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

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

Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection

Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes ($\approx$ hydrodynamic modes) of the underlying physical system, much more than quasi one- and two-dimensional patterns are. The reason is the lack of damping boundaries. This paper compares two analytic techniques to derive the patten dynamics from hydrodynamics, which are usually equivalent but lead to different results when applied to multiple homogeneous soft modes. Dielectric electroconvection in nematic liquid crystals is introduced as a model for three-dimensional pattern formation. The 3D pattern dynamics including soft modes are derived. For slabs of large but finite thickness the description is reduced further to a two-dimensional one. It is argued that the range of validity of 2D descriptions is limited to a very small region above threshold. The transition from 2D to 3D pattern dynamics is discussed. Experimentally testable predictions for the stable range of ideal patterns and the electric Nusselt numbers are made. For most results analytic approximations in terms of material parameters are given.Comment: 29 pages, 2 figure

On the surface-type elastic constant K24 in nematics

In the present paper a novel method is presented, allowing us to measure the saddle-splay elastic constant K24 and consequently the mixed splay-bend elasticity K12, in the frame of the continuum-theory. On a weakly anchored nematic cell with a pure bend distortion a twist deformation is superimposed, due to a magnetic field greater than Freedericksz' threshold. The free energy term of the K13-type is rigorously zero, whereas the term affected by K24 is different from zero, and is dependent only on the twist angles at the walls, and not on their first derivatives. Such a situation allows us to solve the variational problem and to evaluate K24, by measuring the shift of the critical field, provided the anchoring strengths at both walls are suitably chosen