Current flexoelectric

Let us now calculate the flexoelectric current occurring in the deformed cell. The edges of the cell are clamped so that the deformable length of the cell is L, and the surfaces are positioned parallel to the xy plane at z = 0 and z = d (thus d is the thickness of the LC layer). The nematic fills the electrode area X x y in the centre of the cell (Fig. 3.7a). Flexing is realized by translating the centre of the cell (at a = 0) with respect to the edges of the substrates by S along z (Fig. 3.7b). This translation causes a deformation of the substrate, which on the one hand can be described by the local displacement w x) from the non-deformed state (plane plates). 

Flexing of the cell corresponds to a harmonic displacement of the cell centre, i.e. S = S osin(wt). Thus the current generated by flexoelectricity is... 

It can be seen immediately from Eq. (3.22) that for a homeotropic orientation (0 = 1, = 0) the current depends on the splay flexoelectric... 

We would like to emphasize that for an imperfect orientation (0 < 1, < 7r/2) the flexoelectric current depends both on 63 and ei [see... 

The 63 values obtained from the measm-ements on ClPbislOBB using Eq. (3.27) are plotted in Fig. 3.12. It can be seen that 63 deduced from these measm-ements is in satisfactory agreement with that obtained from the direct flexoelectric effect based on polarization current detection imder an apphed cm-vatm-e strain (also plotted in Fig. 3.12). 

A.G. Petrov, Flexoelectricity and mechanotransduction. In ed. O.P. Hamil, Current Topics in Membranes, vol. 58 Mechanosensitive channels, Elsevier/Academic Press, 2007. pp. 121-150. 

We measure pyroelectric coefficient y = dP/dT, using heating the hybrid cell by short ( 10 ns) laser pulses, as shown in Fig. 10.13. The only difference from the surface polarization measurements is using a hybrid cell instead of uniform (planar or homeotropic) cells [28]. The laser pulse produces a temperature increment about AT 0.05 K and the flexoelectric polarization changes. To compensate this change, a charge passes through the external circuit and the current i = dqldt is measured by an oscilloscope. From the identity (A is cell area)... 

It should be noted that there is currently some discrepancy between the values of the flexoelectric coefficients derived by various methods even for the same material, in particular, in MBBA. This may be caused by difficulties in calculating the real values of the anchoring energy of the molecules to the surface, or by not allowing for the sinrface polarization of the nematic liquid crystal caused by the polar nature of its molecules [189]. 

We should also note that the visualization of defects by a nematic liquid crystal, based on the flexoelectric effect in a spatially nonuniform field, is significantly more efiicient than in the dynamic scattering mode [81, 82], because of the higher contrast, the lower visualization voltages (3 to 4 times), and the lower leakage current (about 10 times) [84-86]. 

The above comments represent only some particularly chosen topics and events in the mathematical development of the continuum theory for liquid crystals, focusing especially on nematic and smectic C materials. In a book of this scope it is inevitable that some major topics have not been included, such as soliton-like behaviour in nematics or the flexoelectric effect, and many important contributions to the field have been omitted for the sake of brevity. Nevertheless, readers should have no difficulty in accessing these topics in the current literature if they have been armed with the material presented in subsequent Chapters. Interested readers can find more extensive details on the development of liquid crystals in the historical review by Kelker [143] or the forthcoming volume in this book series by Sluckin. Dunmur and Stegemeyer [253]. 

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