Propagation of dynamic nuclear polarization across the xenon cluster boundaries: elucidation of the spin-diffusion bottleneck

Earlier Dynamic Nuclear Polarization (DNP) experiments with frozen xenon/1-propanol/trityl mixtures have demonstrated spontaneous formation of pure xenon clusters above 120 K, enabling spectrally-resolved real-time measurements of (129)Xe nuclear magnetization in the clusters and in the surrounding radical-rich matrix. A spin-diffusion bottleneck was postulated to explain the peculiar time evolution of (129)Xe signals in the clusters as well as the apparent discontinuity of (129)Xe polarization across the cluster boundaries. A self-contained ab initio model of nuclear spin diffusion in heterogeneous systems is developed here, incorporating the intrinsic T1 relaxation towards the temperature-dependent equilibrium polarization and the spin-diffusion coefficients based on the measured NMR line widths and the known atomic densities in each compartment. This simple model provides the physical basis for the observed spin-diffusion bottleneck and is in a good quantitative agreement with the earlier measurements. A simultaneous fit of the model to the time-dependent NMR data at two different DNP frequencies provides excellent estimates of the cluster size, the intrinsic sample temperature, and (129)Xe T1 constants. The model was also applied to the NMR data acquired during relaxation towards the thermal equilibrium after the microwaves were turned off, to estimate T1 relaxation time constants inside and outside the clusters. Fitting the model to the data during and after DNP provides consistent estimates of the cluster size.