WAHUHA pulse

Figure 15.13. Rotating-frame diagrams for the Lee-Goldberg and WAHUHA pulse sequences.

FIGURE 7.7 Pictorial representation of the effect of the WAHUHA pulse cycle. A series of 90° pulses applied as indicated causes M to spend a period 2r along each of the Cartesian axes in the rotating frame. The average orientation of M during the period 6r is thus along the diagonal at 54.7° from the z axis, as shown. 

FIg. 3.3.11 The WAHUHA pulse cycle, (a) Timing diagram, (b) Time-evolution operators in the rotating coordinate frame, (c) Rotations in the rotating coordinate frame (RCF). 

To consider the efficiency of dipolar decoupling in more detail, a WAHUHA pulse sequence is taken as an example [Hael]. One pulse cycle (cf. Table 3.3.1) leads to the time evolution operator (cf. eqn (3.3.22))... 

For the WAHUHA pulse sequence the average Hamiltonian is given by... 

This equation is sometimes called the magic-angle condition, because when it fulfilled, the spins precess about the cube diagonal which is at the magic angle with respect to Bo. Therefore, the WAHUHA pulse sequence decouples the homonuclear dipole-dipole interaction in first order (cf. Section 3.4.3). 

Figure 4. The WAHUHA experiment a. The action of a TT/2 rf pulse applied to a spin system along the +x axis in the rotating frame b. the action of a ir/2 pulse applied along -x1 axis. c. The WAHUHA pulse sequence.

Schaefer and coworkers, in another chapter in this text, used 1h - 13(j dipole-dipole "line shapes" obtained in a very clever way to investigate rotational motion of the aromatic rings in polystyrene. The method used a WAHUHA pulse sequence to decouple proton-proton dipolar interactions, cross polarization to enhance signal acquisition and an overall sampling technique synchronous with the sample rotation. The dipole-dipole interaction was mapped in rotational sideband spectra obtained from 16 "normal" CP/MAS spectra. The method, though somewhat involved, provided a measure of dipole-dipole line-shapes which can be interpreted in terms of side-chain rotation in the polymer. 

The pulse sequence for this experiment is shown in Figure 1 [8]. The evolution of the carbon magnetization due to chemical shift effects is refocused after two rotor periods by a carbon 180° pulse applied after the first rotor period. Under high-speed spinning conditions, this removes the effect of the chemical shift tensor. The H- C dipolar evolution time is varied with the number of WAHUHA pulse sequences. The spinning speed is chosen so that an integral number of WAHUHA cycles exactly fits into one rotor period. In our experiments, this number was sixteen. (Each WAHUHA cycle took 33 fJsec, with 3-psec 100° pulses, so that sample spinning was at 1894 Hz. 

Figure 43 The WAHUHA pulse sequence [5] used for homonoclear decoupling in solids. All pulse angles are 90°. The ri. phases are indicated above them. The middle four pulses illustrated form the repeat unit of the sequence, s marics a sampling point...

WAHUHA Pulse sequence of Waugh, Huber, and Haeberlen... 

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