Effects of dielectric decrement on surface potential in a mixed electrolyte solution**Project supported by the National Natural Science Foundation of China (Grant Nos. 41501240, 41530855, 41501241, and 41877026), the Natural Science Foundation of Chongqing CSTC (Grant No. cstc2018jcyjAX0318), and the Fundamental Research Funds for the Central Universities, China (Grant No. XDJK2017B029).

Abstract

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.