Director Distortions Research Articles

Lyotropic Chromonic Liquid Crystals for Biological Sensing Applications

ABSTRACT We describe director distortions in the nematic liquid crystal (LC) caused by a spherical particle with tangential surface orientation of the director and show that light transmittance through the distorted region is a steep function of the particle's size. The effect allows us to propose a real-time microbial sensor based on a lyotropic chromonic LC (LCLC) that detects and amplifies the presence of immune complexes. A cassette is filled with LCLC, antibody, and antigen-bearing particles. Small and isolated particles cause no macroscopic distortions of the uniformly aligned LCLC. Upon antibody-antigen binding, the growing immune complexes disrupt the uniformity of the director and cause detectable optical transmittance between crossed polarizers.

Modeling dislocations and disclinations with finite micropolar elastoplasticity

Aspects of a constitutive model for characterizing crystalline metals containing a distribution of dislocation and disclination defects are presented. Kinematics, balance laws, and general kinetic relations are developed – from the perspective of multiscale volume averaging – upon examination of a deforming crystalline element containing a distribution of displacement discontinuities in the form of translational and rotational lattice defects, i.e., dislocations and disclinations. The macroscopic kinematic description is characterized by a three-term multiplicative decomposition of the deformation gradient. The micro-level description follows from an additive decomposition of an affine connection into contributions from populations of dislocations and disclinations to the distortion of the lattice directors. Standard balance equations apply at the macroscopic scale, while momentum balances reminiscent of those encountered in micropolar elasticity (i.e., couple stress theory) are imposed at the micro-level on first and second order moment stresses associated with geometrically necessary defects. Thermodynamic restrictions are presented, and general features of kinetic relations are postulated for time rates of inelastic deformations and internal variables. Micropolar rotations are incorporated to capture physics that geometrically necessary dislocations stemming from first order gradients of elastic or plastic parts of the total deformation gradient may alone be unable to reflect, including evolution of defect substructure at multiple length scales and incompatible lattice misorientation gradients arising in ductile single crystals subjected to nominally homogeneous deformation.

Real-time microbe detection based on director distortions around growing immune complexes in lyotropic chromonic liquid crystals

We describe director distortions in the nematic liquid crystal (LC) caused by a spherical particle with tangential surface orientation of the director and show that light transmittance through the distorted region is a steep function of the particle's size. The effect allows us to propose a real-time microbial sensor based on a nontoxic lyotropic chromonic LC (LCLC) that detects and amplifies the presence of immune complexes. A cassette is filled with LCLC, antibody, and antigen-bearing particles. Small and isolated particles cause no macroscopic distortions of the LCLC. Upon antibody-antigen binding, the growing immune complexes distort the director and cause detectable optical transmittance between crossed polarizers.

Offset of Multiple-Beam Interference inside Anisotropic Multilayered Structure: Determination of Polar Anchoring Strength at Nematic Liquid Crystal-Wall Interface

An optical technique for eliminating the inaccuracy in the measurement of retardation caused by multiple-beam interference in anisotropic multilayer-structured thin film is developed by the detailed analysis of obliquely incident transmission ellipsometry. The director distribution of a nematic liquid crystal inside a conventional sandwich-type cell which constitutes glass substrates, alignment films and transparent electrodes can be accurately determined without taking complicated multilayer analysis into account. As a typical application, a novel method of determining of the polar anchoring strength at the nematic liquid crystal-wall interface is proposed. The accurate measurement of the director distortion of a NLC without information on the refractive indices of ITO films, alignment films and glass substrates results in the realization of polar anchoring strength with a high accuracy. This technique can be used to achive a strong polar anchoring reaching the order of 10-3 J/m2.

