Bjerrum length

Template:Linkless The Bjerrum length refers to the approximate distance within which electrostatic interactions dominate thermal motions for two charges, usually with the value of 0.7 nanometre in pure water. It is expected that two charged species lying a distance of greater than 0.7 nm apart in a pure aqueous medium will feel a force smaller than the background thermal forces.

In standard units, the Bjerrum length is given by

$\lambda _{B}={\frac {e^{2}}{4\pi \epsilon k_{B}T}}$,

where $e$ is the elementary charge, $\epsilon$ is the dielectric constant of the medium, $k_{B}$ is the Boltzmann constant, and $T$ is the absolute temperature in kelvins. For water at room temperature (T = 300 K), $\epsilon \approx 80\epsilon _{0}$, where $\epsilon _{0}$ is the vacuum permittivity.

In Gaussian units the expression for $\lambda _{B}$ simplifies as $4\pi \epsilon _{0}=1$ in those units. It becomes

$\lambda _{B}={\frac {e^{2}}{\epsilon _{r}k_{B}T}}$,

where $\epsilon _{r}=\epsilon /\epsilon _{0}$ is the relative dielectric constant.