Direct force measurements involving oppositely charged micron-sized particles were carried out across aqueous solutions of different multivalent ions with the atomic force microscope (AFM). The measurements could be interpreted quantitatively with Poisson-Boltzmann (PB) theory. Thereby, the surface potentials and regulation properties of the particles are extracted from the forces between the same types of particles. This information is then used to predict force profiles 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 surprisingly reliable down to distances of about 5 nm. An example of this analysis is shown in Figure 1 below, which also indicates the importance of charge regulation. Similar findings were made for a wide range of different multivalent ions. The possibility to accurately predict force profiles in the presence of multivalent ions with PB theory is at odd with various reports in the literature, which state that this theory should fail in such situation due to neglect of ion correlations. We suspect that ion correlations only induce deviations at smaller distances.
F. J. Montes Ruiz-Cabello, G. Trefalt, P. Maroni, M. Borkovec (2014) Accurate predictions of forces in the presence of multivalent ions by Poisson-Boltzmann theory, Langmuir 30, 4551-4555
