Sub-T relaxations

The strong sub-T relaxation observed for the 1,4-CHDM derived amorphous polyesters and copolyesters makes them though and high resistant to compared with other related polyesters (11). Specifically, PECT copolyesters display high impact strength, comparable to that of polycarbonate of bisphenol A. 

The effect of copolymer composition on free volume and gas permeability of PECT copolymers as well as PET and PCT homopolymers was studied by Hill et al. (97). The free volume was studied by positron annihilation lifetime spectroscopy (PALS) in order to determine the relative size and concentration of free volume cavities in the copolymers. The logarithm of the permeability to oxygen and carbon dioxide increased linearly with the %mol content of 1,4-CHDM units in the copolymer, which was in agreement with the free volume cavity size and relative concentration observed by PALS measurements. Light et al. (98) studied the effect of sub-T relaxations on the gas transport properties of PET, PCT and PECT polyesters. They observed that modification of PET with 1,4-CHDM increased the magnitude of the p-relaxation, as well as the diffusion and solubility coefficients for oxygen and CO. ... 

Several studies on thin polymer films also indicated a sub-T Arrhenius-type relaxation process, which was related to the motion within a distinct surface layer of higher mobility or to increased heterogeneity [35, 44, 63, 64], yielding Ea 100 kJ/mol [44] and Ea = 185 3 kJ/mol [14]. Lateral force microscopy measurements on thin PS films [63] found a thickness dependent surface y -relax-ation process, with Ea = 55 kJ/mol for a 65 nm thick film. Fast sub-T -relaxations at surfaces of thin polymer films were measured by AFM, including the relaxation of... 

To develop an understanding of the sub-T relaxational processes of PSF and the nature of molecular motions involved, new forced torsional dynamic medianical data for PSF samples with well-controlled thermal histories were studied. To assist in the assignment of molecular motions, geometry optimized CNDO/2 (Complete Neglect of Differential Overlap) and molecular orbital (MO) calculations of model compounds were used to predict energy barriers to rotation. These energy barriers are compared to the activation energies determined from the dynamic mechanical data for each relaxation. Details of the CNDO/2 and molecular mechanics techniques used may be found elsewhere. 

Reorientations produce characteristic maxima in the relaxation rate, which may be different for the various symmetry species of CD4. The measured relaxation rates exhibit dependence on two time constants at low temperatures, but also double maxima for both relaxation rates. We assume that molecules may move over some places (adsorption sites) on the cage walls and experience different local potentials. Under the assumption of large tunnelling splittings the T and (A+E) sub-systems relax at different rates. In the first step of calculation the effect of exchange between the different places was considered. Comparison with experimental data led to the conclusion that we have to include also a new relaxation process, namely the contribution from an external electric field gradient. It is finally quite understandable to expect that such effect appears when CD4 moves in the vicinity of a Na+ ion. 

Results presented in Fig. 13.8 could have been interpreted as an effect of crosslink density on toughening. But this is an incorrect concept, because crosslink density can be increased by the use of a low-molar-mass aliphatic diepoxide. This would decrease the matrix Tg and increase its toughenabil-ity, in spite of the increase in crosslink density. But also, it may be stated that at the same Tg — T, other factors related to the chemical structure, such as sub-Tg relaxations, will play a role on toughening mechanisms. 

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. 

Landry and Henrichs [63] applied dynamic mechanical spectroscopy and H NMR to investigate sub-T motion in polycarbonate(PC)/PMMA and PC/poly(cyclohexylene dimethylene terephthalate)(PCHDMT). Examination of H NMR spectra and relaxation times led them to conclude that local... 

Figure 6. Percent stress relaxation of quenched Fiberite 934 epoxy resins as a function of sub-T annealing time ...

Glass transition temperature Nominal relaxation time at Tg Relaxation time of sub-T motion at Tg... 

Poly(p-phenylene sulfide) (PPS) (T 558 K) exhibits only weak sub-Tg relaxational processes. Dynamic-mechanical data [68,70] suggest a low-temperature (5)... 

Fig. 2.29 ( ). In the same figure are shown the Rouse relaxation times, tr (a), and the sub-Rouse relaxation times, t r (o), obtained from the peaks of tan (5 in Fig. 2.28. The dashed and dotted curves drawn through them are fits to tr and Tsr data produced by using the WLF equation. The two vertical arrows at T = Ta,sR and T = rsR,R divide the temperature into three regimes, I, II, and III. In regime I, the mechanical responses obtained by measurements of creep compliance [210] or stress relaxation [2] are mainly in the range /g < J(t) < 10 Pa and hence contributed by the local segmental relaxation. Thus it is appropriate to fit the creep data in regime I to Eq. (2.33) with 1 — = 0.55 to determine t . Shift factors aj used for time-...

The plot of the influence of modifying the frequency of analysis / versus the reciprocal of the peak temperatures of E" or tan d, for all experiments at all frequencies, displays different behaviors for sub-T transitions and the glass-rubber relaxation, as shown in Figure 12.4. Typically, a linear behavior is found for sub-T transitions, which can be analyzed using an Arrhenius model (Eq. (12.7)), from which the apparent activation energy Ea can be obtained, as shown in Eq. (12.8), where Tq is a time reference scale (in seconds), and R is the ideal gas constant (8.31JK mor ). 

Figure 12.4 Arrhenius plots for sub-T (fitted to Arrhenius equation) and glass—rubber relaxation (fitted to VFTH equation).

As one can see in Figure 16, where two fit functions are included, our ansatz for Pi(t) can describe the data very well, except for the sub-picosecond vibra-tionally dynamics, which, however, has a negligible contribution to the spin-lattice relaxation time. From this information, we can then calculate the T times for different positions along the chain. 

Figure 8.2.10 (A) Pulse sequence used for selective excitation of each of the four samples in turn. The RF pulses are frequency-selective and applied at different resonant offsets via phase modulation in the time domain. (B) Normal 1H spectrum of (a) the four samples, and the resulting sub-spectra of 0.5 M (b) 1-propanol, (c) 2-propanol, (d) acetic acid and (e) ethanol in D2O. Since the four spectra are acquired within the relaxation time 77 eff, which is typically set to be3Ti, there is an increase in efficiency by a factor of four. Reprinted with permission from Hou, T., Smith, J., MacNamara, E., Macnaughton, M. and Raftery, D., Anal. Chem., 73, 2541-2546 (2001). Copyright (2001) American Chemical Society...

Another recent study makes use of the participation of the T2 state in the S - TISC process in anthracene [31]. 1,3-Octadiene was used to intercept some of the T2 states before they relaxed to Tx and the decrease in 7, yield was used to estimate the T2 lifetime. Further, this study compensated for the effects of static and time-dependent quenching that comes into play at the relatively large quencher concentrations that are required when quenching sub-nanosecond-lifetime transients. The lifetimes obtained (given in Table 5) were significantly less than previously estimated from other quenching studies and are in line with the lifetimes implied from the T-T fluorescence quantum yields discussed above. 

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. 

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