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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 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].

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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, $ε r$ is the relative dielectric constant of the medium and $ε 0$ is the vacuum permittivity. For water at room temperature ( $T = 300$ K), $\epsilon_r \approx 80$ , so that $\lambda_B \approx 0.7$ nm.