On the Adsorption of a Polymer Chain

Abstract

Two chain conformations have been used to describe the behaviour of a polymer molecule in the vicinity of a liquid-solid interface. The one comes from the study of the chain in the presence of an absorbing wall where the probability for the polymeric units to reach the wall is zero while the second one appears if a reflecting wall is present where the probability for the polymeric units to reach the wall is large. In the real situation a lot of other conformations can be realised depending on the interaction energy between the polymeric units and the interface. For high repulsions the probability to find the monomers at the interface gets reduced and a picture reminding the absorbing wall conformation emerges. Reducing the repulsion more and more units are adsorbed. There is a critical energy below of which the majority of polymeric units go to the adsorbed state. At this critical point reflecting wall statistics are suitable to describe the conformation of the chain. We use the reflecting wall probability as a zeroth order solution in order to describe the general problem in the presence of polymer-interface interactions. We work in the neighbourhood of the adsorption-desorption phase transition point and we give expressions for the average amount of polymeric units adsorbed at the interface and the extension of the adsorbed chain into the solution.