Larmor frequency analysis

The purpose of this section is to review the parameters influencing the proton relaxation of a nanomagnet suspension. It will include an analysis of NMRD profiles, which provide the relaxivity dependence with the external held, expressed in proton Larmor frequency units. 

Commercially available instruments include electromagnets of 2.114 and 2.35 Tesla (1 Tesla = 10 kilogauss). For these fields, the range of Larmor frequencies for nuclei of interest in organic structure analysis can be obtained from Fig. 2.35, e.g. ... 

Fig. 2.35. Magnetic field strength and Larmor frequency range for some nuclei of interest in organic structure analysis.

Usually, spin-lattice relaxation experiments are performed at one or a few magnetic fields. The spectral density can thus be determined at only a few Larmor frequencies, so that a detailed analysis of its temperature variation is not possible. Here, an analysis of the spin-spin relaxation times, T, can provide further information about the spectral density, since T2 1 S2(to = 0). Often, the Cole-Davidson distribution Gco(lnT2) [34] is chosen to interpolate the relaxation around the maximum. However, one has to keep in mind that the spectral density close to Tg contains additional contributions from secondary relaxations, such as the excess wing and/or the (i-process discussed in the following sections. In Section IV.C we give an example of a quantitative description of 7) (T) at T > 7 obtained by approximating the spectral density S2(co) using dielectric data. 

The Larmor frequency is dependent on the magnetic field at the loeation of the nucleus, which depends on the influence of nearby atoms. Thus the NMR frequency depends on the ehemieal structure of the molecules in a sample of material. NMR is therefore a useful tool for ehemieal analysis. 

NMR has become such an invaluable technique for studying the structure of atoms and molecules because nuclei represent ideal noninvasive probes of their electronic environment. If all nuclei of a given species responded at their characteristic Larmor frequencies, NMR might then be useful for chemical analysis, but little else. The real value of NMR to chemistry comes from minute differences in resonance frequencies dependent on details of the electronic structure around a nucleus. The magnetic field induces orbital angular momentum in the electron cloud around a nucleus, thus, in effect, partially shielding the nucleus from the external field B. The actual or local value of the magnetic field at the position of a nucleus is expressed as... 

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