Clausius–Mossotti relation

The Clausius–Mossotti relation expresses the dielectric constant (relative permittivity) ε_r 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]

$\frac{\epsilon_\mathrm{r} - 1}{\epsilon_\mathrm{r} + 2} = \frac{N \alpha}{3}$

where

• $\epsilon_r = \epsilon/\epsilon_0$ is the dielectric constant of the material
• $\epsilon_0$ is the permittivity of free space
• $N$ is the number density of the molecules (number per cubic meter), and
• $\alpha$ 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:

$\frac{\epsilon_\mathrm{r} - 1}{\epsilon_\mathrm{r} + 2} = \sum_i \frac{N_i \alpha_i}{3}$

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. Atkins, Peter; de Paula, Julio (2010). "Chapter 17". Atkins' Physical Chemistry. Oxford University Press. pp. 622–629. ISBN 978-0-19-954337-3.