Magnetization-recovery curve

NMR relaxometry Free induction decay (T2 ) or solid echo Spin echo decay (T2) Magnetization recovery curve (7)) Eads (1998)... 

Fig, 8. I3C magnetization recovery curves of the crystalline and amorphous methylene carbons in zinc salt of ethylene ionomers after ageing at room temperature for a long time (E-0.054MAA-0.9Zn) and annealing at 80 °C for 78 hours (E-0.054MAA-0.9Zn-ann), and low-density polyethylene (LDPE) at room temperature. 

An estimate of the average xenon diffusion constant in PMP can be made from the coalescence of peaks if independent domain size information(S,77j is available. A domain size for the amorphous region can be determined by fitting the proton magnetization recovery curve shown in Figure 11. The equation describing the recovery of the magnetization(26j is... 

Fig. 1.—Diagrammatic Representation of the Recovery of Magnetization along the z-Axis (Mj), from Its Initial Value (-M ) to +Mo, Following Its Inversion by a 180° Pulse. The exponential recovery curve shown in [A] depicts the return of magnetization that would be found in a typical inversion-recovery experiment. The curve in [B] would be obtained from a three-pulse sequence, and is a plot of which decreases from an initial value of...

To lessen experimental time, the null-point method may be employed by locating the pulse spacing, tnun, for which no magnetization is observed after the 180°-1-90° pulse-sequence. The relaxation rate is then obtained directly by using the relationship / , = 0.69/t n. In this way, a considerable diminution of measuring time is achieved, which is especially desirable in measurements of very low relaxation-rates, or for samples that are not very stable. In addition, estimates of relaxation rates for overlapping resonances can often be achieved. However, as the recovery curves for coupled spin-systems are, more often than not, nonexponential, observation of the null point may violate the initial-slope approximation. Hence, this method is best reserved for preliminary experiments that serve to establish the time scale for spin-lattice relaxation, and for qualitative conclusions. 

Our procedure for a relaxation time run is to specify the number of points to be taken on the recovery curve, the time interval between those points, the number of FID s to be accumulated per point, and then turn the data acquisition over to the computer. Further embellishments include the fact that we calculate the recovery curve from integrals of selected parts of the on-resonance FID s and that we alternate the functions of the two digitizers with each pulse sequence to cope with the differences between the digitizers. After a specified number of FID s are accumulated at a given value of delay between the combs, a new value of delay is transmitted to the timer and the next point is measured. At the end of such a run, there will be a table of the magnetization recovery as a function of time. 

The recovery curve for the magnetization associated with the Gaussian component along with the fit to obtain a domain. 

Fig. 7.2.1 Pulse sequences for T and related magnetization filters, typical evolution curves of filtered magnetization components, and schematic filter transfer functions applicable in the slow motion regime. Note that the axes of correlation times start at Tc = Wo (a) Saturation recovery filter, (b) Inversion recovery filter, (c) Stimulated echo filter.

Rg. 2.16 The pulse sequence used to determine spectra under dipolar decoupling conditions. Note that only the envelope curve of the FID is shown, not the high-frequency oscillations within it. This is what is usually recorded Fourier analysis then yields the spectrum as frequency shifts from the irradiating frequency. For all pulse sequences, the recovery time Tr between repeated applications of the sequence must be long compared with T. (Adapted from Nuclear Magnetic Resonance in Solid Polymers by V. J. McBrierty and K. J. Packer. Cambridge University Press, 1993.)... 

Equation (1.4) reveals that when the magnetization is fully tipped into the x y plane by a 90° pulse, the magnetization will recover to. 3% of its equilibrium value along z at r = ST). The 7 relaxation time can be measured with an inversion-recovery experiment, where a 180° pulse inverts the magnetization to the negative z axis and allows the magnetization to recover for various times until the curve described by Eq. (1.5) is adequately characterized ... 

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