Abstract
Force profiles as well as aggregation and deposition rates are studied for asymmetrically charged particles and surfaces in aqueous electrolytes theoretically. Interactions are calculated within the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, whereby the electrostatic part is modeled at Poisson-Boltzmann (PB) level. Unequally charged surfaces are examined, from the symmetric system, where both surfaces are equally charged, to fully asymmetric systems, where the surfaces are oppositely charged. Charged-neutral systems, where one surface is charged and the other is neutral, emerge as an essential scenario. In this case, the choice of boundary conditions used for solving the PB equation is crucial, whereby constant charge and constant potential boundary conditions lead to either fully repulsive or fully attractive forces. Consequently, charge regulation has a major influence on particle aggregation and deposition rates too. In the charge-neutral case, substantial shifts in the critical coagulation concentration (CCC) are observed when the regulation properties are changed. In the presence of multivalent ions, these systems behave similarly to the symmetrically charged ones. The CCC decreases with the square of the valence in weakly charged systems, while unrealistically high charge densities are needed to recover the classical Schulze-Hardy limit, which predicts a sixth power dependence on valence.
Highlights
Interactions between charged surfaces in aqueous solutions are of substantial importance in material and environmental sciences
Double layer forces between charged surfaces can be often quantitatively described by Poisson−Boltzmann (PB) theory down to distances of a few nanometers.[9−14] When these forces are added to van der Waals forces, one arrives to the theory developed by Derjaguin, Landau, Verwey, and Overbeek (DLVO).[15,16]
The interactions were described as a sum of electrostatic and van der Waals forces as summarized by the DLVO theory
Summary
Interactions between charged surfaces in aqueous solutions are of substantial importance in material and environmental sciences. Charge regulation effects may be extremely important in such asymmetric systems, especially when one of the particles is almost electrically neutral In such situations, forces may vary from repulsive to attractive depending on the boundary conditions.[20,37]. We analyze the effect of charge asymmetry, and subsequently the importance of charge regulation effects We show that these effects may qualitatively change the interactions, and dramatically modify the heteroaggregation and deposition behavior in such systems. We find that dependencies on the counterion valence are similar to the case of symmetrically charged particles
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