Relaxation dielectric properties

The observation of slow, confined water motion in AOT reverse micelles is also supported by measured dielectric relaxation of the water pool. Using terahertz time-domain spectroscopy, the dielectric properties of water in the reverse micelles have been investigated by Mittleman et al. [36]. They found that both the time scale and amplitude of the relaxation was smaller than those of bulk water. They attributed these results to the reduction of long-range collective motion due to the confinement of the water in the nanometer-sized micelles. These results suggested that free water motion in the reverse micelles are not equivalent to bulk solvation dynamics. 

Time Constant Analysis, r is the relaxation time of the corrosion process and is dependent on the dielectric properties of the interface. r is given by r = R P, but can be measured independently r = wz"max Since and P vary with surface area in exactly opposite fashion, r (or wzBmax) should be independent of surface area. To verify that this is indeed the case, we examined the corrosion of N80 steel in uninhibited 15% HC1 at 65 C. With increasing exposure time, we observed a continuous decrease in R (hence an increase in corrosion rate) and a concomitant increase in P. And, as expected, wz"max did not vary at all (see Figure 8). 

Single-step perturbation methods have also been applied to electrostatic processes. One study probed the dielectric properties of several proteins at a microscopic level [41,42], Test charges were inserted at many different positions within or around each protein, and a dielectric relaxation free energy was computed, which is related to a microscopic dielectric susceptibility (see Sect. 12.3). 

In contrast with Eq. (5), Eq. (11) gives the frequency behavior in relation to the microscopic properties of the studied medium (polarizability, dipole moment, temperature, frequency of the field, etc). Thus for a given change of relaxation time with temperature we can determine the change with frequency and temperature of the dielectric properties - the real and imaginary parts of the dielectric permittivity. 

According to the value of the frequency of the field, and the relaxation time band in relation to the temperature considered, one can find the three general changes with temperature of the dielectric properties. Fig. 1.7 gives the three-dimensional curves describing the dielectric properties in relation to frequency and temperature. 

Considerable progress has been made in going beyond the simple Debye continuum model. Non-Debye relaxation solvents have been considered. Solvents with nonuniform dielectric properties, and translational diffusion have been analyzed. This is discussed in Section II. Furthermore, models which mimic microscopic solute/solvent structure (such as the linearized mean spherical approximation), but still allow for analytical evaluation have been extensively explored [38, 41-43], Finally, detailed molecular dynamics calculations have been made on the solvation of water [57, 58, 71]. 

Table 1.1 Relaxation times (20°C) and dielectric properties of some common organic solvents10...

Table 1.3 Relaxation times and dielectric properties as a function of temperature for EtOH...

The origin of this relaxation is in heterogeneity of the ceramic, in which anisotropically shaped grains exhibit strong variation in their piezoelectric and dielectric properties in different directions. As discussed in [17], in such heterogeneous materials Maxwell-Wagner like processes may lead to a behavior shown in Figure 13.6. 

PTC) is a family of polymers whose thermal properties, Tg, unperturbed dimensions and partial specific volumes has been reported [248-252], The dielectric properties of these polymers were recently studied [253-256], Relaxational studies on poly(thiocarbonate)s are scarce, but on the contrary there is much information about relaxation processes of the analogues poly(carbonate)s (PC). Therefore the study of PTC is an interesting approach to get confidence about the motions responsible of the relaxational behavior of these polymers. 

In order to obtain the excellent dielectric properties desirable for electronic applications the growth rate of coatings is limited to about 10 pm per hour at 300 °C, but well adherent layers can be grown at much higher rates if the requirements on dielectric strength are relaxed and temperatures of 400-500 °C allowed147. Since the depostion takes place simultaneously on the whole surface, only several hours should be necessary to redeposit a 100200 pm thick coating 34). 

M. S. Skaf, T. Fonseca and B. M. Ladanyi, Wave-vector-dependent dielectric relaxation in hydrogen-bonding liquids a molecular-dynamics study of methanol, J. Chem. Phys., 98 (1993) 8929-45 B. M. Ladanyi and M. S. Skaf, Wave vector-dependent dielectric relaxation of methanol-water mixtures, J. Phys. Chem., 100 (1996) 1368-80 M. S. Skaf, Molecular dynamics simulations of dielectric properties of dimethyl sulfoxide Comparison between available potentials, J. Chem. Phys., 107 (1997) 7996-8003. 

A. Water and Tissue Water. The dielectric properties of pure water have been well established from dc up to microwave frequencies, approaching the infrared (3). For all practical purposes they are characterized by a single relaxation process centered near 20 GHz at room temperature. Static and infinite frequency permittivity values are, at room temperature, close to 78 and 5, respectively. Hence, the microwave conductivity increase predicted by Eq. (1) is close to 0.8 mho/cm above 20 GHz, much larger than typical low-frequency conductivities of biological fluids which are about 0.01 mho/cm. The dielectric properties of water are independent of field strength up to fields of the order 100 kV/cm. 

Characteristic frequencies may be found from dielectric permittivity data or, even better, from conductivity data. The earlier data by Herrick et al. (6) suggest that there is no apparent difference between the relaxation frequency of tissue water and that of the pure liquid (7). However, these data extend only to 8.5 GHz, one-third the relaxation frequency of pure water at 37°C (25 GHz), so small discrepancies might not have been uncovered. We have recently completed measurements on muscle at 37°C and 1°C (where the pure water relaxation frequency is 9 GHz), up to 17 GHz. The dielectric properties of the tissue above 1 GHz show a Debye relaxation at the expected frequency of 9 GHz (8 ) (Figure 3). The static dielectric constant of tissue water as determined at 100 MHz compares with that of free water if allowance is made for the fraction occupied by biological macromolecules and their small amount of bound water (1, 9). 

At microwave frequencies the dielectric properties of tissues are dominated by the water relaxation centered near 20 GHz. The magnitude of this water dispersion in tissues is typically diminished by some 20 dielectric units due to the proteins which displace a corresponding volume of water. 

The dielectric properties of tissues and cell suspensions will be summarized for the total frequency range from a few Hz to 20 GHz. Three pronounced relaxation regions at ELF, RF and MW frequencies are due to counterion relaxation and membrane invaginations, to Maxwell-Wagner effects, and to the frequency dependent properties of normal water at microwave frequencies. Superimposed on these major dispersions are fine structure effects caused by cellular organelles, protein bound water, polar tissue proteins, and side chain rotation. 

The epoxy resin data and the post-cure data, taken together, show that the dipolar relaxation is associated with the temperature dependence of the polymer chain mobility in the vicinity of the glass transition. The WLF analysis of the dipolar relaxation during cure has not been carried out. In order to complete the analysis, correlated measurements of Tg, extent of cure, and dielectric properties must be made as functions of cure time and temperature. In the absence of such definitive studies, various indirect methods have been employed to analyze dielectric relaxations in curing systems, as described below. 

In Section 4, we have examined, from a fundamental point of view, how temperature and cure affect the dielectric properties of thermosetting resins. The principal conclusions of that study were (1) that conductivity (or its reciprocal, resistivity) is perhaps the most useful overall probe of cure state, (2) that dipolar relaxations are associated with the glass transition (i.e., with vitrification), (3) that correlations between viscosity and both resistivity and dipole relaxation time are expected early in cure, but will disappear as gelation is approached, and (4) that the relaxed permittivity follows chemical changes during cure but is cumbersome to use quantitatively. 

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