Accurate predictions of forces in the presence of multivalent ions by Poisson-Boltzmann theory.

Forces between positively and negatively charged colloidal particles across aqueous salt solutions containing multivalent ions are measured directly with the atomic force microscope (AFM). The measurements are interpreted quantitatively with Poisson-Boltzmann (PB) theory. Thereby, the surface potentials and regulation properties of the particle surfaces are extracted from symmetric measurements between the same types of particles. This information is used to predict force profiles in the asymmetric situations involving different types of particles without any adjustable parameters. These predictions turn out to be very accurate, which demonstrates that the mean-field PB theory is reliable down to distances of about 5 nm. While various reports in the literature indicate that this theory should fail due to neglect of ion correlations, such effects seem important only at higher concentrations and smaller distances.