The solid effect of dynamic nuclear polarization in liquids

Abstract

Abstract. The solid-state effect of dynamic nuclear polarization (DNP) is operative also in viscous liquids where the dipolar interaction between the electronic and nuclear spins is partially averaged. The proper way to quantify the degree of averaging, and thus calculate the efficiency of the effect, should be based on the time-correlation function of the dipolar interaction. Here we use the stochastic Liouville equation formalism to develop a general theoretical description of the solid effect in liquids. The derived expressions can be used with different dipolar correlations functions depending on the assumed motional model. At high magnetic fields, the theory predicts DNP enhancements at small offsets, far from the classical solid-effect positions that are displaced by one nuclear Larmor frequency from the electronic resonance. The predictions are in quantitative agreement with such enhancement peaks observed at 9.4 T (Kuzhelev et al., 2022). These non-canonical peaks are not due to thermal mixing or the cross effect but exactly follow the dispersive component of the EPR line.

The solid effect of dynamic nuclear polarization in liquids – accounting for g-tensor anisotropy at high magnetic fields

“…). In liquids, where the random molecular motion modulates the dipolar interaction between the electronic and nuclear spins, these rate constants are no longer available analytically but can be calculated numerically for motional models with known dipolar spectral densities , as reviewed below in Sect. .…”

“….) Even leaving power broadening aside, however, we know that in liquids the SE lines of the DNP spectrum should also be broader than the EPR line width because of the fluctuations of the dipolar interaction . Although showed how to quantify this additional motional broadening in the case of translational molecular diffusion, the theoretical treatment there assumed a Lorentzian EPR line and is thus not directly applicable to the experiments in Fig.…”

“…Finally, in Sect. we remind the reader how these expressions should be modified in the presence of random modulation of the dipolar interaction, as relevant for liquids .…”

“…In liquids, changes in time because of molecular diffusion. The treatment of SE-DNP for a time-dependent in was developed under the assumption that the nuclear is orders of magnitude larger than the correlation time of the electron–nucleus dipolar interaction, which is practically always the case in liquids. For the same analysis to apply to solids, nuclear spin diffusion, which analogously to molecular diffusion in liquids spreads out the nuclear polarization across the sample, should be much faster than the nuclear .…”

“…Recently, presented a time-domain description of SE which, like semi-classical relaxation theory, allows for different dynamical processes to modulate the relevant spin interactions. By interfacing this description with the spectral density of isotropic translational diffusion , it was possible to treat SE-DNP in the presence of molecular translation as relevant to homogeneous liquids . The requirement that the dipolar interaction should not be completely averaged out by the molecular dynamics during the electronic restricts liquid-state SE-DNP to viscous media, where the tumbling of the polarizing agent may similarly be too slow to average the anisotropies of its magnetic tensors.…”