Clausius-Mosotti

In this case, the scattering serves as a means for counting the number of molecules (or particles, or objects) per unit volume (N/V). It is seen that the polarizability, a, will be greater for larger molecules, which will scatter more. If we take the Clausius-Mosotti equation [16] ... 

This result, called the Clausius-Mosotti equation, gives the relationship between the relative dielectric constant of a substance and its polarizability, and thus enables us to express the latter in terms of measurable quantities. The following additional comments will connect these ideas with the electric field associated with electromagnetic radiation ... 

The Clausius-Mosotti equation with n written for can be used to... 

The Clausius-Mosotti equation relates the polarizability of a substance to... 

Pq the dipole or orientation polarisation P itself is defined by the Clausius-Mosotti Equation... 

The quantity on the left side of the equation is called the molar polarization, and this expression is the Clausius—Mosotti equation. On the right side the quantity a is the polarizability, which measures the ease with which an induced moment is... 

The linear polarizability, a, describes the first-order response of the dipole moment with respect to external electric fields. The polarizability of a solute can be related to the dielectric constant of the solution through Debye s equation and molar refractivity through the Clausius-Mosotti equation [1], Together with the dipole moment, a dominates the intermolecular forces such as the van der Waals interactions, while its variations upon vibration determine the Raman activities. Although a corresponds to the linear response of the dipole moment, it is the first quantity of interest in nonlinear optics (NLO) and particularly for the deduction of stracture-property relationships and for the design of new... 

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

The ratio S/r qan be estimated in some cases by using the Clausius-Mosotti fimction as... 

Hence there exists a relationship between AE and the dielectric constant e which is correlated with a by the Clausius-Mosotti equation ... 

Use the Clausius-Mosotti equation from physical chemistry (Atkins 1994, Chapter 22) to introduce refractive index n... 

For n close to unity (gases), the Clausius-Mosotti equa- A n2 M + cos2x)... 

The molar polarization of the solvent, P, is given by the Clausius-Mosotti expression P = V(s - l)/(s + 2), similar to the expression for the molar refraction. It is the molar polarization that relates the relative permittivity to the dipole moment p and the polarizability a ... 

In the particular cases for which y = 1 /3e0 rearrangement of Eq. (2.87) leads to the Clausius-Mosotti relationship, here in SI units... 

The capacitance may change with temperature not only because the dimensions of the capacitor change but also because the permittivity of the dielectric changes. To gain some insight into the sources of the variation in permittivity with temperature, the Clausius-Mosotti equation (Eq. (2.88)) can be differentiated with respect to temperature to give... 

For a number of dielectrics with e, > 30, TC is negative and within 15% of —aLer as illustrated by the examples given in Table 5.6. Eq. (5.34) suggests that the temperature variation of polarizability is small compared with the volume expansion coefficient in these cases. Lower-permittivity oxides have positive TC s and in their case the temperature coefficient of polarizability can be assumed to exceed the volume expansion coefficient. However, the extent to which the Clausius-Mosotti equation can be applied to ionic solids is open to debate. 

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. 

The relationship between the dipole moment of a material and its dielectric constant (the Clausius-Mosotti-Debye relationship) is ... 

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... 

Onsager equation — (b) The Onsager equation is an extension of the Debye-Clausius-Mosotti equation, and it relates the - dielectric constant er with the -> dipole moment p ... 

This relation has been used for both static and optical fields in the derivation of the well-known Clausius-Mosotti and Lorenz-Lorentz equa-... 

The linear and non-linear polarizabilities of organic molecules are usually determined from measurements of macroscopic susceptibilities of liquid solutions. Classical examples are the measurements of the refractive index, n, or the relative permittivity of pure organic liquids and their interpretation by the well-known Lorentz-Lorenz and Clausius-Mosotti equations. These... 

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

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... 

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