Exact solution of the unidimensional Poisson-Boltzmann equation for a 1:2 (2:1) electrolyte

The unidimensional Poisson-Boltzmann equation for a 1:2 (2:1) electrolyte has been solved analytically. The results have been compared with those obtained from the linearized equation. It is shown that in physiological conditions the difference may be greater than 10%. The value of the derivative of the potential in x=0, (dpsi/dx)x=0, has been used by many authors in the evaluation of the superficial charges of biological membranes. The value of (dpsi/dx)x-0 have also been compared with the ones derived from the linearized equation. The difference may be greater than 25%. Our results suggest that the linearization of the Poisson-Boltzmann equation for a 1:2(2:1) electrolyte may be greatly misleading.