Ionic Strength Effects in Polyelectrolyte Brushes: The Counterion Correction

We propose a means of accounting for the contribution of counterions to the ionic strength within a polyelectrolyte brush, which is then incorporated into models treating the effects of electrostatic interactions, chain stretching, and curvature on the layer thickness for chains attached to a spherical particle. Combining an electrostatic wormlike chain model originated by Odijk, Fixman, and co-workers with the blob model of Daoud and Cotton predicts without adjustable parameters the layer thickness for a wide range of ionic strengths and particle radii. A simplified scaling version that neglects stiffening due to electrostatic interactions greatly underestimates the layer thickness but captures the dependence on ionic strength reasonably.