Dielectric constant in relation

Fig. 29. Dielectric behavior of an ideal polar material, (a) Effect of frequen r on the static value of the dielectric constant, in relation to the dipole contribution, and on the dissipation factor and loss index as frequency is reduced the dielectric constant reaches its highest static value and the dissipation factor and loss index reach a minimum, (b) Debye curves representing a set or distribution of relaxation times, e s = Static dielectric constant e oo = high frequency dielectric constant t = dielectric relaxation time and n = optical index of refraction, m = 27zf = angular frequency. The broadened loss curve caused by multiple relaxation time is shown by the dashed curve.

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

The ratio of permittivity with the dielectric to the permittivity in vacuum, e/eo, is called the relative permittivity, s, or dielectric constant. The dielectric constant is a material property. Some values of dielectric constants for common ceramic and glass insulators are given in Table 6.3. Since a polarizable material causes an increase in charge per unit area on the plates of a capacitor, the capacitance also increases, and it can be shown that the dielectric constant is related to the capacitance and displacement in vacuum and with the dielectric material as follows ... 

Equation 1.7 demonstrates that the force of attraction between oppositely charged particles is inversely related to the dielectric constant. The data in Table 1.14 show that water possesses the highest dielectric constant in comparison to the other liquids reported in the table. This explains why, for example, gypsum (CaS04 2H20) dissolves in water at 2.2 g L-1 while its solubility in alcohol is negligible. 

The selective resolution enhancement in derivative spectroscopy is pushed even further in the fourth derivative mode. As in the case of second derivative spectroscopy, the amplitude and the position of the derivative spectral bands of the aromatic amino acids are related to the polarity of the medium. We have undertaken a systematic investigation of these spectral features of the N-acetyl O-ethyl esters of tyrosine and tryptophan in various solvents of different polarity (from cyclohexane to water). Astonishingly, a simple relationship between the spectral parameters of the fourth derivatives and the dielectric constant was found [11]. As shown in Figure 5, for tyrosine it is the position of >.max, and for tryptophan it is the derivative amplitude which depends linearly on the dielectric constant er. Since in addition the fourth derivative spectra of these model compounds do not depend significantly on pressure (at least up to 500 MPa), these spectral features may be used as an intrinsic probe to sense the dielectric constant in the vicinity of tyrosine and tryptophan. 

The dielectric constant of a solvent plays a significant role in solubility and stability of the solute. Few studies relating to the dielectric constant of the solvent medium to the photodegradation rate have been undertaken. Thoma and Klimek (8) reported that the improvement in the photostability of nifedipine noted by them is due to an increase in dielectric constant in both ethanol/water and propylene glycol/water mixtures. 

The ease and the stereochemical course of hydrogenation of a,p-unsaturated ketones are particularly influenced by the nature of the solvent and the acidity or basicity of the reaction mixture. Some efforts have been made to rationalize the effect of the various parameters on the relative proportions of 1,2- to 1,4-addition, as well as on the stereochemistry of reduction. For example, the product distribution in -octalone hydrogenation in neutral media is related to the polarity of the solvent if the solvents are divided into aprotic and protic groups. The relative amount of cis- -decalone decreases steadily with decreasing dielectric constant in aprotic solvents, and increases with dielectric constant in protic solvents, as exemplified in Scheme 21 (dielectric constants of the solvents are indicated in parentheses). Similar results were observed in the hydrogenation of cholestenone and of testosterone. In polar aprotic solvents 1,4-addition predominates, whereas in a nonpolar aprotic solvent hydrogenation occurs mainly in the 1,2-addition mode. 

Dielectric relaxation, as the name implies, is concerned with the time, frequency, and/or temperature dependence of the dielectric constant. Since the magnitude of the dielectric constant is related to the molecular structure, its dependence on time, frequency, and/or temperature generally reflects molecular motion. In the case of homogeneous polymers, the dielectric relaxation technique may therefore be used as a probe for the study of transitions and relaxations in a manner analogous to that already discussed for mechanical relaxation. In this chapter we are concerned with the application of dielectric relaxation to amorphous polymers, and we attempt to point out differences between the dielectric and mechanical relaxation techniques. 

It remains now to relate the molecular quantities ccq and p to the macroscopic polarizability or dielectric constant, which can be measured experimentally. This is a very difficult task and will not be carried out in a rigorous fashion here. Rather, we start our discussion with an approximate equation, given by Debye, which describes the complex dielectric constant in terms of molecular properties. We rationalize the form of the equation through the Clausius-Mosotti equation and then show how e (o)) and s"((o) can be derived from this expression. Additional factors that were not included in Debye s original work, such as the effect of the reaction field and orientation correlation-which are important in condensed phases-will also be discussed... 

Conductometric measurements were feasible down to 50 volume percent of THF, and the dissociation constants of lithium ion-pairs were determined from those data. The log Kdiss were shown to be linear with reciprocal of the appropriate dielectric constant - a relation commonly reported284) although not obvious. The solvating power of a medium is not determined uniquely by the bulk dielectric constant, D the more sophisticated Kirkwood function (D - l)/(2 D + l)329) could provide a better measure of that property. However, since the Kirkwood function is nearly linear with 1/D in the investigated range of dielectric constants, the discrimination between them is not practical. 

The presence of dispersed particles may significantly affect the value of dielectric constant of disperse system. In some cases, e.g. in non-aggregated (non-flocculated) inverse emulsions (Chapter VIII,3), the dielectric constant is related to the volume fraction of droplets in the emulsion, VKi, by the Bruggerman relationship... 

Our second self-imposed restriction consists of taking the phrase dielectric constant in its narrowest sense, and confining ourselves to the relation between polarization and electric field in the strict zero-frequency, zero-field limit. Thus, for example, we do not consider index of refraction, dielectric saturation, or dielectric relaxation. 

These equations relating e and h 2) were derived in Section II and provide useful routes to e. If h 2) is exact, both (3.7) and (3.8) must yield the same dielectric constant. In fact, however, self-consistency holds under much weaker conditions, which are satisfied by several approximate theories. 

There has been much controversy in the past several years concerning the relation of the dispersion of the dielectric constant to the molecular dipole-moment correlation function (see Titulaer and Duetch, 1974). Fatuzzo and Mason (1967) have shown that the autocorrelation function of the net dipole moment of a sphere imbedded in a medium of the same dielectric constant is related to the frequency-dependent dielectric constant by... 

We have, in (9.1), implicitly assumed the material to be isotropic, which is not a bad approximation for an ice crystal, so that in the integral we may replace co d by its average value J. Then, recalling that the dielectric constant is related to the induced moment per unit volume by... 

The optical properties of a medium are characterized by the optical susceptibility, This parameter is closely related to the refractive index and the dielectric constant. In an isotropic medium at optical frequencies (co), the relationship between the linear susceptibility, the refractive index (n), and the dielectric constant (2) can be expressed as ... 

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