The Design of Experimentally Robust Pulse Sequences in Solid-State NMR

Abstract

Solid-state NMR is a powerful tool for the study of the structural and dynamic properties of materials and biomolecules. The strength of solid-state NMR lies in the ability to coherently manipulate the system Hamiltonian with the use of radio-frequency pulse sequences and magic-angle spinning. This controlled perturbation is performed by introducing multiple periodic time dependencies and allows for the measurement of the correlation between nuclei and the identification of their local electronic environment. In order to get reliable information and efficient experimental performance, the pulse sequences need to be robust towards experimental uncertainties. Additionally, they need to be highly specific to extract the desired interaction. In this thesis, a variety of widely-used pulse sequences are examined with respect to pulse imperfections and possible approaches based on a theoretical understanding obtained by Floquet theory are presented to tailor the pulse sequences in order to make them more reliably applicable. In the first part of this thesis, the practical compensation of pulse imperfections is studied and previously developed concepts are extended. A published theoretical model of these imperfections, also known as pulse transients, is applied to physically measured pulse shapes to find the origin of pulse imperfections in the spectrometer. Additionally, small adjustments to the experimental setup are presented that ease the implementation of pulse-transient compensation. The second part of this thesis focuses on recoupling sequences, which are pulse sequences designed to reintroduce the dipolar coupling, yielding important information about the spatial proximity of two nuclei. One type of sequence, which includes Radio-Frequency Driven Recoupling or Rotational Echo Double Resonance, uses an isolated pi pulse as a recoupling element. These sequences are widely used due the ease of experimental implementation. Phase cycles are previously proposed modifications to stabilize these sequences. In this thesis, these phase cycles are analysed using the concept of effective Floquet Hamiltonians and numerical simulations to determine their robustness towards pulse imperfections. The advantages and disadvantages of various phase cycles are discussed and the experimental influence of pulse transients is understood using the theoretical concepts developed. A different kind of recoupling sequence uses symmetry-based pulse trains and is known as C or R sequence. A Floquet description of the recoupling sequence of interest, R26, shows inherent flaws in the design of the sequence that are also demonstrated experimentally. The influence of pulse transients is investigated and unexpected results are shown that are in stark contrast to the results found for RFDR and REDOR. A commonly used phase cycle shows great robustness towards any kind of experimental imperfection but calculations of the dipolar scaling coefficient show less recoupling efficiency than the basic sequence. In the third part of this thesis, homo- and heteronuclear decoupling sequences are discussed. Decoupling sequences are designed to remove residual terms in the Hamiltonian that cause line broadening and thus these types of sequences are used to enhance spectral resolution. The homonuclear decoupling sequence frequency-switched Lee-Goldburg for proton-detected experiments is studied. Efficient decoupling is essential for proton detection because without it the lines are too broad to be distinguishable and do not yield reasonable information. This study focuses on the origin of performance degradation of the Lee-Goldburg sequence. Through the use of analytical calculations, numerical simulations, and experimental modifications, the residual line broadening is analysed. A concise conclusion of the origin of the performance degradation is presented for the first time, and it is understood why this sequence is still limited in its use. The heteronuclear decoupling sequence two-pulse phase modulation is investigated with respect to pulse transients. The requirement for the experimental use is a straightforward optimization and the implementation should be robust towards different conditions. Theoretical concepts to describe simple decoupling sequences with discrete phase modulations are presented and extended to understand the influence of pulse transients. The difference between continuous phase modulation and discrete phase jumps as well as a commonly used phase cycle of the basic two-pulse sequence is investigated theoretically and experimentally. In conclusion, this thesis generalises the concepts of pulse transients and the compensation, and draws conclusions on their influence on different kinds of pulse sequences. The removal of pulse imperfections allows the developed theoretical concepts to be validated more accurately and inherent drawbacks of the pulse sequences are found experimentally. This results in suggested modifications and tailoring of the sequence to accommodate the experimental needs of more complex biological systems.