Twisted Wall Research Articles

Model for the director and electric field in liquid crystal cells having twist walls or disclination lines

Two examples of the director structure and electric field in patterned electrode liquid crystal cells are studied using a recently developed calculational model. First, a display cell that exhibits a homeotropic to multidomainlike transition with twist wall structures has been considered for a liquid crystal with positive dielectric anisotropy. The model elucidates the behavior of the electric field. Calculations show good agreement between the model and direct computer solution of the Euler–Lagrange equations, but the model is at least 30 times faster. Second, the possibility that a cell has ±1/2 disclination lines instead of a wall defect is probed. A temperature dependent estimate for the size of the defect core is given, and the total free energy of the cell with disclination lines was calculated and compared with the corresponding value for the same cell with wall defect structure.

Defect Nucleation and Annihilation in Sheared Polymeric Liquid Crystals

ABSTRACTShear–induced nucleation and annihilation of topological defects due to hydrodynamic instability in nematic liquid crystals is a phenomenon of both scientific interest and practical importance. We use a complete generalized non-linear second order tensor Landau-de Gennes model that takes into account short range order elasticity, long-range elasticity and viscous effects, to simulate the nucleation and annihilation of twist inversion walls in flow-aligning nematic polymers subjected to shear flow. Shearing a homogeneous nematic sample perpendicular to the director results in an linear instability that maybe symmetric at low shear rates, and antisymmetric at higher shear rates. At even higher shear rates the onset of nonlinearities results in the nucleation of a parallel array of twist inversion walls, such that asymmetry prevails. By increasing the shear rate the following director symmetry transition cascade is observed: symmetric → antisymmetric → asymmetric → symmetric. The nucleation of the parallel array of twist inversion walls in the asymmetric mode is due to the degeneracy in reorientation towards the shear plane. The annihilation of twist walls is mediated by twist waves along the velocity gradient direction. Twist walls annihilate by three mechanisms: wall-wall annihilations, wall-wall coalescence, and wall-bounding surface coalescence. The annihilation rate increases with increasing shear rate and at sufficiently high rates the layered structure is replaced by a homogeneously aligned system. The role of short range and long range elasticity on defect nucleation and annihilation is characterized in terms of the Deborah and Ericksen numbers. Close form solutions to approximated equations are used to explain the numerical results of the full Landau-de Gennes equations of nematodynamics.

Cholesteric elastomers: deformable photonic solids.

A mechanical strain applied to a monodomain cholesteric elastomer modulates and eventually unwinds the helical director distribution. There are similarities with the classical problem of an electric field applied to a cholesteric liquid crystal, but also differences. Frank elasticity is of minor importance unless the gel is very weak. The interplay is rather between the director being helically anchored to the rubber elastic matrix and the external mechanical field. Stretching perpendicular to the helix axis induces the uniform unwound state via the elimination of sharp, pinned twist walls above a critical strain. Below the critical strain the coarsening of the director distribution is not accompanied by an increase but rather by an affine decrease in the pitch. Unwinding through conical director states occurs when the elastomer is stretched along the helical axis. Finally we consider cholesteric elastomers in a classical device geometry with an electric field applied along the pitch axis and hence transverse to the director orientation.

Untwisting of a cholesteric elastomer by a mechanical field

A mechanical strain field applied to a monodomain cholesteric elastomer will unwind the helical director distribution. There are similarities with the classical problem of an electric field applied to a cholesteric liquid crystal but also differences. Frank elasticity is of minor importance unless the gel is very weak. The interplay is between the director being helically anchored to the rubber elastic matrix and the external mechanical field. Stretching perpendicular to the helix axis induces the uniform unwound state via the elimination of sharp, pinned twist walls above a critical strain. Unwinding through conical director states occurs when the elastomer is stretched along the helical axis.

