Dielectric relaxation modes

If the aqueous phase contains electrolytes, a relaxation due to the Maxwell-Wagner-Sillars effect will be observed. Since the electrolyte is not incorporated in the clathrate structures, an increased electrolyte concentration in the remaining free water will result, thus changing the dielectric relaxation mode. In Fig. 42 we note that the relaxation time r decreases from the initial 1000 100 ps to a final level of 200 20 ps during hydrate formation. The experimental value of 200 ps corresponds roughly to a 3% (w/v) NaCl solution, as compared with the initial salt concentration of 1% (w/v). 

Figure 6.6. Schematic presentation of the frequency dependences of e and e" for typical dielectric relaxation modes in polymers. The traces of relaxation mechanisms with higher molecular mobility (shorter relaxation time) are recorded at higher frequencies. Compare with the isochronal dielectric spectrum of Fig. 6.4. Considering the temperature dependence of the dielectric strength (Ae), it becomes clear that the Ae values measured from isothermal or isochronal isothermal spectra alone are not necessarily equal.

Thus, four active dielectric relaxation modes are prechcted, corresponding to the reorientational motions of ai(=(F F()) with respect to the rdference frame defined by the LC potential, giving two modes for e,(<0) and two for e Jlocal order paranwter S (and hence depend on sample temperature). 

In addition to the dielectric relaxation modes of anisotropic 3D fluids, just as nematic liquid crystals, helical SmC liquid crystals (see Chapter 1, Figure 1.11) have interesting low-frequency dielectric modes that are related... 

Fig. 4. Comparison of the two dielectric relaxation modes (upper spectrum) and the two volume relaxation modes at lOO C (lower spectrum from Kovacs et al., ref. 69).

FIGURE 24.10 Dielectric relaxation times from Figures 24.7 through 24.9 plotted versus 7V, with mode independent -y = 3.0 (1,4-polyisoprene), = 2.5 (polypropylene glycol), and = 2.65 (polyoxyhutylene). 

Consequently, this relaxation time is predicted to be nearly independent of the number of arms. Dielectric relaxation experiments for stars up to 18 arms by Boese et al. [95] show this behavior. The rotational relaxation time, however, can be considered similar to longest internal modes, i.e., it depends on the overall size and, assuming free draining... 

Fig. 4.7 Temperature dependence of the mean relaxation time (r) divided by the rheological shift factor for the dielectric normal mode (plus) the dielectric segmental mode (cross) and NSE at Qinax=l-44 A (empty circle) and Q=1.92 A (empty square) [7] (Reprinted with permission from [8]. Copyright 1992 Elsevier)...

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 the simplest model investigated, including a single Debye mode (X(f) -exp(-t/ r, ), xL being the longitudinal dielectric relaxation time), the spectral effect was found to be small and negative -0.2 <[Pg.332]

As recalled in the Appendix, the rate of tensile relaxation is principally controlled by the slowest modes, while that for dielectric relaxation is most commonly dominated by the fastest modes. Hence, Eq. (49) may not be without interest in certain physical applications. 

As has been pointed out before,13 14,39 the important contributions to the dielectric relaxation are therefore from the fastest modes. 

An alternative approach that was used in the past was to treat the photoelectrochemical cell as a single RC element and to interpret the frequency dispersion of the "capacitance" as indicative of a frequency dispersion of the dielectric constant. (5) In its simplest form the frequency dispersion obeys the Debye equation. (6) It can be shown that in this simple form the two approaches are formally equivalent (7) and the difference resides in the physical interpretation of modes of charge accumulation, their relaxation time, and the mechanism for dielectric relaxations. This ambiguity is not unique to liquid junction cells but extends to solid junctions where microscopic mechanisms for the dielectric relaxation such as the presence of deep traps were assumed. 

In the copolyamides under consideration, the dipoles that are responsible for the dielectric relaxations are associated with the C = 0 groups of the amide functions. Due to the quasi-conjugated character of the CO - NH bond, the amide group takes on a rigid plane conformation in such a way that the dielectric relaxations of copolyamides should correspond to motional modes that involve amide groups and not only the carbonyls, in contrast to what happens with the ester groups encountered in polyethylene fere-phthalalc (Sect. 4.1.2). 

Adachi K, Kotaka T (1993) Dielectric normal-mode relaxation. Prog Polym Sci 18(3) 585-622... 

Current applications have so far avoided these more detailed formulations of the dielectric relaxation, and the scheme of decomposition into collective modes is simplified to two terms only, which here we denote as fast and slow ... 

Our calculations show that to achieve good accuracy with Eqs. (4.233) and (4.234) in a wide range of temperature and frequency variations, it is necessary to retain at least five (odd k= 1, 3,..., 9) lower modes of the spectrum. We remark that the first three relaxational modes have once been evaluated both numerically [109] and analytically [82] in studies of dielectric relaxation in nematic liquid crystals, where the forms of the potential and of the basic equation coincide with those given by our Eqs. (4.224) and (4.225), respectively. 

Comparison of the dielectric and viscoelastic relaxation times, which, according to the above speculations, obey a simple relation rn = 3r, has attracted special attention of scholars (Watanabe et al. 1996 Ren et al. 2003). According to Watanabe et al. (1996), the ratio of the two longest relaxation times from alternative measurements is 2-3 for dilute solutions of polyisobu-tilene, while it is close to unity for undiluted (M 10Me) solutions. For undiluted polyisoprene and poly(d,/-lactic acid), it was found (Ren et al. 2003) that the relaxation time for the dielectric normal mode coincides approximately with the terminal viscoelastic relaxation time. This evidence is consistent with the above speculations and confirms that both dielectric and stress relaxation are closely related to motion of separate Kuhn s segments. However, there is a need in a more detailed theory experiment shows the existence of many relaxation times for both dielectric and viscoelastic relaxation, while the relaxation spectrum for the latter is much broader that for the former. 

Adachi K, Kotaka T (1993) Dielectric normal mode relaxation. Prog Polym Sci 18 585—622 Adelman SA, Freed KF (1977) Microscopic theory of polymer internal viscosity Mode coupling approximation for the Rouse model. J Chem Phys 67(4) 1380-1393 Aharoni SM (1983) On entanglements of flexible and rodlike polymers. Macromolecules 16(11) 1722-1728... 

Fig. 26. Temperature dependence of various properties of myoglobin crystals , frequency of the O-D band maximum (IR) —, dielectric relaxation time of water (schematic) ---—, Lamb-Mossbauer factor,/o, after subtracting the harmonic mode (sche-...

Since the reduced spectrum x"( ) clearly shows the low-ftequency Raman modes, we introduced a simple model to analyze the spectral profile of x"(.v) for obtaining the quantitative information. The model is composed of two damped harmonic oscillator modes and one Debye type relaxation mode (liquid water) or one Cole-Cole type relaxation mode (aqueous solution). Cole-Cole type relaxation is usually adopted in analyzing the dielectric relaxation. The formula of Cole-Cole type relaxation is represented as ... 

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