In addition, our model provides more realistic description of the chain adsorption problem due to the fact that it operates with the actual binding point interaction between the polymer segments and the adsorbing surface, rather than the extended adsorption potential that adequately describes only the case of physical polymer adsorption. We believe that the above features make the present approach valuable contribution to the field of studying the density structure of non-uniform polymer systems.

Despite a long history of using lattice-based models for the description of the polymer adsorption onto a planar surfaces, only few of this models can be credited for giving an adequate description of the polymer segment-segment interactions. Most advanced of these models are based on the approaches of Hoove,[@Hoove] Silberberg,[@Silberberg] Roe,[@Roe] and Scheutjens and Fleer (SF).[@Scheutjens-Fleer] Each of these models have severe limitations, SF being the most advanced and adequate for describing many relevant experimental situations. The main advantage of the SF model over the approaches of Roe and Silberberg is in the provided possibility to describe the actual distribution of *finite* chains on a lattice in the presence of an external field. This theory, however, relies on the Flory-Huggins model [@Flory; @Huggins] for the enthalpy 