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

Abstract

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.

On the effect of discrete charges adsorbed at the interface on nonionic liquid film stability: charges in the film

“…Having this in mind, the simple analytical asymptotics can be derived from equation (8) for the potential of the electrostatic field induced in the dielectric film by single point charge, located near the interface with the electrolyte solution:…”

“…holds. Condition (10) is the consequence of the simultaneous requirements for smallness of arguments of exponential functions in (8) and for holding of the inequality 1 + κ 2 /λ 2 1 in (5). Evidently, the condition (10) for highly concentrated solutions is satisfied already at small film thicknesses and thus might be applied for the analysis of electrostatic potentials and interaction forces in the case of polymolecular wetting films.…”

“…1, when simultaneously for the entire range of λ values, essential for integral (8), the relation λ κ holds, represents another asymptotic limit. One may then put…”

“…Understanding of the polarization effects and the electrostatic forces arising due to the presence of ionized and polar molecules or charged nanoparticles in the vicinity of interfaces is of considerable interest both in science and technology. During the last decades the theoretical analysis of this problem was given in numerous papers (see for example [1][2][3][4][5][6][7][8][9][10][11][12]), taking into account uniform and nonuniform smeared charge distribution as well as discrete charges. The main attention was attracted by the systems containing the charges embedded into an aqueous electrolyte half-space or thin film as the most relevant to colloid science, biophysics and biochemistry.…”

Image-charge forces in thin interlayers due to surface charges in electrolyte

“…Extensive studies in this area have been conducted for decades [1][2][3][4][5][6][7]. The focus in the theoretical studies of recent decades was on the systems important for colloid physics, biophysics, or biochemistry, in which the charges are located either in the vicinity of a single interface between bulk electrolyte and dielectric phases, or in the nanosize films of electrolytes, or, finally, in the dielectric interlayers confined (at least on one boundary) by an electrolyte solution [8][9][10][11][12][13][14][15][16][17][18][19][20].…”