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.

Bath-Induced Zeno Localization in Driven Many-Body Quantum Systems

We study a quantum interacting spin system subject to an external drive and coupled to a thermal bath of vibrational modes, uncorrelated for different spins, serving as a model for dynamic nuclear polarization protocols. We show that even when the many-body eigenstates of the system are ergodic, a sufficiently strong coupling to the bath may effectively localize the spins due to many-body quantum Zeno effect. Our results provide an explanation of the breakdown of the thermal mixing regime experimentally observed above 4-5 K in these protocols.

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.

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.

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

Recently it has been shown that experimental electron-electron double resonance (ELDOR) spectra of amorphous glasses containing free radicals with inhomogeneously broadened electron paramagnetic resonance (EPR) spectra can be analyzed using a set of coupled rate equations for the electron polarizations of frequency bins composing these spectra, named the eSD (electron spectral diffusion) model. The rate matrix defining these equations has elements depending on the microwave, the spin-lattice relaxation rates and on eSD rate constants responsible for polarization exchange. In this study, we show that in addition to the static dipolar flip-flop terms in the Hamiltonian a zero-quantum electron cross-relaxation mechanism can be responsible for the polarization exchange process in our samples. This conclusion was reached by calculating the EPR lineshapes of a system of 11 coupled electrons exposed to microwave irradiation using an eigenstate population rate equation derived from the spin density vector rate equation in Liouville space. These equations involve all terms of the Hamiltonian and in addition rate constants representing longitudinal relaxation and cross-relaxation mechanisms as well as MW irradiation. The results of these calculations are compared with the results obtained from the eSD model.

Dynamic Nuclear Polarization of Long-Lived Nuclear Spin States in Methyl Groups

We have induced hyperpolarized long-lived states in compounds containing ¹³C-bearing methyl groups by dynamic nuclear polarization (DNP) at cryogenic temperatures, followed by dissolution with a warm solvent. The hyperpolarized methyl long-lived states give rise to enhanced antiphase ¹³C NMR signals in solution, which often persist for times much longer than the ¹³C and ¹H spin-lattice relaxation times under the same conditions. The DNP-induced effects are similar to quantum-rotor-induced polarization (QRIP) but are observed in a wider range of compounds because they do not depend critically on the height of the rotational barrier. We interpret our observations with a model in which nuclear Zeeman and methyl tunnelling reservoirs adopt an approximately uniform temperature, under DNP conditions. The generation of hyperpolarized NMR signals that persist for relatively long times in a range of methyl-bearing substances may be important for applications such as investigations of metabolism, enzymatic reactions, protein-ligand binding, drug screening, and molecular imaging.

Dynamic Nuclear Polarization of β-Cyclodextrin Macromolecules

¹H dynamic nuclear polarization and nuclear spin-lattice relaxation rates have been studied in amorphous complexes of β-cyclodextrins doped with different concentrations of the TEMPO radical. Nuclear polarization increased up to 10% in the optimal case, with a behavior of the buildup rate (1/T_POL) and of the nuclear spin-lattice relaxation rate (1/T_1n) consistent with a thermal mixing regime. The temperature dependence of 1/T_1n and its increase with the radical concentration indicate a relaxation process arising from the modulation of the electron-nucleus coupling by the glassy dynamics. The high-temperature relaxation is driven by molecular motions, and 1/T_1n was studied at room temperature in liquid solutions for dilution levels close to the ones typically used for in vivo studies.