Anchoring condition

Fig. 3 Principle anchoring conditions of nematic liquid crystals at nanoparticle surfaces (a) planar anchoring, and (b) vertical (or homeotropic) anchoring...

Disclination lines are energetically disfavored because they produce gradients in the director profile and Frank stresses. So if the sample is left alone, the disclination lines and loops spontaneously shrink in length and annihilate one another (see Fig. 10-22) until no disclinations are left—except for any that are pinned by any impurities in the fluid or by wall irregularities, and those trapped because of incompatibilities in anchoring conditions at surfaces (Chuang et al. 1991 Nagaya et al. 1992). 

Under steady shearing, these trapped disclinations should play the role of an anchoring condition, much like the role solid walls play in the flow properties of small-molecule nematics. A scaling analysis of this problem in Section 10.2.5 gives an equation, (10-28), for the steady-state shear viscosity for flow between surfaces with strong, homeotropic anchoring ... 

Consider the shear flow geometry in Fig. 1, with three different anchoring conditions on the top and bottom planes. The initial condition is a uniform n field consistent with the wall anchoring. Cases (a) and (b) are similar in which n lies initially in the y-z plane. In both cases, the LE theory predicts an in-plane tumbling instability and an out-of-plane twist instability. ... 

Fig. 1 Geometry for shear flow, with three possible anchoring conditions on the top and bottom planes (a) n fixed along the flow direction (planar anchoring) (b) n fixed along the velocity gradient (homeotropic anchoring) and (c) n fixed along the vorticity direction (log rolling).

There have been several theoretical investigations analysing the nematic distortions of the LC surrounding anisotropic particles for different anchoring conditions at the LC-particle interface. In modelling the surface-anchoring free-energy density fa it is usual to adopt the Rapini-Papular expressions, which can be written as... 

Name and identifier Anchoring conditions Cleavage conditions References... 

We have not considered here alignment techniques, such as SiOx deposition or alignement by monolayer (Langmuir) deposition on surfaces. Details on these techniques of surface alignment can be found elsewhere [5-9]. We also do not discuss recently introduced active (command) surfaces, where the anchoring conditions are controlled by light [55], electrochemistry [56] and electric field [57]. 

Static force [45,50,51,57] and friction properties [45,46,51,57-59] have been extensively studied in thermotropic nematics. The surface anchoring conditions were symmetric, with both mica sheets inducing either planar or homeotropic alignment. Bare mica naturally induces planar anchoring on cyanobiphenyls such as 5CB the liquid crystal optical axis orients at abont 7t/6 with respect to the slow optical direction of a (birefringent) freshly cleaved mica sheet [60]. A homeotropic ahgnment can be obtained by adsorbing a mono-layer of surfactant [45,50] on mica. 

We stress however that this deduction is based on the elastic theory for the nematics, that fails to explain the forces in planar samples. Moreover, the discussion does not take into account the specific curved geometry of the SFA, which is not compatible with the hybrid anchoring conditions. In particular, even by considering a finite anchoring strength, a line defect is expected at the center of the cell (as sketched tentatively in Fig. 3.22), that has not been observed yet. 

It has been known for a long time that the surface ordering of a nematic (or other non-polar) liquid crystal is influenced by the ferroelectric domains of the anchoring substrate. In a work by M. Glogarova at al. [69], it is shown how the properties of a liquid crystal cell can be modulated and stabilized using a ferroelectric material as an anchoring substrate. These results motivated us to consider that the EFM technique could be efficiently used to create surfaces with variable anchoring conditions on a micrometric scale. 

Fig. 2.8 Smectic 8CB confined inside a closed rectangular microchannel with mixed anchoring conditions [47], Three microchannel walls impose homeotropic anchoring, while the fourth wall imposes planar anchoring as shown in the schematic illustration in (e). The microchannels are 20 (a), 10 (b), 60 (c) and 40 (d) pm wide and 3.8 (a, b), 10 pm (c, d) deep. Scale bars are 5 pm in (a) and (b) and 10 pm in (c) and (d). Reprinted with permission [47]. Copyright 2006, American Chemical Society...

Fig. 7.8. Even homeotropic boundary conditions allow for a standing helix structure. Thus, homeotropic anchoring conditions will not ensure a long-term stable lying helix structure for the flexoelectro-optic effect. ...

Another reason for the moderate popularity of the field among experimentalists is that fiexoelectricity-driven effects are rare their detection mostly requires unusual surface (anchoring) conditions, moreover, the flexo-electric coefficients are small (in the range of pC/m), thus are not easily measurable and the results are often contradictory. 

Equation for the Period. The solution of eq. (4.2) is not unique, because an arbitrary phase shift of the periodic solution is possible. So the additional equation, which is required for the computation of the period, has to be an anchor equation that fixes the phase. Depending on the considered system, different anchor conditions may be appropriate ... 

In most liquid crystal devices, the liquid crystals are sandwiched between two substrates coated with ahgnment layers. In the absence of externally applied fields, the orientation of the hquid crystal in the cell is determined by the anchoring condition of the alignment layer [26-28]. 

We consider the possible deformations of a nematic liquid crystal confined between two parallel substrates with tangential anchoring condition (parallel to the substrates but no preferred direction on the plane of the substrate). We use the one elastic constant approximation (A n = K22 = Kss = K), the elastic energy is given by... 

Because of the anchoring condition, the liquid crystal director is parallel to the plane of the substrate and depends on the coordinates x and y on the plane. The liquid crystal director is described by... 

We consider a nematic liquid crystal confined in a cylinder with a radius of R. The anchoring condition on the surface of the cylinder is perpendicular, as shown in Figure 1.21. The liquid crystal director aUgns along the radial axis direction, as shown in Figure 1.21(a), and is described by n =f. The elastic deformation of the liquid crystal director is splay with the strength of 5= 1. The elastic energy is... 

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