  Polymer solutions exhibit peculiar properties near surfaces: polymer chains
either adsorb onto or can be repelled by the wall. Only a few techniques are
able to probe their structure in the vicinity of solid substrates, because of
the small length scales over which liquids are influenced by the wall. In this
paper, we use neutron reflectivity measurements at the interface between a
polystyrene semidilute solution in a good solvent and a smooth sapphire
surface. We show that polymer chains are globally depleted from the solid
surface, but contrary to what is generally assumed, this does not prevent some
chains to still adsorb on the wall. We also observe that the Newtonian flow of
the solution has a negligible effect on the size of the depletion layer, which
is a hypothesis often made but rarely measured in the literature.
