Spin-diffusion lattice relaxation time

Maryott A. A., Farrar T. C., Malmberg M. S. 35C1 and 19F NMR spin-lattice relaxation time measurements and rotational diffusion in liquid CIO3F. J. Chem. Phys. 54, 64-71 (1971). 

Zi(Air, x) and 7)(N2, x) are spin-lattice relaxation times of nitroxides in samples equilibrated with atmospheric air and nitrogen, respectively. Note that W(x) is normalized to the sample equilibrated with the atmospheric air. W(x) is proportional to the product of the local translational diffusion coefficient D(x) and the local concentration C(x) of oxygen at a depth x in the membrane, which is in equilibrium with the atmospheric air ... 

Reif 97) has observed the effects of point defects on nuclear resonance lines of Br , Br, Na , and Li in cubic crystals. The effect of temperature on the line widths and spin-lattice relaxation times was investigated for various impurity levels in AgBr and found to be quite pronounced due to vacancy association and diffusion. 

Clearly by working with typical spatial resolutions of approximately 30-50 pm, individual pores within the material are not resolved. However, a wealth of information can be obtained even at this lower resolution (53,54,55). Typical data are shown in Fig. 20, which includes images or maps of spin density, nuclear spin-lattice relaxation time (Ti), and self-diffusivity of water within a porous catalyst support pellet. In-plane spatial resolution is 45 pm x 45 pm, and the image slice thickness is 0.3 mm. The spin-density map is a quantitative measure of the amount of water present within the porous pellet (i.e., it is a spatially resolved map of void volume). Estimates of overall pellet void volume obtained from the MR data agree to within 5% with those obtained by gravimetric analysis. 

Figure 2. Fluorine NMR relaxation times for a sample of Linde molecular sieve 13X containing about 6.6 molecules of SFg per cage O, spin lattice relaxation time , spin-spin relaxation time T2 characterized by exponential decay V and A, T2 characterizedby two relaxation times ticked O, decay as r2. Solid lines are theory to the left of 10Z/T = 6 based on molecular diffusion to the right of 10Z/T controlled by Tu. For dashed lines see text (20)...

Molecular motions in low molecular weight molecules are rather complex, involving different types of motion such as rotational diffusion (isotropic or anisotropic torsional oscillations or reorientations), translational diffusion and random Brownian motion. The basic NMR theory concerning relaxation phenomena (spin-spin and spin-lattice relaxation times) and molecular dynamics, was derived assuming Brownian motion by Bloembergen, Purcell and Pound (BPP theory) 46). This theory was later modified by Solomon 46) and Kubo and Tomita48 an additional theory for spin-lattice relaxation times in the rotating frame was also developed 49>. 

The interest in alkaloids of the nicotine group continues. Convenient syntheses of 7V-CD3-labelled nicotine and nicotine analogues have been described.38 The 13C n.m.r. spin-lattice relaxation times of nicotine have been analysed in terms of anisotropic rotational diffusion constants. The results agree best with a dihedral angle of H(2 )-C(2 )-C(3)-C(2) of ca 0°.39 Dithiodinicotyrine , obtained... 

Some measurements have been made of self diffusion in pure ethylene and in ethylene-sulfur hexafluoride mixtures (22), but these measurements were made very close to the critical temperature and up to pressures of only about 100 bar. Proton spin-lattice relaxation times (T.) of ethylene have been measured at temperatures from 0°C to 50°C and pressures up to about 2300 bar (13). The relaxation time values were -M0—50 sec for much of the region studied. Several relaxation mechanisms contribute to this long relaxation time and make both the measurement and analysis of the relaxation times very difficult. For these reasons, we decided to limit our study to the measurement of the self-diffusion coefficient in supercritical ethylene (60. 

Self diffusion coefficients of deuterated toluene were measured, rather than protonated toluene in order to minimize the experimental difficulties associated with very long proton spin lattice relaxation times (T- ). Since the value of the T1 determines the length of time between pulse sequences, a long relaxation time leads to prohibitively long measurement times. Previous measurements (36-38) of proton and deuterium relaxation times in liquid toluene have been made as a function of temperature and pressure. The relaxation is due to dipolar interactions in protonated toluene and quadrupolar interactions in toluene-dg. Therefore, the relaxation times can be expected to increase with increasing temperature. However, the quadrupolar relaxed deuterium T. values are smaller than the proton T1... 

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. 

Moving from structure to dynamics, we recall the NMR results, [Ty91, Ya91a] which indicate that the molecules in solid Ceo tumble rapidly at room temperature but freeze at lower temperatures. Considering the structural data reviewed above, one would expect a more-or-less continuous rotational diffusion in the room temperature fee phase, and either small oscillations or molecular jumps between favorable orientations in the low temperature phase. This difference was very clearly seen in the overall spin-lattice relaxation time near the orientational phase transition.[Ty91b] It was also found that the... 

The spin-lattice relaxation time 7] as a function of temperature T in liquid water has been studied by many researchers [387-393], and in all the experiments the dependence T (T) showed a distinct non-Arrhenius character. Other dynamic parameters also have a non-Arrhenius temperature dependence, and such a behavior can be explained by both discrete and continuous models of the water structure [394]. In the framework of these models the dynamics of separate water molecules is described by hopping and drift mechanisms of the molecule movement and by rotations of water molecules [360]. However, the cooperative effects during the self-diffusion and the dynamics of hydrogen bonds formation have not been practically considered. 

Deuterium diffusion was studied in VDX, where 0.4 < x < 0.6, by means of 2H NMR measurements.599 1H and 51V spin-lattice relaxation times for TaV2Hx, where x < 0.18, were consistent with two co-existing proton-jump processes.600 3H, 2H and 51V spin-lattice relaxation times were also determined for NbVCrHo.3, NbVCrD0.3g and NbV 14Cro.6Ho.6 in the temperature range 11-424 K.601 A DFT/broken symmetry approach has been used to study exchange... 

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