Relaxation solids, contributions

The complex structure of biomolecules is the main reason for their elaborate molecular dynamics that is very likely inhomogeneous across the molecule in both time scale and amplitude. The different relaxation processes contributing to relaxation in solid proteins were identified and relaxation became a popular tool for amino acids,solid... 

The reliable estimation of residual water in dried solids is of importance but is beset by several problems, mainly related to the shape and interpretation of DSC heating traces, as illustrated in Figure 11 for a typical aqueous mixture, maximally frozen, from which any relaxation enthalpy contribution has been removed by annealing." The drawn-out DSC heating trace represents the superposition of several distinct processes Tg of the mixture, the heat of dilution, produced by ice... 

Fig. 7 Reduced storage modulus [G ( )1 plotted on double logarithmic scales versus the reduced frequency cotq for a 3-D topologically-regular cubic (40 x 40 x 40) network cross-linked from Rouse chains of 20 beads each (solid line). Also shown are the contributions to the [G (ffl)] that come from intrachain relaxation (solid line with circles) and interchain relaxation (solid line with stars)...

In contrast to -conditions a large number of NSE results have been published for polymers in dilute good solvents [16,110,115-120]. For this case the theoretical coherent dynamic structure factor of the Zimm model is not available. However, the experimental spectra are quite well described by that derived for -conditions. For example, see Fig. 42a and 42b, where the spectra S(Q, t)/S(Q,0) for the system PS/d-toluene at 373 K are shown as a function of time t and of the scaling variable (Oz(Q)t)2/3. As in Fig. 40a, the solid lines in Fig. 42a result from a common fit with a single adjustable parameter. No contribution of Rouse dynamics, leading to a dynamic structure factor of combined Rouse-Zimm relaxation (see Table 1), can be detected in the spectra. Obviously, the line shape of the spectra is not influenced by the quality of the solvent. As before, the characteristic frequencies 2(Q) follow the Q3-power law, which is... 

The diverging longest relaxation time, Eq. 1-6, sets the upper limit of the integral. The solid (gel) contribution is represented by Ge. The crossover to any specific short-time behavior for A < A0 is neglected here, since we are mostly concerned with the long-time behavior. 

The presented approach loses its applicability when exchange becomes infrequent and CD4 localized. As in solids we have the dominating contribution from incoherent tunnelling to the relaxation at low temperatures. 

Fig. 30. Hydrogen spin lattice relaxation time T, in a-Si H against temperature for flake samples removed from their substrate (solid line) and for a-Si H on quartz substrates two weeks after deposition (triangles). The circle data points are for the quartz substrate samples ten months after deposition. The magnitude of the 40 K minimum of T, is inversely portional to the number of H2 molecules contributing to the relaxation process (Van-derheiden et al., 1987). 

Table 4.1. Various processes contributing to the spectral line broadening for local vibrations. Frequencies of collectivized local vibrations QK (solid arrows) are supposed to exceed phonon frequencies oiRq (dashed arrows) Ok > max oncq. For an extremely narrow band of local vibrations, diagrams A and B respectively refer to relaxation and dephasing processes, whereas diagrams C account for the case realizable only at the nonzero band width for local vibrations.

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)...

If the paramagnetic center is part of a solid matrix, the nature of the fluctuations in the electron nuclear dipolar coupling change, and the relaxation dispersion profile depends on the nature of the paramagnetic center and the trajectory of the nuclear spin in the vicinity of the paramagnetic center that is permitted by the spatial constraints of the matrix. The paramagnetic contribution to the relaxation equation rate constant may be generally written as... 

In the standard mathematical expressions for the contribution of quadrupolar relaxation to the relaxation rates of the quadrupolar nucleus (in nuclear magnetic resonance), rapid isotropic motion is assumed to occur. This behavior, in most cases, will not be true in the solid or liquid crystalline state ". ... 

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