The solid-state DNP effect in liquids
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 develop a general theoretical description which can take 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. JACS, 144, 1164 (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.
Status: open (until 08 Apr 2023)
- RC1: 'Comment on mr-2023-2', Gunnar Jeschke, 19 Mar 2023 reply
- RC2: 'Comment on mr-2023-2', Anonymous Referee #2, 23 Mar 2023 reply
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This manuscript presents a very elegant theory on DNP under slow-tumbling conditions in liquid solution via a mechanism that is historically known as the solid effect. For a paper discussing high-level spin dynamics theory, it is astonishingly clear. The reader is helped gently over the hurdles on the path to understanding (example: pointing out the outer product with identity operators or the identity matrix in Eq. (53)). The theory is sound and it explains observations recently made by Kuzhelev et al. Compared to an earlier approach that the author calls “more ambitious”, the new theory leads to much simpler results. Although still elaborate, it is one of these theories that appear straightforward after someone has found how to do it. I do not have many remarks and I did not find any serious problem. In principle, this manuscript could be published as is (just correct the typo). The author might want to consider whether any of the following remarks could still improve it.
At some points of my review I refer to the companion paper “Dynamic view of the solid-state DNP effect” (https://doi.org/10.5194/mr-2023-1).
1. Line 35: You refer to the companion paper and discuss the case where the mw nutation frequency approaches the nuclear Larmor frequency. This case is the basis of NOVEL DNP (https://doi.org/10.1016/0022-2364(88)90190-4). You may want to point this out.
2. Line 50: You describe thermal mixing as a DNP process that involves two electron spins and one nuclear spin. Common usage of this term is that it involves several electron spins, not necessarily only two.
3. I understand that the current manuscript needs to repeat some material of the companion paper in order to be self-contained. For my taste, you repeat too much. No derivations are required here. You could simply state the key results of the companion paper before Section 3, where the new derivations and results are described. I would substantially shorten Section 2. Basically, you only need to introduce notation and equations used in later Sections or for generating Figure 3.
4. Line 338: “partial derivative with respect to the time dependence, at fixed ζ.” The reader might be puzzled here, as for any molecule, ζ is generally time dependent, too. Of course, it is mathematically sound to do it this way and average over ζ in the end. However, maybe you want to remind the reader at this point that you are talking about evolution of an ensemble state that contains all orientations. Not all readers might be as familiar with the SLE that they find this obvious.
5. You rightly point out that, with the experimental parameters that you have, you cannot determine the contact distance with sufficient accuracy. However, in principle it may be feasible to determine all parameters that you need (with some effort for B1). Of course, the FFHS model is still a strong simplification. Nevertheless, determining the contact distance within this model may be of interest. Maybe you want to stress this.
Line 436: “hallow” should read “hollow”