Fingerprint patterning of solid nanoparticles embedded in a cholesteric liquidcrystal

Metallic nanoparticles dispersed in a cholesteric liquid crystal can order in accordance withthe helical structure of the chiral phase. Since the liquid crystals we used havea glassy state, the nanostructures may be examined by transmission electronmicroscopy. The platinum nanoparticles form periodic ribbons which mimic thewell-known fingerprint cholesteric texture. The particles do not decorate the pristinetexture but create a novel structure with a larger periodicity. The distance betweenthe ribbons is directly correlated to the helical pitch which therefore becomes asimple control parameter to tune the structuring of nanoparticles. Investigations ofcross-sections show how the particles are arranged in the volume; a selective segregationproceeds at the periphery of the film and the particle ordering is localized close tothe film–air interface. On the fingerprint patterning of nanoparticles, we do ananalogy with the positive staining of polymer films with heavy-metal-containingcompounds for transmission electron microscopy investigations and we discuss theaccumulation of particles in the sites with the highest energy of director distortions.

Measurements of the azimuthal anchoring energy at a polyimide-nematic interface with a new transmitted light method

A new transmitted light method has been used to measure the azimuthal anchoring energy coefficientWat the interface between the nematic liquid crystal 5CB and a rubbed polyimide substrate. This method overcomes the typical drawbacks of the transmitted light methods and provides an unambiguous measurement of the director rotation at the surface. The contributions of the bulk director distortion are very small and can be easily separated from those due to the anchoring. The measurements can be performed also in the critical case of somewhat strong anchoring. The small optical anisotropy of the orienting layer(polyimide)can be also taken into account.

Fully leaky guided mode study of the flexoelectric effect and surface polarization in hybrid aligned nematic cells

The fully leaky guided-mode optical-waveguide technique has been used to characterize the tilt profiles in two E7-filled hybrid-aligned nematic cells. The director distortion was measured with ac and dc voltages applied perpendicular to the substrates. By comparing the tilt profiles with model profiles produced using a free-energy minimization program, the flexoelectric coefficient of E7 at 20 °C has been measured as +1.5±0.2×10−11 C m. The effect of surface polarization in the cells has also been observed. This surface polarization is attributed to the influence of the homeotropic surface. The dipole alignment imbalance of the liquid crystal at the homeotropic surface has then been estimated.

Effect of director distortions on morphologies of phase separation in liquid crystals.

We study phase separation from a nematic liquid crystal with spatially nonuniform director gradients. Particles of a phase-separated component, which is either an isotropic fluid (silicone oil) or a nonmesogenic photopolymer, accumulate in the regions with the strongest director distortions, thus reducing the overall energy of the system.

Elastic Constants of an Achiral Smectic-C Material

A Freedericksz transition technique was used to measure the elastic constants of a smectic-C material with positive dielectric anisotropy. The layer geometry was determined via x-ray scattering and the Freedericksz transition was monitored both optically and from the field-dependent intensity of the Bragg peaks. The splay elastic constant, k 11, was measured across the nematic phase range and correlated with the B 2 c -director distortion in the smectic-C phase. An estimate of the sum of the layer bending elastic constants was also made and it was found that $ 21 + $ 11 is negative and takes a value around 10 m 4 N.

Collective effects in doped nematic liquid crystals

We studied the collective elastic interaction in a system of many macroparticles embedded in a nematic liquid crystal. A theoretical approach to the interaction of macroparticles via deformation of the director field [1] is developed. It is found that the director field distortion induced by many particles leads to the screening of the elastic pair interaction potential. This screening strongly depends on the shape of the embedded particles: it exists for anisotropic particles and is absent for spherical ones. Our results are valid for the homeotropic and the planar anchoring on the particle surface and for different Frank constants. We apply our results to cylindrical particles in a nematic liquid crystal. In a system of magnetic cylindrical grains suspended in a nematic liquid crystal, the external magnetic field perpendicular to the grain orientation results in inclining the grains to the director and induces an elastic Yukawa-law attraction between the grains. The appearance of this elastic attraction can explain the cellular texture in magnetically doped liquid crystals in the presence of the magnetic field [2].

Structure of spontaneous periodic deformations in hybrid aligned nematic layers.

