Optical dielectric permittivity

Typically, another transparency region exists o>a < co < cox where co, called the optical frequency, denotes the lower bound of the electronic (optical) absorption spectrum. Provided this transparency band is wide (say, co0/cox < 102 typically cox > 1016 s-1 and coa 1013—1014 s 1), one can define the optical dielectric permittivity, sx = 1 +477. ... 

In Eq. (28) e is the charge of the electron, r the radius of the reactant, Avo-gadro s number, and d the reactant-electrode distance. The solvent was considered here as a continuous medium with a fast electronic polarization characterized by the optical dielectric permittivity and a slower oscillatory plus orientational polarization characterized by the static dielectric permittivity... 

For the spectroscopic applications, it would be again instructive to separate the noninertial and inertial components of the electrostatic polarization of the dielectric medium. The first of them corresponds to the electrostatic polarization of the electron charge distribution in the solvent that is supposedly instantaneous as compared to any electronic or conformational transition of the solute. The second component arises from the orientational polarization of the solvent molecules in the electrostatic field of the solute. The noninertial polarization can be described by the optical dielectric permittivity of the solvent that corresponds to the infinite frequency of external electromagnetic field (e Ud) whereas the inertial polarization represents the slow, orientational part of the total dielectric constant of the solvent, s. In order to separate the noninertial polarization, it is helpful to determine the solute charge density as the sum of the respective nuclear and electronic parts... 

In all the previous equations n is the refractive index of the pure solute (i.e. of the aldehyde under study), whereas e and e p, are the static or optical dielectric permittivities of the solvent, which is water in this case. 

The effect of solvent polarity and polarizability on the C60 reduction potentials was examined [69] by correlating the potentials with (Cj—l)/(2fis + 1) and (fiop-l)/(2eop + 1) respectively, where fig and Cop are the static and optical dielectric permittivity of the solvent. The 8op usually approximated as the square of the refractive index n. Both parameters define the so-called polarity function / /[70,71] ... 

Tantalum and niobium are added, in the form of carbides, to cemented carbide compositions used in the production of cutting tools. Pure oxides are widely used in the optical industiy as additives and deposits, and in organic synthesis processes as catalysts and promoters [12, 13]. Binary and more complex oxide compounds based on tantalum and niobium form a huge family of ferroelectric materials that have high Curie temperatures, high dielectric permittivity, and piezoelectric, pyroelectric and non-linear optical properties [14-17]. Compounds of this class are used in the production of energy transformers, quantum electronics, piezoelectrics, acoustics, and so on. Two of... 

Crystals with one of the ten polar point-group symmetries (Ci, C2, Cs, C2V, C4, C4V, C3, C3v, C(, Cgv) are called polar crystals. They display spontaneous polarization and form a family of ferroelectric materials. The main properties of ferroelectric materials include relatively high dielectric permittivity, ferroelectric-paraelectric phase transition that occurs at a certain temperature called the Curie temperature, piezoelectric effect, pyroelectric effect, nonlinear optic property - the ability to multiply frequencies, ferroelectric hysteresis loop, and electrostrictive, electro-optic and other properties [16, 388],... 

The compounds K5Nb3OFi8 and Rb5Nb3OFi8 display promising properties for their application in electronics and optics. The compounds can be used as piezoelectric and pyroelectric elements due to sufficient piezo- and pyroelectric coefficients coupled with very low dielectric permittivity. In addition, the materials can successfully be applied in optic and optoelectronic systems due to their wide transparency range. High transparency in the ultraviolet region enables use of the materials as multipliers of laser radiation frequencies up to the second, and even fourth optical harmonic generation. 

