Interplay between Depletion and Double-Layer Forces Acting between Charged Particles in Solutions of Like-Charged Polyelectrolytes.

Direct force measurements between negatively charged silica particles in the presence of a like-charged strong polyelectrolyte were carried out with an atomic force microscope. The force profiles can be quantitatively interpreted as a superposition of depletion and double-layer forces. The depletion forces are modeled with a damped oscillatory profile, while the double-layer forces with the mean-field Poisson-Boltzmann theory for a strongly asymmetric electrolyte, whereby an effective valence must be assigned to the polyelectrolyte. This effective valence is substantially smaller than the bare valence due to ion condensation effects. The unusual aspect of the electrical double layer in these systems is the exclusion of the like-charged polyelectrolyte from the vicinity of the surface, leading to a strongly nonexponential diffuse ionic layer that is dominated by counterions and has a well-defined thickness. As the oscillatory depletion force sets in right after this layer, this condition can be used to predict the phase of the oscillatory depletion force.