Clausius-Mosotti theory

The quantity sr is directly sensitive to the detailed chemical composition of the sample. However, the quantitative theory that relates the observed er to the concentrations and dipole moments of the various polar segments present has proved quite difficult to use. The simplest approach is based on the Clausius-Mosotti equation as modified for permanent moments by Debye28). The Debye approach, although overly simple, revealed that sr should decrease with increasing temperature, and should reflect changing concentrations of polar constituents during a reaction. 

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... 

The weakness of the simple theory is highlighted if we solve the Debye version of the Clausius-Mosotti relation (2.44) for e, neglecting the contribution of a0 ... 

P. Mazur and L. Jansen. On the theory of molecular polarization II. Effects of molecular interactions on the Clausius-Mosotti function for systems of spherical nonpolar molecules. 

In the earliest and crudest theories, those ot Clausius-Mosotti and Debye,12 the reaction field was completely ignored, so that theoretical predictions were not confirmed by the experimental facts except for gaseous dielectrics, and eventually for extremely dilute solutions of polar molecules in nonpolar solvents. 

A more general statistical treatment has been given by Kirkwood for two simplified cases. He has shown30 that for nonpolar gases at low pressures Clausius-Mosotti s equation is a first approximation. Nevertheless, by refining Kirkwood s theory,... 

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. 

The first solvent property applied to eorrelate reaetivity data was the statie dieleetrie eonstant s (also termed 8 ) in the form of di-electrie funetions as suggested from elementary eleetrostatie theories as those by Bom (1/s), Kirkwood (s-l)/(2e+l), Clausius-Mosotti (s-l)/(s+2), and (8-1 )/( + ). A sueeessful eorrela-tion is shown in Figure 13.1.1 for the rate of the Sn2 reaetion of p-nitrofluorobenzene with... 

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