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 homeotropic and planar anchoring. The two competing orientations are metastable over a broad parameter range. Hence such surfaces can be used to generate bistable surfaces.
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…
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.
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 …
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…
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 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 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.
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 …
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.
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…
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…
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 …
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.
We report on a novel method of dynamically controlling the boundary conditions at the surface of a nematic liquid crystal using a surface flexoelectric effect. By moving the surface directors we show that one is able to manipulate defects which lie near the surface. This can be used to produce switching of a nematic liquid crystal device between two states with very similar free energies. This results in a bistable device that can retain either state with no applied voltage. Switching between the states occurs when the movement of the surface directors rotates those in the bulk which are then …
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 have studied the nucleation and the physical properties of a -1/2 wedge disclination line near the free surface of a confined nematic liquid crystal. The position of the disclination line has been related to the material parameters (elastic constants, anchoring energy and favored anchoring angle of the molecules at the free surface). The use of a planar model for the structure of the director field (whose predictions have been contrasted to those of a fully three-dimensional model) has allowed us to relate the experimentally observed position of the disclination line to the relevant propert…
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…
The anchoring of nematic liquid crystals on surfaces with grafted liquid crystalline chain molecules is studied by computer simulations and within a mean field approach. The computer simulations show that a swollen layer of collectively tilted chains may induce untilted homeotropic (perpendicular) alignment in the nematic fluid. The results can be understood within a simple theoretical model. The anchoring on a layer of mutually attractive chains is determined by the structure of the interface between the layer of chain molecules and the solvent. It is controlled by an interplay between the at…
We investigate the origin of secondary disclinations that were recently described as a new evidence of a biaxial nematic phase in an oxadiazole bent-core thermotropic liquid crystal C7. With an assortment of optical techniques such as polarizing optical microscopy, LC PolScope, and fluorescence confocal polarizing microscopy, we demonstrate that the secondary disclinations represent non-singular domain walls formed in an uniaxial nematic during the surface anchoring transition, in which surface orientation of the director changes from tangential (parallel to the bounding plates) to tilted. Eac…
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 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 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…
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…
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…
Partially wetting nematic liquid crystal (NLC) films on substrates are unstable to dewetting-type instabilities due to destablizing solid/NLC interaction forces. These instabilities are modified by the nematic nature of the films, which influences the effective solid/NLC interaction. In this work, we focus on the influence of imposed substrate anchoring on the instability development. The analysis is carried out within a long-wave formulation based on the Leslie-Ericksen description of NLC films. Linear stability analysis of the resulting equations shows that some features of the instability, …
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…
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…
Here we study theoretically the dynamics of a 2D and a 3D isotropic droplet in a nematic liquid crystal under a shear flow. We find a large repertoire of possible nonequilibrium steady states as a function of the shear rate and of the anchoring of the nematic director field at the droplet surface. We first discuss homeotropic anchoring. For weak anchoring, we recover the typical behaviour of a sheared isotropic droplet in a binary fluid, which rotates, stretches and can be broken by the applied flow. For intermediate anchoring, new possibilities arise due to elastic effects in the nematic flui…
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…
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…
The anchoring of the nematic liquid crystal N-(p-methoxybenzylidene)-p-butylaniline (MBBA) on Langmuir-Blodgett monolayers of fatty acids (COOHC$_{n}$H$_{2n+1}$) was studied as a function of the length of the fatty acid alkyl chains, $n$ ($n = 15, 17, 19, 21$). The monolayers were deposited onto ITO-coated glass plates which were used to assemble sandwich cells of various thickness that were filled with MBBA in the nematic phase. The mechanism of relaxation from the flow-induced quasi-planar to the surface-induced homeotropic alignment was studied for the four decreases linearly with increasin…
Nematic shells are colloidal particles coated with nematic liquid crystal molecules which may freely glide and rotate on the colloid's surface while keeping their long axis on the local tangent plane. We describe the nematic order on a shell by a unit director field on an orientable surface. Equilibrium fields can then be found by minimising the elastic energy, which in general is a function of the surface gradient of the director field. We learn how to extract systematically out of this energy a fossil component, related only to the surface and its curvatures, which expresses a curvature pote…
We present experiments where anisometric colloidal microparticles dispersed in a nematic liquid crystal cell with homeotropic anchoring conditions are dynamically assembled by means of liquid-crystal-enabled electrophoresis (LCEEP) using an AC electric field perpendicular to the confining plates. A nematic host with negative dielectric anisotropy leads to a driving force parallel to the cell plates. We take advantage of the resulting gliding anchoring conditions and the degeneracy in the direction of particle motion to design reconfigurable trajectories using a photosensitive anchoring layer (…
We study the optical properties of gold nanoparticles coated with a nematic liquid crystal whose director field is distributed around the nanoparticle according to the anchoring conditions at the surface of the nanoparticle. The distribution of the nematic liquid crystal is obtained by minimization of the corresponding Frank free-energy functional whilst the optical response is calculated by the discrete-dipole approximation. We find, in particular, that the anisotropy of the nematic liquid-crystal coating does not affect much the (isotropic) optical response of the nanoparticle. However, for …
The temperature behaviour of the anchoring energy of nematic liquid crystal MBBA at the substrates with oblique SiO evaporation and director orientation at the interface have been studied by means of magnetic Freedericksz transition technique. The temperature dependence of the coefficients in the phenomenological model of surface anchoring energy has been determined.
