In the frequency domain, the dielectric -relaxation displays a broad and in the most cases symmetric loss peak with half widths of four to six decades [41]. The variety of molecular environments (structural heterogeneity) of the [Pg.20]

Various model available to fit the non-Debye relaxation profiles Width of loss pe also provide the measure of dynmnic heterc eneity Dielectric intensity/strength or a-peak decreases as crystallization progresses with time) Exact identity of molecular relaxor needs complementary analysis [Pg.457]

These relationships are known as the Debye formulae. The Debye process has a relaxation time distribution, which is symmetrical around /niax= niax/2n and has a full width at half-maximum of 1.14 decades in frequency for the dielectric loss. In most cases, the half width of measured loss peaks is much broader than the predicted by eqn [26] and in addition, their shapes are asymmetric and with a high-frequency tail. This is the non-Debye (or nonideal) relaxation behavior found in many glass formers. In the literature, several empirical model funaions, mostly generalization of the Debye function, have been developed and tested which are able to describe broadened and/or asymmetric loss peaks. Among these empirical model functions, the most important are the Kohlrausch-Williams-Watts (KWW), Cole-Cole (CC), Cole-Davidson (CD), and the Havriliak-Negami (HN) function. The HN function, with two shape parameters, is the most commonly used funaion in the frequency domain. [Pg.828]

As illustrated in some of these figures, all the a-loss peaks are well-fitted by the one-sided Fourier transform of the KWW over the main part of the dispersion. Thus, the experimental fact of constant dispersion at constant xa can be restated as the invariance of the fractional exponent KWW (or the coupling parameter n) at constant xa. In other words, xa and (or n) are co-invariants of changing thermodynamic conditions (T and P). If w is the full width at half-maximum of the dielectric loss peak normalized to that of an ideal Debye loss peak, there is an approximate relation between w and n given by n= 1.047(1 — w-1) [112], [Pg.508]

Thus, from both the DSC and the dielectric relaxation data cited earlier, the crossover of r y of PI in the HAPB of 35% and 20% PI with PtBS from VFT to Arrhenius dependences is not found at any temperature. This is the most direct proof that the confinement scenario is unreal. Arrese-lgor et al. (2010) admitted that the crossover predicted by the confinement scenario is not observed on Xaf of PI in the HAPB, but still maintained a vestige of confined dynamics by invoking the marked decrease of the intensity and increase of width as temperature decreases of the a-loss peak of PI in the 20% PI blend. [Pg.251]

This function is assumed to represent the superposition of many Debye functions [Eq. (6.5)] with various relaxation times (Bottcher and Bordewijk 1978). In terms of the Havriliak-Negami model, a complete description of a real (non-Debye) relaxation process in a polymer requires calculation of four parameters the dielectric strength (Ae), a parameter related to the relaxation time of the process at the temperature of the scan (xhn), and two shape parameters (0 < ttHN < 1 and 0 < Phn 1). The latter describe the width and the asymmetry of the loss peak, respectively, but lack a physical meaning. [Pg.505]

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