Effects of dielectric decrement on surface potential in a mixed electrolyte solution

Surface potential is an important parameter related to the physical and chemical properties of charged particles. A simple analytical model for the estimation of surface potential is established based on the Poisson–Boltzmann theory with the consideration of the dielectric decrement in mixed electrolyte. The analytical relationships between surface potential and charge density are derived in different mixed electrolytes with monovalent and bivalent ions. The dielectric decrease on the charged surface strongly affects the surface potential at a high charge density with different ion strengths and concentration ratios of counter-ions. The surface potential based on the Gouy–Chapman model is underestimated because of the dielectric decrement on the surface. The diffuse layer can be regarded as a continuous uniform medium only when the surface charge density is lower than 0.3 C·m-2. However, the surface charge densities of many materials in practical applications are higher than 0.3 C·m-2. The new model for the estimation of surface potential can return to the results obtained based on the Gouy–Chapman model at a low charge density. Therefore, it is implied that the established model that considers the dielectric decrement is valid and widely applicable.

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/m^2.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/m^2.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.