Clausius-Mosotti relationship

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 Born model with integral or partial charges assumes that the ions have zero polaris-ability. This is reasonable for small cations such as Li" or Mg + but can introduce significant errors for other systems. One pxropjerty that clearly demonstrates this is the high-frequency dielectric constant. At a suitably high frequency only the electrons can keep up with the external field and the dielectric constant is given by the Clausius-Mosotti relationship ... 

The shell model the ions are described by a core, including the nucleus and the inner electrons, and a zero-mass shell representing the valence electrons (Dick and Overhauser, 1958). The core and the shell bear opposite charges. They are harmonically coupled by a spring of stiffness k. The electric field / exerted by neighbouring ions shifts the shell with respect to the core position. If Y is the shell charge, induces a dipole moment equal to SY Ik. The ion polarizability ot in the model, is thus equal to o = Y jk. The value of k may be deduced from the value of the optical dielectric constant eClausius-Mosotti relationship ... 

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 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... 

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

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... 

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. 

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 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 refractive index of a (transparent) fluid is a function of the fluid density. The relationship is exactly described by the Clausius-Mosotti equation for gases, this equation reduces to a simple, linear relationship between the refractive index, n, and the gas density, p, known as the Gladstone-Dale formula. Therefore, refractive index variations occur in a fluid flow in which the density changes, for example, because of compressibility (high-speed aerodynamics or gas dynamics), heat release (convective heat transfer, combustion), or differences in concentration (mixing of fluids with different indices of refraction). 

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