Influence of weak anchoring on flow instabilities in nematic liquid crystals

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 prealigned 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 two types of instability arise 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 the two instabilities regimes is obtained.     

Influence of weak anchoring on flow instabilities in nematic liquid crystals

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 prealigned 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 two types of instability arise 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 the two instabilities regimes is obtained.     

Modelling of the simple shear flow of a flow-aligning nematic

The shear flow induced deformations of a nematic liquid crystal layer have been modelled numerically for the case of flow-aligning nematics. The director deviation from the plane of shear, which was predicted earlier for special surface orientation angles, has been confirmed. This deformation takes a form of director rotation about the axis perpendicular to the layer plane. As a result, transverse flow of the nematic arises. The rotation angle is close to pi at sufficiently strong shear stress, and the director is oriented at the usual flow alignment angle in a significant part of the layer. The director coming out of the shear plane should not be treated as a separate effect taking place during the flow, but rather as a way in which the usual flow-aligned structure is achieved.     

Equivalent anchoring energy formula of a NLC on a grating surface and VCT effect

The voltage-controlled twist (VCT) effect shows that a grating surface, with its particular anchoring properties, has the potential to become a new surface anchoring for liquid crystal devices. In order to describe these properties an equivalent anchoring energy is introduced. The alignment of a nematic liquid crystal (NLC) on such a grating originates from two mechanisms, so each produces a term in the equivalent anchoring energy. One is the interaction potential between NLC molecules and the molecules on the substrate surface, from which we derive the expression of the corresponding term. The other is the increased elastic strain energy, for which we adopt the result of Berreman. The equivalent anchoring energy obtained is a function of pitch λ and amplitude δ of the grating surface. Both the corresponding strength parameter and the easy direction are functions of λ and δ. The hybrid aligned nematic cell proposed by. Bryan-Brown et al. is studied by the use of our formula, and the distribution of the director, the saturation state and the saturation voltage are calculated in detail. The results are consistent with experimental data, especially the values of λ and δ. The VCT effect can therefore be explained.     

Dynamic behaviour at a nematic liquid crystal-rubbednylon interface using evanescent wave photon correlation spectroscopy

Photon correlation spectroscopy of light scattered by director fluctuations from an evanescent optical wave propagating in the nematic liquid crystal 5CB is used to study the interfacial dynamic behaviour of the liquid crystal. The intensity correlation function of light scattered by interfacial orientation fluctuations is measured by illuminating to give a short optical penetration depth within the nematic. These surface scattering correlation functions strongly differ from the bulk correlation function and are interpreted in terms of a nematic surface orientation mode arising from the coupling between the director field and the fluid velocity. It is shown that the analysis of the surface mode gives a method for measuring anchoring energies in liquid crystals. The anchoring energy obtained for rotation of the director away from the rubbing direction about an axis normal to the surface for 5CB at a rubbed nylon surface is 7.14±0.7 × 10-² ergcm-².     

Orientational instability of nematic liquid crystal in a homeotropic cell with boundary conditions controlled by an electric field

We study the orientational instability of the director in a homeotropic nematic liquid crystal (NLC) cell in a DC electric field. The electric field is applied along or perpendicular to a cell surface depending on whether anisotropy of dielectric permittivity of NLC is positive or negative. The easy axis on one of the cell polymer substrates is allowed to deviate in perpendicular to the substrate plane due to the influence of the NLC and the electric field. It was established that the orientational instability of the director can have a threshold as well as be thresholdless which depends on the character of the coupling of the easy axis with the electric field. The temporal behaviour of a director and the easy axis during transition to the stationary state after turning on electric field and returning to the initial homogeneous state after turning off the field was investigated. In the case of the negative anisotropy of the static permittivity, the comparison of experimental and calculated time dependences of the easy axis reorientation angle let us to estimate values of the mobile easy axis viscosity coefficient and coupling parameter describing the coupling between the easy axis and the electric field.     

On the non-symmetric planar aligned NLC cell

The planar aligned nematic liquid crystal cell with different anchoring for the two substrates (i.e. a non-symmetric NLC cell) is investigated by an analytical method. We deduce the basic equations and the boundary conditions of the tilt angle θ of the LC director. Expressions for threshold and saturation magnetic field are obtained, and numerical results of these two quantities with variation in anchoring parameters of the two substrates are given. A symmetry breaking parameter Δ is introduced and the relations between Δ and applied field, as well as the two sets of anchoring parameters are discussed in detail. A feasible experimental plan for measurement of anchoring strengths of a series of different substrates is proposed.     

