Forces between charge regulated surfaces inside an electrolyte solution

We study the interaction between two charge-regulated surfaces immersed in a 1:1 electrolyte solution, analyzing how this interaction varies with the ionic strength and pH of the solution. This system can be thought to represent two like-charged colloidal particles with radii much larger than the Debye length. Our theoretical approach is based on a recently developed theory that modifies the traditional Poisson-Boltzmann equation to account for the discrete nature of surface groups. We demonstrate that charge regulation has a significant impact on the interaction forces between the surfaces compared to systems with fixed surface charges. Notably, unlike unregulated surfaces, increasing the salt concentration can lead to a stronger repulsive force between the surfaces.