- Bjerrum length
The

**Bjerrum length**is the separation at which theelectrostatic interaction between two

elementary charges is comparable in magnitude to the thermal energy scale,$k\_B\; T$, where $k\_B$ is theBoltzmann 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 relativedielectric constant of the mediumand $epsilon\_0$ is thevacuum 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**

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