Clausius-Mosotti expression

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 ... 

With this value of a, the Clausius-Mosotti expression may be written for eR as... 

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 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... 

From the Clausius-Mosotti equation (Equation 22.16), the relationship between the dielectric polarizabilities and the measured dielectric constant can be expressed by Equation 22.17. 

The molar refractivity is the volume of the substance taken up by each mole of that substance. In SI units, MR is expressed as m /mol. MR is a molecular descriptor of a liquid, which contains both information about molecular volume and polarizability, usually defined by the Lorenz-Lorentz equation [Lorentz, 1880a, 1880b] (also known as the Clausius-Mosotti equation) ... 

It remains now to relate the molecular quantities ccq and p to the macroscopic polarizability or dielectric constant, which can be measured experimentally. This is a very difficult task and will not be carried out in a rigorous fashion here. Rather, we start our discussion with an approximate equation, given by Debye, which describes the complex dielectric constant in terms of molecular properties. We rationalize the form of the equation through the Clausius-Mosotti equation and then show how e (o)) and s"((o) can be derived from this expression. Additional factors that were not included in Debye s original work, such as the effect of the reaction field and orientation correlation-which are important in condensed phases-will also be discussed... 

It is now easy to understand the origin of equation (7-31). One sees that it is of the form of the Clausius-Mosotti equation where the complex dielectric constant rather than % or eR values is used. The complex formulation introduces a frequency dependence, which appears in the last term of equation (7-31). One would expect the time-dependent contribution to be related to the difference between instantaneous and long-time behavior and, indeed, this is correct, because the factor multiplying the frequency dependence in equation (7-31) is merely the difference between equations (7-47) and (7-40). In fact, these two expressions may be combined with equation (7-47) to yield... 

The dependence of the relative permittivity of a gas, e, on the molar volume can be expressed by the Clausius-Mosotti equation ... 

Real molecules are always polarizable. When these particles have a permanent dipole moment (py) they are characterized by the set pj, Xj) the polarizability may be expressed in terms of the dielectric permittivity (e< )y of the induced high-frequency polarization (by the Clausius-Mosotti equation). 

The degree to which an electromagnetic wave is slowed down upon entering a given medium depends upon the characteristics of the electronic environment it encounters. This is a function of the individual molecular electron clouds, as well as the number of molecules per unit volume, N (particle density). If the medium contains N molecules per unit volume, the magnitude of the charge distortion in the molecules by the electromagnetic field of the radiation is limited by their polarizibility, a, and the dielectric constant, 8, of the medium. The relationship between these parameters is expressed in the Clausius-Mosotti equation ... 

The first quantity, denoted d, is expressed in C.m V while the second quantity [a] is the absolute polarizability expressed in cubic meters (m ). The polarizability of a dielectric material, containing n atoms per unit volume (m" ) and having a relative dielectric permittivity , is given by the Clausius-Mosotti equation ... 

In this expression e is the equilibrium dielectric constant while V is the volume of the sphere. The theoretical objective is to relate M to some molecular quantity. The earliest interpretation was in terms of molecular polarizability of the individual molecules in the sphere. This polarizability is due to the mobility of the electronic cloud that surrounds all atoms or molecules and is given by the Clausius-Mosotti equation ... 

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