Donnan phenomena in membranes with charge due to ion adsorption. Effects of the interaction between adsorbed charged groups

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Abstract
A physical model for the modified Donnan phenomenon associated with ion adsorption on localized membrane sites is presented. This model accounts for the dependence of the concentration of adsorbed ions on electrolyte concentration and pH as it is influenced by the electrostatic interaction between adsorbed ions. The equilibrium thermodynamic concepts employed are based on the Donnan formalism for the ion equilibria between membrane and solution, and the Bragg–Williams approximation for an adsorption isotherm that incorported interaction between adsorbed ions. Our results include the concentration of charged groups in the membrane, the pH of the membrane phase solution, and the Donnan potential as functions of the pH and the electrolyte concentration of the external solution for different degrees of the electrostatic interaction. These magnitudes are of considerable interest in biopolymers, membranes, and conducting polymers.