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 ClausiusâMossotti relation is typically rewritten to show the
molecular polarizability volume which has units of volume [m3].[2] Confusion may arise from the practice of using the shorter name "molecular polarizability" for both and within literature intended for the respective unit system.
The ClausiusâMossotti 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.[4] For example, the ClausiusâMossotti relation is accurate for N2 gas up to 1000 atm between 25 °C and 125 °C.[5] Moreover, the ClausiusâMossotti 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.[6]
LorentzâLorenz equation
The LorentzâLorenz equation is similar to the ClausiusâMossotti relation, except that it relates the refractive index (rather than the dielectric constant) of a substance to its
polarizability. The LorentzâLorenz 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 LorentzâLorenz equation is (in
Gaussian-CGS units)
where n is the refractive index, N is the number of molecules per unit volume, and is the mean polarizability.
This equation is approximately valid for homogeneous solids as well as liquids and gases.
When the square of the refractive index is , as it is for many gases, the equation reduces to:
or simply
This applies to gases at ordinary pressures. The refractive index n of the gas can then be expressed in terms of the
molar refractivityA 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.
References
^Rysselberghe, P. V. (January 1932). "Remarks concerning the ClausiusâMossotti Law". J. Phys. Chem. 36 (4): 1152â1155.
doi:
10.1021/j150334a007.
^
abAtkins, Peter; de Paula, Julio (2010). "Chapter 17". Atkins' Physical Chemistry. Oxford University Press. pp. 622â629.
ISBN978-0-19-954337-3.
^Corson, Dale R; Lorrain, Paul (1962). Introduction to electromagnetic fields and waves. San Francisco: W.H. Freeman. p. 116.
OCLC398313.
O. F. Mossotti, Discussione analitica sull'influenza che l'azione di un mezzo dielettrico ha sulla distribuzione dell'elettricitĂ alla superficie di piĂč corpi electrici disseminati in esso, Memorie di Mathematica e di Fisica della SocietĂ Italiana della Scienza Residente in Modena, vol. 24, p. 49-74 (1850).