Bjerrum length - Revision history

Carl McBride: Added category

2014-03-25T18:20:25Z

Added category

← Older revision		Revision as of 20:20, 25 March 2014
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	==References==		==References==
	<references/>		<references/>
			[[category: electrostatics]]

Carl McBride: Added an example (water)

2014-03-25T18:19:45Z

Added an example (water)

← Older revision		Revision as of 20:19, 25 March 2014
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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/>

Carl McBride: Created page with "The '''Bjerrum length''' $(l_B)$ is the distance for which the electrostatic potential energy between two charges, $e$ , is equal to the thermal energy sc..."

2014-03-25T17:20:49Z

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..."

New page

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 scale <math>k_BT</math>. Using [[Coulomb's law]], one sets

:<math>k_BT = \frac{e^2}{4\pi\varepsilon_0 \varepsilon_r} \frac{1}{|\mathbf{r}_1 - \mathbf{r}_2|}</math>

leading to

:<math>l_B = \frac{e^2}{4\pi\varepsilon_0 \varepsilon_r k_BT} </math>

==See also==
*[[Debye length]]
==References==
<references/>

Bjerrum length - Revision history

Carl McBride: Added category

Carl McBride: Added an example (water)

Carl McBride: Created page with "The '''Bjerrum length''' (l_B) is the distance for which the electrostatic potential energy between two charges, e, is equal to the thermal energy sc..."

Carl McBride: Created page with "The '''Bjerrum length''' $(l_B)$ is the distance for which the electrostatic potential energy between two charges, $e$ , is equal to the thermal energy sc..."