Dilute and semidilute polymer solutions near an adsorbing wall

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Abstract
The variation of the monomer density ρ with distance z from an impenetrable and adsorbing wall is studied for polymer solutions with excluded volume interaction. Both the limits of weak and strong overlap between the polymer chains are considered. For comparison, solutions of ideal noninteracting chains and chains with an excluded volume interaction of the mean‐field type are also discussed. The main emphasis is on a temperature region near the adsorption temperature Ta below which a single long chain, fixed with one end close to the wall, condenses a finite fraction of its monomers to the wall. The relation to an n‐component field theory in a half‐space is used to show that in this temperature region ρ(z) displays crossover scaling behavior involving two macroscopic lengths. The power law exponents for the z dependence in the various regions determined by the two lengths are obtained as well as the qualitative form of the whole profile ρ(z) for various limits of interest.