Spin-lattice relaxation correlation

Schreiner, L. J., J. C. MacTavish, L. Miljkovic, M. M. Pintar, R. Blinc, G. Lahajnar, D. Lasic and L. W. Reeves. 1985. NMR line-shape spin-lattice relaxation correlation study of Portland cement hydration./. Am. Ceram. Soc. 68,10-16. 

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. 

Given the specific, internuclear dipole-dipole contribution terms, p,y, or the cross-relaxation terms, determined by the methods just described, internuclear distances, r , can be calculated according to Eq. 30, assuming isotropic motion in the extreme narrowing region. The values for T<.(y) can be readily estimated from carbon-13 or deuterium spin-lattice relaxation-times. For most organic molecules in solution, carbon-13 / , values conveniently provide the motional information necessary, and, hence, the type of relaxation model to be used, for a pertinent description of molecular reorientations. A prerequisite to this treatment is the assumption that interproton vectors and C- H vectors are characterized by the same rotational correlation-time. For rotational isotropic motion, internuclear distances can be compared according to... 

The second separation method involves n.O.e. experiments in combination with non-selective relaxation-rate measurements. One example concerns the orientation of the anomeric hydroxyl group of molecule 2 in Me2SO solution. By measuring nonselective spin-lattice relaxation-rat s and n.0.e. values for OH-1, H-1, H-2, H-3, and H-4, and solving the system of Eq. 13, the various py values were calculated. Using these and the correlation time, t, obtained by C relaxation measurements, the various interproton distances were calculated. The distances between the ring protons of 2, as well as the computer-simulated values for the H-l,OH and H-2,OH distances was commensurate with a dihedral angle of 60 30° for the H-l-C-l-OH array, as had also been deduced by the deuterium-substitution method mentioned earlier. 

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. 

However, there is no indication that the presence of the observed signals correlates with the polymerization efficiency of the catalyst. In fact, systems which exhibit these signals are less effective catalysts and in some cases do not even polymerize ethylene under the chosen conditions. In contrast, systems without EPR signals correlated to Ti species are foimd to be catalytically active. It has to be emphasized at this point that the lack of an ESR signal associated to Ti + ions, in cases where no additional argon or electron bombardment has been applied, cannot be interpreted as an indication of the absence of Ti + centers at the surface. It has been discussed in the literature that small spin-lattice-relaxation times, dipole coupling, and super exchange may leave a very small fraction of Ti " that is detectable in an EPR experiment [115,116]. From a combination of XPS and EPR results it unhkely that Ti " centers play an important role in the catalytic activity of the catalysts. 

Figure 1 Schematic representation of the 13C (or 15N) spin-lattice relaxation times (7"i), spin-spin relaxation (T2), and H spin-lattice relaxation time in the rotating frame (Tlp) for the liquid-like and solid-like domains, as a function of the correlation times of local motions. 13C (or 15N) NMR signals from the solid-like domains undergoing incoherent fluctuation motions with the correlation times of 10 4-10 5 s (indicated by the grey colour) could be lost due to failure of attempted peak-narrowing due to interference of frequency with proton decoupling or magic angle spinning.

Figure 2 Schematic representation of carbon spin-lattice relaxation time, T,c, and spin-spin relaxation time under CPMAS or DDMAS condition, T2C, as a function of correlation times.

Fig. 1.50. Relaxation time as a function of the molecular correlation time for two spectrometer frequencies 60 MHz and 220 MHz. rSGR, spin-lattice relaxation time rSSR, spin-spin relaxation time (Fig. 2.24 from [ 1.105]).

The reason why one chose to follow the main liquid-crystalline to gel phase transition in DPPC by monitoring the linewidth of the various or natural abundance resonance is evident when we consider the expressions for the spin-lattice relaxation time (Ti) and the spin-spin relaxation time T2). The first one is given by 1/Ti oc [/i(ft>o) + 72(2ft>o)] where Ji coq) is the Fourier transform of the correlation function at the resonance frequency o>o and is a constant related to internuclear separation. The relaxation rate l/Ti thus reflects motions at coq and 2coq. In contrast, the expression for T2 shows that 1/T2 monitors slow motions IjTi oc. B[/o(0) -I- /i(ft>o) + /2(2u>o)], where /o(0) is the Fourier component of the correlation function at zero frequency. Since the linewidth vi/2 (full-width at half-maximum intensity) is proportional to 1 / T2, the changes of linewidth will reflect changes in the mobility of various carbon atoms in the DPPC bilayer. 

Also spin-lattice relaxation times T and spin-spin relaxation times T2 were measured as a function of pressure on different selectively deuterated DPPC (at C2, Cg and Ci3, respectively) by Jonas and co-workers (Fig. 14). The spin-latticed relaxation time T is sensitive to motions with correlation times tc near Uo i e., motions with correlation times in the range from 10 to 10 " s. In comparison with Ti, the spin-spin relaxation time T 2 is more sensitive to motions with correlation times near (e qQlh), i.e., in the intermediate to slow range (10 " to 10 s). The Ti and T2 values obtained showed characteristic changes at various phase transition pressures, thus indicating abrupt changes... 

Activation volumes were derived from pressure dependent NMR experiments using the equation A E = —kT d In T dp]T, where 7) is the spin—lattice relaxation time. A Evalues for the H and NMR experiments were close to each other as well as to the values based on conductivity. These results imply that the electrical transport is correlated with water molecule rotation. There is a trend of increasing A E with decreasing water content. 

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