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The nonsingular soliton-like defects in plane nematic liquid crystal (NLC) layers and spherical NLC drops are experimentally detected and studied when the interaction of NLC molecules with a bounding surface is varied. The dynamics and the annihilation of nonsingular defects of opposite signs on a plane surface are investigated. Periodic transformations of the soliton-like defects in NLC drops in an electric field are detected. The theory of elasticity is used to show that the surface energy taken into account in the total free energy of NLC in the case of weak anchoring leads to the possibility of nonsingular solutions of a director equilibrium equation. The calculated pictures of director distribution in a plane NLC layer and in a spherical NLC drop characterized by weak surface anchoring agree well with the results of polarized light optical observations.

The spatiotemporal dynamics of oscillating electroconvective structures appearing in a nematic liquid crystal (NLC) under the combined action of applied alternating (ac) and direct (dc) electric voltages has been experimentally studied. It is established that an increase in the dc component of the applied voltage leads to synchronization of the hydrodynamic mode with the orientational twist mode of the NLC director. The synchronization parameter and the phase shift of the modes are determined as function of the applied dc voltage. The results confirm the flexoelectric mechanism of synchronization.

We describe the dynamics of zigzag oscillations in a system of convective rolls in a nematic liquid crystal above the electroconvection threshold under the action of an ac voltage with a biased position of the mean value. It is found that an increase in the contribution from the constant component leads to a substantial increase in the spatiotemporal ordering of zigzag rolls and their synchronization with the homogeneous twist mode. The results confirm the flexoelectric mechanism of locking.

We present a systematic study of defects in thin films of cylinder-forming block copolymers upon long-term thermal or solvent annealing. In particular, we consider in detail the peculiarities of both classical and specific topological defects, and conclude that there is a strong "defect structure-chain mobility" relationship in block copolymers. In the systems studied, representative defect configurations provide connectivity of the minority phase in the form of dislocations with a closed cylinder end or classical disclinations with incorporated alternative, nonbulk structures with planar symmetry. In solvent-annealed films with enhanced chain mobility, the neck defects (bridges between parallel cylinders) were observed. This type of nonsingular defect has not been identified in block copolymer systems before. We argue that topological arguments and 2D defect representation, sufficient for lamellar systems, are not sufficient to determine the stability and mobility of defects in the cylindrical phase. In-situ scanning force microscopy measurements are compared with the simulations based on the dynamic self-consistent mean field theory. The close match between experimental measurements and simulation results suggests that the lateral defect motion is diffusion-driven. In addition, 3D simulations demonstrated that the bottom (wetting) layer is only weakly involved into the structure ordering at the free surface. Finally, the morphological evolution is considered with the focus on the motion and interaction of the representative defect configurations.

We report the results on the orientational dynamics and instabilities in nematic liquid crystal MBBA induced by decaying Poiseuille flow. The experiments were carried out in the rectangular wedge-shape LC cell with thickness varying perpendicular to the flow direction and the confining plates provided homeotropic alignment of a nematic liquid crystal. Increasing the values of initial pressure difference the orientational instability corresponding to the escape of the director out of the shear plane was observed for the first time. This ‘‘out-of-plane’’ transition takes place at some critical pressure difference DPc which depends on the local thickness of NLC layer. The results of numerical simulations of governing nematodynamic equations are in a good agreement with experimental data on the threshold of ‘‘out-of-plane’’ instability.

The temperature behaviour of the anchoring energy of nematic liquid crystal MBBA at the substrates with oblique SiO evaporation and director orientation at the interface have been studied by means of magnetic Freedericksz transition technique. The temperature dependence of the coefficients in the phenomenological model of surface anchoring energy has been determined.

