Scaling theory of polymer adsorption

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Abstract
We discuss the equilibrium properties of flexible chains adsorbed on a flat surface, assuming that a) adsorption is weak, resulting in large thicknesses D for the adsorption layer, b) the chains are very long, c) the solvent is good, so that excluded volume effects become important (contrary to an early opinion of Hoeve). The repulsion between monomers are incorporated through a scaling theory which goes beyond the usual mean field (Flory-Huggins) approximations. The central assumption is that polymer concentrations in the first layer and in the next layers scale in the same way, (although they do differ by a constant factor). We can then predict the surface exponents of interest in terms of standard exponents for self avoiding walks; for the latter we use the Flory values. One then finds three regimes of adsorption : (i) In the dilute limit (separate coils) D is independent of the polymerization index N, and varies with the strength of the effective monomer surface attraction (measured by a small parameter δ) according to D ∼ δ -3/2 instead of D ∼ δ-1 in mean field. (ii) There is a semi dilute regime where the coils begin to overlap, but where D remains essentially the same. (iii) The most important case corresponds to the plateau in the adsorption isotherm : here we show that the correlations inside the layer are similar to those in a three dimensional system. Then D ∼ Nδ(ln cB) -1 where cB is the bulk concentration. The dependence on N is stronger than in mean field (D ∼ N1/2) but not incompatible with existant data