Quadrupolar spin relaxation

In 207p j Of jfj X NMR spectra, the observation of indirect nuclear oipb-X spin-spin coupling may be affected by fast relaxation either of the ovpb or of the X nucleus (see Fig. 4 for X = "B with moderately fast quadrupolar spin relaxation ). The broadening of o pb satellites in X NMR spectra, recorded at high field strength Bq, may indicate highly anisotropic surroundings of the o Pb... 

NMR spin relaxation is not a spontaneous process, it requires stimulation by a suitable fluctuating field to induce an appropriate spin transition to reestablish equilibrium magnetization. There are four main mechanisms for obtaining relaxation dipole-dipole (most significant relaxation mechanism for I = 1/2 nuclei), chemical shift anisotropy, spin rotation, and quadrupolar (most significant relaxation mechanism for I > 1/2 nuclei) (Claridge, 1999). 

The spin spin relaxation time T2a can be measured by a quadrupolar echo pulse train 90° — x — 90° — (2t — 90°) if the pulse spacing x < C 2/Av is satisfied (i.e., the deuteron spin relaxes as if the quadrupolar splitting Av is absent or if a non-selective excitation is achieved). Due to the large quadrupolar splitting often encountered in LC, the above condition for x cannot be fulfilled experimentally and the two lines relax independently (i.e., r> 21 Av or selective excitation of half of the doublet exists). The quadrupolar echo pulse train then measures50... 

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). 

Carper, W. R. (1999). Direct determination of quadrupolar and dipolar NMR correlation times from spin-lattice and spin-spin relaxation rates. Concept Mag. Res. 11, 51-60. 

Since the effects of a perturbation on the relaxation rate are mechanism-specific, clarity about the active spin relaxation mechanism is essential. While there is no doubt about the overwhelming dominance of quadrupolar relaxation for Na, Rb, and Rb,... 

More recently Tarasov et al. provided unambiguous evidence for the superposition of scalar and quadrupolar spin-lattice relaxation mechanisms in the case of Al in the corresponding mixed tetrahalogenoaluminates AlCl Br4 . (244) From the temperature dependence of Ti( Al) in AICl4 and AlBr the scalar contributions to the Al relaxation rates are determined, providing the following estimates for the respective scalar coupling constants J( Al- Cl) 650 Hz and J( Al- Br) = 750 Hz. 

Nevzorov AA, Trouard TP, Brown ME. Lipid bilayer dynamics from simultaneous analysis of orientation and frequency dependence of deuterium spin-lattice and quadrupolar order relaxation. Phys. Rev. E 1998 58 2259-2281. 

Nuclei with spin quantum number I > can possess electric quadrupole moments. The nuclear quadrupole is directly coupled to the nuclear spin and the electrostatic interaction dominates the nuclear spin relaxation. The quadrupolar interaction is simply the first non-vanishing term in the Taylor expansion of the electrostatic interaction between the charge distribution of the nucleus and that of its surrounding. It can be expressed as a direct product between the nuclear quadrupole tensor and the electric field gradient (EFG) at the nucleus [6]. 

In recent years there has been much interest in the use of supercritical fluids (SCFs) as replacements for conventional liquid solvents, particularly in separation science, but also as reaction media. In addition to their environmental benefits, SCFs have further advantages over conventional liquid solvents, and these are briefly outlined in Section 2. The remainder of the chapter describes the use of SCFs as a medium for NMR spectroscopic studies. First we look briefly at motives for such NMR studies and the techniques employed. We then examine in more detail chemical shifts and nuclear spin relaxation in SCFs. The lower relaxation rates associated with SCFs and consequent sharper lines obtained for quadrupolar nuclei make SCFs excellent solvents. Section 8 describes some NMR studies of organometallic reactions in SCFs. Here the miscibility of supercritical solvents with gaseous reagents proves to be a tremendously useful feature in, for example, homogeneous catalysis. Finally we comment on future possibilities for NMR studies in SCFs. 

Again, only few results are related to relaxation of metal nuclei in clusters. T values have been reported only for Co [21,28] and range between 1 ms and 50 ps. Linewidths, directly related to the spin-spin relaxation, are sometimes given for quadrupolar nuclei Co [29-31], Cu [32], Mo [33,34]. Relaxation times have been used for structural determination [21] or for the investigation of the dynamic behaviour of clusters [28] no special use of the linewidth is reported, however. 

Study of relaxation times for spin I = ill nuclei in the quadrupole nutation NMR experiment has confirmed that they are inversely proportional to the linewidths of the quadrupole nutation NMR spectra/ In the end, a useful generalization is that, if the relaxation is fast, then the spectral lines will be broad Therefore, the relaxation times, Ti and Tz, for spin-lattice and spin-spin relaxations respectively, can be of very crucial importance as parameters in the NMR study of quadrupolar nuclei. 

We begin, in Section 2, with a detailed theoretical examination of the physics of quadrupolar, spin-5 nuclei, using the matrix operator formalism to discuss the various NMR experiments used in biological spectroscopy of quadrupolar ions and the biexponential relaxation of these ions. The effect of interaction of the Rb+ ion with its chemical environment on relaxation characteristics of the 87 Rb nucleus is considered in Section 3. Section 4 deals with methods of differentiating between intra- and extracellular species of ions. In Section 5 we discuss the kinetics of Rb+ in a variety of tissues, as studied by 87Rb NMR. Where appropriate, studies of 23Na and 39K are also cited. 

Here, Hz is the Zeeman term, Hq is the quadrupolar interaction term for nuclei with 1 1, Hd is the dipolar interaction term for nuclei with 1 = 1/2, Hs is the electron shielding term and Hj is the J-coupling term. Spin relaxations will be induced by the time fluctuations of these interaction terms. For example, H spin-lattice relaxation behaviour is dominated by Hq, whereas Hq mainly determines the relaxation process of the H or magnetization in organic materials. In some cases without significant contributions from Hq and Hq, the time fluctuations of Hs and Hj also induce spin relaxation for example, the magnetization of a carbonyl carbon with a large chemical shift anisotropy relaxes due to the contribution from the time fluctuation of Hs. Nevertheless, since the main interest of polymer scientists is NMR, we focus on the description of the relaxation process in this chapter. 

The spin relaxation of most quadrupolar nuclei is completely given by the interaction of the nuclear quadrupole moment, eQ, with the electric-field gradient (e.f.g.) at the nucleus. To a good approximation the e.f.g. is generated in most molecular liquids exclusively by intramolecular charges. The interaction fluctuates in time because of the reorientation of the X—D or... 

Fig. 4. 62.8 MHz 207Pb H NMR spectrum of a solution of Li[Me3Pb-BH3] in tetra-hydrofuran, measured at various temperatures (extensive decomposition occurs above -30 °C).21 The signal shows splitting due to indirect nuclear 207Pb-uB spin-spin coupling as indicated (nB /= 3/2). At lower temperature, the lifetime of the "B spin states becomes increasingly shorter owing to efficient quadrupolar nB nuclear spin relaxation, and consequently the splitting of the 207Pb NMR signal starts to collapse.

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