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The forced phase locking in a system of the oscillating electroconvective rolls that form in a nematic liquid crystal layer in a dc electric field is studied. As a result of the action of an additive ac electric field with a small amplitude, the system of oscillators is found to be divided into clusters, where oscillations are fully phase locked. The electroconvective rolls in neighboring clusters oscillate in antiphase and the clusters are separated by Ising walls. The phase locking is shown to be maximal at the forcing frequency that is close to the double frequency of the natural oscillations of rolls. A model is proposed to describe spatially distributed phase oscillators, and it takes into account the symmetries of a system of electroconvective rolls and external forcing. The results of numerical simulations agree well with the experimental data.

The actin cytoskeleton and its response to external chemical stimuli is fundamental to the mechano-biology of eukaryotic cells and their functions. One of the key players that governs the dynamics of the actin network is the motor protein myosin II. Based on a phase space embedding we have identified from experiments three phases in the cytoskeletal dynamics of starved Dictyostelium discoideum in response to a precisely controlled chemotactic stimulation. In the first two phases the dynamics of actin and myosin II in the cortex is uncoupled, while in the third phase the time scale for the recovery of cortical actin is determined by the myosin II dynamics. We report a theoretical model that captures the experimental observations quantitatively. The model predicts an increase in the optimal response time of actin with decreasing myosin II-actin coupling strength highlighting the role of myosin II in the robust control of cell contraction.

The structural transformations in a nematic liquid crystal (NLC) layer with a hybrid orientation (planar director orientation is created on one substrate and homeotropic director orientation is created on the other) are studied. In the case of a dc voltage applied to the NLC layer, the primary instability is flexoelectric. It causes the appearance of flexoelectric domains oriented along the director on the substrate with a planar orientation. When the voltage increases further, an electroconvective instability in the form of rolls moving almost normal to flexoelectric domains develops along with these domains. Thus, the following spatially periodic structures of different natures coexist in one system: equilibrium static flexoelectric deformation of a director and dissipative moving oblique electroconvection rolls. The primary instability in the case of an ac voltage is represented by electroconvection, which leads to moving oblique or normal rolls depending on the electric field frequency. Above the electroconvection threshold, a transition to moving “abnormal” rolls is detected. The wavevector of the rolls coincides with the initial director orientation on the substrate with a planar orientation, and the projection of the director at the midplane of the NLC layer on the layer plane makes a certain angle with the wavevector. The results of numerical calculations of the threshold characteristics of the primary instabilities agree well with the obtained experimental data.

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.

We report on Leidenfrost patterns and boiling with compressed sulfur hexafluoride ( $$\hbox {SF}_6$$ ). The experiments were carried out in a large aspect ratio Rayleigh–Benard convection cell, where the distance between the horizontal plates is comparable with the capillary length of the working fluid. Pressures and temperatures were chosen such that the bottom plate was above and the top plate was below the liquid–vapor transition temperature of $$\hbox {SF}_6$$ . As a result, $$\hbox {SF}_6$$ vapor condenses at the top plate and forms drops that grow in size. Leidenfrost patterns are formed as the drops do not fall but levitate by the vapor released in the gap between the hot bottom plate and the colder drops. When the size of these drops became too large, one or more vapor bubbles—chimneys—form inside them. We determine the critical size for the formation of a chimney as a function of the capillary length. For even larger drops and extended puddles many disconnected chimneys occur that can grow to sizes large enough for the formation of new drops inside them. By varying the temperatures and the pressure in the system, we observe various such patterns. When the area covered by a puddle becomes large it touches the hot bottom plate locally and boils off rapidly. This can be attributed to a local reduction of the bottom plate surface temperature below the Leidenfrost temperature.

We investigate flexodomains, which are observed in planar layers of certain nematic liquid crystals, when a dc voltage $U$ above a critical value ${U}_{c}$ is applied across the layer. They are characterized by stationary stripelike spatial variations of the director in the layer plane with a wave number $p(U)$. Our experiments for different nematics demonstrate that $p(U)$ varies almost linearly with $U$ for $Ug{U}_{c}$. That is confirmed by a numerical analysis of the full nonlinear equations for the director field and the induced electric potential. Beyond this numerical study, we demonstrate that the linearity of $p(U)$ follows even analytically, when considering a special parameter set first used by Terent'ev and Pikin [Sov. Phys. JETP 56, 587 (1982)]. Their theoretical paper serves until now as the standard reference on the nonlinear analysis of flexodomains, since it has arrived at a linear variation of $p(U)$ for large $U\ensuremath{\gg}{U}_{c}$. Unfortunately, the corresponding analysis suffers from mistakes, which in a combination led to that result.

