Weak anchoring boundary condition

Weak boundary anchoring decreases Tr time and increases ra- This could be well understood, if we allow for boundary conditions corresponding to a finite anchoring energy W. For small angles (p it has the following form [5] ... 

This calculation assumes that the torques of opposing plates are insufficient to disturb the orientation of the director at the surface such a condition is known as strong anchoring. In practice the strength of surface interactions may have to be considered, and in the example given, weak anchoring would cause the director orientation close to the boundary surfaces to depart from a linear dependence on position, as illustrated in Fig. 8. 

The above discussion of the Fredericks transition can be extended to include (1) pretilt at the boundaries where the boundary conditions (p 0) = (j) L) = 0 are replaced by (p 0) = (p L) = < o (2) the tilted fields where the magnetic field is applied across the sample at a fixed angle (3) weak anchoring where the director is weakly anchored to both boundary plates. A more detailed discussion can be found in Stewart (2004) and Virga (1994). 

Liquid crystals in confined geometries are known to be influenced by the orientation of the director at the boundaries. Section 2.6 introduces various ideas on boundary conditions and the concepts of strong and weak anchoring of the director at the boundaries. Finally, Section 2.7 gives a simplifying reformulation of... 

As a special example, consider again n and i/ in equations (2.229) and (2.230) and now suppose that the anchoring at the interface or boundary is weak. Straightforward substitutions coupled with the identity given by (2.233) (with id replaced by vp) simplify the condition in (2.239) to... 

---