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Register a new userPatterns driven by combined AC and DC electric fields in nematic liquid crystals
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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 electro-hydrodynamic 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.
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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.
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-Benard 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.
We present in this paper a detailed analysis of the flexoelectric instability of a planar nematic layer in the presence of an alternating electric field (frequency $omega$), which leads to stripe patterns (flexodomains) in the plane of the layer. This equilibrium transition is governed by the free energy of the nematic which describes the elasticity with respects to the orientational degrees of freedom supplemented by an electric part. Surprisingly the limit $omega to 0$ is highly singular. In distinct contrast to the dc-case, where the patterns are stationary and time-independent, they appear at finite, small $omega$ periodically in time as sudden bursts. Flexodomains are in competition with the intensively studied electro-hydrodynamic instability in nematics, which presents a non-equilibrium dissipative transition. It will be demonstrated that $omega$ is a very convenient control parameter to tune between flexodomains and convection patterns, which are clearly distinguished by the orientation of their stripes.
We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response can dramatically enhance the field coupling leading to the stabilization of the vortex beam when the amplitude of the second beam exceeds some threshold value. We develop a variational approach to describe this effect analytically.
We analyze the interaction with uniform external fields of nematic liquid crystals within a recent generalized free-energy posited by Virga and falling in the class of quartic functionals in the spatial gradients of the nematic director. We review some known interesting solutions, i. e., uniform heliconical structures, which correspond to the so-called twist-bend nematic phase and we also study the transition between this phase and the standard uniform nematic one. Moreover, we find liquid crystal configurations, which closely resemble some novel, experimentally detected, structures called Skyrmion Tubes. Skyrmion Tubes are characterized by a localized cylindrically-symmetric pattern surrounded by either twist-bend or uniform nematic phase. We study the equilibrium differential equations and find numerical solutions and analytical approximations.
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