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

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.