Electron-driven spin diffusion supports crossing the diffusion barrier in MAS DNP

Modelling and correcting the impact of RF pulses for continuous monitoring of hyperpolarized NMR

Monitoring the build-up or decay of hyperpolarization in nuclear magnetic resonance requires radio-frequency (RF) pulses to generate observable nuclear magnetization. However, the pulses also lead to a depletion of the polarization and, thus, alter the spin dynamics. To simulate the effects of RF pulses on the polarization build-up and decay, we propose a first-order rate-equation model describing the dynamics of the hyperpolarization process through a single source and a relaxation term. The model offers a direct interpretation of the measured steady-state polarization and build-up time constant. Furthermore, the rate-equation model is used to study three different methods to correct the errors introduced by RF pulses: (i) a 1 / cos⁡ n - 1 θ correction (θ denoting the RF pulse flip angle), which is only applicable to decays; (ii) an analytical model introduced previously in the literature; and (iii) an iterative correction approach proposed here. The three correction methods are compared using simulated data for a range of RF flip angles and RF repetition times. The correction methods are also tested on experimental data obtained with dynamic nuclear polarization (DNP) using 4-oxo-TEMPO in 1 H glassy matrices. It is demonstrated that the analytical and iterative corrections allow us to obtain accurate build-up times and steady-state polarizations (enhancements) for RF flip angles of up to 25∘ during the polarization build-up process within ± 10  % error when compared to data acquired with small RF flip angles (< 3 ∘ ). For polarization decay experiments, corrections are shown to be accurate for RF flip angles of up to 12∘ . In conclusion, the proposed iterative correction allows us to compensate for the impact of RF pulses offering an accurate estimation of polarization levels, build-up and decay time constants in hyperpolarization experiments.

Nuclear spin diffusion in the central spin system of a GaAs/AlGaAs quantum dot

The spin diffusion concept provides a classical description of a purely quantum-mechanical evolution in inhomogeneously polarized many-body systems such as nuclear spin lattices. The central spin of a localized electron alters nuclear spin diffusion in a way that is still poorly understood. Here, spin diffusion in a single GaAs/AlGaAs quantum dot is witnessed in the most direct manner from oscillatory spin relaxation dynamics. Electron spin is found to accelerate nuclear spin relaxation, from which we conclude that the long-discussed concept of a Knight-field-gradient diffusion barrier does not apply to GaAs epitaxial quantum dots. Our experiments distinguish between non-diffusion relaxation and spin diffusion, allowing us to conclude that diffusion is accelerated by the central electron spin. Such acceleration is observed up to unexpectedly high magnetic fields - we propose electron spin-flip fluctuations as an explanation. Diffusion-limited nuclear spin lifetimes range between 1 and 10 s, which is sufficiently long for quantum information storage and processing.

Triangulating Dopant-Level Mn(II) Insertion in a Cs2NaBiCl6 Double Perovskite Using Magnetic Resonance Spectroscopy

