Homonuclear Decoupling Techniques

The discussion in section 3.2.1 of the effect of magic angle spinning is valid for the chemical shift anisotropy and heteronuclear dipolar coupling interactions. In the case of a system in which the homonuclear dipolar coupling between several nuclear spins has a significant effect, such as the dense networks of1H nuclei studied in later chapters, magic angle spinning serves only to reduce the dipolar coupling, and hence reduce the line width. The spinning frequency required to achieve this effect is very high, requiring the use of very small rotors capable of achieving such high MAS frequencies. An alternative is to combine MAS with homonuclear decoupling sequences, which reduce the dipolar interaction by rotation of the nuclear spins.

This technique is known as CRAMPS (combined rotation and multiple pulse spec- troscopy). For the crystalline organic solids studied in later chapters, the use of CRAMPS techniques typically provides 1H line widths comparable to, or better than, those obtained at high MAS frequencies. Homonuclear dipolar decoupling can be achieved using a wide variety of sequences. Several such schemes are based on the Lee-Goldburg condition [10], in which the effective field experienced by the nuclear spins is aligned at the magic angle with respect to the B0 field. In the case of the

frequency switched Lee-Goldburg (FSLG) sequence [16], this is achieved by applying a train of rf pulses of flip angle 2π. The pulses are applied off-resonance, with the offset alternating by ±∆ω. If the relationship between ∆ω and the nutation frequencyω1 is

chosen such that ∆ω=ω1/

√

2, then it can be shown that the Lee-Goldburg condition is met.

3.2. SOLID-STATE NMR TECHNIQUES 55 0 π/2 π 3π/2 2π Phase Time

Figure 3.6: Continuous phase profile of a DUMBO pulse. The rf amplitude remains constant while the phase is varied.

DUMBO [18, 95] (decoupling using mind boggling optimisation) scheme. In contrast to Lee-Goldburg based sequences, DUMBO uses on-resonance rf pulses to achieve homonuclear decoupling. The sequence is applied as a series of discrete pulses of con- stant ω1, but with varying phase, following the shape of a continuously varying phase

pattern. The sequence was derived from the BLEW-12 scheme [96], which consists of twelve 90◦ pulses, with phase shifts of 90◦ between each pulse. This sequence was expressed as a Fourier series, the coefficients for which were computationally optimised to produce the DUMBO sequence. Further optimisation, performed experimentally, led to the development of the eDUMBO-122[19] sequence, which is optimised for mod-

erately fast MAS conditions (specifically 22 kHz - although a lower spinning frequency of 12.5 kHz is generally used in experiments presented in later chapters, for reasons which will be discussed in detail in the next section). The continuous phase shape of a DUMBO sequence is shown in figure 3.6.

Homonuclear decoupling sequences may be used in either a windowed or windowless fashion. Windowless sequences are applied continuously, and are therefore useful during delays in a pulse sequence, in which magnetisation is allowed to freely evolve, for example during t1 in a two dimensional experiment. Windowed decoupling is used

during the acquisition period. Since the same coil is used to apply rf pulses and measure the magnetisation of the sample, it is necessary to alternate between periods of decoupling and data acquisition. A schematic pulse sequence for a simple one-pulse experiment with windowed DUMBO decoupling during acquisition is shown in figure 3.7. Also shown in this figure are the pre-pulses of flip anglesθand−θ. These pulses are necessary to rotate the magnetisation into a tilted transverse plane while the decoupling

1H

π

2

n

Figure 3.7: Pulse sequence diagram illustrating windowed decoupling. Acquisition is represented by the single dot int2. The bracketed section is repeatedntimes until the

required number of data points has been acquired. sequence is applied, then back into the transverse plane.

The use of windowed decoupling sequences often results in the presence of an arte- fact in the NMR spectrum at the frequency of therf pulses. As a result, it is necessary to choose a frequency slightly off resonance, such that the artefact does not interfere with spectral peaks. Typically offsets are chosen such that there is a small separation between the artefact and lowest frequency peak of the order of between one and two ppm. The magnitude of the artefact peak can be minimised by optimising the duration and phase of the pre-pulses.

An additional complication when performing experiments that use homonuclear decoupling is the scaling effect on the spectrum. This is caused by the evolution of the magnetisation outside of the usual transverse plane (about a tilted axis relative to the B0 magnetic field). The result is a spectrum in which the chemical shift axes are

compressed by a factor related to the effective field experienced by the nuclear spins during decoupling. If the decoupling sequence has been applied under ideal conditions, such that the effective field is aligned at the magic angle to the B0 field, this scaling

factor will be equal to 1/√3≈0.58. In practice, this factor will vary slightly between experiments and as such it is necessary to record a spectrum without decoupling in order to ensure that the scaling factor used is correct and the spectrum is properly calibrated. This is typically done at a high MAS frequency, and while the resulting spectrum usually has inferior resolution to the CRAMPS spectrum, it is normally sufficient to obtain an accurate scaling factor, provided that at least two known resonances are resolved.