0$, the chain will be in the all trans state. At any finite temperature, because of thermal perturbations, a long polymer will be in a coiled state, same as for a completely flexible polymer when $U_f = 0$. A first order phase transition was found to take place [@Flory1956] in the many chain system at a constant density when the excluded volume interactions are taken into account. In the framework of this theory, the persistence of a chain can be described by the flexibility energy $U_f$, whereas the finite thickness of this chain is associated with the size of the lattice cell. Note that the proposed lattice model is restricted to only nearest-neighbor interactions among segments described by the potential $V$ that has the same strength irrespective whether nearest neighbors are connected by a bond or not. Our polymer melt possesses a finite compressibility captured by means of voids distributed in such a way that a constant chemical potential is maintained throughout the system. Apart from the first layer, $z$ is assumed to be independent of distance from the adsorbing surface. In addition, the stiffness of the model chains is considered to be independent of the local chain density in 