Coupling flexoelectric

Practically aU other methods developed for the measurement of flexo-coefficients are indirect . These exploit the fact that the polarization resulting from the splay-bend distortion couples linearly with an applied electric field E. This contributes to the total free energy of the sample, and hence alters the distortion of the director field compared to that in the absence of flexoelectric polarization. An external electric field of course acts on the dielectric anisotropy (As) of the nematic, which, like the orientational or-... 

Although most of the scientists working on liquid crystals may think that flexoelectricity is a special property of liquid crystals, it was actually first discussed in 1964 for crystals as a response to strain (stress) gradients. The direct and converse flexoelectric coupling constants Cijki were described with a fourth-rank tensor, as... 

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

In the most simple chiral polar tilted smectics, ferroelectric liquid crystals, the flexoelectric phenomenon influences the structure of the SmC phase only quantitatively. It affects the elastic and chiral couplings and consequently slightly changes the transition temperature to the tilted phase and the pitch of the helicoidal modulation. 

The simple expression for / means that the response time will be inversely proportional to the field, r oc 1/ PE) when there is flexoelectric coupling. This is the same dynamics as in ferroelectric liquid crystal (FLC) switching. In the cholesteric case the expression for / is somewhat more complicated and, as we will see below, it turns out that r is independent of E. 

Figure 4.23a reports the schematics of the radial deformation of the perovskite ABO3 nanowire crystal lattice due to spontaneous flexoeffect. The deformation occurs from square cross section to rectangular and inclined parallelogram one. The radial distributions of spontaneous shear strain Upz inside the nanorod for flexoelectric couplings/14 = 1 V and 5 V are presented, respectively, in Fig. 4.23b, c for PbTiOB parameters. 

It is seen, that since the critical temperature Tcr(R) in Eq. (4.2 depends on the flexoelectric coupling coefficient /44, the average polarization P3 and all other related physical properties have to be dependent on the flexoelectric coefficient f44. Note, that P3 and other physical properties can be found by the conventional minimization of the free energy (see Eq. (4.23)). 

The main effect from the flexoelectric coupling is the altering of transition temperature via the renormalization of the extrapoiation iength and the gradient term (see Eq. (4.22)). Due to the same reasons flexoelectric coupling leads to the renormalization of correlation radius as ... 

Here and are, respectively, coupling tensors of piezoelectric and piezomagnetic effects q j and q are the bulk electro- and magnetostriction coefficients. The flexomagnetic and flexoelectric coupling energy is... 

Tensors and are the forth-rank tensors of flexomagnetic and flexoelecttic couplings respectively. Flexoelectric effect exists for arbitrary symmetry. 

The flexoelectric domain instability takes place due to the linear coupling between the flexoelectric polarization P and the external electric field E. The corresponding term in the nematic free energy F gives... 

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