  Surface interactions are responsible for many properties of condensed matter,
ranging from crystal faceting to the kinetics of phase transitions. Usually,
these interactions are polar along the normal to the interface and apolar
within the interface. Here, we demonstrate that polar in-plane surface
interactions of a ferroelectric nematic NF produce polar monodomains in
micron-thin planar cells and stripes of an alternating electric polarization,
separated by 180 degree domain walls, in thicker slabs. The surface polarity
binds together pairs of these walls, yielding a total polarization rotation by
360 degrees. The polar contribution to the total surface anchoring strength is
on the order of 10%. The domain walls involve splay, bend, and twist of the
polarization. The structure suggests that the splay elastic constant is larger
than the bend modulus. The 360 degree pairs resemble domain walls in cosmology
models with biased vacuums and ferromagnets in an external magnetic field.
