Electron-Electron Cross-Relaxation and Spectral Diffusion during Dynamic Nuclear Polarization Experiments on Solids

Full optimization of dynamic nuclear polarization on a 1 tesla benchtop polarizer with hyperpolarizing solids

Hyperpolarization by dissolution dynamic nuclear polarization (dDNP) provides the opportunity to dramatically increase the weak nuclear magnetic resonance (NMR) signal of liquid molecular targets using the high polarization of electron radicals. Unfortunately, the solution-state hyperpolarization can only be accessed once since freezing and melting of the hyperpolarized sample happen in an irreversible fashion. A way to expand the application horizon of dDNP can therefore be to find a recyclable DNP alternative. To pursue this ambitious goal, we recently introduced the concept of recyclable hyperpolarized flow (HypFlow) DNP where hyperpolarization happens in porous hyperpolarizing solids placed in a compact benchtop DNP polarizer at a magnetic field of 1 T and a temperature of 77 K. Here we aim to optimize the radical concentrations immobilized in hyperpolarizing solids with the objective of generating as much polarization as possible in a timeframe (<1 s) compatible with future recyclable DNP applications. To do so, the solid-state DNP enhancement factors, build-up rates and DNP spectra of different hyperpolarizing solids containing various nitroxide radical loadings (20-74 μmol cm-3) are compared against the DNP performance of varying nitroxide concentrations (10-100 mM) solvated in a glassy frozen solution. We demonstrate that in <1 s, polarization enhancement goes up to 56 and 102 with surface-bound and solvated radicals, respectively, under the optimized conditions. For the range of nitroxide concentrations used cross effect DNP seems to be the dominant mechanism under benchtop conditions. This was deduced from the electron paramagnetic resonance (EPR) lineshape of TEMPOL investigated using Q-band EPR measurements.

Unified understanding of the breakdown of thermal mixing dynamic nuclear polarization: The role of temperature and radical concentration

We reveal an interplay between temperature and radical concentration necessary to establish thermal mixing (TM) as an efficient dynamic nuclear polarization (DNP) mechanism. We conducted DNP experiments by hyperpolarizing widely used DNP samples, i.e., sodium pyruvate-1-13C in water/glycerol mixtures at varying nitroxide radical (TEMPOL) concentrations and microwave irradiation frequencies, measuring proton and carbon-13 spin temperatures. Using a cryogen consumption-free prototype-DNP apparatus, we could probe cryogenic temperatures between 1.5 and 6.5 K, i.e., below and above the boiling point of liquid helium. We identify two mechanisms for the breakdown of TM: (i) Anderson type of quantum localization for low radical concentration, or (ii) quantum Zeno localization occurring at high temperature. This observation allowed us to reconcile the recent diverging observations regarding the relevance of TM as a DNP mechanism by proposing a unifying picture and, consequently, to find a trade-off between radical concentration and electron relaxation times, which offers a pathway to improve experimental DNP performance based on TM.

Spectral diffusion of electron spin polarization in glasses doped with radicals for DNP

Spectral diffusion of electron spin polarization plays a key part in dynamic nuclear polarization (DNP). It determines the distribution of polarization across the electron spin resonance (ESR) line and consequently the polarization that is available for transfer to the nuclear spins. Various authors have studied it experimentally by means of electron-electron double resonance (ELDOR) and proposed and used macroscopic models to interpret these experiments. However, microscopic models predicting the rate of spectral diffusion are scarce. The present article is an attempt to fill this gap. It derives a spectral diffusion equation from first principles and uses Monte Carlo simulations to determine the parameters in this equation. The derivation given here builds on an observation made in a previous article on nuclear dipolar relaxation: spectral diffusion is also spatial diffusion and the random distribution of spins in space limits the former. This can be modelled assuming that rapid flip-flop transitions between a spin and its nearest neighbour do not contribute to diffusion of polarization across the ESR spectrum. The present article presents predictions of the spectral diffusion constant and shows that this limitation may lower the spectral diffusion constant by several orders of magnitude. As a check the constant is determined from first principles for a sample containing 40 mM TEMPOL. Including the limitation then results in a value that is close to that obtained from an analysis of previously reported ELDOR experiments.