Lead-free metal halide double perovskites are gaining increasing attention for optoelectronic applications. Specifically, doping metal halide double perovskites using transition metals enables broadband tailorability of the optical bandgap for these emerging semiconducting materials. One candidate material is Mn(II)-doped Cs₂NaBiCl₆, but the nature of Mn(II) insertion on chemical structure is poorly understood due to low Mn loading. It is critical to determine the atomic-level structure at the site of Mn(II) incorporation in doped perovskites to better understand the structure-property relationships in these materials and thus to advance their applicability to optoelectronic applications. Magnetic resonance spectroscopy is uniquely qualified to address this, and thus a comprehensive three-pronged strategy, involving solid-state nuclear magnetic resonance (NMR), high-field dynamic nuclear polarization (DNP), and electron paramagnetic resonance (EPR) spectroscopies, is used to identify the location of Mn(II) insertion in Cs₂NaBiCl₆. Multinuclear (²³Na, ³⁵Cl, ¹³³Cs, and ²⁰⁹Bi) one-dimensional (1D) magnetic resonance spectra reveal a low level of Mn(II) incorporation, with select spins affected by paramagnetic relaxation enhancement (PRE) induced by Mn(II) neighbors. EPR measurements confirm the oxidation state, octahedral symmetry, and low doping levels of the Mn(II) centers. Complementary EPR and NMR measurements confirm that the cubic structure is maintained with Mn(II) incorporation at room temperature, but the structure deviates slightly from cubic symmetry at low temperatures (<30 K). HYperfine Sublevel CORrelation (HYSCORE) EPR spectroscopy explores the electron-nuclear correlations of Mn(II) with ²³Na, ¹³³Cs, and ³⁵Cl. The absence of ²⁰⁹Bi correlations suggests that Bi centers are replaced by Mn(II). Endogenous DNP NMR measurements from Mn(II) → ¹³³Cs (<30 K) reveal that the solid effect is the dominant mechanism for DNP transfer and supports that Mn(II) is homogeneously distributed within the double-perovskite structure.

Electron-decoupled MAS DNP with N@C60

Frequency-chirped microwaves decouple electron- and 13C-spins in magic-angle spinning N@C60:C60 powder, improving DNP-enhanced 13C NMR signal intensity by 12% for 7 s polarization, and 5% for 30 s polarization. This electron decoupling demonstration is a step toward utilizing N@C60 as a controllable electron-spin source for magic-angle spinning magnetic resonance experiments.

Hybrid quantum-classical simulations of magic angle spinning dynamic nuclear polarization in very large spin systems

Solid-state nuclear magnetic resonance can be enhanced using unpaired electron spins with a method known as dynamic nuclear polarization (DNP). Fundamentally, DNP involves ensembles of thousands of spins, a scale that is difficult to match computationally. This scale prevents us from gaining a complete understanding of the spin dynamics and applying simulations to design sample formulations. We recently developed an ab initio model capable of calculating DNP enhancements in systems of up to ∼1000 nuclei; however, this scale is insufficient to accurately simulate the dependence of DNP enhancements on radical concentration or magic angle spinning (MAS) frequency. We build on this work by using ab initio simulations to train a hybrid model that makes use of a rate matrix to treat nuclear spin diffusion. We show that this model can reproduce the MAS rate and concentration dependence of DNP enhancements and build-up time constants. We then apply it to predict the DNP enhancements in core–shell metal-organic-framework nanoparticles and reveal new insights into the composition of the particles’ shells.

Racing toward Fast and Effective 17O Isotopic Labeling and Nuclear Magnetic Resonance Spectroscopy of N-Formyl-MLF-OH and Associated Building Blocks

Solid-state ¹H, ¹³C, and ¹⁵N nuclear magnetic resonance (NMR) spectroscopy has been an essential analytical method in studying complex molecules and biomolecules for decades. While oxygen-17 (¹⁷O) NMR is an ideal and robust candidate to study hydrogen bonding within secondary and tertiary protein structures for example, it continues to elude many. We discuss an improved multiple-turnover labeling procedure to develop a fast and cost-effective method to ¹⁷O label fluoroenylmethyloxycarbonyl (Fmoc)-protected amino acid building blocks. This approach allows for inexpensive ($0.25 USD/mg) insertion of ¹⁷O labels, an important barrier to overcome for future biomolecular studies. The ¹⁷O NMR results of these building blocks and a site-specific strategy for labeled N-acetyl-MLF-OH and N-formyl-MLF-OH tripeptides are presented. We showcase growth in NMR development for maximizing sensitivity gains using emerging sensitivity enhancement techniques including population transfer, high-field dynamic nuclear polarization, and cross-polarization magic-angle spinning cryoprobes.