Flow-aligning and tumbling in small-molecule liquid crystals: pure components and mixtures

The results of an experimental study to measure the tumbling parameter, λ, for various small-molecule liquid crystals and their mixtures are presented. The methods used include textural observations (twist walls), a direct method, a rheological method, and the oscillatory method developed by Mather, Pearson, and Burghardt in 1995. The single-component results are compared with a molecular theory derived in 1995 by Archer and Larson as well as Kroger and Sellers, which predicts the temperature dependence of λ, while the results from the binary mixtures are compared to a continuum theory derived by Rey in 1996, giving the concentration dependence of λ. The results from the four experimental methods agree with each other for single-component liquid crystals, but not for mixtures. This suggests a failure of the single director Leslie-Ericksen theory to describe the rheology of liquid crystal mixtures.

The cholesteric-nematic transition in droplets subjected to electric fields

We have observed the behaviour of chiral nematic droplets with positive dielectric anisotropy subjected to electric fields. With increasing field, the Frank-Pryce spherulitic director configuration is distorted progressively into a quasi-cylindrical spiral twist wall. As the field increases further this wall progressively unwinds, resulting in a confined cholesteric-nematic transition. Measurements of the pitch versus electric field show that, despite the confinement, the pitch is still described by the theory for the unconfined cholesteric-nematic transition.

The origin of stress-oscillation damping during start-up and reversal of torsional shearing of nematics

Using a controlled-temperature shear cell mounted on a polarizing microscope, we observe the behavior of nematic 4,4′-n-octyl-cyanobiphenyl (8CB) during start-up and reversal of shearing in a torsional parallel-plate geometry and correlate this behavior with rheological measurements. During the start-up, a sequence of birefringent rings, or “twist walls”, are observed that originate at the sample edge and propagate radially inward. Each twist wall is a thin region in which the director is twisted out of the plane of the velocity and velocity-gradient directions. The radial variation of in-plane orientation can be explained by the variation of strain in the parallel-plate device. A high Ericksen-number solution of the Leslie-Ericksen equations predicts a damped oscillatory shear stress response which agrees quantitatively with the measured stress oscillations out to an edge strain of around 50. The damping of the stress oscillations is due to the nonuniformity of strain in the parallel-plate geometry. On reversal of the flow, if the strain, γ, is smaller than about 500 units, the damping of stress oscillations is reversed; this correlates with an outward radial migration of twist walls. When γ > 500, disclinations nucleate and spoil the reversibility of stress damping.

The origin of stress-oscillation damping during startup and reversal of torsional shearing of nematics

Using a controlled-temperature shear cell mounted on a polarizing microscope, we observe the behavior of nematic 4,4′-n-octyl-cyanobiphenyl (8CB) during start-up and reversal of shearing in a torsional parallel-plate geometry and correlate this behavior with rheological measurements. During the start-up, a sequence of birefringent rings, or “twist walls”, are observed that originate at the sample edge and propagate radially inward. Each twist wall is a thin region in which the director is twisted out of the plane of the velocity and velocity-gradient directions. The radial variation of in-plane orientation can be explained by the variation of strain in the parallel-plate device. A high Ericksen-number solution of the Leslie-Ericksen equations predicts a damped oscillatory shear stress response which agrees quantitatively with the measured stress oscillations out to an edge strain of around 50. The damping of the stress oscillations is due to the nonuniformity of strain in the parallel-plate geometry. On reversal of the flow, if the strain, γ, is smaller than about 500 units, the damping of stress oscillations is reversed; this correlates with an outward radial migration of twist walls. When γ > 500, disclinations nucleate and spoil the reversibility of stress damping.

