Isoelectric point of an ion-penetrable membrane

The surface potential of an ion-penetrable planar membrane is calculated for the case in which acidic and basic groups are present in the membrane. It is found that when both acidic and basic groups are not uniformly distributed in the direction normal to the membrane, the isoelectric point (the pH value at which the surface potential becomes zero) of the membrane varies with the electrolyte concentration, whereas if both groups are uniformly distributed, the isoelectric point is independent of the electrolyte concentration. As a simple example, we treat a membrane consisting of two layers, in which acidic groups are distributed in the outer layer and basic groups are in the inner layer. Simple equations determining the membrane surface potential as a function of pH and electrolyte concentration and the dependence of the isoelectric point on the electrolyte concentration are presented.