Abstract
<p>Nuclear Magnetic Resonance (NMR) is the most ubiquitous spectroscopic method in use today. Often obtaining sharper lineshape is essential for chemists to distinguish different resonance peaks, for physicists to manipulate prolonged quantum coherence, and for radiologists to produce higher resolution in medical imaging, etc. This dissertation represents two methods of achieving sharp lines via Low-power Excitation and Delayed-Acquisition. First, a theoretical description of low-power excitation in inhomogeneously broadened spin systems is developed in the framework of linear response theory. Linear response theory is shown to break down for spin resonance frequencies on the order of excitation bandwidth even when the overall excitation is still within the linear response regime. This breakdown is due to the fact that radiofrequency (RF) interaction cannot be treated as a small perturbation for spins resonate in the pulse bandwidth no matter how small the excitation is. A remedy has been found by enforcing unitarity of linear response propagator producing correct behavior for spins resonate in the pulse bandwidth. The nature of the spin-echo generated by a <span style="font-family: "Times New Roman"; font-size: medium;">π</span>-pulse applied immediately after a low-power pulse is also investigated. Experimental demonstrations of the theoretical predictions are provided using an inhomogeneously broadened 1:99 v/v H<sub>2</sub>O/D<sub>2</sub>O solution. Furthermore, linear response theory developed for inhomogeneous systems is applied to the problem of low-power excitation in homogeneously broadened dipolar spin systems. The application of a low-power pulse generates a broad signal with a “dip” at the RF transmitter frequency that deepens with increasing nominal flip angles. A <span style="font-family: "Times New Roman"; font-size: medium;">π</span>-pulse applied after the low-power excitation refocuses dephasing due to B<sub>0</sub> inhomogeneity, anisotropic bulk magnetic susceptibility, and chemical shift anisotropy, while dephasing due to nonzero chemical shift differences is only partially refocused. Contrary to previous observations, experiments in powdered hexamethylbenzene demonstrate that these “long-lived” signals can exist even in the absence of nonzero chemical shift differences. Additional experimental demonstrations in powdered and single-crystalline adamantane and ferrocene samples are also presented. Finally, delayed-acquisition as a common technique for improving spectral resolution is studied providing an alternative source of differential “dephasing” under delayed-acquisition that is based solely upon the mathematical properties of the line shape and is independent of the underlying spin dynamics and/or complexity. Signals associated with frequencies where the lineshape either changes sharply and/or is non-differentiable at some finite order dephase at a much slower rate producing sharp spectrum lines upon the application of acquisition delay. Experiments employing delayed-acquisition to study interfaces in biphasic samples, to measure spatially-dependent longitudinal relaxation, and to highlight sharp features in NMR spectra are presented.
</p>