Quadrupolar interactions relaxation mechanisms

There is arbitr iriness in describing phenomena as either physical or chemical, but in some sense the nuclear relaxation mechanisms we have discussed to this point are physical mechanisms, based as they are on rotational motions of molecules, magnetic dipole-dipole interactions, quadrupolar interactions, and so on. Now we discuss a nuclear relaxation mechanism that is chemical in origin. 

S has a moderate quadrupolar moment, eQ, arising from its non-spherical charge distribution. The interaction between the nuclear quadrupole moment and the electric field gradient, which is generated at the nucleus itself by the surrounding electronic distribution, is modulated by molecular reorientational motion and provides the only effective relaxation mechanism in liquid. The resulting relaxation times are on the order of milliseconds. 

The minimum in the spin-lattice relaxation time is more difficult to account for. It cannot be attributed to the onset of the diffusional motion, because the jump frequency does not match the Larmor frequency at the temperature where diffusion becomes important. For this reason it is necessary to postulate an additional kind of motion in the lithium-vanadium bronze—a side-to-side jumping from one side of the channel to the other. In the structure there are sites on both sides of the channel roughly 2 A. apart which are equivalent but only one of which is occupied to fulfill stoichiometry. This kind of motion should start at a lower temperature than the above diffusion and lead to a correlation frequency that matches the Larmor frequency at the spin-lattice time minimum. Because of modulation of quadrupolar interaction, side-to-side motion could provide an effective spin-lattice relaxation mechanism. 

In early years of NMR, extensive studies of molecular dynamics were carried out using relaxation time measurements for spin 1/2 nuclei (mainly for 1H, 13C and 31P). However, difficulties associated with assignment of dipolar mechanisms and proper analysis of many-body dipole-dipole interactions for spin 1/2 nuclei have restricted their widespread application. Relaxation behaviour in the case of nuclei with spin greater than 1/2 on the other hand is mainly determined by the quadrupolar interaction and since the quadrupolar interaction is effectively a single nucleus property, few structural assumptions are required to analyse the relaxation behaviour. 

Relaxation via quadrupolar coupling. Nuclei with 15= 1 have an electric quad-rupole moment (due to non-spherical nuclear charge distribution) which is capable of interacting with local electric field gradients that occur in tumbling molecules with an asymmetric electric charge distribution. Therefore this relaxation mechanism is... 

For a real spin system, the most important problem in the calculation and analysis of the relaxation is the mechanism of fluctuation. Generally, all interactions contribute to relaxation. For spin-1/2 systems, the chemical shift and dipolar interactions are comparable and both contribute to relaxation the separation of the two contributions is generally difficult and therefore a more demanding problem is how to obtain the correct information of motion in a spin-1/2 system. Whereas for a quadrupolar system, the quadrupolar interaction is dominant and in most cases only this interaction should be considered in relaxation. The relaxation mechanism is relatively simple and so there have been more applications of quadrupole relaxation to the extraction of dynamical information in solids. is especially unique for this purpose because both dipolar and shielding interactions are weak. There are large quantities of work on this subject which have been reviewed in a recent paper by Hoatson and Vold. ... 

Temperature Dependence of Spin-Lattice Relaxation. The spin-lattice relaxation rate T ) is comprised of various contributions to the relaxation process, including homo- and heteronuclear dipolar interactions, quadrupolar interactions, chemical shift anisotropy, spin-rotation, and others (10). When the relaxation mechanism is dominated by inter- and intramolecular dipole-dipole interactions, the will increase with temperature, pass through a maximum, and decrease with increasing temperature. Since the relaxation rate is the inverse of the relaxation time, the Ti will decrease, pass through a minimum (Timin), and then increase with increasing temperature (77). The T lmin values are proportional to the internuclear distances. 

As already discussed above chlorine, bromine and iodine nuclei all have I > 1 and possess large electric quadrupole moments. It is therefore not surprising that in a majority of systems studied by NMR the dominant relaxation mechanism is due to quadrupolar interactions. The only exceptions encountered so far concern certain paramagnetic systems. 

Relaxation of nuclear spins occurs under two modes longitudinal and transverse relaxation characterized respectively by time constants T- and T2. The quadrupolar interaction i.e. the interaction of the quadn olar moment of the nucleus witH the electric field gradient present at the sodium site, provides the predominant relaxation mechanism. Due to the rather symmetrical environment of the solvated sodium ion - for instance (Na )6H20 " weak electric field gradient is expected. Upon complexation by a bionolecule, the alkali ion coordinates both with solvent and substrate molecules, which both increase the electric field gradient, and decreases by a considerable amount the cation rotational motion. Both these effects generate a relaxation rate enhancement. 

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