Modified Göuy–Chapman theory for an ion-penetrable charged membrane

Abstract

The classic Göuy–Chapman theory is modified to describe the electrical potential distribution in an ion-penetrable charged membrane by taking the sizes of the charged species into account. We show that for a negatively charged membrane, if the density of fixed charge is low, a reverse in electrical potential may occur if cations are smaller than both anions and fixed groups. Also, only one plane of zero charge (PZC) exists. If a membrane is positively charged, there may exist zero to two PZC, depending upon the fixed charge density and the relative magnitudes of anions and fixed groups. Under a critical condition determined mainly by the sizes of the charged species, a unique PZC exists in the inner plane of fixed charge. The present model is capable of explaining why microorganisms can adjust the degree of dissociation of the ionogenic groups in their cell membranes to absorb nutritive ingredients and to shun toxic species by fluctuations in the extent to which specific ions penetrate the membranes.