Relaxation spin-rotation

The spin-rotation interaction arises from magnetic fields generated at a nucleus by the motion of a molecular magnetic moment that arises from the electron distribution in the molecule. The Hamiltonian for this interaction is given by 

The theory developed initially by Hubbard93 for spherical top molecules in liquids shows that collisions cause the molecule to experience changes in the magnitude and direction of its angular momentum, which then causes the fluctuations required to create magnetic fields oscillating at the Larmor frequency. For a small molecule in a liquid it can be shown that 

Spin-rotation interaction is known to be the dominant relaxation mechanism for 13C in CS2 (except at very high fields and low temperatures) and is important for 13C in methyl groups, which reorient rapidly by internal rotation, even in large molecules. 

Molecules or groups which rotate very rapidly have associated with them a molecular magnetic moment generated by the rotating electronic and nuclear 

The quadrupolar relaxation mechanism is only directly relevant for those nuclei that have a nuclear spin quantum number, I, greater than V2 (quadrupolar nuclei) and is often the dominant relaxation process for these. This can also be a very efficient mechanism and the linewidths of many such nuclei can be hundreds or even thousands of hertz wide. The properties of selected nuclei with I V2 are summarised in Table 2.3. Whilst the direct observation of these 

Isotope Spin Natural abundance Quadrupole moment NMR frequency Relative sensitivity 

The observation of such nuclei is generally most favourable for those of low quadrupole moment and high natural abundance which exist in more highly symmetric environments those listed in italics are considered the least favoured of the available isotopes. The NMR frequencies are quoted for a 400 MHz instrument (9.4 T magnet) and sensitivities are relative to H and take account of both the intrinsic sensitivity of the nucleus and its natural abundance. 

The broad resonances of many quadrupolar nuclei means field inhomogeneity makes a negligible contribution to linewidths so the methods described previously for measuring relaxation times are no longer necessary. For small molecules at least, T2 and Ti are identical and can be determined directly from the half-height linewidth. The broad resonances together with the sometimes low intrinsic sensitivity and low natural abundance of quadrupolar nuclei are the principal reasons for their relatively low popularity for NMR studies relative to spin-Vz nuclei. The very fast relaxation of certain quadrupolar nuclei can also make their direct observation difficult with conventional high-resolution spectrometers see Section 4.5. 

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McClung RED 1996 Spin-rotation relaxation theory Encyclopedia of Nuclear Magnetic Resonance ed D M Grant and R K Harris (Chichester Wiley) pp 4530-5... 

For liquids, the dominant relaxation mechanism is the nuclear-nuclear dipole interaction, in which simple motion of one nucleus with respect to the other is the most common source of relaxation [12, 27]. In the gas phase, however, the physical mechanism of relaxation is often quite different. For gases such as the ones listed above, the dominant mechanism is the spin-rotation interaction, in which molecular collisions alter the rotational state of the molecule, leading to rotation-induced magnetic fluctuations that cause relaxation [27]. The equation governing spin-rotation relaxation is given by... 

Whereas in CF4 we can ignore the surface relaxation term, this term is significant for c-C4F8 at 291 K, with the relative weighting becoming increasingly important as we add additional molecular layers, as shown below. This is equivalent to Eq. (3.5.6), with the bulk fluid term set to the spin-rotation relaxation of the bulk gas. It is clear that in such a system, in comparison with CF4 at 294 K, the effect of liquid phase surface relaxation cannot be ignored. 

The story is even more complicated than we have suggested, because carbon can relax by more than one mechanism. Protons rely on dipole-dipole relaxation, which also works well for protonated carbons but badly for non-proton-ated carbons. But carbon also for example makes use of spin-rotation relaxation, which is particularly active for methyl groups. And the magnetic field dependence of the various mechanisms also differs. We realize that relaxation is a very difficult subject, and if you want to know more then there are plenty of textbooks available ... 

Yaouanc, A. and de Reotier, P.D. (2010) Muon Spin Rotation, Relaxation, and Resonance Applications to Condensed Matter, Oxford University Press, Oxford. 

