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 \del^2 \phi = \rho_{free ions)
+
\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(\bold{r})
+
\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>