Direct observation of hyperpolarization breaking through the spin diffusion barrier

Dynamic nuclear polarization (DNP) is a widely used tool for overcoming the low intrinsic sensitivity of nuclear magnetic resonance spectroscopy and imaging. Its practical applicability is typically bounded, however, by the so-called "spin diffusion barrier," which relates to the poor efficiency of polarization transfer from highly polarized nuclei close to paramagnetic centers to bulk nuclei. A quantitative assessment of this barrier has been hindered so far by the lack of general methods for studying nuclear polarization flow in the vicinity of paramagnetic centers. Here, we fill this gap and introduce a general set of experiments based on microwave gating that are readily implemented. We demonstrate the versatility of our approach in experiments conducted between 1.2 and 4.2 K in static mode and at 100 K under magic angle spinning (MAS)-conditions typical for dissolution DNP and MAS-DNP-and directly observe the marked dependence of polarization flow on temperature.

Scaling analyses for hyperpolarization transfer across a spin-diffusion barrier and into bulk solid media

By analogy to heat and mass transfer film theory, a general approach is introduced for determining hyperpolarization transfer rates between dilute electron spins and a surrounding nuclear ensemble. These analyses provide new quantitative relationships for understanding, predicting, and optimizing the effectiveness of hyperpolarization protocols, such as Dynamic Nuclear Polarization (DNP) under magic-angle spinning conditions. An empirical DNP polarization-transfer coefficient is measured as a function of the bulk matrix 1H spin density and indicates the presence of two distinct kinetic regimes associated with different rate-limiting polarization transfer phenomena. Dimensional property relationships are derived and used to evaluate the competitive rates of spin polarization generation, propagation, and dissipation that govern hyperpolarization transfer between large coupled spin ensembles. The quantitative analyses agree closely with experimental measurements for the accumulation, propagation, and dissipation of hyperpolarization in solids and provide evidence for kinetically-limited transfer associated with a spin-diffusion barrier. The results and classical approach yield general design criteria for analyzing and optimizing polarization transfer processes involving complex interfaces and composite media for applications in materials science, physical chemistry and nuclear spintronics.

Solvent-free dynamic nuclear polarization enhancements in organically modified mesoporous silica

High-field dynamic nuclear polarization is a powerful tool for the structural characterization of species on the surface of porous materials or nanoparticles. For these studies the main source of polarization are radical-containing solutions which are added by post-synthesis impregnation of the sample. Although this strategy is very efficient for a wide variety of materials, the presence of the solvent may influence the chemistry of functional species of interest. Here we address the development of a comprehensive strategy for solvent-free DNP enhanced NMR characterization of functional (target) species on the surface of mesoporous silica (SBA-15). The strategy includes the partial functionalization of the silica surface with Carboxy-Proxyl nitroxide radicals and target Fmoc-Glycine functional groups. As a proof of principle, we have observed for the first time DNP signal enhancements, using the solvent-free approach, for 13C{1H} CPMAS signals corresponding to organic functionalities on the silica surface. DNP enhancements of up to 3.4 were observed for 13C{1H} CPMAS, corresponding to an experimental time save of about 12 times. This observation opens the possibility for the DNP-NMR study of surface functional groups without the need of a solvent, allowing, for example, the characterization of catalytic reactions occurring on the surface of mesoporous systems of interest. For 29Si with direct polarization NMR, up to 8-fold DNP enhancements were obtained. This 29Si signal enhancement is considerably higher than the obtained with similar approaches reported in literature. Finally, from DNP enhancement profiles we conclude that cross-effect is probably the dominant polarization transfer mechanism.

