Dielectric relaxation spectra

Fig. XIV-2. Dielectric relaxation spectrum of a water-in-oil emulsion containing water in triglyceride with a salt concentration of 5 wt % at a temperamre of 25°C. The squares are experimental points and the lines are fits to Eq. XIV-4. (From Ref. 9.)...

Ac Is a measure of the Intensity of the dielectric relaxation spectrum (the relaxation strength) and it Is in turn related to the number of relaxing dipoles (N) per unit volume by the equatlon(2ZjJi, ... 

Qualitative predictions of the classical Marcus theory of ET have been confirmed for a wide variety of systems. Given this success, theory is now challenged to calculate absolute ET rates on the basis of separately obtainable parameters. Regarding the solvent, the input is the dielectric relaxation spectrum. It can be measured or even calculated independently to a high degree of accuracy. Intramolecular modes participating in the ET... 

Figure 24. Comparison between TSDC (solid line) and dielectric relaxation spectroscopy (dotted lines) data for a side-chain liquid-crystalline polysyloxane. For the dielectric relaxation spectrum, the loss factor is plotted for different frequencies. The graphics were adapted from [179]. The left scheme shows the structure of a side-chain LCP, consisting of the main chain, the spacers and the mesogenic groups (elliptic shapes). The molecular origins of the a and 5 relaxations are also represented.

Taylor HE (1956) The dielectric relaxation spectrum of glass. Trans Faraday Soc 52 873... 

Although the Cole-Cole plot was first introduced in the context of a dielectric relaxation spectrum, it helped discover that the molecular mechanism underlying both dielectric relaxation and stress relaxation are substantially identical (44). Figure 8.13 provides an illustration, with temperature instead of frequency. Specifically, the same molecular motions that generate a frequency dependence for the dielectric spectrum are also responsible for the relaxation of orientation in polymers above Tg. Subsequently the Cole-Cole type of plot has been applied to the linear viscoelastic mechanical properties of polymers, especially in the vicinity of the glass transition, including the dynamic compliance and dynamic viscosity functions. 

Figure 7.16 Dielectric relaxation spectrum of a 47.7 kDa Mw di-polyisoprene having nonparallel dipoles due to one inversion at the molecular center, dissolved in 700 Da polybutadiene at a concentration of 27 g/1, using original measurements by Watanabe, etal.Cil), with simple-exponential and power-law fits.

Figure 7.17 Dielectric relaxation spectrum of a 21 kDa triblock copolymer (58 g/1 in hexadecane) in which the central 3 kDa is the type-A c -polyisoprene and the two terminal ends are 8 kDa dielectrically inert polybutadienes, using original measurements by Adachi, et al.(2). The high- and low-frequency features are here interpreted as segmental motion and whole-chain reorientation, respectively.

In the dielectric relaxation spectrum up to five different kinds of motion were found. There are up to three local motions y-relaxation),... 

Usually, the depolarization current is measured to avoid the dc conductivity contribution. The dielectric relaxation spectrum is then obtained by Fourier transform or approximate formulas, e.g., the Hamon approximation [14]. By carefully controlling the sample temperature and accurately measuring the depolarization current, precision measurements of the dielectric permittivity down to 10" Hz are possible [18]. In fast time domain spectroscopy or reflectometry, a step-like pulse propagates through a coaxial line and is reflected from the sample section placed at the end of the line. The difference between... 

In order to obtain information about molecular dynamics from a dielectric relaxation spectrum, the complex dielectric permittivity is related to the correlation function of the electric dipole moment m, of the ith species and the dipole moment Mj of a small (in comparison with the whole sample) macroscopic volume V surrounding m,. Mj is the sum of permanent dipole moments in this volume Mi N being the number of dipole moments in the volume. The... 

The a- and ajS-processes are characterized by a broad asymmetric dielectric relaxation spectrum, which can be well represented by the Kohlrausch Williams-Watts (KWW) decay function (cf. eqn. (4.17)). The major factor leading to the broad DR spectra for a- and ajS-relaxations is that chain segments relax in cooperation with their environment. In order to explain the mechanism of this relaxation, the concepts of defect diffusion and free-volume fluctuation are used. For example, Bendler has proposed a model in which the KWW function is interpreted as the survival probability of a frozen segment in a swarm of hopping defects with a stable waiting-time distribution At for defect motion. 

Fig. 4.22. Schematic representation of a discotic polymer liquid crystal investigated by Vallerien et al Arrows indicate rotations of the ester groups responsible for dielectric relaxation spectrum of this material. (From Ref. 106, with permission of Steinkopff Verlag.)...

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