Anchoring Energies for Nematics

Anchoring energies for nematics D2 External Field On Method... 

FIGURE 4.39. Temperature dependence of the anchoring energy for homogeneously oriented 5CB in the nematic and isotropic phases (figures at the curves are related to various samples with different quality of orientation). 

Yokoyama, H., and Van Sprang, H. A. A novel method for determining the anchoring energy function at a nematic liquid crystal-wall interface from director distortions at high fields./. Appl. Phys. 57, 4520 (1985). 

For consistency we go back to the problem of the twisted cell discussed in Section 8.3.2, however, the director angles cp at the boundaries will be not constant but can be changed due to elastic and external torques. Let a nematic layer be confined by two plane surfaces with coordinates zj = —plane through angle cp (there is no tilt, the angle 9 = ti/2 everywhere, and the azimuthal anchoring energy is finite). 

FIGURE 3.2. Temperatmre dependences of the orientational order parameter at the interface with a substrate (5o) for a semi-infinite nematic layer. Parameter g characterizes the potential of the substrate (proportional to the anchoring energy) [5], Qc = 0.10078. 

The anchoring energy was shown to depend on cell thickness [61] (see also [3, 59]). The thinner the cell the higher the anchoring energy. It is a type of the nonlocality effect discussed in [1]. One of the possible microscopic reasons for the effect is the field of the space charge of the ions adsorbed at opposite interfaces. Such a field can stabilize or destabihze the director in the surface layers in accordance with a sign of the dielectric anisotropy and initial orientation of the nematic [62]. In any case, it results in an increase of an apparent value of Ws in thin cells. 

Only few data are available for other liquid crystal phases (apart from nematics). For example, the azimuthal anchoring energy was recently measured in the ferroelectric smectic C phase [75]. 

It should be noted that there is currently some discrepancy between the values of the flexoelectric coefficients derived by various methods even for the same material, in particular, in MBBA. This may be caused by difficulties in calculating the real values of the anchoring energy of the molecules to the surface, or by not allowing for the sinrface polarization of the nematic liquid crystal caused by the polar nature of its molecules [189]. 

The flexoelectric distortion in Hybrid Aligned Nematic (HAN) configuration was studied [190, 191]. In HAN cells the director is homeotropic on one of the substrates and homogeneous on the other. The measme-ments of transmitted intensity in HAN samples allow us to evaluate for MBBA both a nematic anchoring energy W for the homeotropic orientation VF 6 X 10 erg/cm and the sum of the flexoelectric moduli 11 + 33 —4.5 X 10 dyn / [191]- In an electric field normal to the initial director plane, the flexoelectric effect results in the appearance of twist deformation, observed by the rotation of linearly polarized light [190]. 

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