Polyelectrolyte Overcompensation of Charged Planar Surfaces
Abstract
Mean-field theory is used to model polyelectrolyte adsorption and overcompensation of charged surfaces. Simple scaling laws are derived for surface overcharging and support the existence of four different regimes. (i) For strongly charged polyelectrolytes, the overcharging by polyelectrolytes is found to scale like the bare surface charge. (ii) For intermediate charged polyelectrolytes, the overcompensation is shown to scale like the bare surface charge multiplied by the monomer charged fraction. (iii) Weakly charged polyelectrolytes do not overcompensate the surface charge, and finally, (iv) very weakly charged polyelectrolytes are depleted altogether from the charged surface. Addition of salt is also investigated and is shown to increase the adsorbed layer thickness but decrease the amount of adsorbed polyelectrolytes. The simple scaling results are supported by full numerical solutions of the mean-field equations.Keywords
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