Orientational transition in a nematic liquid crystal at a patterned surface.

We consider a semi-infinite nematic in contact with a periodic patterned surface with alternate planar and homeotropic stripes. Extending the work of Barbero, we find the free energy (assuming K1 = K3) for the situations where the easy direction on the planar stripe is either perpendicular or parallel to the length of the stripes. We find the bulk free energy difference between the structures to be proportional to square root(K2/K1) and so we consider the possibility of a spontaneous transition between the two states if the azimuthal anchoring energy is sufficiently weak and K1 not equal K2. We compute the critical azimuthal anchoring energy for such a transition in terms of the relative width of the stripes and the period of the pattern and find it to be approximately 10(-6) J m(-2), comparable to experimental values.