilted nematic texture. The effect of the groove depth and the anchoring strengths on the location and the order of phase transitions between different nematic textures is studied. A zenithally bistable nematic device is investigated by confining a nematic liquid crystal betwee…
Disclination lines in nematic liquid crystals can exist in different geometric conformations, characterised by their director profile. In certain confined, colloidal and even more prominently in chiral nematics, the director profile may vary along the disclination line. We construct a robust geometric decomposition of director profile variations in closed disclination loops based on a quaternion description and use it to apply topological classification to linked loops with arbitrary variation of the profile. The description bridges the gap between the known abstract classification scheme deri…
We revisit the classic problem of the structure of the isotropic-nematic interface within Ginzburg-Landau-de Gennes theory, refining previous analytic treatments of biaxiality at the interface. We compare our analysis with numerical results obtained through a highly accurate spectral collocation scheme for the solution of the Landau-Ginzburg-de Gennes equations. In comparison to earlier work, we obtain improved agreement with numerics for both the uniaxial and biaxial profiles, accurate asymptotic results for the decay of biaxial order on both nematic and isotropic sides of the interface and a…
