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We develop a theory describing density profile of the semi-flexible polymersabsorbed onto a planar surface. The theoretical analysis consists of two parts.As a first part, we calculate a density profile of the adsorbed polymers bydeveloping an extension of the Bethe-Peierls approximation to the case ofnonhomogeneous systems. This approach relies on the combination of the singlechain adsorption theory and the lattice version of the self-consistent fieldtheory. Semi-flexibility of a chain is described by incorporating a finitecoordination number of the lattice into the consideration, in the spirit of theprevious Silberberg approach. The developed lattice theory incorporates theinteraction between nearest-neighbor pairs of segments and finite chain length.The theory is completely mapped into the Scheutjens-Fleer theory in the limitof infinite coordination number. As a second part of the developed approach, wecalculate the configurational entropy to investigate how the density structureof the semi-flexible polymers near the surface relates to possible reduction ofglass transition temperature near nonabsorbing surface and enhancement near thestrongly attractive surface.

Theoretical estimation of density profile of semiflexible polymers  adsorbed on a surface and thermodynamic glass transition scenario by means of  the Bethe-Peierls approximation