Relaxation data

Figure C3.5.10. Frequency-dependent vibronic relaxation data for pentacene (PTC) in naphthalene (N) crystals at 1.5 K. (a) Vibrational echoes are used to measure VER lifetimes (from [99]). The lifetimes are shorter in regime I, longer in regime II, and become shorter again in regime III. (b) Two-colour pump-probe experiments are used to measure vibrational cooling (return to the ground state) from [1021.

Analogous studies on dienophiles 5.1c and 5.1g in SDS and Zn(DS)2 lead to essentially the same conclusions. Figure 5.9 shows the relaxation data for 5.1g in Zn(DS)2 solutions. The corresponding data for 5.1c could not be measured due to solubility problems. Analogously, Figure 5.10 shows the relaxation data of 5.1c and 5.1g in SDS solutions. 

Fig. 49. Illustration of the time—temperature superposition principle as based on stress—relaxation data for polyisobutylene (299,300). To convert Pa to...

Molecular modeling is an indispensable tool in the determination of macromolecular structures from NMR data and in the interpretation of the data. Thus, state-of-the-art molecular dynamics simulations can reproduce relaxation data well [9,96] and supply a model of the motion in atomic detail. Qualitative aspects of correlated backbone motions can be understood from NMR structure ensembles [63]. Additional data, in particular residual dipolar couplings, improve the precision and accuracy of NMR structures qualitatively [12]. 

This is a stress relaxation problem and strictly speaking stress relaxation data should be used. However, for most purposes isometric curves obtained from the creep curves are sufficiently accurate. By considering the 1.5% isometric curve shown in Fig. 2.8 it may be seen that the initial stress is 16 MN/m2 and the stress after 1 week is 7 MN/m2. 

Usually, nuclear relaxation data for the study of reorientational motions of molecules and molecular segments are obtained for non-viscous liquids in the extreme narrowing region where the product of the resonance frequency and the reorientational correlation time is much less than unity [1, 3, 5]. The dipolar spin-lattice relaxation rate of nucleus i is then directly proportional to the reorientational correlation time p... 

Here, the J terms are the spectral densities with the resonance frequencies co of the and nuclei, respectively. It is now necessary to find an appropriate spectral density to describe the reorientational motions properly (cf [6, 7]). The simplest spectral density commonly used for interpretation of NMR relaxation data is the one introduced by Bloembergen, Purcell, and Pound [8]. 

Cole and Davidson s continuous distribution of correlation times [9] has found broad application in the interpretation of relaxation data of viscous liquids and glassy solids. The corresponding spectral density is ... 

Another way to describe deviations from the simple BPP spectral density is the so-called model-free approach of Lipari and Szabo [10]. This takes account of the reduction of the spectral density usually observed in NMR relaxation experiments. Although the model-free approach was first applied mainly to the interpretation of relaxation data of macromolecules, it is now also used for fast internal dynamics of small and middle-sized molecules. For very fast internal motions the spectral density is given by ... 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

Viscoelastic stress-relaxation data are usually presented in one of two ways. In the first, the stress manifested as a function of time. Families of such curves may be presented at each temperature of interest. Each curve representing the stress-relaxation behavior of the material at a different level of... 

The resulting data can then be presented as a series of curves much like the isometric stress curves in Fig. 2-27. A relaxation modulus similar to the creep modulus can also be derived from the relaxation data. It has been shown that using the creep modulus calculated from creep curves can approximate the decrease in load from stress relaxation. 

Predictions can be made on creep behavior based on creep and relaxation data. 

There is generally a less-pronounced curvature when creep and relaxation data are plotted log-log. Tliis facilitates extrapolation and is commonly practiced, particularly with creep modulus and creep-rupture data. 

Viscoelastic and rate theory To aid the designer the viscoelastic and rate theories can be used to predict long-term mechanical behavior from short-term creep and relaxation data. Plastic properties are generally affected by relatively small temperature changes or changes in the rate of loading application. 

Note that the term y in Eqs. 2-15 and 2-16 has a different significance than that in Eq. 2-14. In the first equation it is based on a concept of relaxation and in the others on the basis of creep. In the literature, these terms are respectively referred to as a relaxation time and a retardation time, leading for infinite elements in the deformation models to complex quantities known as relaxation and retardation functions. One of the principal accomplishments of viscoelastic theory is the correlation of these quantities analytically so that creep deformation can be predicted from relaxation data and relaxation data from creep deformation data. 

In computing ordinary short-term characteristics of plastics, the standard stress analysis formulas may be used. For predicting creep and stress-rupture behavior, the method will vary according to circumstances. In viscoelastic materials, relaxation data can be used in Eqs. 2-16 to 2-20 to predict creep deformations. In other cases the rate theory may be used. 

By the comparison of T1 relaxation data in solution and in the solid state it is realised that the relaxation time increases disproportionally when going from solution to... 

Table 2. 13C NMR chemical shifts and relaxation data T1 of cellulose acetate in solid state and a in acetone-d6 soution at 298 K. Spectrometer JEOL FX-200, frequency 50 MHz...

Table 3. Chemical shifts and relaxation data T1 for wetted cellulose and cellulose acetate (DS = 1.97).

