Dipolar Order Induced Electron Spin Hyperpolarization

The structure of coupled electron spin systems is of fundamental interest to many applications, including dynamic nuclear polarization (DNP), enhanced nuclear magnetic resonance (NMR), the generation of electron spin qubits for quantum information science (QIS), and quantitative studies of paramagnetic systems by electron paramagnetic resonance (EPR). However, the characterization of electron spin coupling networks is nontrivial, especially at high magnetic fields. This study focuses on a system containing high concentrations of trityl radicals that give rise to a DNP enhancement profile of 1H NMR characteristic of the presence of electron spin clusters. When this system is subject to selective microwave saturation through pump-probe ELectron DOuble Resonance (ELDOR) experiments, electron spin hyperpolarization is observed. We show that the generation of an out-of-equilibrium longitudinal dipolar order is responsible for the transient hyperpolarization of electron spins. Notably, the coupled electron spin system needs to form an AX-like system (where the difference in the Zeeman interactions of two spins is larger than their coupling interaction) such that selective microwave irradiation can generate signatures of electron spin hyperpolarization. We show that the extent of dipolar order, as manifested in the extent of electron spin hyperpolarization generated, can be altered by tuning the pump or probe pulse length, or the interpulse delay in ELDOR experiments that change the efficiency to generate or readout longitudinal dipolar order. Pump-probe ELDOR with selective saturation is an effective means for characterizing coupled electron spins forming AX-type spin systems that are foundational for DNP and quantum sensing.

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.

The CW-EPR Capabilities of a Dual DNP/EPR Spectrometer Operating at 14 and 7 T

High-field electron paramagnetic resonance (EPR) measurements are indispensable for a better understanding of dynamic nuclear polarization (DNP), which relies on polarization transfer between electron and nuclear spins. DNP experiments are typically performed at high > 7 T magnetic fields and low ≤ 100 K temperatures, while EPR instrumentation capable of EPR measurements under these conditions is scarce. In this paper, we describe the CW EPR capabilities of a dual DNP/EPR spectrometer that is designed to carry out EPR experiments under "DNP conditions" at 14 and 7 T. In the first part, we present the design of this instrument, highlighting the choices made to allow for both DNP and EPR operations. The spectrometer uses a sweepable cryogen-free magnet with NMR-grade homogeneity, a closed-cycle cooling system, a quasi-optical induction mode bridge, and a superheterodyne receiver system. The probe design is optimized for low heat load and fast sample exchange under cryogenic conditions. The spectrometer can operate in frequency and field sweep modes, including wide field sweeps using the main coil of the magnet. In the second part, we present EPR spectra acquired over a wide range of samples and operating conditions, illustrating the CW EPR capabilities of the instrument.

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.

Nitrogen Substitutions Aggregation and Clustering in Diamonds as Revealed by High-Field Electron Paramagnetic Resonance

Diamonds have been shown to be an excellent platform for quantum computing and quantum sensing applications. These applications are enabled by the presence of defects in the lattice, which are also known as color centers. The most common nitrogen-based defect in synthetic diamonds is the paramagnetic nitrogen substitution (P1) center. While the majority of quantum applications rely on nitrogen-vacancy (NV) centers, the properties of the latter are heavily influenced by the presence and the spatial distribution of the P1 centers. Hence, understanding the spatial distribution and mutual interactions of P1 centers is crucial for the successful development of diamond-based quantum devices. Unlike NV centers, P1 centers do not have a spin-dependent optical signature, and their spin-related properties, therefore, have to be detected and characterized using magnetic resonance methods. We show that using high-field (6.9 and 13.8 T) pulsed electron paramagnetic resonance (EPR) and dynamic nuclear polarization (DNP) experiments, we can distinguish and quantify three distinct populations of P1 centers: isolated P1 centers, weakly interacting ones, and exchange-coupled ones that are clustered together. While such clustering was suggested before, these clusters were never detected directly and unambiguously. Moreover, by using electron-electron double resonance (ELDOR) pump-probe experiments, we demonstrate that the latter clustered population does not exist in isolation but coexists with the more weakly interacting P1 centers throughout the diamond lattice. Its presence thus strongly affects the quantum properties of the diamond. We also show that the existence of this population can explain recent hyperpolarization results in type Ib high-pressure, high-temperature (HPHT) diamonds. We propose a combination of high-field pulsed EPR, ELDOR, and DNP as a tool for probing the aggregation state and interactions among different populations of nitrogen substitution centers.