Site-specific dynamic nuclear polarization in a Gd(III)-labeled protein

Dynamic nuclear polarization (DNP) of a biomolecule tagged with a polarizing agent has the potential to not only increase NMR sensitivity but also to provide specificity towards the tagging site. Although the general concept has been often discussed, the observation of true site-specific DNP and its dependence on the electron-nuclear distance has been elusive. Here, we demonstrate site-specific DNP in a uniformly isotope-labeled ubiquitin. By recombinant expression of three different ubiquitin point mutants (F4C, A28C, and G75C) post-translationally modified with a Gd3+-chelator tag, localized metal-ion DNP of 13C and 15N is investigated. Effects counteracting the site-specificity of DNP such as nuclear spin-lattice relaxation and proton-driven spin diffusion have been attenuated by perdeuteration of the protein. Particularly for 15N, large DNP enhancement factors on the order of 100 and above as well as localized effects within side-chain resonances differently distributed over the protein are observed. By analyzing the experimental DNP built-up dynamics combined with structural modeling of Gd3+-tags in ubiquitin supported by paramagnetic relaxation enhancement (PRE) in solution, we provide, for the first time, quantitative information on the distance dependence of the initial DNP transfer. We show that the direct 15N DNP transfer rate indeed linearly depends on the square of the hyperfine interaction between the electron and the nucleus following Fermi's golden rule, however, below a certain distance cutoff paramagnetic signal bleaching may dramatically skew the correlation.

Combining fast magic angle spinning dynamic nuclear polarization with indirect detection to further enhance the sensitivity of solid-state NMR spectroscopy

Dynamic nuclear polarization (DNP) and indirect detection are two commonly applied approaches for enhancing the sensitivity of solid-state NMR spectroscopy. However, their use in tandem has not yet been investigated. With the advent of low-temperature fast magic angle spinning (MAS) probes with 1.3-mm diameter rotors capable of MAS at 40 ​kHz it becomes feasible to combine these two techniques. In this study, we performed DNP-enhanced 2D indirectly detected heteronuclear correlation (idHETCOR) experiments on ¹³C, ¹⁵N, ¹¹³Cd and ⁸⁹Y nuclei in functionalized mesoporous silica, CdS nanoparticles, and Y₂O₃ nanoparticles. The sensitivity of the 2D idHETCOR experiments was compared with those of DNP-enhanced directly-detected 1D cross polarization (CP) and 2D HETCOR experiments performed with a standard 3.2-mm rotor. Due to low CP polarization transfer efficiencies and large proton linewidth, the sensitivity gains achieved by indirect detection alone were lower than in conventional (non-DNP) experiments. Nevertheless, despite the smaller sample volume the 2D idHETCOR experiments showed better absolute sensitivities than 2D HETCOR experiments for nuclei with the lowest gyromagnetic ratios. For ⁸⁹Y, 2D idHETCOR provided 8.2 times better sensitivity than the 1 D⁸⁹Y-detected CP experiment performed with a 3.2-mm rotor.

Full-Scale Ab Initio Simulation of Magic-Angle-Spinning Dynamic Nuclear Polarization

Theoretical models aimed at describing magic-angle-spinning (MAS) dynamic nuclear polarization (DNP) NMR have great potential in facilitating the in silico design of DNP polarizing agents and formulations. These models must typically face a trade-off between the accuracy of a strict quantum mechanical description and the need for using realistically large spin systems, for instance, using phenomenological models. Here, we show that the use of aggressive state-space restrictions and an optimization strategy allows full-scale ab initio MAS-DNP simulations of spin systems containing thousands of nuclei. Our simulations are shown to reproduce experimental DNP enhancements quantitatively, including their MAS rate dependence, for both frozen solutions and solid materials. They also reveal the importance of a previously unrecognized structural feature found in some polarizing agents that helps minimize the sensitivity losses imposed by the spin diffusion barrier.

