Poisson–Boltzmann equation

The Poisson - Boltzmann equation - named after Siméon Denis Poisson and Ludwig Boltzmann - describes the electrostatic interactions between molecules in liquids with dissolved ions. It is primarily in the areas of physical chemistry and biophysics of great importance. Here it is used to model the implicit solvation. With this method, it is possible to calculate the effects of solvents on the structure and interactions of molecules in solutions of different ionic strength is approximately. Since the Poisson - Boltzmann equation for complex systems is not solved analytically, various computer programs have been developed to solve them numerically. The Poisson - Boltzmann equation is used in particular for biologically relevant systems such as proteins, DNA or RNA.

The equation can be written using SI units as follows:

Denotes the location-dependent dielectric conductivity, the electrostatic potential, the charge density of the solvent, the concentration of the ion at an infinite distance to the solvent, the charge on the ion, the charge of a proton, is the Boltzmann constant and temperature. is a measure of the accessibility of the location to the ions of the solution. Small potential equation can be linearised and thus dissolved more easily.

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• APBS PB solver
• Zap - A Poisson-Boltzmann electrostatics solver

• Physical chemistry
• Electrostatics