Analysis of transient periodic textures in nematic polymers

A numerical solution of the Leslie-Ericksen equations for nematic liquid crystals is obtained for in-plane rotation of a strong magnetic field. A transient periodic orientation develops as a result of in-plane director motion and the induced shear flow. At long times the in-plane director orientation results in steady splay-bend inversion walls. A linear stability analysis shows that the inversion walls are unstable to perturbations out of the plane for elastic coefficients characteristic of nematic polymers. Calculations of transmitted light intensity through crossed polarizers for the computed orientation development predict the evolution of a banded texture, as observed experimentally.     

Twist viscosities and flow alignment of biaxial nematic liquid crystal phases of a soft ellipsoid-string fluid studied by molecular dynamics simulation

We have calculated the twist viscosity and the alignment angle between the director and the stream lines in shear flow of a liquid crystal model system, which forms biaxial nematic liquid crystals, as functions of the density, from the Green-Kubo relations by equilibrium molecular dynamics simulation and by a nonequilibrium molecular dynamics algorithm, where a torque conjugate to the director angular velocity is applied to rotate the director. The model system consists of a soft ellipsoid-string fluid where the ellipsoids interact according a repulsive version of the Gay-Berne potential. Four different length-to-width-to-breadth ratios have been studied. On compression, this system forms discotic or calamitic uniaxial nematic phases depending on the dimensions of the molecules, and on further compression a biaxial nematic phase is formed. In the uniaxial nematic phase there is one twist viscosity and one alignment angle. In the biaxial nematic phase there are three twist viscosities and three alignment angles corresponding to the rotation around the various directors and the different alignments of the directors relative to the stream lines, respectively. It is found that the smallest twist viscosity arises by rotation around the director formed by the long axes, the second smallest one arises by rotation around the director formed by the normals of the broadsides, and the largest one by rotation around the remaining director. The first twist viscosity is rather independent of the density whereas the last two ones increase strongly with density. One finds that there is one stable director alignment relative to the streamlines, namely where the director formed by the long axes is almost parallel to the stream lines and where the director formed by the normals of the broadsides is almost parallel to the shear plane. The relative magnitudes of the components of the twist viscosities span a fairly wide interval so this model should be useful for parameterisation experimental data.     

On a Possible Mechanism for the Spontaneous Freedericksz Effect

Kaznacheev and Sonin have presented a model to explain the so-called spontaneous Freedericksz transition in nematic liquid crystals (1983, Sov. Phys. solid Sr, 25, 528; 1984, Ibid, 26, 486). A surface polarization, coupled with the negative anisotropy of the nematic, turns the two homeotropic anchoring plates into planar anchoring plates. We show that this model, correctly solved, cannot explain the observed critical thickness. The spontaneous Freedericksz transition is in fact the surface instability of a hybrid cell with weak planar anchoring.     

Interplay between shear flow and elastic deformations in liquid crystals

We study shear flow in liquid crystal cells with elastic deformations using a lattice Boltzmann scheme that solves the full, three-dimensional Beris-Edwards equations of hydrodynamics. We consider first twisted and hybrid aligned nematic cells, in which the deformation is imposed by conflicting anchoring at the boundaries. We find that backflow renders the velocity profile non Newtonian, and that the director profile divides into two regions characterized by different director orientations. We next consider a cholesteric liquid crystal, in which a twist deformation is naturally present. We confirm the presence of secondary flow for small shear rates, and are able to follow the dynamical pathway of shear-induced unwinding, for higher shear rates. Finally, we analyze how the coupling between shear and elastic deformation can affect shear banding in an initially isotropic phase. We find that for a nematic liquid crystal, elastic distortions may cause an asymmetry in the dynamics of band formation, whereas for a cholesteric, shear can induce twist in an initially isotropic sample.     