Multi Electron Spin Cluster Enabled Dynamic Nuclear Polarization with Sulfonated BDPA

Dynamic nuclear polarization (DNP) can amplify the solid-state nuclear magnetic resonance (NMR) signal by several orders of magnitude. The mechanism of DNP utilizing α,γ-bisdiphenylene-β-phenylallyl (BDPA) variants as Polarizing Agents (PA) has been the subject of lively discussions on account of their remarkable DNP efficiency with low demand for microwave power. We propose that electron spin clustering of sulfonated BDPA is responsible for its DNP performance, as revealed by the temperature-dependent shape of the central DNP profile and strong electron-electron (e-e) crosstalk seen by Electron Double Resonance. We demonstrate that a multielectron spin cluster can be modeled with three coupled spins, where electron J (exchange) coupling between one of the e-e pairs matching the NMR Larmor frequency induces the experimentally observed absorptive central DNP profile, and the electron T1e modulated by temperature and magic-angle spinning alters the shape between an absorptive and dispersive feature. Understanding the microscopic origin is key to designing new PAs to harness the microwave-power-efficient DNP effect observed with BDPA variants.

Large cross-effect dynamic nuclear polarisation enhancements with kilowatt inverting chirped pulses at 94 GHz

Dynamic nuclear polarisation (DNP) is a process that transfers electron spin polarisation to nuclei by applying resonant microwave radiation, and has been widely used to improve the sensitivity of nuclear magnetic resonance (NMR). Here we demonstrate new levels of performance for static cross-effect proton DNP using high peak power chirped inversion pulses at 94 GHz to create a strong polarisation gradient across the inhomogeneously broadened line of the mono-radical 4-amino TEMPO. Enhancements of up to 340 are achieved at an average power of a few hundred mW, with fast build-up times (3 s). Experiments are performed using a home-built wideband kW pulsed electron paramagnetic resonance (EPR) spectrometer operating at 94 GHz, integrated with an NMR detection system. Simultaneous DNP and EPR characterisation of other mono-radicals and biradicals, as a function of temperature, leads to additional insights into limiting relaxation mechanisms and give further motivation for the development of wideband pulsed amplifiers for DNP at higher frequencies.

Highly bioresistant, hydrophilic and rigidly linked trityl-nitroxide biradicals for cellular high-field dynamic nuclear polarization

Cellular dynamic nuclear polarization (DNP) has been an effective means of overcoming the intrinsic sensitivity limitations of solid-state nuclear magnetic resonance (ssNMR) spectroscopy, thus enabling atomic-level biomolecular characterization in native environments. Achieving DNP signal enhancement relies on doping biological preparations with biradical polarizing agents (PAs). Unfortunately, PA performance within cells is often limited by their sensitivity to the reductive nature of the cellular lumen. Herein, we report the synthesis and characterization of a highly bioresistant and hydrophilic PA (StaPol-1) comprising the trityl radical OX063 ligated to a gem-diethyl pyrroline nitroxide via a rigid piperazine linker. EPR experiments in the presence of reducing agents such as ascorbate and in HeLa cell lysates demonstrate the reduction resistance of StaPol-1. High DNP enhancements seen in small molecules, proteins and cell lysates at 18.8 T confirm that StaPol-1 is an excellent PA for DNP ssNMR investigations of biomolecular systems at high magnetic fields in reductive environments.

