Slow motion regime

Fig. 3. Variation of the completely reduced dipole-dipole spectral density (see text) for the model of a low-symmetry complex for S = 3/2. Reprinted from J. Magn. Reson., vol. 59,Westlund, RO. Wennerstrom, H. Nordenskiold, L. Kowalewski, J. Benetis, N., Nuclear Spin-Lattice and Spin-Spin Relaxation in Paramagnetic Systems in the Slow-Motion Regime for Electron Spin. III. Dipole-Dipole and Scalar Spin-Spin Interaction for S = 3/2 and 5/2 , pp. 91-109, Copyright 1984, with permission from Elsevier.

For a fixed value of Tc, the frequency dependence of either term is a Lorentzian centred at zero frequency. In the tc dependence two regimes are distinguished In the fast motion regime (coiTc spectral density is proportional to tc and does not depend on the measuring frequency a>i, whereas in the slow motion regime (a>iTc > l) it is proportional to ( Tc) i.e. the relaxation rate exhibits dispersion. 

In contrast to critical behaviour, where the NMR relaxation rate shows a max-imiun (or a corresponding Ti minimiun) at Tc, thermally activated slowing down provides a Ti minimiun for lTc = 1, i.e. at the border between the fast motion and the slow motion regimes. Since according to Eq. 11 In(rc) is proportional to T Ti is usually plotted in logarithmically versus T", as for example shown in Fig. 11a. The slopes above and below the minimum are proportional to the activation energy E, . In Fig. 11b a typical tempera-... 

This suppression scheme has been shown to work well together with HMQC experiments of small molecules at natural abundance. Even cleaner spectra are obtained, if the BIRD sequence is combined with HSQC experiments already containing a spin-lock purge pulse. Drawbacks of the BIRD pulse scheme are the fact that the relaxation delay between scans cannot be chosen freely anymore and that complete suppression of all C-bound proton signals is impossible, if they have different relaxation times. Furthermore, the BIRD pulse scheme is not applicable to molecules in the slow motional regime, since negative NOEs between the inverted proton spins and the non-inverted C-bound proton spins would reduce the magnetization of the latter. 

R is always smaller than 1. If qEA 0. A 2D NMR experiment, thus always the measurement of R(x —> oo), and always the determination of qEA, in the slow motion regime, where the determination of qEA from line shape is no longer possible. 

At lower temperatures, the A - - B and A B intra-H-bond exchange time becomes low on the NMR time scale so that we are in the slow motion regime (Am 1). The deuteron NMR frequency now depends on the instantaneous value of the pseudo-spin S,z... 

Rotational motion of a nitroxide modulates the anisotropic electron-nuclear magnetic dipolar interaction, giving rise to electron relaxation that affects the EPR spectral line shape. At X-band frequency, the spectra are sensitive to motions with correlation times in the range of 10-11 < rc < 10-7, but also reflect the anisotropy of the motion. Figure 5B shows simulated EPR spectra for isotropic motion in the fast, intermediate, and slow motional regimes and illustrates the high sensitivity of the line shape to motional rate. 

Figure 5 Plot of 7i and T2 as a function of Tc at three different Larmor frequencies. The region where T and T2 diverge is the slow-motion regime and characterizes relaxation properties of most biomolecules...

Transverse nuclear relaxation due to director fluctuations in liquid crystals for the slow motion regime has been considered this leads to an analysis in detail of the transverse magnetization decay in different kinds of experi-... 

Fig. 7.2.1 Pulse sequences for T and related magnetization filters, typical evolution curves of filtered magnetization components, and schematic filter transfer functions applicable in the slow motion regime. Note that the axes of correlation times start at Tc = Wo (a) Saturation recovery filter, (b) Inversion recovery filter, (c) Stimulated echo filter.

Of particular importance for detection of chemical or physical change in polymer materials are mobility filters, which are sensitive to differences in the numbers of molecules within a given window of correlation times. Within reasonable approximation such filters are relaxation filters. Here, Tj filters are sensitive to differences in the fast motion regime while T2 and Tip filters are sensitive to the slow motion regime. Which time window is of importance can be seen from Fig. 5.7 [101]. It shows a double-logarithmic plot of the mechanical relaxation strengths Hi(t) for two carbon-black filled styrene-butadiene rubber (SBR) samples as a function of the mechanical relaxation time T. They have been measured by dynamic mechanical relaxation spectroscopy. In terms of NMR, the curves correspond to spectral densities of motion. But the spectral densities relevant to NMR are mainly those referring... 

Two-dimensional nuclear Overhauser effect spectroscopy (NOESY) has proven to be a valuable technique in determining the conformations of large polypeptides and oligonucleotides. The slow motional regime in which such molecules lie (where wt> 1) causes the zero quantum transition to be extremely important in determining the rate of cross-relaxation. Crossrelaxation in the homonuclear case is described by the expression ... 

Having taken the trouble to see how the relaxation rates in a two-spin system depend on molecular motion, we are now in a position to predict the behaviour of the NOE itself as a function of this motion and of intemuclear separation. Taking the rale constant Eq. (8.4) and substituting these into that for the NOE Eq. ((8.2)) produces the curve presented in Fig. 8.8 for the theoretical variation of the homonuclear NOE as a function of molecular tumbling rates as defined by (where u>o is the spectrometer observation frequency, approximately equal to uii and ujs). Note this is for a two-spin system, which relaxes solely by the dipole-dipole mechanism and as such represents the theoretically maximum possible NOE. The curve has three distinct regions in it, which we shall loosely refer to as the fast, intermediate and slow motion regimes. For those molecules that tumble rapidly in solution (short those in the extreme narrowing limit), the NOE has a... 

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