Amorphous Debye peak

The high-frequency (3, 7,. .. subsidiary peaks in amorphous polymers are characteristically very broad with a half-height width of several decades (compared with 1.14 decades for a single Debye relaxation process), although a good, linear Arrhenius plot is usually obtained, suggesting a non-co-operative mechanism. Figure 3.8 shows the Arrhenius plot for the /3-relaxation of poly(epichlorhydrin),... 

Careful investigations revealed that the VDOS varies as the square of the frequency below 10 cm for deoxyMb solutions, as predicted from a Debye model, but reveal significant deviations from Debye behavior at higher frequencies, reminiscent of the boson peak observed in amorphous solids. Interestingly, these deviations were not observed for deoxyMb crystals. 

The XRD pattern of pure gum Arabica powder specimen is shown in Figure 12.3. It shows the overall amorphous nature of gum Arabica. The intensity peak corresponds to 26 = 18.893° is the peak in Radial Distribution Function (RDF). The Debye-Scherrer equation given in Equation 12.2 is employed to compute coherent length ... 

Figure 12.11 shows the modulus spectra obtained from the data recorded by the impedance analyzer between the frequency range 5 Hz - 9.5 MHz, and the peak of the curve does not coincide to that of impedance spectra [21]. Therefore, it may be concluded that the dielectric response corresponds to the non-Debye theory of dielectric loss. This indicates the complete amorphous behaviour of powdered gum Arabica specimen. 

The width of the dielectric loss peak given by equation (9.28b) can be shown to be 1.14 decades (see problem 9.3). Experimentally, loss peaks are often much wider than this. A simple test of how well the Debye model fits in a particular case is to make a so-called Cole-Cole plot, in which s" is plotted against e. It is easy to show from equations (9.28) that the Debye model predicts that the points should lie on a semi-circle with centre at [(fis + oo)/2, 0] and radius (e — Soo)/2- Figure 9.3 shows an example of such a plot. The experimental points lie within the semi-circle, corresponding to a lower maximum loss than predicted by the Debye model and also to a wider loss peak. A simple explanation for this would be that, in an amorphous polymer, the various dipoles are constrained in a wide range of different ways, each leading to a different relaxation time r, so that the observed values of s and e" would be the averages of the values for each value of r (see problem 9.4). 

Amorphous and vitreous carbon The first attempt of modelling the structure of a-C vacuum-deposited films using the continuous network approach was made by Kakinoki et al (I960). Their experimental technique (electron diffraction, Smax 35 A ) yielded a carefully measured/(s) curve (Figure 2.31) and a RDF of high resolution which showed two well defined but rather broad peaks at r = 1.50 and r2 = 2.54 k. Using Debye s Eq. (2.2) the authors tried to match without success the whole measured I(s) function by a calculated curve for a spherically symmetrical array of atoms in which only these two interatomic distances were present. 

XRD is a fast and nondestructive test which is frequently used to characterise thermoset materials and their composites. Crystalline materials are characterised by sharp peaks, whereas amorphous materials show broad humps. Thus, the degree of crystallinity can be estimated. When a crystalline material such as clay is dispersed in a thermoset matrix, one can study the intercalation and exfoliation behaviour (see subsequent chapters). If the crystallites of the power are very small, the peaks of the pattern will be broadened. From this broadening one can determine an average crystallite size using the Debye-Scherrer equation ... 

Peak of a-process at Tg, post-Tg signal from rigid amorphous fraction Higher scatter of TW-TSDC peaks under a global peak indicates higher compositional heterogeneity Non-Debye decay functions (e.g., KWW) is inappropriate to describe the TSDC relaxation process measured in temperature scanning mode... 

In many cases - including amorphous polymers - the peaks in dielectric spectra ( " =J co)) are not symmetrical and are broader than predicted by the Debye model (Equation 1.7). To account for asymmetry and broadness of the spectra, modified equations characterized by the addition of exponential parameters to Equation 1.5 have been proposed. For example, the HavrUiak-N ami equation (Equation 1.8) contains two exponents, a and [4] ... 

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