Dielectric constants static

The dielectric properties of a material are properly specified by a symmetric second-rank tensor relating the three components of the electrical displacement vector D to those of the field E. By choosing axes naturally related to the crystal structure the six independent components of this tensor can be reduced to three and, taking account of the hexagonal symmetry of the ice crystal, only two independent components remain. These are the relative permittivities parallel and perpendicular to the unique c-axis direction and we shall denote them by e, and e. We shall discuss the experimental determination of these quantities when we come to consider dielectric relaxation, since some difficulties are involved. For the present we simply note the results which are shown in fig. 9.2. The often-quoted careful measurements of Auty Cole (1952) were made with polycrystalline samples and removed many of the uncertainties in earlier work. They represent, however, a weighted mean of the values of e, and Humbel et al. (1953 J), on the 

Suppose we have a macroscopic system such as an ice crystal, 

Humbel et al. (1953a) H +. Humbel etal. (1953a) --------, Powles 

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 

This very general result is due to Frohlich and may be specialized, as we shall see presently, to give other well-known expressions. Before we do this, however, let us look briefly at the quantity m. If there is no interaction between molecular dipoles then m = m and indeed this can also be shown to hold if each molecule can be treated as a point dipole or as a uniformly polarized sphere. The deviation of m. m ) from is thus a measure of the short-range 

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The size of the exciton is approximately 50 A in a material like silicon, whereas for an insulator the size would be much smaller for example, using our numbers above for silicon dioxide, one would obtain a radius of only 3 A or less. For excitons of this size, it becomes problematic to incorporate a static dielectric constant based on macroscopic crystalline values. 

The dielectric constant (permittivity) tabulated is the relative dielectric constant, which is the ratio of the actual electric displacement to the electric field strength when an external field is applied to the substance, which is the ratio of the actual dielectric constant to the dielectric constant of a vacuum. The table gives the static dielectric constant e, measured in static fields or at relatively low frequencies where no relaxation effects occur. 

Values in parentheses are estimates. Values for band gaps decrease with increasing temperature, whereas values for the static dielectric constant and long wavelength refractive index increase with increasing temperature. 

The addition of salts modifies the composition of the layer of charges at the micellar interface of ionic surfactants, reducing the static dielectric constant of the system [129,130]. Moreover, addition of an electrolyte (NaCl or CaCli) to water-containing AOT-reversed micelles leads to a marked decrease in the maximal solubihty of water, in the viscosity, and in the electrical birefringence relaxation time [131],... 

FIGURE 6. (a) Values of for the solvated electron absorption bands plotted against the mole fraction DMSO for DMSO/H O mixtures, (b) Photon energy of the absorption band maxima for the solvated electron in DMSO/HjO mixtures plotted against the bulk static dielectric constant (25 °C) of the mixture. Non-linear axes showing dielectric constant and mole fraction for (a) and (b) respectively are given as top abscissae. Reproduced by permission of the authors from Reference 30. 

Azo-bridged ferrocene oligomers also show a marked dependence on the redox potentials and IT-band characteristics of the solvent, as is usual for class II mixed valence complexes 21,22). As for the conjugated ferrocene dimers, 2 and 241 the effects of solvents on the electron-exchange rates were analyzed on the basis of the Marcus-Hush theory, in which the t/max of the IT band depends on (l/Dop — 1 /Ds), where Dop and Ds are the solvent s optical and static dielectric constants, respectively (155-157). However, a detailed analysis of the solvent effect on z/max of the IT band of the azo-bridged ferrocene oligomers, 252,64+, and 642+, indicates that the i/max shift is dependent not only on the parameters in the Marcus-Hush theory but also on the nature of the solvent as donor or acceptor (92). 

Here 0 is a step function, L is the distance of closest approach of ions to x = 0, e is the static dielectric constant [the k = 0 Fourier component of e(x, x )], and the inverse dielectric function is defined by... 

