Multiple-pulse echo experiments

P. Gaspard Concerning multiple-pulse echo experiments, I would like to know if there are results on the decay of the amplitude of the echo as the number of pulses increases with equal-time spacing between pulses. If the decay is exponential, the rate of decay may characterize dynamical randomness since it is closely related to the so-called Kolmogorov-Sinai entropy per unit time [see P. Gaspard, Prog. Theor. Phys. Suppl. 116, 369 (1994)]. 

R. Siegel, T. T. Nakashima and R. E. Wasylishen, Signal-to-noise enhancement of NMR spectra of solids using multiple-pulse spin-echo experiments. Concepts Magn. Reson., 2005, 26A, 62-77. 

S. Mukamel In general, multipulse experiments depend on a multitime correlation function of the dipole operator [1], The term x(n) depends on a combination of n + 1 time correlation functions. Their behavior for large n will depend on the model. In some cases (e.g., the accumulated photon echo used by Wiersma) the multiple-pulse sequence is simply used to accumulate a large signal and the higher... 

Fig. 6. Top 2D MAT sequence for correlating isotopic chemical shift and CSA with two separate experiments P+ and P . All pulses following CP are 90°. A four-step phase cycling is used with 6 = —y, x, —y, x. and 62 = —y, x, x, -y. The receiver phases are x, -x, — y, -y for the P+ pulse sequence and x, —x,y, y for the P pulse sequence. (The sign of receiver phases with an asterisk depends on the relation between the pulse phase and the receiver phase of the particular spectrometer in use. These receiver phases must be changed in sign when the quadrature phase cycle (x,y, —x, -y) of the excitation pulse and the receiver phase in a single-pulse test experiment result in a null signal.) Phase alternation of the first H 90° pulse and quadrature phase cycling of the last 13C 90° pulse can be added to the above phase cycle. The time period T can be any multiple of a rotor period except for multiples of 3. Bottom 2D isotropic chemical shift versus CSA spectrum of calcium formate powder with a three-fold MAT echo extension. (Taken from Gan and Ernst178 with permission.)...

Another very important experiment for spectral editing is a heterocorrelation experiment combining MQMAS (in the indirect dimension) with CP. Introducing CP at the MQMAS echo position following a split-fj MQMAS scheme creates a spin-j detected spectra (in the dimension), which is modulated by the isotropic frequency of the quadrupolar nucleus in F. HETCOR has been demonstrated on Na- P pairs, on 2 A1- P pairs and lately on a- H pairs,where proton resolution during F was obtained with the wPMLGS multiple pulse decoupling technique. ... 

Fig. 2. A 2D SLF pulse sequence (A) with S-spin magnetization evolution (B) subject only to heteronuclear dipolar couplings in the q period and detection of chemical shift spectrum in the 2 period. Various multiple pulse (MP) sequences can be used to suppress dipolar coupling among I spins in the laboratory frame during the h period, which enables line-narrowing in the I-S dipolar coupling dimension (i.e., the a>i frequency dimension of the 2D spectrum). This experiment under MAS can be used for separating I-S dipolar sideband patterns by isotropic chemical shifts the re-pulse and the start of the acquisition need to be synchronized with rotational echoes. Other aspects of this pulse sequence are similar to the SLF sequence in Fig. 1.

Chapter 6 introduces the product operator formalism for analysing NMR experiments. This approach is quantum mechanical, in contrast to the semi-classical approach taken by the vector model. We will see that the formalism is well adapted to describing pulsed NMR experiments, and that despite its quantum mechanical rigour it retains a relatively intuitive approach. Using product operators we can describe important phenomena such as the evolution of couplings during spin echoes, coherence transfer and the generation of multiple quantum coherences. 

An external trigger capability for the digitizer is useful for at least two reasons. One is to be able to sample the magnetization at the correct points in a multiple pulse experiment. (An example would be to sample just the tops of the echoes in a CPMG experiment as described in I.C.2.) The other reason is to allow for synchronization of two digitizers, for example, in quadrature detection. 

Phase considerations intrude even in the simplest experiments of observing an FID or an echo. Accurately adjusting the phases of rf pulses can be very important, particularly in experiments involving trains of pulses such as the Carr-Purcell Meiboom-Gill train or the multiple pulse line narrowing sequences. In other sections we have considered how phase shifts originate and how to cope with them. 

The conventional spin-echo experiments, both in the single-pulse refocusing (Carr-Purcell) and multiple-pulse refocusing (CPMG) version, remove the field inhomogeneity, chemical shift and heteronuclear coupling effects, but not the homonuclear /-coulings, which complicated the measurements of T2- Some papers have dealt with suppression of the unwanted... 

In the late 1960s NMR spectroscopists discovered that a vast amount of chemical information could be obtained from experiments based on multiple-pulse sequences. Here, techniques such as im ersion-recoverv and spin-echo NMR enabled the measurement of spin-... 

If more sophisticated experiments are aimed, such as those involving multiple pulse sequences, spin echo detection, rotor synchronization, or 2D methods, additional calibration steps, trial tests, and optimization procedures are required. The reader is referred to the specific literature dealing with each particular method for a proper description of the experimental setup. A general account of these methods can also be found in the monographs by MacKenzie and Smith [4] and Duer [15]. 

To conclude this section on 2D NMR of liquid crystals, some studies of more exotic liquid crystalline systems are pointed out. Polymer dispersed nematic liquid crystals have attracted much attention because of their applications as optical display panels. Deuteron 2D quadrupole echo experiments have been reported [9.28] in the isotropic and nematic phases of / -deuterated 5CB dispersed in polymers. A similar technique was used [9.29] to study two model bilayer membranes. Both studies allow determination of the lineshape F(u ) due to quadrupolar interactions and the homogeneous linewidth L(u ) of the individual lines [9.28]. The 2D quadrupole echo experiment has also been used [9.30] to separate chemical shift and quadrupolar splitting information of a perdeuterated solute dissolved in a lyotropic liquid crystal. The method was compared with the multiple-quantum spectroscopy that is based on the observation of double-quantum coherence whose evolution depends on the chemical shift but not on the quadrupolar splitting. The multiple-quantum method was found to give a substantial chemical shift resolution. The pulse sequences for these methods and their treatment using density matrix formalism were summarized [9.30] for a spin 1=1 system with non-zero chemical shift. Finally, 2D deuteron exchange NMR was used [9.31] to study ring inversion of solutes in liquid crystalline solvents. 

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