Experimental techniques in solid-state NMR – dipolar decoupling

Extensive work with 1_{H in solid-state MAS NMR is a relatively recent phenomenon, especially when}

compared with 1_{H detection in solution. The broadening of} 1_{H lineshapes is a direct consequence of the}

extensive network of homonuclear 1_{H –} 1_{H dipolar couplings which exist in a typical organic sample.}

MAS, even at high spinning frequencies of up to and exceeding 60 kHz, is not sufficient to fully average these couplings and hence significant broadening of resonances, especially those relating to aromatic and alkyl environments, persists. It has been shown, for small organic molecules, that combining MAS

with high performance decoupling schemes can significantly improve the resolution of 1_H

lineshapes.(44) The fate of homonuclear dipolar couplings in solid-state NMR and under MAS was discussed in sections 2.4.4 and 2.4.5.

Specifically, decoupling refers to the process of subjecting a given sample to irradiation at a certain frequency in order to eliminate, fully or partially, the effect of a coupling between certain nuclei. Such a process can either be employed in a homonuclear or heteronuclear fashion. Homonuclear decoupling refers to the situation where both the nucleus to be irradiated and observed belongs to the same spin species, i.e., 1_{H –} 1_{H. For heteronuclear decoupling the opposite is true, i.e.,} 1_{H –} 13_{C. Both types of}

decoupling will be briefly described in the following sections. 3.3.2 Heteronuclear dipolar decoupling

For experiments in which the low natural abundance or ‘dilute’ spin is to be observed, i.e., in a CP MAS experiment (see section 3.4.1 below), it is generally assumed that the X – H heteronuclear dipolar coupling is the most significant internal interaction that needs to be considered. For 13_{C, for instance,}

so as to avoid spinning sidebands), therefore, in order to obtain clearly resolved lines it is necessary to decouple during acquisition.

Heteronuclear decoupling is typically applied in a continuous manner via close-to-resonance high frequency rf irradiation to the abundant spin species (usually 1_{H). The effect of this irradiation is to}

excite continuous transitions between the 𝛼 and 𝛽 states in the 1_{H spins at a rate determined by the}

amplitude of the rf irradiation. If this frequency is high enough, then these transitions are fast when compared to the magnitude of the heteronuclear dipolar coupling, which is subsequently averaged by such transitions. In order to fully average a coupling, the rf nutation frequency must be at least three times higher than the magnitude of the largest X – H heteronuclear dipolar coupling. The nutation frequency is usually set to 100 kHz, which more than satisfies this condition. However, since heteronuclear decoupling is usually applied alongside MAS, the two effects can combine to introduce a periodicity into the dipolar Hamiltonian. This means that at certain ratios of r and 1 (irradiation

frequency), destructive interference may occur which subsequently negates the averaging effect of the decoupling sequence. In order to correct for this, optimised heteronuclear decoupling sequences consisting of rf pulse blocks, in which individual pulses alternate their respective phase, have been developed. Popular examples include the Two Pulse Phase Modulated (TPPM) (170) and SPINAL-64 (171) schemes. TPPM decoupling is continuous and consists of two alternating pulses of flip angle 𝜃𝑝 with phase of 𝜙𝑝 and 𝜙𝑝+ Δ𝜙𝑝 respectively. The values of these phases are determined experimentally, with the optimal values being dependent upon the spinning frequency and the sample under consideration. Other schemes with similar efficiencies were developed in the late 1990s and early

2000s, including FMPM,(172) SPARC,(173) C122-1,(174), amplitude-modulated TPPM,(175) and

methods continue to be developed. (176-178) 3.3.3 Homonuclear dipolar decoupling

The magnitude of 1_{H –} 1_{H homonuclear dipolar coupling is such that, for an ensemble of spins, MAS}

alone is insufficient to fully average the line broadening effect, in its current maximum limit. There exist many schemes which are capable of efficiently decoupling this interaction in conjunction with MAS (CRAMPS), such as the popular DUMBO (decoupling under mind-boggling optimisation) scheme,(45,46,179) which works well at moderate MAS frequencies for small organic molecules such as peptides. For the theory and subtleties of the various schemes there are many excellent reviews,(180) an in-depth discussion here is beyond the scope of this thesis. The first homonuclear decoupling sequence, WAHUHA,(25) is very simply a sequence of /2 pulses with different phases separated by delays, , with the sequence being repeated throughout the acquisition time and FID points being collected at the end of each repetition.

Modern homonuclear decoupling schemes can be applied in a windowed or windowless manner. Early schemes such as Lee-Goldberg were exclusively windowless.(40) Windowed schemes such as

DUMBO-1 allow for periods of free evolution,(45) in which the signal is acquired, alternating with irradiation periods. Windowless decoupling, such as eDUMBO22,(46) is applied during t1 evolution

periods in two-dimensional experiments, with the irradiation being constant over the course of the decoupling period.

Homonuclear decoupling sequences use high nutation frequencies and subsequently require short rise times since the duty cycle, which is the decoupling duration as a percentage of the whole pulse sequence duration, needs to be kept short, in order to avoid damage to the sample or the probe head. Homonuclear decoupling is therefore much more complex when compared to its heteronuclear counterpart. As such much effort is spent in devising high performance, robust homonuclear decoupling schemes, which can be employed under various experimental conditions and still achieve efficient line narrowing in one- and two-dimensional 1_{H spectra.}