Temperature of the a relaxation

Figure 5 Summary plot of the transition temperatures (lower), inverse of the smectic layer spacing (middle), and temperature of the a relaxation (upper) of polybibenzoates as a function of the number of methylene units in the spacer Ti, [Ref. 9] T, , [Ref. 9] A I/d, [Ref. 7] T T , [Ref. 9] open symbols our results.

Analyzer on a sample of roll-oriented nylon tape. The temperature of the a-relaxation declines by about 90°C between dryness and saturation The varia-... 

Cold drawn specimens of nylon 6 have recently been investigated by Owen and Ward who measured static moduli between — 110 C and -t-20°C, and dynamic tan d between — 70°C and -l- 110 C in a vibrating reed instrument. As can be seen from Fig. 15 the pattern of anisotropy changes with temperature, there being a minimum in o and 90, near room temperature, around the draw ratios at which X-ray diffraction indicates a transformation from an form to a more stable y form. These structural changes, and the changes responsible for the rise in the temperature of the a relaxation with orientation, prevented a detailed understanding of the mechanical deformation processes. 

Table 10.2.6 reports the temperatures of the a-relaxation (measured at 10 KHz) and the P-relaxation (measured at 100 Hz) for the reference sample (bulk PMMA) and the different solution-cast films. 

Transitions. Samples containing 50 mol% TFE with ca 92% alternation were quenched in ice water or cooled slowly from the melt to minimize or maximize crystallinity, respectively (24). Internal motions were studied by dynamic mechanical and dielectric measurements, and by nuclear magnetic resonance. The dynamic mechanical behavior showed that the a relaxation occurs at 110°C in the quenched sample in the slowly cooled sample it is shifted to 135°C. The )3 relaxation appears near —25°C. The y relaxation at — 120°C in the quenched sample is reduced in peak height in the slowly cooled sample and shifted to a slightly higher temperature. The a and y relaxations reflect motions in the amorphous regions, whereas the fi relaxation occurs in the crystalline regions. The y relaxation at -120°C in dynamic mechanical measurements at 1 Hz appears at -35°C in dielectric measurements at 10 Hz. The temperature of the a relaxation varies from 145°C at 100 Hz to 170°C at 10 Hz. In the mechanical measurement it is 110°C. There is no evidence for relaxation in the dielectric data. 

The dependence of the relaxation temperatures on the level of absorbed water is known from dynamic mechanical studies (82,87,89) as well as dielectric studies (90). The temperature variations with sorbed moisture of the loss modulus peaks for the three relaxations are shown in Figure 38 (82). The test frequency for the three relaxations varies slightly but is around 1 Hz. The data indicate that the temperature of the a relaxation at a given frequency decreases by about 100°C between dryness and saturation. The relaxation is also shifted to lower temperatures and higher frequencies by absorbed water, while the temperature of the y relaxation is only slightly affected, shifting somewhat to lower temperatures and higher frequencies. 

Figure 20 Temperature dependence of the a-relaxation time scale for PB. The time is defined as the time it takes for the incoherent (circles) or coherent (squares) intermediate scattering function at a momentum transfer given by the position of the amorphous halo (q — 1.4A-1) to decay to a value of 0.3. The full line is a fit using a VF law with the Vogel-Fulcher temperature T0 fixed to a value obtained from the temperature dependence of the dielectric a relaxation in PB. The dashed line is a superposition of two Arrhenius laws (see text).

Fig. 4.8 Temperature dependence of the dielectric characteristic times obtained for PB for the a-relaxation (empty triangle) for the r -relaxation (empty diamond), and for the contribution of the -relaxation modified by the presence of the a-relaxation (filled diamond). They have been obtained assuming the a- and -processes as statistically independent. The Arrhenius law shows the extrapolation of the temperature behaviour of the -relaxation. The solid line through points shows the temperature behaviour of the time-scale associated to the viscosity. The dotted line corresponds to the temperature dependence of the characteristic timescale for the main peak. (Reprinted with permission from [133]. Copyright 1996 The American Physical Society)...

Fig. 4.9 Temperature dependence of the characteristic time of the a-relaxation in PIB as measured by dielectric spectroscopy (defined as (2nf ) ) (empty diamond) and of the shift factor obtained from the NSE spectra at Qmax=l-0 (filled square). The different lines show the temperature laws proposed by Tormala [135] from spectroscopic data (dashed-dotted), by Ferry [34] from compliance data (solid) and by Dejean de la Batie et al. from NMR data (dotted) [136]. (Reprinted with permission from [125]. Copyright 1998 American Chemical Society)...

Fig. 4.15 Momentum transfer (Q)-dependence of the characteristic time r(Q) of the a-relaxation obtained from the slow decay of the incoherent intermediate scattering function of the main chain protons in PI (O) (MD-simulations). The solid lines through the points show the Q-dependencies of z(Q) indicated. The estimated error bars are shown for two Q-values. The Q-dependence of the value of the non-Gaussian parameter at r(Q) is also included (filled triangle) as well as the static structure factor S(Q) on the linear scale in arbitrary units. The horizontal shadowed area marks the range of the characteristic times t mr- The values of the structural relaxation time and are indicated by the dashed-dotted and dotted lines, respectively (see the text for the definitions of the timescales). The temperature is 363 K in all cases. (Reprinted with permission from [105]. Copyright 2002 The American Physical Society)...

