Clausius-Mosotti relation

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

For non-polar materials the relationship between the molar polarisation Pll/ the dielectric constant e and the molecular polarisability a is known as the molar Clausius-Mosotti relation and reads... 

The molar Clausius-Mosotti relation then reads... 

In contrast to molar polarisation calculated from optical refractivities, that calculated from relative permittivities observed at lower frequencies is by no means always independent of temperature. Actually, materials tend to fall into one of two classes. Those in one class show a relatively constant molar polarisation in accord with the simple Clausius-Mosotti relation, whilst the members of the other class, which contains materials with high relative permittivities, show a molar polarisation that decreases with increase in temperature. Debye recognised that permanent molecular dipole moments were responsible for the anomalous behaviour. From theories of chemical bonding we know that certain molecules which combine atoms of different electronegativity are partially ionic and consequently have a permanent dipole moment. Thus chlorine is highly electronegative and the carbon-chlorine... 

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. 

Fig. 4.4. Real part of the dielectric constant ei(127 eV) as a function of density for fluid mercury at constant supercritical temperature 1570 °C (Hensel, 1990). Dashed line represents prediction of Clausius-Mosotti relation, Eq. (4.7).

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