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, $k_{\text{B}}T$ , where $k_{\text{B}}$ is the Boltzmann constant and $T$ is the absolute temperature in kelvins. 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 $\lambda _{\text{B}}={\frac {e^{2}}{4\pi \varepsilon _{0}\varepsilon _{r}\ k_{\text{B}}T}},$ 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 ( $T\approx 293{\text{ K}}$ ), $\varepsilon _{r}\approx 80$ , so that $\lambda _{\text{B}}\approx 0.71{\text{ nm}}$ .

In Gaussian units, $4\pi \varepsilon _{0}=1$ and the Bjerrum length has the simpler form

$\lambda _{\text{B}}={\frac {e^{2}}{\varepsilon _{r}k_{\text{B}}T}}.$

The relative permittivity ε_r of water decreases so strongly with temperature that the product (ε_r·T) decreases. Therefore, in spite of the (1/T) relation, the Bjerrum length λ_B increases with temperature, as shown in the graph.

References

^ "Obituary: Professor Niels J. Bjerrum". Transactions of the Faraday Society. 55: X001. 1959. doi:10.1039/TF959550X001.
^ Russel, William B.; Saville, D. A.; Schowalter, William R. (1989). Colloidal Dispersions. New York: Cambridge University Press.

[1] "Obituary: Professor Niels J. Bjerrum". Transactions of the Faraday Society. 55: X001. 1959. doi:10.1039/TF959550X001.

[2] Russel, William B.; Saville, D. A.; Schowalter, William R. (1989). Colloidal Dispersions. New York: Cambridge University Press.

[1]

[2]

Fahrer / Team für die Suche eingeben:

Fahrer / Team für die Suche eingeben:

Langbahn Team – Weltmeisterschaft

Bjerrum length

See also

References