Simulations of Dynamic Nuclear Polarization pathways in large spin ensembles - Wisniewski, Daniel (2017)
Dynamic Nuclear Polarization (DNP) is a method for signal enhancement in NMR, with numerous applications ranging from medicine to spectroscopy. Despite the success of applications of DNP, the understanding of the underlying theory is still limited. Much of the work on the theory of DNP has been carried out on small spin systems; this is a restriction due to the exponential growth of the Liouville space in quantum simulations. In the work described in this thesis, a methodology is presented by which this exponential scaling can be circumvented. This is done by mathematically projecting the DNP dynamics at resonance onto the Zeeman subspace of the density operator. This has successfully been carried out for the solid effect, cross effect and recently for the Overhauser effect in the solid state (see appendix A.4). The results are incoherent state-dependent dynamics, resembling classical behaviour. Such form of effective dynamics allows the use of kinetic Monte Carlo algorithms to simulate polarization dynamics of very large spin systems; orders of magnitude larger than has previously been possible. We verify the accuracy of the mathematical treatment of SE-DNP and CE-DNP, and illustrate the insight large spin-system simulations provide into the mechanism of DNP. For SE-DNP the mechanism of polarization to the bulk of spin systems is determined to be spin diffusion, and we carried out studies into the efficiency and performance of radicals, with an outlook on radical design. We also show that the Zeeman projection can be applied to heteronuclear spin systems if the nuclear species are close in frequency, and we present a formalism for simulating C-13 nuclear spin systems based on a linear rate approach, enabling simulations of thousands of spins in a matter of minutes. A study into the scaling of the kinetic Monte Carlo algorithm error, and the simulation run time, with respect to an increasing number of spins is also presented. For CE-DNP the error analysis led to establishing a parameter regime in which the effective dynamics are accurate. We show that spin diffusion is the mechanism of transfer of polarization to bulk nuclei. We also show how the effective rates for CE-DNP can be used to understand the efficiency of bi-radicals, point to optimisation possibilities, and hold a potential to aid in bi-radical design. We finally show large scale simulations for CE-DNP bi-radical systems with improved parameters; leading to very rapid build-up of nuclear polarization.