Monte Carlo study of the spin-spin interactions between radicals used for dynamic nuclear polarization

The spectrum of the electron spin-spin interactions largely determines which mechanism is responsible for the growth of the nuclear spin polarization in dynamic nuclear polarization (DNP). When electron spin-spin interactions are weak and their spectrum is narrow, the solid effect (SE) dominates the process. When they are stronger, the cross effect (CE) and thermal mixing (TM) come into play. Then a narrow spectrum favours the CE-that is an exchange of electron Zeeman energy with the nuclear spins-and a broad spectrum also TM-that is an exchange of electron spin-spin interaction energy with the nuclear spins. Moreover, the spectrum of the electron spin-spin interactions critically determines the rate of spectral diffusion of electron spin polarization across the electron spin resonance (ESR) line, and the associated conversion of electron Zeeman energy into electron spin-spin interaction energy. This way electron spin-spin interactions indirectly influence the DNP process. The present work describes Monte Carlo simulations of the spectrum of these interactions for approximately spherical radicals in glasses and analytical approximations of the simulation results. As an example application expressions for the relative strengths of the energy flows due to the CE and TM are derived.

13C Dynamic Nuclear Polarization using SA-BDPA at 6.7 T and 1.1 K: Coexistence of Pure Thermal Mixing and Well-Resolved Solid Effect

SA-BDPA is a water-soluble, narrow-line width radical previously used for dynamic nuclear polarization (DNP) signal enhancement in solid-state magic angle spinning NMR spectroscopy. Here, we report the first study using SA-BDPA under dissolution DNP conditions (6.7 T and 1.15 K). Longitudinal-detected (LOD)-electron spin resonance (ESR) and ¹³C DNP measurements were performed on samples containing 8.4 M [¹³C]urea dissolved in 50:50 water:glycerol (v/v) doped with either 60 or 120 mM SA-BDPA. Two distinct DNP mechanisms, both "pure" thermal mixing and a well-resolved solid effect could clearly be identified. The radical's ESR line width (30-40 MHz), broadened predominantly by dipolar coupling, excluded any contribution from the cross effect. Microwave frequency modulation increased the enhancement by DNP at the lower radical concentration but not at the higher radical concentration. These results are compared to data acquired with trityl radical AH111501, highlighting the unusual ¹³C DNP properties of SA-BDPA.

Study of electron spectral diffusion process under DNP conditions by ELDOR spectroscopy focusing on the 14N solid effect

Electron spectral diffusion (eSD) plays an important role in solid-state, static dynamic nuclear polarization (DNP) with polarizers that have inhomogeneously broadened EPR spectra, such as nitroxide radicals. It affects the electron spin polarization gradient within the EPR spectrum during microwave irradiation and thereby determines the effectiveness of the DNP process via the so-called indirect cross-effect (iCE) mechanism. The electron depolarization profile can be measured by electron-electron double resonance (ELDOR) experiments, and a theoretical framework for deriving eSD parameters from ELDOR spectra and employing them to calculate DNP profiles has been developed. The inclusion of electron depolarization arising from the 14 N solid effect (SE) has not yet been taken into account in this theoretical framework and is the subject of the present work. The 14 N SE depolarization was studied using W-band ELDOR of a 0.5 mM TEMPOL solution, where eSD is negligible, taking into account the hyperfine interaction of both 14 N and 1 H nuclei, the long microwave irradiation applied under DNP conditions, and electron and nuclear relaxation. The results of this analysis were then used in simulations of ELDOR spectra of 10 and 20 mM TEMPOL solutions, where eSD is significant using the eSD model and the SE contributions were added ad hoc employing the 1 H and 14 N frequencies and their combinations, as found from the analysis of the 0.5 mM sample. This approach worked well for the 20 mM solution, where a good fit for all ELDOR spectra recorded along the EPR spectrum was obtained and the inclusion of the 14 N SE mechanism improved the agreement with the experimental spectra. For the 10 mM solution, simulations of the ELDOR spectra recorded along the g z position gave a lower-quality fit than for spectra recorded in the center of the EPR spectrum. This indicates that the simple approach we used to describe the 14 N SE is limited when its contribution is relatively high as the anisotropy of its magnetic interactions was not considered explicitly.

Brute-force solvent suppression for DNP studies of powders at natural isotopic abundance

A method based on highly concentrated radical solutions is investigated for the suppression of the NMR signals arising from solvents that are usually used for dynamic nuclear polarization experiments. The presented method is suitable in the case of powders, which are impregnated with a radical-containing solution. It is also demonstrated that the intensity and the resolution of the signals due to the sample of interest is not affected by the high concentration of radicals. The method proposed here is therefore valuable when sensitivity is of the utmost importance, namely samples at natural isotopic abundance.

