Difference between revisions of "Poisson-Boltzmann equation"

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==Short derivation==
 
==Short derivation==
 
The Poisson equation reads
 
The Poisson equation reads
 +
 
<math>
 
<math>
 
\epsilon_0 \epsilon_r \nabla^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>\rho_{(free ions)} = e \sum_i z_i c_i</math>
+
 
 +
<math>
 +
\rho_{(free ions)} = e \sum_i z_i c_i
 +
</math>.

Revision as of 21:14, 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>.