(412c) Quantitative Scaling Analyses of Polarization Energy Transfer in Solids and across Solid-Solid Interfaces

An energy-conserving constitutive model, with analogies to heat conduction and mass transfer, quantitatively describes the propagation and dissipation of non-equilibrium spin polarization over nanometer to micrometer length scales in diverse heterogeneous solids. The approach provides new insights on hyperpolarization energy transfer processes, which open new opportunities to characterize the compositions and structures of engineering materials, especially near solid-solid interfaces. In these systems, non-equilibrium spin polarization is generated by continuous microwave excitation of unpaired electron spins and transferred via hyperfine interactions to nearby nuclear spins. This produces locally a high level of non-Boltzmann polarization that can be relayed via ¹H–¹H dipole-dipole interactions over distances ranging from <1 nm to >1 μm, depending on the relative rates of generation, spin diffusion, and spin relaxation in a given medium. Thermodynamic scaling analyses lead naturally to dimensionless parameters that have direct analogies to the Thiele modulus, Biot Number, and Damköhler Number and are based solely on measurable or known physical properties.

Complications associated with continuum-level descriptions of hyperfine-induced energy transfer processes, which are intrinsically quantum-mechanical, are overcome by inclusion of a “film" resistance to polarization transfer that is analogous to a heat-transfer coefficient. The constitutive model (with no adjustable parameters) and scaling analyses lead to analytical expressions that account quantitatively for transient and steady-state polarization energy transfer in diverse solids, including glasses, polymer microbeads (100 nm), pharmaceutical compounds, semiconductors, and low-surface-area silicate particles (10 μm). The analyses enable the rate-limiting steps associated with polarization energy transfer kinetics versus polarization conduction to be determined. More importantly, they enable near-surface compositions and structures of heterogeneous materials to be measured and understood for systems that were not previously feasible to investigate, such as in polymers and cements, which will be discussed.