Anchoring homeotropic

FIG. 7 Same as Fig. 5, but for a nematic Gay-Berne film confined between homeotropically anchoring substrates (from Ref. 48). 

T. Gruhn, M. Schoen. A grand canonical ensemble Monte Carlo study of confined planar and homeotropically anchored Gay-Berne films. Mol Phys 95 681-692, 1998. 

Stelzer et al. [109] have studied the case of a nematic phase in the vicinity of a smooth solid wall. A distance-dependent potential was applied to favour alignment along the surface normal near the interface that is, a homeotropic anchoring force was applied. The liquid crystal was modelled with the GB(3.0, 5.0, 2, 1) potential and the simulations were run at temperatures and densities corresponding to the nematic phase. Away from the walls the molecules behave just as in the bulk. However, as the wall is approached, oscillations appear in the density profile indicating that a layered structure is induced by the interface, as we can see from the snapshot in Fig. 19. These layers are... 

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

The concept of local perturbations of the director around nanoparticles, often linked to homeotropic anchoring to the nanoparticle surface, is a concept often brought forward in discussions of thermal, optical and electro-optic properties of nanoparticle-doped nematic liquid crystals, which adds a slightly different perspective to the invisibility of smaller particles in aligned nematics. This appears to be of particular relevance for particles coated with either hydrocarbon chains or pro-mesogenic as well as mesogenic units. 

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 ... 

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).

The unit vector s denotes some preferred orientation of the director at the surface. For homeotropic anchoring it corresponds to the unit vector normal to the surface. W is the couphng constant which merely stands for the strength of the anchoring at the surface of the particle. It varies in the range 10 -10 3 J/m [25]. 

Ellipsometry experiments have been performed at a comparable length scale for small nematic droplets on substrates inducing planar anchoring, the air/nematic free interface giving a homeotropic anchoring [67]. The predicted bent-to-uniform director transition is observed at a critical drop thickness of about 30 nm. The microscopic details of the molecule/molecule and molecule/surface interaction become relevant only for thickness < 1 nm. 

Fig. 8.7. Sketch of different systems characterized by hybrid frustration (a) Confining substrates repared in a way, so that one induces homeotropic anchoring and the other homogeneous planar anchoring, (b) Hybrid frustration due to opposing geometry induced direction of order and the direction induced by anchoring, (c) Liquid crystal in a contact with a solid substrate and with a free LC-air interface.

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...

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