Weak anchoring

A summary of the conclusions from this fitting procedure is as follows. In the very strong anchoring limit (w > 10) the value of does not depend on the history of the system. In the weak anchoring regime we find that... 

Fig. 4.8. Relaxation time r for the fundamental splay fluctuation mode as a function of sample thickness (circles) and best fit of the theoretically predicted relation for weak anchoring (solid line). The aligning layer was UV illuminated photoactive poly-(vinyl-cinnamate), the liquid crystal was 5CB in the nematic phase (T = 32°C) [59].

In the case of weak anchoring, when VF —> 0 and A —> oo, series expansion of the relaxation time of the fundamental mode for gd first order yields... 

Such linear dependence in thin samples has also been experimentally observed (Fig. 4.8) and the obtained anchoring for the shown example is = (9.1 0.9) X10" J/m with A,j = 480 45nm. Note that when measuring weak anchoring, the sample can be slightly thicker, up to a few microns, as again only the sample size relative to the measured extrapolation length is relevant. 

In confined geometries, however, this is not the case. In a planar sample, for example, the magnitude of the wave vector component parallel to the boundaries is arbitrary, whereas the fluctuation wave vector component perpendicular to the boundaries can only have certain values. In this case, the allowed wave vector components are determined by the sample thickness, viscoelastic properties of the liquid crystal, and also by the interaction of a liquid crystal with the aligning surface. If the director is strongly bound to the aligning substrate, it cannot deviate from the induced direction (easy axis) and the fluctuation amphtude at the boundary is zero. On the other hand, if the surface only weakly anchors the director orientation, the director can fluctuate to a certain degree around the easy axis. 

So far we have only considered strong anchoring of the director at the confining plates. The case of weak anchoring, where the director orientation at the plates is sensitive to the distortions in the bulk, has been considered for K = K2. No qualitatively new scenarios only quantitative corrections of Uc and Qc were predicted. These depend on two additional material parameters to describe the surface potential of the director, which in most cases have not been measured. 

In contrast to other bistable nematic modes the surface state of the director does not change in zenithal bistable mode devices, which gives them an important robustness. In other words, while the device is bistable, the director state at the ZBD surface is monostable. This feature gives a smaller temperature dependence than other modes utilizing weak anchoring and multiple surface states. Among the many similarities with FLC devices there is also the fact that the stable states are polarized, i.e. they have a non-zero polarization in bulk. Therefore we anticipate problems with im-... 

H.P. Hinov, Further experimental evidence for the wall structure of the flexoelectric domains in symmetrically weakly-anchored MBBA layers, Mol. Cryst. Liq. Cryst. 89(1), 227-248, (1982). doi 10.1080/00268948208074480... 

Fig. 11.29 Conversed flexoelectric effect in cells with homeotropic (a) and homogeneous (b) director alignment and electric field applied along the cell normal. Weak anchoring energy at the bottom plate allows the flexoelectric deflection of the director 3 at the surface propagating up in the vertical direction (e = 0)...

For weak anchoring and 0 by analogy with a nematic (see Eq. 10.77), the free energy of the distortion includes the elastic term due to the bend-distortion (we assume K = Kn = K s) and the flexoelectric term with an average coefficient e. The second elastic term is due to the cholesteric helical structure (modulus K22). ... 

In a recent article Nehring, Kmetz and Scheffer described effects of weak anchoring on equilibrium configurations of twist cells.1 In order to obtain tractable equations for analytic solution, the three bulk elastic constants were made equal, the field-and-strain-free orientation at the surface was assumed to be parallel to the surface, and only nematic liquids were discussed. That treatment gives useful insights into the nature of the problem but leaves a number of interesting questions unanswered. 

We have used the full Leslie-Ericksen hydrodynamic equatlons2>3 for cholesterics in laminar flow between parallel surfaces, except for the justifiable omission of inertial terms. Use of cholesterics removes the difficulty mentioned in Ref. 1 of obtaining a 90 twist with very weak anchoring. The effects of using models for surface energy other than the symmetric sin (n,np) form used in previous work are investigated. 

To Illustrate the effects of viscous weak anchoring, we have computed the dynamic and optical behavior of cells with rigid anchoring and with weak anchoring. The material chosen for an example Is E-7, a widely used mixture of high dielectric anisotropy made by Anchoring based on surface energies... 

Figures 6 and 7 show response of cells having weak anchoring with constants given in Table 1, using the symmetric energy function (a) and the asymmetric form (c), respectively. The surface tilt as well as midplane tilt are variable.

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