Other Relaxation Mechanisms

Yj is the magnetogyric ratio of the observed nucleus, is the Bohr magneton, 

R is the distance between the observed nucleus and the paramagnetic centre, 

The time constants characterizing the rate of fluctuation of the interactions are affected by the rates of several processes, 

When the g-tensor no longer is isotropic and when the decay of the electronic longitudinal and transverse magnetizations no longer can be described by simple exponential decays, the nuclear relaxation in paramagnetic complexes becomes more complicated. A detailed account of these cases is considered outside the scope of the present review and the reader is referred to original articles on this subject [33, 34,35,36]. 

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Here, is the magnetization of spin i at thermal equilibrium, p,j is the direct, dipole-dipole relaxation between spins i and j, a-y is the crossrelaxation between spins i and j, and pf is the direct relaxation of spin i due to other relaxation mechanisms, including intermolecular dipolar interactions and paramagnetic relaxation by dissolved oxygen. Under experimental conditions so chosen that dipolar interactions constitute the dominant relaxation-mechanism, and intermolecular interactions have been minimized by sufficient dilution and degassing of the sample, the quantity pf in Eq. 3b becomes much smaller than the direct, intramolecular, dipolar interactions, that is. 

A deviation from the value of l.S indicates that other relaxation mechanisms contribute to the relaxation of spin i. The extent of intramolecular dipole-dipole interactions for spin i is given by ... 

When other relaxation mechanisms are involved, such as chemical-shift anisotropy or spin-rotation interactions, they cannot be separated by application of the foregoing relaxation theory. Then, the full density-matrix formalism should be employed. 

Two factors contribute to r K. One is the ratio of the magnetogryric ratios of the two different spins, and the other depends on relaxation mechanisms. Provided that the relaxation mechanism is purely dipole-dipole, may approach zero. Assuming that the dipolar mechanism is operational (no quadrupolar nuclei with I > 1/2 are present), r has the value ys/ 2y and is regarded as rimax. In the homonuclear case we have r max = 1/ 2. Usually one chooses nuclei where ys > y/ to ensure that the NOE is significant. For observation of 13C for instance, if the protons in the molecule are double irradiated, the ratio is 1.99 and 1 + r max equals approximately 3. To repeat a statement made above, proton broad-band irradiation enhances the intensity of the 13C nucleus, which otherwise has very low receptivity. 

The experiment is applied for the evaluation of C T, values. T, values are usually used to optimize insensitive C experiments, i.e. to adjust the length of the preparation time in other NMR experiments. To deduce structural information it is usual to interpret the dipolar part of the longitudinal relaxation time (T, ). To separate the dipolar contribution from the contributions of other relaxation mechanisms, it is necessary to perform further experiments (gated decoupling experiments) to evaluate the heteronuclear NOE values. T °° may be exploited in a qualitative way to differentiate between carbon nuclei in less or highly mobile molecular fragments. In a more detailed analysis reliable T, values can be used to describe the overall and internal motions of molecules. 

At the other limit of correlation times, Eqs. 8.6 and 8.9 show that for small tc, the denominators approach unity, and T2 = T,.The region of Tc< 1 /(o0 is often called the extreme narrowing condition. Note that we are considering here only dipolar interactions. Other relaxation mechanisms discussed subsequently may cause T2 to be smaller than 7), even under the extreme narrowing condition. 

When other relaxation mechanisms compete with dipolar relaxation (often the case, as we see subsequently), the magnitude of rj is reduced according the fraction of the total relaxation rate represented by the dipolar contribution ... 

In homo-dinuclear systems, such as two copper(ll) ions, no large effects are expected on the electron relaxation rates as the two metal ions relax at the same rate. However, some other relaxation mechanisms are operative, giving rise to faster electron relaxation rates (dementi and Luchinat, 1998). Consequently, nuclear relaxation is slower than in single copper(ll) systems. Several examples from model complexes are available (Brink et al., 1996 Murthy et al., 1997), as well as from a copper(ll)-substituted zinc enzyme, the aminopeptidase from Aeromonas proteolytica (Holz et al., 1998). In contrast, few NMR studies on native copper proteins containing two coupled copper (II) ions have been reported so far (Bubacco cf a/., 1999). 

The increase in linewidth between MePOZ/MePTZ to MePSZ is due to the spin-orbit coupling effect of Se. (In the case of MePTZ, the increased SOC with respect to MePOZ is not manifest in the linewidth, because other relaxation mechanisms dominate). 

