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.     

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.     

Orientational Behaviour of the Nematic Director upon Macroscopic Rotation at the Magic Angle

The ¹⁹F N.M.R. spectrum of 1,2,2,2-tetrachloro-l,l-difluoroethane has been studied in the nematic liquid crystal ZLI1167 (Merck) upon rotation at the magic angle. The director of the liquid crystal is oriented perpendicular to the spinning axis when the angle between the rotation axis and the magnetic field is less than the magic angle and parallel when this angle is more than the magic angle. It is shown that exactly at the magic angle the spectrum corresponds to a frequency modulated powder pattern. This powder pattern leads to an understanding of the orientational behaviour of the director when a nematic is spun at the magic angle.     

Shear-induced rotations in a weakly anchored nematic liquid crystal

We analyse the instability dynamics of a nematic liquid crystal under steady plane Couette flow. Weak anchoring for molecules of the nematic at the boundaries with an easy axis perpendicular to the flow plane is assumed. Orientation of the director along the easy axis is our basic state. Previously (Tarasov et al., 2001, Liq. Cryst. 28, 833), it was found that the critical shear rate of the primary instability of the basic state strongly decreases with anchoring strength. In the present study our interest was to examine the effect of the anchoring strength on the nematic dynamics in the regime with a slightly supercritical shear rate. It was found that for weaker anchoring the director rotates more strongly and the relaxation time of the amplitude of the basic state perturbations significantly increases. Results obtained can be used for experimental measurements of the anchoring strengths.     

Shear flow induced deformations of planar cholesteric layers

The shear flow induced deformation of the planar cholesteric structure is modelled numerically, taking into account long pitch flow-aligning material. Three pitch-to-thickness ratios in five configurations are considered. Unwinding of the cholesteric helix due to the flow alignment is found. This process has a threshold character, when the mid-plane director is perpendicular to the plane of shear; otherwise it is continuous. The transverse component of the flow is always present. At high stress, the director in the prevailing part of the layer is oriented at the flow-aligning angle.     

An unusual chevron structure in an achiral smectic C liquid crystal device

The layer structure that occurs in an achiral smectic C liquid crystal device has been investigated as a function of temperature using the small angle X-ray scattering facility at the Synchrotron Radiation Source, Daresbury UK. The material studied shows a direct phase transition from the nematic to the smectic C phase. The layer structure proposed on the basis of the diffraction data is relatively complex, containing regions with chevron, quasi-bookshelf and curved structures. A rationale for the formation of the structure is presented, relying on both the phase transition characteristics of the system and the anisotropic layer elasticity in the smectic C phase. Qualitative analysis indicates that the layer constant A is greater than A 21, i.e. layer flexing is easier perpendicular to the plane of the director than parallel to it. It is also demonstrated that the surface chevron angle is several degrees different from the tilt angle of the smectic C phase at temperatures well below the smectic C to nematic phase transition. 12     

Analysis of shear flow alignment of nematic liquid crystals at low shear stress based on catastrophe theory

The low stress shear flow alignment of a nematic liquid crystal in the presence of strong anchoring at the boundaries is analysed. Layers with pretilted director orientation are taken into account. Two kinds of symmetric deformations are assumed. They differ in the director distribution in the vicinity of the boundaries. The analysis is carried out using an expansion of the free energy of the layer in powers of the maximum deformation angle. The results have qualitative character. The condition for the threshold behaviour and the stability of the solutions are discussed. The deformation may develop continuously or discontinuously. The transition between two kinds of deformation is predicted. The facts already known are confirmed and supplemented.     

The director distribution in a spinning nematic mesophase subject to a statis magnetic field

We have determined the probability distribution function for the director in a spinning nematic mesophase subject to a static magnetic field using electrons resonance spectroscopy. For low spinning speeds the director is found to be inclined to the magnetic field as predicted by a continum theory analysis of the system; there is however a small spread in the angle made by the director with the field. This is inhomogeneity in the director alignment increases smoothly as the angular velocity of the mesophase is increased until at high speeds the director adopts an isotropic distribution mesophase which account for the dispersion in the director produced by sample rotation.     

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.     

Manipulation of the director in bicellar mesophases by sample spinning: a new tool for NMR spectroscopy.

It is shown that bicellar nematic liquid-crystalline phases can be oriented with the director (the normal to the bicellar plane) at an arbitrary angle to the applied magnetic field by sample rotation around one axis (variable-angle sample spinning) or around two axes successively (switched-angle spinning). This promises to open novel possibilities for NMR studies of bicelles and proteins incorporated into bicelles or dissolved in a solution containing bicelles, including the correlation of several orientations in a two-dimensional NMR experiment.     

