Overcharging and Free Energy Barriers for Equally Charged Surfaces Immersed in Salt Solutions.

Samuel Stenberg,Jan Forsman

doi:10.1021/acs.langmuir.1c02268

Abstract

The stability of dispersions containing charged particles may obviously be regulated by salt. In some systems, the effective charge, as measured by the potential some small distance away from the particles, can have a sign opposite to the bare surface charge. If charge reversal takes place, there is typically a salt concentration regime within which colloidal stability increases with added salt. These experimental findings on dispersions have been corroborated by atomic force microscopy investigations, where an attraction is found at short separations. This attraction is stronger than expected from standard DLVO theory, and there has been considerable debate concerning its origin. In this work, we use simple coarse-grained models of these systems, where the bare surfaces carry a uniform charge density, and ion-specific adsorption is absent. Our hypothesis is that these experimental observations can be explained by such a simplistic pure Coulomb based model. Our approach entails grand canonical Metropolis Monte Carlo (MC) simulations as well as correlation-corrected Poisson-Boltzmann (cPB) calculations. In the former case, all ions have a common size, while the cPB utilizes a point-like model. We devote significant attention on apparent surface charge densities and interactions between large flat model surfaces immersed in either a 2:1 salt or a 3:1 salt. In contrast to most of the previous theoretical efforts in this area, we mainly focus on the weak long-ranged repulsion and its connection to an effective surface charge. We find a charge reversal and a concomitant development of a free energy barrier for both salts. The experimentally observed nonmonotonic dependence of colloidal stability on the salt concentration is reproduced using MC simulations as well as cPB calculations. A strong attraction is observed at short range for all investigated cases. We argue that in our model, all non-DLVO aspects can be traced to ion–ion correlations.

Highlights

The intricate behavior of colloid and surface interactions in multivalent electrolyte solutions has been studied using both experimental[1−9] and theoretical.[10−25] approaches
Because we always insert and remove electroneutral groups of ions, the surface charge potential needs not be considered in these processes and not in any Monte Carlo (MC) steps
In corrected Poisson-Boltzmann (cPB), and PB, calculations, electroneutrality is maintained via a Donnan potential as has been previously described.[41] energy density functional theory (DFT)

Summary

■ INTRODUCTION

The intricate behavior of colloid and surface interactions in multivalent electrolyte solutions has been studied using both experimental[1−9] and theoretical.[10−25] approaches. For low concentrations of monovalent salt, screening of the particle charge is inefficient, that is, the outer counterion layer is very diffusive (in an aqueous solution) This generates a long-ranged free energy barrier, which is often strong enough to prevent flocculation. These observations were corroborated by AFM measurements, with a repulsion at low and high concentrations of a multivalent salt, but a monotonic attraction at intermediate concentrations This overall response was found when the counterions are oligomeric[9] or polymeric.[5] We note that in the stability studies, the systems are canonical, that is, there is no infinitely large “bulk” solution, from (or to) which additional charge can be added. In the main paper, we have used an adjusted value

■ RESULTS AND DISCUSSION

■ CONCLUSIONS

■ REFERENCES