Dipolar echo

The faithful representation of the shape of lines broadened greatly by dipolar and, especially, quadrupolar interactions often requires special experimental techniques. Because the FID lasts for only a very short time, a significant portion may be distorted as the spectrometer recovers from the short, powerful rf pulse. We saw in Section 2.9 that in liquids a 90°, t, 180° pulse sequence essentially recreates the FID in a spin echo, which is removed by 2r from the pulse. As we saw, such a pulse sequence refocuses the dephasing that results from magnetic field inhomogeneity but it does not refocus dephasing from natural relaxation processes such as dipolar interactions. However, a somewhat different pulse sequence can be used to create an echo in a solid—a dipolar echo or a quadrupolar echo—and this method is widely employed in obtaining solid state line shapes (for example, that in Fig. 7.10).The formation of these echoes cannot readily be explained in terms of the vector picture, but we use the formation of a dipolar echo as an example of the use of the product operator formalism in Section 11.6. 

As a second example, we look at echoes. We saw in Chapter 9 that a 180° pulse refocuses not only chemical shifts and the effects of magnetic field inhomogeneity but also spin coupling provided that the pulse does not also disturb the spin state of the coupled nucleus (see Fig. 9.2) However, in a homonuclear spin system a nonselective pulse does effect spin states. We found in Chapter 7 that dipolar interactions have the same mathematical from as indirect spin coupling, and it is known that a 180° pulse does not produce an echo in a solid because spin states are disturbed. However, it is possible to obtain a solid echo or dipolar echo by applying the pulse sequence 90, T, 90r It is very difficult to rationalize an echo from... 

Fig. 6.1.9. 200 MHz spectra of H pertaining to spin diffusion experiments on a nylon 6,6 PBZT blend (VanderHart [46]). Left, magnetization gradient created by dipolar echo sequence with spacing 30 [xs, thus, initially favoring the PBZT portion of the blend. Right, results of spin diffusion observed using CRAMPS to obtain high resolution proton NMR of the blend, and observation of magnetization transfer between the phenyl protons of the PBZT, and the methylene protons of the nylon 6,6.

N. Boden, Y. K. Levine, D. Lightowlers, and R. T. Squires, "NMR dipolar echoes in liquid crystals," Chem. Phys. Letters 31, 511 (1975) "Internal molecular disorder in the nematic and smectic phases of thermotropic liquid crystals studied by NMR SPDE experiments," ibid 34, 63-68 (1975). 

Blinc, R., M. Burgar, G. Lahajnar, M. Rozmarin, V. Rutar, I. Kocuvan and J. Ursic (1978). NMR Relaxation Study of Adsorbed Water in Cement and C3S Pnstes Journal of the American Ceramic Society 61 (1-2) 35-37. Bloembergen, N., E. M. Purcell and R. V. Pound (1948). Relaxation Effects in Nuclear Magnetic Resonance Absorption . Physical Review 73 679-712. Boden, N., Y. K. Levine and R. T. Squires (1974). NMR Dipolar Echoes in Solids Containing Spin-12 Pairs . Chemical Physics Letters 28 (4) 523-525. 

In addition to sample rotation, a particular solid state NMR experiment is further characterized by the pulse sequence used. As in solution NMR, a multitude of such sequences exist for solids many exploit through-space dipolar couplings for either signal enhancement, spectral assignment, interauclear distance determination or full correlation of the spectra of different nuclei. The most commonly applied solid state NMR experiments are concerned with the measurement of spectra in which intensities relate to the numbers of spins in different environments and the resonance frequencies are dominated by isotropic chemical shifts, much like NMR spectra of solutions. Even so, there is considerable room for useful elaboration the observed signal may be obtained by direct excitation, cross polarization from other nuclei or other means, and irradiation may be applied during observation or in echo periods prior to... 

Rotational-echo double-resonance (REDOR)(75,79) is a new solid-state NMR technique which is sensitive to through-space carbon-nitrogen interactions between selectively 13C and 15N-enriched sites separated by up to 5A (20-22). The parameter directly measured in a REDOR experiment is the heteronuclear dipolar coupling constant DCN, which is in itself proportional to the inverse third power of the intemuclear distance, rCN. It is this dependence on (icn)3 which accounts both for REDOR s ability to accurately measure short distances and its insensitivity to longer-range interactions. As a technique which can probe, in detail, intermolecular interactions over a distance range of 5A, REDOR is well suited to studying the distribution of small selectively-labeled molecules in polymer delivery systems. 

The REDOR experiment has formed the basis for a large number of ideal pulse type recoupling experiments, and later finite pulse variants, for heteronuclear dipolar recoupling. These include experiments such as frequency selective REDOR (FS-REDOR) [80], TEDOR (Transferred Echo DOuble Resonance) [25], and 3D variants of TEDOR [81, 82], which have found important applications, e.g., for measurement of intemuclear 13C-15N distances in biological solids. We should also mention that rotor-encoded variants of TEDOR, such as REPT, HDOR [83], and REREDOR [84], have been proposed for 1H13C dipolar recoupling under high-speed MAS conditions. 

Rotational-echo double resonance (REDOR), originally introduced by Gullion and Schaefer [102], is a method to recouple heteronuclear spin pairs. The sequence relies on a train of rotor-synchronized n pulses applied to the I spin to interrupt the spatial averaging of the heteronuclear dipolar coupling under MAS to give a nonvanishing dipolar Hamiltonian over a full rotor cycle (Fig. 11.8). Typically, REDOR data are collected by col-... 

Gullion, T. and Schaefer, J. (1989) Detecbon of weak heteronuclear dipolar coupling by rotabonal-echo doubleresonance nuclear magnebc resonance. Adv. Magn. Reson., 13, 57-83. 

Gullion, T. (1997) Measurement of heteronuclear dipolar interacbons by rotabonal-echo, double-resonance nuclear magnebc resonance. Magn. Reson. Rev., 17, 83-131. 

Gullion, T. (1995) Measurement of dipolar interacbons between spin-1 /2 and quadrupolar nuclei by rotabonal-echo, adiababc-passage, double-resonance NMR. Chem. Phys. Lett., 246, 325-330. 

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