# Difference between revisions of "Poisson-Boltzmann equation"

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Chakraborty (Talk | contribs) |
Chakraborty (Talk | contribs) |
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==Short derivation== | ==Short derivation== | ||

The Poisson equation reads | The Poisson equation reads | ||

− | <math>\epsilon_0 \epsilon_r \nabla^2 \phi = \rho_{(free ions)}</math> | + | <math> |

+ | \epsilon_0 \epsilon_r \nabla^2 \phi = \rho_{(free ions)} | ||

+ | </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 21:13, 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>