Dispersions of nanoparticles in ferroelectric liquid crystals (FLCs) predominantly focused on induced or altered electro-optic effects, but also on the alignment of FLCs. Raina and co-workers reported on a gradual decrease of the dielectric permittivity, e, by doping with SiC>2 nanoparticles at frequencies up to 1 kHz and a rather minor increase of as well as an increase in optical transmission at frequencies above 2 kHz [279]. Liang et al. used BaTiC>3 nanoparticles (31 nm in diameter after grinding commercially available 90 nm nanoparticles Aldrich) and showed, perhaps expectably, a twofold increase in the spontaneous polarization... 

The first term, which contains the the static dielectric permittivities of the three media , 2, and 3, represents the Keesom plus the Debye energy. It plays an important role for forces in water since water molecules have a strong dipole moment. Usually, however, the second term dominates in Eq. (6.23). The dielectric permittivity is not a constant but it depends on the frequency of the electric field. The static dielectric permittivities are the values of this dielectric function at zero frequency. 1 iv), 2 iv), and 3(iv) are the dielectric permittivities at imaginary frequencies iv, and v = 2 KksT/h = 3.9 x 1013 Hz at 25°C. This corresponds to a wavelength of 760 nm, which is the optical regime of the spectrum. The energy is in the order of electronic states of the outer electrons. 

The Hamaker constant is determined by the dielectric permittivities and the optical properties of the interacting media. 

It is impossible, apparently, to discuss the phenomena of elasticity, optical anisotropy and dielectric permittivity of polymer without referring to motion of the Kuhn s segments. Indeed, for example, from the time of classical... 

Dipole moment, dielectric permittivity, optical absorption, and index of refraction are determined for chromophores by standard methods. 

The optical response of a monomolecular layer consists of scattered waves at the frequency of the incident wave. Since the surface model is a perfect infinite layer, the scattered waves are reflected and transmitted plane waves. In the case of a 3D crystal, we have defined (Section I.B.2) a dielectric permittivity tensor providing a complete description of the optical response of the 3D crystal. This approach, which embodies the concept of propagation of dressed photons in the 3D matter space, cannot be applied in the 2D matter system, since the photons continue propagating in the 3D space. Therefore, the problem of the 2D exciton must be tackled directly from the general theory of the matter-radiation interaction presented in Section I. 

Clausius-Mossotti equation — Named after Clausius and Ottaviano Fabrizio Mossotti (1791-1863). It relates the electron -> polarizability a of an individual molecule to the optical -> dielectric constant (relative permittivity) r of the bulk material. 

Solvent permittivity — is an index of the ability of a solvent to attenuate the transmission of an electrostatic force. This quantity is also called the -> dielectric constant. -> permittivity decreases with field frequency. Static (related to infinite frequency) and optical op (related to optical frequencies) permittivities are used in numerous models evaluating the solvation of ions in polar solvents under both static and dynamic conditions. Usually the refractive index n is used instead of op (n2 = eop), as these quantities are available for the majority of solvents. The theory of permittivity was first proposed by Debye [i]. Systematic description of further development can be found in the monograph of Frohlich [ii]. Various aspects of application to reactions in polar media and solution properties, as well as tabulated values can be found in Fawcetts textbook [iii]. 

If vdielectric permittivity in vacuum will then be equal to 80. This is the so-called static permittivity. The permittivity of the vaccum is 0.855x 10 C m. The static dielectric permittivity near the ion or the surface of the charged electrodes, however, will exhibit smaller values. For instance, in the case of water at the electrode surface is assumed to approach 6. When applying the Marcus theory [8] both static and optical permittivities are used in calculations. These parameters therefore are listed in Table 1. In other calculations and correlations of the rate constants of electrode reactions and the dynamic relaxation properties of the solvents, the relaxation time of the solvents is used (Thble 1). 

This is given by g = gexdex, where gex is the exciton generation rate and /ex the exciton dissociation probability. The position dependence of gex can be found by solving Maxwell s equations for light absorption in the thin, layered device structure. Because of the low thicknesses and low dielectric permittivity, absorption is strongly influenced by optical interference. In an effective medium, tj x can be treated as a... 

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