Microscopic Approach to Determination of the Flexoelectric Coefficients

The molecular-statistical approach to calculating the flexoelectric coeflS-cients was developed independently in [198, 199]. Parameters a, 6, and Oq are introduced to define the pear or banana shape of the molecules (Fig. 4.33). Next, by specifying a definite splay or bend deformation, it is possible to calculate the fraction of the molecules which achieve the preferred orientation of their dipoles in order to ensure the maximum packing density. The excess number AN = — N-) of the molecules with dipole 

An attempt has been made [201] to isolate that part of the general frequency dependence of the flexoelectric effect which is caused solely by the frequency characteristics of the polarization of the medium, i.e., by the frequency dependence of the flexoelectric coefficient. It was also shown that when a quadrupole mechanism dominates (the experiments were conducted in a nonuniform field), dispersion of the flexoelectric coefficient is absent in the dipole relaxation frequency range (in MBBA). At the same time, such a dispersion was detected for a three-ring phenylbenzoate. This is consistent with the considerable contribution of the Meyer dipole mechanism to the observed flexoelectric effect. 

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) 

This correlates [200] with neither the dipole mechanism of the flexoelectric effect (Fig. 4.29), which gives 

The temperature dependence (4.79) is perhaps caused by an improper allowance for the anchoring energy which plays an important role in the flexoelectric distortion [28, 29]. 

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