Many theoretical and experimental studies indicate that a propagation block represents an important factor in spiral wave initiation in excitable media. The analytical and numerical results we obtained for a generic two-component reaction-diffusion system demonstrate quantitative conditions for the propagation block in a one-dimensional and a two-dimensional medium due to a sharp spatial increase of the medium's excitability or the coupling strength above a certain critical value. Here, we prove that this critical value strongly depends on the medium parameters and the geometry of the inhomogeneity. For an exemplary two-dimensional medium, we show how the propagation block can be used to initiate spiral waves by a specific choice of the size and shape of the medium's inhomogeneity.

We present results from moist convection in a mixture of pressurized sulfur hexa-flouride (liquid and vapor) and helium (gas) to model the wet and dry components of the earth's atmosphere. To allow for homogeneous nucleation, we operate the experiment close to critical conditions. We report on the nucleation of microdroplets in the wake of large cold liquid drops falling through the supersaturated atmosphere and show that the homogeneous nucleation is caused by isobaric cooling of the saturated sulfur hexaflouride vapor. Our results carry over to atmospheric clouds: falling hail and cold rain drops may enhance the heterogeneous nucleation of microdroplets in their wake under supersaturated atmospheric conditions. We also observed that under appropriate conditions settling microdroplets form a rather stable horizontal cloud layer, which separates regions of super and sub critical saturation., 6 pages, 3 figures

Self-sustained waves of electrophysiological activity can cause arrhythmia in the heart. These reentrant excitations have been associated with spiral waves circulating around either an anatomically defined weakly conducting region or a functionally determined core. Recently, an ablation procedure has been clinically introduced that stops atrial fibrillation of the heart by destroying the electrical activity at the spiral core. This is puzzling because the tissue at the anatomically defined spiral core would already be weakly conducting, and a further decrease should not improve the situation. In the case of a functionally determined core, an ablation procedure should even further stabilize the rotating wave. The efficacy of the procedure thus needs explanation. Here, we show theoretically that fundamentally in any excitable medium a region with a propagation velocity faster than its surrounding can act as a nucleation center for reentry and can anchor an induced spiral wave. Our findings demonstrate a mechanistic underpinning for the recently developed ablation procedure. Our theoretical results are based on a very general and widely used two-component model of an excitable medium. Moreover, the important control parameters used to realize conditions for the discovered phenomena are applicable to quite different multicomponent models.

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.

Ferrofluid flow along a tube of radius R in a constant axial magnetic field is revisited. Our analytical solution and numerical simulations predict a transition from an initially axial flow to a steady swirling one. The swirl dynamo arises above some critical pressure drop and magnetic field strength. The new flow pattern consists of two phases of different symmetry: The flow in the core resembles Poiseuille flow in a rotating tube of the radius r_{*}

The effect of superposed dc and ac applied voltages on two types of spatially periodic instabilities in nematic liquid crystals, flexoelectric domains (FD) and electroconvection (EC), was studied. The onset characteristics, threshold voltages and critical wave vectors, were determined. We found that in general the superposition of driving with different time symmetries inhibits the pattern forming mechanisms for FD and EC as well. As a consequence the onset extends to much higher voltages than the individual dc or ac thresholds. A dc bias induced reduction of the crossover frequency from the conductive to the dielectric EC regimes and a peculiar transition between two types of flexodomains with different wavelengths were detected. Direct measurements of the change of the electrical conductivity and its anisotropy, induced by the applied dc voltage component, showed that the dc bias substantially affects both parameters. Taking into account the experimentally detected variations of the conductivity in the linear stability analysis of the underlying nemato-hydrodynamic equations, a qualitative agreement with the experimental findings on the onset behavior of spatially periodic instabilities was obtained., 16 pages, 18 figures

