  The effect of confinement on the orientational structure of a nematic liquid
crystal model has been investigated by using a version of density-functional
theory (DFT). We have focused on the case of a nematic confined by opposing
flat surfaces, in slab geometry (slit pore), which favor planar molecular
alignment (parallel to the surface) and homeotropic alignment (perpendicular to
the surface), respectively. The spatial dependence of the tilt angle of the
director with respect to the surface normal has been studied, as well as the
tensorial order parameter describing the molecular order around the director.
For a pore of given width, we find that, for weak surface fields, the alignment
of the nematic director is perpendicular to the surface in a region next to the
surface favoring homeotropic alignment, and parallel along the rest of the
pore, with a interface separating these regions (S phase). For strong surface
fields, the director is distorted uniformly, the tilt angle exhibiting a linear
dependence with the distance normal to the surface (L phase). Our calculations
reveal the existence of a first-order transition between the two director
configurations, which is driven by changes in the surface field strength, and
also by changes in the pore width. In the latter case the transition occurs,
for a given surface field, between the S phase for narrow pores and the L phase
for wider pores. A link between the L-S transition and the anchoring transition
observed for the semi-infinite case is proposed. We also provide calculations
with a phenomenological approach that yields the same main result that DFT in
the scale length where this is valid.
