Pulse Inversion recovery

Figure 3. Partial 100-MHz 2H NMR spectra of methyl p-D-glucopyranoside, showing the single selective determination of the spin-lattice relaxation rate of H-l using a two-pulse inversion recovery sequence. All spectra were monitored as for those in Figure 2 except for pulse delay — 25 sec. The duration of the selective 180°-pulse was 38 msec (13 Hz bandwidth). The time interval (sec) between the selective 180°- and 90° -pulses are indicated to the right of each...

Spin- spin relaxation is usually determined applying spin echoes (Hahn-Echo, CPMG method), which delete other influences such as Bo inhomogeneity. The spin-lattice relaxation time Ti is measured by detecting the relaxation after inverting Mo by a 180° pulse (inversion recovery method). 

The values of the time constants and are important in understanding both internal and overall motional behavior of the sample molecule. values are measured by the inversion recovery pulse sequence ... 

The technique for measurement which is most easily interpreted is the inversion-recovery method, in which the distribution of the nuclear spins among the energy levels is inverted by means of a suitable 180° radiofrequency pulse A negative signal is observed at first, which becomes increasingly positive with time (and hence also with increasing spin-lattice relaxation) and which... 

The chemical shifts are obtained from the spectra of the T1 measurements in relation to the signal for the methyl carbon (20.6 ppm). The T1 measurements were performed using the inversion recovery (IR) method (180 deg. (12.7 us)-tau — 90 deg. (6.1 us)) with MAS 2200 scans were collected and the pulse delay time was veryshort, + 10 sec. 

Fig. 7. A C-13 relaxation time measurement of solid state wetted cellulose acetate (6% by weight water) using the inversion recovery (IR) method at 50.1 MHz and spinning at 3.2 kHz at the magic angle (54.7 deg) with strong proton decoupling during the aquisition time (136.3 ms), (upper part of the Figure). Tau represents the intervals between the 180 deg (12.2 us) inverting and 90 deg (6.1 us) measuring pulse. 2200 scans were collected and the pulse delay time was 10 s, Cf. Table 3 and Ref.281...

The most popular, and also a very accurate, experimental method for measuring nonselective spin-lattice relaxation-rates is the inversion recovery (180°-r-90°-AT-PD)NT pulse sequence. Here, t is the variable parameter, the little t between pulses, AT is the acquisition time, PD is the pulse delay, set such that AT-I- PD s 5 x T, and NT is the total number of transients required for an acceptable signal-to-noise ratio. Sequential application of a series of two-pulse sequences, each using a different pulsespacing, t, gives a series of partially relaxed spectra. Values of Rj can... 

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...

Another method used to measure relaxation rates is the three-pulse (180°-t-90°-AT-PD—90°)nt sequence. This method is similar to the inversion recovery, with the addition of a third 90° pulse after the pulse... 

Selective, spin-lattice relaxation-rates are measured by the inversion-recovery technique. A rather weak, 180° pulse of very long duration (10-50 ms) inverts a multiplet (single-selective) or two multiplets (double-selective) in the spectrum of asperlin (1 see Fig. 2 ) and the recovery of the... 

It is important to avoid saturation of the signal during pulse width calibration. The Bloch equations predict that a delay of 5 1] will be required for complete restoration to the equilibrium state. It is therefore advisable to determine the 1] values an approximate determination may be made quickly by using the inversion-recovery sequence (see next paragraph). The protons of the sample on which the pulse widths are being determined should have relaxation times of less than a second, to avoid unnecessary delays in pulse width calibration. If the sample has protons with longer relaxation times, then it may be advisable to add a small quantity of a relaxation reagent, such as Cr(acac) or Gkl(FOD)3, to induce the nuclei to relax more quickly. 

Inversion recovery A pulse sequence used to determine spin-lattice relaxation times. 

The idea of exploration of relaxation correlation was first reported in 1981 by Peemoeller et al. [23] and later by English et al. [24] using an inversion-recovery experiment detected by a CPMG pulse train. This pulse sequence is shown in Figure 2.7.1. 

T, values can be easily determined using pulse sequences which form part of the standard computer software, the most common one being the so-called inversion-recovery experiment. 

This experiment uses two pulses, 180° and 90°, separated by a delay time x which is varied. For each delay a certain number of FIDs are accumulated the result is a series of spectra in which the individual signals have different intensities. Figure 9 shows the result of an inversion-recovery experiment carried out on 1. 

