these calculations, we assume that polymers experience ideal glass transition at the point where the configurational entropy vanishes. The described model mimics the the apparent glass transition in dense systems. As we intend to show in what follows, this relatively simple model provides an effective tool for studying the glass transition in confined geometries.

The paper is organized as follows. In Section \[SecTheory\] we describe the mathematical procedure that rationalizes the mentioned generalization of the Bethe-Peierls approximation to the case of nonhomogeneous chain systems. In Section \[GlasTransSec\] we introduce the calculation method of the configuration entropy along with the equations for the contact densities. In Section \[SecResults\] we present the calculated density profiles, along with the corresponding values of the configurational entropy given as a function of the bulk polymer density observed far away from the adsorbing surface. Finally, Sec. \[SecConcl\] presents our conclusions.

Density profile of semi-flexible chain in presence of adsorbing surface: Mathematical model {#SecTheory}
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In performing the first step of the program outlined in the Introduction, in this Section we intend to calculate the density profile of semi-flexible chains adsorbed onto a planar substrate. For the sake of notational convenience we distinguish between the segments positioned 