Electric potential distributions around discrete charges in a dielectric membrane—electrolyte solution system

Within the framework of the linearized Debye-Hückel theory an exact solution of the problem of calculating the electric potential caused by discrete fixed charges located at arbitrary positions with respect to a dielectric membrane-solution interface is presented. It takes into account the existence of an electrolyte solution on both sides of the membrane. Asymmetric ionic conditions are allowed for. For some interesting typical cases of fixed charge locations and electrolyte ionic strengths electric potential distributions were calculated and discussed. It is shown that, if the fixed charges were at or in front of the membrane surface, the characteristic distance of the electric potential decay was comparable to the Debye-Hückel length. At the opposite membrane surface only very small electric potentials can be observed. If, however, the fixed charge was placed below the membrane surface the electric potential in lateral direction and towards the other membrane surface largely increased. This effect was very sensitive to the position of the fixed charge with respect to the membrane surface.