Charged Membranes: Poisson–Boltzmann Theory, The DLVO Paradigm, and Beyond

Employing simple physical models, electrostatic properties of charged membranes in aqueous solutions are reviewed. In particular, it is shown how the well-known Poisson–Boltzmann (PB) equation governs the equilibrium ionic profiles for different boundary conditions at the membrane. The discussion is separated into the single charged membrane case and that of two interacting charged membranes, with counterions only and in presence of a salt reservoir. A modification of the PB theory is presented to treat the extremely high counterion concentration in the vicinity of a charge membrane. In addition, charge-regulation boundary condition is examined and its effects on the ionic profiles and the osmotic pressure for two membranes are discussed. The last part offers a brief review of the ever-present van der Waals interactions, as well as a short account of the limitations inherent in the mean-field PB theory.