Heteronuclear Polarization Transfers Between Spin-locked and Anti-Longitudinal Spin States in the NMR of Liquids and Spinning Solids

Recently, Pang et al reported a novel polarization transfer scheme applicable to three-spin systems, whereby a rotating-frame NMR analogue of the cross effect could transfer polarization between; e.g., two 13Cs and an 15N in a single crystal. The present work furthers this scheme to the case of powder NMR under magic angle spinning (MAS) conditions, as well as to solution NMR. It is found that in all such cases a second-order average Hamiltonian can transfer polarization between non-equivalent, coupled abundant spins (e.g., two 1Hs) prepared in anti-longitudinal magnetization states, and the spin-locked magnetization of a rare spins (e.g., one 13C). The average Hamiltonian for such three-spin (S1-S2) to I transfer was derived for both liquids and solids, and found in good quantitative agreement with numerical simulations and experiments. At an optimal transfer condition whereby an I-spin RF irradiation field matches the S1-S2 chemical-shift-difference, a maximum polarization enhancement equal to the ratio of gyromagnetic ratios is achieved; as explained and demonstrated in the study, ca. half of this can be effectively obtained for I = 13C in powdered solids and in multi-spin systems in solutions. All such processes display an oscillatory nature, meaning that the transverse spin-locked polarization of a rare spin can become anti-longitudinal magnetization of abundant spins -without ever pulsing on the latter. The roles played by many-body interactions, RF inhomogeneities, and interferences of other coherences during the execution of these novel forms of cross-polarization were investigated, and are exemplified with experiments and simulations.