Dielectric loss peaks, secondary

Figure 2. Secondary dielectric loss peaks (1 kHz) in cured I.

The dielectric loss behavior of both polyethylene s Y transi-tion and polycarbonate s 0-transltion was enhanced by the presence of unassociated water. The area under the associated loss peak was found to increase in direct proportion to the concentration of unassociated water. In addition a secondary dielectric loss peak associated with frozen clustered water occurred in polycarbonate about 40°C below Its g-transition. Liquid clustered water at... 

The dielectric loss peak of secondary relaxations is extremely broad due to the variety of molecular environments (structural heterogeneity) of the relaxing unit, and, consequently, a variety of energy barriers, being more or less symmetrical. 

By combining the results of several methods (dynamic mechanical, dielectric, NMR, etc.), it is usually possible to determine quite reliably the structural units whose motions give rise to secondary relaxations. If dynamic mechanical measurements alone are employed, the usual procedure is that the chemical constitution is systematically altered and correlated with the dynamic mechanical response spectra, i.e. with the temperature-dependence of the G" and G moduli. If the presence of a certain group in polymers is marked by the formation of a loss peak characterized by a certain temperature position, size and shape etc., then the conclusion may be drawn that the motional units responsible for the secondary relaxation are identical or related with that group. Naturally, the relations obtained in this way are empirical and qualitative. 

Figure 6. Master curve of the dielectric loss data of l,l -bis(p-methoxyphenyl)cyclohexane (BMPC). The spectra measured under pressure were shifted on the frequency scale to superpose with the a-loss peak at T = 248 K and ambient pressure. The secondary relaxation of BMPC is not a JG relaxation (its loss peak frequency is pressure-insensitive), and it is not temperature-pressure-superposable along with the a-loss peak.

Figure 39. Dielectric loss for PPG dimer at pressures (from right to left) of 67.6, 248.7, 335.7, 520, and 510 MPa. The last one was measured after 12 hours of aging. There is a pressure-independent secondary peak at 104 Hz, which exhibits a negligible response to aging.

In the previous subsection, we have provided conceptually the rationale and experimentally some data to justify the expectation that the primitive relaxation time To of the CM should correspond to the characteristic relaxation time of the Johari-Go Id stein (JG) secondary relaxation Xjg- Furthermore, it is clear from the CM relation, Ta = ( "to)1 1- , given before by Eq. 6 that To mimics Ta in behavior or vice versa. Thus, the same is expected to hold between Xjg and Ta. This expectation is confirmed in Section V from the properties of tjg- The JG relaxation exists in many glass-formers and hence there are plenty of experimental data to test the prediction, xjG T,P) xo(T,P). Broadband dielectric relaxation data collected over many decades of frequencies are best for carrying out the test. The fit of the a-loss peak by the one-sided Fourier transform of a Kohlrausch function [Eq. (1)] determines n and Ta, and together with tc 2 ps, To is calculated from Eq. 6... 

If the first scenario were real, the slower secondary relaxation should express its presence as an excess wing on high frequency side of the a- relaxation peak. To check this we superimposed dielectric loss spectra of octa-O-acetyl-lactose measured above and below Tg to that obtained at T=353 K. Next we fitted a master curve constructed in this way to the Kohlrausch-Williams-Watts function... 

However, it is difficult to interpret this in such a way. One can see that the coupling parameter n estimated for the a- relaxation peak of octa-O-acetyl-lactose is significant (it means that the distribution of a-relaxation times is quite broad). It implies that the separation between maxima of dielectric loss of the expected secondary relaxation and main structural relaxation peaks should be significant. Consequently, the p- mode should be clearly visible in the dielectric loss spectra. However, in the case of octa-O-acetyl-lactose the y- relaxation... 

However, it has to be pointed out that it is only an approximate calculation, because we did not consider intermolecular hydrogen bonds which surely also make the structure of lactose more rigid. In such a case the activation energy of the slower secondary relaxation should be comparable to that for the y-relaxation (Ea=44 kJ/mol). This may imply that the slower secondary relaxation seen in lactose may be undetectable in the case of acethyl derivative of this disaccharide, because maxima of both secondary relaxations can be too close to each other. In fact, the inspection of the dielectric loss spectra obtained for octa-0-acetyI-Iactose below its glass transition temperature (see Fig. 2) showed that there is only one secondary relaxation peak. However, a detailed analysis of the y- loss peak revealed that probably two secondary processes contribute to it. 