Theoretical Aspects of the Cross Effect Enhancement of Nuclear Polarization under Static Dynamic Nuclear Polarization Conditions

In this study, we perform quantum calculations of the spin dynamics of a small spin system that includes nine coupled electrons and one nucleus placed in an external magnetic field and exposed to microwave irradiation. This is an extension of a previous work in which we have demonstrated on a system of 11 coupled electron spins the dynamics of the electron polarizations composing the electron paramagnetic resonance (EPR) line during static dynamic nuclear polarization (DNP) experiments. There we have shown that the electron polarizations are determined by a spectral diffusion process, induced by the dipolar interaction and cross-relaxation. Additionally, we showed that a distinction had to be made between strong and weak dipolar-coupled systems relative to the inhomogeneity of the EPR line with only the first behaving according to the thermal mixing DNP (with two electron spin temperatures) description. The EPR spectra in the weak and strong dipolar interaction cases show different types of spectral features. In the extended spin system, we again make a distinction between weak and strong electron-electron interactions and show that the DNP spectra for the two cases are different in nature but that the DNP spectra can be derived in all cases from the EPR line shapes using the indirect cross effect.

Dynamic nuclear polarization via the cross effect and thermal mixing: B. Energy transport

The fundamental process of dynamic nuclear polarization (DNP) via the cross effect (CE) and thermal mixing (TM) is a triple spin flip, in which two interacting electron spins and a nuclear spin interacting with one of these electron spins flip together. In the previous article (Wenckebach, 2018) these triple spin flips were treated by first determining the eigenstates of the two interacting electron spins exactly and next investigating transitions involving these exact eigenstates and the nuclear spin states. It was found that two previously developed approaches-the scrambled states approach and the fluctuating field approach-are just two distinct limiting cases of this more general approach. It was also shown that triple spin flips constitute a single process causing two flows of energy: a flow originating in the electron Zeeman energy and a flow originating in the mutual interactions between the electron spins. In order to render their definitions more precise, the former flow was denoted as the CE and the latter as TM. In this article the treatment is extended to a glass containing N_I equivalent nuclear spins I=12 and N_S randomly distributed and oriented electron spins S=12. Rate equations are derived for the two flows of energy to the nuclear spins. The flow originating in the electron Zeeman energy-i.e. the CE-is found to lead to the same stationary state as was previously predicted by the scrambled states approach, though the rate may be smaller due to limitations imposed by conservation of energy. The flow originating in the mutual interactions between the electron spins-i.e. TM-is found to involve the full spectrum of the mutual interactions between the electron spins, while the fluctuating field approach only accounts for the component of this spectrum at the nuclear magnetic resonance (NMR) frequency. Still, TM is found to induce equal spin temperature for different nuclear spin species during nuclear spin-lattice relaxation and, at least in some cases also during polarization. It is also confirmed that TM couples local nuclear spins near the electron spins so strongly to the mutual interactions between electron spins, that they may constitute a single energy reservoir (Cox et al., 1973). Hence such local nuclear spins may have to be included in treatments of the dynamics of the electron spins.

Experimental quantification of electron spectral-diffusion under static DNP conditions

Dynamic Nuclear Polarization (DNP) is an efficient technique for enhancing NMR signals by utilizing the large polarization of electron spins to polarize nuclei. The mechanistic details of the polarization transfer process involve the depolarization of the electrons resulting from microwave (MW) irradiation (saturation), as well as electron-electron cross-relaxation occurring during the DNP experiment. Recently, electron-electron double resonance (ELDOR) experiments have been performed under DNP conditions to map the depolarization profile along the EPR spectrum as a consequence of spectral diffusion. A phenomenological model referred to as the eSD model was developed earlier to describe the spectral diffusion process and thus reproduce the experimental results of electron depolarization. This model has recently been supported by quantum mechanical calculations on a small dipolar coupled electron spin system, experiencing dipolar interaction based cross-relaxation. In the present study, we performed a series of ELDOR measurements on a solid glassy solution of TEMPOL radicals in an effort to substantiate the eSD model and test its predictability in terms of electron depolarization profiles, in the steady-state and under non-equilibrium conditions. The crucial empirical parameter in this model is ΛeSD, which reflects the polarization exchange rate among the electron spins. Here, we explore further the physical basis of this parameter by analyzing the ELDOR spectra measured in the temperature range of 3-20 K and radical concentrations of 20-40 mM. Simulations using the eSD model were carried out to determine the dependence of ΛeSD on temperature and concentration. We found that for the samples studied, ΛeSD is temperature independent. It, however, increases with a power of ∼2.6 of the concentration of TEMPOL, which is proportional to the average electron-electron dipolar interaction strength in the sample.