Director distribution and surface anchoring potential in Grandjean-Cano wedge

Theoretical and experimental studies of the director distribution of a chiral nematic liquid crystal placed in a wedge-shaped cell with weak surface anchoring were performed. We measured local value of pitch as function of position inside each Grandjean-Cano zone by registering selective reflection spectra from narrow stripes cut from each Cano zone. We also measured the rotation of the polarisation plane as function of thickness of the wedge sample. These data allowed determination of the angle between the local director and the easy direction on the surface. The obtained director distributions in individual Cano zones were compared with the results of theory and thus used for restoration of the actual shape of the surface anchoring potential.     

Experimental study of the molecular reorientation induced by the ordinary wave in a nematic liquid crystal film

When an s-polarized laser beam impinges on a homeotropically aligned film of nematic liquid crystal at small incident angle, undamped oscillations of the molecular director may be produced. At high beam intensities the oscillations break up into deterministic chaos. Although this effect has been known for a long time and the route to chaos has been qualitatively analysed, no detailed study of the actual molecular director motion has been carried out. We have designed an experimental apparatus to monitor the dynamics of the molecular director, as described by its two polar angles. We observed different dynamical regimes, depending on the laser intensity: steady states, ocillations, rotation and, at the highest laser intensities, deterministic chaos. Moreover, the transitions between the oscillation and rotation regimes are characterized by intermittency.     

Convective director structures upon continuous rotation of nematic side group polymers

We present the first study of convective director structures in nematic side group polymers. A thin liquid crystal cell (10-500 μm) was continuously rotated about an axis perpendicular to the field of a 7T NMR magnet. The director behaviour was followed by deuteron NMR as well as by polarization microscopy. While by optical studies the development of periodic director structures can be directly monitored, the analysis of the NMR lineshape gives detailed information about the director distribution in these structures. The development of the structures depends sensitively on the rotation frequency and is discussed in terms of non-linear amplification of long wavelength director fluctuations due to the coupling between director rotation and viscous flow of the nematic.     

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.     

Convective director structures upon continuous rotation of nematic side group polymers

Abstract

We present the first study of convective director structures in nematic side group polymers. A thin liquid crystal cell (10–500 μm) was continuously rotated about an axis perpendicular to the field of a 7T NMR magnet. The director behaviour was followed by deuteron NMR as well as by polarization microscopy. While by optical studies the development of periodic director structures can be directly monitored, the analysis of the NMR lineshape gives detailed information about the director distribution in these structures. The development of the structures depends sensitively on the rotation frequency and is discussed in terms of non-linear amplification of long wavelength director fluctuations due to the coupling between director rotation and viscous flow of the nematic.     

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.     

Simulation of texture evolution for nematic liquid crystalline polymers under shear flow

The development of microstructure in nematic liquid crystalline polymers under shear flow is investigated through computational simulation. By using a tensorial expression for the elastic torque, the nemato-dynamic equation is numerically resolved. The simulation shows that elastic anisotropy has a strong influence on the evolution of the director and that the ‘log-rolling’ orientation of the directors emerges for tumbling nematics if the twist constant is smaller than the splay and the bend constants, even though one starts from a structure in which the directors are aligned within the velocity and velocity gradient plane. The interaction of wedge disclination pairs subject to a shear flow field is also simulated. The generation, multiplication and interaction of inversion wall defects during shearing have been revealed. In general the wall moves to the boundaries and is absorbed by the boundaries. When two walls of opposite orientation meet, a loop may form, then shrink, and finally collapse. Correspondingly, if they have the same orientation, commutation will occur.     

Simulation of texture evolution for nematic liquid crystalline polymers under shear flow

The development of microstructure in nematic liquid crystalline polymers under shear flow is investigated through computational simulation. By using a tensorial expression for the elastic torque, the nemato-dynamic equation is numerically resolved. The simulation shows that elastic anisotropy has a strong influence on the evolution of the director and that the 'log-rolling' orientation of the directors emerges for tumbling nematics if the twist constant is smaller than the splay and the bend constants, even though one starts from a structure in which the directors are aligned within the velocity and velocity gradient plane. The interaction of wedge disclination pairs subject to a shear flow field is also simulated. The generation, multiplication and interaction of inversion wall defects during shearing have been revealed. In general the wall moves to the boundaries and is absorbed by the boundaries. When two walls of opposite orientation meet, a loop may form, then shrink, and finally collapse. Correspondingly, if they have the same orientation, commutation will occur.     

Simulations of liquid crystals in Poiseuille flow

Lattice Boltzmann simulations are used to explore the behavior of liquid crystals subject to Poiseuille flow. In the nematic regime at low shear rates we find two possible steady-state configurations of the director field. The selected state depends on both the shear rate and the history of the sample. For both director configurations there is clear evidence of shear thinning, a decrease in the viscosity with increasing shear rate. Moreover, at very high shear rates or when the order parameter is large, the system transforms to a ‘log-rolling state’ with boundary layers that may exhibit oscillatory behavior.