In electromagnetism, the Clausius–Mossotti relation, named for O. F. Mossotti and Rudolf Clausius, expresses the dielectric constant (relative permittivity, εr) of a material in terms of the atomic polarizability, α, of the material's constituent atoms and/or molecules, or a homogeneous mixture thereof.
It is equivalent to the Lorentz–Lorenz equation, which relates the refractive index (rather than the dielectric constant) of a substance to its polarizability.
where 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:[3]
In the CGS system of units the Clausius–Mossotti relation is typically rewritten to show the molecular polarizability volume
[2] Confusion may arise from the practice of using the shorter name "molecular polarizability" for both
within literature intended for the respective unit system.
The Clausius–Mossotti relation assumes only an induced dipole relevant to its polarizability and is thus inapplicable for substances with a significant permanent dipole.
It is applicable to gases such as N2, CO2, CH4 and H2 at sufficiently low densities and pressures.
[5] Moreover, the Clausius–Mossotti relation may be applicable to substances if the applied electric field is at a sufficiently high frequencies such that any permanent dipole modes are inactive.
The Lorentz–Lorenz equation is named after the Danish mathematician and scientist Ludvig Lorenz, who published it in 1869, and the Dutch physicist Hendrik Lorentz, who discovered it independently in 1878.
The most general form of the Lorentz–Lorenz equation is (in Gaussian-CGS units) where n is the refractive index, N is the number of molecules per unit volume, and
This equation is approximately valid for homogeneous solids as well as liquids and gases.
The refractive index n of the gas can then be expressed in terms of the molar refractivity A as: where p is the pressure of the gas, R is the universal gas constant, and T is the (absolute) temperature, which together determine the number density N.