Poisson-Boltzmann equation

The Poisson-Boltzmann equation describes the ion distribution in an electrolyte solution outside a charged interface. It relates the mean-field potential to the concentration of electrolyte.

Short derivation

The Poisson equation reads <math> \epsilon_0 \epsilon_r \del^2 \phi = \rho_{free ions) </math> where the charge distribution is <math> \rho_{free ions) = e \sum_i z_i c_i(\bold{r}) </math>