Dielectric relaxation parameter plots

The DISPA analysis described above is based on comparison of an experimental curve to a reference circle. Although that display is qualitatively useful in identifying the correct line-broadening mechanism, the analogous Cole-Cole plotS in dielectric relaxation continues as a popular display mode after nearly 40 years), a display in vyhich the same experimental DISPA data is compared to a straight line could better help to determine quantitatively the line-broaoen-ing parameter(s) of that mechanism. 

Circular plots aid in studying polarization effects as function of frequency (52). If a single dielectric relaxation time is involved, the plot of the loss index against the dielectric constant (for fi equencies fi om just above and below those for which polarization occurs) is a semicircle with its center on the dielectric constant axis (Fig. 30a). If more than one dielectric relaxation time is involved, it is still possible to plot the loss index against the dielectric constant axis (Fig. 30b). A new parameter is required, the storage coefficient, a, which is the complement... 

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... 

The s parameter following this procedure is found to be between 0.91 and 0.95 and the conductivity increases x 10 x S cm-1. The activation energy, for this conductive process, obtained from the Arrhenius plot was equal to 100.5 kJ mol-1 (1.04 eV). As usual, the dielectric strength of the a -relaxation Ae = eoa — < coa, decreases when the temperature increases. The shape parameter for both parameters are nearly temperature independent. 

Figure 46. Linearized plots of the three parameters xa, vmin, and %min, determined from the MCT analyses of the relaxation spectrum in the high-temperature regime. Plotted are the scaling law amplitude (SLA) as indicated (a) from the dielectric spectra of glycerol (cf. Fig. 18a) (adapted from Ref. 136) (b) from the light scattering spectra of 2-picoline (cf. Fig. 18b) (from Ref. 183).

Progressive changes in the dielectric behavior are found with increasing metal salt concentration, with the a process rapidly increasing in its temperature location until at 18% it is amalgamated completely with, or obscured by, the d process which then dominates the dielectric response. Frequency plane data for this d relaxation in the 18 mol % zinc chloride sample are shown in Figure 5. The relaxation is much sharper than a normal main-chain relaxation with the data giving excellent Cole-Cole (8) circular arc plots with the breadth parameter = 0.14. This reflects... 

Figure 22 shows Arrhenius plots of the relaxation times for the a- and approcesses obtained by the peak frequency of the dielectric loss e" for P2CS thin films with d = 3.7 nm. The peak frequencies/ and/a, are evaluated fi-om the frequency dependence of the dielectric loss due only to the a- and approcesses that are reproduced from Eq. (12) with best-fit parameters. The peak frequency of As"(f, Ta) after isothermal aging at a given aging temperature Ta for 30 h and with... 

Figure 6.30. Schematic plots of (a) the real part e of dielectric permittivity and (b) the loss factor e" versus frequency with cure time (tc) as a parameter (Tcure = constant). The higher the frequency /i, the shorter the time at which the dipolar component (a relaxation) appears as a drop in e (f) and as a maximum in "(/). Experimental evidence of the low-frequency shift of the a relaxation with the increase of U is provided by Eloundou et al. (2002).

Here e , is the high frequ y limit of s, So is the static dielectric constant (low frequency limit of s ). So - Soo = A is the dielectric increment, fR is the relaxation frequency, a is the Cole-Cole distribution parameter, and P is the asymmetry parameter. The relaxation frequency is related to the relaxation time by fa = (27It) A simple exponential decay of P (oc,P = 0) is characterised by a single relaxation time (Debye-process [1]), P = 0 and 1 < a < 0 describe a Cole-Cole-relaxation [2] with a symmetrical distribution function of t whereas the Havriliak-Negami equation (EQN (4)) is used for an asymmetric distribution of x [3]. The symmetry can be readily seen by plotting s versus s" as the so-called Cole-Cole plot [4-6]. 

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