Ordoelectric polarization

A change of the order parameter modulus S (r) can also create polarization, for example due to transformation of the ellipsoidal shape of Q tensor in space. In this case we deal with the so-called ordoelectric polarization [14]. Indeed, decreasing S value results in less extended (less prolate) ellipsoid form without reorientation of its principal axes. Such a transformation may be caused by a scatter of the rigid molecular quadrupoles with respect to the director axis the stronger the scatter, the lower is the quadmpole order S and the less prolate ellipsoid Q. This is illustrated by Fig. 10.12 in sketch (a) the order parameter is stronger at the surface and... 

Fig. 10.12 Ordoelectric surface polarization. In sketch (a) the order parameter is iarger at the surface and smaller in the bulk in sketch (b) the order parameter is smaiier at the surface than in the bulk. Corresponding gradient curves S z) for a nematic liquid crystal are qualitatively pictured in the bottom sketches. Vectors and m show the directions of the surface polarization...

According to Eq. (10.16) the gradient of the order parameter amplitude V5(z) will inevitably result in the surface ordoelectric polarization ... 

The flexoelectric polarization Pf depends on the curvature of the director field (div n and curln) at constant modulus of the order parameter S. For uniform director orientation ( =constant), Pf=0. A simplified molecular picture of the phenomenon is shown in Fig. 15 a, b. Equation (39) defines the so-called ordoelectric polarization Pq, which depends on the gradient of the nematic orientational order parameter S (quadrupo-lar in nature) and does not vanish for a uniform director distribution. For instance. 

---