# Bjerrum length

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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

$lambda_B = frac\left\{e^2\right\}\left\{4pi epsilon_0 epsilon_r k_B T\right\}$,

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

$lambda_B = frac\left\{e^2\right\}\left\{epsilon_r k_B T\right\}$.

References

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