Magnetic fields static

If we neglect interaction of the electronic and/or nuclear spins with an external magnetic field (which can be treated correctly only within the framework of a relativistic CO theory see Section 1.5), the one-electron Hamiltonian of a system in the presence of a magnetic field H can be written in the form 

10 Magnetic, Electrical, and Mechanical Properties of Polymers 

In the simplest case H = const. For instance, if H = where z is the direction of the long axis of the chain, one obtains 

With allowance for equations (10.5) and (10.6) the matrix elements of in an LCAO approximation can then be expressed as 

If H remains a constant vector but points in a general direction, then 

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Figure Bl.15.5. Effect of small-amplitude 100 kHz field modulation on the detector output current. The static magnetic field is modulated between the limits and The corresponding detector current varies between the limits 1 and/. The upper diagram shows the recorded 100 kHz signal as a fiinction of B. After [3].

Fig. 2. Interaction of nucleus (electron) with static magnetic field, Bq, where the bulk magnetization, M, is (a) parallel to Bq and to the -axis, and (b), upon apphcation of a 90° radio frequency pulse along x, M perpendicular to Bq and to the -axis. See text.

The presence of a static magnetic field within a plasma affects microscopic particle motions and microscopic wave motions. The charged particles execute cyclotron motion and their trajectories are altered into heUces along the field lines. The radius of the helix, or the T,arm or radius, is given by the following ... 

Chemical shift relates the Larmor frequency of a nuelear spin to its ehemieal environment The Larmor frequency is the preeession frequency Vg of a nuclear spin in a static magnetic field (Fig. 1.1). This frequency is proportional to the flux density Bg of the magnetic field vglBg = const.)... 

Figure 1.1. Nuclear precession nuclear charge and nuclear spin give rise to a magnetic moment of nuclei such as protons and carbon-13. The vector n of the magnetic moment precesses in a static magnetic field with the Larmor frequency vo about the direction of the magnetic flux density vector Bo...

Relaxation refers to all processes which regenerate the Boltzmann distribution of nuclear spins on their precession states and the resulting equilibrium magnetisation along the static magnetic field. Relaxation also destroys the transverse magnetisation arising from phase coherenee of nuelear spins built up upon NMR excitation. 

Spin-lattice relaxation is the steady (exponential) build-up or regeneration of the Boltzmann distribution (equilibrium magnetisation) of nuelear spins in the static magnetic field. The lattice is the molecular environment of the nuclear spin with whieh energy is exchanged. 

For an oriented polymer, the magnitude of the observed second moment static magnetic field H0, which can be conveniently defined by the polar and azimuthal angles A, transverse isotropy, to which the following discussion is limited, the observed second moment will depend only on the angle A, there being no preferred orientation in the plane normal to the 3 direction. The treatment follows that originally presented by McBrierty and Ward 9>. 

The significant improvements in sensitivity achieved during the last 5 years have been because of improved probe design and radiofrequency circuits. Since the probe needs to be located very close to the sample, it must be made of a material with a low magnetic susceptibility, for otherwise it would cause distortions of the static magnetic field thereby adversely affecting line shape and resolution. Much research has therefore been undertaken by NMR spectrometer manufacturers to develop materials that... 

Figure 1.10 (a) The dispersion mode line should have zero amplitude at resonance, (b) The deuterium lock keeps a constant ratio between the static magnetic field and the radiofrequency. This is achieved by a lock feedback loop, which keeps the frequency of the deuterium signal of the solvent unchanged throughout the experiment. 

Fig. 9.5 Illustration of the dipolar interaction. (A and B) The magnetic field induced by spin I adds up to the static magnetic field Bo and leads to a shift of the resonance frequency of the close-by spin S. Since spins parallel and...

Fig. 4.1.4 Porosity distribution within a horizontal layer of the Bentheimer sample. Axis z- is parallel with the static magnetic field.

Fig. 4.5.1 Photograph of the NMRI probe designed to generate a concentric cylinder shear flow. The cylinder axis is parallel to the direction of the static magnetic field B0. The front of the probe is inserted into the magnet...

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