Cation binding to membranes: Competition between mono-, di- and trivalent cations

The binding of mono-, di- and trivalent cations to negatively charged surfaces is studied within the framework of a modified Gouy-Chapman equation. For any given combination of ions of the above valences, the existence and uniqueness of the solution for the surface potential is shown. The treatment provides the surface potential and charge density. For a system containing only monovalent and divalent ions, analytical solutions are given. When trivalent ions are also present, a procedure based on numerical integration is described. The distance dependence of the electrostatic potential for planar surfaces is given. The calculations provide the amount of cations tightly bound and the amount trapped in the double layer region. The competition between cations for binding to surfaces is elucidated.