Dielectric relaxation regions

Several dielectric relaxation regions are usually observed for partially crystalline polymers. They arise from motions within the crystals, on their surfaces or in the amorphous regions of the material. Particularly interesting materials, which have been widely studied, are oxidized low density and high density polyethylenes, polyoxymethylene, nylons and poly(vinylidene difluoride) (for reviews see refs. 6, 7, 10, 11, 44, 49, 58). It is useful to consider the theory for the reorientational motion of a chain in a crystal as was first described by Frohlich and developed by Tuijnman, Booij, Williams, Lauritzen and Hoffman and by Boyd and co-workers and which has been applied to the relaxation in partially crystalline polyethylene (see ref. 63 for a review). 

Dielectric measurements were used to evaluate the degrees of inter- and intramolecular hydrogen bonding in novolac resins.39 The frequency dependence of complex permittivity (s ) within a relaxation region can be described with a Havriliak and Negami function (HN function) ... 

Several methods are successfully applicable in this field, e.g. dielectric relaxation methods 164>, IR investigations in the near, fundamental, and far IR regions 165>, RAMAN spectroscopy 166>, NMR spectroscopy 32-34-16 ), and ultrasonic absorption i 8-i70). 

The dielectric constant is generally different in the crystalline and amorphous phases. In this case, Xc in Eq. (95) does not mean the volume fraction of the crystalline phase itself. Furthermore, the amorphous phase exhibits dielectric relaxation in the region where the mechanical relaxation occurs. Considering this effect, Xc should be taken as a complex quantity with a negative imaginary part. However, the inequality (100) is valid in so far as the dielectric loss tangent is smaller than the mechanical one. The inequality (101) holds more generally because the effect of dielectric relaxation enhances the positive value of d"jd. ... 

A detailed comparative study of dielectric behaviour of smectic and nematic polymers was carried out for polymers of acrylic and methacrylic series, containing identical cyanbiphenyl groups (polymers XI and XII) 137 138>. The difference in structural organization of these polymers consists in a more perfect layer packing of smectic polymer XI (see Chaps. 4.1 and 4.2) with antiparallel orientation of CN-dipoles. This shifts the relaxation process of CN-dipole reorientation to a low frequency region compared to nematic polymer XII. Identification of Arrhenius plots for dielectric relaxation frequencies fR shows that for a smectic polymer the value of fR is a couple of orders lower than for a nematic polymer (Fig. 21). Though the values... 

Figure 1 indicates the dielectric behavior of practically all tissues. Two remarkable features are apparent exceedingly high dielectric constants at low frequencies and three clearly separated relaxation regions a, 3, y of the dielectric constant at low, medium, and very high frequencies. Each of these relaxation regions is in its simplest form characterized by equations of the Debye type... 

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 nature of the frequency dependence of Mott-Schottky plots for semiconductor electrodes has been discussed in the electrochemical literature for more than three decades (see e.g. reviews [6, 84]). It has been speculated that it can be caused by the following factors (1) frequency dependence of dielectric relaxation of the space charge region [85], (2) roughness of the electrode surface [84], (3) slow ionization of deep donors (acceptors) in the space charge region in the semiconductor [86], and (4) effect of surface states. 

The analysis of the dynamics and dielectric relaxation is made by means of the collective dipole time-correlation function (t) = (M(/).M(0)> /( M(0) 2), from which one can obtain the far-infrared spectrum by a Fourier-Laplace transformation and the main dielectric relaxation time by fitting < >(/) by exponential or multi-exponentials in the long-time rotational-diffusion regime. Results for (t) and the corresponding frequency-dependent absorption coefficient, A" = ilf < >(/) cos (cot)dt are shown in Figure 16-6 for several simulated states. The main spectra capture essentially the microwave region whereas the insert shows the far-infrared spectral region. 

FIG. 13.24 Frequency-temperature correlation map for dynamic mechanical, dielectric and NMR measurements on Polyisobutylene. The a and P relaxation regions are shown. Measurements ( ) NMR (O) Dielectric ( ) Mechanical. The full lines are the WLF equation (curved) and the Eyring Equation (straight). From Schlichter (1966). Courtesy John Wiley Sons, Inc. 

The dielectric relaxation properties in a sodium bis(2-ethylhexyl) sulfosuc-cinate (AOT)-water-decane microemulsion near the percolation temperature threshold have been investigated in a broad temperature region [47,143,147]. The dielectric measurements of ionic microemulsions were carried out using the TDS in a time window with a total time interval of 1 ps. It was found that the system exhibits a complex nonexponential relaxation behavior that is strongly temperature-dependent (Figure 8). 

The third relaxation process is located in the low-frequency region and the temperature interval 50°C to 100°C. The amplitude of this process essentially decreases when the frequency increases, and the maximum of the dielectric permittivity versus temperature has almost no temperature dependence (Fig 15). Finally, the low-frequency ac-conductivity ct demonstrates an S-shape dependency with increasing temperature (Fig. 16), which is typical of percolation [2,143,154]. Note in this regard that at the lowest-frequency limit of the covered frequency band the ac-conductivity can be associated with dc-conductivity cio usually measured at a fixed frequency by traditional conductometry. The dielectric relaxation process here is due to percolation of the apparent dipole moment excitation within the developed fractal structure of the connected pores [153,154,156]. This excitation is associated with the selfdiffusion of the charge carriers in the porous net. Note that as distinct from dynamic percolation in ionic microemulsions, the percolation in porous glasses appears via the transport of the excitation through the geometrical static fractal structure of the porous medium. 

Fig. 3.7 Dielectric relaxation curves for poly(vinylchloride) in the a-relaxa-tion region. From Ishida (1960) with permission from Dr Dietrich Steinlcopff Vertag.

Relaxation times and dispersion amplitudes" change when ions are added. If ion pairs are formed, a new relaxation region appears on the solvent relaxation spectrum on the low-frequency side. Figure 4.105 shows the dielectric absorption spectrum of LiBr in acetonitrile, and how a maximum is developed in the low-frequency region as the concentration of solute increases and ion pairs are formed. Association constants can be determined from these data and contribute to the identification of the ion pan-present. 

As reasonably expected, the agreement between Xq and I/t, is especially good in the low-temperature region. Furthermore, the other eigenvalues are proven to correspond to frequencies much higher than the characteristic frequency of the first band. Therefore, this theoretical result reproduces the experimental data which, at microwave frequencies, can be fitted by a single dielectric relaxation time. 

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