Clausius–Mossotti relation

The Clausius–Mossotti relation connects a material’s relative permittivity to molecular number density and polarizability: (εᵣ − 1)/(εᵣ + 2) = Nα/(3ε₀) in SI units.

Lorentz local field: The effective electric field acting on a molecule in a dielectric, accounting for the surrounding polarized medium. Its spherical-cavity correction produces the factor (εᵣ + 2)/3 in the relation.
Relative permittivity: The ratio of a material’s permittivity to the permittivity of vacuum. It is the bulk electrical property predicted from molecular polarizability and density.
Refractive index: The ratio of light’s phase velocity in vacuum to its phase velocity in a medium. At optical frequencies, the relation connects molecular polarizability to refractive index through εᵣ ≈ n².
Maxwell–Garnett theory: An effective-medium model for the permittivity of inclusions dispersed in a host material. It generalizes local-field reasoning to heterogeneous mixtures rather than a uniform molecular medium.
Electric polarizability: A measure of how readily an atom or molecule develops an electric dipole in response to an electric field. The relation uses molecular polarizability to predict bulk permittivity.
Number density: The number of particles per unit volume. It sets how many polarizable molecules contribute to the material’s response.
Lorentz–Lorenz equation: A relation between a material’s refractive index, molecular number density, and molecular polarizability. It is the optical counterpart obtained by applying the same local-field reasoning.
Bruggeman effective medium approximation: A self-consistent model for the effective permittivity of a mixture whose components are treated symmetrically. It offers a mixture model where the Clausius–Mossotti relation assumes one uniform material.
Electric susceptibility: A dimensionless measure of how strongly a material polarizes in response to an applied electric field. The equation can be expressed through susceptibility, χₑ = εᵣ − 1.
Molecular polarizability: The proportionality between an isolated molecule’s induced dipole moment and the local electric field. This microscopic quantity is the α appearing in the relation.

Linked from 3 pages

PolarizabilityRelated: It connects microscopic polarizability with bulk dielectric behavior.