Angle-Averaged Dipolar Interactions

The Boltzmann angle-averaged interaction potential is generally referred to as the orientation or Keesom interaction and represents one of the three 6th power of distance relationships involved in the total van der Waals interaction. 

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These trends are similar to what is observed in simpler model fluids with purely spherically s3mimotric interactions [298, 313], which is to some extent expected because the gas liquid transition in Stockmayer fluids is mainly driven by the isotropic LJ (12,6) interactions underlying this model. We show in Ref. 307 that the main effects of HS matrices on the condensation can be reproduced when the dipolar model fluid is approximated by a fluid with angle-averaged dipolar interactions that are not only spherically symmetric but also short-ranged (they decay in proportion to for r — cx)). This notion is particularly important for future simulation studies on adsorbed dipolar fluids. 

The geometric term in Equation 4.5 vanishes when =54°44 the magic angle. The dipolar interaction (also referred to as dipolar coupling) should average to zero if the sample is spun at this angle with respect to the static field. However, to completely eliminate the dipolar interactions the speed of rotation must be several times the static linewidth, typically several lOOkHz which is not currently possible. Most commercial MAS systems are capable of rotating 4mm sample rotors at a speed of 10-15 kHz or so. 

Since dipolar interaction is a distance-dependent interaction, the heteronuclear interaction between spins 1 and S can be exploited to get information about the distance between these nuclei. Heteronuclear dipolar interactions that are averaged by magic angle spiiming can be reintroduced by suitable dephasing pulses that are synchronized with the sample spinning. It is a difference spectroscopy... 

In general, multiple pulse techniques sufficiently average the dipolar interactions, compress the chemical shift scale, but they do not affect heteronuclear dipolar interactions and the chemical shift anisotropy. A combination of both multiple pulse techniques and magic angle spinning, so-called CRAMPS (Combined Rotational And Multiple Pulse Spectroscopy) is found to yield satisfactory results in the solid state H NMR of solids 186). The limitations of all these techniques, from the analytical point of view, arises from the relatively small chemical shift range (about 10 ppm) as compared with some other frequently studied nuclei. However, high resolution H NMR of solids is useful in studies of molecular dynamics. 

Often, in liquid-phase as well as in single-crystal NMR work, the samples are deliberately spun, often at special orientations (magic angle) relative to B. This will average out dipolar interactions, often narrowing the observed lines by substantial amounts. For example, see Ref. 3, Section 7.10 and Ref. 4, Chapter 8. Under some circumstances, additional lines (spinning sidebands) are generated by the MAS technique.32-34... 

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