Nematic Liquid Crystal Director Research Articles

The Interaction of Poled Thin Film Ferroelectrics with Nematic Liquid Crystals

Nematic liquid crystals (NLCs) have been widely used to image the static and dynamic domain structure that occurs in poled ferroelectric crystals. The interaction mechanism is influenced by both the coupling of the ferroelectric polarisation with the NLC and the effect on the surface anchoring of the NLC director due to the ferroelectric substrate. This paper reports the formation and observation of poled structures in thin film ferroelectric ceramic systems incorporated in a novel liquid crystal device architecture. Hybrid display devices combining thin film oxide ferroelectrics (OFEs) with NLCs are described. The OFEs are of the lead zirconate-lead titanate, Pb(Zr0.30Ti0.70)O3(PZT 30/70) system, are under 1 μm thick, transparent and are combined with commercially available NLCs. Visualisation of poled domains within the OFE is demonstrated. The mechanism of coupling the polarisation of the OFE with the orientation of the NLC is described and preliminary results are discussed.

Modelling Nematic Liquid Crystal Alignment on Asymmetric Surface Grating Structures

Static nematic liquid crystal director configurations have been calculated numerically for alignment over an asymmetric grooved surface profile. The results demonstrate the existence of a low pretilt regime, where the director field follows the contours of the grating, and a high pretilt regime, where the director field shows a characteristic defect structure. The relative energies of the distorted director field have been calculated for the two regimes. The profile of a real surface has been implemented in the model and the predicted values of the pretilt are commensurate with those measured experimentally.

Singularities of a Variational Wave Equation

We analyze several aspects of the singular behavior of solutions of a variational nonlinear wave equation which models orientation waves in a massive nematic liquid crystal director field. We prove that smooth solutions develop singularities in finite time. We construct exact travelling wave solutions with cusp singularities, and use them to illustrate a phenomena of accumulation and annihilation of oscillations in sequences of solutions with bounded energy. We also prove that constant solutions of the equation are nonlinearly unstable.

On a completely integrable nonlinear hyperbolic variational equation

We show that the nonlinear partial differential equation, ( u t +uu x ) xx =1/2( u x 2 ) x , is a completely integrable, bi-variational, bi-Hamiltonian system. The corresponding equation for w=u xx belongs to the Harry Dym hierarchy. This equation arises in two different physical contexts in two nonequivalent variational forms. It describes the propagation of weakly nonlinear orientation waves in a massive nematic liquid crystal director field, and it is the high-frequency limit of the Camassa-Holm equation, which is an integrable model equation for shallow water waves. Using the bi-Hamiltonian structure, we derive a recursion operator, a Lax pair, and an infinite family commuting Hamiltonian flows, together with the associated conservation laws. We also give the transformation to action-angle coordinates. Smooth solutions of the partial differential equation break down because their derivative blows up in finite time. Nevertheless, the Hamiltonian structure and complete integrability appear to remain valid globally in time, even after smooth solutions break down. We show this fact explicitly for finite dimensional invariant manifolds consisting of conservative piecewise linear solutions. We compute the bi-Hamiltonian structure on this invariant manifold which is obtained by restricting the bi-Hamiltonian structure of the partial differential equation.

On a completely integrable nonlinear hyperbolic variational equation

We show that the nonlinear partial differential equation, ( u t+uu x) xx =1/2( u x 2) x , is a completely integrable, bi-variational, bi-Hamiltonian system. The corresponding equation for w=u xx belongs to the Harry Dym hierarchy. This equation arises in two different physical contexts in two nonequivalent variational forms. It describes the propagation of weakly nonlinear orientation waves in a massive nematic liquid crystal director field, and it is the high-frequency limit of the Camassa-Holm equation, which is an integrable model equation for shallow water waves. Using the bi-Hamiltonian structure, we derive a recursion operator, a Lax pair, and an infinite family commuting Hamiltonian flows, together with the associated conservation laws. We also give the transformation to action-angle coordinates. Smooth solutions of the partial differential equation break down because their derivative blows up in finite time. Nevertheless, the Hamiltonian structure and complete integrability appear to remain valid globally in time, even after smooth solutions break down. We show this fact explicitly for finite dimensional invariant manifolds consisting of conservative piecewise linear solutions. We compute the bi-Hamiltonian structure on this invariant manifold which is obtained by restricting the bi-Hamiltonian structure of the partial differential equation.

Polarization dynamics of an ordinary light wave interacting with a nematic liquid crystal

Abstract Experimental observations and theoretical calculations of the interaction of an ordinary light wave with a homeotropically aligned nematic liquid crystal (NLC) are presented. It was observed that by increasing the light power, aperiodic, damped, periodic and stochastic oscillations of the polarization of the light wave take place. Theoretically, the self-consistent problem of the interaction of the director of a homeotropic NLC with a plane light wave of ordinary type was treated and the change in the polarization state of the transmitted-light wave was calculated. Calculations reproduced the existence of aperiodic, damped and periodic oscillations, in qualitative agreement with the experimental results.

