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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, kBT, where kB is the Boltzmann constant and T is the absolute temperature in Kelvin. It could be seen as one screening effect about the electrostatic interaction in a certain media[1]. It is the correlation range of two charges, such as the attraction range between people in social network[2].

In standard units, the Bjerrum length is given by=

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

where e is the elementary charge, εr is the relative dielectric constant of the medium and ε0 is the vacuum permittivity. For water at room temperature (T = 300 K), $\epsilon_r \approx 80$, so that $\lambda_B \approx 0.7$ nm.

In Gaussian units, 4πε0 = 1 and the Bjerrum length has the simpler form

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

1. ^ http://www.uic.edu/classes/phys/phys450/MARKO/N005.html
2. ^ http://www.urbandictionary.com/define.php?term=bjerrum+length