Interaction dipolar, nuclear

Aside from the question of the precise model by which relaxation times are interpreted there is the more practical problem of isolating that part of the relaxation specifically caused by diffusion. The contributions of exchange processes (see below), spin-rotation interaction (9), and spin diffusion (9) can be identified by temperature dependences different from that which is solely the result of the motionally modulated nuclear dipolar interaction as sketched above, and corrections can be made. The molecular rotation contributions to dipolar relaxation can be removed or corrected for by (a) isotopic substitution methods (19), (b) the fact that rotation is in some cases much faster than diffusion, and its relaxation effects are shifted to much lower temperatures (7, 20), and (c) doping with paramagnetic impurities as outlined above. The last method has been used in almost all cases reported thus far, more by default than by design, because commercial zeolites are thus doped by their method of preparation this... 

Owing to the differences in both the nature and magnitude of the homo-and hetero-nuclear dipolar interactions, the process of eliminating the dipolar interactions to obtain a high resolution spectrum in the solid state is slightly different for protons and carbons, respectively, and will be reviewed separately in following... 

If i and j are different nuclei (for instance 13C and H) the hetero-nuclear dipolar interaction, which is often strong, can be removed by dipolar decoupling, which consists of irradiation nucleus j (say H) at its resonance frequency while observing nucleus i (say 13C). The time-averaged value of the Hamiltonian is then zero. 

Here /, is the 13C nuclear spin, S is the unpaired electronic spin, and A j- is the Fermi contact hyperfine coupling tensor. This coupling is identical for all 13C nuclei as long as the C60 ion is spherical, but becomes different for different nuclei after the Jahn-Teller distortion leading to an inhomogeneous frequency distribution. The homogeneous width of the 13C NMR lines is, on the other hand, mainly determined by the electron-nuclear dipolar interaction... 

The information that can be extracted from solid-state NMR spectra is encoded via spin interactions such as the chemical shielding, the quadrupolar interaction and the homo-and hetero-nuclear dipolar interactions [1,9-10]. Some knowledge of the spin interactions that determine the features of the spectra are thus of prime importance. 

A pulse scheme recovering the zero-quantum Hamiltonian was proposed by Baldus and Meier.142 It is weakly dependent on spectral parameters and a faithful measure of internuclear distances. This sequence is based on the former rotor-synchronized R/L-driven polarization transfer experiments.143,144 It uses the LG or FS-LG, which is used to decouple the high-7 spins, and combined MAS and RF irradiation of low-7 spins to decouple the hetero-nuclear dipolar interactions. With phase-inversion and amplitude attenuation in the rotating frame and refocusing pulses in the laboratory frame part of the pulse sequence, a zero-quantum average Hamiltonian can be obtained with optimum chemical-shift/offset independence. 

Both of these interactions are small in relation to the resolution obtained in the studies of N2 in its3 + state. The effect of the nuclear dipolar interaction was included as an estimated correction, but was not actually determined in the spectroscopic analysis. 

The constant b therefore contains contributions from two quite different magnetic interactions, the Fermi contact and the electron-nuclear dipolar interactions. Interpretation of the magnitudes of these constants in terms of electronic structure theory always involves the separate assessment of these different effects, so that we prefer to use an effective Hamiltonian which separates them at the outset. Consequently the effective magnetic hyperfine Hamiltonian used throughout this book is... 

The electron-nuclear dipolar interaction (see equation (10.76)) for the phosphorus nucleus is as follows ... 

In the case of rapid reactions of lanthanide complexes if Tie the electron spin relaxation time is short compared to the rotational reorientation time, rr, the electron—nuclear dipolar interaction will give rise to nuclear relaxation rates given by [27]... 

Relaxation of nitrogen nuclei apparently is governed by modulation of the electron-nuclear dipolar interaction, the so-called END mechanism. The nitrogen nuclear relaxation probability can be greater than the electron spin-lattice relaxation probability. See, for example, the paper by Popp and Hyde [45]. One consequence of this process is that it can alter the apparent relaxation time of the electron since it gives rise to parallel relaxation pathways. One must distinguish between apparent and actual electron spin-lattice relaxation probabilities. 

So far, only nuclei like and with strong homonuclear dipolar couplings have been considered. Dilute nuclei like exhibit mostly hetero-nuclear dipolar interactions, which are of the order of 10 kHz and thus much smaller. They can easily be removed by dipolar decoupling in a double resonance circuit. However, the chemical shift anisotropy (typically 100-200 ppm) still limits the spatial resolution and the low abundance the signal-to-noise [22-24]. 

There is another important term contributing to K ab when the electron-nuclear dipolar interaction is on.)... 

Another factor in solid-state spectroscopy is that some interactions not encountered in the spectral analysis of liquids contribute to the solid-state spectrum. These inelude the through-space coupling of magnetic spins, known as the nuclear dipolar interaction, and the... 

The fine structure of atomic line spectra and the hyperfine splittings of electronic Zeeman spectra are non-symmetric for those atomic nuclei whose spin equals or exceeds unity, / > 1. The terms of the spin Hamiltonian so far mentioned, that is, the nuclear Zeeman, contact interaction, and the electron-nuclear dipolar interaction, each symmetrically displace the energy, and the observed deviation from symmetry therefore suggests that another form of interaction between the atomic nucleus and electrons is extant. Like the electronic orbitals, nuclei assume states that are defined by the total angular momentum of the nucleons, and the nuclear orbitals may deviate from spherical symmetry. Such non-symmetric nuclei possess a quadrupole moment that is influenced by the motion of the surrounding electronic charge distribution and is manifest in the hyperfine spectrum (Kopfer-mann, 1958). 

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