Proton Spin Relaxation of a Liquid Crystal with a Glassy Cholesteric State

Abstract Field-cycling and standard pulsed NMR techniques have been used to study the frequency dependence of the longitudinal proton spin relaxation time T x in the crystalline estradiol compound (+)3,1,7-ß-bis-(4n-butoxybenzoyloxy)-estra-1,3,5-(10)-trien or BET, which is a mesogenic material with a chiral molecular structure. From the measured Larmor frequency and temperature depen-dences we conclude that, at low NMR frequencies in the cholesteric phase, T1 reflects in addition to the relaxation process familiar from nematic liquid crystals (director fluctuation modes) another slow mechanism theoretically predicted for cholesteric systems, namely diffusion induced rotational molecular reorientation. These relaxation processes are not or much less effective in the crystalline and glassy state, where they are frozen. Also the high NMR frequency relaxation dispersion strongly differs between the cholesteric mesophase and the not liquid crystalline samples. This is interpreted by a change from essentially translational self-diffusion to rotational diffusion controlled proton relaxation.

Solitons Generated by Pressure Gradients in Nematic Liquid Crystals

Abstract Equations of motion of director and velocity of nematic liquid crystals under pressure gradients are derived from the Ericksen-Leslie theory. Under suitable approximations, these coupled equations are reduced to a single (2 + 1) nonlinear partial differential equation for the director angle. Boundary effects are taken into account. Similarity analysis of this equation is presented. Properties of steady-state solutions are discussed. Numerical solutions are obtained. Traveling solutions of the (2 + 1) equation are given numerically showing the existence of solitons propagating along the direction of the pressure gradient (in both directions). Corresponding optical interference patterns of these solitons under both monochromatic and white lights are calculated. Good agreement between our theoretical results and recent experiments are obtained.

Possible boundary discontinuities of the tilt angle in nematic liquid crystals

The boundary energy term, introduced by Dubois-Violette and Parodi, which depends on the first derivatives of the nematic liquid crystal director, is considered. Il is shown that if it is written as a purely surface term, the problem of finding stable director configurations cannot be solved. Further information is required about the interaction forces giving rise to this energy term. On the basis of a simple model for such an interaction, it is shown that its main effect is to give a non negligible variation of the tilt angle in a thin boundary layer, when the easy axis is tilted. It is also shown that all the previously used methods for finding the stable director configurations, when surface energy terms dependent on the director derivatives are present, must be reconsidered L'etude amene a la conclusion que toutes les methodes utilisees precedemment pour trouver les configurations stables du directeur doivent etre reconsiderees lorsque les energies de surface contiennent des termes en gradient de l'orientation du directeur

Hysteresis of Light Induced Fréedericks Transition due to the Static Electric Field

Abstract It is shown that when a quasistatic electric field (not inducing the Freedericks transition) is applied to a cell with a nematic liquid crystal (NLC), a hysteresis can arise in the dependence of the NLC director reorientation on the intensity. The critical tension of the static field inducing hysteresis is calculated.

Effects of hydrodynamic motion on the establishment of orientational optical nonlinearity in a liquid crystal

Extensive research is on hand on orientational optical nonlinearity in the mesophase of nematic liquid crystal (NLC), but in all studies on the dynamics of orientation effects it has been usual to employ a dissipative function in the simple form R =0.5y1(~n/3t) 2, where n is the NLC director. This does not incorporate the effects of hydrodynamic motion in the NLC on the establishment of the optical nonlinearity, although the motion of the liquid itself may accompany the director rotation, as occurs for example in SB deformation [I] (see also review [2]), in which the effect is important and the viscosity YI should be replaced by some effective value y ef, which incorporates the effects of the inverse NLC flow, i.e., the changes in velocity V of the NLC during direct reorientation. For small SB deformations in static fields, the effective viscosity y1 ef takes the form [i] ef 2 ef o T t X y : G 3 / ~ b , Y:B = y:--a~/~qc, where the subscripts S and B relate correspondingly to the S and B effects, ~c and ~b are the Mesovich viscosity coefficients, y~ =~a -~2; and ui are the Lesley coefficients. Here we examine the effects of the reverse flow on the settling time for the giant optical nonlinearity and the light-induced Fredericks transition.

The Orientational Optical Non-linearity of Liquid Crystals. I. Nematics

Abstract The optical non-linearity of a nematic liquid crystal (NLC) is considered. The strongest effect studied is due to the local turn of NLC director. The possibility of wavefront conjugation by four-wave interaction in a NLC is considered. Strong effects of self-focusing in a NLC due to the orientational mechanism of non-linearity are predicted.

354. Beam probing of rf beam-plasma interactions: A B Canuara and F W Crawford, J Appl Phys, 36 (10), Oct 1965, 3132–3135

The effects of anchoring phenomenon on the electric Frederiks transition threshold field in a nematic liquid crystal doped with ferroelectric nanoparticles are discussed. The polarizability of these nanoparticles in combination with confinement effects cause the drastic effects on the ferronematic systems. This study is based on Frank free energy and Rapini–Papoular surface energy for ferronematic liquid crystal having finite anchoring condition. In the case of different anchoring boundary conditions, the Euler–Lagrange equation of the total free energy is numerically solved by using the finite difference method together with the relaxation method and Maxwell construction to select the physical solutions and therefore investigate the effects of different anchoring strengths on the Frederiks transition threshold field. Maxwell construction method is employed to select three periodic solutions for nematic liquid crystal director at the interfaces of a slab. In the interval from zero to half-π, there is only one solution for the director orientation. In this way, NLC director rotates toward the normal to the surface as the applied electric field increases at the walls. Our numerical results illustrate that above Frederiks transition and in the intermediate anchoring strength, nematic molecules illustrate the different orientation at slab boundaries. We also study the effects of different anchoring strengths, nanoparticle volume fractions and polarizations on the Frederiks transition threshold field. We report that decreasing in the nanoparticle polarization results in the saturation Frederiks threshold. However, this situation does not happen for the nanoparticles volume fraction.