Linewidths, transverse

To extract information about xj from NMR data, the transverse relaxation time Tj may be used as well as the longitudinal time T. For gaseous nitrogen it was done first with Ti in [81] and confirmed later [82] when T was measured and used for the same goal. The NMR linewidth of 15N2 is the inverse of T2, and the theory, relating to Ti to x.1, is well known [39, 83]. For the case of diatomic and linear molecules the formula is... 

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 ...

Bell et al. (2002) investigated the relationship between water mobility as measured by oxygen-17 NMR (transverse relaxation rate obtained from linewidth at half-height) and chemical stability in glassy and rubbery polyvinylpyrrolidone (PVP) systems. Reported results suggest that water mobility in PVP model systems was not related to Tg. The study did not find a link between water mobility and reaction kinetics data (half-lives) for degradation of aspartame, loss of thiamin and glycine, and stability of invertase. 

In order to realize the extremely small linewidths, attainable because of the temporal coherence of induced emission, care must be taken to ensure that the threshold condition for induced oscillation is fulfilled for only one mode. The transverse modes can be eliminated by an appropriate choice of the cavity dimensions, introducing... 

If the spectrum involves only one resonance (or if linewidths do not allow for the separation of several resonances), a single experiment can be run with acquisition of the amplitude of each echo along the pulse train (for sensitivity enhancement, accumulations can be carried out). This experiment is especially valuable for determining the relative proportions of two species which differ by their transverse relaxation time, for instance the two types of water (free and bound), if exchange between these two states is sufficiently slow. For this type of measurement, a low resolution spectrometer (without any shim system) proves to be quite sufficient. 

The spectrum obtained by FT of the whole train of decaying echoes consisfs of a series of spikelets separated by the frequency vcpMG = l/ra. The envelope of these sidebands is defined by the second-order quadrupolar CT lineshape under MAS. The linewidth of each spikelet is determined by the true transverse relaxation time (T2) of the material, which is a measure of the decay time of the amplitude of the echoes in the... 

Since its first description in 1971 [35], gel-phase NMR was applied to peptide chemistry by Manatt and coworkers [36, 37], These authors used 13C NMR to determine the extent of chloromethylation of crosslinked polymers and 19F NMR to monitor protection-deprotection reactions. These two nuclei are the most commonly used in these types of studies, mainly because of their significant chemical shift dispersion, which can alleviate in part the resolution loss due to the non ideal linewidth obtained in the gel state. Apart from restricted molecular motion, that shortens T2 because of an efficient transverse relaxation, other sources of line-broadening derive from magnetic susceptibility variations within the sample (due to the physical heterogeneity of the system) and residual dipolar couplings. 

Thus we cannot escape the depressing reality that 7 2 will get shorter and linewidth will get bigger as we increase the size of the protein studied. The reduced T2 is not only a problem for linewidth, but also causes loss of sensitivity as coherence decays during the defocusing and refocusing delays (1/(2J)) required for INEPT transfer in our 2D experiments. The only ray of hope comes in the form of a new technique called TROSY (transverse relaxation optimized spectroscopy), which takes advantage of the cancellation of dipole-dipole relaxation by CSA relaxation to get an effectively much longer 7 2 value we will briefly discuss TROSY at the end of this chapter. 

Zeeman broadening can be reduced by motional averaging providing that the rate at which the atom transverse the trap is large compared to the Zeeman frequency spread. The average linewidth is given by... 

In addition to the induced magnetic field, the migration rate can greatly influence the NMR signal intensity and linewidth. Unlike in LC, the rate of migration of each band in CE is characteristic of electrophoretic mobility and so each move past the detector at different rates. The effective longitudinal (7ie(f) and transverse relaxation (T a) times of NMR nuclei in a flow system can be related to the residence time of the analyte (x) in the detector and the relaxation times (7 b 7 2) under static conditions [45] ... 

At fast flow rates, the saturation of signals is avoided because spins leave the NMR active region, thus leading to an increase in S/N. The NMR linewidth is related to transverse relaxation time and, in a flow system, the linewidth is further influenced by the residence time. As a result, short residence times at fast flow rates yield broader NMR signals with low S/N. Ideally, detection of each analyte should be optimized using suitable acquisition parameters to obtain NMR spectra with comparable S/N. In addition, the overall temperature change in buffer by Joule heating may also contribute to linewidth increase [44],... 

From Eq. (10) it is evident that, in the inhnite magnetic field limit, the transverse relaxation rate (and therefore the linewidth) is proportional to the correlation time. Consequently the same nucleus at the same distance from the metal would have a linewidth one order of magnitude larger in Type II copper proteins than in blue copper proteins. As an example, a proton at 5 A from the metal in a system with Tj 10 s (e.g., copper. 

Several formalisms have been applied to relaxation in exchanging radicals. Principal among these are modifications of the classical Bloch equations (8, l ) and the more rigorous quantum mechanical theory of Redfield al. (8 - IJ ). When applied in their simplest form, as in the present case for K3, both approaches lead to the same result. Since the theory has been elegantly described by many authors (8 - 12 ), only those details which pertain to the particular example of K3 will be presented here. Secular terms contribute to the ESR linewidth (r) and transverse relaxation time (T ) by an amount... 

Table IV. Temperature variation in correlation time (T(.), secular linewidth, r(M, k), and transverse relaxation time (T2) for M = -h. The Larmor frequency o)o/2Tr = 9.3 GHz. For an explanation, see text.

The main factor which allows observation of the NMR signals is the rather small magnitude of hyperfine couplings involved. Small A values will not greatly affect the transverse relaxation time T2 of the proton [equation (18)] and thus the NMR bandwidth will not be greatly increased. Byers and Williams (56) have studied some dimeric cupric complexes which are models for copper dimer units in proteins. Interest was particularly centred around the possibility that, if appreciable copper(ii) interactions occur, a mechanism for mutual fast relaxation is provided which in turn may lead to much narrower linewidths and measurable paramagnetic shifts. The systems are illustrated in [6]. 

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