Hahn spin echo sequence

The intense water signal and the broad protein resonances were suppressed by a combination of continuous secondary Irradiation at the water frequency and the Hahn spin-echo sequence (0[90 x-t-180 y-t-collect]). 

In principle, Ti and T2 can be measured experimentally by the inversion recovery sequence (180°—x—90°) and the Hahn spin-echo sequence, respectively. In practice, these experiments can be easily performed only when the 33S signal is very narrow. If the signal is broad, the difficulties in obtaining 33S spectra with a good S/N make the direct measurements very time-consuming and less precise. The problem can be easily circumvented because T2 (and Ti) can be obtained with good precision directly from line width. 

Fig. 9. (A) Selective excitation and destruction of magnetization using a magnetic field gradient pulse. PGSE sequences used for diffusional attenuation of the solvent signal, based on the Hahn spin-echo sequence (B) and the stimulated-echo sequence (C). In the Hahn spin-echo sequence the magnetization is always subject to spin-spin relaxation. However, in the stimulated-echo sequence the delays can be set such that A is mainly contained in t2 where the relaxation is longitudinal and thus this sequence is preferable for large solute molecules since the condition T2 < usually holds.

To minimize signal loss due to spin-spin relaxation, it is often preferable with larger solute molecules to use a stimulated-echo-based sequence (see Fig. 9C) in lieu of the Hahn spin-echo sequence, for which the attenuation equation is given by... 

The Hahn spin-echo sequence consists of a 90° pulse followed after a time T by a 180° pulse. The second pulse refocuses the magnetization, and the spin echo is formed after a time 2r.) Vary r to allow T2 to be determined by... 

We consider the coherence evolution of uncoupled spins 7=1/2 during the pulsed gradient Hahn spin echo sequence schematically shown in Fig. 2a. A suitable basis for the treatment is the spherical product operator formalism. Explanations, definitions, and rules of the spin operator formahsm needed in this context can be found in Ref [2]. Times just before and immediately after RF (radio frequency) and field gradient pulses will be indicated by minus and plus signs, respectively. 

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).

Both find their origin in the spin-echo sequence, devised hy Hahn in 1952 and used for the determination of relaxation times. 

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. 

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 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.

The rf part of the pulse sequence generates a Hahn spin echo at time 2x. In imaging jargon the time from the center of the 90° pulse to the center of the echo is called the echo time (or time to echo) TE = 2x (where x is the spectroscopist s usual symbol for the time from the 90° pulse to the 180° pulse). The time from the center of the 90° pulse to the center of the next 90° pulse is called the repetition time (or time to repeat) TR. Spectroscopists know TR as the time equal to the recycle delay plus the time taken by the pulsing and data sampling. 

The combination of homonuclear Hartmann-Hahn transfer with homonuclear double- or zero-quantum spectroscopy yields the so-called DREAM experiment (double-quantum relay enhancement by adiabatic mixing Berthault and Perly, 1989) and the zero-quantum-(ZQ) TOCSY experiment (Kessler et al., 1990a), respectively. Multiplet-edited HOHAHA spectra can be obtained by adding a spin-echo sequence to the Hartmann-Hahn mbdng period (Davis, 1989a). 

Static spin echo decay spectroscopy also forms the basis for the measurement of magnetic dipole-dipole interactions between two unlike nuclei I and S. While this interaction is refocused by the Hahn spin echo, it can be recoupled by applying a 7i-pulse to the S-spins during the dipolar evolution period [12]. This manipulation inverts the sign of the heterodipolar Hamiltonian, and thereby interferes with the ability of the Hahn spin echo technique to refocus this interaction. The corresponding pulse sequence, termed SEDOR spin echo double resonance) shown in Fig. 4, compares the I-spin echo intensity as a function of dipolar evolution time (a) in the absence and (b) in the presence of the ti(S) pulses. Experiment (a) produces a decay F(2ti)/Fo, which is dominated by homonuclear dipole-dipole interactions, while experiment (b) results in an accelerated decay, reflecting the contribution from the heteronuclear I-S dipole-dipole interaction, which is now re-introduced into the spin Hamiltonian. For multi-spin systems, a Gaussian decay is expected ... 

Providing the echo interval in WATERGATE is kept short to minimize /-modulation, T2 relaxation and molecular diffusion effects (i.e. note the similarity with the Hahn spin-echo-based PGSE sequence in Fig. 9B), the desired resonances are retained in the spectrum with near-full intensity while the water peak should be suppressed by a factor of at least 1(1. Scalar coupling evolution can be refocused if the ir pulse in the WATERGATE sequence excites only some of the solute resonances but not the scalar coupled partners (for example amide resonances). ... 

Many NMR experiments are described using this model. For example, the Hahn spin-echo experiment involves measurement of the signal (or echo ) following a 90°, t, 180°, T sequence, t being the interval between two pulses. The behavior of the spin system in the spin echo experiment is shown in Figure 6. 

All these sequences include a (90°) preparation pulse which flips the magnetization of the spin system into the xy plane. The evolution period is then the period of free precession of the spin system in the xy plane, in the Hahn spin echo experiment (Fig. 6). The almost infinite variations in the mixing strategies serve the purpose of bringing out those features of the correlated motions in the system of coupled spins which one wishes to observe. 

SE indicates use of a Hahn spin-echo T2 measurement is by the CPMG sequence. 

The self-diffusion coefficients described below were measured by the pulsed-field technique proposed by Stejskal and Tanner. The pulse sequence applied is a modification of the classical Hahn spin-echo experiment for the determination of the spin-spin relaxation time,72- Fourier transformation of the second half of the spin-echo permits the simultaneous study of complex mixtures. The limit for the number of compounds that can be measured in one experiment is set solely by the requirement that there is at least one... 

Setting up a Hahn spin-echo pulse sequence and calibrating the gradient-coil constant, k... 

Slichter s spin echo approach is a variation on the spin echo double resonance (SEDOR) experiment originally proposed by Hahn I03. To see how this experiment works, consider the spin echo sequences shown in Fig 53. The first case, Fig 53a, describes Hahn s original echo experiment 103. In a hetero-nuclear case (always observing the rare spin) any heteronuclear dipolar interactions (along with the chemical shift and inhomogeneous line broadening processes) will be refocused as a result of this sequence. The second example. Fig 53b, is Hahn s SEDOR experiment (74). Here, the heteronuclear dipole-dipole interaction is not refocused because of the application of the second tt pulse to... 

This provides the basis for measuring A- Let us consider the pulse sequence introduced by Stejskal and Tanner in the 1960s (Figure la) by modifying the Hahn spin-echo pulse sequence. ... 

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