Spin-lattice correlation rates

Figure 29.8 Comparison of spin-lattice correlation rates measured by NMR relaxometry [51] with those calculated by AIM/DOIT [7] for solid benzoic acid isotopomers with mobile Hhl (top), HD (center), and DD (bottom) pairs. Measurements are depicted by symbols the broken and dot-dash lines represent theoretical results for two limiting cases, the solid curve being their geometric mean [7].

Usually, nuclear relaxation data for the study of reorientational motions of molecules and molecular segments are obtained for non-viscous liquids in the extreme narrowing region where the product of the resonance frequency and the reorientational correlation time is much less than unity [1, 3, 5]. The dipolar spin-lattice relaxation rate of nucleus i is then directly proportional to the reorientational correlation time p... 

The measurement of correlation times in molten salts and ionic liquids has recently been reviewed [11] (for more recent references refer to Carper et al. [12]). We have measured the spin-lattice relaxation rates l/Tj and nuclear Overhauser factors p in temperature ranges in and outside the extreme narrowing region for the neat ionic liquid [BMIM][PFg], in order to observe the temperature dependence of the spectral density. Subsequently, the models for the description of the reorientation-al dynamics introduced in the theoretical section (Section 4.5.3) were fitted to the experimental relaxation data. The nuclei of the aliphatic chains can be assumed to relax only through the dipolar mechanism. This is in contrast to the aromatic nuclei, which can also relax to some extent through the chemical-shift anisotropy mechanism. The latter mechanism has to be taken into account to fit the models to the experimental relaxation data (cf [1] or [3] for more details). Preliminary results are shown in Figures 4.5-1 and 4.5-2, together with the curves for the fitted functions. 

The significance of n.m.r. spectroscopy for structural elucidation of carbohydrates can scarcely be underestimated, and the field has become vast with ramifications of specialized techniques. Although chemical shifts and spin couplings of individual nuclei constitute the primary data for most n.m.r.-spectral analyses, other n.m.r. parameters may provide important additional data. P. Dais and A. S. Perlin (Montreal) here discuss the measurement of proton spin-lattice relaxation rates. The authors present the basic theory concerning spin-lattice relaxation, explain how reliable data may be determined, and demonstrate how these rates can be correlated with stereospecific dependencies, especially regarding the estimation of interproton distances and the implications of these values in the interpretation of sugar conformations. 

One of the classical NMR methods used to determine molecular correlation times is provided by spin-lattice relaxation experiments. The spin-lattice relaxation rate 1 /T is determined by transitions among the Zeeman levels. For a liquid, the expression for the spin-lattice relaxation rate [81] is... 

Here, K% is a constant related to the NMR coupling constant,. S 2 is the spectral density associated with the second-rank orientational correlation function g2(f). If g2(f) is an exponential function, such as in rotational diffusion, Eq. (16) reduces to the famous Bloembergen-Purcell-Pound (BPP) expression for the spin-lattice relaxation rate [81,82]. 

In supercooled liquids the BPP expression usually fails to reproduce the observed spin-lattice relaxation times. Instead of a single correlation time x2, it is found that a distribution of correlation times G(lnx2) exists. Indication for a distribution G(lnx2) resulting from a superposition of subensembles with different x2 were reported for supercooled liquids close to Tg [11,349,350]. This implies the existence of a distribution of spin-lattice relaxation rates. Correspondingly, the relaxation function 4>,w (t) of the z-magnetization is... 

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... 

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,... 

Sturz and DoUe measured the temperature dependent dipolar spin-lattice relaxation rates and cross-correlation rates between the dipolar and the chemical-shift anisotropy relaxation mechanisms for different nuclei in toluene. They found that the reorientation about the axis in the molecular plane is approximately 2 to 3 times slower than the one perpendicular to the C-2 axis. Suchanski et al measured spin-lattice relaxation times Ti and NOE factors of chemically non-equivalent carbons in meta-fluoroanihne. The analysis showed that the correlation function describing molecular dynamics could be well described in terms of an asymmetric distribution of correlation times predicted by the Cole-Davidson model. In a comprehensive simulation study of neat formic acid Minary et al found good agreement with NMR relaxation time experiments in the liquid phase. Iwahashi et al measured self-diffusion coefficients and spin-lattice relaxation times to study the dynamical conformation of n-saturated and unsaturated fatty acids. 

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