Irreversible Adsorption of a Concentrated Polymer Solution

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Abstract
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: aΦ7/24 N5/6 and that the concentration profile (z) varies as: Φ7/10(a/z)2/5 for aΦ−3/4 < z < h.