We study the anchoring and anchoring transitions in the
nematicsubstrate system using the Landaude Gennes formalism.
The free energy functional is expanded around the bulk tensor
nematic order parameter up to the secondorder terms. This
quadratic approximation is used to find an explicit condition
for anchoring directions in a semiinfinite 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 homeotropicconical transition and
a first order or continuous planarconical transition. It also
predicts that the geometrical measure of the anchoring strength
is always positive and does not diverge even at a continuous
anchoring transition.
