Raimondi, FC
(2020)
Large-scale Simulation of Cross Effect Dynamic Nuclear Polarisation Dynamics and Relaxation of a Tempol-doped Water/Glycerol Sample Below 30K.
PhD thesis, University of Nottingham.
Abstract
Dynamic nuclear polarisation (DNP) provides significant signal enhancement com- pared to conventional thermal polarisation techniques used in typical nuclear magnetic resonance applications. Of the possible DNP mechanisms, the cross effect (CE), involving triple spin flips between two interacting electrons and a nucleus upon ir- radiation with a microwave field, is the most efficient at low temperatures and microwave irradiation amplitudes. In silico optimisation of parameters affecting CE enhancement, such as radical concentration and design, require simulation of large spin systems. However, the computational expense of solving the full Liouville-von Neumann equation for such systems makes this approach intractable after only a few spins. In the first part of this thesis, it is shown that the non-equilibrium nuclear polarisation buildup in the static CE case is effectively driven by incoherent 3-spin Markovian dissipative processes. These processes can be modelled using a classical kinetic Monte Carlo simulation algorithm, whose computation time scales favourably with system size. With this theoretical approach, it has been shown that it is possible to simulate systems consisting of over 120 spins in a timely fashion, allowing the study of many-body effects such as spin diffusion. It has also enabled predictive simulations that examine the effect of certain parameters on the CE DNP enhancement.
Simulations on cubic grids of 125 nuclear spins with varying degrees of linear randomisation on the spins’ positions show that optimal enhancement is achieved for randomisations of 5% to 10%. The addition of glassing agents to the solvent to en- sure even distribution of radical in the sample therefore also affects the polarisation enhancement by altering the dipolar matrix in the bulk. The same 125-spin cubic grid (with 0% randomisation) is used to verify that the removal of protons with high secular interactions has a positive impact on the polarisation enhancement, while the removal of protons with high pseudo-secular interactions has a negative impact. Knowledge of how protons in the immediate vicinity of electrons affect the polarisation dynamics can aid in the design of radical molecules.
In many cases, the experimentally more relevant CE DNP mechanism is magic angle spinning (MAS) DNP, where the sample is spun at frequencies up to ∼100kHz. While the Hamiltonians of the CE under static and MAS conditions are almost identical, save for the time dependence acquired by some of the terms under MAS, the mechanisms leading to CE DNP have little in common. The kinetic Monte Carlo algorithm developed previously can therefore no longer be used. Furthermore, because the MAS dynamics are periodic with the rotor period, the problem of prohibitively long simulation times is exacerbated by the need to track dynamics within a rotor period as well as stroboscopically. In the fast simulation algorithm presented here, the polarisation-exchanging dynamics within a rotor period are modelled using a highly efficient Landau-Zener formalism. These dynamics are calculated only once to deter- mine the average propagator in a period, which is then used in conjunction with a correction term accounting for the slow nuclear buildup over many periods to calculate the long-time stroboscopic dynamics.
To illustrate the versatility of the fast simulation algorithm, sweeps of the microwave frequency, static field strength & MAS spinning frequency were performed for the 52 structural protons of bTbk. Parameter sweeps such as these are a key building block in the development of an optimised CE DNP experiment. In another simulation, 100 solvent protons are added to the structural protons of bTbk to examine how the bTbk-solvent dynamics depend on the proton concentration in the solvent. It is shown that if the proton relaxation rate is relatively high, the radical and solvent evolve independently. This could pave the way to even faster simulation algorithms that replace the radical with a single representative nucleus and focus on the solvent dynamics. This is useful because experimentally, it is generally the solvent protons that are observed, since the radical protons are too strongly hyperfine shifted for the receiver coil to pick them up.
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