The Clausius-Mosotti relation

Knowing the local field operating at each molecule from Equation (2.29) above, we may now calculate the individual contributions to the polarisation from Equation (2.7)  

Again substituting for P from Equation (2.5), we obtain the Clausius-Mosotti 

If Mw is the molar mass of the material and p is its density, this equation may be written  

Orientation of molecules is much too slow to contribute to polarisation at these high frequencies. Then substituting (2.34) in (2.33) gives a quantity that is usually called the molar refraction of the material  

Equation (2.35), known as the Lorenz-Lorentz relation, provides a method of calculating the molecular polarisability from a macroscopic, observable quantity, the refractive index. We must make the proviso that we stay away from any resonant absorption frequency, where the refractive index is anomalously high. If the refractive index refers to optical frequencies, the polarisability a will be purely electronic in origin. In practice, electronic polarisabilities derived in this way are remarkably insensitive to temperature and pressure, even for highly condensed phases in which intermolecular forces must be large. This is illustrated for the particular case of xenon in Table 2.1. 

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Based on this concept, the dielectric constant is modified by application of the Clausius-Mosotti relation ... 

Let us consider an essentially non-polar polymer, e.g. polyethylene, CH3-(CH2) -CH3. The density of solid polyethylene covers a range from 0.92 to 0.99 Mgm-3 depending on the extent of chain branching which determines its crystallinity. We may therefore test the validity of the Clausius-Mosotti relation. From published tables of bond polarisabilities, the Clausius-Mosotti relation for an assembly of -CH2- units becomes... 

Oxide dielectric polarizabihties can be measured directly from dielectric constants of some of the simple oxides using the Clausius-Mosotti relation (equation 2) or derived indirectly from the dielectric constants of complex oxides and the oxide additivity rule (equation 3). Table 1 summarizes the accurately known values of oxide polarizabilities. These values can be used to check the oxide additivity rule. 

This relationship between the dielectric constant and the molecular polari-sability is known as the Clausius-Mosotti relation. It can usefully be written in terms of the molar mass M and density p of the polymer in the form... 

The apparent oscillator strength is proportional to the integrated intensity under the molar absorption curve. To derive the formula, Chako followed the elassieal dispersion theory with the Lorentz-Lorenz relation (also known as the Clausius-Mosotti relation), assuming that the solute molecule is located at the center of the spherical cavity in the continuous dielectric medium of the solvent. Hence, the factor derived by Chako is also called the Lorentz-Lorenz correction. Similar derivation was also presented by Kortiim. The same formula was also derived by Polo and Wilson from a viewpoint different from Chako. 

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