Relaxation rate table

The substrates of step 1 do not interact with the enzyme-bound manganese, as shown by the fact that they do not lower the enhanced eflFect of Mn on the relaxation rate of water 10, 11), The substrates of step 2 (pyruvate, oxalacetate, and a-ketobutyrate) are coordinated by the enzyme-bound Mn, as demonstrated indirectly by decreases in the water relaxation rates (Table I) 10, 11) and directly by enhancements of the relaxation rates of the carbon-bound protons of these substrates (Table... 

Figure 5 illustrates the stress relaxation of methylvinylsilicone vulcanizates containing ionic liquids. Addition of ionic liquids to the rubber caused the lower stress during the relaxation process. However, those stresses decreased more significantly for ionic liquids containing samples, which was reflected by relaxations rates (Table 3). The... 

Table 4.5-1 gives values for the fit parameters and the reorientational correlation times calculated from the dipolar relaxation rates. 

Table I reports the observed NMR linewidths for the H/3 protons of the coordinating cysteines in a series of iron-sulfur proteins with increasing nuclearity of the cluster, and in different oxidation states. We have attempted to rationalize the linewidths on the basis of the equations describing the Solomon and Curie contributions to the nuclear transverse relaxation rate [Eqs. (1) and (2)]. When dealing with polymetallic systems, the S value of the ground state has been used in the equations. When the ground state had S = 0, reference was made to the S of the first excited state and the results were scaled for the partial population of the state. In addition, in polymetallic systems it is also important to account for the fact that the orbitals of each iron atom contribute differently to the populated levels. For each level, the enhancement of nuclear relaxation induced by each iron is proportional to the square of the contribution of its orbitals (54). In practice, one has to calculate the following coefficient for each iron atom ...

Scheme 1.—Occurrence of Ring Protons Expected to Have a Major Influence on the Relaxation Rates (R,) of the Anomeric Protons (H-1) of Aldopyranoses and Derivatives (4-25, Table I) in the C, or C4, Conformation.

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. 

For a rigidly held, three-spin system, or when existing internal motion is very slow compared to the overall molecular tumbling, all relaxation methods appear to be adequate for structure determination, provided that the following assumptions are valid (a) relaxation occurs mainly through intramolecular, dipolar interactions between protons (b) the motion is isotropic and (c) differences in the relaxation rates between lines of a multiplet are negligibly small, that is, spins are weakly coupled. This simple case is demonstrated in Table V, which gives the calculated interproton distances for the bicycloheptanol derivative (52) of which H-1, -2, and -3 represent a typical example of a weakly coupled, isolated three-spin... 

Table 14. Representative values of relaxation rate constants for [Fe(6-Mepy)2(py)tren](C104)j doped into PSS ...

Stress-Jump Experiments. The results of stress-jump experiments for HM-HEC monolayers with various compositions are shown in Table II, where the relaxation rate constants, ctRT, were calcu-... 

The segmental mobility of the polymer in the monolayer is enhanced by the solvation of the hydrophobes with toluene (9) the relaxation rate constant at the toluene/aqueous interface was three times that at the air/aqueous interface, as shown by Experiments Numbers 1 and 2 in Table II. 

Their q-values, either calculated from the experimental conditions or chosen for best fit, and their corresponding relaxation rate constants, obtained from separate stress-jump experiments, are listed in Table III. 

The second and third relaxation processes were coupled, where the observed rate constants differed by a factor of 3 to 7 and the rate constant for each relaxation process varied linearly with the DNA concentration.112 This dependence is consistent with the mechanism shown in Scheme 2, where 1 binds to 2 different sites in DNA and an interconversion between the sites is mediated in a bimolecular reaction with a second DNA molecule. For such coupled kinetics, the sum and the product of the two relaxation rate constants are related to the individual rate constants shown in Scheme 2. Such an analysis led to the values for the dissociation rate constants from each binding site, one of the interconversion rate constants and the association rate constant for the site with slowest binding dynamics (Table 2).112 The dissociation rate constant from one of the sites was similar to the values that were determined assuming a 1 1 binding stoichiometry (Table 1). 

In addition to the use of quadrupolar splitting, the spin relaxation rate can also be used to calculate the specific surface area ratios for pulps beaten to different degrees and the results for an unbleached pulp agree closely and confirm the 250% increase in surface area measured by isotherm data (Table 5.4). 

Table 5.4 A comparison of specific surface area ratio calculated from quadrupole splitting (Aq), spin-lattice relaxation rate (Rf, half-height linewidth (Avj/2) and isotherm data for an unbleached linerboard pulp beaten to various degrees.

Table 1.2. Values of Relaxation Rate Constants (k) for Various Single Equilibria System k...

If in the relaxation systems listed in Table 1.2 one of the reactants A or B and one of the products C or D is in large excess, that is if pseudo first-order conditions obtain, the relaxation expression is identical with the rate law obtained starting from pure reactants (1.148). For conditions other than these however, the simplified treatment with relaxation conditions is very evident, as can be seen, for example, in the simple expression for the first-order relaxation rate constant for the A -I- B C -i- D scheme compared with the treatment starting from only A and B, and when pseudo first-order conditions cannot be imposed.""... 

As pointed out above, the RPA theory predicts that the dynamics of the respective homopolymers should be observed at high Q in the Rouse regime. While the experiment shows that the predicted Q dependencies are reproduced well by the data, the absolute values for the observed relaxation rates disagree with the predictions (see Table 6.2). In particular the observed Rouse factors for PE are considerably smaller than predicted, (Wf )expt=2xl0 s" compared to Wf pa=3.8x 10 A s at T=473 K. At low Q values, the two blocks display the same single chain dynamics. 

Table II reports the contact coupling constant for different aqua ion systems at room temperature. The contact coupling constant is a measure of the unpaired spin density delocalized at the coordinated protons. The values were calculated from the analysis of the contact contribution to the paramagnetic enhancements of relaxation rates in all cases where the correlation time for dipolar relaxation is dominated by x and Tig > x. In fact, in such cases the dispersion due to contact relaxation occurs earlier in frequency than the dispersion due to dipolar relaxation. In metalloproteins the contact contribution is usually negligible, even for metal ions characterized by a large contact contribution in aqua ion systems. This is due to the fact that the dipolar contribution is much larger because the correlation time increases by orders of magnitude, and x becomes longer than Tig. Under...

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