Spin Refocusing

Without spin refocusing, the simulations show that R2 reaches a plateau for diameters above 0.02 pm. The corresponding maximum relaxation rate of about 100 s is predicted by the Static Dephasing Regime (SDR) model 22, 23), which assumes that, as depicted above, transverse relaxation is only attributed to differences in precession frequencies of static spins. The relaxation rate is then given by ... 

After a time r, a 180° RF pulse reverses the spin precession. A second gradient pulse of equal duration 8 and magnitude g follows to tag the spins in the same way. If the spins have not changed their position in the sample, the effects of the two applied gradient pulses compensate each other, and aU spins refocus. If the spins have moved due to self-diffusion, the effects of the gradient pulses do not compensate and the echo-amplitude is reduced. The decrease of the amplitude A with the applied gradient is proportional to the movement of the spins and is used to calculate the self-diffusion coefficient. 

Figure 6. The Hahn spin echo experiment in the rotating frame, (a) Tipping of M into the x y plane by 90° pulse, (b) Decrease in M,. as spins dephase. (c) Application of a second (180°) pulse, (d) Increase in M. as spins refocus , (e) Complete refocusing, (f) Decay in M,. as spins dephase. From [2].

It was shown in section 6.2.6 that the spin echo applied to one spin refocuses the offset this conclusion is not altered by the presence of a coupling so the offset will be ignored in the present calculation. This greatly simplifies things. 

In a heteronuclear experiment (separate pulses shown on the / and S spins) a 180° pulse on the S spin refocuses the IS coupling over the period 28. The gradient pulses shown are used to "clean up" the inversion pulse. 

Figure Bl.14.1. Spin warp spin-echo imaging pulse sequence. A spin echo is refocused by a non-selective 180° pulse. A slice is selected perpendicular to the z-direction. To frequency-encode the v-coordinate the echo SE is acquired in the presence of the readout gradient. Phase-encoding of the > -dimension is achieved by incrementmg the gradient pulse G...

In electron-spin-echo-detected EPR spectroscopy, spectral infomiation may, in principle, be obtained from a Fourier transfomiation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of tire echo is used as the main source of infomiation in ESE experiments. Recording the intensity of the two-pulse or tliree-pulse echo amplitude as a function of the external magnetic field defines electron-spm-echo- (ESE-)... 

The spin-echo experiment therefore leads to the refocusing not only of the individual nuclear resonances but also of the field inhomogeneity components lying in front or behind those resonances, a maximum negative amplitude being observed at time 2t after the initial 90° pulse. The frequency of rotation of each signal in the rotating frame will depend on its chemical shift and after the vector has been flipped by the 180° pulse, it... 

Figure 2.2 Effect of 180 pulse on phase imperfections resulting from magnetic field inhomogeneities. Spin-echo generated by 180 refocusing pulse removes the effects of magnetic field inhomogeneities.

Figure 2.3 Spin-echo experiment. The behavior of nucleus X in an AX spin system is shown. (A) Application of the second 180° pulse to nucleus X in the AX hetero-nuclear system results in a spin-flip of the two X vectors across the x -axis. But the direction of rotation of the two X vectors does not change, and the two vectors therefore refocus along the —y axis. The spin-echo at the end of the t period along the -y axis results in a negative signal. (B) When the 180° pulse is applied to nucleus A in the AX heteronuclear system, the spin-flip of the X vectors...

Hence it is clear that if the two delay periods before and after the 180° pulses are kept identical, then refocusing will occur only when a selective 180° pulse is applied. This can happen only in a heteronuclear spin system, since a 180° pulse applied at the Larmor frequency of protons, for instance, will not cause a spin flip of the C magnetization vectors. 

Will the vectors of a doublet be refocused at time 2t in a spin-echo experiment ... 

Nuclei resonating at different chemical shifts will also experience similar refocusing effects. This is illustrated by the accompanying diagram of a two-vector system (acetone and water), the nuclei of which have different chemical shifts but are refocused together by the spin-echo pulse (M, = magnetization vector of acetone methyl protons, M(v = magnetization vector of water protons). 

The basic INEPT spectrum cannot be recorded with broad-band proton decoupling, since the components of multiplets have antiphase disposition. With an appropriate increase in delay time, the antiphase components of the multiplets appear in phase. In the refocussed INEPT experiment, a suitable refocusing delay is therefore introduced that allows the C spin multiplet components to get back into phase. The pulse sequences and the resulting spectra of podophyllotoxin (Problem 2.21) from the two experiments are given below ... 

A 90° Gaussian pulse is employed as an excitation pulse. In the case of a simple AX spin system, the delay t between the first, soft 90° excitation pulse and the final, hard 90° detection pulse is adjusted to correspond to the coupling constant JJ x (Fig- 7.2). If the excitation frequency corresponds to the chemical shift frequency of nucleus A, then the doublet of nucleus A will disappear and the total transfer of magnetization to nucleus X will produce an antiphase doublet (Fig. 7.3). The antiphase structure of the multiplets can be removed by employing a refocused ID COSY experiment (Hore, 1983). 

Spin-echo The refocusing of vectors in the xy-plane caused by a (t-180°-t) pulse sequence produces a spin-echo signal. It is used to remove field inhomogeneity effects or chemical shift precession effects. 

The reference scan is to measure the decay due to spin-lattice relaxation. Compared with the corresponding stimulated echo sequence, the reference scan includes a jt pulse between the first two jt/2 pulses to refocus the dephasing due to the internal field and the second jt/2 pulse stores the magnetization at the point of echo formation. Following the diffusion period tD, the signal is read out with a final detection pulse. The phase cycling table for this sequence, including 2-step variation for the first three pulses, is shown in Table 3.7.2. The output from this pair of experiments are two sets of transients. A peak amplitude is extracted from each, and these two sets of amplitudes are analyzed as described below. 

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