For Si- H experiments the maximum NOE is — 2-52. (229) This occurs when the DD mechanism dominates the relaxation, and decreases when other relaxation mechanisms are prominent. In situations where the NOE is equal to — 1 no NMR is observed because, by definition, the signal is nulled into the baseline. 

With the advent of FT NMR and subsequently multinuclear spectrometers broadband proton decoupling has become widespread and is usually accompanied by a NOE which is often substantial [equation (16)] and can provide a useful gain in sensitivity. However, the dependence upon the competition between dipole-dipole and other relaxation mechanisms means that the NOE can vary from one site to another which militates against reliable intensity measurements. In these circumstances it is desirable to be able to quench the NOE, and this may also be necessary for nuclei with a negative magnetogyric ratio for which a really unfortunate combination of relaxation times can lead to zero signal intensity. 

Paramagnetic relaxation, when present, dominates over the other relaxation mechanisms due to the enormous magnitude of the electron spin as compared to the nuclear spins and the fast relaxation of the electron spin. Thus, it is important to ensure that no source of paramagnetic relaxation is present (in particular, molecular oxygen is a potential disturbance) when performing relaxation measurements [4]. 

Thus the rate of dipole-dipole relaxation is greater for longer Xc values which corresponds to high viscosity, t), and low temperature, T, and of course the converse is true for spin-rotation relaxation. The low viscosity of SCFs (and, frequently, use of higher temperatures) should clearly lead to enhanced spin-rotation and reduced dipole-dipole relaxation. In the studies of SCFs mentioned above and for in SC CO2 the decrease in relaxation time as temperature was increased showed that spin-rotation had become the dominant relaxation pathway (for all other relaxation mechanisms increasing temperature results in a lengthening of T whereas in the case of the much larger hexadecane, dipole-dipole relaxation remained dominant. In the latter study the authors point out that spin-rotation relaxation dominates for the C resonance in CO2. In the study of SC H2O by Lamb and Jonas [16] it was noted that under supercritical conditions the proton T values were not affected by addition of O2, unlike in normal solvents. 

For the individual interested in molecular motion, the important feature of spin-lattice relaxation (or other relaxation mechanisms) is the dependency on molecular motion to provide an efficient energy pathway for relaxation. Thus, molecular motions at the Larmor frequency for individual carbon atoms in a molecular framework may be mapped by Tj measurements. Since the frequency of molecular motion is temperature dependent, additional thermodynamic and kinetic information may be obtained by measuring Tj values for different carbons over a range of temperatures. In the paper by Lyerla and coworkers in this volume, measurements made for the first time over a... 

We now return to discussing some other relaxation mechanisms which involve random motions of molecules, namely the scalar relaxation of the first and second kinds, quadrupolar relaxation, chemical shift anisotropy relaxation, and spin rotation relaxation. 

Finally, we consider spin rotation interaction which is important only for small spherical molecules under conditions in which they are relatively free to rotate in the absence of other relaxation mechanisms. It is most common in gaseous samples (and it is indeed a major source of relaxation in molecular and atomic beam experiments) but exists also in liquids and even some solids. 

There are a couple of special methods of separating the contribution of dipolar relaxation in solution. One is by the NOE factor which is the fractional difference in the signal intensity of one spin with and without irradiation applied to another spin system. For a sample containing protons and carbon-13 in the motionally narrowed limit, this factor should be 2 if the relaxation takes place through the dipolar and the scalar interactions. Thus, the departure from 2 of the NOE factor is an indication of other relaxation mechanisms. Clearly, any other pairs of spin systems with NOE s can be treated this way, with appropriate limiting NOE factors. See, for example, Noggle and Shirmer listed in Appendix A for more details. 

As a conclusion, the whole temperature dependence of at the X-band cannot be ascribed to only the Q-I D diffusive motion or the model by [164], Denis and co-workers suggested more complicated relaxation mechanisms for ir ns-(CH), at the X-band [191], Thus, a complete interpretation of 7 at the X-band in the whole temperature range is still open to question. From the situation of the diffuse/lrap model one can predict TyJ behaviour below 100 K and at high frequencies, such as at X-band that the effect of the finite extension of the soliton severely suppresses the relaxation following the exp ( —l/F") rule [6,185], Such a suppression and the observation that oc w at the X-band and low temperatures [151] implies that far enough below 100 K the Q-l-D relaxation dies out and other relaxation mechanisms, for example via phonons, dominate the obseiwed relaxation. 

In practice, NOE enhancements will vary, with a twofold (200%) signal increase being the theoretical maximum enhancement for observation with decoupling. Other relaxation mechanisms besides that due to the dipolar interaction will diminish the observed enhancement, q. 

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