ABSTRACT We use computer simulations to investigate the behavior of a weak polyelectrolyte nanogel in a solution containing divalent salt. In our simulations, we systematically vary the bulk pH value and the bulk concentration of divalent salt, allowing us to study the influence of charge regulation and divalent ions on the ionization behavior, ion partitioning, and nanogel swelling. With regard to the ionization behavior, we observe that, with an increasing concentration of divalent salt, the suppression of ionization becomes weaker. Moreover, we find that the strongly non‐uniform ionization profile observed in the absence of divalent counterions becomes increasingly uniform as the concentration of divalent salt is increased. We also study the partitioning of monovalent and divalent counterions between the nanogel and the bulk solution; our analysis shows that the uptake of divalent ions may be enhanced by up to tenfold as compared to the mean‐field prediction. Finally, we consider the influence of divalent ions on the pH‐dependent swelling behavior of the nanogel. Here, we observe a two‐stage swelling driven by charge regulation and ion partitioning. Overall, our results highlight the complex interplay of ionization equilibria, valency effects, and ion partitioning in weak polyelectrolyte systems.
Beyer et al. (Sun,) studied this question.