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, , where is the Boltzmann constant and is the absolute temperature in kelvins. 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

where is the elementary charge, is the relative dielectric constant of the medium and is the vacuum permittivity. For water at room temperature (), , so that .

In Gaussian units, and the Bjerrum length has the simpler form


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