Polarizability and refractive index

In view of these results, two observations may be made (a) as a corollary to studies of protein ultraviolet spectra in any particular nonaqueous solvent, the spectral properties of relevant simple compounds in that solvent must be investigated and (5) any changes in protein spectra produced as a result of modification of the native protein conformation in a particular nonaqueous solvent must be superimposed on changes resulting simply from the replacement of the aqueous environment by the nonaqueous one of generally different polarizability and refractive index. In the extreme case, for example, it may make little or no difference spectrally whether the aromatic chromophores remain internally bound within the protein molecule, or whether they become exposed to the solvent, and hence no useful information about protein conformations can be expected. More studies have to be made to clarify to what extent spectral changes can be useful in the investigation of proteins in nonaqueous solvents. 

Since relative dielectric constants and refractive indices are related according to the MaxweU theory, = er, polarizability and refractive index can be expressed one as a function of the other by... 

The very high ionization potential and the low polarizability of the fluorine atom imply that fluorinated compounds have only weak intermolecular interactions. Thus, perfluoroalkylated compounds have very weak surface energies, dielectric constants, and refracting indexes. 

An analysis of the t(30) values, using multivariate statistical methods, has been carried out by Chastrette et al. [193]. According to this analysis, the x(30) values of non-HBD solvents are measures of the dipolarity and polarizability as well as the cohesion of the solvents. Another analysis of x(30) values in terms of functions of the dielectric constant sf and refractive index ( d) of forty non-HBD solvents has been given by Bekarek et al he emphasizes the predominant influence of the f(fir) term on the iix(30) parameter of those solvents [194]. For further correlations of the x(30) values with other empirical parameters of solvent polarity, see Section 7.6. 

Table 5.16. Calculated electric-dipole polarizability for COj " and refractive index n of calcite in sodium D light, for carbon-oxygen distance = 1.29 A...

BekSrek and coworkers40 related the effect of the medium on the spectrum of 2-nitroaniline to the relative permittivity and refractive index of the solvents. In subsequent work, BekSrek and coworkers52 53 employed several probes, including 5, 8, 9, 10 and 15 as well as some that have not been mentioned previously 3-nitro-AAAAdimethylaniline (46), 4-nitroso-A ,A -dimethy I aniline (47) and Af-(2-nitrophenyl)piperidine (48), as probes to explore the polarity/polarizability and HBA/EPD properties of a large number of polar and non-polar aprotic aliphatic solvents. The wavenumbers could be fitted to expressions similar to equations 10 and 11, but with a cross-term of the permittivity and refractive index included (equation 12) ... 

According to the accepted photo-physical concepts on the influence of the medium on emission spectra, the effects observed may be divided into general (non-specific) and specific ones.7 General effects result in changes in orientation polarizability of the emitter microenvironment whose value depends on dielectric constant and refractive index of the medium. Maximum spectral shift is observed for the emitters with maximum changes in dipole moments upon excitation and in the medium with... 

Another property of wide interest for alkanes is a measure of polarizability, the molar refraction which is based upon the experimental measurement of liquid density and refractive index. For a data set of high experimental quality, the following QSAR is obtained (equation 19) ... 

A master table is presented containing the formulae of colloidal scattering for the characteristic quantities r, Rgo, Re, and /Zgox in terms of polarizability a, permittivity t and refractive index p of the components in the Rayleigh and Rayleigh-Debye approximations is given. 

Densities (p) and refractive indexes (n) for various solvents were taken from standard tables [12-14], and the refractive indices of solvent mixtures were calculated according to classical [15] volume additivity of polarizabilities, namely. 

This was necessary since neither the polarity, (eq — l)/(2fio +1). nor the polarizability, (n — )/(2n + ), parameter could alone account for the observed spectral shifts (fio and n are the dielectric constant and refractivity index respectively). 

Equations (10.17) and (10.18) show that both the relative dielectric constant and the refractive index of a substance are measurable properties of matter that quantify the interaction between matter and electric fields of whatever origin. The polarizability is the molecular parameter which is pertinent to this interaction. We shall see in the next section that a also plays an important role in the theory of light scattering. The following example illustrates the use of Eq. (10.17) to evaluate a and considers one aspect of the applicability of this quantity to light scattering. 

Polarizability Attraction. AU. matter is composed of electrical charges which move in response to (become electrically polarized in) an external field. This field can be created by the distribution and motion of charges in nearby matter. The Hamaket constant for interaction energy, A, is a measure of this polarizability. As a first approximation it may be computed from the dielectric permittivity, S, and the refractive index, n, of the material (15), where is the frequency of the principal electronic absorption... 

In Raman spectroscopy the intensity of scattered radiation depends not only on the polarizability and concentration of the analyte molecules, but also on the optical properties of the sample and the adjustment of the instrument. Absolute Raman intensities are not, therefore, inherently a very accurate measure of concentration. These intensities are, of course, useful for quantification under well-defined experimental conditions and for well characterized samples otherwise relative intensities should be used instead. Raman bands of the major component, the solvent, or another component of known concentration can be used as internal standards. For isotropic phases, intensity ratios of Raman bands of the analyte and the reference compound depend linearly on the concentration ratio over a wide concentration range and are, therefore, very well-suited for quantification. Changes of temperature and the refractive index of the sample can, however, influence Raman intensities, and the band positions can be shifted by different solvation at higher concentrations or... 

The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in the medium, and is the square root of the relative permittivity of the medium at that frequency. When measured with visible light, the refractive index is related to the electronic polarizability of the medium. Solvents with high refractive indexes, such as aromatic solvents, should be capable of strong dispersion interactions. Unlike the other measures described here, the refractive index is a property of the pure liquid without the perturbation generated by the addition of a probe species. 

---