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.     

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.     

Experimental study of the director pattern dynamics in the vicinity of the Fréedericksz twist geometry

We present an experimental study of the transient periodic structures appearing in the nematic director field in the magnetically induced reorientation of the director in the vicinity of the twist Fréedericksz geometry. Thin nematic samples (50?µm thick) were exposed to magnetic fields of variable intensity and orientation relative to the surface aligning direction of the sample. The director reorientation was induced by a rapid rotation of the sample in the static magnetic field producing a misalignment between the director and the magnetic field. The director field was optically monitored during the reorientation process and the transient periodic structures were characterized. Two types of periodic structures could be identified, namely bands and walls. Walls grow from bands close to the twist Fréedericksz geometry. The time dependence of the wave length and inclination of the periodic structures was obtained as a function of the magnetic field intensity and orientation relative to the surface aligning direction of the sample. The results for the bands are compared with the predictions of a model that we specifically developed to account for the non-orthogonal field orientations. It is seen that our model can account rather well for the experimental results considering that it uses only the field rotation time as adjustable parameter. All other model parameters are known.     

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.     

Field-induced alignment of the nematic director: studies of nuclear magnetic resonance spectral oscillations in the limit of fast director rotation

Time-resolved NMR spectroscopy is a powerful method to investigate field-induced rotation of the director in a nematic liquid crystal. The method requires that the director does not rotate significantly during the acquisition of the free induction decay and hence the NMR spectrum. We have extended the method to systems where this is not the case and the observed NMR spectra are now found to contain novel oscillatory features. To understand these oscillations, we have developed a model combining both director and spin dynamics. In addition to increasing the information content of the time-resolved NMR spectra, it also proves possible to determine the field-induced relaxation time from a single spectrum.     

Electric-field driven director oscillations in a nematic liquid crystal: a NMR investigation

We have investigated the oscillatory behavior of the nematic director for 4-pentyl-4'-cyanobiphenyl (5CB) when it is subjected to a static magnetic field and a sinusoidal electric field. In these experiments the two fields were inclined at about 50 degrees and the frequency of the electric field was varied from several hertz to approximately 1000 Hz. The director orientation was measured using time-resolved deuterium NMR spectroscopy since this has the advantage of being able to determine the state of director alignment in the sample. In fact, for all of the frequencies studied the director is found to remain uniformly aligned. Since the diamagnetic and dielectric anisotropies are both positive the director oscillates in the plane formed by the two fields. These oscillations were observed to continue for many cycles, indicating that the coherence in the director orientation was not lost during this motion. The maximum and minimum angles made by the director with the magnetic field were determined, as a function of frequency, from the NMR spectrum averaged over many thousand cycles of the oscillations. At low frequencies (several hertz) these limiting angles are essentially independent of frequency but as the frequency increases the two angles approach each other and become equal at high frequencies, typically 1000 Hz. Our results are well explained by a hydrodynamic theory in which the sinusoidal time dependence of the electric field is included in the torque-balance equation. This analysis also shows that, for a range of frequencies between the high and low limits, these NMR experiments can give dynamic as well as static information concerning the nematic phase.     

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.     

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.     

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.     

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.     

Polar electro-optic switching in droplets of an achiral nematic liquid crystal

A polar electro-optic response is observed in droplets of an achiral nematic liquid crystal in coexistence with the isotropic phase. Between crossed polarizers each pancake-shaped droplet shows extinction brushes in the form of a centred cross aligned with the polarizer axes. An applied electric field E induces a rotation of the crosses about the field direction, with about half the droplets switching clockwise and the other half anticlockwise. The sense of rotation in each droplet changes when E is reversed. We propose that a twisted bipolar director structure is stabilized in the droplets by a relatively large splay elastic constant and tangential boundary conditions. The molecules twist along the diameter of the droplets, perpendicular to the applied field, which results in a linear rotation of the director by the inverse flexoelectric effect. Since the molecules are achiral, the handedness of the twist, and hence the sense of the switching, in any droplet is arbitrary.     

Polar electro-optic switching in droplets of an achiral nematic liquid crystal

A polar electro-optic response is observed in droplets of an achiral nematic liquid crystal in coexistence with the isotropic phase. Between crossed polarizers each pancake-shaped droplet shows extinction brushes in the form of a centred cross aligned with the polarizer axes. An applied electric field E induces a rotation of the crosses about the field direction, with about half the droplets switching clockwise and the other half anticlockwise. The sense of rotation in each droplet changes when E is reversed. We propose that a twisted bipolar director structure is stabilized in the droplets by a relatively large splay elastic constant and tangential boundary conditions. The molecules twist along the diameter of the droplets, perpendicular to the applied field, which results in a linear rotation of the director by the inverse flexoelectric effect. Since the molecules are achiral, the handedness of the twist, and hence the sense of the switching, in any droplet is arbitrary.     

