We investigate the effects of image charges, interfacial charge discreteness, and surface roughness on spherical electric double layer structures in electrolyte solutions with divalent counterions in the setting of the primitive model. By using Monte Carlo simulations and the image charge method, the zeta potential profile and the integrated charge distribution function are computed for varying surface charge strengths and salt concentrations. Systematic comparisons were carried out between three distinct models for interfacial charges: (1) SURF1 with uniform surface charges, (2) SURF2 with discrete point charges on the interface, and (3) SURF3 with discrete interfacial charges and finite excluded volume. By comparing the integrated charge distribution function and the zeta potential profile, we argue that the potential at the distance of one ion diameter from the macroion surface is a suitable location to define the zeta potential. In SURF2 model, we find that image charge effects strongly enhance charge inversion for monovalent interfacial charges, and strongly suppress charge inversion for multivalent interfacial charges. For SURF3, the image charge effect becomes much smaller. Finally, with image charges in action, we find that excluded volumes (in SURF3) suppress charge inversion for monovalent interfacial charges and enhance charge inversion for multivalent interfacial charges. Overall, our results demonstrate that all these aspects, i.e., image charges, interfacial charge discreteness, their excluding volumes, have significant impacts on zeta potentials of electric double layers.

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A generalized image charge formulation is proposed for the Green's function of a core-shell dielectric nanoparticle for which theoretical and simulation investigations are rarely reported due to the difficulty of resolving the dielectric heterogeneity. Based on the formulation, an efficient and accurate algorithm is developed for calculating electrostatic polarization charges of mobile ions, allowing us to study related physical systems using the Monte Carlo algorithm. The computer simulations show that a fine-tuning of the shell thickness or the ion-interface correlation strength can greatly alter electric double-layer structures and capacitances, owing to the complicated interplay between dielectric boundary effects and ion-interface correlations.

The polarization-induced charges of a dielectric sphere are studied for charged colloidal systems in electrolyte solutions with a primitive model. The method of constructing multiple-image charges is used to approximate the polarization potential of a microion outside the sphere; it is based on a numerical discretization of the potential's analytical integral representation, and can systematically approximate the exact potential with desired accuracy by varyiation of the number of point images. Different aspects of the image effects are then investigated by Monte Carlo simulations for several colloidal systems, in both salt-free and salty environments. Furthermore, we studied the influence of discrete surface charges of different valences, and demonstrate that the polarization charges can significantly strengthen charge reversal for the colloid-microion complex, especially for multivalent interfacial ions.