Bjerrum length

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, $k_{B}T$ , where $k_{B}$ is the Boltzmann constant and $T$ is the absolute temperature in Kelvin. 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

$\lambda_B = \frac{e^2}{4\pi \varepsilon_0 \varepsilon_r \ k_B T},$

where $e$ is the elementary charge, $\varepsilon _{r}$ is the relative dielectric constant of the medium and $\varepsilon _{0}$ is the vacuum permittivity. For water at room temperature ( $T = 300 \mbox{ K}$ ), $\varepsilon_r \approx 80$ , so that $\lambda_B \approx 0.7 \mbox{nm}$ .

In Gaussian units, $4\pi\varepsilon_0 = 1$ and the Bjerrum length has the simpler form

$\lambda_B = \frac{e^2}{\varepsilon_r k_B T}.$

References

↑ http://www.rsc.org/delivery/_ArticleLinking/DisplayArticleForFree.cfm?doi=TF959550X001&JournalCode=TF
↑ Russel, William B.; Saville, D. A.; Schowalter, William R. (1989). Colloidal Dispersions. New York: Cambridge University Press.

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