Magnetic dipole interaction principles

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

Apart from electric and magnetic dipole transitions, time-dependent interactions involving higher-pole electric and magnetic moments can, in principle, occur. However, no examples of such transitions appear in this book they are of academic rather than practical interest. 

In general, NMR relaxation is mainly induced by dipole-dipole interaction and is greatly affected by the internuclear distance of the nuclear spins fluctuating in the magnetic field. However, an interatomic distance of more than ca. 5 A does has almost no effect on the NMR relaxation as seen from Eq. (1) since Ha is proportional to r. Thus, the NMR relaxation times, in principle, provide information about the interatomic distance r, if r is less than ca. 5 A. From such a background, we are concerned with the miscibility between the LDS and PCS portions in blended LDS/PCS samples. The intermolecular distance between the LDS and PCS portions in blended... 

For the sake of simplicity, we will restrict our discussion to the interaction of polar molecules (i.e., of molecules that carry a permanent electric dipole moment) with electric fields. However, we note that the same arguments and principles hold for the interaction of particles with a magnetic dipole moment with magnetic fields. 

Within degenerate perturbation theory at the nonrelativistic level, there are in principle two contributing terms arising from expectation values of the spin-Zeeman (O Eq. 11.50) and the magnetic dipole operator (O Eq. 11.44), respectively. The latter can be shown to be zero, and the effect of the spin-Zeeman operator is to recover the free-electron g factor, ge. Thus, within a purely nonrelativistic picture, there would be no effect of the electronic structure of the molecule on the interaction between an external magnetic field and the magnetic moment of the unpaired electron. 

Some years ago it was discovered that by dispersing monosized nonmagnetic spheres/particles in a ferrofluid, it was possible to produce a system of interacting magnetic dipoles which has been called "magnetic holes". The concept is very simple and corresponds to the magnetic analogue of Archimedes principle as shown schematically in Fig. 15. 

In principle there are many different processes whereby spin-lattice relaxation is mediated - all of them have in common the interaction of the rapidly processing nuclear spin with some fluctuating magnetic field generated in the lattice - but fortunately in practice the relaxation of most protons of sugars occurs exclusively by just one mechanism, the dipole-dipole mechanism. We shall return somewhat later to the full formulation of this mechanism, but for the present the somewhat simplified version shown in [1] will reveal why this particular relaxation mechanism is relevant to studies of the anomeric effect. According to [1] the efficiency with which a donor... 

The most important interactions between the unpaired electron and the magnetic nuclei can be of two kinds dipole-dipole (anisotropic) interactions, that depend on the molecular orientation with respect to the external field, and Fermi contact or isotropic interactions (spherically symmetric). The latter are purely quantum mechanical, and arise when there is a non-zero probability of finding the electron at a particular magnetic nucleus. Hence, the interaction (coupling) will in principle be larger the more s-character there is in the singly occupied molecular orbital on the particular atom (JV). 

For spin 1/2 nuclei the principle Ti mechanism is often dipole-dipole relaxation, which results from interactions between two nuclei with magnetic spins. Its efficiency is inversely proportional to the sixth power of the intemuclear distance. In C spectra of organic molecules, protons provide the main source of such relaxation. Where a C... 

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