On the validity of the elastic model for the nematic surface anchoring energy

The intrinsic uniform and non-uniform contributions to the anisotropic part of the surface energy are considered. Our analysis shows that the uniform part can be separated into an intrinsic and an extrinsic term. The first one is due to the nematic-nematic interaction only, whereas the second one is due to the nematic-substrate interaction. They are found to be of the same order of magnitude (≈1 erg cm²). The non-uniform part takes its origin from the spatial variation of the elastic constants. By means of a semi-microscopic model it is shown that, in the framework of perfect nematic order, the extrapolation length of the elastic origin is microscopic. On the contrary, if the spatial variation of the scalar order parameter is taken into account, simple calculations indicate that the extrapolation length is of the order of the coherence length in the nematic phase.     

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, W ₁ and W ₂. We demonstrate that W ₁ is equal to the tilt angle strength A_θ , and W ₂ corresponds to the difference between A_θ and the azimuthal strength A_? . Thus A_θ –A_? 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_? . Previously proposed formulae are discussed from our point view.     

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.     

New method for measuring polar anchoring energy of nematic liquid crystals

A new method for measuring a polar anchoring energy of nematic liquid crystals (LCs) is proposed. A variation of LC tilt angle on the surface with an applied electrical field was determined by a reflective method. The twisted LC cell configuration was selected to compensate a contribution of the induced birefringence in the reflective spectra. The electrical field controlled reflectance was used to analyse the potential form of the polar anchoring energy and to define the anchoring strength. The proposed method is applicable for 2–5 μm thick LC cells.     

Director configurations in nematic droplets with tilted surface anchoring

The polymer dispersed nematic liquid crystal (LC) with the tilted surface anchoring has been studied. The droplet orientational structures with two point surface defects – boojums and the surface ring defect – are formed within the films. The director tilt angle α = 40° ± 4° at the droplet interface and LC surface anchoring strength W_s ~ 10^–6 (J m^?2) have been estimated. The bipolar axes within the studied droplets of oblate ellipsoidal form can be randomly oriented are oriented randomly relatively to the ellipsoid axes as opposed to the droplets with homeotropic and tangential anchoring.     

Dynamics of surface anchoring breaking in a nematic liquid crystal

Abstract

We present a simple dynamical model which describes the time dependence of the threshold electric field for breaking the surface anchoring of nematics. This model includes a surface friction, resulting from volume hydrodynamic dissipation. Experimental data with AC and DC pulsed fields are explained by this model. For DC, the threshold difference versus the field polarity is well-described by the flexo-electric effects in a uniform field for short times and in a non-uniform field for long times.     

Dynamics of surface anchoring breaking in a nematic liquid crystal

We present a simple dynamical model which describes the time dependence of the threshold electric field for breaking the surface anchoring of nematics. This model includes a surface friction, resulting from volume hydrodynamic dissipation. Experimental data with AC and DC pulsed fields are explained by this model. For DC, the threshold difference versus the field polarity is well-described by the flexo-electric effects in a uniform field for short times and in a non-uniform field for long times.     

Dependence of the anchoring energy on the applied voltage in a nematic cell

A nematic liquid crystal cell in the shape of a slab of thickness d and containing ionic impurities is considered in the presence of a dc voltage. A complete theoretical model to determine the electric field distribution across the sample is used to explain the experimental dependence of the effective anchoring energy of the cell on the applied voltage, in the limit of high voltage.     

Invited Lecture. Experimental studies of the anchoring energy of nematic liquid crystals

An analysis is given of experimental techniques for measuring the anchoring energy, W, of nematic liquid crystals with solid surfaces. Two novel methods for measuring W in homeotropically oriented samples are discussed. The first is based on the stabilization of the flexoelectric distortion by a magnetic field. In the second the thickness dependence of the phase delay for the light beam transmitted through a wedge-form cell with the hybrid orientation of a nematic should be measured. New experimental data on thickness and temperature dependences of the anchoring energy for homogeneously oriented 5CB are also presented. The anchoring energy was even measured for thin interface layers in the isotropic phase and its critical behaviour near the N-I transition is also discussed. New data were also obtained for the anchoring energy of nematics at crystalline surfaces.     

Slow relaxation processes in nematic liquid crystals at weak surface anchoring

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.     

Converse flexoelectric effect in homeotropic nematic layers with asymmetric surface anchoring

The dc electric field-induced deformations of conducting flexoelectric nematic layers were studied numerically. Asymmetric boundary conditions expressed by different anchoring strengths on the limiting surfaces were assumed. Nematic material was characterised by negative dielectric anisotropy. Both signs of the sum of flexoelectric coefficients were taken into account. The electric properties of the layer were described in terms of a weak electrolyte model. Mobility of cations was assumed to be one order of magnitude lower than that of anions. Quasi-blocking electrode contacts were assumed. The threshold voltages for the deformations and the director distributions in the deformed layers were calculated for low, moderate and high ion concentrations. The director distributions were also determined. The results show that asymmetry caused by difference between the anchoring strengths and by difference between mobilities of anions and cations lead to two threshold values for a given layer corresponding to two polarities of the bias voltage. Additionally, the values of both thresholds depend on the sign of the flexoelectric parameter. In every case under consideration, the threshold is significantly lowered when the ion concentration is high.     

