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

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.