Scaling laws of polyelectrolyte adsorption

Adsorption of charged polymers (polyelectrolytes) from a semidilute solution to a charged surface is investigated theoretically. We obtain simple scaling laws for (i) the amount of polymer Γ adsorbed to the surface and (ii) the width D of the adsorbed layer, as a function of the fractional charge per monomer P and the salt concentration c_b. For strongly charged polyelectrolytes (p ≲ 1) in a low-salt solution, both Γ and D scale P^-1/2. In high-salt solutions D ∼ c_b^1/2/p whereas the scaling behavior of Γ depends on the strength of the polymer charge. For weak polyelectrolytes (p ≪ 1 we find that Γ ∼ P/c_b^1/2, and for strong polyelectrolytes Γ ∼ c_b^1/2/P. Our results are in good agreement with adsorption experiments and with numerical solutions of mean-field equations.