An enhanced dielectric loss maximum was observed at -85°C when a polysulfone sample which contained 0.76 wt. % unassociated water and no detectable level of clustered water (<0.01 wt. %) was run (Fig. 6, curve A). An apparent low temperature broadening of the dielectric loss dispersion was noted for another polysulfone specimen with 0.76 wt. % unassociated water and an additional 0.04 wt. % clustered water (Fig. 6, curve B). However, when a polysulfone sample which contained the same amount of unassociated water as the two prior samples but had 0.16 wt. % clustered water was analyzed, it had a significantly more intense loss peak centered near -105°C (Fig. 6, curve C). We believe that this shift in loss maximum and increase in loss intensity is caused by the development of an additional secondary loss peak about 20° below the 3-transition (Figure 6). In earlier work we had observed the same phenomenon in polycarbonate where the new loss peak occurred about 40 below its 3-transition as a separate loss peak. 

The dielectric strength. As, which is proportional to the area under the loss peak, is much lower for the secondary processes, relative to the a relaxation analysed in the next section. This is a common pattern foimd in both polymer materials and glass formers. The P secondary process is even more depleted in linear polymers that contain the dipole moment rigidly attached to the m chmn, such as polycarbonate [78-80] and poly(vinyl chloride) (the behaviour of this polymer was revisited in ref [81] where the secondary relaxation motions are considered as precursors of the a-relaxation motions). Polymers with flexible polar side-groups, like poly(n-alkyl methacrylate)s, constitute a special class where the P relaxation is rather intense due to some coupling vnth main chain motions. 

McCnun et al. (1967) have listed the various secondary relaxations observed in PMMA. The one that has been most widely studied is the p-relaxation of the COOCH3 ester side group. It has been studied extensively both by dielectric relaxation and by mechanical relaxation. We consider here only the latter mechanical relaxations, which are summarized in Fig. 5.10, where the relaxation information is plotted as either the temperature of the loss peak in dynamic experiments at constant frequency or as the frequency of the loss peak in experiments conducted at constant temperature. All results are plotted along the slanted P-line. The figure also shows on the left side a steep line that represents the a-relaxation. This should not have appeared on this kinetic plot, and its slope is too steep to show its characteristic curvature representing the WLF form of relaxation. It is included only to show the relative positions of the specific secondary relaxations against the a-relaxation. 

In addition to knowing the temperature shift factors, it is also necessary to know the actual value of ( t ) at some temperature. Dielectric relaxation studies often have the advantage that a frequency of maximum loss can be determined for both the primary and secondary process at the same temperature because e" can be measured over at least 10 decades. For PEMA there is not enough dielectric relaxation strength associated with the a process and the fi process has a maximum too near in frequency to accurately resolve both processes. Only a very broad peak is observed near Tg. Studies of the frequency dependence of the shear modulus in the rubbery state could be carried out, but there... 

Figures 3-5 that the dielectric relaxation again reveals only a single a relaxation for the mixtures. These are, however, noticeably broader than the a relaxation of the pure polymers. The temperatures of the loss maxima, when plotted (Figure 7) as a function of wu the weight fraction of PPO in the mixtures, do not display the smooth monotonic increase in T0 vs. Wi that was shown by both the Vibron and the DSC results. Instead, there is a pronounced increase in Tg above = 0.5 to give a sigmoid curve for this relation. Some reservations should be attached to this observation inasmuch as data for only three polyblend compositions are available nevertheless a qualitatively similar phenomenon is observed in the analysis of the intensity of the y peak (below). Further, if only the stronger maxima in the dynamical mechanical data are considered— i.e.y if the secondary peaks and shoulders which led to the identification of two phases are omitted—then a similar sigmoid curve is found. The significance of this observation is discussed later.

Dielectric permittivity and loss for both polymers under study can be observed on Figs. 2.17 and 2.18. In both figures a prominent peak corresponding to the dynamic glass transition temperature can be observed, which at low frequencies is overlapped by conductivity effects. Moreover, in both polymers a broad secondary peak is observed at about -50°C. This peak is more prominent in P2tBCHM which is in good... 

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