Optimizing nitroxide biradicals for cross-effect MAS-DNP: the role of g-tensors' distance

Nitroxide biradicals are common polarizing agents used to enhance the sensitivity of solid-state NMR experiments via Magic Angle Spinning Dynamic Nuclear Polarization (MAS-DNP). These biradicals are used to increase the polarization of protons through the cross-effect mechanism, which requires two unpaired electrons with a Larmor frequency difference greater than that of the protons. From their early conception, the relative orientation of the nitroxide rings has been identified as a critical factor determining their MAS-DNP performance. However, the MAS leads to a complex DNP mechanism with time dependent energy level anti-crossings making it difficult to pinpoint the role of relative g-tensor orientation. In this article, a single parameter called "g-tensors' distance" is introduced to characterize the relative orientation's impact on the MAS-DNP field profiles. It is demonstrated for the first time how the g-tensors' distance determines the nuclear hyperpolarization and depolarization properties of a given biradical. This provides a new critical parameter that paves the way for more efficient bis-nitroxides for MAS-DNP.

Recent developments in MAS DNP-NMR of materials

Solid-state NMR spectroscopy is a powerful technique for the characterization of the atomic-level structure and dynamics of materials. Nevertheless, the use of this technique is often limited by its lack of sensitivity, which can prevent the observation of surfaces, defects or insensitive isotopes. Dynamic Nuclear Polarization (DNP) has been shown to improve by one to three orders of magnitude the sensitivity of NMR experiments on materials under Magic-Angle Spinning (MAS), at static magnetic field B₀ ≥ 5 T, conditions allowing for the acquisition of high-resolution spectra. The field of DNP-NMR spectroscopy of materials has undergone a rapid development in the last ten years, spurred notably by the availability of commercial DNP-NMR systems. We provide here an in-depth overview of MAS DNP-NMR studies of materials at high B₀ field. After a historical perspective of DNP of materials, we describe the DNP transfers under MAS, the transport of polarization by spin diffusion and the various contributions to the overall sensitivity of DNP-NMR experiments. We discuss the design of tailored polarizing agents and the sample preparation in the case of materials. We present the DNP-NMR hardware and the influence of key experimental parameters, such as microwave power, magnetic field, temperature and MAS frequency. We give an overview of the isotopes that have been detected by this technique, and the NMR methods that have been combined with DNP. Finally, we show how MAS DNP-NMR has been applied to gain new insights into the structure of organic, hybrid and inorganic materials with applications in fields, such as health, energy, catalysis, optoelectronics etc.

Endogenous dynamic nuclear polarization NMR of hydride-terminated silicon nanoparticles

Silicon nanoparticles (SiNPs) are intriguing materials and their properties fascinate the broader scientific community; they are also attractive to the biological and materials science sub-disciplines because of their established biological and environmental compatibility, as well as their far-reaching practical applications. While characterization of the particle nanostructure can be performed using ²⁹Si solid-state nuclear magnetic resonance (NMR) spectroscopy, poor sensitivity due to low Boltzmann population and long acquisition times hinder in-depth studies of these potentially game-changing materials. In this study, we compare two dynamic nuclear polarization (DNP) NMR protocols to boost ²⁹Si sensitivity in hydride-terminated SiNPs. First, we assess a traditional indirect DNP approach, where a nitroxide biradical (AMUPol or bCTbk) is incorporated into a glassing agent and transferred through protons (e^- → ¹H → ²⁹Si) to enhance the silicon. In this mode, electron paramagnetic resonance (EPR) spectroscopy demonstrated that the hydride-terminated surface was highly reactive with the exogenous biradicals, thus decomposing the radicals within hours and resulting in an enhancement factor, ε, of 3 (T_B = 15 s) for the 64 nm SiNP, revealing the surface components. Secondly, direct DNP NMR methods were used to enhance the silicon without the addition of an exogenous radical (i.e., use of dangling bonds as an endogenous radical source). With radical concentrations <1 mM, ²⁹Si enhancements were obtained for the series of SiNPs ranging from 3 to 64 nm. The ability to use direct ²⁹Si DNP transfer (e^- → ²⁹Si) shows promise for DNP studies of these inorganic nanomaterials (ε = 6 (T_B = 79 min) for 64 nm SiNPs) with highly reactive surfaces, showing the sub-surface and core features. These preliminary findings lay a foundation for future endogenous radical development through tailoring the surface chemistry, targeting further sensitivity gains.