Symbolic Computation Of Average Hamiltonians,Analytical Solution And Quantitative Subjects Of Cross Polarization Dynamics

This thesis includes three projects:1. Symbolic Computation of Average HamiltonianAverage Hamiltonian Theory, presented by U. Haeberlen and J. S. Waugh in1968, is one of the most important theories in the NMR history. By intro-ducing a toggling frame, we are able to separate the RF interaction from the main Hamiltonian, making it possible to calculate average Hamiltonians asso-ciated with the spin interactions only. AHT has be successfully applied to the experiments of multiple pulses, spin echo, composite pulses, CP dynamics, magic angle spinning, multiple quantum coherence, spin decoupling, dipolar recoupling, as well as quantum computing.The importance of Average Hamiltonian is well known. High order Aver-age Hamiltonians are necessary for high accuracy analysis, but the complex of computation is employed especially for second order Average Hamiltonian, only a few second order Average Hamiltonian were obtained in NMR history.In this chapter we present a general framework of automatic symbolic com-putation to calculate the Average Hamiltonians up to the second order. To demonstrate this work, we calculate a very challenge problem in the NMR field, the second order AH with finite pulse width of WAHUHA sequence, which was never acquired because of its inconceivable complexity. All procedures are pro-grammed using Computer Algebra System (CAS). Our work can be easily used to solve similar questions in quantum mechanics; it will promote theoretical analysis in other fields subsequently.2. Analytical Solution of Cross Polarization DynamicsCross Polarization experiment was introduced by Hartman and Hahn in1962, where the dynamics is the key to understand the subject. The first ana-lytic solution under Hartman-Hahn match for stationary sample was derived by Richard R. Ernst (1991Nobel Prize winner in Chemistry) et al. After the intro- duction of magic angle spinning, the dynamics becomes much more complicated. By transferring the Hamiltonian into a new rotating frame, John S. Waugh(1983Wolf Prize winner in Chemistry,2011Welch Prize winner in Chemistry) got the effective Hamiltonian and the new condition of Hartman-Hahn match, which leads to an analytic solution of CP dynamics under very fast magic angle spinning speed. For both results, the effective Hamiltonians are time-independent in the rotating frame, respectively. Under conventional MAS speed, the Hamiltonian is no longer time-independent in any rotating frame. Because of the time-dependent Hamiltonian, the analytic solution of CP dynamics has not been derived until now. Our work resolves this tough problem and therefore draws a completed period in this field.3. Quantitative Subjects of Cross PolarizationA novel scheme that combines the cross-polarization (CP) with a single-pulse (SP) experiment is developed to quantitatively analyze compositions of multi-phase polymers with marked difference in phase mobility. The CPSP method is able to record both CP and SP spectra in one experiment and avoid excessive long relaxation delay, saving considerable experimental time. The quantification of CP spectrum is done by measuring the enhancement factor of CP with a reciprocity relation, while the quantification of SP is derived directly from the Boltzmann distribution in thermo equilibrium. The relative mole composition obtained from a poly(styrene)-poly(isoprene) diblock copolymer matches well with the known value.