Magnetic field,nucleus

The shielding at a given nucleus arises from the virtually instantaneous response of the nearby electrons to the magnetic field. It therefore fluctuates rapidly as the molecule rotates, vibrates and interacts with solvent molecules. The changes of shift widi rotation can be large, particularly when double bonds are present. For... 

Section 13 4 The energy required to flip the spin of a proton from the lower energy spin state to the higher state depends on the extent to which a nucleus is shielded from the external magnetic field by the molecule s electrons... 

Shielding (Section 13 4) Effect of a molecule s electrons that decreases the strength of an external magnetic field felt by a proton or another nucleus... 

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.

Nuclear magnetic resonance (nmr) requires an atomic nuclei that can absorb a radio-frequency signal impinging it in a strong magnetic field to give a spectmm. The field strength at which the nucleus absorbs is a function of both the nucleus and its immediate electronic environment. The atoms normally used for nmr analysis are as follows (34) H, F, P, Si, and Of these, the most commonly used in polymer analyses are... 

It is convenient to reference the chemical shift to a standard such as tetramethylsilane [TMS, (C//j)4Si] rather than to the proton fC. Thus, a frequency difference (Hz) is measured for a proton or a carbon-13 nucleus of a sample from the H or C resonance of TMS. This value is divided by the absolute value of the Larmor frequency of the standard (e.g. 400 MHz for the protons and 100 MHz for the carbon-13 nuclei of TMS when using a 400 MHz spectrometer), which itself is proportional to the strength Bg of the magnetic field. The chemical shift is therefore given in parts per million (ppm, 5 scale, Sh for protons, 5c for carbon-13 nuclei), because a frequency difference in Hz is divided by a frequency in MHz, these values being in a proportion of 1 1O. ... 

In the absence of an external magnetic field, the 21 + 1 energy states of a nucleus are of identical energy (they are said to be degenerate) and, therefore, are equally populated at thermal equilibrium in any assemblage of such nuclei. In the presence of an applied steady field Ho, these 21 + states will assume different energy... 

Consider a nucleus with magnetic moment pi in a magnetic field Ho- According to classical mechanics the rate of change of the angular momentum G is the torque T. 

A more recent implementation, which completely eliminates the gauge dependence, is to make the basis functions explicitly dependent on the magnetic field by inclusion of a complex phase factor refening to the position of the basis function (usually the nucleus). 

There are a number of NMR methods available for evaluation of self-diffusion coefficients, all of which use the same basic measurement principle [60]. Namely, they are all based on the application of the spin-echo technique under conditions of either a static or a pulsed magnetic field gradient. Essentially, a spin-echo pulse sequence is applied to a nucleus in the ion of interest while at the same time a constant or pulsed field gradient is applied to the nucleus. The spin echo of this nucleus is then measured and its attenuation due to the diffusion of the nucleus in the field gradient is used to determine its self-diffusion coefficient. The self-diffusion coefficient data for a variety of ionic liquids are given in Table 3.6-6. 

All nuclei in molecules are surrounded by electrons. When an external magnetic field is applied to a molecule, the electrons moving around nuclei setup tiny local magnetic fields of their own. These local magnetic fields act in opposition to the applied field so that the effective field actually felt by the nucleus is a bit weaker than the applied field. 

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