We study the consistent inclusion of ionic size-asymmetry for a wide range of macroparticle charges in the primitive model of an electrical double layer around a spherical colloid using (1) Monte-Carlo simulations, (2) the hybrid integral-equation formalism of hypernetted-chain (HNC) and mean-spherical approximation (MSA), and (3) the Gouy–Chapman theory modified for unequal ionic radii. In our simulations, for a weakly charged macroion, we observe surface charge amplification from adsorption of like-charged ions, as well as charge reversal due to overcompensation of the bare nanoparticle charge by counterions. When the nanoparticle charge increases, we detect both asymmetric neutralization and asymmetric electrostatic screening that depend on the sign of the macroion's valence. Specifically, there exists a higher reduction of the original bare charge and a smaller electrostatic potential for the case of negative nanoparticles with positive small counterions, versus the case of positive nanoparticles with negative large counterions. These coarse-grained results are in agreement with the predictions of asymmetric charge renormalization (P. González-Mozuelos and M. Olvera de la Cruz, Phys. Rev. E, 2009, 79, 031901), in which the aqueous solvent is explicitly taken into account. Results from the Gouy–Chapman theory modified for unequal ionic radii differ notably from our obtained Monte-Carlo data, while good agreement exists between simulation results and HNC/MSA-treatment findings.

The ionic adsorption around a weakly charged spherical colloid, immersed in size-asymmetric 1:1 and 2:2 salts, is studied. We use the primitive model (PM) of an electrolyte to perform Monte Carlo simulations as well as theoretical calculations by means of the hypernetted chain/mean spherical approximation (HNC/MSA) and the unequal-radius modified Gouy–Chapman (URMGC) integral equations. Structural quantities such as the radial distribution functions, the integrated charge, and the mean electrostatic potential are reported. Our Monte Carlo “experiments” evidence that near the point of zero charge, the smallest ionic species is preferentially adsorbed onto the macroparticle, independently of the sign of the charge carried by this tiniest electrolytic component, giving rise to the appearance of the phenomena of charge reversal (CR) and overcharging (OC). Accordingly, colloidal CR, due to an excessive attachment of counterions, is observed when the macroion is slightly charged and the coions are larger than the counterions. In the opposite situation, i.e., if the counterions are larger than the coions, the central macroion acquires additional like-charge (coions) and hence becomes “overcharged,” a feature theoretically predicted in the past [F. Jiménez-Ángeles and M. Lozada-Cassou, J. Phys. Chem. B 108, 7286 (2004)]. In other words, here we present the first simulation data on OC in the PM electrical double layer, showing that close to the point of zero charge, this novel effect surges as a consequence of the ionic size asymmetry. We also find that the HNC/MSA theory captures well the CR and OC phenomena exhibited by the computer experiments, especially as the macroion’s charge increases. On the contrary, even if URMGC also displays CR and OC, its predictions do not compare favorably with the Monte Carlo data, evidencing that the inclusion of hard-core correlations in Monte Carlo and HNC/MSA enhances and extends those effects. We explain our findings in terms of the energy-entropy balance. In the field of electrophoresis, it has been generally agreed that the charge of a colloid in motion is partially decreased by counterion adsorption. Depending on the location of the macroion’s slipping surface, the OC results of this paper could imply an increase in the expected electrophoretic mobility. These observations aware about the interpretation of electrokinetic measurements using the standard Poisson–Boltzmann approximation beyond its validity region.

The hypernetted chain/mean spherical approximation (HNC/MSA) integral equation for a totally asymmetric primitive model electrolyte around a spherical macroparticle is obtained and solved numerically in the case of size-asymmetric systems. The ensuing radial distribution functions show a very good agreement when compared to our Monte Carlo and molecular-dynamics simulations for spherical geometry and with respect to previous anisotropic reference HNC calculations in the planar limit. We report an analysis of the potential versus charge relationship, radial distribution functions, mean electrostatic potential, and cumulative reduced charge for representative examples of 1:1 and 2:2 salts with a size-asymmetry ratio of 2. Our results are collated with those of the modified Gouy–Chapman (MGC) and unequal radius modified Gouy–Chapman (URMGC) theories and with those of HNC/MSA in the restricted primitive model (RPM) to assess the importance of size-asymmetry effects. One of the most striking characteristics found is that, contrary to the general belief, away from the point of zero charge the properties of an asymmetric electrical double layer (EDL) are not those corresponding to a symmetric electrolyte with the size and charge of the counterion, i.e., counterions do not always dominate. This behavior suggests the existence of a new phenomenology in the EDL that genuinely belongs to a more realistic size-asymmetric model where steric correlations are taken into account consistently. Such novel features cannot be described by traditional mean-field theories such as MGC, URMGC, or even by enhanced formalisms, such as HNC/MSA, if they are based on the RPM.

Significance: Colloids constitute the basic components of many everyday products and are integrated into the fabric of modern society. Understanding their assembly is key for nanotechnological and biotechnological advances. At the single-particle level, colloids commonly possess electric charge. Consequently, the structure to which they conform is strongly influenced by electrostatic interactions. In solution, these interactions are modified by the presence of ions. We have developed a model for computing the corresponding effective electrostatic interactions as well as the osmotic pressure. Our model extends the applicability of Derjaguin−Landau−Verwey−Overbeek theory to dense systems in which many-body effects are crucial. This will allow previously impossible, mesoscale studies of colloidal assembly to be performed analytically or by simulation with implicit ions models.