  Mean-field theory is used to model polyelectrolyte adsorption and the
possibility of overcompensation of charged surfaces. For charged surfaces that
are also chemically attractive, the overcharging is large in high salt
conditions, amounting to 20-40% of the bare surface charge. However, full
charge inversion is not obtained in thermodynamical equilibrium for physical
values of the parameters. The overcharging increases with addition of salt, but
does not have a simple scaling form with the bare surface charge. Our results
indicate that more evolved explanation is needed in order to understand
polyelectrolyte multilayer built-up. For strong polymer-repulsive surfaces, we
derive simple scaling laws for the polyelectrolyte adsorption and overcharging.
We show that the overcharging scales linearly with the bare surface charge, but
its magnitude is very small in comparison to the surface charge. In contrast
with the attractive surface, here the overcharging is found to decrease
substantially with addition of salt. In the intermediate range of weak
repulsive surfaces, the behavior with addition of salt crosses over from
increasing overcharging (at low ionic strength) to decreasing one (at high
ionic strength). Our results for all types of surfaces are supported by full
numerical solutions of the mean-field equations.
