Indirect dipolar interaction

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. 

Nuclear spins can be considered as dipoles that interact with each other via dipolar couplings. While this interaction leads to strongly broadened lines in soUd-state NMR spectroscopy, it is averaged out in isotropic solution due to the fast tumbUng of the solute molecules. In Uquid-state NMR spectroscopy, the dipolar interaction can only be observed indirectly by relaxation processes, where they represent the main source of longitudinal and transverse relaxation. 

The fact that dynamic 13C polarization is only possible through the indirect way via tire 1H spins suggests the mechanism of polarization transfer. Since the polarization transfer between the electrons and nuclei are driven by the dipolar interactions between them, and the fraction of the guest triplet molecules was small, it would be natural to assume that the polarization of the electron spins in the photo-excited triplet state is given to those H spins which happen to be close to the electron spins, and then the 1H polarization would be transported away over the whole volume of the sample by spin diffusion among the 1H spins. 

It should now be evident that the experimental tensor may be expressed as the sum of an isotropic term resulting from the contact interaction, and a tensor resulting from dipolar interactions and any indirect coupling via the orbital angular momentum. This may be written in the form of an equation ... 

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. 

The next step is to define the Hamiltonian for the system. For NMR it is easy to write down the Hamiltonian for a set of nuclei in a molecule that is tumbling rapidly. We know that each nucleus interacts with the magnetic field as we discussed in Chapter 2, that direct dipolar interactions average to zero and need not be considered, and that indirect spin coupling between any pair of nuclei can be handled as a scalar product. All of these factors are included in the Hamiltonian given. 

As a second example, we look at echoes. We saw in Chapter 9 that a 180° pulse refocuses not only chemical shifts and the effects of magnetic field inhomogeneity but also spin coupling provided that the pulse does not also disturb the spin state of the coupled nucleus (see Fig. 9.2) However, in a homonuclear spin system a nonselective pulse does effect spin states. We found in Chapter 7 that dipolar interactions have the same mathematical from as indirect spin coupling, and it is known that a 180° pulse does not produce an echo in a solid because spin states are disturbed. However, it is possible to obtain a solid echo or dipolar echo by applying the pulse sequence 90, T, 90r It is very difficult to rationalize an echo from... 

Figure 15 presents the pulse sequence for a general separated local field (SLF) experiment.133-136 The basic principle of the SLF technique is that a spinning-sideband pattern, from which the heteronuclear dipolar coupling can be extracted, is obtained in the indirect dimension for each resolved resonance in the direct dimension, i.e., the dipolar interaction is separated from the chemical shift interaction. In the original SLF papers, a homonuclear decoupling method is applied in t, but recently McElheny et al. 

There are two kinds of spin-spin interaction, direct (through space) and indirect (through bond). The direct couplings, known as dipolar interactions, are anisotropic. A similar formalism may be used to describe the dipolar coupling under MAS as was used to describe the chemical shift (Eqs. (1) and (2))... 

Relaxation-mediated magnetization transfer is often dominated by the effects of a strongly coupled proton bath. The influence of the corresponding homonuclear and heteronuclear dipolar interactions may indirectly enhance the rate of polarization exchange between rare spins such as by a process called proton-driven spin diffusion... 

The anisotropy of the indirect (ind) spin-spin coupling of nuclei can lead to a term Dcalled a pseudodipolar interaction, which enters the spin Hamiltonian of Eq. (1) in the same way as the direct dipolar interactions of Eq. (2).4 Thus we may write... 

S H one, leading to the usual inversion of the proton signal. If the dipolar coupling between the proton and fluorine spins is an appreciable relaxation process for the fluorine nuclei, then when the proton performs an H+ transition in relaxing towards the thermal equilibrium distribution, there will be a probability that the fluorine spin will perform a simultaneous F+ transition due to the term H+F+ in the fluorine-proton dipolar interaction Hamiltonian. Thus in addition to any fluorine enhancement due to the direct fluorine electron interaction, there will be an additional positive enhancement due to the indirect three-spin interaction. 

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