Clausius-Mossotti

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... 

Another way to obtain a relative permitivity is using some simple equations that relate relative permitivity to the molecular dipole moment. These are derived from statistical mechanics. Two of the more well-known equations are the Clausius-Mossotti equation and the Kirkwood equation. These and others are discussed in the review articles referenced at the end of this chapter. The com-... 

Wetting and capillarity can be expressed in terms of dielectric polarisabilities when van der Waals forces dominate the interface interaction (no chemical bond or charge transfer) [37]. For an arbitrary material, polarisabilities can be derived from the dielectric constants (e) using the Clausius-Mossotti expression [38]. Within this approximation, the contact angle can be expressed as ... 

After a little manipulation we derive the Clausius-Mossotti equation... 

The derivation of the Clausius-Mossotti equation follows as above, except that the quantity in square brackets has to replace a, and we obtain finally... 

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... 

It is also worth noting that Equation 9.1 indicates a connection between C44, hardness, and e. The dielectric constant, e depends on the polarizability, a of each alkali halide through the Clausius-Mossotti equation ... 

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. 

Many authors have discussed a dielectric catastrophe and the Mott transition in terms of the Clausius-Mossotti relationship... 

Clausius-Mossotti equation). In this expression, V designates the mole volume and Ae, Be, Cf,... are the first, second, third,... virial dielectric coefficients. A similar expansion exists for the refractive index, n, which is related to the (frequency dependent) dielectric constant as n2 = e (Lorentz-Lorenz equation, [87]). The second virial dielectric coefficient Be may be considered the sum of an orientational and a polarization term, Be = B0r + Bpo, arising from binary interactions, while the second virial refractive coefficient is given by just the polarization term, B = Bpo at high enough frequencies, the orientational component falls off to small values and the difference Be — B may be considered a measurement of the interaction-induced dipole moments [73],... 

Clausius-Mossotti equation). The AE, BE,. .., are the first, second,. .., dielectric virial coefficients, given by... 

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 ... 

If (RIV) = 1, the resultant force on the localized electron vanishes, the electron is set free, and the system acquires metallic status. The previous statements may be recast in slightly different form using the venerable Clausius-Mossotti relationship (81), where... 

Fortunately, they are several species of low-loss dielectric ceramics with tailored temperature coefficient of dielectric constant, which can be made lower than 1 ppm/K for a certain temperature window around room temperature. Physically, this can be accomplished either by intrinsic compensation of the temperature dependence of thermal volume expansion V(T) and lattice polarizability a(T) via the Clausius-Mossotti relation ... 

Having obtained statistically converged results for the dipole polarizability of liquid argon, we now consider the resulting values for the dielectric constant. Again, we use the three theoretical models and simply obtain the dielectric constant e, from the dipole polarizability, using the Clausius-Mossotti equation [34] ... 

When combined with the classical Clausius-Mossotti theory of a dielectric medium, this version of the local response model gives the correct asymptotic form of the polarization potential of a spherical atom, —a(0)/2r4, where... 

Using the cgs system the Clausius-Mossotti relation becomes... 

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