^{1}and Songi Han

^{2,a)}

### Abstract

Nitroxide free radicals are the most commonly used source for dynamic nuclear polarization (DNP) enhanced nuclear magnetic resonance(NMR)experiments and are also exclusively employed as spin labels for electron spin resonance(ESR)spectroscopy of diamagnetic molecules and materials. Nitroxide free radicals have been shown to have strong dipolar coupling to in water, and thus result in large DNP enhancement of NMR signal via the well known Overhauser effect. The fundamental parameter in a DNP experiment is the coupling factor, since it ultimately determines the maximum NMR signal enhancements which can be achieved. Despite their widespread use, measurements of the coupling factor of nitroxide free radicals have been inconsistent, and current models have failed to successfully explain our experimental data. We found that the inconsistency in determining the coupling factor arises from not taking into account the characteristics of the ESR transitions, which are split into three (or two) lines due to the hyperfine coupling of the electron to the nuclei (or ) of the nitric oxide radical. Both intermolecular Heisenberg spin exchange interactions as well as intramolecular nitrogen nuclear spin relaxation mix the three (or two) ESR transitions. However, neither effect has been taken into account in any experimental studies on utilizing or quantifying the Overhauser driven DNP effects. The expected effect of Heisenberg spin exchange on Overhauser enhancements has already been theoretically predicted and observed by Bates and Drozdoski [J. Chem. Phys.67, 4038 (1977)]. Here, we present a new model for quantifying Overhauser enhancements through nitroxide free radicals that includes both effects on mixing the ESR hyperfine states. This model predicts the maximum saturation factor to be considerably higher by the effect of nitrogen nuclear spinrelaxation. Because intramolecular nitrogen spin relaxation is independent of the nitroxide concentration, this effect is still significant at low radical concentrations where electron spin exchange is negligible. This implies that the only correct way to determine the coupling factor of nitroxide free radicals is to measure the maximum enhancement at different concentrations and extrapolate the results to infinite concentration. We verify our model with a series of DNP experimental studies on NMR signal enhancement of water by means of as well as isotope enriched nitroxide radicals.

The authors thank Dr. Ralph Weber and Dr. Art Heiss (Bruker Biospin) for providing us with measurements and for steady support. Dr. Evan McCarney is acknowledged for the many helpful discussions on experiment and theory development. Both Mark Lingwood and Dr. Evan McCarney heavily contributed to the DNP instrumental setup. This work was supported by the Materials Research Laboratory program of the National Science Foundation under Grant No. DMR00-80034 and The Institute for Collaborative Biotechnologies through Grant No. DAAD19-03-D-0004 from the U.S. Army Research Office.

I. INTRODUCTION

II. THEORY

A. Overhauser effect

B. Including effect of Heisenberg spin exchange into DNP

C. Including effect of nitrogen nuclear spin relaxation into DNP

III. MATERIALS AND METHODS

A. Samples and preparation

B. Experimental setup

C. Data processing

IV. EXPERIMENTAL RESULTS

A. Testing the low concentration approximation of measuring

B. Concentration dependence of enhancements

C. Actual achieved enhancements

V. CONCLUSION AND IMPLICATIONS

### Key Topics

- Electron paramagnetic resonance spectroscopy
- 58.0
- Spin relaxation
- 37.0
- Nuclear spin
- 30.0
- Nuclear magnetic resonance
- 26.0
- Classical spin models
- 15.0

## Figures

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.

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 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.

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.

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 .

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 .

## Tables

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.

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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