We analyse the influence of a surface viscosity on the orientational dynamics of a nematic liquid crystal subjected to an oscillatory Couette flow. Approximate analytical solutions of nematohydrodynamic equations for small flow amplitudes are calculated and compared with the results of full numerical simulations. The range of flow frequencies where the surface viscosity has strong influence on the optical response is determined., 8 pages, 2 figures

This contribution deals with three types of orientational phenomena generated by oscillatory #ow in nematic liquid crystals: (1) Uniform orientational instabilities in the geometry where the director is initially oriented within the #ow plane. The instability occurs under rectilinear Poiseuille #ow and not under Couette #ow. (2) The "rst instability under rectilinear Couette #ow is a bifurcation to a stationary roll pattern with the roll axis perpendicular to the #ow direction. The threshold amplitude has been measured for homeotropic alignment and calculated by linear stability analysis. (3) An interesting slow director precession and nonlinear waves which arise in homeotropically aligned nematics exposed to an elliptical shear #ow in the bend FreH edericksz distorted state. The experimental data are compared with a theoretical analysis. The precession can also be generated by oscillatory compression. ( 2000 Elsevier Science B.V. All rights reserved.

We consider planarly oriented nematic liquid crystal subjected to plane, rectilinear, oscillatory Couette or Poiseuille flow in the case, when the director is initially perpendicular to the flow plane. Using the Galerkin method we found the critical amplitude of the flow at which the homogeneous instability develops. The analytical approximations for the frequency dependence of the critical amplitude for different types of flow are obtained. The results are compared with experimental data.

The optical response of the nematic liquid crystal confined between plates with strong homeotropic and weak planar anchoring (hybrid geometry) under the oscillatory shear has been investigated. Critical shear amplitude above that the director deviates from the planar orientation at the substrate with weak anchoring was found and the dependence of the tilt angle on the displacement amplitude was obtained. The anchoring strength and surface viscosity for the SiO-evaporated substrate was estimated.

Phase separation in binary mixtures in the presence of Janus particles has been studied in terms of a Cahn-Hilliard model coupled to the Langevin equations describing the particle dynamics. We demonstrate that the phase separation process is arrested leading to unexpected regular stripe patterns in the concentration field. The underlying pattern forming mechanism has been elucidated: The twofold absorption properties on the surface of Janus particles with respect to the two components of a binary mixture trigger in their neighborhood spatial concentration variations. They result in an effective interaction between the particles mediated by the binary mixture. Our findings open a route to design composite materials with nanoscale lamellar morphologies where the pattern wavelength can be tuned by changing the wetting properties of the Janus particles., 5 pages, 4 figures

Optical methods are most convenient to analyze spatially periodic patterns with wavevector $\bm q$ in a thin layer of a nematic liquid crystal. In the standard experimental setup a beam of parallel light with a 'short' wavelength $\lambda \ll 2 \pi/q$ passes the nematic layer. Recording the transmitted light the patterns are either directly visualized by shadowgraphy or characterized more indirectly by the diffraction fringes due to the optical grating effects of the pattern. In this work we present a systematic short-wavelength analysis of these methods for the commonly used planar orientation of the optical axis of liquid crystal at the confining surfaces. Our approach covers general 3D experimental geometries with respect to the relative orientation of $\bm q$ and of the wavevector $\bm k$ of the incident light. In particular the importance of phase grating effects is emphasized, which are not accessible in a pure geometric optics approach. Finally, as a byproduct we present also an optical analysis of convection rolls in Rayleigh-B\'enard convection, where the refraction index of the fluid is isotropic in contrast to its uniaxial symmetry in nematic liquid crystals. Our analysis is in excellent agreement with an earlier physical optics approach by Trainoff and Cannell [Physics of Fluids {\bf 14}, 1340 (2002)], which is restricted to a 2D geometry and technically much more demanding., Comment: 22 pages

The dynamics of microphase separation and the orientation of lamellae in diblock copolymers is investigated in terms of a mean-field model. The formation of lamellar structures and their stable states are explored and it is shown that lamellae are stable not only for the period of the structure corresponding to the minimum of the free energy. The range of wavelengths of stable lamellae is determined by a functional approach, introduced with this work, which is in agreement with the results of a linear stability analysis. The effects of the interaction of block copolymers with confining plane boundaries on the lamellae orientation are studied by an extensive analysis of the free energy. By changing the surface property at one boundary, a transition from a preferentially perpendicular to a parallel lamellar orientation with respect to the boundaries is found, which is rather independent of the distance between the boundaries. Computer simulations reveal, that the time scale of the lamellar orientational order dynamics, which is quantitatively characterized in terms of an orientational order parameter and the structure factor, depends significantly on the properties of the confining boundaries as well as on the quench depth.

