Analytical solutions of the nonlinear Poisson–Boltzmann equation in mixture of electrolytes

The Poisson–Boltzmann theory is still considered as an exact theory under low or even moderate electrolyte concentrations. As of today, however, just the analytical solutions in a single electrolyte were obtained, while people often meet mixed electrolytes in practical applications. Thus the analytical solutions of Poisson–Boltzmann equation (PBE) in different mixed electrolytes are still an important issue. The analytical solutions of PBE in mixed electrolytes with monovalent and bivalent counterions were firstly derived in the present study. The potential distribution and concentration profile curves in EDL were obtained with one dimensional space by the analytical solutions of PBE. The potential distribution curves of different mixtures showed that the power of the screen surface charge for bivalent counterion was stronger than that for monovalent counterion, thus the concentration of bivalent counterion in EDL was larger than that of monovalent counterion.