Net equilibrium magnetization

In NMR experiments the signal intensity is proportional to the net equilibrium magnetization or polarization, Mo, given by ... 

The application of a properly timed rf pulse disturbs the net equilibrium magnetization aligned parallel to the magnetic field Hq. The return of nuclear magnetization to equilibrium for solid polymers depends on the chain mobility and is monitored by the FID. The crystalline phase content can be extracted by deconvoluting the decay curve into portions corresponding to crystalline and noncrystalline components. Crystallinity determination of various polyethylene samples by FID NMR based on two- and three-component approaches, as well as... 

As a result of magnetic inter-particle interactions, each nanoparticle will feel a net local interaction field that can be modelled by a time-dependent local applied field, Hint(t). If the time variation of the local interaction field is either very fast or very slow compared to the relevant characteristic times (e.g., i) of the particle, then Hi t(t) can in turn be modelled as a static local field, that will, of course, depend on temperature and macroscopic applied field. The distributions of particle positions, orientations, and supermoments will determine the distribution of local interaction fields. These interaction fields are present in zero applied field and dramatically affect the behaviors of the individual nanoparticles and, consequently, of the sample as a whole. They achieve this in two important ways. First, they change the equilibrium magnetic properties of the sample, giving rise, for example, to superferromagnetic ordering or interaction Curie-Weiss behaviors (see below). Second, and possibly more importantly, they affect dynamic response, via their influence on SP dwell times. 

Figure 4. Precession of an ensemble of identical nuclei (/ = 1 /2) at thermal equilibrium. The net macroscopic magnetization, M, is oriented along the z axis (the direction of H), components of magnetization along x and y being zero (the dipoles are randomly oriented in the x, y plane).

The direction in which these vectors point can be specified by giving each a phase - arbitrarily the angle measured around from the x-axis. It is immediately clear that if these phases are random the net transverse magnetization of the sample will be zero as all the individual contributions will cancel. This is the situation that pertains at equilibrium and is shown in (a) in the figure above. 

Those familiar with the routine acquisition of 13c NMR spectra are aware of the consequences of the nuclear Overhauser effect (NOE). Saturation of protons has the effect of increasing the net 13c magnetization of those carbons relaxed by the protons of up to a factor of three times the equilibrium magnetization. Most analytical or survey 13c spectra are obtained with continuous broadband proton decoupling and any resultant NOE. Characteristics of this mode of operation are, (1) the possibility of variable NOE, (2) repetition rate governed by 13c T and (3) both protonated and non-protonated carbons are detected. The first aspect makes quantitation difficult. The second affects net sensitivity, and the third has the prospect of having undesirable signals in certain situations. 

The observed signal in the time domain is called a free induction decay (FID) because it is measured free of a driving if field. It is a decaying voltage because the net nuclear magnetic field decays as the nuclei return to their equilibrium value (Fig. 6.5). 

At equilibrium, the transverse magnetization equals zero. A net magnetization vector rotated off the -axis creates transverse magnetization. 

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