Macroscopic nuclear spin diffusion constants of rotating polycrystalline solids from first-principles simulation

Non-commutative perturbation theory for spin dynamics explains the factorization properties of RIDME background

The intermolecular hyperfine relaxation-induced dipolar modulation enhancement (ih-RIDME) experiment has a promising potential to quantitatively characterize the nuclear environment in the 0.8-3 nm range around an electron spin. Such information about the spatial arrangement of nuclei is of great interest for structural biology as well as for dynamic nuclear polarization (DNP) methods. In order to develop a reliable and sensitive spectroscopic tool, a solid data model needs to be established. Here, we attempt to provide a theoretical explanation for the experimentally observed properties of the ih-RIDME signal. Our main approach uses a perturbation expansion of the Baker-Campbell-Hausdorff formula during the transverse evolution of the electron spin, treating the nuclear dipolar Hamiltonian as a perturbation. We show that a product structure of the ih-RIDME signal follows directly from the statistical independence of the perturbation terms and the multinuclear hyperfine coupling, and that this signal composition is expected when the mixing time exceeds the 95% decay of the Hahn echo.

Magic Angle Spinning Solid-State 13C Photochemically Induced Dynamic Nuclear Polarization by a Synthetic Donor-Chromophore-Acceptor System at 9.4 T

Solid-state photochemically induced dynamic nuclear polarization (photo-CIDNP) is a nuclear magnetic resonance spectroscopy technique in which nuclear spin hyperpolarization is generated upon optical irradiation of an appropriate donor-acceptor system. Until now, solid-state photo-CIDNP at high magnetic fields has been observed only in photosynthetic reaction centers and flavoproteins. In the present work, we show that the effect is not limited to such biomolecular samples, and solid-state 13C photo-CIDNP can be observed at 9.4 T under magic angle spinning using a frozen solution of a synthetic molecular system dissolved in an organic solvent. Signal enhancements for the source molecule larger than a factor of 2300 are obtained. In addition, we show that bulk 13C hyperpolarization of the solvent can be generated via spontaneous 13C-13C spin diffusion at natural abundance.

Optimal sensitivity for 1H detected relayed DNP of organic solids at fast MAS

Dynamic nuclear polarization (DNP) combined with high magnetic fields and fast magic angle spinning (MAS) has opened up a new avenue for the application of exceptionally sensitive 1H NMR detection schemes to study protonated solids. Recently, it has been shown that DNP experiments at fast MAS rates lead to slower spin diffusion and hence reduced DNP enhancements for impregnated materials. However, DNP enhancements alone do not determine the overall sensitivity of a NMR experiment. Here we measure the overall sensitivity of one-dimensional 1H detected relayed DNP experiments as a function of the MAS rate in the 20-60 kHz regime using 0.7 mm diameter rotors at 21.2 T. Although faster MAS rates are detrimental for the DNP enhancement on the target material, due to slower spin diffusion, we find that with increasing spinning rates the gain in sensitivity due to 1H line-narrowing and the folding-in of sideband intensity compensates a large part of the loss of overall hyperpolarization. We find that sensitivity depends on the atomic site in the molecule, and is maximised at between 40 and 50 kHz MAS for the sample of L-histidine.HCl·H2O studied here. There is a 10-20 % difference in sensitivity between the optimum MAS rate and the fastest rate currently accessible (60 kHz).

1H Detected Relayed Dynamic Nuclear Polarization

Recently, it has been shown that methods based on the dynamics of ¹H nuclear hyperpolarization in magic angle spinning (MAS) NMR experiments can be used to determine mesoscale structures in complex materials. However, these methods suffer from low sensitivity, especially since they have so far only been feasible with indirect detection of ¹H polarization through dilute heteronuclei such as ¹³C or ²⁹Si. Here we combine relayed-DNP (R-DNP) with fast MAS using 0.7 mm diameter rotors at 21.2 T. Fast MAS enables direct ¹H detection to follow hyperpolarization dynamics, leading to an acceleration in experiment times by a factor 16. Furthermore, we show that by varying the MAS rate, and consequently modulating the ¹H spin diffusion rate, we can record a series of independent R-DNP curves that can be analyzed jointly to provide an accurate determination of domain sizes. This is confirmed here with measurements on microcrystalline l-histidine·HCl·H₂O at MAS frequencies up to 60 kHz, where we determine a Weibull distribution of particle sizes centered on a radius of 440 ± 20 nm with an order parameter of k = 2.2.