De Pristo A. E., Rabitz H. Scaling theoretic deconvolution of bulk relaxation data state-to-state rates from pressure-broadening linewidths,... 

Relaxation data may be analyzed by two general methods a two-parameter, linear regression and a three-parameter, nonlinear, fitting procedure. " " The first method requires an accurate experimental determination of Mo, which is both difficult and time-consuming. Furthermore, the... 

The relaxation data for the anomeric protons of the polysaccharides (see Table II) lack utility, inasmuch as the / ,(ns) values are identical within experimental error. Obviously, the distribution of correlation times associated with backbone and side-chain motions, complex patterns of intramolecular interaction, and significant cross-relaxation and cross-correlation effects dramatically lessen the diagnostic potential of these relaxation rates. 

If all nuclei are assigned and the spectral parameters for the conformational analysis are extracted, a conformation is calculated - usually by distance geometry (DG) or restrained molecular dynamics calculations (rMD). A test for the quality of the conformation, obtained using the experimental restraints, is its stability in a free MD run, i.e. an MD without experimental restraints. In this case, explicit solvents have to be used in the MD calculation. An indication of more than one conformation in fast equilibrium can be found if only parts of the final structure are in agreement with experimental data [3]. Relaxation data and heteronuclear NOEs can also be used to elucidate internal dynamics, but this is beyond the scope of this article. 

Fig. 3.5.1 Spin-lattice relaxation data for (a) CF4 and (b) c-C4F8 gas as a function of pressure. The solid curve is the model prediction. Data for CF4 were measured at 181, 294 and 362 K. Small temperature variations were measured for each data point, and were...

Fig. 4.1.3 Intrinsic magnetization determined by the relaxation data corresponding to the selected voxel in the Bentheimer sample.

R. M. Kroeker, R. M. Henkelman 1986, (Analysis of biological NMR relaxation data with continuous distributions of relaxation-times),/. Mag. Reson. 69, 218. 

NMR provides one of the most powerful techniques for identification of unknown compounds based on high-resolution proton spectra (chemical shift type integration relative numbers) or 13C information (number of nonequivalent carbon atoms types of carbon number of protons at each C atom). Structural information may be obtained in subsequent steps from chemical shifts in single-pulse NMR experiments, homo- and heteronuclear spin-spin connectivities and corresponding coupling constants, from relaxation data such as NOEs, 7) s 7is, or from even more sophisticated 2D techniques. In most cases the presence of a NOE enhancement is all that is required to establish the stereochemistry at a particular centre [167]. For a proper description of the microstructure of a macromolecule NMR spectroscopy has now overtaken IR spectroscopy as the analytical tool in general use. 

The 50.31 MHz 13C NMR spectra of the chlorinated alkanes were recorded on a Varian XL-200 NMR spectrometer. The temperature for all measurements was 50 ° C. It was necessary to record 10 scans at each sampling point as the reduction proceeded. A delay of 30 s was employed between each scan. In order to verify the quantitative nature of the NMR data, carbon-13 Tj data were recorded for all materials using the standard 1800 - r -90 ° inversion-recovery sequence. Relaxation data were obtained on (n-Bu)3SnH, (n-Bu)3SnCl, DCP, TCH, pentane, and heptane under the same solvent and temperature conditions used in the reduction experiments. In addition, relaxation measurements were carried out on partially reduced (70%) samples of DCP and TCH in order to obtain T data on 2-chloropentane, 2,4-dichloroheptane, 2,6-dichloroheptane, 4-chloroheptane, and 2-chloroheptane. The results of these measurements are presented in Table II. In the NMR analysis of the chloroalkane reductions, we measured the intensity of carbon nuclei with T values such that a delay time of 30 s represents at least 3 Tj. The only exception to this is heptane where the shortest T[ is 12.3 s (delay = 2.5 ). However, the error generated would be less than 10%, and, in addition, heptane concentration can also be obtained by product difference measurements in the TCH reduction. Measurements of the nuclear Overhauser enhancement (NOE) for carbon nuclei in the model compounds indicate uniform and full enhancements for those nuclei used in the quantitative measurements. Table II also contains the chemical... 

For folded proteins, relaxation data are commonly interpreted within the framework of the model-free formalism, in which the dynamics are described by an overall rotational correlation time rm, an internal correlation time xe, and an order parameter. S 2 describing the amplitude of the internal motions (Lipari and Szabo, 1982a,b). Model-free analysis is popular because it describes molecular motions in terms of a set of intuitive physical parameters. However, the underlying assumptions of model-free analysis—that the molecule tumbles with a single isotropic correlation time and that internal motions are very much faster than overall tumbling—are of questionable validity for unfolded or partly folded proteins. Nevertheless, qualitative insights into the dynamics of unfolded states can be obtained by model-free analysis (Alexandrescu and Shortle, 1994 Buck etal., 1996 Farrow etal., 1995a). An extension of the model-free analysis to incorporate a spectral density function that assumes a distribution of correlation times on the nanosecond time scale has recently been reported (Buevich et al., 2001 Buevich and Baum, 1999) and better fits the experimental 15N relaxation data for an unfolded protein than does the conventional model-free approach. 

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