Fig. 9 Spectra of compound 1 obtained from an inversion-recovery experiment. Pulse sequence fixed delay - 180° pulse - variable delay x - 90° pulse - acquisition of FID...

Because the excitation/detection coil is in the x-y plane and the longitudinal component relaxes along the z axis, T cannot be measured directly from an NMR spectrum, but must be obtained using a pulse sequence. The most commonly used pulse sequence to measure T is an inversion recovery pulse sequence (Kemp, 1986). Other commonly used pulse sequences for measuring 7j are given in Ernst et al. (1987). 

A number of pulse-sequence methods are available for measurement of Ti values, and those most commonly used are the methods of saturation recovery (s.r.F.t.),69,70 progressive saturation (p.s.F.t.),71 inversion recovery (i.r.F.t.),72 and the Freeman-Hill modification of in-... 

FIGURE 31. Typical data set for measurement of the spin-lattice relaxation times of the sp2-hybridized carbon atoms of, 6-carotene at 11.7 T. The chemical shift values are shown across the bottom of the figure. The t-value for each spectrum is the delay time in the inversion-recovery pulse sequence. Reprinted with permission from Reference 49. Copyright (1995) American Chemical Society... 

Abbreviations D, self-diffusion coefficient ge, gradient-echo IR, inversion recovery IRFT, inversion recovery fourier transform MRS, magnetic resonance spectroscopy PD, proton density PFGSE, pulsed field gradient spin echo se, spin-echo. 

Fig. 1. Top Scheme of an inversion recovery experiment 5rielding the longitudinal relaxation time (inversion is achieved by mean of the (re) radiofrequency (rf) pulse, schematized by a filled vertical rectangle). Free induction decays (fid represented by a damped sine function) resulting from the (x/2) read pulse are subjected to a Fourier transform and lead to a series of spectra corresponding to the different t values (evolution period). Spectra are generally displayed with a shift between two consecutive values of t. The analysis of the amplitude evaluation of each peak from — Mq to Mq provides an accurate evaluation of T. Bottom the example concerns carbon-13 Tl of irans-crotonaldehyde with the following values (from left to right) 20.5 s, 19.8 s, 23.3 s, and 19.3 s.

Users of any NMR instrument are well aware of the extensive employment of what is known as pulse sequences. The roots of the term go back to the early days of pulsed NMR when multiple, precisely spaced RF excitation pulses had been invented (17,98-110) and employed to overcome instrumental imperfections such as magnetic field inhomogeneity (Hahn echo) or receiver dead time (solid echo), monitor relaxation phenomena (saturationrrecovery, inversion recovery, CPMG), excite and/or isolate specific components of NMR signals (stimulated echo, quadrupole echo), etc. Later on, employment of pulse sequences of increasing complexity, combined with the so-called phase-cycling technique, has revolutionized FT-NMR spectroscopy, a field where hundreds of useful excitation and detection sequences (111,112) are at present routinely used to acquire qualitatively distinct ID, 2D, and 3D NMR... 

There are important FFC sequences in which the preparatory sub-sequence sections includes RF pulses. A typical example is the FFC version of the classical inversion recovery sequence (IR). 

Fig. 28. FFC Inversion Recovery sequence. In the upper case the sample is first prepolarized in a filed Bp, then switched to the acquisition field Ba where the first RF pulse of 180° is applied and the sample magnetization is inverted. The field is then switched to B,. and the sample is allowed to relax for the variable time t. Finally, the field is switched again to the acquisition value and the magnetization is sampled by any of the sample-detection methods (here, a simple FID following a 90° RF pulse). Notice that, as shown in the lower diagram, in the special case when Bp = Ba it is possible to neatly avoid the extra switching interval prior to the inversion pulse.

The classical Jeener Broekaert sequence (133) is used to determine the dipolar-order relaxation time (in systems of spin 1/2 nuclides) and the Tiq relaxation time (in systems with spin 1 nuclides) of spin 1 nuclides with quadrupolar contributions to 7. Its FFC version is similar to the Inversion Recovery, except that the first 180° pulse is replaced by the sequence 90, — 5 — 45, the detection pulse becomes 45 and a special phase cycle is required. We shall not dwell on the details and purpose of the sequence since they go beyond the scope of this chapter. We wish to underline, however, the fact that sequences of this type require a close coordination of the preparatory sub-sequence with the signal-detection sub-sequence in order to isolate not just a particular magnetization component but a particular relaxation pathway. 

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