Polar anchoring strength

From Equation 5.11 we have the boundary condition at z = 0, which is 

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Nastishin, YA, Polak, RD, Shiyanovskii, SV, Bodnar, VH Lavrentovich, OD (1999). Nematic polar anchoring strength measured by electric field techniques. Journal of Applied Physics, Vol. 86, No. 8, (Oct), pp. 4199-4213. 

As discussed in Chapter 1, photo-polymers that have been unidirectionally modified by exposure to linearly polarized light have the ability to induce alignment of liquid crystals [37-41]. This works presumably via anisotropic van der Waals forces [38], similar to the alignment on conventionally rubbed polymer layers [18,22]. In spite of this similarity, generally there are large differences found between the surface anchoring strengths of these two types of... 

Figure I4. Pretransitional ordering transmitted polarized light intensity / as a function of T for different anchoring strengths u = 1 (large dots), w = 0.5 (medium dots), and w = 0.1 (small dots). lo denotes the intensity of the incoming light.

The FLC free energy should also include the surface terms, which are the polar Wp = —Wp(Pi/) and dispersion Wd = —Wd(Pi/) contributions, where Wp and Wd are the corresponding anchoring strength coefficients. 

Reference [68] gives the phase diagrams of different FLC states (helical and uniform) for various relationships between the polar and dispersion contributions (in terms of reduced anchoring strength coeflSicients)... 

Methods of computer simulation show that the electric field threshold of bistability (7.74) depends both on polar and dispersion anchoring strength coefficients [75, 158]. With increasing anchoring we have to increase the switching amplitude of the electric field (Fig. 7.27). For Wj = 0 it is possible to write the following relationship for the bistability threshold [75] ... 

Figure 3. Free energy per unit length in term.s of anchoring strength for the pianar polar (PP) and non-planar escaped radial (ER) structures (one-constant approximation, Kfi=K). The critical radius for the structural transition is given by the intersection points of the energy graphs. (Reproduced from Crawford et al. 11911.)...

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