Pulse sequences Hahn-echo sequence

Fig. 17. NMR spectrum obtained using a single 90° pulse without H decoupling in pure DPPC bilayers at 50 °C and 1 bar (a) and P NMR spectra obtained using a fully phase-cycled Hahn echo sequence with inversely gated H decoupling in pure DPPC bilayers at 50 °C and 1 bar in the LC phase (b), 1 kbar in the GI phase (c), 1.75 kbar in the interdigitated Gi gel phase (d), 2.5 kbar in the GII gel phase (e), 3.7 kbar in the GUI gel phase (f), and 5.1 kbar in the GX gel phase (g) (after Refs. 4, 18).

For the basic PFGE experiment a spin-echo experiment (either the two-pulse Hahn echo sequence, Fig. la, or the three-pulse stimulated echo sequence. Fig. lb) is combined with two magnetic field gradient pulses with duration 8 and separated by the time duration A. The gradient pulses generate a magnetic... 

Fig. 4. The CPMG pulse sequence. An echo is formed halfway between two consecutive K pulses. The echo amplitude (or the Fourier transform of the half-echo) provides an evaluation of T2 less affected by translational diffusion than in the simple Hahn sequence. The phase change of k pulses with respect to the initial Jt/2 pulse cancels the effect of (re) pulse imperfections.

The rf power is reduced by a factor of four as compared to that of the Hahn-echo sequence for a given pulse width. 

Fig. 7.2.12 [Capl] Schemes for compensation of gradient moments. Left gradient waveforms without refocusing pulses. Right gradient waveforms for use in Hahn-echo sequences.

Consider again the Hahn echo sequence (7t/2)Q-T-(/t)9Q-x-echo. It should not give rise to any echoes in a dipolar system of one kind of spins in solids because the second pulse simply inverts all spins and, consequently, the local fields as well. A sequence which does result in an echo, however, is (7t/2)0-T-(7t/2)9Q-x-echo, xsolid echo and, under the condition t< the trailing half of the echo is equal to the FID (Powles and Strange, 1963). Therefore, the... 

Hahn echo sequences work regardless of the relative phases of the two pulses so that the solid echo sequence (7i/2)Q-x-(7i/2)gQ can induce Hahn echoes in an isotropic non-viscous liquid as well as the echoes from two identical n/2 pulses. Therefore, two different contributions to an echo can exist for the solid echo in a sample like a liquid crystal which has both a liquid and solid character (Cohen-Addad, 1974 Cohen-Addad, and Vogin, 1974). 

The possibility of echo formation is improved if there is a second kind of spins present in the solid. In fact, even the Hahn echo sequence can produce an echo in the solid in that case (Warren and Norberg, 1967). Basically, the 71 pulse inverts only one kind of nuclei in the presence of the local... 

Figure 18. The time evolution of the fluorescence intensity after the application of the Hahn echo sequence for different values of the waiting time T. The zero of the time axis corresponds to the end of the third microwave pulse. The solid lines are a result of a calculation using Eq. (11). Curve a) corresponds to a r of 0.2, b) r = 2 ps and c)...

Figure 4 A schematic depiction of the (A) one-pulse, (B) Hahn-echo, and (C) QCPMG pulse sequences. In this diagram, jr denotes a 180° pulse, nil represents a 90° pulse, T is a delay, and is the time associated with an individual echo. A/ is the number of loops or echoes in the QCPMG pulse sequence.

Fig. 7. Schematic diagram of the events during a two-pulse Hahn echo sequence. Re and Im refer to the so-called real and imaginary NMR signal components, that is, the two channels of the quadrature phase-sensitive detector. Ideally, 0, = 90° and 02 1 0°, with phase cycling of and 02- dashed regions of the NMR signals following the pulses represent the deadtime of the receiver. From Ranee and Byrd (1983).

