at the ends of a chain and the rest of the segments that we call hereafter the end segments and the middle segments, respectively. The adsorption interaction between polymer segments and the substrate is described by the binding energy $U_s<0$ that can be alternatively characterized by the characteristic adsorption length $L_A\sim (\beta U_s)^{-1}$, $\beta$ being the reciprocal temperature expressed in units of the Boltzmann constant $k_B$. For the sake of simplicity, we assume that the total width $D$ of the adsorbed film is much larger than $L_A$, so that the profile of the chain density in the described film comprised of the chains saturates to its bulk value observed far away from the adsorbing surface.

Note that there are essential differences between the behavior of the end segments and middle segments caused by the fact that confining surface restricts the location of these types of segments in different ways. First restriction on the possible locations of the both types of segments is caused by the limitations imposed by the surface on the coordination number. The restriction equally applies to both types of segments. The second restriction caused by the connectivity of chains, in contrary, differs for the end and middle 