Clausius-Mossotti relation

Clausius-Mossotti relation
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Clausius-Mossotti_relation".

The Clausius–Mossotti equation is named after the Italian physicist Ottaviano-Fabrizio Mossotti, whose 1850 book analyzed the relationship between the dielectric constants of two different media, and the German physicist Rudolf Clausius, who gave the formula explicitly in his 1879 book in the context not of dielectric constants but of indices of refraction. The same formula also arises in the context of conductivity, in which it is known as Maxwell's formula. It arises yet again in the context of refractivity, in which it is known as the Lorentz–Lorenz equation.

Clausius–Mossotti factor

The Clausius–Mossotti factor can be expressed in terms of complex permittivities:

$K(\omega) = \frac{\epsilon^*_p - \epsilon^*_m}{\epsilon^*_p + 2\epsilon^*_m}$

$\epsilon^* = \epsilon + \frac{\sigma}{i\omega} = \epsilon - \frac{i\sigma}{\omega}$

Legend
$ε$ is the permittivity
(where the subscript p refers to a lossless dielectric sphere suspended in a medium m)
$σ$ is the conductivity
$ω$ is the angular frequency of the applied electric field
i is the square root of -1

In the context of electrokinetic manipulation, the real part of the Clausius-Mossotti factor is a determining factor for the dielectrophoretic force on a particle, where as the imaginary part is a determining factor for the electrorotational torque on the particle. Other factors are, of course, the geometries of the particle to be manipulated and the electric field.

References

Konstantin Z. Markov, Elementary Micromechanics of Heterogeneous Media, Chapter 1 in the collection: Heterogeneous Media: Modelling and Simulation, edited by Konstantin Z. Markov and Luigi Preziosi, Birkhauser Boston, 1999, pp. 1–162.
Michael Pycraft Hughes, AC Electrokinetics: Applications for Nanotechnology, Nanotechnology 11, 2000, pp. 124–132.
J. Gimsa (2001): Characterization of particles and biological cells by AC-electrokinetics, in: A.V. Delgado (ed.) Interfacial Electrokinetics and Electrophoresis. Marcel Dekker Inc., New York, ISBN: 0-8247-0603-X, pp. 369-400.

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