Relaxation data for

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...

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... 

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. 

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...

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. 

To continue the investigation, carbon detected proton T relaxation data were also collected and were used to calculate proton T relaxation times. Similarly, 19F T measurements were also made. The calculated relaxation values are shown above each peak of interest in Fig. 10.25. A substantial difference is evident in the proton T relaxation times across the API peaks in both carbon spectra. Due to spin diffusion, the protons can exchange their signals with each other even when separated by as much as tens of nanometers. Since a potential API-excipient interaction would act on the molecular scale, spin diffusion occurs between the API and excipient molecules, and the protons therefore show a single, uniform relaxation time regardless of whether they are on the API or the excipients. On the other hand, in the case of a physical mixture, the molecules of API and excipients are well separated spatially, and so no bulk spin diffusion can occur. Two unique proton relaxation rates are then expected, one for the API and another for the excipients. This is evident in the carbon spectrum of the physical mixture shown on the bottom of Fig. 10.25. Comparing this reference to the relaxation data for the formulation, it is readily apparent that the formulation exhibits essentially one proton T1 relaxation time across the carbon spectrum. This therefore demonstrates that there is indeed an interaction between the drug substance and the excipients in the formulation. 

Figure 5.16 Typical stress relaxation data for concentrated charge dispersions. Two models are shown, one based on a model for the relaxation spectra (Equation 5.59) and one based on an extended exponential (Equation 5.51)...

Fig. 12.2 Summary of the, 5N relaxation data for the / ARK PH domain measured at 500 MHz (see Ref. [23]) a R, b R2, and c hetero-nuclear NOE versus protein sequence.

Gd3+ chelate compounds with bulk solvent waters. Table 8.2 lists r1 relaxivity data for the two Gd C60 derivatives under a variety of aqueous solution conditions. 

Also displayed in Table II are spin-lattice relaxation data for liquidlike (CH2) groups that were observable in DPMAS experiments. Both the dependence on temperature and the particular Ti values suggested rapid segmental motions within long runs of methylene groups, quite similar to the dynamic behavior reported for soft-segment CH2 s in synthetic polyesters (19). 

Relaxation data for water in highly pure 70-/ diameter NaX crystals are shown in Figure 6, before and after elutriation with water to separate the desired size fraction. Note the maxima in the three sets of T2 data and the decrease on raising the temperature further. This effect is caused... 

The decrease in the amount of complex with increasing temperature in Fig. 9 is qualitatively in accordance with the temperature effect on the complex formation shown in Figs. 7 and 8, except that the temperature effect appears even below 20 "C in Fig 5 while in Fig 9 the decrease in the amount of complex only begins at 20 °C. This exception may arise from the dependence of the stability of the complex on the soaking temperature. The stress relaxation data for these specimens measured in water, shown in Fig. 10, are useful to study the reason why the amount of complex begins to decrease at about 20 °C. The data in Fig. 10 were obtained under 20% extension and the same heating conditions as in Fig 9. Although the stress values are quite different between two specimens... 

Fig. 6. Proton Tj relaxation data for crosslinked polybutadiene samples with average number of repeat units per network chain 44 (A) and 14 (O), compared with the computed results from the modified BPP equation (assuming Gaussian distribution and the model based bn spin diffusion to locations of rapid spin-lattice relaxation) (reprinted from Ref.541 with permission)...

The adsorption and desorption kinetics of surfactants, such as food emulsifiers, can be measured by the stress relaxation method [4]. In this, a "clean" interface, devoid of surfactants, is first formed by rapidly expanding a new drop to the desired size and, then, this size is maintained and the capillary pressure is monitored. Figure 2 shows experimental relaxation data for a dodecane/ aq. Brij 58 surfactant solution interface, at a concentration below the CMC. An initial rapid relaxation process is followed by a slower relaxation prior to achieving the equilibrium IFT. Initially, the IFT is high, - close to the IFT between the pure solvents. Then, the tension decreases because surfactants diffuse to the interface and adsorb, eventually reaching the equilibrium value. The data provide key information about the diffusion and adsorption kinetics of the surfactants, such as emulsifiers or proteins. 

