Nuclear spin diffusion in dynamic nuclear polarization of crystalline nanoscale silicon particles

Hyperpolarized nanoparticles offer high polarization levels with room-temperature relaxation times exceeding half an hour. In this work, we demonstrate that the achievable hyperpolarization enhancement and relaxation (decay) time at room temperature are largely independent of the particle size contrary to previous assumptions. This is explained through first-principles spin-diffusion coefficient calculations and finite-difference polarization simulations. The simulated zero-quantum (flip-flop) linewidth governing the spin diffusion is found to agree with the experimentally accessible single-quantum (single spin flip, e.g., radio-frequency pulse) linewidth. The transport of hyperpolarization from strongly hyperfine-coupled spins toward the bulk is believed to be responsible for the slow polarization dynamics including the long room-temperature decay time. The linewidth and spin-diffusion simulations are extended to other cubic crystal structures and analytical expressions, which only require insertion of the gyromagnetic ratio, lattice constant, isotope abundance, and measured spectral density distribution (nuclear linewidth). The presented simulations can be adjusted to study spin diffusion in other materials.