Anchoring energy transition

Such an antisymmetric distortion differs from the symmetric distortion characteristic of the Frederiks transition. It is instructive to compare these two cases. In Fig. 11.28 the space distributions of the director n and its x-projection rix = sinfl 9 are pictured for the Fredericks transition (a) and flexoelectric effect (b) the anchoring energy at both surfaces is infinitely strong in case (a) and finite in case (b). 

Fig. 11.28 Comparison of the distortion profile (molecular picture below and angle 3(z) above) for the Frederiks transition with infinite anchoring energies (a) and flexoelectric effect with finite anchoring energies (b) (homeotropic initial director alignment in both cases)...

The dependencies 6 ocd and 8 ocE agree well with experiment [30]. Therefore, in principle, we can find from the measured value of the cell retardation because usually 33 is known from the Frederiks transition threshold. However, in a real experiment it is almost impossible to have zero anchoring energy. For the finite anchoring energy, we can only find ratio ej,/W and the accuracy of determination... 

The theory of the local Prederiks transition [85, 86] considers the competition of two terms, the surface anchoring energy due to the short range forces W responsible for one type of orientation (homeotropic in the previous example), and the long-range Van der Waals forces U z) integrated over their penetration radius... 

Let us go back to the discussion of the Frederiks transition in a homogeneously oriented nematic with positive dielectric anisotropy (splay distortion). A conventional sandwich cell is used which is very convenient in this case, because the Kerr effect is not observed when the light wave vector coincides with the field direction. Let us imagine that we are measuring the temperature dependence of the anchoring energy of the nematic using the saturation field for the complete director reorientation. For 5CB we have the left part of Fig. 4.39 [226]. 

The bistability phenomena in the FLC structures will be considered below.) The results of these two methods coincide with each other to an accuracy of 30%. The anchoring energy of an FLC mixture (ZhK-224) for different conducting surfaces is shown in Table 7.2. The values of Wd, measured according to (7.40), (7.41), were shown to depend linearly on the temperature near the A C phase transition point... 

Finally, we will discuss some consequences of the 13 term on elastic deformations in nematic phases. First, if is of the same order as other elastic constants, it will be effective in much more situations than will K24. In fact, in most cases where K24 is effective, will have to be considered as well. This has been pointed out for stripe domains in hybrid aligned films [190], surface transitions in nematics on solid surfaces [224], nematic droplets [47] and cylindri-cally confined nematics [214]. Many authors have emphasized the modification of the apparent surface anchoring energy by the term (see above). 

The above analysis assumes that the undulations of the layers vanish at the boundaries. Ishikawa and Lavrentovich [131] have modelled a lamellar system of cholesteric liquid crystal which allows layer undulations near the boundaries. This was achieved by adding a finite surface anchoring energy to a bulk energy that is essentially of the same form as that stated above for SmA. This idea could perhaps also be modified to model general SmA or SmC liquid crystals. The results in [131] seem to indicate that the incorporation of finite surface anchoring leads to a decrease in the theoretical threshold for the onset of the Helfrich-Hurault transition. 

Fig. 4.10 Anchoring energy coefficients W p (solid line) and (dotted line) as a function of temperature for nematic 5CB on rubbed Nylon. Tni the transition temperature from the nematic to isotropic phase. Reprinted with permission from [27]. Copyright by the American Physical Society...

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