Bjerrum length

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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.

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