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:

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

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:

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

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

References

• C.J.F. Böttcher, Theory of electric polarization, Elsevier Publishing Company, 1952