Periodic deformations, arising spontaneously in hybrid nematic layers were investigated numerically. So called splay stripes, which appear when the surface anchoring energy of the planar alignment was greater than that of the homeotropic alignment, were considered. Conical degeneration of the anchoring is assumed. The role of the layer thickness d and the anchoring strength W was studied by means of the dimensionless control parameter gamma=Wd/k(11) defined for each boundary. The saddle-splay elastic constant k(24) was varied within the limits given by general Ericksen inequalities. The director distributions were calculated. Two structures with different properties were distinguished: one for k(24)<0 (mode 1) and the other for k(24)>0 (mode 2). For given nematic liquid crystal parameters, mode 1 existed when gamma exceeds some critical value. Below this critical gamma, the director distortion decayed and the spatial period simultaneously diverged to infinity. As a result mode 1 disappeared and the homogeneously planar orientation was realized. The width of the stripes also increased infinitely for high gamma. No upper limit of the gamma range in which mode 1 could exist was found. Mode 2 existed for gamma ranging from 0 to a certain critical value. Above this limit the periodic structure was replaced by the homogeneous hybrid alignment as a consequence of an infinite increase of the stripes' width. When k(24)>0 was sufficiently small, the gamma range was bounded from below, and a homogeneously planar orientation appeared for low gamma. The visibility of the stripes between crossed polarizers was estimated by calculations of light transmission. In general, the stripes for k(24)<0 turned out to be more distinct than that for k(24)>0.

Homeotropic polar anchoring energy of a nematic liquid crystal using the fully leaky waveguide technique

Optical excitation of a series of fully leaky guided modes has been used to explore the director distortion of a hybrid-aligned nematic liquid crystal with a negative dielectric anisotropy (Merck-BDH, MLC 6608) under application of an ac electric field. Hybrid alignment is realized by the use of a lecithin film on the top glass plate and rubbed polyimide on the bottom plate, both plates having indium–tin–oxide coatings. Continuum theory is used to model the director profile through the cell. Fitting the fully leaky guided mode data both in transmission and reflection using optical multilayer theory together with continuum modeling gives the director profile both with and without applied fields. From this fitting the changes in the surface tilt angle and its gradient are obtained. Using this information the polar anchoring coefficient of the homeotropic surface Wθ is deduced. At 23.1 °C we find Wθ=(4.6±0.2)×10−4 J m−2.

Phase-shift error as a result of molecular alignment distortions in a liquid-crystal point-diffraction interferometer

We report the observation of nematic director distortions around the diffracting element of a liquid-crystal point-diffraction interferometer. The observed director field distortions are similar to those reported in the literature for other liquid-crystal guest-host systems. We show how the alignment distortion changes as a function of the voltage applied to the liquid-crystal cell, leading to an observed phase-shift error. Tailoring of surface anchoring conditions and judicious choice of phase-shift algorithm can improve device accuracy.

Fully leaky guided wave determination of the polar anchoring energy of a homogeneously aligned nematic liquid crystal

Optical excitation of a series of fully leaky guided modes has been used to explore the director distortion of a homogeneously aligned nematic liquid crystal (Merck-BDH E7) under application of an ac electric field (1 kHz) normal to the cell wall. Homogeneous alignment is realized by rubbed polyimide films on glass plates with indium–tin–oxide coatings. By using continuum theory to model the director profile through the cell to fit the fully leaky guided mode reflectivity and transmissivity data, both with and without applied fields, the changes of surface tilt angle and its gradient can be obtained from which the polar anchoring coefficient, Wθ, is derived. At 26.8 °C we find that Wθ=1.2×10−4 Jm−2.

Lattice modelling of nematodynamics

The microstructures of textured nematics under shear are investigated by means of a director lattice model incorporating linear shear response as well as elastic interactions between neighbouring directors. The model can be understood as a lattice implementation of the so-called nematodynamics equation for a constant uniaxial order parameter. The dimensionless number governing the model is found to be a mesoscale Ericksen number, which scales with the square of the lattice cell size. It is shown that the predicted microstructure depends strongly on the scale of that number. In particular, disclination loops are found to grow for a range of mesoscale Ericksen numbers, while below or above that they disappear. We apply the model to investigate the director profiles of tumbling nematics. If the orientations are restricted to lying in the vorticity plane, we reproduce the director wind-up layers and distortion saturation predicted theoretically. In the full three-dimensional case an initially polydomain director field evolves to a vorticity-aligned state up to a critical Ericksen number, above which in-plane orientations with distortion saturation are found. The simulations hence reproduce the transition from log-rolling to flow aligning with increasing shear rate observed experimentally.