The effect of replacing a benzene ring with a saturated six-membered ring on the mesomorphic properties of 4,4′-disubstituted diphenyldiacetylenes

We present new results of experimental investigations of azimuthal director reorientation dynamics for a nematic liquid crystal on solid substrates. Two types of substrate with weak anchoring were studied: glass/polystyrene and glass/UV‐activated dye. Slow and fast relaxation processes were observed in both cases under the action of a strong ‘in‐plane’ electric field. The slow surface reorientation and memory effects were controlled by two parameters: the electric voltage and the excitation time. It was established that the increase of the excitation time results in a slowing of the relaxation of the system to the initial state after turning off the electric field. A phenomenological model of a gliding of easy axes is proposed to explain the slow relaxation process.     

Static periodic distortion above bend Freedericksz transition in nematics

The linearized mathematical model developed by Allender, Hornreich and Johnson [1987, Phys. Rev. Lett., 59, 2654], for explaining the appearance of the magnetic field induced stripe phase (SP) above the bend Freedericksz threshold in a nematic close to the smectic transition, is generalized to the case of uniform tilt θ₁ of the nematic director n₀ away from the homeotropic with the field H acting normal to n₀. Calculations of SP threshold and domain wave vector Q are presented for different elastic ratios and tilts θ₁, by exact computation of the ground state homogeneous deformation (HD) under the rigid anchoring hypothesis. Approximate estimates based on energetics, explicitly taking into account the modal symmetry of perturbations, agree well with the results of exact calculations based on the solution of torque equations. For homeotropic alignment (θ₁ = 0) calculations predict that the SP domain width should decrease when the sample is heated away from the smectic transition point; at a given temperature when H is rotated through a small angle with respect to the sample planes the domains should grow wider. These points can be verified experimentally. It is also shown that for sufficiently high initial tilt θ₁ away from the homeotropic director alignment, SP may be quenched. Materials, such as nematic polymers, which exhibit static periodic domains (PD) in splay geometry (of the kind discovered by Lonberg and Meyer, 1985, Phys. Rev. Lett., 55, 718) may also show SP for director tilts θ₁ close to the homeotropic. It appears possible to make tentative predictions regarding the effects of weak anchoring and oblique magnetic fields on the SP threshold and domain wave vector.     

Oscillating Poiseuille flow in photo-aligned liquid crystal cells

We present an experimental study of thin liquid crystal (LC) layers under the action of a harmonically varied pressure gradient. Optical measurements were performed to register the linear oscillations of a nematic director related to homeotropic and homeoplanar (hybrid) initial states. In the latter case one of the inner surfaces of the rectangular channels was treated by ultraviolet light to provide a relatively weak planar anchoring. The optical response of hybrid and homeotropic LC cells under an oscillating pressure gradient was investigated in relation to on the amplitude and frequency of the pressure gradient. A hydrodynamic model is developed taking into account the LC polar anchoring strength and the surface viscosity responsible for a fast LC surface dynamics. Our estimates show that the thickness of the boundary layer corresponding to the surface viscosity does not exceed 10^-6 m, and further experiments are needed with thinner LC cells and higher frequency oscillations to achieve a more precise value. An oscillating Poiseuille flow in the hybrid cell was found to be useful for characterizing elastic and viscous properties of a weakly anchoring LC surface layer in a fast surface dynamic process.     

Nemato-capillarity theory and the orientation-induced Marangoni flow

The macroscopic equations of nemato-capillarity, including the interfacial linear momentum balance equation and the interfacial director torque balance equation, are presented. The interfacial linear momentum balance equation for isotropic fluid-nematic liquid crystals involves the surface divergence of the surface stress tensor. It is shown that the surface stress tensor for isotropic fluid-nematic interfaces is, in most cases of interest, dominated by elastic modes. It is found that the anisotropic elastic contribution to the surface stress tensor gives rise to bending stresses, not observed in interfaces between isotropic fluids. In addition it is found that the anisotropic contribution to the surface elasticity also gives rise to tangential forces. Thus when the director orientation deviates from the easy axis of an isotropic fluidnematic interface and the deviation has surface gradients, an orientation-driven Marangoni flow can exist. The strength of this novel effect is proportional to the anchoring energy of the interface, and the direction of flow is from low energy regions towards high energy regions, that is, from regions where the director is aligned along the easy axis towards regions where the director deviates from the easy axis.     

