Difference between revisions of "Poisson-Boltzmann equation"
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Chakraborty (Talk | contribs) (New page: =Derivation= The Poisson-Boltzmann equation describes the ion distribution in an electrolyte solution outside a charged interface.) |
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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. | |
| − | The Poisson-Boltzmann equation describes the ion distribution in an electrolyte solution outside a charged interface. | + | ==Short derivation== |
| + | The Poisson equation reads | ||
| + | <math> | ||
| + | \epsilon_0 \epsilon_r \del^2 \phi = \rho_{free ions) | ||
| + | </math> | ||
| + | where the charge distribution is | ||
| + | <math> | ||
| + | \rho_{free ions) = e \sum_i z_i c_i(\bold{r}) | ||
| + | </math> | ||
Revision as of 21:08, 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 \del^2 \phi = \rho_{free ions) </math> where the charge distribution is <math> \rho_{free ions) = e \sum_i z_i c_i(\bold{r}) </math>
