Principles of Surface Potential Estimation in Mixed Electrolyte Solutions:Taking into Account Dielectric Saturation

The dielectric properties between in-particle/water interface and bulk solution are significantly different, which are ignored in the theories of surface potential estimation. The analytical expressions of surface potential considering the dielectric saturation were derived in mixed electrolytes based on the nonlinear Poisson-Boltzmann equation. The surface potentials calculated from the approximate analytical and exact numerical solutions agreed with each other for a wide range of surface charge densities and ion concentrations. The effects of dielectric saturation became important for surface charge densities larger than 0.30 C/mbegin{document}$ ^2 $end{document}. The analytical models of surface potential in different mixed electrolytes were valid based on original Poisson-Boltzmann equation for surface charge densities smaller than 0.30 C/mbegin{document}$ ^2 $end{document}. The analytical model of surface potential considering the dielectric saturation for low surface charge density can return to the result of classical Poisson-Boltzmann theory. The obtained surface potential in this study can correctly predict the adsorption selectivity between monovalent and bivalent counterions.