Field-cycling NMR detection of magnetoacoustically manipulated nematic ordered states: Memory effects

The proton spin–lattice relaxation time (T₁) dispersion was studied under simultaneous sonication in the nematic phase of 5CB. It appears that metastable ordered states subject to a memory effect can be induced by the combined action of an amplitude-modulated ultrasonication and a pulsed magnetic field. We argue that the acoustic amplitude modulation adds instability to the nematic phase through director order fluctuation enhancement. Different manipulated states of the director were unambiguously identified by the Larmor frequency dispersion of T₁. The field-cycling NMR technique was used for T₁ measurements.     

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.     

Chiral nematic liquid crystals in cylindrical cavities. A classification of planar structures and models of non-singular disclination lines

A part of homotopy theory is applied to classify planar structures in chiral nematic liquid crystals confined to cylindrical cavities. The resulting classification is exact in the approximation of undeformed chiral nematic surfaces. Within this approach the relative stability of possible planar structures with surface and bulk disclination lines is discussed. The number and the shape of these disclinations, which in some cases form spiral structures, are predicted. Further approximate analytical expressions for non-singular director fields close to disclination lines with integral strength are introduced. Our predictions, which are also in agreement with some previously suggested pictures of such director fields, are used to improve stability considerations of the confined planar chiral nematic structures in tubes and droplets.     

The structure and conformations of 2-thiophenecarboxaldehyde obtained from partially averaged dipolar couplings.

The proton NMR spectra of samples of 2-thiophenecarboxaldehyde dissolved in a nematic liquid crystalline solvent, including those from all five singly labelled 13C isotopomers, have been obtained. These have been analysed to yield sets of partially averaged dipolar couplings which have been used to determine the structure and the relative amounts of the cis and trans forms, which are the two minimum-energy structures generated by rotation about the ring-aldehyde bond. A procedure for applying vibrational corrections to the dipolar couplings in the presence of large amplitude motions is discussed.     

Chiral nematic liquid crystals in cylindrical cavities. A classification of planar structures and models of non-singular disclination lines

Abstract

A part of homotopy theory is applied to classify planar structures in chiral nematic liquid crystals confined to cylindrical cavities. The resulting classification is exact in the approximation of undeformed chiral nematic surfaces. Within this approach the relative stability of possible planar structures with surface and bulk disclination lines is discussed. The number and the shape of these disclinations, which in some cases form spiral structures, are predicted. Further approximate analytical expressions for non-singular director fields close to disclination lines with integral strength are introduced. Our predictions, which are also in agreement with some previously suggested pictures of such director fields, are used to improve stability considerations of the confined planar chiral nematic structures in tubes and droplets.     

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.     

Analysis of the degree of nematic ordering within dense aqueous dispersions of charged anisotropic colloids by 23Na NMR spectroscopy

Aqueous dispersions of Laponite, a synthetic clay neutralized by sodium counterions, are used as a model of charged anisotropic colloids to probe the influence of the shape of the particle on their organization within a macroscopic nematic phase. Because of the large fraction of condensed sodium counterions in the vicinity of the clay particle, (23)Na NMR is a sensitive probe of the nematic ordering of the clay dispersions. We used line shape analysis of the (23)Na NMR spectra and measurements of the Hahn echo attenuation to quantify the degree of alignment of the individual clay particles along a single nematic director. As justified by simple dynamical simulations of the interplay between the sodium quadrupolar relaxation and its diffusion through the porous network limited by the surface of the clay particles, we probe the degree of ordering within these clay nematic dispersions by measuring the variation of the apparent (23)Na NMR relaxation rates as a function of the macroscopic orientation of the clay dispersion within the magnetic field.     

Proton N.M.R. lineshape in nematic microdroplets

The dependence of the proton N.M.R. absorption spectrum on nematic director configuration and molecular self-diffusion in nematic submicrondroplets is analysed. The lineshape is evaluated numerically for radial and bipolar director configuration. The motional averaging is taken into account by means of a numerical simulation of the molecular diffusion which induces slow molecular reorientations due to non-uniform orientational ordering in the droplet. This diffusion process strongly affects the absorption spectra of the radial configuration, whereas spectra of the bipolar configuration are only slightly influenced. The possibility of determinating the submicrometre nematic droplet structures using the proton N.M.R. lineshape is discussed.