# Difference between revisions of "Poisson-Boltzmann equation"

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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 $\epsilon_0 \epsilon_r \nabla^2 \phi = \rho_{free ions)$ where the charge distribution is $\rho_{free ions) = e \sum_i z_i c_i(\)$