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 investigate a number of complex patterns driven by the electro-convection instability in a planarly aligned layer of a nematic liquid crystal. They are traced back to various secondary instabilities of the ideal roll patterns bifurcating at onset of convection, whereby the basic nemato-hydrodynamic equations are solved by common Galerkin expansion methods. Alternatively these equations are systematically approximated by a set of coupled amplitude equations. They describe slow modulations of the convection roll amplitudes, which are coupled to a flow field component with finite vorticity perpendicular to the layer and to a quasi-homogeneous in-plane rotation of the director. It is demonstrated that the Galerkin stability diagram of the convection rolls is well reproduced by the corresponding one based on the amplitude equations. The main purpose of the paper is, however, to demonstrate that their direct numerical simulations match surprisingly well new experiments, which serves as a convincing test of our theoretical approach.

This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is presented, for both statics and dynamics, and its validity tested self-consistently. As is well known, the mean-field approximation breaks down below four spatial dimensions, where it can be replaced by a scaling phenomenology. The Ginzburg-Landau formalism can then be used to justify the phenomenological theory using the renormalization group, which elucidates the physical and mathematical mechanism for universality. In the second part of the paper it is shown how near pattern forming linear instabilities of dynamical systems, a formally similar Ginzburg-Landau theory can be derived for nonequilibrium macroscopic phenomena. The real and complex Ginzburg-Landau equations thus obtained yield nontrivial solutions of the original dynamical system, valid near the linear instability. Examples of such solutions are plane waves, defects such as dislocations or spirals, and states of temporal or spatiotemporal (extensive) chaos.

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 effect of superimposed ac and dc electric fields on the formation of electroconvection and flexoelectric patterns in nematic liquid crystals was studied. For selected ac frequencies, an extended standard model of the electrohydrodynamic instabilities was used to characterize the onset of pattern formation in the two-dimensional parameter space of the magnitudes of the ac and dc electric field components. Numerical as well as approximate analytical calculations demonstrate that depending on the type of patterns and on the ac frequency, the combined action of ac and dc fields may either enhance or suppress the formation of patterns. The theoretical predictions are qualitatively confirmed by experiments in most cases. Some discrepancies, however, seem to indicate the need to extend the theoretical description.

Electroconvection in twisted nematics has been studied experimentally and theoretically. The frequency dependence of the threshold voltage and rolls period for the different twist angles as well as the Lifshitz point versus the twist angle have been measured. The experimental results agree well with the predictions of linear stability analysis. Various types of secondary instabilities were found above the roll instability depending on the twist angle. The transition from 1D structure to the 2D domain pattern was investigated.

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.

~Received 19 March 1998! The response of a homeotropically aligned nematic liquid crystal layer to oscillatory rectilinear shear ~Couette flow ! was investigated for frequencies f between 0.01 and 200 Hz and layer thickness d between 10 and 130 mm. Below the onset of instability the cell was placed between crossed polars and light transmission was studied using a parallel light beam. The experimental results for the transmitted light intensity agree quantitatively with numerical solutions of the nematodynamic equations for different cell thicknesses, oscillation frequencies, and amplitudes. For frequencies between 25 and 150 Hz the critical oscillation amplitude for the onset of a spatial pattern, observed in polarized white light, could be reached. The pattern consisted of stationary rolls perpendicular to the direction of the oscillation. The experimentally obtained frequency dependence of the critical shear amplitude for the roll instability for different cell thicknesses is compared with an existing theory and the results of numerical calculations. @S1063-651X~98!09411-2# Nematic liquid crystals ~NLCs! exhibit interesting flow phenomena due to the coupling between the local molecular orientation ~director n ˆ! and the velocity field v. The flow properties of NLCs are characterized by Leslie viscosity coefficients a 1 ,...,a6 , two of which a 2(,0) and a 3 are important in describing the coupling between flow and director orientation @1‐4#. In the case of steady, plane, parallel shear flow, e.g., along the x axis with a velocity field v x(z )( v y 5 v z 50) and in the absence of other torques, the director will tend to align in the flow plane ( x-z plane! at a fixed angle u fl 56arctan(a3 /a2) 1/2 with the x axis if a 3,0 ~the 6

