Double-layer properties of an ion-penetrable charged membrane: Effect of sizes of charged species

In this paper we have proposed a double-layer model, which takes the sizes of the charged species into account, for an ion-penetrable charged membrane immersed in an electrolyte solution. Analytical expressions for the electrical potential distribution, the potential drop across the membrane, and the net penetration charge into the membrane are derived for the case in which the linearized Gouy-Chapman model is employed. We will show that, if charged species have different sizes, the behavior of a positively charged membrane is unsymmetrical to that of a negatively charged membrane. Also, the larger the counterions, the greater the potential drop across a membrane and the smaller the net penetration charge into a membrane; the reverse is true for co-ions.