Hahn-echo

A typical decay of the HE of a single molecule is given in Fig. 19. This figure shows the HE intensity as a function of ti (ti = T2), where ti is the waiting time between the first two pulses. The dotted curve represents a fit with a mono- 

In the following we will discuss the HE decay (spin dephasing) times T2 for different molecules [37]. The histogram in Fig. 20 compares T2 for 9 different molecules. The figure shows that the decay times and thus the homogeneous linewidths for different molecules differ by about a factor of three. 

The use of analytical models for spin dephasing in the solid state [39, 40] is not appropriate for the present case because they do not account for the specific distribution of nuclear spins around the electron spin. In order to consider the real matrix structure close to the chromophore we simulated the HE decay curves numerically by using the known crystal structure [9] and the nuclear flip-flop rate IE as a parameter. The echo decay is calculated as 

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Fig. 3.3.3 (a) Hahn echo ]H intensity during heating cycle of cyclohexane filling the pores of catalyst pellets, (b) Pore size distribution obtained from (a) in comparison with BET measurements. 

As increasing the time interval between the single-shot DNP operation and the aH NMR measurement, the intensity of the magic echo was found to decrease. Instead, the intensity of the 1H Hahn echo grew up, as demonstrated in Figure 19B-D). The fact that the inhomogeneous character in the aH spectra increased with time shows that the spin polarization had been transferred to the place where the H spins were dilute, that is surrounded by the 2H spins in the heavily deuterated host material. 

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) ... 

In the limit of zero gradient, the sequence reduces to the Hahn echo, and it is conventional to expand the echo amplitude as a multiple exponential function of T, and define, the usual transverse relaxation times, T,... 

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. 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... 

RAPT signal-enhancement method (top) and a simple two-pulse Hahn-echo experiment (bottom). Both spectra were acquired at 11.75T, with the same experimental conditions. Reproduced from Cahill et al., ° Copyright 2009, with permission from Wiley. 

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 A1.3.3 Hahn Echo NMR signal of canola at 20 MHz obtained by a minispec mq20.

Figure A1.3.4 Semi-log plot of Spin Echo amplitude with changing Hahn Echo experiment interval, x, for an oilseed containing excess moisture (therefore some is free) and oil. Extrapolation of the fitted lines (dashed) to x = 0 gives amplitudes for excess (free) moisture (Aw and oil A0 modified from Schmidt, 1991).

Ranee, M. and Byrd, R.A. 1983. Obtaining high-fidelity spin-1/2 powder spectra in anisotropic media Phase-cycled Hahn Echo spectroscopy. J. Magnetic Resonance 52 221-240. 

Spent grain, (i-glucan quantitation, 751 Spin Echo, 23, 24 (fig.), 25. See also Hahn Echo... 

Create a Hahn-echo sequence with 16/32 ns in one channel and optimize the echo intensity. Do the same in a second channel and adjust its phase 180° to the first cannel. Both channels are used for the two-step phase cycle. Running the experiment with the two-step phase cycle eliminates receiver offsets and allows reading off the real echo signal intensity, which is important for accurately determining Vx in spin counting experiments (Section 5.1). 

Figure 7.5 [15] Susceptibility contrast in EPDM samples at 363 K (a) 2D Hahn-echo image acquired with the sequence of Figure 7.4a (b) 2D gradient-echo image acquired...

In the Cohen-Addad-Sotta model [23, 25] the Hahn-echo decay is expressed without the assumption of dangling chains by the expression ... 

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