Bjerrum length

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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_BT, where k_B is the Boltzmann constant and T is the absolute temperature in Kelvin.

In standard units, the Bjerrum length is given by

,

where e is the elementary charge, ε is the dielectric constant of the medium and ε₀ is the vacuum permittivity. For water at room temperature (T = 300 K), , so that nm.

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

,

where ε_r = ε / ε₀ is the relative dielectric constant.