It is noteworthy that the neutron work in the merging region, which demonstrated the statistical independence of a- and j8-relaxations, also opened a new approach for a better understanding of results from dielectric spectroscopy on polymers. For the dielectric response such an approach was in fact proposed by G. Wilhams a long time ago [200] and only recently has been quantitatively tested [133,201-203]. As for the density fluctuations that are seen by the neutrons, it is assumed that the polarization is partially relaxed via local motions, which conform to the jS-relaxation. While the dipoles are participating in these motions, they are surrounded by temporary local environments. The decaying from these local environments is what we call the a-process. This causes the subsequent total relaxation of the polarization. Note that as the atoms in the density fluctuations, all dipoles participate at the same time in both relaxation processes. An important success of this attempt was its application to PB dielectric results [133] allowing the isolation of the a-relaxation contribution from that of the j0-processes in the dielectric response. Only in this way could the universality of the a-process be proven for dielectric results - the deduced temperature dependence of the timescale for the a-relaxation follows that observed for the structural relaxation (dynamic structure factor at Q ax) and also for the timescale associated with the viscosity (see Fig. 4.8). This feature remains masked if one identifies the main peak of the dielectric susceptibility with the a-relaxation. 

With the exception of local main-chain motions, the above-mentioned types of molecular motions have been investigated on a series of hydrophilic polymethacrylates and polyacrylates by means of dynamic mechanical measurements carried out with a torsional pendulum. For this purpose, the constitution of polymethacrylates was systematically altered and correlated with the dynamic mechanical response spectra. It was established for a series of copolymers of poly(2-hydroxyethyl methacrylate) that the temperature of the y relaxation (140 K 1 Hz), assigned to the motion of 2-hydroxyethyl... 

The parameters for P4tBCHM are summarized in Table 2.6 The temperature dependence of the a relaxation in the frequency domain can be conveniently analyzed by means of the Vogel-Fulcher-Tamman-Hesse (VFTH) equation [88-90] which was empirically formulated as ... 

The relaxation process associated with the dynamic glass transition, the a relaxation, and the P relaxation, as a shoulder of the a relaxation can be observed in all these figures. At low temperatures another relaxation labeled as y relaxation can be observed. In the case of PCHpM, the maximum of the y relaxation is well away from the temperature range. Heijboer and Pineri [36,57] have reported that the maximum for this polymer is at about 100 K for 1 Hz. In the case of PCHpMM and PCOcM, the y relaxation can be observed which may be analyzed by using the Fuoss-Kirkwood (F-K) equation ... 

Figures 2.31 and 2.32 show the dielectric permittivity and loss for poly(cyclobutyl methacrylate) (PCBuM) and poly(cyclobutylmethyl methacrylate) (see Scheme 2.5). In these figures the a relaxation is associated to the glass transition temperature and the p relaxation appear as a shoulder of the a relaxation.

On the other hand, as in the analysis of the previous systems the temperature dependence of the a relaxation follow the Vogel-Fulcher-Tamman-Hesse (VFTH) [88-90], The 7% values obtained are 337 5 and 274 5 for PBCHM and PBCHMM respectively. By this way and using equation (2.31) the m parameter obtained are 1579 and 1804 and the relative free volumes at Tg are 3.2 and 2.6% for PCBuM and PCHBMM, respectively, in good agreement with the free volume theory. 

The s parameter following this procedure is found to be between 0.91 and 0.95 and the conductivity increases x 10 x S cm-1. The activation energy, for this conductive process, obtained from the Arrhenius plot was equal to 100.5 kJ mol-1 (1.04 eV). As usual, the dielectric strength of the a -relaxation Ae = eoa — < coa, decreases when the temperature increases. The shape parameter for both parameters are nearly temperature independent. 

Figures 2.71 and 2.72 show conductivity contributions perhaps also overlapped by interfacial effects which are present for the peak at higher temperatures than that of the a relaxations. However there is not a clear correlation between the position of the peak and the length or shape of the side groups in these polymers.

As a general comment about the dynamic mechanical relaxational behavior of this polymer, the results are consistent with dielectric data [210] and with the fact that no glass transition phenomenon is observed, at least in the range of temperature studied. This is striking in an amorphous polymer. It is likely that the residual part of the molecule mechanically active above the temperature of the ft relaxation is only a small one, and this is the reason for the low loss observed in the a zone. 

Figures 2.82, 2.83, and 2.84 illustrate the dielectric permittivity and loss for PD-CBI, PDCHpI and PDCOI at different frequencies. The a relaxation associated to the glass transition is clearly observed in these Figures. The P relaxation is also observed as a shoulder in the low temperature side of the a relaxation. Moreover, Y and 5 relaxations are also present depending on the structure of the polymer. Particularly, for PDCHpI only a weak subglass activity is observed in the low range of temperatures.

The rate of the molecular motion responsible for the observed amorphous lineshape changes above -40° must be much less than or much greater than 1-10 kHz (T v) and much less or much greater than 100 MHz (T ) from -40 Zto 260°cl since no minimum was observed in the relaxation data. In addition, the rate must be >1-10 kHz to cause the observed lineshape changes. Therefore, the rate must be greater than 100 MHz. (At these temperatures, the rate of the a relaxation is <<1 Hz). 

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