Flexo-electric effect

Another example of the coupling between microscopic and macroscopic properties is the flexo-electric effect in liquid crystals [33] which was first predicted theoretically by Meyer [34] and later observed in MBBA [35], Here orientational deformations of the director give rise to spontaneous polarisation. In nematic materials, the induced polarisation is given by... 

Note 4 The flexo-electric effect is the analogue of the piezo-electric effect in solids, where the polarization is induced by a strain that produces a translational deformation of the crystal. The flexo-electric effect in a liquid crystal is caused by a purely orientational deformation. 

Fig. 32. Schematic representation of the flexo-electric effect, (a) The structure of an undeformed nematic liquid crystal with pear- and banana-shaped molecules (b) the same liquid crystal subjected to splay and bend deformations, respectively.

Domain corresponding to a periodic deformation caused by the inverse flexo-electric effect in a nematic liquid crystal. 

Fig. 3.12. Comparison of the temperature dependences of the direct and inverse flexo-electric effects for ClPbislOBB.

J. Harden, R. Teeling, J.T. Gleeson, S. Sprunt and A. Jakli, Converse flexo-electric effect in a bent-core nematic Uquid crystal, Phys. Rev. E 78(3), 031702/1-5, (2008). doi 10.1103/PhysRevE.78.031702... 

A. V. Emelyanenko and M. A. Osipov, Theoretical model for the discrete flexo-electric effect and a description for the sequence of intermediate smectic phases with increasing periodicity, Phys. Rev. E 68(5), 051703/1-16, (2003). doi 10.1103/PhysRevE.68.051703... 

Case 3 has been particularly well investigated by Belova [82] with the result that the transmission of a layer in the SAW and the longitudinal electric fields can be smaller than w=0.01. However, in these experiments the optical clearing pattern was found to have high spatial homogeneity along the layer, which is inconsistent with many of the other data reported [35, 38—40]. It is likely that the SAW-created distortion in the nematics is masked by the flexo-electric effect one [68]. 

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. 

Another reason for the moderate popularity of the field among experimentalists is that fiexoelectricity-driven effects are rare their detection mostly requires unusual surface (anchoring) conditions, moreover, the flexo-electric coefficients are small (in the range of pC/m), thus are not easily measurable and the results are often contradictory. 

Besides the elastic and the electric torques the so-called flexoelectric (or flexo) torques on the director play an important role as well. Their effect on pattern-forming instabilities in nematics is the main issue of this chapter. Flexotorques originate from the fact that typically (in some loose analogy to piezoelectricity) any director distortion is accompanied by an electric flexopolarization Pa (characterized by the two ffexocoefScients ei, 63). From a microscopic point of view, finite ei and 03 naturally arise when the nematic molecules have a permanent dipole moment. But also for molecules with a quadrupolar moment, finite ei and 63 are possible (see also Chapter 1 in this book ). Flexopolarization has to be incorporated into the free energy P n) for finite E. It is not surprising that this leads to quantitative modifications of phenomena, which exist also for ci = 63 = 0. Though, for example, the Freedericksz threshold field Ep is not modified, the presence of flexoelectricity leads to considerable modifications of the Freedericksz distorted state for E > Ep- ... 

An external electric field interacts with the local dielectric anisotropy of a blue phase and contributes to the energy of the liquid crystal with the term Ae jAn [95]. Flexo-effects in blue phases have not been discussed yet. 

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