Quadrupole relaxation

N-protonation the absolute magnitude of the Ad values is larger than for Af-methylation <770MR(9)53>. Nuclear relaxation rates of and have been measured as a function of temperature for neat liquid pyridazine, and nuclear Overhauser enhancement has been used to separate the dipolar and spin rotational contributions to relaxation. Dipolar relaxation rates have been combined with quadrupole relaxation rates to determine rotational correlation times for motion about each principal molecular axis (78MI21200). NMR analysis has been used to determine the structure of phenyllithium-pyridazine adducts and of the corresponding dihydropyridazines obtained by hydrolysis of the adducts <78RTC116>. 

It is worth mentioning that >NH protons may often appear somewhat broader than their -OH counterparts, for another reason >NH protons have another relaxation mechanism available to them (quadrupole relaxation) because the 14N nucleus has an electric quadrupole moment. This extra relaxation capability can lead to a shorter relaxation time for >NH protons, and since the natural linewidth of a peak is inversely proportional to the relaxation time of the proton(s) giving rise to it, a shorter relaxation time will give rise to a broader peak. 

Chemists pay much less attention to the NMR relaxation rates than to the coupling constants and chemical shifts. From the point of view of the NMR spectroscopist, however, the relaxation characteristics are far more basic, and may mean the difference between the observation or not of a signal. For the quadrupolar nucleides such as 14N the relaxation characteristics are dominated by the quadrupole relaxation. This is shown by the absence of any nuclear Overhauser effect for the 14N ammonium ion despite its high symmetry, which ensures that the quadrupole relaxation is minimized. Relaxation properties are governed by motional characteristics normally represented by a correlation time, or several translational, overall rotational and internal rotational, and thus are very different for solids, liquids and solutions. 

All nuclear multiplet structures due to coupling of nonequivalent nuclei are, as noted earlier, subject to effects on line shapes by chemical or positional exchange. For those multiplet structures arising from coupling of nuclei, one of which has a nonzero nuclear quadrupole moment, effects of quadrupole relaxation must be considered. For example, if a proton or fluorine atom is bonded to a nitrogen nucleus (I = 1), a triplet resonance will be expected in the proton or fluorine spectrum. For observation of this fine structure it is necessary that the lifetimes of the nuclear spin states of nitrogen (m = 1, 0, —1) be greater than the inverse frequency separation between multiplet components, i.e., t > l/ANx (106). The lifetimes of N14 spin states can become comparable to or less than 1 /A as a result of quadrupole relaxation. When the N14 spin-state lifetimes are comparable... 

Under the assumption of quadrupole relaxation, the form of the transition matrix in Eq. (1) is easily determined. The transition rate is characterized by the time constant... 

Determination of Quadrupole Relaxation Times and Coupling Constants from 13C Spin-Lattice Relaxation Times... 

Engstrdm et al. [112] used molecular dynamics simulations to study quadrupole relaxation mechanism for Li+, Na+, and Cl ions in dilute aqueous solutions. They found that NMR relaxation rate for these ions was determined by the relaxation of water molecules in the first solvation shell. The simulations show nonexponential solvation dynamics which can be modeled by two relaxation time constants < 0.1 ps and x2 lps (see Table 4). 

Ref. 13 contains a more complete discussion of static quadrupolar effects for amphiphilic mesophases. That work also includes a treatment of counterion quadrupole relaxation for liquid crystalline systems a brief outline of this discussion is given in the next section. 

Nuclear quadrupole relaxation may also contribute significantly to spin-relaxation and thus lead to line broadening. These effects depend upon the electric-field gradient at the nucleus which is reduced if the radical is symmetrical. 

Andrasko, J., Bull,T. E., and Lindqvis, I. (1972). Quadrupole relaxation in solutions of humic acids. Chem. Scripta 2, 93-95. 

Lindman, B., and Lindqvis, I. (1969). Nuclear quadrupole relaxation of 8SRB in an aqueous solution of a humic acid. Acta Chem. Scand. 23, 2215-2216. 

Rheological properties are particularly sensitive and for some solubilizates, such as a-methylnaphthalene, the solutions may become viscoelastic the appearence of viscoelasticity often depends on subtle effects in chemical structure29). Certain spectroscopic features are strongly influenced. Thus the H and 13C NMR line widths show large increases, the 81 Br quadrupole relaxation may be strongly affected and there may be the appearance of linear dichroism, birefringence and conductance anisotropy for flowing systems. 

Fig. 12a-e. Non-monopole (quadrupole) relaxation and shape distortion of a core hole in open shell type of situations (a) Lowest order self-energy diagram (b) one-electron picture of the pulling down of empty levels below the Fermi level (c) shape distortion of one-electron orbitals due to quadrupole relaxation (d, e) schematic core level spectra in the case of (d) closed and (e) open ground state shell structure (d)... 

It is interesting to note that in the quadrupole relaxation process discussed in Section 3.4 (Fig. 12) the core hole can be regarded as fluctuating between the different degenerate orbital magnetic sublevels. In this way, the core hole can form a static quadrupole moment and induce a quadrupole screening charge distribution. 

The spin-lattice relaxation of nuclei with /> 1 /2 is mainly due to nuclear quadrupole relaxation and the relaxation time at a temperature of 77 °K is still fairly short (of the order of milliseconds for many nuclei of interest to chemists). Therefore the experimental methods usually applied do not involve relaxation problems. The full RF fields available — for instance, with a superregenerative NQR spectrometer — may be applied successfully, resulting in an improved signal-to-noise ratio for the resonance at 77 °K as compared with room temperature. There are exceptions to this rule (e.g. 14N NQR spectroscopy where saturation problems come into play at 77 °K). 

NMR thus, 19F splittings due to UB—19F coupling, and their disappearance at lower temperatures due to quadrupole relaxation of UB, give a measure of the electric field gradient about boron and, hence, of the adduct structure (27, 28). 

The general theory of quadrupole relaxation is somewhat complex but simplifies for the case of rapid molecular tumbling and axial symmetry of the molecular electric field. The interaction energy between the nucleus and a surrounding electric field gradient (Eq. 7.18) appears quadratically ... 

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. 

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