A. Voit, A. Krekhov, and W. Ko 1hler*Physikalisches Institut, UniVersita¨t Bayreuth,D-95440 Bayreuth, GermanyReceiVed September 22, 2006Phase separation of polymer blends, especially spinodaldecomposition, has fascinated researchers for a long time, anda large body of both experimental and theoretical papers canbe found in the literature. Almost all authors describe the phasebehavior of the blend by means of an equilibrium phase diagram,where the locus of the mixture is fully characterized by itsaverage composition and a constant temperature.Comparatively little work has been done on the phasebehavior of polymer blends subject to nonuniform temperaturefields. Lee et al. studied spinodal decomposition in the presenceof a temperature gradient

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

Pattern forming instabilities induced by ultralow frequency sinusoidal voltages were studied in a rodlike nematic liquid crystal by microscopic observations and simultaneous electric current measurements. Two pattern morphologies, electroconvection (EC) and flexodomains (FD), were distinguished, both appearing as time separated flashes within each half period of driving. A correlation was found between the time instants of the EC flashes and those of the nonlinear current response. The voltage dependence of the pattern contrast $C(U)$ for EC has a different character than that for the FD. The flattening of $C(U)$ at reducing the frequency was described in terms of an imperfect bifurcation model. Analyzing the threshold characteristics of FD, the temperature dependence of the difference $|{e}_{1}\ensuremath{-}{e}_{3}|$ of the flexoelectric coefficients was also determined by considering elastic anisotropy.

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.

The temporal evolution of patterns within the driving period of the ac voltage was studied in the 10-mHz-250-Hz frequency range. It was shown that the stationary electroconvection pattern of the conductive regime transforms into a flashing one at ultralow frequencies, existing only in narrow time windows within the period. Furthermore a transition between electroconvection and flexoelectric domains was detected which is repeating in each half period. The two patterns are well separated in time and in Fourier space. Simultaneous current measurements uncovered that the electric properties of the polyimide orienting layers influence the redistribution of the applied voltage. The experimental findings are in good qualitative agreement with the theoretical predictions based on an extended standard model including flexoelectricity.

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

We present some experiments on electrohydrodynamic convection (EHC) in nematic liquid crystals with a planar, but twisted configuration (MBBA). The threshold voltage is shown to depend only weakly on the twist angle. A theoretical analysis of the onset behaviour agrees well with the experiments. More sensitive is a secondary transition to modulation structures, which are not easily observed in untwisted geometries. A rough estimate of the secondary instability based on the behaviour of the most rapidly growing modulation mode seems to account well for the observations. Additional theoretical investigations for materials with positive dielectric anisotropy concerning the competition between the Freedericksz transition and EHC are included. We predict the existence of a crossover codimension-2 point, which could easily be tested by variation of the twist angle

It is demonstrated that the key findings of the paper by Y.G. Marinov and H.P. Hinov, Eur. Phys. J. E 31, 179-189 (2010), are in direct conflict with the general physical background of flexoelectric domains. This is caused by a methodological error in the theoretical analysis of the paper.

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.

Anomalous diffusion is predicted for Brownian particles in inhomogeneous viscosity landscapes by means of scaling arguments, which are substantiated through numerical simulations. Analytical solutions of the related Fokker-Planck equation in limiting cases confirm our results. For an ensemble of particles starting at a spatial minimum (maximum) of the viscous damping we find subdiffusive (superdiffusive) motion. Superdiffusion occurs also for a monotonically varying viscosity profile. We suggest different substances for related experimental investigations., Comment: 15 pages

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.

