Clausius-Mossotti formula

Herz3 calculated the true specific volume (=space occupied by the molecules per ml. of liquid) by the Clausius-Mossotti formula ... 

In order to analyze carefully the frequency-dependent ellipsometric measurements described in the previous section, a precise determination of the frequency dependence of the dielectric constant e is needed. While, the dielectric constant of nonpolar polymers is nearly constant over a wide range of frequencies, that of polar materials decreases with increasing frequency (50), In the optical range, e generally increases with the frequency and this behavior is known as normal dispersion. At these high frequencies, the origin of the polarizability is mainly electronic. However, at moderate and low frequencies the dielectric constant is enhanced compared with its optical frequency value due to the motion of the molecular dipoles. This regime is called anomalous dispersion. The orientational and electronic contributions are found in the well-known Clausius-Mossotti formula for instance. In the simplest model, the frequency dependence of the dielectric constant can be described by the Debye formula (50) ... 

According to the Clausius-Mossotti formula, the static dielectric constant of one pure material e can be expressed as [43]... 

This is a simpler model for spherical cells containing imiform cytoplasm and covered with membrane, which is applicable, for example, to nuclei-free cells such as red blood cells and platelets. More complex "double-shell" models requiring a computer-assisted approach should be considered for cells with nuclei, such as monocytes and endothelial cells. For nonspherical cellular shapes geometrical corrections can be introduced into the Clausius-Mossotti formula [9]. 

Clapeyron-Clausius equation, 332, 346, 356 Clausius equations for properties of saturated vapours, 336 -Mossotti formula, 23 cloud formation, 338, 371 coefficient of condensation, 244... 

Several alternative forms of the Clausius-Mossotti equation are encountered. Frequently, the term N is replaced by its reciprocal, the volume of one atom or one formula unit of stmcture, Vin = /N and is set out in terms of a, thus ... 

Lorentz was the first to consider such problems for a reasonably defensible model of induced dipoles derive the local Lorentz field j and from this obtain the venerable Clausius Mossotti (or perhaps more properly Lorentz-Lorenz) formula. As shown schematically in Figure 1 (a) the molecules are assumed to be at sites on a cubic lattice with uniform macroscopic along the z axis. 

Application of high pressure changes the position of the electronic conduction level, Vq (see Section 6.9), and it increases the dielectric constant of the liquid. Both effects have an influence on the ionization energy of a solute. The dependence of Vo(p) is complicated and experimental data must be used. The effect of pressure on the dielectric constant is due to the increase in density and it is well described by the Clausius-Mossotti equation (see Section 1.6). In Figure 8a the photoconductivity spectrum of TMPD in neohexane is shown as a function of pressure. The variation of the photoconductivity threshold with pressure is depicted in Figure 8b. Evaluation of the data by means of Bom s formula (Chapter 7, Equation 94) led to the hypothesis that an additional increase of liquid density around the solute molecule due to fluctuations is responsible for the observed shifts (Katoh et al., 1995). 

Continuum models have a long and honorable tradition in solvation modeling they ultimately have their roots in the classical formulas of Mossotti (1850), Clausius (1879), Lorentz (1880), and Lorenz (1881), based on the polarization fields in condensed media [32, 57], Chemical thermodynamics is based on free energies [58], and the modem theory of free energies in solution is traceable to Bom s derivation (1920) of the electrostatic free energy of insertion of a monatomic ion in a continuum dielectric [59], and Kirkwood and Onsager s... 

---