Analytical Expression for the Electrostatic Disjoining Pressure Taking into Account the Excluded Volume of the Hydrated Ions between Charged Interfaces in Electrolyte

In this work we illustrate how the excluded volume of the hydrated electrolyte ions can be accounted for in the theory of the electric double layer and in the DLVO theory. It is shown that the finite size of the ions affects their distributions and the electric potential not only in the close vicinity of the charged interface but also over all of the electric double layer. We derive the correction to the electrostatic disjoining pressure due to the excluded volume of the ions in the film for the regime of weak overlap of the electric double layers. It is repulsive for large separations and can be accounted for by introducing an effective surface potential. The repulsion for large separations increases with an increase in the volume of the hydrated counterions. We demonstrate that this effect contributes to an increase in the critical coagulation concentration of electrolyte for a charged colloid. By contrast, the small separation asymptotic of the electrostatic disjoining pressure at constant surface potential, which takes into account the excluded volume, predicts a reduced repulsion compared to DLVO theory.