Bjerrum length

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The Bjerrum length (after Danish chemist Niels Bjerrum 1879–1958 [1]) 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. This length scale arises naturally in discussions of electrostatic, electrodynamic and electrokinetic phenomena in electrolytes, polyelectrolytes and colloidal dispersions. [2]

In standard units, the Bjerrum length is given by

\lambda_B = \frac{e^2}{4\pi \varepsilon_0 \varepsilon_r \  k_B T},

where e is the elementary charge, \varepsilon_r is the relative dielectric constant of the medium and \varepsilon_0 is the vacuum permittivity. For water at room temperature (T = 300 \mbox{ K}), \varepsilon_r \approx 80, so that \lambda_B \approx 0.7 \mbox{nm}.

In Gaussian units, 4\pi\varepsilon_0 = 1 and the Bjerrum length has the simpler form

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


  1. ^
  2. ^ Russel, William B.; Saville, D. A.; Schowalter, William R. (1989). Colloidal Dispersions. New York: Cambridge University Press.