| dc.description.abstract | In this chapter, Floquet theory was employed to describe the SAP (Selective Averaging Pulse) experiment. Restriction of the CP (Cross Polarization) contact time to part of the rotor period and the application of additional 90° pulses act as extra modulations on the Hamiltonian, which is already time-dependent due to magic angle spinning (MAS).
The Fourier expansion of the matrix elements reintroduces time-independent coupling terms for the dipolar interaction, enabling flip-flop transitions between the dressed eigenstates of the Floquet Hamiltonian. By using a numerical diagonalisation procedure, the intensity of the S spin was obtained for a range of matching conditions (??S – ??I) for both the standard CP experiment and the SAP experiment. Results obtained for typical crystallite orientations are observed to be in qualitative agreement with experimental observations reported in Chapter 2 of this thesis.
Estimation of Dipolar Couplings and Order Parameters
A method for estimating dipolar couplings and order parameters along C–H bond axes in liquid crystals and oriented samples, based on the transient oscillations observed in cross-polarisation experiments, has been presented. A two-dimensional NMR method, which utilises the concept of cross depolarisation, has also been shown to be useful in estimating transient oscillation frequencies.
Order parameters estimated for MBBA using this technique are in reasonable agreement with previous measurements. The method utilises spectra of natural abundance, comparing favourably with deuterium NMR. Sample spinning is not required, as the liquid crystal provides resolved spectra even for the static sample due to its orientation in the magnetic field.
The disadvantage of the method could arise from spin-diffusion, which may smear out the oscillations and lead to large errors in estimating dipolar couplings. For example, no information on the methyl carbons in MBBA could be obtained. On the other hand, the spin-diffusion time constants for the ?-, ?-, and ?-carbons show correlation to the mobility of different segments of the molecule, providing additional information.
Energy Exchange Between Zeeman and Dipolar Reservoirs
The exchange of energy between the Zeeman and dipolar reservoirs in the rotating frame has been studied in the case of ammonium dihydrogen phosphate. Three experiments were carried out in which magnetisation from the I spin was transferred to the S spin with the involvement of the dipolar reservoirs in the transfer process.
The description of the process in terms of quasi-equilibrium constants leads to a better understanding of the experimental results. | |
