Amorphous relaxation spectrum

Fig. 23. (a) Partially relaxed spectrum of the a-methylene carbon at 0 °C, obtained as a tt/2 single pulse sequence with = 0.8 s, and (b) transversally relaxed spectrum for 600 ps and (c) difference spectrum obtained by subtracting (b) from (a). Spectrum (a) represent all noncrystalline contribution and (b) and (c) represent the contributions of the amorphous and crystalline-amorphous interphases, respectively... 

Spectrum (a) shows the DD/MAS 13C NMR spectrum of the a-methylene carbon that was obtained by a single pulse sequence with a repetition time of 0.8 s. This is 0.8 s is longer than 5 times the Tic of the noncrystalline component and much shorter than Tic of the crystalline component (cf. Table 10). Hence, this spectrum represents the contribution from the noncrystalline component that consists of amorphous and crystalline-amorphous interphases. Spectrum (b) is a partially relaxed spectrum transversely for 600 ps. Since 600 ps is much longer... 

The crystalline phase affects the viscoelastic dynamic functions describing the glass-rubber relaxation. For example, the location of this absorption in the relaxation spectrum is displaced with respect to that of the amorphous polymer and greatly broadened. Consequently, the perturbing effects of crystal entities in dynamic experiments propagate throughout the amorphous fraction. The empirical Boyer-Beaman law (32)... 

The (3 relaxation in polyethylene, which is most prominent in the low-crystallinity LDPE, is associated with the amorphous regions and almost certainly corresponds to what would be a glass transition in an amorphous polymer a diiference in its position in mechanical and dielectric spectra is therefore not surprising. The a relaxation, as discussed in section 7.6.3, is associated with helical jumps in the crystalline regions and, provided that the lamellar thickness is reasonably uniform, might be expected to correspond to a fairly well-defined relaxation time and to a narrow peak in the relaxation spectrum. The dielectric peak is indeed quite narrow, because the rotation of the dipoles in the crystalline regions is the major contribu-... 

Some secondary relaxations in amorphous polymers have fundamental implications for the dynamics of the glass transition. There are several characteristics of this class of p-relaxations in polymeric as well as in nonpolymeric glass-formers. One characteristic is the tendency of the p-relaxation spectrum to merge into the... 

In the introductory section on amorphous polymers (Section 7.1.1), we considered the relaxation spectrum of amorphous polymers and noted that it was quite complex. The normal mode theories, now to be discussed, attempt to predict the relaxation spectrum for amorphous polymers, as well as the time-temperature equivalence. 

In the range of time or frequency where the mecheinical response of an amorphous polymer varies from that of a soft rubber to that of a hard glass, the relaxation spectrum (which determines time or frequency dependence) has been obtained experimentally for about two dozen polymers Its form depends somewhat on chemical structure, but these relations are still not well understood. At the low frequency or long time end, it can be approximated by the Rouse spectrum and a match here can furnish values of the monomeric friction coefficient, a measure of the location of the transition zone on the time or frequency scale. 

As a liquid is cooled at a finite rate, the relaxation time spectrum will shift to longer times and a temperature region will eventually be reached where the sample is no longer in volume equilibrium. If the sample continues to be cooled at this rate it will become a glass. A glass is a nonequilibrium, mechanically unstable amorphous solid. If the sample is held at a fixed temperature near Tg the volume will relax towards its equilibrium value. In this section we will restrict our attention to equilibrium liquids at temperatures near... 

Phase structure. It was confirmed in the previous section that the bulk iPP crystal consists of three phases the crystalline, noncrystalline amorphous phase and crystalline-amorphous interphase. Hence, it is also assumed that the bulk sPP crystal forms a three-phase structure in a similar manner. The question here is whether the sPP crystal involves such a phase structure in forming a gel or not In order to study this problem, we have analyzed 13C NMR spectra of the sPP gel. The noncrystalline contributions to each resonance of CH2, CH and CH3 carbons in the DD/MAS 13C NMR spectrum of the gel can be seen, as indicated by the arrows in Fig. 27, where their assignment as noncrystalline resonances was confirmed by the spin-lattice and spin-spin relaxation times as described above with relation to the results in Table 13. We carried out the line-decomposition analysis of the resonance lines of the methine and methyl carbons, since these resonances are most pertinent for the present purpose because of the simplicity of the spectral shape. 

On the other hand, in the solid-state high resolution 13C NMR, elementary line shape of each phase could be plausibly determined using magnetic relaxation phenomenon generally for crystalline polymers. When the amorphous phase is in a glassy state, such as isotactic or syndiotactic polypropylene at room temperature, the determination of the elementary line shapes of the amorphous and crystalline-amorphous interphases was not so easy because of the very broad line width of both the elementary line shapes. However, the line-decomposition analysis could plausibly be carried out referring to that at higher temperatures where the amorphous phase is in the rubbery state. Thus, the component analysis of the spectrum could be performed and the information about each phase structure such as the mass fraction, molecular conformation and mobility could be obtained for various polymers, whose character differs widely. 

FID contains information about the chemical environment of each nucleus. The curve-fitting for the observed FIDs gives the individual spin-spin relaxation characteristics in different phases crystalline, amorphous and interfacial.4-9 Such a resolution into several components has been long attempted on a broadline spectrum of solid PE.10-13 These results will reflect the sample morphologies. 

Process 1 The early stage of heating causes the relaxation shift of the interfacial chains into amorphous, which leads to the decrease in integral intensity (crystallinity). However, the residual crystalline molecules inside the lamellae still maintain their hindered molecular motion thus, the integral width of the spectrum exhibits a constant level. 

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