Irreversible Adsorption of a Concentrated Polymer Solution

We study the adsorption of long, linear polymer chains from a melt or a semi-dilute solution onto a solid wall, the adsorption of a monomer on a surface site being irreversible. Using scaling arguments, we derive the concentration profile and the extension of the polymer layer, which has been washed out with pure solvent. Let us consider, Φ the volume fraction of the initial semi-dilute solution (Φ = 1 in the case of the melt), a the monomer size and N the degree of polymerization of the chains. Our main result is that the extension h of the profile scales as: a Φ 7/24 N 5/6 and that the concentration profile ϕ( z ) varies as: Φ 7/10 ( a/z ) 2/5 for a Φ −3/4 < z < h .