Electric Clausius-Mossotti

For static electric properties, the bulk property of interest is the dielectric polarization P. The magnitude of P can be estimated from (for example) the Clausius-Mossotti relation... 

This equation is not valid for liquids or crystals, but only for substances for which the dielectric constant is very close to unity, as for gases. For other substances an equation derived by consideration of the effect of the induced moments of neighboring molecules upon the molecule undergoing polarization must be considered. In a polarized medium each molecule is affected by the electric field in the region occupied by the molecule, called the local field. For many substances the local field is satisfactorily represented by the Clausius-Mossotti expression, derived in 1850. Each molecule is considered to occupy a spherical cavity. The part of the substance outside the spherical cavity undergoes polarization in the applied field. A simple calcula-... 

Now let us calculate the alteration of the potential energy U in the case of polarisation by an electric field 2 or. The orientation field Bor depends on the external electric field E which is given by Clausius-Mossotti EOT = (e + 2)/3 E or with somewhat better results by Gnsager32 ... 

Molecular distortion polarizability is a measure of the ease with which atomic nuclei within molecules tend to be displaced from their zero-field positions by the applied electric field. (3) Orientation polarizability is a measure of the ease with which dipolar molecules tend to align against the applied electric field. The electron polarizability of an individual molecule is related to the -> permittivity (relative) of a dielectric medium by the -> Clausius-Mossotti relation. 

GpF2<7m) l2. Both the real and imaginary parts of the Clausius-Mossotti factor govern the movement of particles in AC electric field, but in different... 

DEP force. The frequency dependence and the direction of the DEP force are governed by the real part of the Clausius-Mossotti factor. If the particle is more polarisable than the medium, (Re[/cm] > 0). the particle is attracted to high intensity electric field regions. This is termed as positive dielectrophoresis (pDEP). Conversely, if the particle is less polarisable than the medium, (Re[/cm] < 0), the particle is repelled from high intensity field regions and negative dielectrophoresis (nDEP) occurs. Therefore the real part of the Clausius-Mossotti factor characterizes the frequency dependence of the DEP force, as demonstrated in Fig. 1. 

In practice, it is difficult to measure the DEP force due to the effects of Brownian motion and electrical field-induced fluid flow [3]. Instead, the DEP crossover frequency can be measured as a function of medium conductivity and provides sufficient information to determine the dielectric properties of the suspended particles. The DEP crossover frequency,is the transition frequency point where the DEP force switches from pDEP to nDEP or vice versa. According to Eq. (6), the crossover frequency is defined to be the frequency point where the real part of the Clausius-Mossotti factor equals zero ... 

In 1906, J. C. Maxwell Garnett used the Maxwell Garnett theory, equation (12), for the first time to descibe the color of metal colloids glasses and of thin metal films. Equation (12) can be deviated from the Rayleigh scattering theory for spherical particles [21], or from the Lorentz-Lorenz assumption for the electrical field of a sphere and the Clausius-Mossotti Equation by using the polarizability of an metal particle if only dipole polarization is considered [22]. 

This frequency, co, dependent factor, K((u), dynamically reflects the polarizability of a particle (subscript p) in a conductive medium (subscript m). The Clausius-Mossotti factor is a ratio of complex permittivities, of the form H = s — ia/oj, where co is the frequency, s is the dielectric constant, and a is the electrical conductivity of the medium. As can be seen, the complex K(ffl) factor has an imaginary component, which is out of phase with the applied electric field, while the real component is in phase [1, 4]. The imaginary... 

An induced dipole moment P- can be created in a non-polar molecule or added to the permanent dipole moment in a polar molecule, when the molecule is placed in an electric field. The proximity of a strongly polar molecule can bring about such an effect. Total dipole moment is the sum of permanent and induced dipoles, and is defined as molar polarisation by the Clausius-Mossotti Equation (49). 

This is the Langevin equation which describes the degree of polarization in a sample when an electric field, E, is applied at temperature T. Experimentally, a poling temperature in the vicinity of Tg is used to maximize dipole motion. The maximum electric field which may be applied, typically 100 MV/m, is determined by the dielectric breakdown strength of the polymer. For amorphous polymers p E / kT 1, which places these systems well within the linear region of the Langevin function. The following linear equation for the remanent polarization results when the Clausius Mossotti equation is used to relate the dielectric constant to the dipole moment 41). 

The direction and rate of rotation relative to the electric field is dependent on the imaginary coirponent of the Clausius-Mossotti factor (Im [AT(< >)]). When this component is positive the direction of rotation is opposite of the direction of the rotating field and vice versa for a negative value of Im[AT( y)]. By properly applying a nonuniform electric field and controlling the real and imaginary parts of the Clausius-Mossotti factor, a particle can be simultaneously manipulated by dielectrophoresis and electrorotation. 

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