Flexoelectric effect measurement

Converse flexoelectric effects (i.e. voltage-generated curving) have been demonstrated in uranyl-acetate-stabilized phosphatidylserine BLMs by real-time stroboscopic interferometric measurements the obtained satisfactory agreement between the converse and the direct (i.e. curvature-generated voltage) flexoelectric coefficients have been in accord with the Maxwell relationship [8]. 

This chapter is concerned with experimental measurements of flexo-electric coefficients. After a brief introduction to flexoelectricity in nematic liquid crystaJs, some applications exploiting the flexoelectric effect and the influence of this effect on electrohydrodynamic instabilities are pointed out. Flexoelectricity axises in samples with a splay-bend distortion in the director field and as such its measurement is not as direct as for dielectric constants. The theoretical background needed to analyse electro-optic experiments and extract the flexocoefficients is outlined in Section 2.2. Various experimental techniques that have been developed are described in Section 2.3. These involve cells in which the alignment of the nematic director is homeotropic, or planar or hybrid. In the first case, the interdigitated electrode technique is particularly noteworthy, as it has been used to establish several features of flexoelectricity (1) the effect can arise purely from the quadrupolar nature of the medium, and (2) the dipolar contribution relaxes at a relatively low frequency. 

Though this type of periodic structure with multiple arches of the director is difficult to generate in a nematic, it is already present in a cholesteric liquid crystal when viewed in a plane whose normal makes an oblique angle with the helical axis. The flexoelectric effect changes the periodicity of this structure under a DC field applied normal to the helical axis, effectively rotating the latter. This can be used in tmn to measure (ei — 63). ... 

In this chapter we consider several important aspects of the flexoelectric effect for chiral polar smectic liquid crystals and for the variety of phases. First, we discuss the reason for indirect interlayer interactions, which extend to more distant layers, and the lock-in to multi-layer structures. Second, although it was believed for a long time that polarization in tilted chiral smectics is always perpendicular to the tilt with the smectic layer normal, a component in the direction of the tilt may exist. And third, in multi-layer structures, the flexoelectricaUy induced polarization can be extremely large but is difficult to measure. 

What are the other possibilities for measuring the flexoelectric effect We could consider dielectric coupling in a high-frequency electric field. 

In more complex chiral polar smectics, antiferroelectric liquid crystals, there are many consequences of the flexoelectric effect. It influences interlayer interactions and causes indirect interactions between more distant layers to appear and become important. The phenomenon is the reason for the appearance of commensurate structures that extend up to six layers. In addition, longitudinal polarization, i.e. the polarization that has a component parallel to the tilt, exists in more complex structures such as the SmCpi2, the SmC jj and the SmC phases. Unfortunately it seems that flexoelectric polarization cannot be detected separately from other phenomena by simple means. A way of measuring the flexoelectric contribution in tilted polar smectics still seems to be an open question. 

One of the experimental methods for studying the orientation of the liquid crystal in the flexoelectric effect is to measure the retardation of the liquid crystal cell, which is given by... 

The most direct method of finding the coefficient en would be to fill the space between the metallic coaxial cylinders with a liquid crystal having pear-shaped molecules, with the surfaces of the cylinders having been pretreated for homeotropic orientation and to measure the potential difference between the cylinders. In fact, because of the difference in radii of the cylinders, the nematic liquid crystal structure proves to be splay deformed, and if the molecules have even a small longitudinal dipole moment the plates of the coaxial capacitor would be charged. However, despite its apparent simplicity, this experiment is, in fact, complicated because of the screening of the potential caused by the flexoelectric effect by firee charges from the liquid crystal and the atmosphere. 

Assuming that arises from the third-order hyperpolarizability, elements of give information about the degree of orientational order. Measurements of electric-field-induced second-harmonic generation (EFISH) have been carried out [88] on 5CB, showing the expected temperature dependence. In liquid crystals, may originate from order or flexoelectric effects, or other mechanisms resulting in electric polarization. 

The flexoelectro-optic effect in cholesterics (which is described in more detail in Chapter 7 by Rudquist and Lagerwall ) offers another way to measure 61 — 63. A tight-pitch helical structure can easily be induced in nematics by adding a few per cent of chiral dopant. Recently this technique has been adopted to test the flexoelectric response of another BC nematic, 4-cyano-l,3-phenylene bis [4-[4 -(hexyl) benzoyloxy] benzoate] (C6ban). ... 

Many bent-core molecules do not have nematic phases, but may be added to calamitic nematics to tune the flexoelectric behaviour. Several groups have reported measurement results in such guest-host systems ° using either HAN cells or the flexoelectro-optic effect mentioned above. It was found that some BC compounds used as dopants in small (< 10%) concentration may effectively increase ei —es of the host. ° Other, mainly asymmetric, BC compounds had hardly any influence on ei - - es of the host nematic. ... 

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