Quadrupolar from spin-lattice relaxation times

A function closely related to QCC is the Li quadrupolar splitting constant (QSC), defined as QSC = (1 -h/7 /3) x( Li), where r is the asymmetry parameter. The Li QSC values can be estimated from the Li and C(para) spin-lattice relaxation times. The QSC values are correlated with the effects of structure, solvent and temperature on association in solution for aryllithium compounds (155, 171, 172). Conclusions can be drawn about the structure of the associated species in cases where no supporting XRD evidence is available. ... 

The procedures for recording spectra of heteronuclei often differ considerably from those for H and (which would today be considered routine ) since it is necessary, even for routine measurements, to adjust the experimental conditions to suit the special properties of the nuclei to be observed. For example, the spin-lattice relaxation times for some nuclides, such as N, are very long, whereas for others (especially those with an electric quadrupole moment, such as N) they are very short. Also, the spectra observed for some nuclides contain interfering signals caused by other materials present, for example the glass of the sample tube ("B, Si), the spectrometer probe unit ( Al) or the transmitter/receiver coil. For many nuclides the sample temperature and its constancy are important factors for example, quadrupolar nuclides such as O give narrower signals when the temperature is increased. 

Other effects frequently encountered in inorganic systems that can severely affect line shape involve relaxation processes arising from interactions of nuclear quadrupole moments with electric field gradients. For quad-rupolar nuclei (I 1), the quadrupolar contribution to the spin-lattice relaxation time Ti is given approximately by... 

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. 

Inversion-recovery deuterium NMR spectra were obtained by performing a 180°-r-90° pulse sequence, followed by the quadrupolar echo sequence (12). Spin lattice relaxation times were estimated from the null points in the inversion-recovery spectra. 

Some appreciation for the nitrogen nuclear characteristics may be obtained from Table 1. Because the relative sensitivities are comparable, the approximately 300-fold higher natural abundance of would seem to make it the nucleus of choice. It is even more sensitive than at natural abundance. However, like all nuclei with spin quantum number I > 1/2, possesses an electric quadrupole moment that arises from a nonspherical electric charge distribution in the nucleus itself. When placed in an electric field gradient, such as that characteristic of most molecular electron distributions, a quadrupolar nucleus experiences random fluctuating electric fields. The characteristic frequencies of these motions have components at the resonance frequency and hence afford an efficient relaxation mechanism. As a result, spin-lattice relaxation times (Tj ) are very short, 0.1-10 ms. Because Tj = To for in most molecules Lie in solution, linewidths are corres-... 

The T and T2E relaxation times have been measured on macroscopi-cally aligned samples over a wide temperature range. The spin-spin relaxation times T2E are most sensitive to motions with correlation times of the same order of magnitude as the reciprocal of the quadrupolar coupling constant, i.e. in the range from 10" to 10"" s, whereas the spin-lattice relaxation times T depend on motions with correlation times of the order of the reciprocal of the Larmor frequency, i.e. in the range from 10" to 10" s. 

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. 

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. 

Both the 1 B and B n.m.r. spectra of 1.2-D2-I.Z-CgBio lO were used In a study of B quadrupole coupling.Spin-lattice (T].) relaxation times were aeaured. It was concluded that Ti values were dominated by the quadrupolar relaxation mechanism whereas there was a substantial boron-boron scalar contribution to 2 times. The quadrupole coupling constants from this solution study were In good agreement with the data from a solid state B n.q.r. Investigatlon b solid state B, and... 

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