glassy dynamics in sufficiently thin layers is rather significantly affected by the molecular weight of glass forming of polymers and layer thickness. [@Tress] The chain length is believed to affect $T_g$ only via the free volume associated with chain ends. [@Ferry; @deGennes_glass] In this scenario the glass transition temperature is solely determined by length of typical loop adsorbed by both ends onto the surface. In the present study, the effect of chain length is investigated and the loops are taken into account. Note that in a typical experimental situation, the glass transition is considered to be primary caused by rapid cooling of the system below the glass transition temperature. We however consider the system at constant temperature fixed slightly below or above the bulk $T_g$ and study the thermodynamics of the system near the surface.

The above described need in the understanding of a physical nature of the glass transition in non-uniform polymer systems calls for an adequate theoretical approach to this important problem. The present work aims at providing such a theoretical model based on the detailed investigation of the density profiles of semiflexible polymers in presence of adsorption interactions with the substrate confining the polymer system. With the 