Bjerrum length

The Bjerrum length is the separation at which the electrostatic interaction between two
elementary charges is comparable in magnitude to the thermal energy scale,$k\_B\; T$, where $k\_B$ is the Boltzmann constant and $T$ is theabsolute temperature in Kelvin. It could be seen as one screening effect about the electrostatic interaction in a certain media [ [http://www.uic.edu/classes/phys/phys450/MARKO/N005.html Screening of Electrostatic Interactions ] ] .

In standard units, the Bjerrum length is given by

$lambda\_B\; =\; frac\{e^2\}\{4pi\; epsilon\_0\; epsilon\_r\; k\_B\; T\}$,

where $e$ is the elementary charge, $epsilon\_r$ is the relative dielectric constant of the mediumand $epsilon\_0$ is the vacuum permittivity.For water atroom temperature ($T\; =\; 300$ K), $epsilon\_r\; approx\; 80$, so that$lambda\_B\; approx\; 0.7$ nm.

In Gaussian units, $4piepsilon\_0=1$ and the Bjerrum length has the simpler form

$lambda\_B\; =\; frac\{e^2\}\{epsilon\_r\; k\_B\; T\}$.

References