  A self consistent field theory for compressible polymer mixtures is developed
by introducing elements of classical density functional theory into the
framework of the Helfand theory. It is then applied to study free surfaces of
binary (A,B) polymer blends. Density profiles in the one- and two-phase region
are calculated as well as chain end distributions and chain orientations of the
minority and the majority component. In the ideally symmetric mixture, in which
the individual properties of polymers A and B are the same and both have the
same surface energy, polymers of the minority component segregate to the
surface, where they are exposed to less polymers of the majority component.
This effect can only be captured correctly, if one accounts for the fact that
the monomer-monomer interaction has finite range. As a consequence, the
Flory-Huggins-parameter varies in space and depends on the concentration
profiles and their derivatives. The surface segregation calculated with such an
ansatz, without any fit parameter, is in reasonable quantitative agreement with
data from recent Monte Carlo simulations.
