Modeling the surface charge evolution of spherical nanoparticles by considering dielectric discontinuity effects at the solid/electrolyte solution interface.

It is well known that the electrostatic repulsions between charges on neighboring sites decrease the effective charge at the surface of a charged nanoparticle (NP). However, the situation is more complex close to a dielectric discontinuity, since charged sites are interacting not only with their neighbors but also with their own image charges and the image charges of all neighbors. Titrating site positions, solution ionic concentration, dielectric discontinuity effects, and surface charge variations with pH are investigated here using a grand canonical Monte Carlo method. A Tanford and Kirkwood approach is used to calculate the interaction potentials between the discrete charged sites. Homogeneous, heterogeneous, and patch site distributions are considered to reproduce the various titrating site distributions at the solid/solution interface of spherical NPs. By considering Coulomb, salt, and image charges effects, results show that for different ionic concentrations, modifications of the dielectric constant of NPs having homogeneous and heterogeneous site distributions have little effect on their charging process. Thus, the reaction field, due to the presence of image charges, fully counterbalances the Coulomb interactions. This is not the case for patch distributions, where Coulomb interactions are not completely counterbalanced by the reaction field. Application of the present model to pyrogenic silica is also performed and comparison is made with published experimental data of titration curves at various ionic concentrations.