Large Room Temperature Bulk DNP of 13C via P1 Centers in Diamond

We use microwave-induced dynamic nuclear polarization (DNP) of the substitutional nitrogen defects (P1 centers) in diamond to hyperpolarize bulk ¹³C nuclei in both single crystal and powder samples at room temperature at 3.34 T. The large (>100-fold) enhancements demonstrated correspond to a greater than 10 000-fold improvement in terms of signal averaging of the 1% abundant ¹³C spins. The DNP was performed using low-power solid state sources under static (nonspinning) conditions. The DNP spectrum (DNP enhancement as a function of microwave frequency) of diamond powder shows features that broadly correlate with the EPR spectrum. A well-defined negative Overhauser peak and two solid effect peaks are observed for the central (m _I = 0) manifold of the ¹⁴N spins. Previous low temperature measurements in diamond had measured a positive Overhauser enhancement in this manifold. Frequency-chirped millimeter-wave excitation of the electron spins is seen to significantly improve the enhancements for the two outer nuclear spin manifolds (m_I = ±1) and to blur some of the sharper features associated with the central manifold. The outer lines are best fit using a combination of the cross effect and the truncated cross effect, which is known to mimic features of an Overhauser effect. Similar features are also observed in experiments on single crystal samples. The observation of all of these mechanisms in a single material system under the same experimental conditions is likely due to the significant heterogeneity of the high pressure, high temperature (HPHT) type Ib diamond samples used. Large room temperature DNP enhancements at fields above a few tesla enable spectroscopic studies with better chemical shift resolution under ambient conditions.

A transition from solid effect to indirect cross effect with broadband microwave irradiation

Dynamic nuclear polarization (DNP) at high magnetic fields has become a prominent technique for signal enhancement in nuclear magnetic resonance (NMR). In static samples, the highest DNP enhancement is usually observed for high radical concentrations in the range of 15-40 mM. Under these conditions, the dominant DNP mechanism for broad-line radicals is the electron-electron spectral-diffusion-based indirect cross effect (iCE). To further increase the DNP performance, broadband microwave irradiation is often applied. Until now, the theory of iCE was not rigorously combined with broadband microwave irradiation. This paper fills this gap by extending the iCE theory to explicitly include broadband irradiation. We demonstrate that our theory allows for quantitative fitting of the DNP spectra lineshapes using four different datasets acquired at 3.4 T and 7 T. We find that the DNP mechanism changes with an increase in the excitation bandwidth. While with narrowband continuous-wave irradiation the DNP mechanism is a combination of the solid effect (SE) and iCE, it shifts toward iCE with increasing excitation bandwidth until, at high bandwidth, the iCE completely dominates the DNP spectrum - this effect was not accounted for previously.

Three mechanisms of room temperature dynamic nuclear polarization occur simultaneously in an ionic liquid

For the first time, several mechanisms of dynamic nuclear polarization, namely Overhauser, solid effect and cross effect/thermal mixing, have been identified in an ionic liquid with a nitroxide radical at ambient temperatures.

Solid-state MAS NMR at ultra low temperature of hydrated alanine doped with DNP radicals

Magic angle spinning (MAS) nuclear magnetic resonance (NMR) experiments at ultra low temperature (ULT) (≪ 100 K) have demonstrated clear benefits for obtaining large signal sensitivity gain and probing spin dynamics phenomena at ULT. ULT NMR is furthermore a highly promising platform for solid-state dynamic nuclear polarization (DNP). However, ULT NMR is not widely used, given limited availability of such instrumentation from commercial sources. In this paper, we present a comprehensive study of hydrated [U-¹³C]alanine, a standard bio-solid sample, from the first commercial 14.1 Tesla NMR spectrometer equipped with a closed-cycle helium ULT-MAS system. The closed-cycle helium MAS system provides precise temperature control from 25 K to 100 K and stable MAS from 1.5 kHz to 12 kHz. The ¹³C CP-MAS NMR of [U-¹³C]alanine showed 400% signal gain at 28 K compared with at 100 K. The large sensitivity gain results from the Boltzmann factor, radio frequency circuitry quality factor improvement, and the suppression of its methyl group rotation at ULT. We further observed that the addition of organic biradicals widely used for solid-state DNP significantly shortens the ¹H T₁ spin lattice relaxation time at ULT, without further broadening the ¹³C spectral linewidth compared to at 90 K. The mechanism of ¹H T₁ shortening is dominated by the two-electron-one-nucleus triple flip transition underlying the Cross Effect mechanism, widely relied upon to drive solid-state DNP. Our experimental observations suggest that the prospects of MAS NMR and DNP under ULT conditions established with a closed-cycle helium MAS system are bright.

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.

