Flexoelectric coefficients temperature dependence

Fig. 3.13. Relative temperature dependences for the BC nematic lODClPBCP fluid monomer, for a BC nematic swollen in a calamitic liquid crystal elastomer (BCN-LCE) and a BC nematic elastomer (BCLCE). The flexoelectric coefficient of an LCE is also shown (note that it is not distinguishable from the horizontal axis at the present scale due to the three orders of magnitude difference).

Critical radius Rcr is the solution of equation TeriRcrJu) = 0. Its dependence on flexoelectric coefficients fAA for different temperatures is shown in Fig. 4.27. Solid curves have been calculated numerically from Eq. (4.22) while flexoelectric effect renormalizes both critical temperature and radius. 

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 renormalized correlation radius dependences on nanowire radius and flexoelectric coefficients /44 are reported in Fig. 4.28a-d for PbTiOs material parameters at room temperature. 

We already discussed this case in relation to the surface polarizafimi (Section 10.1.3). Generally both dipolar and quadrupolar mechanisms contribute to Py but the temperature dependence of the corresponding coefficients is different, oc S(T) for the quadrupolar mechanism, but Cd oc S (T) for the dipolar one. The flexoelectric coefficients have the dimension of (CGSQ/cm or C/m) and the order of magnitude, e 10 CGS units (or 3 pC/m). The flexoelectricity is also observed in the SmA phase [27]. 

Fig. 11.26 A scheme of a hybrid cell that supports the splay-bend distortion and manifests the flexoelectric polarization (a) and an experimental temperature dependence of the sum of flexoelectric coefficients in the nematic phase of liquid crystal 5CB (b)...

With a short laser pulse, the derivative dTIdt is just a jump, therefore, pyroelectric coefficient y(I) can be easily calculated at any temperature of the nematic phase. An example of the Pj(X) dependence is shown in Fig. 11.26b. The maximum value of e for 5CB is 3.610 CGS (or -12 pC/m). It means that the molecular quadrupole has the form shown in the Inset to the same figure. There are some other methods to find the sum of the flexoelectric coefficients based, e.g., on the electro-optical techniques but they are not as straightforward as the pyroelectric technique. 

The temperature dependence of flexoelectric moduli in MBBA was studied [202]. The coefficient 633 was shown to depend on temperatures even weaker than the order parameter S(T)... 

In this expression only the coefiBcient of the term quadratic in the primary parameter is temperature dependent, whereas the coefficient of the P term is constant this is so because it is not the interaction between the electric polarization that leads to a phase transition. The coefficient is of the form = Aq T - Tqa), where Tqa is the smectic-C-smectic-A transition temperature, Kj is the elastic constant, and A is the coefficient of the so-called Lifshitz term responsible for the helicoidal stmcture. p and C are the coefficients of the flexoelectric and piezoelectric bilinear couplings between the tilt and the polarization. The coefficients A and C are dependent on the chiral character of the molecules. For nonchiral molecules, A and C are zero minimization of the free energy given in Equation (4.94) yields a system where the director axis is homogeneously tilted below the transition temperature T. There is no linear coupling between the tilt and the polarization, and thus, P. For temperatures... 

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