Dynamic NMR line shapes

The combination rate constant k was derived from the exchange rate constant which was measured by dynamic NMR line shape analysis. The combination rate constant Is about 3 x 10 H s l at 20 with a low enthalpy of activation, about 2 kcal/mole (see Experimental for more details). The high rate of exchange In the 2-alkoxy-... 

Pulsed deuteron NMR is described, which has recently been developed to become a powerftd tool for studying molectdar order and dynamics in solid polymers. In drawn fibres the complete orientational distribution function for the polymer chains can be determined from the analysis of deuteron NMR line shapes. By analyzing the line shapes of 2H absorption spectra and spectra obtained via solid echo and spin alignment, respectively, both type and timescale of rotational motions can be determined over an extraordinary wide range of characteristic frequencies, approximately 10 MHz to 1 Hz. In addition, motional heterogeneities can be detected and the resulting distribution of correlation times can directly be determined. 

It should be also noted that the dynamic NMR line width Avayn = is always small (Fig. 11a) as compared to the static glassy line width induced by the inhomogeneous nature of the spectrum. Therefore the nanocluster dynamics can be locally seen only by T2 measurements, and not by ID line shape data which reflect the static glassy nature of the relaxor state characterized by the Edwards-Anderson order parameter. 

NMR is a powerful technique for providing information about the distribution and dynamics of local RFs, characteristic of such systems. While the quadrupole-perturbed NMR line shape analysis gives details about the distribution of local RFs, spin-lattice relaxation (SLR) studies can give information on the dynamics in the frustrated state of these systems. From the literature, it can be seen that most of the NMR experiments have been carried out in RADP mixed systems and its deuterated analogues. ETFI group published a number of results21-23 on various mixed crystals. 

Dynamics of typical reorganizing systems that have been investigated using NMR line shape analysis include first-order degenerate processes such as degenerate bond rotations (equation 1), first-order interconversions where A and B are different species (equation 2), bimolecular group transfer (equation 3) and mutual exchange (equation 4). 

For calculating the c elements for an NMR spectrum subject to dynamic effects, all the NMR parameters should be known together with a range of trial values for the rate constants. Then, via an iterative procedure, comparison of calculated and observed NMR line shapes provides the rate constants. As of this writing software for solving these density matrix equations is readily available and easily managed using any current PC. 

FIGURE 1. Left proton NMR, 300 MHz, CHiLi portion of (R)-2-methylbutyllithium, 1.5 M in pentane at different temperatures. Right calculated NMR line shapes taking into account the dynamics of inversion. Reprinted with permission from Reference 17. Copyright (1976) American Chemical... 

Some examples which show the dynamic effects of alkyl and silyl substituents on barriers to rotation in allyllithium compounds 26 to 32 are listed in Table 7. These results were obtained from proton NMR line shape data. The procedure for compounds 26, 28, 29 and 32, which exhibited rotation around their C — CH2 bonds, is diagrammed by structure 33 in which hydrogens A, B and X are all nonequivalent and each couples to the others. Rotation averages the A and B shifts as well as the coupling constant between them and 3./(Ha.Hx) averages with 37(HB,HX), (Figure 15). At the same time, the Hx resonance... 

Rotation around Ca — Ci. The third reorganization process which has been investigated is rotation around the Ca— Q(Ar) bond. The ortho carbons are nonequivalent at 245 K in 39, 41 and 42. With increasing temperature these doublets average. Dynamic parameters obtained from the NMR line shapes are listed in Table 9. 

TABLE 10. Dynamics of reorganization of allylic lithium TMEDA complexes, 0.3 M in diethyl ether-4io from 13C NMR line shape analysis... 

We have shown how organolithium compounds adopt a variety of structures which differ in state of aggregation and degree of solvation. These species interconvert rapidly at equilibrium by different mechanisms, such as intermolecular C—Li exchange ligand transfer and dissociation-recombination processes as well as first-order reorganizations such as inversion and rotation. Dynamics of many of these processes have been determined by our methods of NMR line shape analysis. 

When the H- H dipole-dipole interaction can be measured for a specific pair of H nuclei, studies of the temperature dependence of both the H NMR line-shape and the H NMR relaxation provide a powerful way of probing the molecular dynamics, even in very low temperature regimes at which the dynamics often exhibit quantum tunnelling behaviour. In such cases, H NMR can be superior to quasielastic neutron scattering experiments in terms of both practicality and resolution. The experimental analysis can be made even more informative by carrying out H NMR measurements on single crystal samples. In principle, studies of both the H NMR lineshape and relaxation properties can be used to derive correlation times (rc) for the motion in practice, however, spin-lattice relaxation time (T measurements are more often used to measure rc as they are sensitive to the effects of motion over considerably wider temperature ranges. 

Nuclear magnetic resonance (NMR) spectra can yield information on magnetic properties, rotational states and of the symmetry of both the molecules and then-environment. Mostly, is used as a probe, but in alkali salts, alkali atoms as Na or Li have also been applied. The effect of molecular dynamics, including pseudorotations, on the NMR line shape is thoroughly discussed in [20,28],... 

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