Difference between revisions of "Poisson-Boltzmann equation"

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(New page: =Derivation= The Poisson-Boltzmann equation describes the ion distribution in an electrolyte solution outside a charged interface.)
 
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=Derivation=
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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.
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==Short derivation==
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The Poisson equation reads
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<math>
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\epsilon_0 \epsilon_r \del^2 \phi = \rho_{free ions)
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</math>
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where the charge distribution is
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<math>
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\rho_{free ions) = e \sum_i z_i c_i(\bold{r})
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</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>