Bjerrum length


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 theabsolute temperature in Kelvin. It could be seen as one screening effect about the electrostatic interaction in a certain media [ [http://www.uic.edu/classes/phys/phys450/MARKO/N005.html Screening of Electrostatic Interactions ] ] .

In standard units, the Bjerrum length is given by

lambda_B = frac{e^2}{4pi epsilon_0 epsilon_r k_B T},

where e is the elementary charge, epsilon_r is the relative dielectric constant of the mediumand epsilon_0 is the vacuum permittivity.For water atroom temperature (T = 300 K), epsilon_r approx 80, so thatlambda_B approx 0.7 nm.

In Gaussian units, 4piepsilon_0=1 and the Bjerrum length has the simpler form

lambda_B = frac{e^2}{epsilon_r k_B T}.

References


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