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This paper discusses the little-known fact that Donnan's equilibrium criteriaestablished over 100 years ago neglected the coupling between ionconcentrations and the osmotic pressure. Such coupling can be treated based ongeneral thermodynamic considerations including the solvent equilibrium, leadingto a membrane potential that consists of not only the classical Donnanpotential term but also an additional term due to the osmotic pressure, and theexistence of a membrane potential even when the impermeable species are notcharged. This coupled treatment is in conflict with the well-establishedPoisson-Boltzmann equation and Nernst-Planck equation, but is consistent withthe extension of these equations including the solvent effects by Freise andSchlogl, enables us to view the electrical double layer equilibrium as Donnanequilibrium.

Donnan Equilibrium Revisited: Coupling between Ion Concentrations, Osmotic Pressure, and Donnan Potential