Dipolar interactions residual coupling

Instead of measuring only the time-dependent dipolar interaction via NOE, it is also possible to determine dipolar couplings directly if the solute molecule is partially aligned in so-called alignment media. The most important resulting anisotropic parameters are RDCs, but residual quadrupolar couplings (RQCs), residual chemical shift anisotropy (RCSA) and pseudo-contact shifts (PCSs) can also be used for structure determination if applicable. 

The first combined 13C- H MAS/CP experiment was performed by Schaefer and Stejskal (23). The double-resonance procedure decouples the strong heteronuclear dipolar interactions and indirect J couplings, while the weak 13C signal is enhanced by proton polarization transfer. The residual spectral width of several kHz arises from 13C chemical shift anistropy and weak 13C- 3C dipolar interactions between 1.1 % abundant 13C nuclei. Both of these interactions are removed by MAS. 

Figure 7.7 Fast but anisotropic segmental motion results in a solid-like contribution to the NMR signal. This contribution is expressed in terms of a fractional contribution q of the second moment M2 of the rigid lattice line of a single chain or residual dipolar interactions between protons. The line splitting caused by the dipole-dipole interaction depends on the orientation angle q of the internuclear vector of the coupling protons in the magnetic field B(). The distribution of orientation angles changes with the...

In elastomer samples with macroscopic segmental orientation, the residual dipolar couplings are oriented as well, so that also the transverse relaxation decay depends on orientation. Therefore, the relaxation rate 1/T2 of a strained rubber band exhibits an orientation dependence, which is characteristic of the orientational distribution function of the residual dipolar interactions in the network. For perfect order the orientation dependence is determined by the square of the second Legendre polynomial [14]. Nearly perfect molecular order has been observed in porcine tendon by the orientation dependence of 1/T2 [77]. It can be concluded, that the NMR-MOUSE appears suitable to discriminate effects of macroscopic molecular order from effects of temperature and cross-link density by the orientation dependence of T2. 

For elastomers and rubbery-like materials well above the T, the high molecular mobility reduces the dipolar couplings dramatically. The WISE experiment allows one to investigate site-selectively residual dipolar interactions and thus molecular dynamics by editing the corresponding proton slices of the 2D data set. 

RDCs belong to the so-called anisotropic NMR parameters which cannot be observed in isotropically averaged samples as, for example, is the case in liquids. Besides RDCs, a number of other anisotropic parameters can be used for structure elucidation, like residual chemical shift anisotropy, residual quad-rupolar couplings for spin-1 nuclei, or pseudo-contact shifts in paramagnetic samples. Here, we will focus on RDCs where we give a brief introduction into the dipolar interaction, then into the averaging effects with the description by the alignment tensor and concepts to deal with the flexibility of molecules. For the other anisotropic NMR parameters, we refer the reader to ref 19 for an introduction and to refs. 6-8 for a detailed description. 

A simple model of an elastomer network is depicted in Fig. 7.1.8. The segmental motion of inter-cross-link chains is fast but anisotropic at temperatures of 100-150 K above the glass transition temperature The end-to-end vector R of such a chain reorients on a much slower timescale because it appears fixed between seemingly static cross-link points. As a result of the fast but anisotropic motion, the dipolar interaction between spins along the cross-link chains is not averaged to zero, and a residual dipolar coupling remains [Cohl, Gotl, Litl]. 

In the absence of a significant Cq, the indirect spin-spin interaction between quadrupolar and spin-1/2 nuclei manifests itself in the spectrum of the latter as a multiplet consisting of 2/-I-1 evenly spaced peaks. However, if Uq is a significant fraction of vq, the spin states for the quadrupolar nucleus are not quantized precisely in the direction of Bo and hence MAS does not completely average the dipolar interaction between the nuclei. The effect, referred to as residual dipolar coupling, manifests itself as distortions in the multiplet structure in the NMR... 

The residual dipolar coupling also manifests itself in NMR spectra of dipolar-coupled quadrupolar spin pairs.Wu and Yamada also observed residual dipolar coupling attributed to the N- B dipolar interaction in the NMR spectra of MAS samples of triethanolamine borate. More recently, the effect of the N- B, "B- B, and Mn- Mn residual dipolar interactions on the B and Mn NMR line shapes acquired through MQMAS were also demonstrated. ... 

Phase diagram studies by NMR are generally based on the fact that the rapid molecular dynamics causes an elimination of any spin interactions to an extent that is directly related to the degree of anisotropy of the structure. The most important use of NMR is to distinguish between phases that give residual dipolar or quadrupolar interactions and phases that do not in general, this also marks the difference between optically anisotropic and optically isotropic phases. Whether residual couplings are seen depends on the extension of the anisotropic domains (microcrystallite sizes) in combination with the rate of molecular diffusion. 

Residual dipolar coupling (RDC) partial average of a dipolar interaction between two nuclei in a molecule with anisotropic rotational diffusion resulting from its partial orientation in a magnetic field... 

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