The nonlinear response of a nematic slab subjected to a rectilinear low-frequency oscillatory Couette and Poiseuille flow is investigated theoretically. We find that under Poiseuille flow and with appropriate alignment conditions by surface anchoring and/or magnetic field a state with slow, spontaneous director rotation appears. This may provide a model for the slow director rotations observed in high-frequency Couette flow. \textcopyright{} 1996 The American Physical Society.

We calculate the threshold of electrohydrodynamic convection (EHC) for nematic liquid crystals with negative dielectric anisotropy, where one allows for different director orientations at the upper and lower confining plates (hybrid cells). Besides the planar versus homeotropic case we present for the first time an analysis of continuous tilt at one plate. The predistorted ground state strongly influences the EHC character and the roll orientation. One observes a generic nonstationary behaviour and in particular the interesting scenario of drifting oblique rolls.

Generalizing a recently introduced approximation scheme valid when the director relaxation time is large compared to the inverse frequency of an oscillatory flow, we derive equations for the time-averaged torques on the director for a prescribed plane shear flow. Whereas for a linear flow field (simple Couette flow) the average torques vanish, one has for Poiseuille flow (and more general flow fields) torques that tend to orient the director essentially perpendicular to the flow plane. For flow-aligning materials the orientation parallel to the flow is also (weakly) stable. Including the effect of homeotropic surface alignment we estimate the threshold of the oscillation amplitude for the out-of-plane transition. The results are essentially recovered (and improved) by direct numerical simulations

The viscoelastic properties of a binary mixture of a mesogenic side-chain block copolymer in a low molecular weight nematic liquid crystal are studied for mass concentrations ranging from the diluted regime up to a liquid crystalline gel state at about 3%. In the gel state, the system does not flow, exhibits a polydomain structure on a microscopic level, and strongly scatters light. Below the gelation point, the system is homogeneous and behaves like a usual nematic, so the continuum theory of liquid crystals can be applied for interpreting the experimental data. Using the dynamic Fr\'eedericksz transition technique, the dependence of the splay elastic constant and the rotational viscosity on the polymer concentration have been obtained. Comparing the dynamic behavior of block copolymer solutions with the respective homopolymer solutions reveals that, above a mass concentration of 1%, self-assembling of the block copolymer chain segments in clusters occurred, resulting in a gel state at higher concentrations. The effective cluster size is estimated as a function of the concentration, and a scaling-law behavior near the sol-gel transition is confirmed. This technique may serve as an alternative method for determining the gelation point.

Using a simple averaging method we show that under plane oscillatory shear a net torque acts on the director of a nematic liquid crystal leading to unexpected flow alignment. Under quite general conditions the usual flow-alignment orientations are unstable, and the ori- entation parallel to the shear (perpendicular to the velocity) becomes most stable within the shear plane. The effect drops out exactly under (unrealistic) linear shear unless the director has a nontrivial space dependence. An explicit application to plane Poiseuifle flow is presented. Pre- liminary experimental data are shown which demonstrate a transition under planar oscillatory shear from a homeotropically aligned nematic to a spatially homogeneously deformed state.

The experimental investigation of surface polarization by modulation spectroscopy of electro-reflection from the nematic liquid crystal-semiconductor interface and capacitance modulation spectroscopy of direct piezoeffect in nematics has been carried out. The models of surface polarization with induced polar order parameter have been suggested.

The problem of disclinations streamlining by the flow of nematic liquid crystal (NLC) was investigated theoretically. Distributions of the flow velocity for defects with different topological indices were found numerically.

For many years it has been commonly accepted that electroconvection (EC) as primary instability in nematic liquid crystals for the "classical" planar geometry requires a positive anisotropy of the electric conductivity, sigma(a), and a slightly negative dielectric anisotropy, epsilon(a). This firm belief was supported by many experimental and theoretical studies. Recent experiments, which have surprisingly revealed EC patterns at negative conduction anisotropy as well, have motivated the theoretical studies in this paper. It will be demonstrated that extending the common hydrodynamic description of nematics by the usually neglected flexoelectric effect allows for a simple explanation of EC in the "nonstandard" case sigma(a)

We consider instabilities, either homogeneous or periodic in space, which develop in a nematic liquid crystal layer under rectilinear oscillatory Couette flow for planar surface alignment of the director perpendicular to the flow plane. On the basis of a numerical and analytical linear stability analysis we determine the critical amplitude of the oscillatory flow, the wave number, and the symmetry of the destabilizing mode and present a comprehensive phase diagram of the flow instabilities. In particular it is found that by varying the frequency of the Couette flow the instability changes its temporal symmetry. This transition is shown to be related to the inertia effects of the nematic fluid, which become more important with increasing flow frequency. We also show that an electric field applied perpendicularly to the nematic layer can induce an exchange of instabilities with different spatial and temporal symmetries. The theoretical results are compared with experiments, when available.