Consonni, R. and Cagliani, L. R. (2007). NMR relaxation data for quality characterization of Balsamic vinegar of Modena. Talanta 73,332-339. 

Figure 1.37 presents relaxation data for polycarbonate at various temperatures [8], Create a master curve at 25°C by graphically sliding the curves at the various temperatures horizontally until they line up. 

Spin-Lattice RelaxAtion Data for Alkali Metal Atoms ... 

The shift in the two tensors is expected to be effective for carbohydrate molecules bearing a number of polar groups and hydrogen-bonding centers. Hence, serious difficulty for quantitative analysis may arise if the molecule does not contain three or more nonequivalent C—H vectors that relax predominantly via the overall motion. If this fact is ignored, qualitative treatment may lead to an erroneous motional description. Thus, one should be very cautious in interpreting the relaxation data for overall motion, especially when discrepancies well outside the experimental error are observed for the T, values. When the relaxation times are nearly similar and within the experimental error, isotropic motion may be considered as a first approximation to the problem. 

Figure 2. Rotating-frame relaxation data for normal alkanes vs. temperature (9)...

Relaxation data for the methyl carbon could be measured only down to ca. -125°C below this temperature line broadening was too severe to obtain results. The near equal values observed for the Ti and Tip over much of the limited temperature interval is in accord with the methyl motion being on the high temperature side of the Ti-minimum. 

Further use of relaxation data, now studying the water and the ligand protons34 36, leads to an estimate of the outer sphere hydration of the lanthanides. We know there are no water molecules in the first coordination sphere of course. These outer sphere relaxation data for the different cations are proportional to susceptibilities and electron relaxation times and become very useful in the study of the inner sphere hydration of other complexes M(dipic) (H20)x and M(dipic)2(H20)y, see below. Note that there is no evidence of further association of the Ln(III) tris-dipicolinate complexes with small cations such as sodium ions. Later we shall show that these anions can bind to biological cationic surfaces and act as shift or relaxation probes. 

We can turn finally to the mono dipicolinate complexes. The same analysis as above shows that in solution the M(dipic) complexes are isostructural. The exact structure has been determined using shift and relaxation data as above, see Refs. 34—36. Knowledge of the relaxation data for both ligand and water protons and the known relaxation of the contribution to water relaxation from the outer sphere then permits calculation of the number of water molecules in M(dipic)(H20)n. We have shown that n = 6 for all the lanthanides. 

Table 3. I3C NMR chemical shift and relaxation data for thyroxine...

One of the most widely used tools to assess protein dynamics are different heteronuclear relaxation parameters. These are in intimate connection with internal dynamics on time scales ranging from picoseconds to milliseconds and there are many approaches to extract dynamical information from a wide range of relaxation data (for a thorough review see Ref. 1). Most commonly 15N relaxation is studied, but 13C and 2H relaxation are the prominent tools to characterize side-chain dynamics.70 Earliest applications utilized 15N Ti, T2 relaxation as well as heteronuclear H- N) NOE experiments to characterize N-H bond motions in the protein backbone.71 The vast majority of studies applied the so-called model-free approach to translate relaxation parameters into overall and internal mobility. Its name contrasts earlier methods where explicit motional models of the N-H vector were used, for example diffusion-in-a-cone or two- or three-site jump, etc. Unfortunately, we cannot obtain information about the actual type of motion of the bond. As reconciliation, the model-free approach yields motional parameters that can be interpreted in each of these motional models. There is a well-established protocol to determine the exact combination of parameters to invoke for each bond, starting from the simplest set to the most complex one until the one yielding satisfactory description is reached. The scheme, a manifestation of the principle of Occam s razor is shown in Table l.72... 

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