Importance of Charge Regulation in Attractive Double-Layer Forces between Dissimilar Surfaces

Direct force measurements between oppositely charged latex particles in aqueous electrolyte solutions were carried out with a multiparticle colloidal probe technique based on atomic force microscopy. Force profiles between two dissimilarly charged surfaces can be only described when charge regulation effects are taken into account, while constant charge or constant potential boundary conditions are inappropriate. Surface potentials and regulation parameters are determined from force data obtained in symmetric systems with the Poisson-Boltzmann theory and constant regulation approximation. The resulting quantities are used to predict the force profiles in asymmetric systems, and good agreement between theory and experiment is found. These findings show that charge regulation is important to quantify double-layer forces in asymmetric systems.

Figure 1

Force profiles measured with the AFM in symmetric systems involving two individual particles. Sulfate latex (left column) and amidine latex (right column) for different ionic strengths at (a) $p\mathrm{H}$ 4.0 and (b) $p\mathrm{H}$ 5.6. Solid lines are best fits with PB theory with charge regulation and including the van der Waals force. The left inset in (b) compares the fit to the CR boundary conditions and the conditions of CC and CP. The amidine particles at $p\mathrm{H}$ 5.6 are neutral and interact by van der Waals forces. The right inset in (b) shows the expected scaling behavior.

Figure 2

Force profiles measured with the AFM in asymmetric systems between two individual dissimilar sulfate and amidine latex particles. Ionic strength of $0.2\mathrm{m}M$ (left column) and $1.0\mathrm{m}M$ (right column) at (a) $p\mathrm{H}$ 4.0 and (b) $p\mathrm{H}$ 5.6. The solid lines are predictions of the PB model with CR approximation. All parameters were obtained from force measurements in symmetric systems. The importance of charge regulation is evident from the large differences between CC and CP boundary conditions.