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 study the equilibrium configuration of a nematic liquid crystal bounded by a rough surface. The wrinkling of the surface induces a partial melting in the degree of orientation. This softened region penetrates the bulk up to a length scale which turns out to coincide with the characteristic wave length of the corrugation. Within the boundary layer where the nematic degree of orientation decreases, the tilt angle steepens and gives rise to a nontrivial structure, that may be interpreted in terms of an effective weak anchoring potential. We determine how the effective surface extrapolation len…
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…
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 consider the effective pseudo-Casimir interaction forces mediated by a nematic liquid-crystalline film bounded by two planar surfaces, one of which imposes a random (disordered) distribution of the preferred anchoring axis in the so-called easy direction. We consider both the case of a quenched as well as an annealed disorder for the easy direction on the disordered surface and analyze the resultant fluctuation-induced interaction between the surfaces. In the case of quenched disorder, we show that the disorder effects appear additively in the total interaction and are dominant at intermedi…
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…
The effective interaction between spherical colloids in nematic liquid crystals is investigated in the framework of the Landau-de Gennes theory. The colloids differ through their interaction with the nematic. While both particles induce quadrupolar far-field distortions in the nematic matrix, with unlike quadrupole moments, one favours homeotropic and the other degenerate planar anchoring of the nematic director. In the strong anchoring regime the colloids with homeotropic anchoring are accompanied by an equatorial disclination line defect, known as "Saturn-ring", while the colloids with degen…
Monte Carlo simulation, experiment and continuum theory are used to examine the anchoring exhibited by a nematic liquid crystal at a patterned substrate comprising a periodic array of rectangles that, respectively, promote vertical and planar alignment. It is shown that the easy axis and effective anchoring energy promoted by such surfaces can be readily controlled by adjusting the design of the pattern. The calculations reveal rich behavior: for strong anchoring, as exhibited by the simulated system, for rectangle ratios $\geq 2$ the nematic aligns in the direction of the long edge of the rec…
As an approach to the motion of particles in an anisotropic liquid, we analytically study the Stokes drag of spherical particles in a nematic liquid crystal. The Stokes drag of spherical particles for a general anisotropic case is derived in terms of multipoles. In the case of weak anchoring, we use the well-known distribution of the elastic director field around the spherical particle. In the case of strong anchoring, the multipole expansion may be also used by modifying the size of a particle to the size of the deformation coating. For the case of zero anchoring (uniform director field) we f…
The influence of capillary flow on the alignment of the nematic liquid crystal MBBA on fatty acid Langmuir-Blodgett monolayers was studied by optical second-harmonic generation. The surface dipole sensitivity of the technique allows probing the orientation of the first liquid crystal monolayer in the presence of the liquid crystal bulk. It was found that capillary flow causes the first monolayer of liquid crystal molecules in contact with the fatty acid monolayer to be oriented in the flow direction with a large pretilt (78 degrees), resulting in a quasi-planar alignment with splay-bend deform…
