Electrical interactions between two ion-penetrable charged membranes: Effect of sizes of charged species

A diffuse double-layer model for evaluation of the electrical interactions between two particles each covered by an ion-penetrable charged membrane in an electrolyte solution is proposed by taking the sizes of charged species into account. We show that the ionic sizes have a significant effect on the electrical interaction force between two particles. For constant fixed charge density, the corresponding point charge model will underestimate the interaction force, and the reverse is true for constant. membrane potential. The deviation due to the assumption of point charges is more serious for constant fixed charge density than that for constant membrane potential. It is found that the smaller the counterions, the greater the interaction force, and the reverse is true for co-ions.