Conformation of a non-interacting polymer near a “sticky” wall

We consider the statistical mechanics of a polymer, with freely rotating bonds, confined in a half space by an impenetrable wall with which the polymer may interact. We derive an asymptotic expression for the average number of beads adsorbed on the wall, the mean square end-to-end separations of the beads on the wall, the position of the centre of mass of the polymer and the density distribution of beads off the wall as a function of the adsorption energy parameter W. We find that a phase transition occurs at a critical value of W(=Wc).