Electrostatic repulsion of ion penetrable charged membranes: role of Donnan potential

A model is proposed for the electrostatic repulsion between two ion-penetrable charged membranes in which fixed charges are uniformly distributed. This model assumes that the electric potential far inside the membrane is always equal to the Donnan potential, independent of the membrane separation. In this respect the present model completely differs from usual models for the electrostatic interaction of colloidal particles which assume that the surface potential or the surface charge density remains constant during interaction. It is shown that the rise in potential in the interacting membranes caused by their approach is greatly suppressed so that the potential in the membrane does not exceed the Donnan potential. Numerical results of the calculation of the repulsion by the non-linear Poisson-Boltzmann equation are displayed as a function of the membrane separation and an approximate formula is also derived.