  We present a density functional study of Lennard-Jones liquids in contact
with a nano-corrugated wall. The corresponding substrate potential is taken to
exhibit a repulsive hard core and a van der Waals attraction. The corrugation
is modeled by a periodic array of square nano-pits. We have used the modified
Rosenfeld density functional in order to study the interfacial structure of
these liquids which with respect to their thermodynamic bulk state are
considered to be deep inside their liquid phase. We find that already
considerably below the packing fraction of bulk freezing of these liquids,
inside the nanopits a three-dimensional-like density localization sets in. If
the sizes of the pits are commensurate with the packing requirements, we
observe high density spots separated from each other in all spatial directions
by liquid of comparatively very low density. The number, shape, size, and
density of these high density spots depend sensitively on the depth and width
of the pits. Outside the pits, only layering is observed; above the pit
openings these layers are distorted with the distortion reaching up to a few
molecular diameters. We discuss quantitatively how this density localization is
affected by the geometrical features of the pits and how it evolves upon
increasing the bulk packing fraction. Our results are transferable to colloidal
systems and pit dimensions corresponding to several diameters of the colloidal
particles. For such systems the predicted unfolding of these structural changes
can be studied experimentally on much larger length scales and more directly
(e.g., optically) than for molecular fluids which typically call for
sophisticated X-ray scattering.
