Complex permittivity changes

A jumpwise volume change in the transition correlates with a jumpwise change in the shear equilibrium modulus, the refractive index, the stress-optical coefficient and in the components of complex permittivity e and complex modulus G. ... 

These results led us to analyze the relationship between carrier-wave frequency and power density. We developed a mathematical model (6) which takes into account the changes in complex permittivity of brain tissue with frequency. This model predicted that a given electric-field intensity within a brain-tissue sample occurred at different exposure levels for 50-, 147-, and 450-MHz radiation. Using the calculated electric-field intensities in the sample as the independent variable, the model demonstrated that the RF-induced calcium-ion efflux results at one carrier frequency corresponded to those at the other frequencies for both positive and negative findings. In this paper, we present two additional experiments using 147-MHz radiation which further test both negative and positive predictions of this model. 

A relationship was then developed that defines the power densities at various carrier frequencies which would give the same average internal electric field intensity in the sample. These developments were necessary because the relative complex permittivity of the tissue and the wavelength of radiation change with carrier frequency. Finally, using the complex permittivity values reported by Foster et al. (10), relationships were derived for incident power densities at 50, 147,... 

Keeping the average electric field intensity the same within a spherical model of chick-brain in buffer solution at different incident carrier wave frequencies requires that incident power density be changed with frequency to compensate for the change in complex permittivity and wavelength with frequency. The resulting Equations (3) and (A) relate corresponding values of P. at carrier frequencies of 50, 1A7, and A50 MHz. 1... 

The dielectric constant is a natural choice of order parameter to study freezing of dipolar liquids, because of the large change in the orientational polarizability between the liquid and solid phases. The dielectric relaxation time was calculated by fitting the dispersion spectrum of the complex permittivity near resonance to the Debye model of orientational relaxation. In the Debye dispersion relation (equation (3)), ij is the frequency of the applied potential and t is the orientational (rotational) relaxation time of a dipolar molecule. The subscript s refers to static permittivity (low frequency limit, when the dipoles have sufficient time to be in phase with the applied field). The subscript oo refers to the optical permittivity (high frequency limit) and is a measure of the induced component of the permittivity. 

Such illustration, calculated from Eqs. (199) and (200), is given in Fig. 43 for water at the temperature 27°C. The employed model parameters are close to those presented in Table I for H20 at this temperature. In Fig. 43a we depict the loss-contribution e" (v) to the total complex permittivity s. We take two values of the frequency factor p , introduced in Eq. (176b). The solid curve 1 refers to p =0.65. The dashed curve 2 in Fig. 4a refers to p = 1 (without change of the rest of the parameters). 

Hence, transformations of Maxwell equations, the change of orientational distribution functions to the form, close to the Boitzmann distribution with account of classical equations of motions yield the complex susceptibility /(co) determined by unperturbed collision-free motion of an individual particle in a given static potential well. In our approach, the complex permittivity e(co) is found as a simple rational function of this susceptibility /(co). 

Let the resolvation process proceeds at substantial abundance of the component A in mixed solvent and initial concentrations HA (HA" ) and B to be equal. The output of the process can be calculated from the equation similar to equation [9.66]. The large value of K s in all considered processes of proton resolvation indicates the effect of permittivity change on the yield of complex HB formation. The output of resolvated proton in process [9.104] proceeding in methanol equals 100%, whereas in the same process in low polarity solvent (e.g., methanol-hexane), with abundance of the second component, the equilibrium is shifted to the left, resulting in solvate output of less than 0.1%. K s values in single alcohol solvents are large, thus the output of reaction does not depend on solvent exchange. 

Cavity perturbation techniques are used for resonator-based sensing systems [7]. When the complex permittivity or permeability of a region within the resonator is changed, the resonant frequency is shifted and the shift. A/, is given by... 

Dielectric cure monitoring generally relies on measin-ement of the ionic conductivity (a in eq. 19). The conductivity during cure of epoxy-amine systems have been characterized to establish relationships between conductivity and viscosity (103,104), conductivity and Tg (104), and relationships to the conversion of epoxide (103). Recently, models were established to relate changes in the dipole component of the complex permittivity to the advancement of cure through the Tg-con version relationship, expanding the capabilities of dielectric sensing to monitor cure (102). 

Figure 3. Changes of a) impedance and b) complex permittivity during NET-formation (after 3 hours) compared with unstimulated neutrophils.

Michaels et al. [2, 3] found that the stoichiometric NaPSSA BTAC complex, when completely free of extraneous electrolytes, exhibits a high dc resistivity (approximately 10 ° Q. cm). The value of e measured at 100 Hz changes from 50 to 5 (for water-saturated PEC) and from about 5 to 3 (for dried PEC) at 0.1 MHz. When doped with simple electrolytes like NaBr, the absolute values of the complex permittivity as well as the dependence of s and e" on frequency change significantly. Eigure 2 shows the influence of the dopant salt [2]. 

At present, the major focus of the researchers is on the nanocomposite materials based on the nanoparticles of metals and their compounds stabilized within a polymeric dielectric matrix [1-4]. The dielectric and optical properties of these materials have been demonstrated to be highly dependent on the size, structure, and concentration of the nanopartides, as well as on the type of polymeric matrix [5-8]. These have shown the possibility of the purposeful change of parameters of the nanocomposite materials such as electrical conductivity, complex permittivity, refraction coefficient, and so on. It is believed that these materials would demonstrate low acoustic impedance because they are based on the polymeric matrix [9]. At that, the impedance value should be varied within certain limits by adjusting the parameters of the embedded nanopartides. All of these would allow one to use these materials for low disturbing substrates in various devices based on the waves in thin piezoelectric plates [10]. 

The dynamics of lubricant interaction with added water is even more complicated. In addition to high-frequency permittivity changes described by Eq. 7-7, the entire impedance spectrum undergoes a complicated pattern of time-dependent changes. The low-frequency impedance changes caused by water will be discussed in a later section of this chapter. In the bulk solution a complex kinetics of water-oil interactions occurs, combining several mutually dependent processes of emulsification of free nonbound water, formation of inverse micelles, and evaporation of free and micellated water [21]. 

In aqueous electrolyte solutions the molar conductivities of the electrolyte. A, and of individual ions, Xj, always increase with decreasing solute concentration [cf. Eq. (7.11) for solutions of weak electrolytes, and Eq. (7.14) for solutions of strong electrolytes]. In nonaqueous solutions even this rule fails, and in some cases maxima and minima appear in the plots of A vs. c (Eig. 8.1). This tendency becomes stronger in solvents with low permittivity. This anomalons behavior of the nonaqueous solutions can be explained in terms of the various equilibria for ionic association (ion pairs or triplets) and complex formation. It is for the same reason that concentration changes often cause a drastic change in transport numbers of individual ions, which in some cases even assume values less than zero or more than unity. 

One way to achieve such improvements is by doping of aluminum oxide with properly selected impurities. These could be introduced by implantation into aluminum and subsequent transfer into the oxide during anodization.331 Alternatively, complex anions containing impurity atoms could be introduced into the anodizing bath [see Section IV(2)]. The incorporated anions influence the dielectric permittivity, E, of the oxide.176 Hence, one can manipulate the E value by changing the electrolyte concentration and anodization regime.91 According to the published data, rare-earth-doped... 

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