segments. Specifically, the configuration with the end points placed near the surface makes this configuration more entropically favorable than the equivalent configurations with middle segments placed in the same positions. the above difference can be quantitatively taken into account by straightforward modification of our previous theory [@2011] developed for uniform polymer systems. Technically, this modification amounts to introducing the correction to the configurational entropy differentiating the end and middle points of the polymer chains described in what follows.

Owing to the added mathematical complexity in describing semi-flexible polymer systems, far less is known about the density profiles of the adsorbed chains that possess a finite stiffness or rigidity. In the present study, we will take the stiffness of a chain into account by employing the Flory lattice model Ref. . The essence of the approximation is to distinguish between trans and gauche states of the model chain: The latter can pass from any lattice site to the directions of the nearest-neighbor sites. The forward direction, the trans state, is energetically more favorable to all other directions, the gauche states. The energy difference $U_f$ between the trans and the gauche state, introduces a local stiffness so that at temperature $T = 