Effective surface charge for symmetric electrolytes in the primitive model double layer

Electrophoretic mobility of model colloids and overcharging: theory and experiment

“…In ®gure 10 the Ád ¡ ¼0 predictions of two approximate integral equation approaches (HNC/MSA and AHNC) are plotted for a particular case (2:2 electrolyte, 0.125 M, aˆ0 :23 nm). The AHNC values have been estimated from [19], ®gure 6. As concluded, there are no remarkable di erences between the two theories within the range of surface charge densities studied (0±25 mC cm ¡ 2 ) but this ®gure also suggests that discrepancies may emerge for j ¼0 j > 30 mC cm ¡ 2 .…”

“…Physically, this means the appearance of exponentially damped oscillatory behaviour for Á …x † as well as the correlation functions, which is interpreted as the occurrence of alternating layers with positive and negative charge even far from the surface. According to some authors [14,17,19], this phenomenon is found irrespective of the magnitude of the surface charge. Attard has also put forward the extended PB approximation, which is essentially the solution of the MSA to the inhomogeneous OZ equation for ions of zero size.…”

Aggregation Processes and Formation of Silico-calco-alkaline Gels under High Ionic Strength

“…Nevertheless, repulsive interactions at the particle surface and effects of counterions' size have been theoretically proposed for such solutions (33)(34)(35). These studies demonstrate that the effective charge density of the particles increases with the counterion size and this increase becomes more important for increasing ionic strength.…”

Zeta-Potential Study of Calcium Silicate Hydrates Interacting with Alkaline Cations

“…Indeed, correlations between the charged species may have to be taken into account to describe the highly charged surface of CSH in concentrated electrolytic solutions. For instance, the anisotropic hypernetted chain (AHNC) theory, which considers electrostatic and steric interactions between charged species, predicts an "effective" surface charge, that is the charge "seen" by ions situated at a large distance from the charged interface, depending strongly on the diameter of the counterions (28), especially at high surface charge. The larger the counterions, the higher the effective surface charge calculated by the AHNC theory, compared to that calculated by neglecting the correlation effects, which leads to an increase in the diffuse-layer potential.…”