Relaxation of quadrupolar nuclei

It is not clear why the 51V resonance should be so sharp the ion cannot have the cubic symmetry that is normally required for slow relaxation of quadrupolar nuclei ( 1.4.10). It is even more surprising that the relatively slow relaxation, and associated narrow linewidth, are o... 

The efficient relaxation of quadrupolar nuclei in solution generally results in self-decoupling, such that quadrupolar effects are generally not observed in NMR spectra of spin-1/2 nuclei. Self-decoupling may also be a factor in NMR spectra of solid samples this often manifests itself as an asymmetric line shape. By decreasing the temperature, the Ti relaxation time of the quadrupolar nucleus may increase sufficiently to allow acquisition of NMR spectra where the effects of residual dipolar coupling are sufficiently resolved. ... 

The study of quadrupolar nuclei can provide unique and very valuable information on a variety of physico-chemical and biological systems. For one thing the relaxation of quadrupolar nuclei is in many ways easier to interpret than the relaxation of non-quadrupolar nuclei, since the former is in many cases caused by purely intramolecular interactions modulated by the molecular motion. Studies of quadrupolar relaxation have therefore furnished important information about molecular reorientation and association in liquids and have played - and will certainly play for many years - an important role in testing new theoretical models of molecular motion in liquids. 

When Wqi / Wq2 the magnetization recovery may appear close to singleexponential, but the time constant thereby obtained is misleading [50]. The measurement of 7) of quadrupolar nuclei under MAS conditions presents additional complications that have been discussed by comparison to static results in GaN [50]. The quadrupolar (two phonon Raman) relaxation mechanism is strongly temperature dependent, varying as T1 well below and T2 well above the Debye temperature [ 119]. It is also effective even in cases where the static NQCC is zero, as in an ideal ZB lattice, since displacements from equilibrium positions produce finite EFGs. 

Spin-spin (transversal) relaxation (relaxation time T2) is the second mechanism which is related to molecular mobility. It influences the half-height line widths w [tv = lj(n T2) in the frequency-domain NMR spectrum and is of some relevance in the NMR spectroscopy of quadrupolar nuclei such as, 2H, 14N, 170, 33S and others. In the context of this section, T2 is of very limited relevance. 

Another important nuclear characteristic is the nuclear quadrupole moment which, possessed by nuclei for which 7 1, has given rise to the important field of nuclear quadrupole resonance spectroscopy. A major importance of the quadrupole moment with respect to NMR absorption resides in the effects of quadrupole coupling constants on nuclear relaxation times and, therefore, on the line widths and saturation characteristics of NMR absorption (9). In addition, in favorable situations, quadrupole coupling constants can be derived from the characteristics of nuclear resonance of quadrupolar nuclei 127). Some examples of these effects will be described in Sections III, IV and VI of this chapter. 

Symmetries of local electrical environments of quadrupolar nuclei (/ 1) profoundly influence relaxation times and resonance line shapes of such nuclei (9, 116). Consider a nucleus for which I = % (Br79, Bn). In the absence of quadrupolar perturbation, the nuclear spin levels are evenly spaced, as shown in I below, and the three possible nuclear resonance transitions have equal energies (Am = 1). If, however, eqQ 0... 

Nuclear relaxation of different nuclei other than the proton can also be used to determine the rotational correlation time. The longitudinal relaxation of the 170 is governed by quadrupolar [68] and dipolar mechanisms [69], 1 /Tlq and 1 /Tld, respectively, both dependant on rotation ... 

Theoretical expressions for spin-lattice relaxation of 2H nuclei (determined by locally axially symmetric quadrupolar interactions modulated by molecular motions) can be derived for specific dynamic processes, allowing the correct dynamic model to be established by comparison of theoretical and experimental results [34,35]. In addition, T, anisotropy effects, which can be revealed using a modified inversion recovery experiment, can also be informative with regard to establishing the dynamic model [34,35]. 

