Difference between revisions of "Poisson-Boltzmann equation"
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\rho_{(free ions)} = e \sum_i z_i c_i | \rho_{(free ions)} = e \sum_i z_i c_i | ||
</math>. | </math>. | ||
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| + | Assuming that the energy of each ion is due to only the electrostatic potential, the Boltzmann distribution dictates that | ||
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| + | <math> | ||
| + | c_i = c_i0 Exp(\frac{-z_i e \phi, k T}) | ||
| + | </math> | ||
Revision as of 21:17, 20 November 2009
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>.
Assuming that the energy of each ion is due to only the electrostatic potential, the Boltzmann distribution dictates that
<math> c_i = c_i0 Exp(\frac{-z_i e \phi, k T}) </math>
