Dynamic view of the solid-state DNP effect
Abstract. The first report of dynamic nuclear polarization (DNP) in liquids via the solid-effect mechanism [Erb, Motchane and Uebersfeld, Compt. rend. 246, 2121 (1958)] drew attention to the similarity between the field profile of the enhancement and the dispersive component of the EPR line. The implications of this similarity, however, were not pursued subsequently as practically at the same time Abragam explained the effect in terms of state mixing by the dipolar interaction. Here we develop a description of the solid effect which is grounded in the dynamics of the electron-nucleus spin system, rather than the static view of state mixing. Our approach highlights the role of the coherences in the polarization transfer, and shows that the offset dependence of the DNP enhancement can be rationalized as the response of two band-pass filters connected in series. The first filter is the power-broadened EPR line; the second filter consists of two parts centered on both sides of the electronic resonance and displaced by one nuclear Larmor frequency from it. Being proportional to the product of the two filters, the DNP enhancement profile acquires its odd symmetry from the dispersive EPR line, as intuited by Erb et al. and in agreement with their phenomenological treatment. The developed time-domain description of the solid effect is extendable to liquids where the dipolar interaction changes randomly in time due to molecular diffusion.
Status: open (until 23 Apr 2023)
- RC1: 'Review of manuscript', Anonymous Referee #1, 29 Mar 2023 reply
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The reviewed manuscript describes an analytically derived description of the so-called solid-state DNP effect. As stated by the author, his main goal was to rehabilitate the approach proposed in the 1958 paper by Erb et al. in Comptes rendus "The nuclear polarization effect in liquids and gases adsorbed on charcoal," in which the antiphase structure of the DNP spectrum, later called the solid effect, is interpreted by the determining contribution of equilibrium dispersion of electron spin magnetization. I believe that this cannot be considered the purpose of the manuscript, since the dispersion extremums in their approach are determined solely by the transverse electron relaxation time T2, whereas the proper mechanism of the solid effect gives a description of the two extremum positions with their dependence on the nuclear Zeeman frequency. Moreover, the approach of Erb et al. (1958), as they themselves wrote, was purely phenomenological, in contrast to the correct explanation given by Abraham and Proctor in the same issue of Comptes rendus (1958). Nevertheless, the result of the peer-reviewed paper may be considered to be that the author has shown that the antiphase (+/-) character of the solid-state effect spectrum is determined by the antiphase character of the magnetization s_x of the stationary electron. Also I find it a very interesting result of the manuscript that the author has reduced the solid-state effect problem to a closed system of equations for the mean values of seven spin operators to obtain the stationary nuclear polarization. Among these seven mean values of the operators there are three projections of electron spin, for which stationary values can easily be found from the Bloch equations without taking into account the coupling of electron and nucleus spins. This is reasonable, because the equilibrium of the electron spin is reached much faster than that of the nuclear spin.
At the same time, I consider completely unjustified and unnecessary all the graphical representations of the differential equations, with which the work is simply overloaded. In my opinion, they provide no new information and distract attention. Extremely much space is given to the usual Bloch equations for the projections of the electron spin, taking into account the microwave field and the calculation of their stationary values, as well as the determination of transition probabilities for the kinetic transition scheme, these well-known solutions are given in all textbooks on magnetic resonance. I believe that the article simply needs to be very significantly reduced as follows:
Thus, the paper can be published only after major revision.