Equilibrium Electric Double Layer of Charged Spherical Colloidal Particles: Effect of Different Distances of Minimum Ion Approach to The Particle Surface

Abstract

A study of the equilibrium double layer surrounding charged spherical particles is presented, considering that ions in the suspending medium have a finite size. It is assumed that each ionic species has a different minimum approach distance to the particle surface, while the distance of minimum approach between ions in the bulk has the same value for all ion species. Numerical calculations made using the network simulation method and including all the features of the considered model are presented, together with rigorous analytical results valid for a flat interface and point ions in the bulk electrolyte solution. It is shown that the double-layer parameters are very sensitive to the difference between the minimum approach distances of co-ions and counterions. For negative particles and greater approach distances for co-ions than for counterions, the potential always increases with this difference and, under appropriate circumstances, attains positive values leading to charge reversal. This phenomenon is favored by a high electrolyte concentration, high counterion valences, and low surface charge (in modulus). An analytical expression relating these parameters to the threshold value of the difference between the minimum approach distances of co-ions and counterions to the particle surface is presented.

Recent developments in electrokinetics of salt-free concentrated suspensions

“…Some of the new approaches concern microscopic descriptions of the previous considerations although restricted mainly to equilibrium conditions. The classical approach of the standard electrokinetic model is a macroscopic description that considers average interactions by mean field approximations [21, [63][64][65][66][67][68][69][70][71][72][73]. Important phenomena like overcharging [74] have no convincing explanation when ion-ion correlations including steric effects are neglected, as the classical approach does, while it has been satisfactorily explained with…”

Predictions of the maximum energy extracted from salinity exchange inside porous electrodes

“…1) must be solved considering both ionic species given by Eq. 11 [41]. Accordingly, new boundary conditions must be used, namely, the continuity of the potential and of the normal component of the electric displacement at the boundary between every pair of regions:…”

“…For our purposes, existing models on the description of the EDL potential profile at interfaces with different geometries [38,34,39,40,41,42,43,44,45] cannot be applied to porous electrodes because such models are usually restricted to dilute suspensions, so that the likely overlap between EDLs from opposite walls of the pores is not considered. Theoretical models including EDL overlap and ionic size effects have been applied to salt free suspensions [42], and are based on cell models, which are appropriate in the case of homogeneous distributions of non-contacting spherical particles [41].…”

“…Theoretical models including EDL overlap and ionic size effects have been applied to salt free suspensions [42], and are based on cell models, which are appropriate in the case of homogeneous distributions of non-contacting spherical particles [41].…”

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

“…Quite recently, López-García et al [42] have extended their previous model to allow for a different distance of closest approach to the particle surface for each ionic species. The most important fact is that it predicts charge reversal under appropriate circumstances by only considering such ionic excluded volume effects.…”