Relaxation time distribution effects

Jaeger, F., Grohmann, E., and Schaumann, G. E. (2006). ll NMR relaxometry in natural humous soil samples Insights in microbial effects on relaxation time distributions. Plant Soil 280, 209-222. 

Dielectric spectroscopy was also used by the same group in order to study the local and global dynamics of the PI arm of the same miktoarm star samples [89]. Measurements were confined to the ordered state, where the dynamics of the PI chain tethered on PS cylinders were observed in different environments since in the SIB case the faster moving PB chains are tethered in the same point as the PI arm. The distribution of segmental relaxation times were broader for SI2 than SIB. The effect was less pronounced at higher temperatures. The PI normal mode time was found to be slower in SIB, when compared to SI2 although both arms had the same molecular weight. Additionally, the normal mode relaxation time distributions of the PI chains tethered to PS cylinders in the miktoarm samples were narrower than in P(S-h-I) systems of lamellar structure. 

The temperature dependence of Tj (Fig. 13) points to a noticeable effect of the nature of adsorbent (phenolic oligomer) on the properties of adsorbed water. Firstly, the value of Ti (1-1.2 s) is nearly half that of free water (in 0.5 1). Secondly, relaxation curves sharply differ in 20- and 400-oersted fields. In the 20-oersted field the dependence Ti = f (T) is stepwise and the steepest part is observed near temperatures corresponding to the phase transition water - ice . The authors suggest that the minimum observed between 0 to -2 °C is connected with the dispersion of the relaxation time distribution. In order to confirm this assumption a classical relaxation analysis using deuterated water and the temperature dependence of longitudinal relaxation time is required. 

Thus, the chain of transitions considered above is effectively reduced to exponential, Debye-like relaxation with the mean relaxation time (x). In other words, the concept of a relaxation time distribution implies Debye-like relaxation of a system. However, it is evident that the relaxation will become nonexponential, should a system be characterized by a complex susceptibility of, say, Cole-Cole type. 

A systematic study of the relaxation of rubbing induced birefringence in PS has been conducted. Extensive and clear experimental evidence have been foimd that show the absence of the physical aging effects in the relaxation of RIB, and the relaxation of RIB involves very small length scales. The RIB relaxation is then modeled by a relaxation times distribution function that depends only on temperature but not on thermal or strain history. An individual birefringence elements model has been proposed and a systematic way has been devised to extract the parameters in the model from specifically designed experiments, namely the Temperature Lag measurements and the Continuous Curve measurements. The results predicted by the model agree well with experiments. 

Chang et al. have compared the stress-relaxation behavior of three miscible blend systems, PS/PPO, PS/PVME, and PMMA/PEO (Chang et al. 1997), for compositions in which one of the components was always in excess. Eor PS/PPO and PS/PVME, the stress-relaxation rates were found to be faster for the blends in comparison with PS alone, whereas the opposite was tme for a PMMA/PEO blend when compared with pure PMMA. Two main effects were discussed packing density and concentration fluctuations. It was noted that for PS/PPO and PS/PVME, addition of the second component leads to a decrease in the packing density of the blend but this is not the case for PMMA/PEO. Concentration fluctuations in the blend, detected via changes in width of the stress-relaxation time distribution, may also be responsible for differences in mechanical response, and their contribution appeared to be particularly significant in the PS/PVME system. 

The effect of the change of the salt concentration on the relaxation time distribution at SDS/PEO 1 9 w/w, shown in Fig. 14, appears larger than may be expected from the change in the phase ctiagram. At both salt concentrations is composition is far beyond the saturation limit. The amplitudes of the scattering peaks should, however, dii tly reflect the relative amounts of material present as free micelles in the polymer-surfactant complex when the main peak areas are equal. 

Spin-lattice relaxation time distributions appeared to be useful to obtain information on crystal size, but they hi lighted the limitations of Ti measurements for the determination of polymorphism. Indeed, for the mixtures with a high tricaprin concentration, there were two well-separated peaks, with a wide difference between the maxima. Therefore, in this case, Ti measurements effectively determine polymorphism. On the other hand, there was only one peak for the 25-75 (w/w) mixture in spite of the presence of two different polymorphic forms as determined by X-Ray Diffraction. Thus determination of polymorphism was not possible here. Consequently, as determination of polymorphism through Ti measurements is based on crystal size, it is not possible to achieve this when crystals are of similar size. However, as p crystals are larger than a crystals, the latter situation rarely occurs. 

The intermolecular association of polymer-bound dodecyl groups is evidenced by an effect of a surfactant molecule added to polymer solutions. Hgure 7 compares relaxation time distributions for the copolymers with, X)d = 2.5 and 10 mol % at a 10.0 g/L polymer concentration in the presence of varying concentrations of n-dodecyl hexaoxyethylene glycol monc tiier (C12E6). In the cai of the copolymer with j >od =... 

The relaxation behavior of the PVC-copolymer (styrene-methyl-methacrylate-acrylonitryle) was studied by the dielectric method. The Cole-Cole parameters, characterizing the distribution of relaxation time (relaxation spectra) and its temperature dependence have been calculated (Figure 7.18). It is seen that with an increase of filler amount, the parameter of relaxation time distribution decreases, i.e., the broadening of the spectra occurs. These effects, similar to analogous effects described in Chapter 5 for filled polymers, are explained by the restriction of molecular mobility of alloy components in the surface layers and by their contribution to the total relaxation spectrum. 

Serghei, A., Tress, M., Kremer, F. Confinement effects on the relaxation time distribution of the dynamic glass transition in ultrathin polymer films. Macromolecules 39, 9385 (2006)... 

With crystalline plastics, the main effect of the crystallinity is to broaden the distribution of the relaxation times and extend the relaxation stress too much longer periods. This pattern holds true at both the higher and low extremes of crystallinity (Chapter 6). With some plastics, their degree of crystallinity can change during the course of a stress-relaxation test. This behavior tends to make the Boltzmann superposition principle difficult to apply. 

For all known cases of iron-sulfur proteins, J > 0, meaning that the system is antiferromagnetically coupled through the Fe-S-Fe moiety. Equation (4) produces a series of levels, each characterized by a total spin S, with an associated energy, which are populated according to the Boltzmann distribution. Note that for each S level there is in principle an electron relaxation time. For most purposes it is convenient to refer to an effective relaxation time for the whole cluster. 

---