# Clausius–Mossotti relation

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The Clausius–Mossotti relation expresses the dielectric constant (relative permittivity) εr of a material in terms of the atomic polarizibility α of the material's constituent atoms and/or molecules, or a homogeneous mixture thereof. It is named after Ottaviano-Fabrizio Mossotti and Rudolf Clausius. It is equivalent to the Lorentz–Lorenz equation. It may be expressed as:[1][2]

${\displaystyle {\frac {\epsilon _{\mathrm {r} }-1}{\epsilon _{\mathrm {r} }+2}}={\frac {N\alpha }{3\epsilon _{0}}}}$

where

• ${\displaystyle \epsilon _{r}=\epsilon /\epsilon _{0}}$ is the dielectric constant of the material
• ${\displaystyle \epsilon _{0}}$ is the permittivity of free space
• ${\displaystyle N}$ is the number density of the molecules (number per cubic meter), and
• ${\displaystyle \alpha }$ is the molecular polarizability in SI-units (C·m2/V).

In the case that the material consists of a mixture of two or more species, the right hand side of the above equation would consist of the sum of the molecular polarizability contribution from each species, indexed by i in the following form:

${\displaystyle {\frac {\epsilon _{\mathrm {r} }-1}{\epsilon _{\mathrm {r} }+2}}=\sum _{i}{\frac {N_{i}\alpha _{i}}{3\epsilon _{0}}}}$

In the CGS system of units the Clausius–Mossotti relation is typically rewritten to show the molecular polarizability volume ${\displaystyle \alpha '=\alpha /(4\pi \varepsilon _{0})}$ which has units of volume (m3).[2] Confusion may arise from the practice of using the shorter name "molecular polarizability" for both ${\displaystyle \alpha }$ and ${\displaystyle \alpha '}$ within literature intended for the respective unit system.

## References

• C.J.F. Böttcher, Theory of electric polarization, Elsevier Publishing Company, 1952
1. ^ Rysselberghe, P. V. (January 1932). "Remarks concerning the Clausius–Mossotti Law". J. Phys. Chem. 36 (4): 1152–1155. doi:10.1021/j150334a007.
2. ^ a b Atkins, Peter; de Paula, Julio (2010). "Chapter 17". Atkins' Physical Chemistry. Oxford University Press. pp. 622–629. ISBN 978-0-19-954337-3.
• R. Clausius, "Die Mechanische Behandlung der Electricität", Vieweg+Teubner Verlag; Wiesbaden, 1879, ISBN 978-3-663-19891-8, https://link.springer.com/book/10.1007%2F978-3-663-20232-5
• O. F. Mossotti, Discussione analitica sull’influenza che l’azione di un mezzo dielettrico ha sulla distribuzione dell’elettricità alla superficie di più corpi elettrici disseminati in esso, Memorie di Mathematica e di Fisica della Società Italiana della Scienza Residente in Modena, vol. 24, p. 49-74 (1850).