Principles for the determination of the surface potential of charged particles in mixed electrolyte solutions

The Gouy–Chapman surface potential is a key parameter for many interfacial phenomena in physical, chemical and biological systems. Existing theoretical approaches allow the determination of the surface potential at a solid–liquid interface only in single electrolyte solutions; however, mixed electrolytes are often encountered in practical applications. The development of a theoretical approach for the determination of the surface potential in mixed electrolyte solutions is therefore a desirable goal. In this study, this important issue was resolved for the first time. Based on the analytical solutions of the nonlinear Poisson–Boltzmann equation in different mixed electrolyte solutions, corresponding mathematical relationships were developed between the surface potential and the mean ionic concentration in the diffuse layer. As the mean ionic concentration in the diffuse layer can be easily determined, the surface potential could be calculated using the newly derived equations. The effects of electrolyte composition on the surface potential were theoretically quantified in the new equations, while only counterionic type was taken into account for mixed electrolyte solutions in the current studies.