Crossover from a Solid Effect to Thermal Mixing 1H Dynamic Nuclear Polarization with Trityl-OX063

Trityl-OX063 is a narrow-line, water-soluble, and biocompatible polarizing agent, widely used for dynamic nuclear polarization (DNP) amplified NMR of ¹³C, but not of the abundant ¹H nuclear spin, for which the ineffective solid effect (SE) is expected to be operational. Surprisingly, we observed a crossover from SE to thermal mixing (TM) DNP of ¹H with increasing Trityl-OX063 concentration at 7 T. We experimentally ascertained diagnostic signatures of TM-DNP that have only been theoretically predicted: (i) an electron paramagnetic resonance (EPR) spectrum that maintains an asymmetrically broadened EPR line from strong e-e couplings and (ii) hyperpolarization, i.e., cooling of select electron-spin populations, manifested in a characteristic pump-probe electron double-resonance spectrum under DNP conditions. Low microwave power requirements, high polarization transfer rates, and efficient DNP at high magnetic fields are the key benefits of TM-DNP.

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.

Cross-Effect Dynamic Nuclear Polarization Explained: Polarization, Depolarization, and Oversaturation

The scope of this Perspective is to analytically describe NMR hyperpolarization by the three-spin cross effect (CE) dynamic nuclear polarization (DNP) using an effective Hamiltonian concept. We apply, for the first time, the bimodal operator-based Floquet theory in the Zeeman-interaction frame for two and three coupled spins to derive the known interaction Hamiltonian for CE-DNP. With a unified understanding of CE-DNP, and supported by empirical observation of the state of electron spin polarization under the given experimental conditions, we explain diverse manifestations of CE from oversaturation, enhanced hyperpolarization by broad-band saturation, to nuclear spin depolarization under magic-angle spinning.

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.

Tuning nuclear depolarization under MAS by electron T1e

The Cross-Effect (CE) Dynamic Nuclear Polarization (DNP) mechanism under Magic Angle Spinning (MAS) induces depletion or "depolarization" of the NMR signal, in the absence of microwave irradiation. In this study, the role of T_1e on nuclear depolarization under MAS was tested experimentally by systematically varying the local and global electron spin concentration using mono-, bi- and tri-radicals. These spin systems show different depolarization effects that systematically tracked with their different T_1e rates, consistent with theoretical predictions. In order to test whether the effect of T_1e is directly or indirectly convoluted with other spin parameters, the tri-radical system was doped with different concentrations of GdCl₃, only tuning the T_1e rates, while keeping other parameters unchanged. Gratifyingly, the changes in the depolarization factor tracked the changes in the T_1e rates. The experimental results are corroborated by quantum mechanics based numerical simulations which recapitulated the critical role of T_1e. Simulations showed that the relative orientation of the two g-tensors and e-e dipolar interaction tensors of the CE fulfilling spin pair also plays a major role in determining the extent of depolarization, besides the enhancement. This is expected as orientations influence the efficiency of the various level anti-crossings or the "rotor events" under MAS. However, experimental evaluation of the empirical spectral diffusion parameter at static condition showed that the local vs. global e-e dipolar interaction network is not a significant variable in the commonly used nitroxide radical system studied here, leaving T_1e rates as the major modulator of depolarization.

Eigenstate versus Zeeman-based approaches to the solid effect

The solid effect is one of the simplest and most effective mechanisms for dynamic nuclear polarization. It involves the exchange of polarization between one electron and one nuclear spin coupled via the hyperfine interaction. Even for such a small spin system, the theoretical understanding is complicated by the contact with the lattice and the microwave irradiation. Both being weak, they can be treated within perturbation theory. In this work, we analyze the two most popular perturbation schemes: the Zeeman and the eigenstate-based approaches, which differ in the way the hyperfine interaction is treated. For both schemes, we derive from first principles an effective Liouville equation that describes the density matrix of the spin system; we then study numerically the behavior of the nuclear polarization for several values of the hyperfine coupling. In general, we obtain that the Zeeman-based approach underestimates the value of the nuclear polarization. By performing a projection onto the diagonal part of the spin-system density matrix, we are able to understand the origin of the discrepancy, which is due to the presence of parasite leakage transitions appearing whenever the Zeeman basis is employed.

