Relaxation glasses

Fig. 3.22 Frequency-dependent dynamic modulus G"(co) from a PE chain of M =800 kg/mol at 509 K. The solid line gives the reptation prediction of G co)-cor . The peak here may not be confused with the a-relaxation of the glass dynamics. It immediately follows from the Fourier transform of strongly depends on molecular weight. The glass relaxation...

The large range of viscosities for glasses is related to its structure. For example, compared to a highly mobile liquid like water, the relaxation time is much longer in glasses. Relaxation time is the time needed for the structural components to adjust to... 

In addition to the intrinsic lack of stationarity, many of the fluctuations in the glass relax so slowly that they appear to be static sources of light scattering on the time scale of the data collection. These static contributions will introduce a heterodyne component into the observed relaxation function. If the fraction of the light which is quasi-static exceeds 90%, then the observed relaxation function can be interpreted as a heterodyne case and an analysis can be carried out. However, it is not clear that this limit is ever reached in practice. Only 60% of the light was slowly relaxing at all in polystyrene. If at least 90% of the slowly relaxing part becomes quasi-static the heterodyne case will still apply to the observed part of the relaxation function. For PMMA and PEMA this is unlikely to be the case at any temperature near Tg. 

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. 

Consider a polymer is quenched from liquid to glass where the sample is annealed. During isothermal annealing, the number of holes is close to a conserved quantity. The local excess of number density of the quenched glass relaxes by spreading slowly over the entire region, and is governed by... 

During isothermal annealing, the frozen-in structure of quenched glass relaxes, and F(r) can be interpreted as the probability that holes have not reached their equilibrium states. The probability of a hole in the ith wave number state having reached equilibrium in a time interval t is (nt/n) (R/l) R/Ll. Thus, we write [12]... 

The a relaxation in both isotactic and syndiotactic PS is broader than that in atactic PS and the actual location of the peak is slightly shifted to higher temperature. The broadening effect was attributed to restrictions imposed by crystallites on the amorphous phases [12,24,25], Nakatani et al. [26] showed how the broadness of a syndiotactic PS sample can be represented by the overlapping of two glass relaxation processes arising from one purely amorphous component and the other amorphous component, which is under restrain owing to the proximity of crystallites. 

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. 

Arrhenius plots demonstrating the effect of temperature on lettuce seed aging rate (squares) and on molecular mobility calculated using the Adam-Gibbs model and heat capacity measurements (open circles) and from rotational motion using electron spin resonance measurements. Data are from Walters et al., (2004) (aging rate), Walters, (2004) (glass relaxation rates) and Buitink et al., (2000) (ESR measurements). 

Figure 6. Low-temperature glass relaxation for reaction specimens taken from mold and quenched in liquid nitrogen at various times during the polymerization. Key 1,1% reacted at 17 s 11, 54% reacted at 40 s 111, 84% reacted at 45 s IV, 95% reacted at 60 s V, 99% reacted at 240 s VI, post-cured 16 h at 140°C.

The molecular origin of vitrification is still a subject of scientific debate, but clues as to the motions involved in the glass relaxation process are provided by the following observations ... 

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

Results of dielectric studies of a series of nanocomposites based on a semiaromatic PA-1 ITIO with HAp helped to explain the structure-property relationships [Sender, 2008], For dry, neat PA-llTlO, a symmetric depolarization peak, detected by TSC near Tg measured by DSC, was attributed to dielectric dynamic glass relaxation. By DDS, two distinct high-temperature processes were distinguished when plotting the experimental data points versus HT. The dependence is displayed in Figure 13.2, where the two dashed lines show the complex dielectric permittivity fitted by the Havriliak-Negami equation ... 

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