Clausius–Mossotti relation

The Clausius- Mossotti equation links the macroscopically measurable quantity permittivity with the microscopic (molecular) size electric polarizability. It is named after the two physicists Rudolf Clausius and Ottaviano Fabrizio Mossotti and reads:

It is

• The molar polarization ( its unit is the molar volume of, eg m3/mol )
• The molar mass (kg / mol)
• The density ( in kg/m3 )
• The Avogadro constant.

The equation is valid for non-polar substances without a permanent dipole moment, ie there is only induced dipoles ( induced polarization ). For substances with permanent dipoles the Debye equation is used, which takes into account the induced polarization and the orientation polarization.

Derivation

Macroscopic polarization is the sum of induced dipoles divided by the observed volume (which corresponds to a polarization dipole ):

The particle number density, polarizability, local electric field strength at the location of the atom / molecule.

The macroscopically measurable quantities electric susceptibility or the dielectric constant represent the relationship between the polarization and the electric field here:

Is obtained by equating the following equation:

In order to make further statements, the local field must be determined.

Side note: For dilute gases, the induced dipoles do not affect the local field is equal to the applied external field and from this:

For a dielectric of higher density, the local field is equal to the applied external field, since all nearby induced dipoles also build up an electric field.

This results in a local electric field by:

Substituted into the above equation:

Switching provides:

Respectively. resolved by:

Now you can still the particle density by macroscopically measurable quantities expressed (density, molar mass and Avogadro's number ):

Inserting provides the Clausius- Mossotti equation:

Respectively. resolved by: