Electrical properties flexoelectricity

The aim of these studies is to understand and control the electrical properties of surfaces on a micrometric scale, that might be extremely useful for the application of these materials in the field of liquid crystal display (LCD) technology. In fact, it is well known that the LC anchoring properties depend not only on the substrate morphology but also on its electrical properties [68]. The electric polarization in nematic and other non-polar liquid crystals has essentially three origins flexoelectricity [65], orderelectricity [66,67] (related to the gradient in the order parameter) and the polarization of the substrate... 

Bent-core liquid crystal elastomers have shown to exhibit large values of flexoelectricity as many as three orders of magnitude larger than liquid crystal elastomers containing rod-shaped molecules [44]. These high responses are attributed to a piezoelectric phenomenon. Liquid crystal elastomers combine elasticity and flexibility inherent to rubbers and the optical and electrical properties of liquid crystals, and are promising materials for applications such as electrooptics, flexible electronics, and actuator technologies for biomedical applications. 

In this chapter, we will be describing different electro-optic techniques that have been developed specifically for measurement of the flexocoeffi-cients. In these techniques, an electric field is applied to a nematic liquid crystal in a cell with well-defined boundary treatments. The net torque on the medium, which involves dielectric, elastic and flexoelectric components, is set to zero both in the bulk and at the two surfaces in order to And the equilibrium director configuration if a DC field is applied. In AC techniques, the above torques are balanced with the viscous torque. The optical properties of the medium are in turn calculated for the distorted profiles and compared with experimental measurements. The flexoelectric, and in some... 

The presence of clusters in BC nematics is now well established from various measmements. Recent studies " have in fact indicated a ferroelectric or an antiferroelectric response to an applied electric field, and an unusual low-frequency (presumably collective) mode has been detected in the dielectric spectra of bent-core nematics, which might also be related to clusters. In spite of the intense studies, however, the exact structure and the physical properties of the clusters are still unknown. Therefore, not surprisingly, a precise physical model for the role of polar clusters in the flexoelectric response of BC nematics and a quantitative estimation of the resulting increment of the flexocoefiicients has not yet been worked out. 

Flexoelectricity is a basic mechano-electric phenomenon in liquid crystal physics. The first hints for the existence of a curvature-polarization tensor in liquid crystals, although with different sjmunetry transformation properties, can be foimd in a manuscript by Freedericksz (1940) that made use of the tensorial analysis method of general relativity and was published only... 

Flexoelectricity is a reciprocal relation between the electrical and mechanical properties of liquid crystalline biostructures. We have underlined in... 

A.G. Petrov, Measurements and interpretation of flexoelectricity. In eds. D.A. Dunmur, A. Fukuda and G.R. Luckhurst, Physical Properties of Liquid Crystals Nematics Vol. 1, EMIS Datareviews Series, Inst. Electrical Engineers, UK, 2001. pp. 251-264. 

According to Eq. (7.1) P is zero for the two cases of uniform director fields and pure twist. Hence both cases can serve as a zero state as far as flexoelectric excitations are concerned. It is important to note that a twist is not associated with a polarization (i.e. C2 is identically zero, cf. Fig. 7.2). An imstrained nematic has a centre of symmetry (centre of inversion). On the other hand, none of the elementary deformations - splay, twist or bend have a centre of symmetry. According to Curie s principle they could then be associated with the separation of charges analogous to the piezoeffect in solids. This is true for splay and bend but not for twist because of an additional symmetry in that case if we twist the adjacent directors in a nematic on either side of a reference point, there is always a two-fold symmetry axis along the director of the reference point. In fact, any axis perpendicular to the twist axis is such an axis. Due to this symmetry no vectorial property can exist perpendicular to the director. In other words, a twist does not lead to the separation of charges. This is the reason why twist states appear naturally in liquid crystals and are extremely common. It also means that an electric field cannot induce a twist just by itself in the bulk of a nematic. If anything it reduces the twist. A twist can only be induced in a situation where a field turns the director out of a direction that has previously been fixed by boundary conditions (which, for instance, happens in the pixels of an IPS display). 

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