Flip angles

Richard Ernst, who won the 1991 Nobel Prize in Chemistry, conclusively demonstrated that the second method of using less-than-90° pulses with no delay times is superior (Ernst and Anderson, 1966). He calculated the ratio 7/7] (max) and related it to the optimum angle of rotation, (the Ernst angle). In this expression, T is the total time between pulses, which 

While the Ernst angle relationship has worked very well for many years, problems can arise if 7/7] (max) moves, for a variety of reasons, off scale (to the left) or if the resulting 

Even if the does not appear to be too short for the relaxation times involved, we saw at the beginning of this section that spectral resolution and fa are inversely related. Desirable H and spectral resolution values are about 0.25 and 1 Hz, respectively, and such numbers, in turn, require /y s of approximately 4 and 1 s, respectively. One remedy for the problem of short is to use a larger number of data points. If np = 65,536 (64K), also is doubled (assuming that sw remains constant). This approach, however, increases both the memory and speed requirements of the spectrometer computer. 

The consequences of this relationship are considerably different for H and NMR. In Section 2-4d, we saw that proton are around 4 s for standard 10-ppm spectral widths at 400 MHz, while those for C are about 0.75 s for common 220-ppm spectral windows at 100 MHz. The numerators of the 7/7 (max) ratio for H and therefore, are considerably different if T is essentially equal to fy ( is in xs, and its contribution to T can be ig-nored). The denominators of this ratio are less different for H and C than one would imagine when quaternary carbons are ignored. The T values of protons and many protonated carbons are similar in magnitude ( 2-3 s) if very small molecules are discounted (Section 5-1). Nonprotonated carbons are another matter and have significantly longer T values. The T % of these carbons, however, are usually considered only indirectly when NMR spectroscopists determine r/7 (max) ratios. 

Because H and are not generally known, the selection of a often is done in the 

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In a coupled spin system, the number of observed lines in a spectrum does not match the number of independent z magnetizations and, fiirthennore, the spectra depend on the flip angle of the pulse used to observe them. Because of the complicated spectroscopy of homonuclear coupled spins, it is only recently that selective inversions in simple coupled spin systems [23] have been studied. This means that slow chemical exchange can be studied using proton spectra without the requirement of single characteristic peaks, such as methyl groups. 

H-NMR studies were performed on a Bruker MSL-400 spectrometer operating in the Fourier transform mode, using a static multinuclei probehead operating at 400.13 MEtz. A pulse length of 1 iis is used for the 90° flip angle and the repetition time used (1 second) is longer than five times Tjz ( H) of the analyzed samples. 

Since there is a slight delay between when a pulse is switched on and when it reaches full power, an error may be introduced when measuring 90° or smaller pulses directly. If the 90° pulse width is required with an accuracy of better than 0.5 fi, then it may be determined more accurately by using self-compensating pulse dusters that produce accurate flip angles even when there are small (<10%) errors in the setting of pulse widths. 

Many subspectral editing techniques alternative to DEPT, such as SEMUT (Subspectral Editing using a Multiple Quantum Trap) (Bildsoe et al., 1983) and SEMUT GL, have been developed that utilize the fact that the transfer of magnetization to unobservable multiple-quantum coherence for CH, CHj, and CH spin systems is dependent on the last flip angle 0. However, these experiments have not been widely used. 

Figure 6.2 Pulse sequences for some common 3D time-domain NMR techniques. Nonselective pulses are indicated by filled bars. Nonselective pulses of variable flip angle are shown by the flip angle )8. Frequency-selective pulses are drawn with diagonal lines in the bars. (Reprinted from J. Mag. Reson. 84, C. Griesinger, et al, 14, copyright (1989), with permission from Academic Press, Inc.)...

Flip angle The angle by which a vector is rotated by a pulse. 

The shape of any rf pulse can be chosen in such a way that the excitation profile is a rectangular slice. In the light of experimental restrictions, which often require pulses as short as possible, the slice shape will never be perfect. For instance, the commonly used 900 pulse is still acceptable, while a 1800 pulse produces a good profile only if it is used as a refocusing pulse. Sometimes pulses of even smaller flip angles are used which provide a better slice selection (for a discussion of imaging with small flip angles, see Section 1.7). 

Fig. 1.20 Gradient-echo based pulse sequences based on low flip angles. When low flip angles and short image repetition times are employed at the expense of transverse magnetization during the course of the complete image acquisition, this represents a FLASH sequence (without ). The combination of flip angle and repetition time can be adjusted in...

Fig. 1.22 RARE sequence. Here the formation of the first spin echo is conventional. The CPMG form of spin echo is used to avoid the accumulation of flip angle errors over the echo train. However, before the second echo can be acquired, the phase-encoding has to be rewound to undo the dephasing of the spins. Therefore, a phase encoding step of equal...

The rf pulses for 27A1 NMR experiments were calibrated using an aqueous solution of A1C13. For the rf power level attenuated by 10 dB, the duration of the 180 "-pulse of the broadband probe was 60 ps. All solids imaging experiments were performed with t => 300 ps and the nominal flip angle a = 90°/(J + 1/2). The two pulses had the same amplitude and for 27A1 MRI were 10- and 20-ps long, respectively. 

Proton NMR and deuteron NMR spectra of soluble fractions and spent solvent mixtures were obtained by using a JE0L FX60Q FT NMR Spectrometer. A flip angle of 45° was used which corresponds to 14 ms for and 75 ms for 2H. The pulse repetition times were 6.0 and 9.0 s, respectively. Chloroform-d was used as the NMR solvent, and chloroform was used as the 2H NMR solvent. 

A) Recorded with 256 increments, 4 transients, and a recovery delay of 1 s. (B) Recorded with 256 increments, 8 transients, and a recovery delay of 0.2 s. The flip angle a was set to 90°. The typical F2 rows (at the 13C chemical shift of C-18, indicated by the horizontal arrows and depicted on the top of the spectra) show the signal enhancements. 

Spectra were determined using a pulse width of 4 yseconds, which corresponds to a flip angle of 18° and a 1 second pulse delay time. The 4000 Hz spectrum was described using 8192 data points. 

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