Dielectric parameter

This fomuila does not include the charge-dipole interaction between reactants A and B. The correlation between measured rate constants in different solvents and their dielectric parameters in general is of a similar quality as illustrated for neutral reactants. This is not, however, due to the approximate nature of the Bom model itself which, in spite of its simplicity, leads to remarkably accurate values of ion solvation energies, if the ionic radii can be reliably estimated [15],... 

Equation 5 is the practical equation for computing power dissipation in materials and objects of uniform composition adequately described by the simple dielectric parameters. 

The apphcation of microwave power to gaseous plasmas is also of interest (see Plasma technology). The basic microwave engineering procedure is first to calculate the microwave fields internal to the plasma and then calculate the internal power absorption given the externally appHed fields. The constitutive dielectric parameters are useful in such calculations. In the absence of d-c magnetic fields, the dielectric permittivity, S, of a plasma is given by equation 10 ... 

Various data sources (44) on plasma parameters can be used to calculate conditions for plasma excitation and resulting properties for microwave coupling. Interactions ia a d-c magnetic field are more compHcated and offer a rich array of means for microwave power transfer (45). The Hterature offers many data sources for dielectric or magnetic permittivities or permeabiHty of materials (30,31,46). Because these properties vary considerably with frequency and temperature, available experimental data are iasufficient to satisfy all proposed appHcations. In these cases, available theories can be appHed or the dielectric parameters can be determined experimentally (47). 

Employing the Davidson-Cole model for propylene carbonate and the Cole-Cole model for propionitrile with the appropriate dielectric parameters from the literature, we have predicted C(t) for these polar aprotic solvents according to the dielectric continuum model. The agreement between the predicted and observed C(t) is not nearly as good as the alcohol examples (see below). 

The values of e and e" of a food material play a critical role in determining the interaction of the microwave electric field with the material. A discussion of these interactions follows. A "map" of foods plotted against their dielectric parameters was introduced by Bengtsson and Risman (1971). Table 1 gives values for the dielectric constant, loss factor and penetration depth, and Figure 1 shows a "map" of these values for common foods. 

A method which circumvents many of the disadvantages of the transmission line and cavity perturbation technique was pioneered by Stuchley and Stuchley (1980). This technique calculates the dielectric parameters from the microwave characteristics of the reflected signal at the end of an open-ended coaxial line inserted into a sample to be measured. This technique has been commercialized by Hewlett Packard with their development of a user-friendly software package (Hewlett Packard 1991) to be used with their network analyzer (Hewlett Packard 1985). This technique is outstanding because of its simplicity of automated execution as well as the fact that it allows measurements to be made over the entire frequency spectrum from 0.3 MHz to 20 GHz. 

Figure 28. Experimental frequency dependences of dielectric parameters recorded for liquid water (a) Real (curve 1) and imaginary (curve 2) parts of the complex permittivity at 27°C. The data are from Refs. 42 (solid lines) and 17 (circles), (b) Absorption coefficient. Solid line and crosses 1 refer to 1°C filled circles 2 refer to 27°C dashed line and squares 3 refer to 50°C. For lines the data from Ref. 17 were employed, for circles the data are from Ref. 42, for crosses and squares the data are from Ref. 53.

Dielectric measurements are insensitive to gelation. This important point is mainly based on experiments with epoxy-amine reactions for which the dielectric parameters are controlled by ionic conductivity. More experiments with other chemistries are needed to reach a more universal conclusion. 

The waveguide system used to measure the dielectric parameters of water and other lossy liquids has been described previously (3J. Basically it involves the measurement of the power profile of a wave reflected from a movable short circuit as it traverses the liquid under test. 

Three dielectric parameters are characteristic of the electrical and viscous properties of tissue water a) the conductance of ions in water, b) the relaxation frequency fc, and c) the static dielectric permittivity eQ observed at f fc =... 

The trends of viscosity and dielectric parameters during the neutralization show that the maximum extension of the polyions occurs when only a part of the ionizable groups are neutralized. 

The relationship between the optical parameters (n, k) and the dielectric parameters (e, e") is given by... 

Dielectric Parameters of Several Polar Solvents Showing Discontinuous Relaxation Time Distributions... 

Calculated and Measured Values of Some Dielectric Parameters of Liquid HjO at Various Temperatures ... 

One should also mention the so-called mean spherical approximation (MSA) treatment of solvent reorganization [25]. McManis and Weaver [125] considered how the solvent radius and dielectric parameters affect the electron transfer within the frame of this theory. The frequency dependence of the effective radius should cause significant deviations from the Marcus expression for the activation energy of... 

Figure 4 Dielectric parameters of poly methyl methacrylate obtained from the Reddish-Hyde spectrometer e - scale on left, e" - scale on right. The l.f. and h.f. instruments overlap at 10 — 10 Hz the a.c. results are careful bridge measurements...

Both static and time-dependent dielectric parameters have been calculated from the computer molecular dynamical model, and they will be discussed in the ensuing sections. 

As we have already mentioned, it is difficult to evaluate dielectric parameters from Eq. (201) because a knowledge of all the eigenvalues X[ and corresponding amplitudes c7k is required. A more simple (from the computational point of view) solution can be given in terms of matrix continued fractions. The general transient response solution of Eq. (172) for t > 0, one can be sought in the form... 

The behavior of the dielectric spectra for the two-rotational-degree-of-ffeedom (needle) model is similar but not identical to that for fixed-axis rotators (one-rotational-degree-of-fireedom model). Here, the two- and one-rotational-degree-of-freedom models (fractional or normal) can predict dielectric parameters, which may considerably differ from each other. The differences in the results predicted by these two models are summarized in Table I. It is apparent that the model of rotational Brownian motion of a fixed-axis rotator treated in Section IV.B only qualitatively reproduces the principal features (return to optical transparency, etc.) of dielectric relaxation of dipolar molecules in space for example, the dielectric relaxation time obtained in the context of these models differs by a factor 2. 

Lane, 1987, Gorto and tgei from dielectric parameters On-line measurements... 

Figure 7. Linear variation of dielectric parameter, K, with n at low water contents (24).

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