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 Gamma 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 less than or similar to 1) in a low-salt solution, both Gamma and D scale as p(-1/2). In high-salt solutions D similar to c(b)(1/2)/p whereas the scaling behavior of Gamma depends on the strength of the polymer charge. For weak polyelectrolytes (p much less than 1) we find that Gamma similar to p/c(b)(1/2), and for strong polyelectrolytes Gamma similar to c(b)(1/2)/p. Our results are in good agreement with adsorption experiments and with numerical solutions of mean-field equations.