Dielectric relaxation data processing

Fig. 4.8 Plot of 8out against 8 using dielectric relaxation data for water in the frequency range 60 10 GHz [G5]. The solid line shows the contribution from the low-frequency relaxation process.

Dielectric relaxation data for a 0.08 M Mg2S04 solution are shown in fig. 4.11. On the basis of an analysis of these data by Barthel and coworkers [29, 32], three relaxation processes may be discerned. The first one, involving the ion pair, occurs between permittivity values of 82.9 and 75.2 and involves a relaxation time of 181 ps. The second process, which is attributed to the slow reorientation of water clusters, takes place between the permittivity values of 75.2 and 8.4 with a relaxation time of 8.4 ps. Finally, the high-frequency process, which occurs between 8.4... 

The dielectric relaxation data for dimethylformamide (DMF) and dimethyl-acetamide (DMA) can be described by two Debye processes [9]. The low-frequency, high-amplitude process is attributed to rotational diffusion. For... 

Given the following dielectric relaxation data for methanol, find the values of the Es, , and td, assuming there is only one relaxation process. 

The identification of the a process as a c-shear relaxation and the p process as interlamellar shear in a drawn and annealed LDPE sheet was nicely confirmed by measurements of the anisotropy of dielectric relaxation [32], Pure polyethylene shows no dielectric response, so experiments were made on specimens that had been lightly decorated with dipoles by means of oxidation, to such a small extent that the overall relaxation behaviour was not significantly affected. The dielectric relaxation data showed marked anisotropy for the relaxation, consistent with its assignment to the c-shear relaxation, but the P relaxation... 

For transport in amorphous systems, the temperature dependence of a number of relaxation and transport processes in the vicinity of the glass transition temperature can be described by the Williams-Landel-Ferry (WLF) equation (Williams, Landel and Ferry, 1955). This relationship was originally derived by fitting observed data for a number of different liquid systems. It expresses a characteristic property, e.g. reciprocal dielectric relaxation time, magnetic resonance relaxation rate, in terms of shift factors, aj, which are the ratios of any mechanical relaxation process at temperature T, to its value at a reference temperature 7, and is defined by... 

Paddison et al. performed high frequency (4 dielectric relaxation studies, in the Gig ertz range, of hydrated Nafion 117 for the purpose of understanding fundamental mechanisms, for example, water molecule rotation and other possible processes that are involved in charge transport. Pure, bulk, liquid water is known to exhibit a distinct dielectric relaxation in the range 10—100 GHz in the form of an e" versus /peak and a sharp drop in the real part of the dielectric permittivity at high / A network analyzer was used for data acquisition, and measurements were taken in reflection mode. 

In all the above three polymers only a single process is apparently observed in the time window for PCS (10-6 to 100 s). The shape of the relaxation function is independent of temperature. The temperature dependence of (r) follows the characteristic parameters observed for mechanical or dielectric studies of the primary (a) glass-rubber relaxation. Relaxation data obtained by many techniques is collected together in the classic monograph of McCrum, Read and Williams41. The data is presented in the form of transition maps where the frequencies of maximum loss are plotted logarithmically... 

Complex dielectric susceptibility data such as those in Figure 15.6 provide a detailed view of the dynamics of polar nanodomains in rls. They define relaxation frequencies, /, corresponding to the e (T) peak temperatures Tm, characteristic relaxation times, r = 1/tu (where uj = 2nf is the angular frequency), and a measure of the interaction among nanodomains as represented by the deviation of the relaxation process from a Debye relaxation. Analysis of data on pmn and other rls clearly shows that their dipolar relaxations cannot be described by a single relaxation time represented by the Debye expression... 

In the temperature interval of —70 to 0°C and in the low-frequency range, an unexpected dielectric relaxation process for polymers is detected. This process is observed clearly in the sample PPX with metal Cu nanoparticles. In sample PPX + Zn only traces of this process can be observed, and in the PPX + PbS as well as in pure PPX matrix the process completely vanishes. The amplitude of this process essentially decreases, when the frequency increases, and the maximum of dielectric losses have almost no temperature dependence [104]. This is a typical dielectric response for percolation behavior [105]. This process may relate to electron transfer between the metal nanoparticles through the polymer matrix. Data on electrical conductivity of metal containing PPX films (see above) show that at metal concentrations higher than 5 vol.% there is an essential probability for electron transfer from one particle to another and thus such particles become involved in the percolation process. The minor appearance of this peak in PPX + Zn can be explained by oxidation of Zn nanoparticles. 

A frequency dependence of complex dielectric permittivity of polar polymer reveals two sets or two branches of relaxation processes (Adachi and Kotaka 1993), which correspond to the two branches of conformational relaxation, described in Section 4.2.4. The available empirical data on the molecular-weight dependencies are consistent with formulae (4.41) and (4.42). It was revealed for undiluted polyisoprene and poly(d, /-lactic acid) that the terminal (slow) dielectric relaxation time depends strongly on molecular weight of polymers (Adachi and Kotaka 1993 Ren et al. 2003). Two relaxation branches were discovered for i.s-polyisoprene melts in experiments by Imanishi et al. (1988) and Fodor and Hill (1994). The fast relaxation times do not depend on the length of the macromolecule, while the slow relaxation times do. For the latter, Imanishi et al. (1988) have found... 

Dielectric relaxation of complex materials over wide frequency and temperature ranges in general may be described in terms of several non-Debye relaxation processes. A quantitative analysis of the dielectric spectra begins with the construction of a fitting function in selected frequency and temperature intervals, which corresponds to the relaxation processes in the spectra. This fitting function is a linear superposition of the model functions (such as HN, Jonscher, dc-conductivity terms see Section II.B.l) that describes the frequency dependence of the isothermal data of the complex dielectric permittivity. The temperature behavior of the fitting parameters reflects the structural and dynamic properties of the material. 

Figure 14. Imaginary part of the dielectric permittivity e,(co) of (a) fluoroaniline (7 — 173 K) and (b) toluene (Tg = 117 K), both type B glass formers showing in addition to the main relaxation (a-process) a secondary relaxation peak (p-process) numbers indicate temperature in K. Unfilled symbols represent data obtained from a broad-band spectrometer [6,153]. Filled symbols represent data from a high-precision bridge [137] interpolations for fluoroaniline (solid lines) were done by applying the GGE distribution (a-process) and a Gaussian distribution (p-process) of relaxation times [142], and these for toluene (dashed lines) were done by the gamma distribution (a-process) and a Gaussian distribution (p-process) [6] (cf. Section IV.C.2).

Figure 35. Time evolution of the secondary dielectric relaxation loss spectrum of DPGDB on isothermal annealing at 173.15 K after rapid cooling from 300 K. From top to bottom, the data were obtained after the sample has been annealed isothermally at 173.15 K for times, ta, equal to 93 s, 745 s, 1353 s, 3752 s, and 7272 s elapsed after the thermal stabilization. Solid circles represent the spectrum obtained by slowly cooling the sample at 0.05 K/min. Vertical arrows show the frequencies of the maximum loss for the JG P- and the y-processes.

The dielectric relaxation processes of matter can be analyzed with an empirical model of dielectric dispersion, for example, the one described by Havriliak-Negami s equation. " We analyzed dielectric data obtained for our samples using a model of complex permittivity k with two dispersions (the main and the low-frequency dispersion of a space charge effect) and conductivity ao (caused by electrode discharge), as follows ... 

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