Quantification of the surface- and bulk-order parameters of a homogeneously aligned nematic liquid crystal using fully leaky guided modes

An optical waveguide technique, involving the excitation of fully leaky guided modes, has been used to quantify the director distortions induced by the application of weak in-plane electric fields to a homogeneously aligned nematic liquid crystal, E7. The twist profile of the nematic is determined by fitting angle-dependent reflectivity and transmission data to multilayer optical theory. By considering the Frank–Oseen free energy in the bulk, with Rapini–Papoular-type anchoring at the surfaces, we have determined accurate values for both the azimuthal anchoring strength Wa and the twist elastic constant k22 as a function of temperature. Values for the temperature-dependent surface and bulk average-order parameters have also been deduced by allowing for a spatially varying nematic-order parameter.

Influence of a surface electric field on the anchoring characteristics of nematic phases at rubbed polyimides

We report measurements of the anchoring energy of 5CB (4-cyano-4′-n-pentyl-biphenyl) at a commercial polyimide (AL1051) with a method using a large applied electric field on thick measurement cells. The experiments reveal a deviation from the expected behavior of the system and cannot be described by the usual Frank elastic bulk energy density plus anchoring surface energy within the thermodynamic limit. We, therefore, discuss the effect of a surface electric field coupled to director distortions by the flexoelectric effect. Numerical calculations show, indeed, that the experiments can be described reasonably by the model. Experiments for thin cells indicate that the Debye screening length does not depend on the cell thickness. We derive an easy way to get an estimate of the Debye screening length from the experiments.

Analysis of Liquid Crystalline Fiber Coatings

A phenomenological model for the spreading of nematic liquid crystals on fibers of circular cross section is presented. The model is used to calculate the wetting thresholds of nematics on fibers for three chracteristic director orientations: axial (undistorted), radial (splay), and azimuthal (bend): the wetting thresholds are given in terms of critical film thickness hc and critical spreading parameter Sc. When the spreading parameter S is greater than the critical value Sc, nematic liquid crystal fiber wetting is similar to that of viscous fluids when director distortions are absent. In other cases when nematic liquid crystals spread on fibers the distortion due to the cylindrical geometry gives rise to Frank elasticity. For symmetric director boundary conditions the characteristic modes of splay and bend increase the magnitude of critical spreading parameter Sc. It is found that when spreading occurs (S>Sc) the equilibrium film thickness decreases with increasing elastic storage. The film thickness for rod-like and disc-like nematics differs because the splay-bend elastic anisotropy is reversed.

NMR Study of Flow and Viscoelastic Properties of PBLG/m-Cresol Lyotropic Liquid Crystal

Director distortion patterns and backflow effects in transient flows of nematic solutions of PBLG/m-cresol are studied by deuteron NMR. The simulation of the observed NMR spectra as a function of time allows to characterise the director field pattern and to evaluate most of the viscoelastic properties of the system. A good agreement with classical rheometry is observed.

Quantification of the azimuthal anchoring of a homogeneously aligned nematic liquid crystal using fully-leaky guided modes

A novel optical guided mode technique, the fully-leaky guided mode technique, has been used to investigate the director distortion under the application of an in-plane electric field of a homogeneously aligned conventional cell filled with the nematic liquid crystal E7. The liquid crystal is aligned using polyimide rubbed along the direction of the gold electrode edges. A weak field is applied across a 3 mm gap between the gold electrodes to induce small changes in the twist angle of the director. These distortions are determined by fitting to the angledependent reflectivity and transmissivity data and are compared with continuum theory. From careful analysis of the results, both the twist elastic constant, k22, and the azimuthal anchoring strength, Wa, of the system are obtained. At 23.5 C for E7 on rubbed polyimide we find that k22=(6.50±0.05)x10-12N and Wa=(2.9±0.2)x10-5 J m-2.