ClausiusMossotti

The Clausius–Mossotti relation is a fundamental result in electromagnetism and physical chemistry that connects the macroscopic dielectric response of a homogeneous, isotropic material to its microscopic molecular properties. It relates the relative permittivity ε_r (or refractive index n) of a material to the number density N of its molecules and the molecular polarizability α.

In SI units, the relation is written as (ε_r − 1)/(ε_r + 2) = (N α)/(3 ε0), where ε0 is the vacuum permittivity. Equivalently, using the refractive index, (n^2 − 1)/(n^2 + 2) = (N α)/(3 ε0). The formula arises from considering the local electric field experienced by a molecule inside a polarized medium (the Lorentz local field) and how individual dipoles contribute to the macroscopic polarization.

The Clausius–Mossotti relation is commonly used to estimate molecular polarizabilities from dielectric measurements or to predict dielectric behavior from known molecular properties. It is most accurate for non-conducting, isotropic media at relatively low to moderate densities and frequencies where dispersion is not essential. Deviations occur for dense liquids, strong intermolecular interactions, anisotropic materials, or significant dispersion; in such cases tensor generalizations or frequency-dependent forms are employed.

History and naming: the relation was derived in the 19th century by Rudolf Clausius and Ottaviano-Fabrizio Mossotti. It is closely related to the Lorentz–Lorenz equation, and in many contexts the two expressions are considered equivalent, differing mainly in unit conventions and interpretation of local-field corrections.