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 electr ical potential distribution, the potential drop across the membrane, and th e net penetration charge into the membrane are derived for the case in whic h the linearized Gouy-Chapman model is employed. We will show that, if char ged species have different sizes, the behavior of a positively charged memb rane is unsymmetrical to that of a negatively charged membrane. Also, the l arger the counterions, the greater the potential drop across a membrane and the smaller the net penetration charge into a membrane; the reverse is tru e for co-ions.