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

TL;DR

This paper revisits Donnan equilibrium, revealing the coupling between ion concentrations and osmotic pressure, leading to a modified membrane potential that includes additional thermodynamic effects often overlooked in classical models.

Contribution

It introduces a coupled thermodynamic framework for Donnan equilibrium that accounts for osmotic pressure and solvent effects, challenging traditional assumptions.

Findings

Membrane potential includes an osmotic pressure term.

Donnan equilibrium can be viewed as an electrical double layer.

Coupled treatment conflicts with classical Poisson-Boltzmann models.

Abstract

This paper discusses the little-known fact that Donnan's equilibrium criteria established over 100 years ago neglected the coupling between ion concentrations and the osmotic pressure. Such coupling can be treated based on general thermodynamic considerations including the solvent equilibrium, leading to a membrane potential that consists of not only the classical Donnan potential term but also an additional term due to the osmotic pressure, and the existence of a membrane potential even when the impermeable species are not charged. This coupled treatment is in conflict with the well-established Poisson-Boltzmann equation and Nernst-Planck equation, but is consistent with the extension of these equations including the solvent effects by Freise and Schlogl, enables us to view the electrical double layer equilibrium as Donnan equilibrium.