In this paper, the structure of the electric double layer in the presence of (mostly) multivalent counterions is investigated through Monte Carlo simulations. Unlike previous similar studies addressing this matter, the difference of this study lies in the use of realistic hydrated ion sizes. Additionally, two different methods for calculating energies in the Metropolis algorithm are applied. The obtained results show that the conclusions of preceding papers must be revised. In particular, our simulations suggest the existence of certain ion layering effects at high surface charge densities, which are not accounted for by integral equation theories in the case of divalent counterions. These layering effects could justify why the overcharging phenomena due to ion size correlations are hardly observable in real colloids with divalent counterions. The existence of charge inversion due to ion size correlations (and without requiring specific counterion adsorption) is probed for trivalent counterions. Moreover, the hypernetted-chain/mean-spherical-approximation is tested under conditions not studied yet.

In this work, we have performed explicit coarse-grained Monte Carlo simulations of thermo-responsive nanogels in salt-free solutions with the help of the bead-spring model of polyelectrolytes and a solvent-mediated hydrophobic interaction potential that captures the swelling behavior of real microgels. As far as we know, such simulations have not been applied to temperature-sensitive charged nanogels yet. Monovalent and divalent counterions have been considered. Charge profiles inside and outside the nanogel have been computed from simulations, revealing an attractive finding for the use of these nanoparticles as potential drug carriers: when charged nanogels collapse, they can sometimes form a hollow sphere, with the charged beads concentrated on the inner and outer surfaces, and some counterions enclosed in the inner space. Simulations also show that the surface electrostatic potential increases when nanogels shrink upon heating. However, the fraction of counterions inside these soft nanoparticles slightly varies with temperature. Charge profiles were also calculated using a Poisson–Boltzmann cell model. Its predictions about the charge profile outside the nanogel, the fraction of counterions inside and the surface electrostatic potential are in fair agreement with simulation data. This suggests that this model provides valuable information about the electric double layer of thermo-responsive nanogels.

In this work, a quantitative comparison between experimental swelling data of thermo-sensitive microgels and computer simulation results obtained from a coarse-grained model of polyelectrolyte network and the primitive model of electrolyte is carried out. Polymer-polymer hydrophobic forces are considered in the model through a solvent-mediated interaction potential whose depth increases with temperature. The qualitative agreement between simulation and experiment is very good. In particular, our simulations predict a gradual shrinkage with temperature, which is actually observed for the microgels studied in this survey. In addition, the model can explain the swelling behavior for different contents of ionizable groups without requiring changes in the hydrophobic parameters. Our work also reveals that the abruptness of the shrinkage of charged gels is considerably conditioned by the number of monomeric units per chain. The swelling data are also analyzed with the Flory-Rhener theory, confirming some limitations of this classical formalism.