Relaxation time map

Figure 8. Example of microwave conductivity transient map PMC relaxation time map taken from a 20- m thin silicon wafer onto which 11 droplets of zeolith suspension were deposited and dried. Reduced lifetimes are clearly observed in the region of droplets. For color version please see color plates opposite this page.

The response from the water and hydrocarbon can be distinguished by measuring the distributions of the diffusion coefficients simultaneously with the distributions of the relaxation times. The resulting distributions are displayed on a two-dimensional diffusion coefficient-relaxation time map and the distributions for... 

The spin-lattice relaxation time map (discussed in Section II.A.2) yields information about the spatial distribution of mean pore size within a given image pixel. Lighter shades in the image correspond to larger mean pore size. Even at this coarse... 

In an investigation of the spin-density (voidage) and spin-lattice relaxation time maps of many pellets, it was found that it was the heterogeneity in pore size, as characterized by the fractal dimension of the Ti map, that was consistent between images of pellets drawn from the same batch 58). The fractal dimensional of these images identifies a constant perimeter-area relationship for clusters of pixels of... 

Here mass transport is of minor importance compared to the changes in relaxation times induced by phase changes such as crystallization of water or lipid, phase separation, gelation and/or macromolecule aggregation and denatur-ation. Since relaxation times are sensitive to temperature, relaxation time maps might also be used to follow temperature changes and heat transport. 

The results are discussed with relation to the relaxation time map. The distribution of Tg in a thin film is discussed in Sect. 6 for multilayered thin films utilizing isotope labeling by neutron reflectivity. Concluding remarks are given in Sect. 7. 

Is the decrease in activation energy sufficient to realize the existence of a crossing point in the relaxation time map If only the change of activation energy occurred, the crossing point in relaxation time map would be realized at extremely high temperature... 

Fig. 24 Relaxation time map of bulk PMPS and PMPS films of different thicknesses confined to nanoporous glass, as observed with dielectric spectroscopy, thermal analysis, and INS [60]...

Fig. 27 Relaxation time map for PS thin films, used to explain the film thickness dependence of Tg. Thin film 2 is thinner than thin film 1.

INS results and ellipsometry results seem to be explained using the schematic sketch of the relaxation time map. INS measurements with different energy resolutions can serve as a self-check for the relaxation time map, and an increase in Tg would be expected with lowering the energy resolution for same sample. Returning to Fig. 22, it was confirmed that Tg increased with lowering energy resolution hence, the schematically prepared relaxation time map is consistent with our results. 

In order to construct a more reliable relaxation time map quantitatively, complementary use of other methods like dielectric relaxation measurements and INS measurements with different energy resolutions are still needed. 

One of the fruitful results of the extensive studies on dynamics of glass-forming materials near Tg in the last decade is relaxation time maps of some glass-form-... 

The characteristic times t of PB determined by many experimental methods are plotted in a relaxation time map (Fig. 9), where 1/ris plotted vs inverse temperature 1/r. This map was first reported by Rossler et al. [84] to summarize the characteristic features of the dynamics of glass-forming materials. 

Fig.9. Relaxation time map of polybutadiene observed with various kinds of methods. Quasielastic neutron scattering (O, ) [32,79], neutron spin echo ( ) [80,82], viscosity ( ) [100],2h NMR(1) [99]...

Richter et al. carried out neutron spin echo measurements at the minimum position of S(Q) on the same polymer (PB) as that described above [82]. The intermediate scattering functions were described by a stretched exponential function as well, but could not be scaled to a master curve using a shift factor a-j. The relaxation times extracted from the observed stretched exponential functions are plotted in the relaxation time map in Fig. 9, from which it is seen that they deviate from the relaxation time of the a-process and the temperature dependence of Tjg is well described by the Arrhenius formula. It was confirmed that the process observed in PB at the minimum position Q ,j in S(Q) is the JG process. The fact that the JG process is observed at Q jjj suggests that the process is not a cooperative motion but an isolated one. 

In order to identify the E-process of PB, the characteristic times are plotted in a relaxation time map (Fig. 22) [ 130]. As mentioned in Sect. 4, the three processes - the a-process, the Johari-Goldstein process, and the fast process - are commonly observed in most glass-forming materials including polymers and small molecules. Therefore, these three processes should not be considered as special features of polymers but as common features of glass-forming materials. On the other hand, the E-process is not observed in the relaxation time map of OTP [84], suggesting that the E-process is characteristic of polymers. 

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