Refractive index, relationship polarization

In this subsection, the connection is made between the molecular polarizability, a, and the macroscopic dielectric constant, e, or refractive index, n. This relationship, referred to as the Lorentz-Lorenz equation, is derived by considering the immersion of a dielectric material within an electric field, and calculating the resulting polarization from both a macroscopic and molecular point of view. Figure 7.1 shows the two equivalent problems that are analyzed. 

Since these complications have prevented a quantitative estimation of the enthalpies and entropies of keto and enol forms in different solvents, a quantitative relationship between AG or Ki, and the solvating ability or polarity of the solvent (expressed in physical characteristics such as the relative permittivity e, the dipole moment fi, the refraction index n, etc.) has not been possible either. Such equations would have the form of Eq. (4-26) ... 

The physical principle of these polarizers rests on the so called Brewster reflection that is theoretically explained by the Fresnel theory of reflection and refraction. Each dielectric medium reflects at a definite angle called Brewster angle, only radiation which is polarized perpendicularly to the plane of incidence. The Brewster angle is determined by the refractive index of the medium according to the relationship tan The... 

For polar substances and mixtures of polar and semi-polar substances the relationship breaks down and no simple functions describe dielectric constant in terms of refractive index. 

In this equation defining P,., n denotes the refractive index extrapolated for infinite wave-length. This extrapolation is usually performed by means of a single ultra-violet absorption frequency. But as the infra-red dispersion is completely neglected in the above, we may expect discrepancies between Pq and P to occur and to be specially conspicuous in the case of polar molecules. We may suppose that the infra-red contribution P — P, together with the dipole moment, increases as the size of the molecule increases. These relationships are illustrated in a particularly beautiful way in the case of... 

While some qualitative inferences about the nature of the interface can be derived directly from the SHG observations, extracting detailed quantitative information from the SHG intensity and polarization data requires the construction of a model of the interface and frequently assumptions about some of the parameters for this model. Parameters such as the interfacial refractive index and roughness need to be determined separately, calculated or more frequently obtained by reasonable assumptions [20,21,23-27]. Some idea of the relationship between the model, assumptions and results is given in Figure 1.2. 

The dielectric properties of the solvents considered here are summarized in table 4.2. These properties are important in evaluating the solvation of ions in polar solvents under both static and dynamic conditions. The relative permittivity of a solvent at high frequencies, Sop, can be calculated from the refractive index, nop, the relationship being... 

A reason for selecting the dielectric constant as the experimental basis for is that the high-frequency value, oo, is due entirely to the polarization of the electrons. Also oo is equal to the square of the refractive index and is easily measured. There is a simple relationship between the average energy gap and ,... 

As shown above, there is a well-defined relationship between refractive index and electric susceptibility. According to Eq. (4.24), the refractive index is a measure of the degree of induced polarization in a given medium. We have to admit, however, in the case of an anisotropic medium that the derivation of the relationship between refractive index, dielectric constant, and permeability is very complex and a nuisance because eri and / n are tensors, and the refractive index is different for each direction of the propagated light. 

HB interactions, is claimed to lie in different responses to solvent polarizability effects. Likewise, in the relationship between the Ji scale and the reaction field functions of the refractive index (whose square is called the optical dielectric constant e ) and the dielectric constant, the aromatic and the halogenated solvents were found to constitute special cases." This feature is also reflected by die polarizability correction term in eq. [13.1.2] below. For the select solvents, the various polarity scales are more or less equivalent. A recent account of the various scales has been given by Marcus, and in particular of by Laurence et al., and of Ey by Reichardt. ... 

When both bordering media are transparent, one can apply transmission spectroscopy in polarized radiation (Section 2.1) or, when there is a difference in the refractive indices of these media, the ATR method and IRRAS. For each type of solid-solid interface, except for the metal-metal interface, one can study the layers in the contact zone by IRRAS or ATR in the transparent spectral range of one of the media in the system. To choose the technique with which to investigate dielectric (semiconductor)-liquid, dielectric (semiconductor)-semiconductor, and dielectric-dielectric interfaces, several factors must be considered, including the region of transparency of the media under study and the relationship between their refractive indices. If the medium with the largest refractive index is the most transparent, one should use the ATR method otherwise IRRAS is more appropriate. 

For polarized measurements the relationship between refractive index and absorbance is critical. Directional absorbance changes lead to birefringence, which in turn will affect strongly the nature of polarized light. The Kramers-Rronig relations come into play for cases like this one (15). They relate the complete electromagnetic absorption spectrum of a material to its refractive index at all frequencies and vice versa. A form of the relation is... 

There are surface-oriented sampling techniques such as internal reflectance (ATR) and external (specular) reflectance, both providing data that are influenced in one way or another by the sample s refractive index (at the measurement wavelength), the refractive index of the sampling medium (in particular, ATR), and the polarization of the infrared beam (in particular, external reflectance). For ideal cases, the mathematical relationship between the recorded spectrum and an idealized absorption (or transmission) spectrum is understood. In these situations, a correction algorithm can be... 

For polar substances or mixtures of polar substances and semi polar substances, however, the relationship breaks down and there is no simple function that describes refractive index in terms of... 

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