Generalised technique for calculation of plane director profiles in bounded nematic liquid crystals

We propose an improved conformal mapping technique for analytical calculation of two-dimensional profiles of the nematic liquid crystal (NLC) director in a cell with a simply connected cross-sectional region. We consider the case of the strong anchoring and the piecewise constant director pretilt on the piecewise smooth curve which bounds the region. Obtained expressions for the director profile explicitly depend on the conformal mapping which maps the region onto the upper half plane of a complex plane. An advantage of our method in comparison with the standard conformal mapping technique is that it does not require the knowledge of the inverse mapping and the calculation of the integral in the Poisson formula. Proposed technique allows to take into account topological defects in the bulk of the NLC on the symmetry axis of the region. As an example of how the method can be used, we find an analytical expression for the director profile in a horizontal cylindrical groove partly filled with the NLC. We consider the case where a disclination line parallel to the axis of the groove occurs in the bulk of the NLC. The equilibrium position of the disclination line is found.     

Disclinations dynamics in confined nematic liquid crystals: strong anchoring

We have investigated the dynamics of pair annihilation of disclination lines in strong anchoring. This work is based on the Frank free energy. The director angle, φ(x, y, z), is obtained by the continuous theory. We show that the form of the viscous force in a confined nematic liquid crystal and in strong anchoring is a function of the initial distance between the two disclination lines. The asymptotic velocity, v _asy, is also a function of the initial distance. Our theoretical result on the asymptotic velocity is in good agreement with previous experimental results.     

Azimuthal director gliding at a strongly anchoring interface of polyimide

A gliding of the director at the interface between a nematic liquid crystal and a solid medium is generally observed at many interfaces giving weak or moderately strong anchoring. This phenomenon is characterized by strongly non-linear dynamics and very long relaxation times (hours-days). The gliding of the director has also been observed very recently at the interface between a rubbed polyimide layer and a nematic liquid crystal which gives strong azimuthal anchoring. However, due to the weak nature of the experimental signals that characterizes the strong anchoring, this latter measurement was appreciably affected by thermal drift. In this paper, we develop a new experimental reflectometric method whereby the thermal drift is appreciably reduced. The method allows us to obtain more accurate signals and to investigate their time dependence. It is shown that the director gliding is well represented by a stretched exponential, as well as in the case of weak anchoring substrates. These measurements confirm that the gliding of the director is a universal phenomenon characterizing any kind of substrate with either weak and strong anchoring.     

The spatial inhomogeneity of rodlike polymeric systems subject to simple shear flow

A novel simulation approach has been developed by the combination of Brownian dynamics and Lebwohl-Lasher nematogen potential, by which we have made preliminary investigation on the spatial inhomogeneity of nematic rodlike polymeric system with planar surface anchoring and subject to simple shear flow. Some rheological behaviors such as the damped oscillation of stresses with time or the negative first normal stress difference at moderate shear rate find good agreement with previous experimental observations reported in literature. The distribution function of rod orientation takes on “breathe-like” time-evolution and is verified not Gaussian-featured. The layered director, order parameter, shear stress and first normal stress difference have also been calculated by statistics, and most importantly, all of these statistic quantities show spatial distribution in different layers and corresponding distribution functions are time-dependent. Therefore, our simulation implies the complicated pattern formation and pattern evolution in this system. It is, hence, very meaningful to further study the spatial inhomogeneity of rodlike polymers under shear flow extensively both in theory and in experiment.     

The formula of anchoring energy for a nematic liquid crystal

The interface energy for a nematic liquid crystal (NLC) is considered as the sum of potential energy between LC molecules and molecules of the substrate surface, and a formula for anchoring energy is derived by elementary principles. The anchoring energy for a NLC should have two terms, the first term is the same as the Rapini-Papoular expression, the second is related to the normal of interface and resultes from the biaxial property of a NLC induced by interface. Hence there are two anchoring coefficients, W₁ and W₂. We demonstrate that W₁ is equal to the tilt angle strength A_θ, and W₂ corresponds to the difference between A_θ and the azimuthal strength A_ϕ. Thus A_θ-A_ϕ is due to the biaxial property of the NLC near the interface. Applying this formula to the twisted NLC cell, we discuss the threshold and saturation field, as well as the maximal tilt angel θ_m with respect to A_θ/A_ϕ. Previously proposed formulae are discussed from our point view.