Flexoelectricity and pattern formation in nematic liquid crystals

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

Thermomechanical effects in uniformly aligned dye-doped nematic liquid crystals

We show theoretically that thermomechanical effects in dye-doped nematic liquid crystals when illuminated by laser beams, can become important and lead to molecular reorientation at intensities substantially lower than that needed for optical Fr\'eedericksz transition. We propose a 1D model that assumes homogenous intensity distribution in the plane of the layer and is capable to describe such a thermally induced threshold lowering. We consider a particular geometry, with a linearly polarized light incident perpendicularly on a layer of homeotropically aligned dye-doped nematics

Separate measurements of the flexoelectric and surface polarization in a model nematic liquid crystal p-methoxybenzylidene-p´-butylaniline : Validity of the quadrupolar approach

The temperature dependences of the surface polarization have been measured at the interface of a conductive glass with both the homogeneously and homeotropically oriented nematic liquid crystal p-methoxybenzylidene-p´-butylaniline. The polarization was found in the field-off regime from the pyroelectric response of a cell to a short laser pulse, absorbed in the bulk of the liquid crystal. The temperature increment was calculated from the measurements of the birefringence induced by the same light pulse. It has been shown that the surface polarization at the homeotropic (mh) and planar (mp) interfaces is directed from an interface into the bulk and from the bulk to an interface, respectively (with a magnitude mh~— 0.3 pC/m and mp' ≈ 0.2 pC/m at 25℃). The experimental data may be explained in terms of the quadrupole model of the order-electric polarization with account of some additional contribution from molecular dipoles. The same technique also allows for the measurements of the z component of the flexoelectric polarization using a pyroelectric response of a hybrid (homeoplanar) aligned nematic cell and proper subtracting of the surface contributions. The flexoelectric polarization has been shown to be opposite to the sum of the surface terms mh + mp and directed from the planar to homeotropic interface. This means that the sum of the flexoelectric coefficients e=(e1 + e3) is positive (e ≅ 1.7 pC/m at 28℃). The temperature dependence of e has been shown to involve a combination of both the quadrupolar and dipolar contributions

Temporal response to harmonic driving in electroconvection

The temporal evolution of the spatially periodic electroconvection (EC) patterns has been studied within the period of the driving ac voltage by monitoring the light intensity diffracted from the pattern. Measurements have been carried out on a variety of nematic systems, including those with negative dielectric and positive conductivity anisotropy, exhibiting "standard EC" (s-EC), those with both anisotropies negative exhibiting "non-standard EC" (ns-EC), as well as those with the two anisotropies positive. Theoretical predictions have been confirmed for stationary s-EC and ns-EC patterns. Transitions with Hopf bifurcation have also been studied. While traveling had no effect on the temporal evolution of dielectric s-EC, traveling conductive s-EC and ns-EC patterns exhibited a substantially altered temporal behavior with a dependence on the Hopf frequency. It has also been shown that in nematics with both anisotropies positive, the pattern develops and decays within an interval much shorter than the period, even at relatively large driving frequencies.Comment: 19 pages, 5 figure

Uniqueness in the Freedericksz transition with weak anchoring

In this paper we consider a boundary value problem for a quasilinear pendulum equation with nonlinear boundary conditions that arises in a classical liquid crystals setup, the Freedericksz transition, which is the simplest opto-electronic switch, the result of competition between reorienting effects of an applied electric field and the anchoring to the bounding surfaces. A change of variables transforms the problem into the equation x = −f(x) for ∈ (−T, T), with boundary conditions x = ± T f(x) at = ∓T, for a convex nonlinearity f. By analyzing an associated inviscid Burgers' equation, we prove uniqueness of monotone solutions in the original nonlinear boundary value problem. This result has been for many years conjectured in the liquid crystals literature, e. g. in E. G. Virga, Variational Theories for Liquid Crystals,Chapman and Hall, London, 1994 and in I. W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction, Taylor and Francis, London, 2003