Influence of the finite size and effective permittivity of ions on the equilibrium double layer around colloidal particles in aqueous electrolyte solution

• We propose a theoretical model that improves the Poisson–Boltzmann equation.
• The model takes into account the finite ion size and the effective ion permittivity effects.
• The model introduces both the Bikerman and the Carnahan–Starling expressions for the ion–ion interactions.
• The presented model greatly amplifies the steric effects.

The equilibrium properties of the electrical double layer surrounding a charged spherical colloidal particle immersed in an aqueous electrolyte solution are examined taking into account the finite ion size. This study includes the representation of the steric interactions among ions using both the Bikerman and the Carnahan–Starling models, an account of all the effects related to the representation of hydrated ions as dielectric spheres (dependence of the electrolyte solution permittivity, on the local ion concentration, and appearance of the Born and the dielectrophoretic forces acting on the ions), and solution of the problem for both high and low surface charge values. We find that the Carnahan–Starling model together with effective ion permittivity related effects appears to be able to provide an interpretation to the electrokinetic potential vs. surface charge dependence in the case of colloidal particles suspended in aqueous electrolyte solutions. On the contrary, for electrode–electrolyte systems, both the Bikerman and the Carnahan–Starling models might be able to explain this dependence.

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