Poisson–Boltzmann equation

<math> \vec{\nabla}\cdot\left[\epsilon(\vec{r})\vec{\nabla}\Psi(\vec{r})\right] = -4\pi\rho^{f}(\vec{r}) - 4\pi\sum_{i}c_{i}^{\infty}z_{i} q \lambda(\vec{r}) \cdot \exp \left[{\frac{-z_{i}q\Psi(\vec{r})}{k_B T}}\right] </math>

or (in mks):

<math>

\vec{\nabla}\cdot\left[\epsilon(\vec{r})\vec{\nabla}\Psi(\vec{r})\right] = -\rho^{f}(\vec{r}) - \sum_{i}c_{i}^{\infty}z_{i} q \lambda(\vec{r}) \cdot \exp \left[{\frac{-z_{i}q\Psi(\vec{r})}{k_B T}}\right] </math>

• http://en.wikipedia.org/wiki/Poisson%E2%80%93Boltzmann_equation

Software

• http://www.poissonboltzmann.org/apbs/
• http://en.wikipedia.org/wiki/DelPhi_%28software%29

• http://www.fetk.org/