Amplification of Dynamic Nuclear Polarization at 200 GHz by Arbitrary Pulse Shaping of the Electron Spin Saturation Profile

Dynamic nuclear polarization (DNP) takes center stage in nuclear magnetic resonance (NMR) as a tool to amplify its signal by orders of magnitude through the transfer of polarization from electron to nuclear spins. In contrast to modern NMR and electron paramagnetic resonance (EPR) that extensively rely on pulses for spin manipulation in the time domain, the current mainstream DNP technology exclusively relies on monochromatic continuous wave (CW) irradiation. This study introduces arbitrary phase shaped pulses that constitute a train of coherent chirp pulses in the time domain at 200 GHz (7 T) to dramatically enhance the saturation bandwidth and DNP performance compared to CW DNP, yielding up to 500-fold in NMR signal enhancements. The observed improvement is attributed to the recruitment of additional electron spins contributing to DNP via the cross-effect mechanism, as experimentally confirmed by two-frequency pump-probe electron-electron double resonance (ELDOR).

Truncated Cross Effect Dynamic Nuclear Polarization: An Overhauser Effect Doppelgänger

The discovery of a truncated cross-effect (CE) in dynamic nuclear polarization (DNP) NMR that has the features of an Overhauser-effect DNP (OE-DNP) is reported here. The apparent OE-DNP, where minimal μw power achieved optimum enhancement, was observed when doping Trityl-OX063 with a pyrroline nitroxide radical that possesses electron-withdrawing tetracarboxylate substituents (tetracarboxylate-ester-pyrroline or TCP) in vitrified water/glycerol at 6.9 T and at 3.3 to 85 K, in apparent contradiction to expectations. While the observations are fully consistent with OE-DNP, we discover that a truncated cross-effect ( tCE) is the underlying mechanism, owing to TCP's shortened T_1e. We take this observation as a guideline and demonstrate that a crossover from CE to tCE can be replicated by simulating the CE of a narrow-line (Trityl-OX063) and a broad-line (TCP) radical pair, with a significantly shortened T_1e of the broad-line radical.

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.

Gadolinium based endohedral metallofullerene Gd2@C79N as a relaxation boosting agent for dissolution DNP at high fields

We show increased dynamic nuclear polarization by adding a low dosage of a S = 15/2 Gd based endohedral metallofullerene (EMF) to DNP samples. By adding 60 μM Gd₂@C₇₉N, the nuclear polarization of ¹H and ¹³C spins from 40 mM 4-oxo-TEMPO increases by approximately 40% and 50%, respectively, at 5 T and 1.2 K. Electron-electron double resonance (ELDOR) measurements show that the high spin EMF shortens the electron relaxation times and increases electron spectral diffusion leading to the increased DNP enhancement.

Anisotropic longitudinal electronic relaxation affects DNP at cryogenic temperatures

We report the observation of anisotropic longitudinal electronic relaxation in nitroxide radicals under typical dynamic nuclear polarization conditions. This anisotropy affects the efficiency of dynamic nuclear polarization at cryogenic temperatures of 4 K and high magnetic fields of 6.7 T. Under our experimental conditions, the electron paramagnetic resonance spectrum of nitroxides such as TEMPOL (4-hydroxy-2,2,6,6-tetramethylpiperidin-1-oxyl) is only partly averaged by electronic spectral diffusion, so that the relaxation times T_1e(ω) vary across the spectrum. We demonstrate how the anisotropy of T_1e(ω) can be taken into account in simple DNP models.

Dynamic nuclear polarization for sensitivity enhancement in modern solid-state NMR

The field of dynamic nuclear polarization has undergone tremendous developments and diversification since its inception more than 6 decades ago. In this review we provide an in-depth overview of the relevant topics involved in DNP-enhanced MAS NMR spectroscopy. This includes the theoretical description of DNP mechanisms as well as of the polarization transfer pathways that can lead to a uniform or selective spreading of polarization between nuclear spins. Furthermore, we cover historical and state-of-the art aspects of dedicated instrumentation, polarizing agents, and optimization techniques for efficient MAS DNP. Finally, we present an extensive overview on applications in the fields of structural biology and materials science, which underlines that MAS DNP has moved far beyond the proof-of-concept stage and has become an important tool for research in these fields.

