Clausius Mossotti field

If we consider the optical response of a molecular monolayer of increasing surface density, the fomi of equation B 1.5.43 is justified in the limit of relatively low density where local-field interactions between the adsorbed species may be neglected. It is difficult to produce any rule for the range of validity of this approximation, as it depends strongly on the system under study, as well as on the desired level of accuracy for the measurement. The relevant corrections, which may be viewed as analogous to the Clausius-Mossotti corrections in linear optics, have been the... 

A particle is subdivided into a small number of identical elements, perhaps 100 or more, each of which contains many atoms but is still sufficiently small to be represented as a dipole oscillator. These elements are arranged on a cubic lattice and their polarizability is such that when inserted into the Clausius-Mossotti relation the bulk dielectric function of the particle material is obtained. The vector amplitude of the field scattered by each dipole oscillator, driven by the incident field and that of all the other oscillators, is determined iteratively. The total scattered field, from which cross sections and scattering diagrams can be calculated, is the sum of all these dipolar fields. 

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-... 

This equation, called the Lorenz-Lorentz equation, was derived in 1880 by combining the Clausius-Mossotti expression for the local field with the idea of molecular polarizability. 

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. 

To describe local field effects associated with a crystalline environment, e.g. Cso arranged in a lattice of cubic symmetry, we use the Clausius-Mossotti relation [93] in the form... 

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 ... 

We now call attention to three closely related approximations. All three use the mean field result for and outside the core, given by (2.66b). The first also uses (2.70). With the use of (2.27) both A and Ay, can be determined for all r. Both approximations violate the core condition (2.65b). The resulting e is easy to compute via (2.15) and yields the Clausius-Mossotti relation. The resulting approximation for A(12) could be called the two-particle Clausius-Mossotti approximation. ... 

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... 

This dielectric force pushes particles toward regirms of high field density or low field density depending on whether the Clausius-Mossotti factor is positive or negative, respectively. In other words, if Op < ct then negative dielectrophoretic motion away from sharp points in electrodes or insulator obstacles is observed the converse is true for positive dielectrophoresis, which is rarely observed in DC-DEP due to other electrokinetic forces. For a truly insulating particle, Op = 0, the Clausius-Mossotti factor is simply 1/2, and motion away from high field... 

The frequency of the applied field, through the real part of Clausius-Mossotti factor... 

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