Dislocations in CaTiO3 perovskite deformed at high-temperature: a transmission electron microscopy study

Dislocation configurations in natural single crystals of CaTiO3 perovskite deformed in high-temperature creep were examined and characterized by transmission electron microscopy. Screw dislocations with Burgers vector [100]pc and [011]pc, dissociated on the \((01\bar 1)_{{\text{pc}}} \) plane, form rectangular networks with extended four-fold nodes in the shape of octagons, a configuration never observed in any of the previously investigated perovskites, except CaGeO3. Screw dislocations with Burgers vector [101]pc and \((\bar 101)_{{\text{pc}}} \) , on the (010)pc plane, react to form a twist wall; the dislocations with Burgers vector [002] produced by the reaction decompose into two perfect dislocations [001]pc. This results in a new configuration, never observed before, with three-fold nodes at the corners of rectangles. Both the octagonal extended nodes and the junctions decomposed into perfect dislocations are seen in samples deformed indifferently by slip on {100}pc or {110}pc planes, but they seem to appear only above 1520 K, in the cubic phase.

Flow patterns and disclination-density measurements in sheared nematic liquid crystals II: Tumbling 8CB

Abstract We examine the behaviour of nematic 4,4′-n-octylcyanobiphenyl (8CB) subjected to steady torsional shear flow at a temperature where this nematic is ‘tumbling’, i.e. the ratio α3/α2 of Leslie viscosities is negative. If the disc rotation speed is gradually increased from zero ( < 10−6 rad s−2), the director eventually departs from the shear plane and becomes oriented radially. However, if the disc rotation speed is increased from rest at higher rates, twist wall defects are created sequentially at the sample meniscus and propagate inward with velocity ≈0.85mm s−1. Eventually, disclinations are nucleated. Disclination density measurements reveal that over similar ranges of values of the Ericksen number Er, samples of 8CB have roughly ten times the disclination density of the flow-aligning nematic, 5CB, reported in the preceding paper. Additionally, a transition from a power-law exponent of 0.5 to 1.0 for the dependence of dimensionless disclination density on Er is observed near Er = 2000, consiste...

Dynamical confinement of twisted soliton pairs in biaxial ferromagnets.

The dynamics of a classical continuum model of a ferromagnet with exchange and anisotropy energies of hard- and easy-axis type is considered. Exact solutions of soliton pairs with vanishing center of mass velocity are presented. They reveal the counterintuitive existence of a family of bound states of a repulsive, twisted domain wall (soliton) pair. These breather states have energies which lie above the continuum of the corresponding scattering states of two solitons

Lines in liquid crystalline phases of biopolymers

DNA, PBLG and xanthan are three polymers which give cholesteric liquid crystalline phases in concentrated solution. We analyzed different structures encountered in these phases that we call « lines » because they all appear, in the polarizing microscope, as illuminated lines in a dark background. They correspond either to molecular discontinuities, or to surfaces separating two phases of different nature or to twist walls which are observed in homeotropic textures where the twist is prevented. The analysis of such structures gives information about the nature of the phase in which they are observed.

Radial Creeping Flow Between Parallel Disks of Rod-like Nematic Liquid Crystals: Textures and Instabilities

ABSTRACTFour solutions to the Leslie-Ericksen equations for nematic liquid crystals are obtained for pressure-driven radial out-flow between concentric parallel disks and homeotropic director wall anchoring. At low pressure drops the in-plane mode is stable; the centerline director orientation is normal to the flow direction. For each radial distance from the entrance hole there is a critical pressure drop at which the elongational torque twist the director out-ofthe- plane of flow ; left and right rotations are possible. The transition results in the appearance of secondary flows in the azimuthal direction. The radius of the boundary between in-plane and out-of-the-plane modes increases with increasing pressure drops. At higher pressure drops a twist wall develops at the centerline. There is a second critical pressure drop at which the wall collapses with the nucleation and growth of a twist disclination loop. The resulting stable director field is in-plane and flow-aligned throughout the cell.

