Four-level energy diagram for two coupled spin ’s, which is appropriate for a coupled electron/proton system. includes both dipolar and scalar transitions, while and are the dipolar relaxation transitions, and is the transition rate in the absence of the radical. Overhauser enhancements are obtained by exciting the electron spin transition , creating a nonequilibrium population distribution of the electron spins. The cross relaxation terms transfer the electron spin polarization from the electron spins to the proton spins.
The coupling factor measured at different concentrations of (a) and (b) 4-oxo-TEMPO dissolved in water using Eq. (1). There is no theoretical dependence of on ; however, Heisenberg electron spin exchange can explain this observed effect. The dotted line shows the actual coupling factor, as determined by extrapolating the vs curve to infinite concentrations. At low concentrations, the exchange model predicts measured by Eq. (1) should converge to the dotted line. The experimental data, however, show that this does not occur for -nitroxide radicals, suggesting nitrogen nuclear relaxation may be important. The data obtained from -nitroxide radicals do seem to converge to the expected limit, so nitrogen nuclear relaxation may not play an important role for the maximum saturation factor .
The 12-level model for coupled electron and protons spins originally proposed by Bates and Drozdoski to explain Overhauser enhancements with nitroxide free radicals. Their model only included the intermolecular electron spin exchange transitions, while the effect of nitrogen nuclear spin transitions have been added in this study. Radiation driven electron transitions are denoted by . is related to the applied radiation power by . Implicit in this diagram is that the hyperfine splitting of the electron transition by the nuclei is small compared to the Zeeman energy so of set I approaches of sets II and III.
Maximum saturation is plotted vs and for the -nitroxide radicals using the model that includes nitrogen nuclear spin relaxation transitions. When both and are unimportant, the maximum saturation is as predicted by the four-level model. However, as either or both of these effects become important, approaches 1, the value expected from a radical with a single electron spin transition. Exchange is more effective at mixing the states than nitrogen nuclear relaxation because two molecules are involved and because sets I and III in Fig. 3 can be mixed without first going through set II.
The black circles represent the experimentally determined maximum enhancements using 4-oxo-TEMPO dissolved in water. The solid curve is the fit to the model proposed by Bates and Drozdoski. While the quality of the fit is quite good, it will underestimate the ratio if nitrogen nuclear spin relaxation is important. However, this fit provides the correct coupling factor . The dotted line shows what the maximum enhancements would be in the absence of electron spin exchange with .
Largest experimentally measured enhancements as well as the calculated maximum enhancements for different concentrations of and 4-oxo-TEMPO dissolved in water at . The percent of maximum saturation is also shown for each sample as well as the ESR absorption linewidth. As concentration increases, the ESR absorption lines of 4-oxo-TEMPO broaden more slowly than those of , thus a higher percent of is obtained, contributing to the larger achieved enhancements. The actual enhancements initially increase as the ESR lines broaden due to an increase in and , but about for , the increase in and with concentration is small while the ESR lines continue to broaden linearly with concentration, thus the actual enhancements decrease. Note that these values of linewidth were not used in the calculation of as these values were measured inside the NMR probe before a DNP experiment. A separate experiment was performed to determine without a NMR probe in the resonant cavity.
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