We discuss the dynamic critical properties of a binary blend of the two polymers poly(dimethyl siloxane) (PDMS) and poly(ethyl-methyl siloxane) (PEMS), and we have investigated experimentally and theoretically patterning and structure formation processes above and below the spinodal in the case of a spatially varying temperature. Asymptotic critical scaling is found close to T c in the range 6 ×10− 4 ≤ e ≤ 0. 2 of the reduced temperature e and a mean field behavior for large values of e. The thermal diffusion coefficient D T is thermally activated but does not show the critical slowing down of the Fickian diffusion coefficient D, which can be described by crossover functions for D. The Soret coefficient \({S}_{\mathrm{T}} = {D}_{\mathrm{T}}/D\) diverges at the critical point with a critical exponent − 0. 67 and shows a crossover to the exponent − 1 of the structure factor in the classical regime. Thermal activation processes cancel out and do not contribute to S T. The divergence of S T also leads to a very strong coupling of the order parameter to small temperature gradients, which can be utilized for laser patterning of thin polymer films. For a quantitative numerical model all three coefficients D, D T, and S T have been determined within the entire homogeneous phase and are parameterized by a pseudospinodal model. It is shown that equilibrium phase diagrams are no longer globally valid in the presence of a temperature gradient, and systems with an upper critical solution temperature (UCST) can be quenched into phase separation by local heating. Below the spinodal there is competition between the spontaneous spinodal demixing patterns and structures imposed by means of a focused laser beam utilizing the Soret effect. Elongated structures degrade to spherical objects due to surface tension effects leading to pearling instabilities. Grids of parallel lines can be stabilized by enforcing certain boundary conditions. Phase separation phenomena in polymer blends belong to the universality class of pattern forming systems with a conserved order parameter. In such systems, the effects of spatial forcing are rather unexplored and, as described in this work, spatial temperature modulations may cause via the Soret effect (thermal diffusion) a variety of interesting concentration modulations. In the framework of a generalized Cahn–Hilliard model it is shown that coarsening in the two-phase range of phase separating systems can be interrupted by a spatially periodic temperature modulation with a modulation amplitude beyond a critical one, where in addition the concentration modulations are locked to the periodicity of the external forcing. Accordingly, temperature modulations may be a useful future tool for controlled structuring of polymer blends. In the case of a traveling spatially periodic forcing, but with a modulation amplitude below the critical one, the coarsening dynamics can be enhanced. With a model of phase separation, taking into account thermal diffusion, essential features of the spatio-temporal dynamics of phase separation and thermal patterning observed in experiments can be reproduced. With a directional quenching an effective approach is studied to create regular structures during the phase separation process. In addition, it is shown that the wavelength of periodic stripe patterns is uniquely selected by the velocity of a quench interface. With a spatially periodic modulation of the quench interface itself, cellular patterns can also be generated.

We present a theoretical analysis of phase separation in the presence of a spatially periodic forcing of wavenumber q traveling with a velocity v. By an analytical and numerical study of a suitably generalized 2d-Cahn-Hilliard model we find as a function of the forcing amplitude and the velocity three different regimes of phase separation. For a sufficiently large forcing amplitude a spatially periodic phase separation of the forcing wavenumber takes place, which is dragged by the forcing with some phase delay. These locked solutions are only stable in a subrange of their existence and beyond their existence range the solutions are dragged irregularly during the initial transient period and otherwise rather regular. In the range of unstable locked solutions a coarsening dynamics similar to the unforced case takes place. For small and large values of the forcing wavenumber analytical approximations of the nonlinear solutions as well as for the range of existence and stability have been derived.

Phase separation under directional quenching has been studied in a Cahn-Hilliard model. In distinct contrast to the disordered patterns which develop under a homogeneous quench periodic stripe patterns are generated behind the quench front. Their wavelength is uniquely defined by the velocity of the quench interface in a wide range. Numerical simulations match perfectly analytical results obtained in the limit of small and large velocities of the quench interface. Additional periodic modulation of the quench interface may lead to cellular patterns. The quenching protocols analyzed in this paper are expected to be an effective tool in technological applications to design nanostructured materials.

Novel behavior in electroconvection (EC) has been detected in nematic liquid crystals (NLCs) under the condition of comparable timescales of the director relaxation and the period of the driving ac voltage. The studied NLCs exhibit standard EC (s-EC) at the onset of the instability, except one compound in which nonstandard EC (ns-EC) has been detected. In the relevant frequency region, the threshold voltage for conductive s-EC bends down considerably, while for dielectric s-EC it bends up strongly with the decrease of the driving frequency. We show that inclusion of the flexoelectric effect into the theoretical description of conductive s-EC leads to quantitative agreement, while for dielectric s-EC a qualitative agreement is achieved. The frequency dependence of the threshold voltage for ns-EC strongly resembles that of the dielectric s-EC., Comment: 13 pages, 14 figures, submitted