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We investigate the effects of image charges, interfacial charge discreteness,and surface roughness on spherical electric double layers in electrolytesolutions with divalent counter-ions in the setting of the primitive model. Byusing Monte Carlo simulations and the image charge method, the zeta potentialprofile and the integrated charge distribution function are computed forvarying surface charge strengths and salt concentrations. Systematiccomparisons were carried out between three distinct models for interfacialcharges: 1) SURF1 with uniform surface charges, 2) SURF2 with discrete pointcharges on the interface, and 3) SURF3 with discrete interfacial charges andfinite excluded volume. By comparing the integrated charge distributionfunction (ICDF) and potential profile, we argue that the potential at thedistance of one ion diameter from the macroion surface is a suitable locationto define the zeta potential. In SURF2 model, we find that image charge effectsstrongly enhance charge inversion for monovalent interfacial charges, andstrongly suppress charge inversion for multivalent interfacial charges. ForSURF3, the image charge effect becomes much smaller. Finally, with imagecharges in action, we find that excluded volumes (in SURF3) suppress chargeinversion for monovalent interfacial charges and enhance charge inversion formultivalent interfacial charges. Overall, our results demonstrate that allthese aspects, i.e., image charges, interfacial charge discreteness, theirexcluding volumes have significant impacts on the zeta potential, and thus thestructure of electric double layers.

Effects of image charges, interfacial charge discreteness, and surface roughness on the zeta potential of spherical electric double layers