Relaxation mechanism measurements

The isothermal curves of mechanical properties in Chap. 3 are actually master curves constructed on the basis of the principles described here. Note that the manipulations are formally similar to the superpositioning of isotherms for crystallization in Fig. 4.8b, except that the objective here is to connect rather than superimpose the segments. Figure 4.17 shows a set of stress relaxation moduli measured on polystyrene of molecular weight 1.83 X 10 . These moduli were measured over a relatively narrow range of readily accessible times and over the range of temperatures shown in Fig. 4.17. We shall leave as an assignment the construction of a master curve from these data (Problem 10). 

Dynamic mechanical measurements were made on PTEE samples saturated with various halocarbons (88). The peaks in loss modulus associated with the amorphous relaxation near —90°C and the crystalline relaxation near room temperature were not affected by these additives. An additional loss peak appeared near —30° C, and the modulus was reduced at all higher temperatures. The amorphous relaxation that appears as a peak in the loss compliance at 134°C is shifted to 45—70°C in the swollen samples. 

Transitions. Samples containing 50 mol % tetrafluoroethylene with ca 92% alternation were quenched in ice water or cooled slowly from the melt to minimise or maximize crystallinity, respectively (19). Internal motions were studied by dynamic mechanical and dielectric measurements, and by nuclear magnetic resonance. The dynamic mechanical behavior showed that the CC relaxation occurs at 110°C in the quenched sample in the slowly cooled sample it is shifted to 135°C. The P 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 CC and y relaxations reflect motions in the amorphous regions, whereas the P relaxation occurs in the crystalline regions. The y relaxation at — 120°C in dynamic mechanical measurements at 1 H2 appears at —35°C in dielectric measurements at 10 H2. The temperature of the CC relaxation varies from 145°C at 100 H2 to 170°C at 10 H2. In the mechanical measurement, it is 110°C. There is no evidence for relaxation in the dielectric data. 

A Relaxation time measurement in the solid (Al) in solution (A2). B Mechanical spectroscopy. C Variable-temperature NMR spectroscopy (coalescence temperature measurement). D Variable-temperature EPR spectroscopy... 

For polyatomic gases in porous media, however, the relaxation rate commonly decreases as the pore size decreases [18-19]. Given that the relaxation mechanism is entirely different, this result is not surprising. If collision frequency determines the Ti, then in pores whose dimensions are in the order of the typical mean free path of a gas, the additional gas-wall collisions should drastically alter the T,. For typical laboratory conditions, an increase in pressure (or collision frequency) causes a proportional lengthening of T1 so the change in T, from additional wall collisions should be a good measure of pore size. 

The shape of the curves for the dilational modulus (Figures 7 and 8) suggests a single relaxation mechanism, probably the unfolding of the demulsifier molecules at the interface. The frequency peak in the e"(f) plot is a measure of the characteristic relaxation time. A shorter relaxation time, by inducing faster film drainage, increases demulsification efficiency. 

The samples were cured with 0.2, 0.4, 0.8 and 1.6 wt.% dicu-myl peroxide. In this way, we obtained twelve different networks with great variations in relaxation Intensities. Dynamic mechanical measurements were performed In torsion in the linear region (deformations smaller than 5 %) with a mechanical spectrometer, using the parallel-plate geometry. The frequency ranged from 0.01 to 15 Hz and the temperature was usually between 300 and 435 K. 

When Wqi / Wq2 the magnetization recovery may appear close to singleexponential, but the time constant thereby obtained is misleading [50]. The measurement of 7) of quadrupolar nuclei under MAS conditions presents additional complications that have been discussed by comparison to static results in GaN [50]. The quadrupolar (two phonon Raman) relaxation mechanism is strongly temperature dependent, varying as T1 well below and T2 well above the Debye temperature [ 119]. It is also effective even in cases where the static NQCC is zero, as in an ideal ZB lattice, since displacements from equilibrium positions produce finite EFGs. 

The 113Cd Ti values estimated for the various peaks varied from 10 to 50 ms and obeyed the qualitative dependence upon 1/R6 (R = Mn-Cd distance) of the dipolar relaxation mechanism expected to be operative. The broad line widths were also shown to have significant contributions from the T2 relaxation induced by Mn++, with both dipolar and contact terms contributing. The 113Cd shifts of the peaks assigned to different shells were measured as a function of temperature, and observed to follow a linear 1/T dependence characteristic of the Curie-Weiss law, with slopes proportional to the transferred hyperfine interaction constant A. 

By now, water exchange has been studied on more than one hundred Gdm complexes with the help of 170 NMR, and the large body of data available has been reviewed recently (48). Variable temperature 170 transverse relaxation rate measurements provide the rate of the water exchange, whereas the mechanism can be assessed by determining the activation volume, AVt, from variable pressure 170 T2 measurements (49,50). The technique of 170 NMR has been described in detail (51). 

A variety of relaxation time studies have been performed on toluene. The choice of deuterated toluene avoids certain complicating factors which affect proton NMR studies, such as, dipolar or spin-spin couplings. The dominant relaxation mechanism is quadrupolar and the relaxation times are determined by the reorientation of the C-D bond vector. Relaxation times such as T, are sensitive to the motions of the solvent around the larmor frequency, which is on the order of 14 MHz in this study. T2 measurements may probe slower motions if the molecule undergoes slow and/or anisotropic motion. The relaxation time results presented in Figure 3 are significantly shorter than those found in bulk toluene solutions (18.19). In bulk toluene, the T and T2 values are equal above the melting temperature (1.2.). In this polymer system T2 < T indicative of slow and/or anisotropic reorientation. 

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