Nuclear spin interaction anisotropy

Motions with rates of the order of the nuclear spin interaction anisotropy can be assessed via lineshape analysis. These are generally motions of intermediate rates, a few kHz to tens of kHz for chemical shift and dipolar interactions, higher for quadrupolar interactions. 

The important nuclear spin interaction in the context of probing molecular reorientation is provided by the quadrupolar interaction (Q) or the chemical shift anisotropy (CSA), and we assume that the spin system is prepared by, for example, isotopic labeling in such a way that only a single interaction is relevant. The ubiquitous presence of dipolar broadening is assumed to be small. For most NMR experiments it suffices to consider the secular part of the... 

Anisotropic nuclear spin interactions, such as chemical shift anisotropy (CSA) and heteronuclear dipolar coupling, are highly valuable in understanding the nature of chemical bonding, structure, dynamics, and function of chemical and biological molecules. For example, chemical shifts of H, N, and nuclei are routinely used in the structural and motional studies of proteins using solution and solid-state NMR methods.Spectra of aligned solid-state... 

One potential problem with chemical shift anisotropy lineshape analysis (or indeed analysis of lineshapes arising from any nuclear spin interaction) is that the analysis results in a description of the angular reorientation of the chemical-shielding tensor during the motion, not the molecule. To convert this information into details of how the molecule moves, we need to know how the chemical-shielding tensor (or other interaction tensor) is oriented in the molecular frame. A further possible complication with the analysis is that it may not be possible to achieve an experiment temperature at which the motion is completely quenched, and thus it may not be possible to directly measure the principal values of the interaction tensor, i.e. anisotropy, asymmetry and isotropic component. If the motion is complex, lack of certainty about the input tensor parameters leads to an ambiguous lineshape analysis, with several (or even many) possible fits to the experimental data. 

MAS is routinely used in solid-state NMR spectroscopy for eliminating the effects of chemical shift anisotropy, heteronuclear dipolar interactions and first-order quadrupolar interactions. In this method the sample is rotated about the axis inclined at 54.74° with respect to the external magnetic field Bq, so that the average of the geometric term in nuclear spin interactions (3 cos 0 — 1) = Except... 

Characterization of the polymer primary structure is best carried out using solution NMR methods due to the increased spectral specificity of solution NMR methods as compared to solid state NMR methods. Solution NMR methods here includes solutions, gels, dispersions, melts, etc. Any method involving dilution, dispersion, increased temperature, etc. that will introduce sufficient motion into the polymer chain such that the unwanted nuclear spin interactions can be averaged to their trace values (zero for dipolar, isotropic chemical shift for the chemical shift anisotropy, scalar coupling for the indirect dipolar interaction, and zero for quadrupolar), on a sufficiently short time scale. 

The aim of this section is to provide an overview about the development and application of solid state NMR spectroscopic techniques for the study of molecular structures and dynamics on the molecular and intermolecular length scale (lA-lOA). In particular, anisotropic magnetic nuclear spin interactions like chemical shielding anisotropy (CSA), magnetic dipolar interaction and quadrupolar interaction are used as probes for interatomic distances and orientations of molecular groups, i.e. structures, and changes of these interactions are monitored and used as a measure of dynamic processes inside the system. 

Instead of averaging away the anisotropic nuclear spin interactions by MAS or multiple pulse sequences, it is possible to take advantage of the anisotropy of these interactions, provided that macro-scopically oriented samples are available. This kind of static solid state NMR approach is entirely different from the experiments discussed above. It can lead to highly resolved H and spectra with narrow lines, whose position carries information about... 

NMR spectroscopy is a powerful technique to study molecular structure, order, and dynamics. Because of the anisotropy of the interactions of nuclear spins with each other and with their environment via dipolar, chemical shift, and quadrupolar interactions, the NMR frequencies depend on the orientation of a given molecular unit relative to the external magnetic field. NMR spectroscopy is thus quite valuable to characterize partially oriented systems. Solid-state NMR... 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

In addition to g tensor anisotropy, EPR spectra are often strongly affected by hyperfine interactions between the nuclear spin I and the electron spin S. These interactions take the form T A S, where A is the hyperfine coupling tensor. Like the g tensor, the A tensor is a second-order third-rank tensor that expresses orientation dependence, in this case, of the hyperfine coupling. The A and g tensors need not be colinear in other words, A is not necessarily diagonal in the coordinate systems which diagonalize g. 

Fig. 4. Quadrupolar powder patterns (a) Spin NMR powder pattern showing that the central -)<- ) transition is broadened only by dipolar coupling, chemical shift anisotropy, and the second-order quadrupolar interactions, (b) Spin 1 NMR powder pattern for a nucleus in an axially symmetric electric field gradient (see text). The central doublet corresponds to 6 = 90° in Eq. (10). The other features of low intensity correspond to 6 = 0° and 6 = 180°. (c) Theoretical line shape of the ) - -) transition of a quadrupolar nuclear spin in a powder with fast magic-angle spinning for different values of the asymmetry parameter t (IS) ...

The characteristic shape of the ESR spectrum of the trapped hole in the different systems is not caused by nuclear hyperfine interaction since Cl35 37 (I = 3/2), S32 (I = 0) and P31 (I = 1/2) have different nuclear spins, yet the spectra are almost identical in all the three cases (Figure 8). Also, photobleached specimens of H3PO4 in H20 and D3PO4 in D20 exhibit identical ESR spectra, and hence there is no hyperfine interaction with the H or D nuclei. The shapes can be attributed to randomly oriented species with g-factor anisotropy. 

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