We study theoretically the slow director precession and nonlinear waves observed in homeotropically oriented nematic liquid crystals subjected to circular or elliptical Couette and Poiseuille flow and an electric field. From a linear analysis of the nematodynamic equations it is found that in the presence of the flow the electric bend Fréedericksz transition is transformed into a Hopf-type bifurcation. In the framework of an approximate weakly nonlinear analysis we have calculated the coefficients of the modified complex Ginzburg-Landau equation, which slightly above onset describes nonlinear waves with strong nonlinear dispersion. We also derive the equation describing the precession and waves well above the Fréedericksz transition and for small flow amplitudes. Then the nonlinear waves are of diffusive nature. The results are compared with full numerical simulations and with experimental data.

We study the homogeneous and the spatially periodic instabilities in a nematic liquid crystal layer subjected to steady plane Couette or Poiseuille flow. The initial director orientation is perpendicular to the flow plane. Weak anchoring at the confining plates and the influence of the external electric and/or magnetic field are taken into account. Approximate expressions for the critical shear rate are presented and compared with semianalytical solutions in case of Couette flow and numerical solutions of the full set of nematodynamic equations for Poiseuille flow. In particular the dependence of the type of instability and the threshold on the azimuthal and the polar anchoring strength and external fields is analyzed.

The stability of the equilibrium configurations of a nematic liquid crystal confined between two coaxial cylinders is analysed when a radial electric field is applied and the flexoelectric effect is taken into account. The threshold for perturbations depending only on the radius r in the cylindrical coordinate system and strong boundary conditions is studied. A new type of orientational transition caused by pure flexoelectric effect is found., 8 pages, 3 figures. To appear in Mol. Cryst. Liq. Cryst. (2001)

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 pre-aligned 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 one has two types of instability 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., Comment: 19 pages, 3 figures

We investigate the orientational behaviour of a homeotropically aligned nematic liquid crystal subjected to an oscillatory plane Poiseuille flow produced by an alternating pressure gradient. For small pressure amplitudes the director oscillates within the flow plane around the initial homeotropic position, whereas for higher amplitudes a spatially homogeneous transition to out-of-plane director motion was observed for the first time. The orientational transition was found to be supercritical and the measured frequency dependence of the critical pressure amplitude in the range between 2 and 20 Hz was in quantitative agreement with a recent theory., 11 pages, 4 figures, submitted to Europhys. Lett

Elliptic shear applied to a homeotropically oriented nematic above the electric bend Freedericks transition (FT) generates slow precession of the director. The character of the accompanying nonlinear waves changes from diffusive phase waves to dispersive ones exhibiting spirals and spatio-temporal chaos as the FT is approached from above. An exact solution of the flow alignment equations captures the observed precession and predicts its reversal for non-flow aligning materials. The FT transforms into a Hopf bifurcation opening the way to understand the wave phenomena., Comment: 4 pages, 4 figures, submitted to PRL

We report experimental and theoretical results on the flexoelectric instability and crossover between flexoelectric domains and electroconvection in a hybrid aligned nematic MBBA under d.c. voltage. At threshold a spatially periodic flexoelectric deformation in the form of longitudinal domains (along the planar director) was observed. With increasing voltage the director deviation out of the initial plane becomes clearly detectable. Observations of tracers show that hydrodynamic flow develops inside the flexoelectric stripe pattern in the form of circular orbits perpendicular to the domain stripes. With further increasing d.c. voltage electroconvection sets in in the form of drifting oblique rolls inside the flexoelectric domains., Comment: 8 pages, 4 figures. To Appear in Mol. Cryst. Liq. Cryst. (2001)