# Poisson-Boltzmann equation

From Soft-Matter

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 \nabla^2 \phi = \rho_{(free ions)}</math> where the charge distribution is <math>\rho_{free ions) = e \sum_i z_i c_i</math>