  We develop a theory describing density profile of the semi-flexible polymers
absorbed onto a planar surface. The theoretical analysis consists of two parts.
As a first part, we calculate a density profile of the adsorbed polymers by
developing an extension of the Bethe-Peierls approximation to the case of
nonhomogeneous systems. This approach relies on the combination of the single
chain adsorption theory and the lattice version of the self-consistent field
theory. Semi-flexibility of a chain is described by incorporating a finite
coordination number of the lattice into the consideration, in the spirit of the
previous Silberberg approach. The developed lattice theory incorporates the
interaction between nearest-neighbor pairs of segments and finite chain length.
The theory is completely mapped into the Scheutjens-Fleer theory in the limit
of infinite coordination number. As a second part of the developed approach, we
calculate the configurational entropy to investigate how the density structure
of the semi-flexible polymers near the surface relates to possible reduction of
glass transition temperature near nonabsorbing surface and enhancement near the
strongly attractive surface.