Spectral diffusion and dynamic nuclear polarization: Beyond the high temperature approximation

Dynamic Nuclear Polarization (DNP) has proven itself most powerful for the orientation of nuclear spins in polarized targets and for hyperpolarization in magnetic resonance imaging (MRI). Unfortunately, the theoretical description of some of the processes involved in DNP invokes the high temperature approximation, in which Boltzmann factors are expanded up to first order, while the high electron and nuclear spin polarization required for many applications do not justify such an approximation. A previous article extended the description of one of the mechanisms of DNP-thermal mixing-beyond the high temperature approximation (Wenckebach, 2017). But that extension is still limited: it assumes that fast spectral diffusion creates a local equilibrium in the electron spin system. Provotorov's theory of cross-relaxation enables a consistent further extension to slower spectral diffusion, but also invokes the high temperature approximation. The present article extends the theory of cross-relaxation to low temperature and applies it to spectral diffusion in glasses doped with paramagnetic centres with anisotropic g-tensors. The formalism is used to describe DNP via the mechanism of the cross effect. In the limit of fast spectral diffusion the results converge to those obtained in Wenckebach (2017) for thermal mixing. In the limit of slow spectral diffusion a hole is burnt in the electron spin resonance (ESR) signal, just as predicted by more simple models. The theory is applied to DNP of proton and ¹³C spins in samples doped with the radical TEMPO.

Dynamic nuclear polarization via thermal mixing: Beyond the high temperature approximation

Dynamic Nuclear Polarization (DNP) via the mechanism of thermal mixing has proven itself most powerful for the orientation of nuclear spins in polarized targets and hyperpolarization for magnetic resonance imaging (MRI). Unfortunately, theoretical descriptions of this mechanism have been limited to using-at least partially-the high temperature approximation, in which Boltzmann factors are expanded linearly. However, the high nuclear spin polarization required and obtained for these applications does not justify such approximations. This article extends the description of thermal mixing beyond the high temperature approximation, so Boltzmann factors are not expanded. It applies for DNP in samples doped with paramagnetic centres, for which the electron spin resonance spectrum is mainly inhomogeneously broadened by g-value anisotropy. It verifies Provotorov's hypothesis that fast spectral diffusion leads to a density matrix containing two inverse spin temperatures: the inverse electron Zeeman temperature and the inverse electron non-Zeeman temperature, while thermal mixing equalizes the nuclear Zeeman temperature and the electron non-Zeeman temperature. Equations are derived for the evolution of these temperatures and the energy flows between the spins and the lattice. Solutions are given for DNP of proton spins in samples doped with the radical TEMPO.

Effect of electron spectral diffusion on static dynamic nuclear polarization at 7 Tesla

Systematic investigation of DNP profiles at high radical concentrations and 7 T show that electron spectral diffusion directly impacts DNP processes.

Colored spectrum characteristics of thermal noise on the molecular scale

Thermal noise is of fundamental importance to many processes. Traditionally, thermal noise has been treated as white noise on the macroscopic scale. Using molecular dynamics simulations and power spectrum analysis, we show that the thermal noise of solute molecules in water is non-white on the molecular scale, which is in contrast to the conventional theory. In the frequency domain from 2 × 10¹¹ Hz to 10¹³ Hz, the power spectrum of thermal noise for polar solute molecules resembles the spectrum of 1/f noise. The power spectrum of thermal noise for non-polar solute molecules deviates only slightly from the spectrum of white noise. The key to this phenomenon is the existence of hydrogen bonds between polar solute molecules and solvent water molecules. Furthermore, for polar solute molecules, the degree of power spectrum deviation from that of white noise is associated with the average lifetime of the hydrogen bonds between the solute and the solvent molecules.

Electron spin dynamics and spin-lattice relaxation of trityl radicals in frozen solutions

Electron spin-lattice relaxation of two trityl radicals, d24-OX063 and Finland trityl, were studied under conditions relevant to their use in dissolution dynamic nuclear polarization (DNP). The dependence of relaxation kinetics on temperature up to 100 K and on concentration up to 60 mM was obtained at X- and W-bands (0.35 and 3.5 Tesla, respectively). The relaxation is quite similar at both bands and for both trityl radicals. At concentrations typical for DNP, relaxation is mediated by excitation transfer and spin-diffusion to fast-relaxing centers identified as triads of trityl radicals that spontaneously form in the frozen samples. These centers relax by an Orbach-Aminov mechanism and determine the relaxation, saturation and electron spin dynamics during DNP.

