Adsorption and depletion of polyelectrolytes from charged surfaces

Mean-field theory and scaling arguments are presented to model polyelectrolyte adsorption from semidilute solutions onto charged surfaces. Using numerical solutions of the mean-field equations, we show that adsorption exists only for highly charged polyelectrolytes in low salt solutions. Simple scaling laws for the width of the adsorbed layer and the amount of adsorbed polyelectrolyte are obtained. In other situations the polyelectrolyte chains will deplete from the surface. For fixed surface potential conditions, the salt concentration at the adsorption–depletion crossover scales as the product of the charged fraction of the polyelectrolyte $f$ and the surface potential, while for a fixed surface charge density, σ, it scales as ${\sigma }^{\text{2/3}}{f}^{\text{2/3}},$ in agreement with single-chain results.