Polar anchoring energy and order parameter at a nematic liquid crystal-wall interface

By measuring the integrated birefringence versus thickness of homogeneous and distorted nematic liquid crystal configurations, we have obtained the anchoring energy and the change of the order parameter at the orientating layer. The measurements were made for planar and tilted orientating SiO layers and for rubbed polyimide. The tilted orientating SiO layer shows the most significant decrease of the order parameter near the interface, which can be explained by its microscopically inhomogeneous alignment.     

Determination of the surface anchoring potential of a nematic in contact with a substrate

We have developed a method for determining the surface anchoring potential for nematics in contact with a substrate that provides director alignment. Our main result is that the surface torque and hence the anchoring potential may be determined from either dielectric or optical phase response of a nematic undergoing a Freedericksz transition. The method is based on the Frank-Oseen continuum theory, and makes no assumptions about the functional form of the potential. We have measured the surface anchoring potential of two types of substrate in contact with the nematic liquid crystal 4-n-pentyl-4′-cyanobiphenyl. The surfaces were ITO-coated float glass, coated either with obliquely evaporated SiO or a buffed polymer film. Comparison of the results obtained from capacitance and optical measurements provides an estimate of the goodness of the method.     

The polar anchoring energy of nematic liquid crystals with polyvinylidene fluoride alignment layer

It has been proved that the high dielectric polyvinylidene fluoride (PVDF) could be used as an alignment layer in liquid crystal device. In this paper, the transmittance, pretilt angle and the polar anchoring energy of the substrates with PVDF alignment layer were researched. Theoretical results and the experimental results about the reflectivity R_SS (polarisation-conserving signals) recorded by full-leaky guided mode in liquid crystal technique are analysed to evaluate the anchoring energy of PVDF alignment layer. The result shows that the polar anchoring energy between PVDF alignment layer and liquid crystal molecules is 2.80 × 10^?4 J/m².     

Surface anchoring of nematic liquid crystal 8OCB on a DMOAP-silanated glass surface

Dynamic light scattering spectroscopy has been used to determine the temperature dependence of the anchoring strength of the nematic liquid crystal 8OCB on DMOAP-silanated glass surfaces inducing homeotropic alignment. Wedge-type glass cells with known thickness profile starting from 150 nm to several microns have been used in the experiments. The relaxation rates of the nematic fluctuations with the wave vector perpendicular to the confining surfaces have been measured as a function of the cell thickness. Fitting of the thickness dependence of the relaxation rate allows for straightforward determination of the surface extrapolation length and therefore also the strength of the surface anchoring, which is 1×10^-4 J m^-2. The overall experimental accuracy of the experiments is discussed.     

The effect of a finite anchoring energy on the transient periodic structures in nematic liquid crystals

Non-equilibrium transient periodic structures have been widely observed in thermotropic and lyotropic nematic liquid crystals. So far only the case of strongly anchored nematics has been considered. Here we investigate the influence of a finite anchoring energy on the non-equilibrium transient pattern in a twist geometry. Both the domain wavelength and the threshold field for the non-equilibrium pattern have been calculated for different values of the anchoring energy.     

Measurement of twist angle and surface torsional anchoring strength in a nematic liquid crystal cell

In this paper a novel method is developed for measuring the twist angle and surface torsional anchoring strength in nematic liquid crystal (NLC) cells. This method is based on a technique developed from the Jones optical propagation matrix. From the measurement, the actual twist angle in NLC cell and the deviation of the LC director on the boundary of the cell from the rubbing direction of the substrate are obtained. A theoretical discussion shows that the surface torsional anchoring strength has a great influence on the value of the deviation, and hence so it can be calculated.     

Influence of anchoring at a nematic cell surface on threshold spatially periodic reorientation of a director

We have analysed the influence of surface director anchoring in a planar flexoelectric nematic cell on the threshold spatially periodic reorientation of the director in an external dc electric field. By minimizing the free energy of the nematic cell we obtained the equations for a director and numerically solved them in the one elastic constant approximation. The dependences of the threshold electric field and the spatial period of director structure on the azimuthal and polar anchoring energy, as well as the flexoelectric parameters, are determined. It is shown that the domain of the flexoelectric parameter values, at which the spatially periodic reorientation of a director takes place, increases with decreasing azimuthal anchoring energy and increasing polar anchoring energy.     

The elastic distortion and stability of biaxial nematic liquid crystal on the surface grooves

Fukuda et al. reexamined the Berreman's model which attributes the surface anchoring to the elastic distortion of the uniaxial nematic liquid crystal induced by the grooves of a surface. They showed that at the variance with the assumption made in the original approach of Berreman, the azimuthal distortion of the director cannot be considered as negligibly small. Now this method is generalized to the biaxial nematic liquid crystals, with some approximations for the elastic constants. We obtain an additional term in the elastic distortion energy per unit area which depends on the second power of the cosine of the angle made between the main director n at infinity and the direction of the surface grooves. This additional term describes the distortion energy of the minor director m induced by the surface grooves when the n director is anchored exactly along the grooves. We have studied the stability of the n director around the grooves, and in one-constant model for each director the stability condition is that the elastic constant of the n director is the maximum.