We study the anchoring and anchoring transitions in the
nematic-substrate system using the Landau-de Gennes formalism.
The free energy functional is expanded around the bulk tensor
nematic order parameter up to the second-order terms. This
quadratic approximation is used to find an explicit condition
for anchoring directions in a semi-infinite system. A finite
system is also studied and a geometrical measure of the anchoring
strength, similar to the extrapolation length, is defined.
Then we study anchoring transitions between the homeotropic,
planar, and conical anchorings. The quadratic approximation
predicts a first order homeotropic-conical transition and
a first order or continuous planar-conical transition. It also
predicts that the geometrical measure of the anchoring strength
is always positive and does not diverge even at a continuous
| A.Poniewierski and A.Samborski JOURNAL of CHEMICAL PHYSICS, Vol. 105 ,7632, (1996)