that is known [@GujratiJCP; @dG] to be non-adequate for the description of many relevant phenomena in non-uniform polymer melts. In addition, to the best of the authors knowledge, SF theory in its conceptional form has never been used to describe the finite stiffness of the chains.

Along with using more advanced in terms of correlations taken into account approximation, the present study remedies this omission by using the modified lattice coordination number that distinguishes between trans and gauche configurations of the polymer chain, as has been suggested previously by Silberberg. [@Silberberg] In our former study,[@2011] we applied the Bethe-Peierls approximation [@Bethe; @Peierls] to the study of the uniform polymer melts and demonstrated the complete agreement of this approach with quasi-chemical approximation. The present work describes an extension of our earlier studies to the case of non-uniform polymer melts in the presence of adsorbing surface. Specifically, we apply the developed formalism for deriving the adsorption isotherm in the described non-uniform many-chain system, which allows us to mimic the density structure of the whole polymer film. Upon analyzing the density structure of the adsorbed semi-flexible chains, we perform a numerical estimation of the configurational entropy of the non-uniform chain layer. In performing 