C. Quadrupolar relaxation of ionic nuclei in aqueous and organic media... 

There are two conceptually different theories for quadrupolar relaxation of ionic nuclei in solution. Deverell (22) rationalized the electric field gradients at the site of the nucleus as arising from distortions of the closed-shell orbitals in the ion due to collisions with solvent molecules and, at higher concentrations, also counter-ions. In another theory developed by Valiev (23) and by Hertz and his coworkers (24) it is assumed that the electric field gradients are caused by the electric dipoles of the surrounding solvate molecules. It is certainly Hertz to whom we owe the detailed understanding of ionic quadrupole relaxation, and because of the fundamental implications that his work has on ionic solvation the important results are briefly summarized here. 

Both AP and Ga have a tightly bound hydrate shell in aqueous solution and both are prone to hydrolysis. In terms of the Hertz electrostatic model for quadrupolar relaxation of ionic nuclei in electrolyte solution (see Section III.C) one therefore expects effective quenching of the electric field gradient caused by the surrounding water dipoles, due to a nearly perfect coordination symmetry. Any contribution to the e.f.g. should therefore arise from outer-sphere solvent dipoles. In terms of the fully orientated solvation (FOS) model this would correspond to a distribution width parameter approaching zero (/. -> 0) with the first term in equation (4) vanishing. This is indeed what Hertz (24) found for both AF" and Ga ", and the experimental infinite dilution relaxation rates ( AP" 7-5 s Ga 350 s ) are remarkably well matched by the computed ones... 

Quadrupolar nuclei constitute most of the magnetic nuclei within the Periodic Table of the elements. However, the lack of suitable instrumentation as well as the misconception of the deleterious nature of these nuclei have impeded a more widespread utilization of their resonances. Quadrupolar relaxation resulting from the interaction of the nuclear quadrupolar moment with finite electric field gradients is the principal source of nuclear relaxation in nearly all compounds. However, albeit generally eonsidered a nuisance, the phenomenon may as well be exploited to the experimenter s advantage. In contrast to spin-j nuclei whose relaxation behaviour is principally dictated by the dynamics of the molecules in solution, structural and electronic effects play the key role in the relaxation process of quadrupolar nuclei. 

H. Versmold, Interaction Induced Magnetic Relaxation of Quadrupolar Ionic Nuclei in Electrolyte Solutions, Mol. Phys., 57 (1986), 201-216. 

J. Vaara, J. Jokisaari, T. T. Rantala, and J. Lounila, Computational and Experimental Study of NMR Relaxation of Quadrupolar Noble Gas Nuclei in Organic Solvents, Mol. Phys., 82 (1994), 13-27. 

In the case of relatively slow relaxation of quadrupolar X nuclei (as defined by the quadrupolar relaxation time and/or large coupling constants... 

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. 

The application of the PFT technique to 14N spectra is less effective than for l5N because of the quadrupolar relaxation of 14N nuclei which results in a large range of signal widths, from less than 1 Hz to several kHz, depending on the molecular environment of the 14N nuclei. The... 

For materials applications, the chemical shifts of methanol and ethylene glycol can be monitored in the liquid state to follow temperature [Hawl]. The most sensitive ehemical shift is the Co resonance of aqueous Co(CN)e with a sensitivity of 0.05 K at 7 T and 0.2 K at 2T [Dorl]. Furthermore, dibromomethane dissolved in a liquid crystal is a temperature sensitive NMR compound [Hed 1 ], and known phase-transition temperatures can be exploited to calibrate the temperature control unit [Hawl J. In temperature imaging of fluids, temperature can be determined from the temperature dependence of the selfdiffusion coefficient but convective motion may arise in temperature gradients [Hedl]. In the solid state, the longitudinal relaxation time of quadrupolar nuclei like Br is a temperature sensitive parameter [Suil, Sui2]. In elastomers, both T2 and Ti depend on temperature (Fig. 7.1.13). In filled SBR, T2 is the more sensitive parameter with a temperature coefficient of about 30 xs/K [Haul]. 

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. 

---