Publications on the temperature dependence of 13C relaxation [190-199] are concerned with simple molecules such as carbon disulfide, iodomethane, and acetonitrile [190-194], Any interpretation of the temperature dependence of relaxation times requires a knowledge of the relative contributions of dipole-dipole and spin-rotation relaxation, as the former becomes progressively slower and the latter steadily faster with increasing temperature. In special cases, such as that of cyclopropane [200], the effects of both contributions can almost cancel each other. 

Raman scattering depolarization of fluorescence Spin-rotation relaxation time... 

The mean square torque is taken from computer experiments. Nevertheless, it could have been found from the infrared bandshapes. Likewise the integral in this expression can be found from the experimental spin rotation relaxation time, or it can be found directly from the computer experiment as it is here. The memory function equation can be solved for this memory. The corresponding angular momentum correlation function has the same form as v /(0 in Eq. (302) with... 

The serial publications listed in Section 1.3 contain a number of articles on various aspects of relaxation. The Encyclopedia of NMR includes 13 articles under titles beginning with the word Relaxation and several other related articles, including Nuclear Overhauser Effect," Carbon-13 Relaxation Measurements,100 Paramagnetic Relaxation in Solution,101 Brownian Motion,102 and Spin—Rotation Relaxation Theory.103 Many of these articles are based on density matrix formulations, which can readily be understood with the background provided in Chapter 11. 

For a spherical top molecule, the spin rotational relaxation is given as [73] ... 

Now, by combining results from MD simulations of stannane, we obtain tj according to equation (37), which we insert into the equation of the spin-rotation relaxation, equation (35). We also insert experimental the into equation (35) so that we can calculate C ff- Stannane is chosen because the SR is the dominating mechanism in the spin I = relaxation of Finally, from C ff, we can... 

Thus the rate of dipole-dipole relaxation is greater for longer Xc values which corresponds to high viscosity, t), and low temperature, T, and of course the converse is true for spin-rotation relaxation. The low viscosity of SCFs (and, frequently, use of higher temperatures) should clearly lead to enhanced spin-rotation and reduced dipole-dipole relaxation. In the studies of SCFs mentioned above and for in SC CO2 the decrease in relaxation time as temperature was increased showed that spin-rotation had become the dominant relaxation pathway (for all other relaxation mechanisms increasing temperature results in a lengthening of T whereas in the case of the much larger hexadecane, dipole-dipole relaxation remained dominant. In the latter study the authors point out that spin-rotation relaxation dominates for the C resonance in CO2. In the study of SC H2O by Lamb and Jonas [16] it was noted that under supercritical conditions the proton T values were not affected by addition of O2, unlike in normal solvents. 

H, and relaxation times have been measured for Sn[ri-C5H3(1,3- Bu2)]2 in toluene and xenon at 300 K (see Table 4, Figure 6). For the most part, relaxation times were longer in xenon (e.g. the values for Sn were 2.6 and 8.4 s in toluene and Xe respectively). However for the quaternary carbons the T values were lower in Xe. Presumably this is because those carbons with no attached protons have no efficient relaxation mechanism in conventional solvents, but undergo efficient spin-rotation relaxation in supercritical solvents. 

Relaxation is a complex phenomenon, depending on many factors [2], such as dipole-dipole relaxation, chemical shift anisotropy, spin-rotation relaxation, quad-rupolar relaxation etc. Examples for macroscopic factors are sample and magnetic field homogenity and the viscosity of the NMR solvent. When running NMR experiments on ionic liquids, we have to deal with three main challenges ... 

For Mn, a sensitivity of 0.016 ppmK was measured for a KMnO4 solution at a Larmor frequency of 19.087 MHz. An extensive study of the temperature dependence of Mn chemical shifts and linewidths contains data for more than 14 compounds.within the series of compounds Mn(CNR)6 the Mn chemical shifts increased linearly with temperature over the range 238 to 318 K, with coefficients between roughly 0.4 and 0.7 ppmK" . The linewidths also decreased monotically with temperature for all R groups, except for methyl and ethyl, corresponding to a dominant quadrupolar relaxation mechanism, where the linewidth is inversely proportional to temperature. The increase in linewidth with temperature for these two smaller complexes was explained by assuming that spin-rotational relaxation was the dominant mechanism. 

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