  We investigate the effects of image charges, interfacial charge discreteness,
and surface roughness on spherical electric double layers in electrolyte
solutions with divalent counter-ions 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 (ICDF) and 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 the zeta potential, and thus the
structure of electric double layers.
