Quadrupole relaxation time, correlation

It is generally accepted that if electric field gradients occur at the nucleus site, the quadrupole relaxation times, and T, of nuclei with nuclear spin / > 1/2 are related to the reorientational correlation time at the extreme-narrowing limit as given below." " 7rAvi/2 = l/T i = 1/7 2 = Stt /IOX (2/ + 3)/ (2/ - 1) X Qq / (4)... 

In 4-substituted AT-ethylpyridinium cations, the observation of coupling between the ethyl CH protons and nitrogen depends on the quadrupole relaxation of the nitrogen, which in turn depends on the nature of the 4-substituent. A roughly linear correlation of (quadrupole relaxation time) with the Hammett a function was observed (see also p. 138). 

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>. 

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. 

While the nuclei 3H and 13C relax predominantly by the DD mechanism, relaxation of a quadrupole nucleus such as deuterium essentially involves fluctuating fields arising from interaction between the quadrupole moment and the electrical field gradient at the quadrupole nucleus [16]. If the molecular motion is sufficiently fast (decreasing branch of the correlation function, Fig. 3.20), the 2H spin-lattice relaxation time is inversely proportional to the square of the quadrupole coupling constant e2q Q/H of deuterium and the effective correlation time [16] ... 

S nuclear quadrupole coupling constants have been determined from line width values in some 3- and 4-substituted sodium benzenesulphonates33 63 and in 2-substituted sodium ethanesulphonates.35 Reasonably, in sulphonates R — SO3, (i) t] is near zero due to the tetrahedral symmetry of the electronic distribution at the 33S nucleus, and (ii) qzz is the component of the electric field gradient along the C-S axis. In the benzenesulphonate anion, the correlation time has been obtained from 13C spin-lattice relaxation time and NOE measurements. In substituted benzenesulphonates, it has been obtained by the Debye-Stokes-Einstein relationship, corrected by an empirically determined microviscosity factor. In 2-substituted ethanesulphonates, the molecular correlation time of the sphere having a volume equal to the molecular volume has been considered. 

The 2-site 120° jump motion for the basal molecules switches between these two hydrogen bonding arrangements and clearly requires correlated jumps of the hydroxyl groups of all three basal molecules. On the assumption of Arrhenius behaviour for the temperature dependence of the jump frequencies, the activation energies for the jump motions of the apical and basal deuterons were estimated to be 10 and 21 kj mol-1, respectively. This dynamic model was further supported by analysis of the dependence of the quadrupole echo 2H NMR lineshape on the echo delay and consideration of 2H NMR spin-lattice relaxation time data. 

The spin-lattice relaxation times Ti due to the quadrupole interaction mechanism can be ctmverted to die rotational correlation times T2R ui a simple maimer. In the extreme narrowing limit attained by nqnd molecular rotational motions, the spin-lattice relaxation rate 1/Tj forthe m nucleus with the spin 1=1 is expressed by... 

To simplify the interpretation of STMAS spectra, it is desirable to remove the CT—>CT correlation signal, particularly when studying nuclei subjected to distribution of local environments or weak quadrupole interactions. Several methods are available to remove the CT CT peak. In the first method, the CT transition is presaturated by a soft pulse, prior to the STMAS sequence (Fig. 12a) [38]. A sequence consisting of a selective soft pulse followed by a delay and a short excitation pulse maybe used for optimising the presaturation pulse. Unfortunately, this simple method only works when aU species present in the sample have very similar transverse relaxation times and quadrupole couphng constants. 

From the comparison of the measured and calculated temperature dependences of the relaxation time (see Fig. 20), it follows that the inelastic phonon scattering is the most essential mechanism of the spin-lattice relaxation for Ge. It is evident that only at low temperatures T < 30K) some other mechanisms (the most probable one is the relaxation due to a small amount of paramagnetic impurities) become dominant. At T > 300/C some additional mechanism of relaxation may also exist. The interaction of the nuclear quadrupole moment with vibrations of the nearest four Ge atoms brings about the main contribution to the spin-lattice relaxation rate. The effective modulation of the EFG by the nearest bond charges is greatly reduced because of strong correlations between their displacements. As the main result of the present investigation of spin-lattice relaxation,... 

In the liquid state, the nuclear quadrupole coupling constant is difficult to determine. In the extreme narrowing case (w2 r2 1), where co is the Larmor frequency and rc is the rotational correlation time, the spin-lattice relaxation time (Tfi) of the quadrupole nucleus in a spherical diamagnetic molecule can be expressed1 by ... 

Here, T2 is the spin-spin relaxation time Av is the linewidth eq is the electric held gradient at the nucleus eQ is the nuclear quadrupole moment and /(rR, rex) is some function of the correlation times rR and rex, for rotational motion and exchange of the ions, respectively. An asymmetry parameter of zero is assumed (18). 

As quadrupole relaxation dominates deuterium relaxation hlgh-resolutlon NMR In liquids will be confined to small and medivun-sized molecules where relaxation broadening Is moderate. Assuming for example a correlation time of 10 sec as it is typical of a molecule of MH 250, a natural line width of 1.5 Hz results based upon a quadrupole coupling constant of 180 kHz. 

Typical pulse sequences, commonly employed in relaxation studies of 1 = 1 spin systems are shown in Fig. 6. The quadrupole echo (QE) sequence (top) [51] provides the spin-spin relaxation time Tjg [52]. Since Tjg is most sensitive to motions with correlation times equal to the inverse quadrupolar coupling constant, quadrupole echo sequences of deuterons ( H) offer a means to study molecular dynamics in the... 

Hirschinger et al [95] also used the anisotropy of spin-lattice relaxation to distinguish the two mechanisms, in this case the relaxation time associated with quadrupolar order, T q. A pulse sequence similar to Figure 8.2(b) was used. Quadrupolar order for the amorphous regions was shown to decay quickly, and for longer values of DE, only crystalline quadrupole order remained. The spectra could be closely simulated by a diffusion model and correlation time of 100 ps. Calculated jump lineshapes possess a central peak that is not present in the experimental data. 

Quadrupole relaxation studies of the mobility of covalent compounds have almost exclusively dealt with the pure compounds and medium effects on halogen quadrupole relaxation are virtually unknown. Furthermore, we have seen in the above description of models of molecular motion in liquids and the interpretation of correlation times that the effect of specific intermolecular forces has in most cases been disregarded. For the understanding of the influence of different types of intermolecular interactions on molecular reorientation, systematic studies of quadrupole relaxation in liquid mixtures should be helpful. Halogen relaxation investigations of this type are nonexistent in the literature but a preliminary investigation in our... 

In conclusion, it appears that quantitative tests of the electronic distortion model for the quadrupole relaxation resulting from ion-solvent interactions are presently not possible since neither the field gradient nor the correlation time may be reliably estimated. A more fruitful approach of investigating if electronic distortion effects contribute to halide ion quadrupole relaxation at infinite dilution would probably be to test the predicted relationship between... 

Arnold and Packer [265] criticized the assumed proportionality between correlation time and viscosity arguing that while viscosity and correlation time for ion quadrupole relaxation both are average values over the system, the weighting of the contributions from different environments is entirely different in the two cases. Arnold and Packer also showed that if relaxation is assumed to result from translational motion it should in certain cases be possible to relate the... 

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