Polyelectrolyte adsorption and charge inversion

We discuss theoretically the adsorption of linear weakly charged polyelectrolyte solutions on an oppositely charged solid surface using the classical self-consistent mean field theory. If the solid surface has an indifferent short range interaction with the polymer (at the crossover point between attraction and repulsion), we show that its charge is always overcompensated by the adsorption of the polymer. At low ionic strength, the overcompensated charge per unit area is proportional to the inverse screening length kappa and the thickness of the adsorbed layer is of the order of the thickness of a single adsorbed chain. At higher ionic strength, the electrostatic interaction is strongly screened and is equivalent to an effective excluded volume. The overcompensated charge is then proportional to the bare surface charge. These results provide a theoretical basis to explain the formation of the polyelectrolyte multilayers that have been made by successive adsorption of polyelectrolyte layers of opposite signs.