# 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.) |
Chakraborty (Talk | contribs) |
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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>