Fig. 2.9.2 Radiofrequency, field gradient and current distributions requires a three-dimen-ionic current pulse sequences for two-dimen- sional imaging sequence [see Figure 2.9.1(a)] sional current density mapping. TE is the Hahn and multiple experiments with the orientation spin-echo time, Tc is the total application time of the sample relative to the magnetic field of ionic currents through the sample. The 180°- incremented until a full 360°-revolution is pulse combined with the z gradient is slice reached. The polarity of the current pulses...

Fig. 2.9.7 Hahn spin-echo rf pulse sequence combined with bipolar magnetic field gradient pulses for hydrodynamic-dispersion mapping experiments. The lower left box indicates field-gradient pulses for the attenuation of spin coherences by incoherent displacements while phase shifts due to coherent displacements on the time scale of the experiment are compensated. The box on the right-hand side represents the usual gradient pulses for ordinary two-dimensional imaging. The latter is equivalent to the sequence shown in Figure 2.9.2(a).

A few relatively recent published examples of the use of NMR spectroscopy for studying polymer degradation/oxidation processes will now be discussed briefly. At the early stages of degradation, the technique can be used to provide chemical identification and quantification of oxidised species for polyolefins, oxidation sites can be identified by the chemical shifts of -CH2- groups a and ji to carbons bonded to oxygen [85]. Spin-spin relaxation times may be determined by a pulse sequence known as the Hahn spin-echo pulse sequence. 

Acquisition of wide static or MAS spectra of the CT is typically made using a two-pulse echo sequence nil t n (the Hahn echo [55,106]). By setting the strength of the rf-field at mrf = Aco/(I+ 1/2), where Aco is the CT linewidth, these sequences selectively irradiate the CT, while minimizing the contributions from the STs [107, 108]. In such case, the opjj frequencies are given by (29) ... 

Fig. 1. The pulse sequences for the pulsed field gradient echo NMR experiment (a) Hahn echo, (b) stimulated or three-pulse sequence.

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... 

Fig. 14. Dependence of the relaxation times T2. and the fractions of protons with different mobility (f.) for unsaturated polyester on the curing time, as measured from broad line NMR ( ), Hahn spin-echo ( ) and Carr-Purcell pulse sequence (O)- Symbol x indicates the initial distribution of styrene and unsaturated polyester protons (adapted from Ref. S5))...

Figure A1.3.2 Hahn Echo (Spin Echo) pulse sequence and schematic NMR signal from an oilseed. Label A1 indicates the position of the water plus oil sampling window. The label A2 indicates the oil-only sampling window.

Figure 2. Pulse sequence diagram of a Hahn spin-echo experiment with field gradient pulses. Rf- and field gradient pulses are denoted by 90°, 180° and FGP, respectively. The FGP pulses have a length 5 and are separated by an interval A as in the spin-echo sequence given in Fig. 1. VD is a time delay which may be variable in which case also A is variable. A PFG NMR experiment may also be performed with variable 5 or gradient strength (G) and fixed A. Normally, 6 is chosen between 0 and 10 ms and A between 0 and 400 ms. The time delay t depends on the T1 relaxation time of the pure oil of the emulsion but is normally between 130 and 180 ms.

Figure 3. High resolution proton NMR spectra of cheese, obtained by application of a Hahn spin echo pulse sequence with and without field gradient pulses. Measurements were performed on a Bruker MSL-300 spectrometer, operating at 300 MHz. The field gradient unit used with this spectrometer was home-built and the strength was calibrated to 0.25 T/m, using a 1-octanol sample for which the diffusion coefficient is known at several temperatures.

Figure 25 H-decoupled 31P NMR powder spectra of DMPC MLV samples as a function of concentration and pH with sorbic acid at (A) pH 4.4 and (B) 7.4 with decanoic acid at (C) pH 4.4 and (D) 7.4, obtained using a Hahn-echo pulse sequence under static condition at 35 °C.The concentrations of the weak acids are 0 (in black), 5 (in light grey) and 10 (in grey) mol %, respectively. Taken from Ref. [101].

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