Sub-glass relaxations

The dielectric analysis of these systems show, that only one peak can be observed corresponding to the dynamic glass transition. The sub-glass relaxations are very small. 

Sub-glass relaxation phenomena are thermally activated processes that exhibit Arrhenius behavior,... 

Sub-glass relaxations for crystalline and amorphous polymers in the frequency domain are described by the empirical Fuoss-Kirkwood equation (35)... 

Sub-glass relaxations fit this equation. Plotting cosh [straight lines from whose slopes (= mEJPi) the evolution of the parameter m with the frequency of the isochrones can be evaluated. The Fuoss-Kirkwood equation also allows determination of the relaxation strength of sub-glass absorptions. 

Most crystalline polymers with metylenic groups in their structure and with a degree of crystallinity below 50% present a sub-glass relaxation whose intensity and location scarcely differ from those observed for the amorphous polymer in the glassy state. The temperature dependence of this relaxation follows Arrhenius behavior, and its activation energy is of the same order as that found for secondary processes in amorphous polymers. 

Sub-glass relaxations are thermally activated processes. Therefore, the temperature dependence of their relaxation times is Arrhenius-type,... 

Similarly, in Amorphous Pol5miers (qv) the drop in modulus accompanying sub-glass relaxations can have an important effect on engineering properties, particularly brittleness and impact resistance. This is discussed below in a section on impact behavior. 

DSC and DTA. They can be used to confirm suspicious glass transitions revealed by DSC and most important, they can further quantify molecular mobility associated with sub-glass transitions. For example, DSC analysis of poly (ethylene 2,6-naphthalene dicarboxylate) (PEN) only revealed the presence of a glass transition around 112 °C (Hardy et al., 2001). DMA analysis of the same sample, however, revealed two secondary relaxations below this glass transition (Hardy et al., 2001). In the case of humic materials, it is not uncommon for DSC to fail to detect clear thermal transitions due to their heterogeneous nature, which contributes to overlap/ broadening or washout of thermal transitions. As such,TMA and DMA represent powerful, complementary tools to DSC. 

Sub-glass (P) relaxations can be obtained in the frequency domain at T < Tg. In principle, a and P dispersions can be obtained in the frequency domain at temperatures slightly higher than the glass transition temperature. However, the low range of frequencies available renders it difficult to detect them by mechanical experiments. 

It is usual to classify the detected relaxation processes, at a fixed frequency, in order of decreasing temperature (or in order of increasing frequency for a fixed temperature). Thus, besides the a main relaxation described in the next section, the P relaxation is located at the highest temperatures, in comparison with the other sub-glass processes, respectively, y and 5 relaxations, with even more local mobility and shorter relaxation times. 

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