Aerodynamics of a twisted wall jet in a co-current flow

Aerodynamics of a twisted wall jet in a co-current flow

Homogeneous electric field threshold switching phenomena in a multiplexible bistable liquid crystal display

An electrically addressed, thermally erased bistable nematic liquid crystal display with a potentially very large multiplexing capacity is described. A simple, uniform electric field geometry produces a nearly ideal electro-optic threshold response, with a very sharply defined threshold field and rapid saturation. The threshold is analytically shown to depend on the binding energy of disclination lines at a spatially finite surface orientational discontinuity. Moreover, the binding energy changes in time as the orientational discontinuity at the binding site is altered by the movement of a twist wall away from the junction. The nature and dynamics of this domain wall are described, as are the different distorted boundary layer configurations that arise in a uniform field geometry. The movement of this wall effectively reduces the binding energy of the disclinations, allowing switching to occur at lower fields. A dramatic voltage reduction is achieved with a short, low voltage pulse applied to prime the device prior to the onset of the switching pulse. This reduction makes 2:1 addressing possible at high speed (2 msec), using row and column voltage levels of approximately ±50 V. Similarly, 3:1 addressing is achieved with select and nonselect levels of 70 and 35 V, respectively. The high addressing speed results from the requirement of only a minimal amount of disclination movement, with the self-propelled annihilation of the detached loops carrying the switching process to completion thereafter.

Les dislocations dans la forsté rite déformée à haute Tempé rature

Abstract Dislocations in forsterite deformed at a high temperature Creep experiments have been performed at high temperatures on forsterite single crystals at moderate stress (8–100 MPa, 1400–1650°C). Samples have been deformed by compression in three simple orientations. Dislocation microstructures are reported here for these three groups of samples. Previous observations were made using a very efficient decoration technique. TEM results confirm the reliability of this technique. Moreover they give a complete identification of Burgers vectors and activated slip systems. For the first orientation, most of the dislocations are ‘a’ edges in glide bands. Tilt walls are also present. The ‘a’ edges are not very straight. For the third orientation, most of the dislocations are ‘c’ screws. Twist walls are numerous. The ‘c’ screws are very straight. The second orientation is intermediate between the first and the third ones. It shows the two types of microstructures in highly variable proportions. These facts she...

Analysis of dynamic diffuse wall based on two-dimensional twist wall

The mechanism and the dynamic properties of the dynamic diffuse wall observed in Garnet bubbles have been analyzed based on two dimensional twist wall with a finite film thickness. The analysis reveals that during wall motion, 360 °-spin twist nucleates inside the wall and propagates along the film thickness. The wall distortion takes place where the 360 °-twist appears. Annihilation and/or accumulation of the 360 °-twist occurs at the film surface. The number of the 360 °-twists contained in a wall increases with increasing drive and in-plane fields, which leads to an increase of the apparent wall width obtained by domain walls observed by transmitted light (Faraday effect). Most of the experimental results may be well interpreted by the present analysis.

Helical disclination lines in smectics a

Abstract It is shown that helical disclination lines exist in smectics A; they can play the role of focal conics for the smectic planes or be true disclination lines. In the latter case, they are a source of screw dislocation lines. Single helices are terminations of twist walls made up of screw dislocation lines. Double helices are equivalent to large screw dislocation lines.

Numerical computation of the director field in a twist wall

Abstract The Eulor-Lagrange equations for a nematic liquid crystal are solved numerically for the boundary conditions which give a twist wall. An approximate solution deduced in previous work is found to represent the numerical solution well.

Twisted domain wall structure for stripe domains in bubble films

A four-parameter variational model is used to calculate the properties of stripe domains in uniaxial magnetic films. The width of the stripes and the thickness of the walls between the stripes are allowed to vary. In addition, the effects of the demagnetizing fields across the walls are included by allowing the spins within the walls to twist out of the wall plane. It is shown that the presence of neighboring walls in this model yields a substantially higher wall energy density in most cases of importance to bubble technology than was previously reported by Schlomann for a similar model of an isolated wall, the stripe wall energy density being over 50 percent higher in the case where the dimensionless anisotropy parameter q = K_{u}/2\piM^{2} is 1.1 and the film thickness to material length ratio h/l is 9. A critical discussion of the significance of wall energies in such models is given, and a method is discussed by which the stripe-width information from this model may be used in interpreting stripe-width data to obtain material parameters to an accuracy hitherto unavailable.