Difference between revisions of "Poisson-Boltzmann equation"
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The Poisson equation reads | The Poisson equation reads | ||
<math> | <math> | ||
| − | \epsilon_0 \epsilon_r \ | + | \epsilon_0 \epsilon_r \nabla^2 \phi = \rho_{free ions) |
</math> | </math> | ||
where the charge distribution is | where the charge distribution is | ||
<math> | <math> | ||
| − | \rho_{free ions) = e \sum_i z_i c_i(\ | + | \rho_{free ions) = e \sum_i z_i c_i(\) |
</math> | </math> | ||
Revision as of 21:09, 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>