Linear absorption and fluorescence spectra for the series of symmetrical cationic polymethines with 5-butyl-7,8-dihydrobenzo[ /]furo 2,3 /lindolium terminal groups are shown in Fig. 14 for solvents of different polarity. It is known that the polarity of solvents can be characterized by their orientational polarizability, which is given by Af = (e- l)/(2e + 1) — (n2 - l )/(2n2 +1), where e is the static dielectric constant and n is the refractive index of the solvent [41], Calculated A/values... 

Before a dislocation on one of the glide planes passes through the complex, the distance between the two charge centers is d = b = a0/>/2. After it has passed by the distance is d = V2(b) = a0. Therefore, if K is the static dielectric constant, and q = electron s charge, the energy difference between the before and after states is AU = (q2/Ka0)(V2-l). 

In the continuum and semicontinuum models of es, long-range forces due to distant solvent molecules are usually represented by the optical and static dielectric constants. In a true continuum model, the continuity is extended to the origin or to the surface of the cavity. In some sense, the continuum and semicontinuum models both contain both short- and long-ranged interactions. The main difference is that in the semicontinuum model, the molecules in the first shell(s) are structured. 

Static coefficient, 15 205 Static dielectric constant (e0), of compound semiconductors, 22 150t, 151 Static electroanalytical measurements, 9 586... 

FIGURE 1.29. Effect of solvation in the case of a saturated and unsaturated bridge separating two identical oxidizable or reducible groups. B — (N eo/4neo)(l — l/es) NA is Avogadro s number, eo is the electron charge, () the permitivity of vacuum, and es the static dielectric constant of the solvent (+) for oxidations, (—) for reductions. 

According to the Kirkwood theory of polar dielectrics, simple relations (23) between molecular dipole moment vectors and the mean-square total dipole moment of water clusters can be used to compute the static dielectric constant of water. As the normalized mean-square total dipole moment increases towards unity, theory predicts decreases in the static dielectric constant. Since MD results indicate that the mean-square total dipole moment of interfacial water is greater than that for bulk water (48), the static dielectric... 

After these preliminary remarks, the term polarity appears to be used loosely to express the complex interplay of all types of solute-solvent interactions, i.e. nonspecific dielectric solute-solvent interactions and possible specific interactions such as hydrogen bonding. Therefore, polarity cannot be characterized by a single parameter, although the polarity of a solvent (or a microenvironment) is often associated with the static dielectric constant e (macroscopic quantity) or the dipole moment p of the solvent molecules (microscopic quantity). Such an oversimplification is unsatisfactory. 

Theoretical investigations of AEV and AEC have indicated that the ratio AEV/AEC is greater than 1 [Zh2, Vo2, Ne2] and may be as high as 3 for the case of hydrogenated silicon clusters [Re3], In a similar calculation for thin silicon films, even-odd oscillations of A v according to the number of Si monolayers have been found [Zh2], For the latter case the ratio AEy/AEc showed values between 1 and 2. The results of a study [Wa5] including the decrease in the static dielectric constant with size are close to the experimentally [Bu2] observed values of about 2 for the ratio AEy/AEc, as shown in Fig. 7.16. In this work [Wa5], it is concluded that the electron-hole pair is confined by the physical dimension of the quantum dot, not by Coulomb attraction. 

In the homogeneous case, Aq is given by (7), where is the electron charge, Dop and Dg the optical and static dielectric constants of the solvent respectively, and a I and 2 e equivalent hard sphere radii of the two reactants (and products). For the electrochemical case, there are two versions for the expression of A., . In Marcus s treatment (Marcus, 1965) the reaction site is assumed to be located at a distance from the electrode equal to its radius, a, and the effect of image forces in the electrode is taken into account (8). In Hush s treatment (Hush, 1961) the reaction site is assumed to be located farther from the electrode surface and the effect of image forces is neglected (9). 

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