Clausius–Mossotti relation
Clausius–Mossotti relation
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]
where
is the dielectric constant of the material
is the permittivity of free space
is the number density of the molecules (number per cubic meter), and
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: (see Lorrain and Corson - Electromagnetic Field and Waves, 1962, 2nd Edition, page 116)
Lorentz–Lorenz equation
The Lorentz–Lorenz equation is similar to the Clausius–Mossotti relation, except that it relates the refractive index (rather than the dielectric constant) of a substance to its polarizability. 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 CGS units)
or simply
