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—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—.—i—i—i—i—i—i—i-5.4 5.2 5.0 4.8 4.6 4.4 4.2 4.0 3.8 3.6 3.4 ppm

—i—i—i—i—i—i—i—i—i—i—i—i—i—i—i—.—i—i—i—i—i—i—i-5.4 5.2 5.0 4.8 4.6 4.4 4.2 4.0 3.8 3.6 3.4 ppm

Figure 8.18

profile anywhere in the spectrum we want. Figure 8.18 shows a stacked plot of spectra of sucrose in D20 with different effective frequencies of the shaped pulse, using the phase ramp (frequency-shifted laminar pulse) to move the center of the excitation profile. The reference frequency and pulse frequency (vr) are the same in all of these spectra. We can cleanly select any of the resolved peaks in the spectrum, with no excitation of other peaks. Only in the case of crowded regions (d-f) do we see any excitation of neighboring peaks.

8.6.2 Selective Annihilation: Watergate

We have seen that the key to selectivity in the PFGSE is whether the spins in question receive a 180° pulse at the center of the spin echo. If they do not, all magnetization (including z magnetization) is destroyed. This can be applied as a strategy for getting rid of unwanted peaks in a spectrum. The most unwanted peak in all of NMR spectroscopy is the water peak in a 90% H20/10% D2O sample. We saw in Chapter 5 how presaturation can be used to selectively saturate the water protons with a long, low-power irradiation at exactly the water resonance frequency. The problem with presaturation is that these saturated H20 protons can exchange with amide NH positions, carrying their lack of magnetization along with them. This "bleaches" these signals, reducing or even removing them from the spectrum. What if we had a shaped pulse that provides a 180° pulse everywhere except the center of the spectral window, where the water peak is positioned? All the peaks of the spectrum will survive the PFGSE, but the water peak will be destroyed by the gradients because its coherence helix is not reversed in the middle of the spin echo. This is better than presaturation because the water magnetization is destroyed quickly at the end of the pulse sequence, just before the start of the FID. Furthermore, the water at any level of the NMR tube still has its full net magnetization—it is only at the level of summing the water magnetization at all levels of the tube that we get cancellation and a zero net magnetization.

(no effect)

Figure 8.19

(no effect)

Figure 8.19

The only problem is that we need to find this magic selective pulse that delivers a 180° rotation everywhere but the center of the spectral window. There are shaped pulses that do this, but it turns out that the simplest solution is a series of six hard pulses separated by equal delays. If we divide the 90° rotation into 13 small rotations of equal angle, the sequence is

where the numbers are multiples of 90/13 = 6.92° and the bar over the number means that the pulse phase is reversed from that of the first three pulses (e.g., —x instead of x). The actual pulse rotations are 20.77° ("3"), 62.31° ("9"), and 131.54° ("19"), and their durations are calculated from the calibrated 90° pulse width.

To understand this sequence, let's start with a very simple set of two pulses separated by a delay. The sequence 90°x-t-90° — x is called a "jump-return" or 1 — 1 sequence and can be used as a selective 90° pulse on everything but the water. The water resonance, which is placed at the center of the spectral window, does not undergo chemical shift evolution during the t delay. So it is rotated from to — y, sits motionless on the — y axis during the t delay, and then returns to . It receives no excitation at all (Fig. 8.19). Now consider a resonance with an offset (vo — vr) of 1/(4t) Hz. Just like the water magnetization, it moves from to —y during the first pulse. But during the t delay, it precesses ccw in the x'-y' plane by an angle 1/(4t) x t = 1/4 cycle or 90°, from the —y' axis to the x' axis. The final 90° pulse has no effect, as the magnetization is on the same axis as the pulse. At the end of the sequence, we have delivered an overall 90° excitation pulse to the spins at this offset. In general, for an offset of Q rad/s (Q = 2n(vo — vr)) we have

Iz —> — Iy — t ^ — IycosQt + IxsinQT —> IzcosQt + IxsinQT

The excitation profile is just a sine function, with positive peaks to the left of the center of the spectral window rising to a peak at an offset of Q = n/(2T) and then falling to another null at Q = n/t. To the right of the center of the spectral window, we see the same thing except that the peaks are negative. At the center (Q = 0), there is no excitation. This is quite a radical distortion of our spectrum, a high price to pay for destroying the water signal.

Now let's return to the "3-9-19" sequence. For the water peak, it's simple. As there is no evolution during the t delays, it is just a sequence of six pulses whose rotation is exactly balanced between ccw rotations (3-9-19) and cw rotations (19 — 9 — 3). The net rotation is zero and the water magnetization ends up on the axis, where it started. Water is not affected by the pulse train. The same is true if the offset is vo — vr = 1/t

Figure 8.20

or — 1/t (Q = 2n/t or —2n/t) as the evolution of the x-y component will be 360° during each t delay, returning the vector to where it started before the t delay. What if the offset is right between these two extremes, at vo — vr = 1/(2t)? The x-y component of the magnetization vector will rotate exactly 180° during the t delay. If the pulses are on the x' axis (or the —x' axis), the net magnetization stays in the y'-z plane and each delay flips it to the opposite side (reversing the y' component). The chemical shift evolution can be thought of as a 180° rotation around the z axis: a "+z pulse." If we divide the 360° rotation around the x' axis in the y'-z plane into 52 equal angles (13 for each 90° rotation), we can describe the position of the net magnetization by a number between 0 and 52 (Fig. 8.20). Now we can "narrate" the effect of the 3-9-19 sequence. Starting from position 13 (the +z axis)

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