Dielectric loss spectrum

A fully realistic picture of solvation would recognize that there is a distribution of solvent relaxation times (for several reasons, in particular because a second dispersion is often observable in the macroscopic dielectric loss spectra [353-355], because the friction constant for various types or modes of solute motion may be quite different, and because there is a fast electronic component to the solvent response along with the slower components due to vibration and reorientation of solvent molecules) and a distribution of solute electronic relaxation times (in the orbital picture, we recognize different lowest excitation energies for different orbitals). Nevertheless we can elucidate the essential physical issues by considering the three time scales Xp, xs, and Xelec-... 

Fodor JS, Hill DA (1994) Determination of molecular weight distribution of entangled cis-polystyrene melts by inversion of normal-mode dielectric loss spectra. J Phys Chem 98(31) 7674-7684... 

Figure 25. (top) Dielectric loss spectra of glycerol, including time domain data, interpolated by applying the GGE distribution, cf. Eq. 36 (solid lines) (bottom) corresponding derivatives of both the data (points) and fit (solid line) (from [142].)... 

The theory starts from description of the dielectric loss spectra, frequency-dependent permittivity of the solvent e uj), in the framework of the Debye model [86], in which the reorientation of the solvent dipoles gives the main contribution to the relaxation of solvent polarization ... 

Returning to anomalous dielectric relaxation, it appears that a significant amount of experimental data on disordered systems supports the following empirical expressions for dielectric loss spectra, namely, the Cole-Cole equation... 

Thus 0), and w depend not only on the barrier height (as in normal diffusion) but also on the anomalous exponent a which substantially modifies the dielectric loss spectra. The characteristic frequency , and (nw given by Eqs. (160) are shown in Fig. 3 as a function of a and E,y. 

Figure 9. Dielectric loss spectra %jj(to) evaluated from the exact continued fraction solution [Eqs. (176) and (A2.3) solid lines] for a = 0.5 and various values of , and compared with those calculated from the approximate Eq. (191) (asterisks). The low- (dotted lines) and high-frequency (dashed lines) asymptotes are calculated from Eqs. (184), (187), and (185), (188), respectively.

Dielectric loss spectra versus coq for various values of a and y... 

Finally, it is apparent that between the low-frequency and very high-frequency bands, at some values of model parameters, a third band exists in the dielectric loss spectra (see, e.g., Fig. 30). This band is due to the high-frequency relaxation modes of the dipoles in the potential wells (without crossing the potential barrier) which will always exist in the spectra even in the noninertial limit (see Section III.B). Such relaxation modes are generally termed the intrawell modes. The characteristic frequency of this band depends on the barrier height v and the anomalous exponent a. 

Figure 30. Representative dielectric loss spectra of BMPC obtained under isothermal conditions and applied pressure as indicated.

Figure 41. The inset shows isothermal dielectric loss spectra of DOP at ambient pressure. The y-relaxation is the only resolved secondary relaxation. The main figure is obtained by time-temperature superposition.

Figure 44. Dielectric loss spectra of PI. The data at 216.0 K (OX 211-15 K ( ), 208.15 K(OX and 204.15 K (V) were obtained using the IMass Time-Domain Dielectric Analyzer. All the other data, which start at 10 Hz and continue up to 100 kHz, were taken with the CGA-83 Capacitance Bridge. There is good agreement of the CGA-83 data at 216.7 K ( ), 212.7 K (I), 208.7 ( ), and...

Polymers that have bulky repeat units can have multiple secondary relaxations. If more than one secondary relaxation is found, then the slowest one has to be the JG relaxation, assuming that the latter is resolved. Excellent illustrations of this scenario are found by dielectric relaxation studies of aromatic backbone polymers such as poly(ethylene terephthalate) (PET) and poly(ethylene 2,6-naphthalene dicarboxylate) (PEN) [43]. The calculated To from the parameters, n and xa, of the a-relaxation are in good agreement with the experimental value of %jq obtained either directly from the dielectric loss spectra or from the Arrhenius temperature dependence of xjg in the glassy state extrapolated to Tg. The example of PET is shown in Fig. 46. 

Figure 54. Dielectric loss spectra with the same maximum peak frequency for different concentrations of tert-butylpyridine (wt%) in tristyrene. For clarity, each spectrum is shifted vertically by a concentration dependent factor K. K = 1, 2, 1.3, 1, and 0.98 for 100%, 60%, 40%, 25%, and 16% TBP, respectively. The x axis is the real measurement frequency, except for the spectra of 100% and 16% TBP, where horizontal shifts of frequency by factors of 1.75 and 0.80, respectively, have been applied.

Dielectric loss spectra /"(m) versus logn/mq), for various values of a and y, are shown in Figs. 11 13. It is apparent that the spectral parameters (the characteristic frequency, the half-width, the shape) strongly depend on both a (which pertains to the velocity space) and y. Moreover, the high-frequency behavior of x"((o) is entirely determined by the inertia of system. It is apparent, just as in Brownian dynamics, that inertial effects produce a much more rapid falloff of x"(to) at high frequencies. Thus the Gordon sum rule for the dipole integral absorption of one-dimensional rotators [14,28], namely... 

As an example, this effect is shown by the isothermal dielectric loss spectra of BIBE at ambient pressure and at elevated pressures in Fig. 4. 

Figure 1. Dielectric loss spectra of 5%wt. CNBz in trystyrene at different temperatures. Continuous lines are from fitting Havriliak-Negami functions, dotted line is a KWW function (n=0.55) fitted to the spectrum at T=221 K. Vertical arrow shows the location for the characteristic frequency of the JG process, VjQ=l/(2tiTjQ) as predicted by Eq.l.

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