Spin Dynamics and Establishing of Internal Quasi-Equilibrium in Dilute Paramagnetic Solids

A brief review is given of the development and experimental verification of the two-temperature quasi-equilibrium concept as applied to EPR in dilute paramagnetic solids. Existing experimental data on spectral diffusion in a dipolar broadened EPR line and excitation transfer inside the electron dipolar reservoir are newly considered. The discussion is supplemented with theoretical arguments based on the concentration and cluster expansion techniques. Conditions and limitations of applicability of the two-temperature quasi-equilibrium model to electron spin systems with random distribution of paramagnetic centers are cleared up.

A versatile and modular quasi optics-based 200GHz dual dynamic nuclear polarization and electron paramagnetic resonance instrument

Solid-state dynamic nuclear polarization (DNP) at higher magnetic fields (>3T) and cryogenic temperatures (∼ 2-90K) has gained enormous interest and seen major technological advances as an NMR signal enhancing technique. Still, the current state of the art DNP operation is not at a state at which sample and freezing conditions can be rationally chosen and the DNP performance predicted a priori, but relies on purely empirical approaches. An important step towards rational optimization of DNP conditions is to have access to DNP instrumental capabilities to diagnose DNP performance and elucidate DNP mechanisms. The desired diagnoses include the measurement of the "DNP power curve", i.e. the microwave (MW) power dependence of DNP enhancement, the "DNP spectrum", i.e. the MW frequency dependence of DNP enhancement, the electron paramagnetic resonance (EPR) spectrum, and the saturation and spectral diffusion properties of the EPR spectrum upon prolonged MW irradiation typical of continuous wave (CW) DNP, as well as various electron and nuclear spin relaxation parameters. Even basic measurements of these DNP parameters require versatile instrumentation at high magnetic fields not commercially available to date. In this article, we describe the detailed design of such a DNP instrument, powered by a solid-state MW source that is tunable between 193 and 201 GHz and outputs up to 140 mW of MW power. The quality and pathway of the transmitted and reflected MWs is controlled by a quasi-optics (QO) bridge and a corrugated waveguide, where the latter couples the MW from an open-space QO bridge to the sample located inside the superconducting magnet and vice versa. Crucially, the versatility of the solid-state MW source enables the automated acquisition of frequency swept DNP spectra, DNP power curves, the diagnosis of MW power and transmission, and frequency swept continuous wave (CW) and pulsed EPR experiments. The flexibility of the DNP instrument centered around the QO MW bridge will provide an efficient means to collect DNP data that is crucial for understanding the relationship between experimental and sample conditions, and the DNP performance. The modularity of this instrumental platform is suitable for future upgrades and extensions to include new experimental capabilities to meet contemporary DNP needs, including the simultaneous operation of two or more MW sources, time domain DNP, electron double resonance measurements, pulsed EPR operation, or simply the implementation of higher power MW amplifiers.

Heteronuclear DNP of protons and deuterons with TEMPOL

Dynamic nuclear polarization (DNP) experiments on samples with several types of magnetic nuclei sometimes exhibit “cross-talk” between the nuclei, such as different nuclei having DNP spectra with similar shapes and enhancements.

Evidence of spin-temperature in dynamic nuclear polarization: an exact computation of the EPR spectrum

We show the validity of the spin-temperature approach for typical radical concentration used in dissolution DNP protocols.

Theoretical aspects of Magic Angle Spinning - Dynamic Nuclear Polarization

Magic Angle Spinning (MAS) combined with Dynamic Nuclear Polarization (DNP) has been proven in recent years to be a very powerful method for increasing solid-state NMR signals. Since the advent of biradicals such as TOTAPOL to increase the nuclear polarization new classes of radicals, with larger molecular weight and/or different spin properties have been developed. These have led to unprecedented signal gain, with varying results for different experimental parameters, in particular the microwave irradiation strength, the static field, and the spinning frequency. Recently it has been demonstrated that sample spinning imposes DNP enhancement processes that differ from the active DNP mechanism in static samples as upon sample spinning the DNP enhancements are the results of energy level anticrossings occurring periodically during each rotor cycle. In this work we present experimental results with regards to the MAS frequency dependence of the DNP enhancement profiles of four nitroxide-based radicals at two different sets of temperature, 110 and 160K. In fact, different magnitudes of reduction in enhancement are observed with increasing spinning frequency. Our simulation code for calculating MAS-DNP powder enhancements of small model spin systems has been improved to extend our studies of the influence of the interaction and relaxation parameters on powder enhancements. To achieve a better understanding we simulated the spin dynamics of a single three-spin system {ea-eb-n} during its steady state rotor periods and used the Landau-Zener formula to characterize the influence of the different anti-crossings on the polarizations of the system and their necessary action for reaching steady state conditions together with spin relaxation processes. Based on these model calculations we demonstrate that the maximum steady state nuclear polarization cannot become larger than the maximum polarization difference between the two electrons during the steady state rotor cycle. This study also shows the complexity of the MAS-DNP process and therefore the necessity to rely on numerical simulations for understanding parametric dependencies of the enhancements. Finally an extension of the spin system up to five spins allowed us to probe the first steps of the transfer of polarization from the nuclei coupled to the electrons to further away nuclei, demonstrating a decrease in the spin-diffusion barrier under MAS conditions.

