Bjerrum length: Difference between revisions
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Carl McBride (talk | contribs) (Created page with "The '''Bjerrum length''' <math>(l_B)</math> is the distance for which the electrostatic potential energy between two charges, <math>e</math>, is equal to the thermal energy sc...") |
Carl McBride (talk | contribs) (Added an example (water)) |
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leading to | leading to | ||
:<math>l_B = \frac{e^2}{4\pi\varepsilon_0 \varepsilon_r k_BT} </math> | :<math>l_B = \frac{e^2}{4\pi\varepsilon_0 \varepsilon_r k_BT} \approx \frac{1.671 \times 10^{-5}}{\varepsilon_r T}</math> | ||
The charges could come in the form of monovalent ions in a solvent. Thus for distances greater than the Bjerrum length, where thermal fluctuations become stronger than electrostatic interactions, it becomes reasonable to introduce a continuum mean-field representation. For [[water]], whose relative permittivity is <math>\varepsilon_r \approx 78</math> at 298K <ref>[http://dx.doi.org/10.1063/1.555977 D. P. Fernández, Y. Mulev, A. R. H. Goodwin and J. M. H. Levelt Sengers "A Database for the Static Dielectric Constant of Water and Steam", Journal of Physical and Chemical Reference Data '''24''' pp. 33-69 (1995)]</ref> one arrives at a value of around <math>l_B \approx 0.72</math> nm. | |||
==See also== | ==See also== | ||
*[[Debye length]] | *[[Debye length]] | ||
==References== | ==References== | ||
<references/> | <references/> | ||
Revision as of 20:19, 25 March 2014
The Bjerrum length is the distance for which the electrostatic potential energy between two charges, , is equal to the thermal energy scale . Using Coulomb's law, one sets
leading to
The charges could come in the form of monovalent ions in a solvent. Thus for distances greater than the Bjerrum length, where thermal fluctuations become stronger than electrostatic interactions, it becomes reasonable to introduce a continuum mean-field representation. For water, whose relative permittivity is at 298K [1] one arrives at a value of around nm.