Dynamic Nuclear Polarization and the Paradox of Quantum Thermalization

Dynamic nuclear polarization (DNP) is to date the most effective technique to increase the nuclear polarization opening disruptive perspectives for medical applications. In a DNP setting, the interacting spin system is quasi-isolated and brought out of equilibrium by microwave irradiation. Here we show that the resulting stationary state strongly depends on the ergodicity properties of the spin many-body eigenstates. In particular, the dipolar interactions compete with the disorder induced by local magnetic fields resulting in two distinct dynamical phases: while for weak interaction, only a small enhancement of polarization is observed, for strong interactions the spins collectively equilibrate to an extremely low effective temperature that boosts DNP efficiency. We argue that these two phases are intimately related to the problem of thermalization in closed quantum systems where a many-body localization transition can occur varying the strength of the interactions.

Simultaneous DNP enhancements of (1)H and (13)C nuclei: theory and experiments

DNP on heteronuclear spin systems often results in interesting phenomena such as the polarization enhancement of one nucleus during MW irradiation at the "forbidden" transition frequencies of another nucleus or the polarization transfer between the nuclei without MW irradiation. In this work we discuss the spin dynamics in a four-spin model system of the form {ea-eb-((1)H,(13)C)}, with the Larmor frequencies ωa, ωb, ωH and ωC, by performing Liouville space simulations. This spin system exhibits the common (1)H solid effect (SE), (13)C cross effect (CE) and in addition high order CE-DNP enhancements. Here we show, in particular, the "proton shifted (13)C-CE" mechanism that results in (13)C polarization when the model system, at one of its (13)C-CE conditions, is excited by a MW field at the zero quantum or double quantum electron-proton transitions ωMW = ωa ± ωH and ωMW = ωb ± ωH. Furthermore, we introduce the "heteronuclear" CE mechanism that becomes efficient when the system is at one of its combined CE conditions |ωa - ωb| = |ωH ± ωC|. At these conditions, simulations of the four-spin system show polarization transfer processes between the nuclei, during and without MW irradiation, resembling the polarization exchange effects often discussed in the literature. To link the "microscopic" four-spin simulations to the experimental results we use DNP lineshape simulations based on "macroscopic" rate equations describing the electron and nuclear polarization dynamics in large spin systems. This approach is applied based on electron-electron double resonance (ELDOR) measurements that show strong (1)H-SE features outside the EPR frequency range. Simulated ELDOR spectra combined with the indirect (13)C-CE (iCE) mechanism, result in additional "proton shifted (13)C-CE" features that are similar to the experimental ones. These features are also observed experimentally in (13)C-DNP spectra of a sample containing 15 mM of trityl in a glass forming solution of (13)C-glycerol/H2O and are analyzed by calculating the basic (13)C-SE and (13)C-iCE shapes using simulated ELDOR spectra that were fitted to the experimental ones.

Effects of the electron polarization on dynamic nuclear polarization in solids

The effect of the electron polarization distribution on the DNP line-shapes: theory and a demonstration on a 40 mM TEMPOL sample.

Direct dynamic nuclear polarization targeting catalytically active 27Al sites

This is the first study demonstrating the viability of targeted ²⁷Al DNP characterization by varying the functional side groups of mono-radical spin probes.

The effect of Gd on trityl-based dynamic nuclear polarisation in solids

The increase in ¹³C polarisation of ¹³C-urea dissolved in samples containing water/DMSO mixtures and trityl radical (OX063) in the presence of Gd³⁺ is explained by changes in electron relaxation, electron spectral diffusion and effective electron–proton hyperfine interaction.