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.

Hyperpolarization transfer pathways in inorganic materials

Dynamic nuclear polarization can be used to hyperpolarize the bulk of proton-free inorganic materials in magic angle spinning NMR experiments. The hyperpolarization is generated on the surface of the material with incipient wetness impregnation and from there it is propagated towards the bulk through homonuclear spin diffusion between weakly magnetic nuclei. This method can provide significant gains in sensitivity for MAS NMR spectra of bulk inorganic compounds, but the pathways of the magnetization transfer into the material have not previously been elucidated. Here we show how two-dimensional experiments can be used to study spin diffusion from the surface of a material towards the bulk. We find that hyperpolarization can be efficiently relayed from surface sites to multiple bulk sites simultaneously, and that the bulk sites also engage in rapid polarization exchange between themselves. We also show evidence that the surface peaks can exchange polarization between different sites in cases of disorder.

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.

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.

Measurement of Proton Spin Diffusivity in Hydrated Cementitious Solids

The study of hydration and crystallization processes involving inorganic oxides is often complicated by poor long-range order and the formation of heterogeneous domains or surface layers. In solid-state NMR, ¹H-¹H spin diffusion analyses can provide information on spatial composition distributions, domain sizes, or miscibility in both ordered and disordered solids. Such analyses have been implemented in organic solids but crucially rely on separate measurements of the ¹H spin diffusion coefficients in closely related systems. We demonstrate that an experimental NMR method, in which "holes" of well-defined dimensions are created in proton magnetization, can be applied to determine spin diffusion coefficients in cementitious solids hydrated with ¹⁷O-enriched water. We determine proton spin diffusion coefficients of 240 ± 40 nm²/s for hydrated tricalcium aluminate and 140 ± 20 nm²/s for hydrated tricalcium silicate under quasistatic conditions.

Linear-scaling ab initio simulations of spin diffusion in rotating solids

We investigated the utility of locally restricting the basis sets involved in low-order correlations in Liouville space (LCL) calculations of spin diffusion. Using well-known classical models of spin diffusion, we describe a rationale for selecting the optimal basis set for such calculations. We then show that the use of these locally restricted basis sets provides the same computational accuracy as the full LCL set while reducing the computational time by several orders of magnitude. Speeding up the calculations also enables us to use higher maximum spin orders and increase the computational accuracy. Furthermore, unlike exact and full LCL calculations, locally restricted LCL calculations scale linearly with the system size and should thus enable the ab initio study of spin diffusion in spin systems containing several thousand spins.

Maximizing nuclear hyperpolarization in pulse cooling under MAS

It has recently been shown how dynamic nuclear polarization can be used to hyperpolarize the bulk of proton-free solids. This is achieved by generating the polarization in a wetting phase, transferring it to nuclei near the surface and relaying it towards the bulk through homonuclear spin diffusion between weakly magnetic nuclei. Pulse cooling is a strategy to achieve this that uses a multiple contact cross-polarization sequence for bulk hyperpolarization. Here, we show how to maximize sensitivity using the pulse cooling method by experimentally optimizing pulse parameters and delays on a sample of powdered SnO₂. To maximize sensitivity we introduce an approach where the magic angle spinning rate is modulated during the experiment: the CP contacts are carried out at a slow spin rate to benefit from faster spin diffusion, and the spin rate is then accelerated before detection to improve line narrowing. This method can improve the sensitivity of pulse cooling for ¹¹⁹Sn spectra of SnO₂ by an additional factor of 3.5.

Large-scale ab initio simulations of MAS DNP enhancements using a Monte Carlo optimization strategy

Magic-angle-spinning (MAS) dynamic nuclear polarization (DNP) has recently emerged as a powerful technology enabling otherwise unrealistic solid-state NMR experiments. The simulation of DNP processes which might, for example, aid in refining the experimental conditions or the design of better performing polarizing agents, is, however, plagued with significant challenges, often limiting the system size to only 3 spins. Here, we present the first approach to fully ab initio large-scale simulations of MAS DNP enhancements. The Landau-Zener equation is used to treat all interactions concerning electron spins, and the low-order correlations in the Liouville space method is used to accurately treat the spin diffusion, as well as its MAS speed dependence. As the propagator cannot be stored, a Monte Carlo optimization method is used to determine the steady-state enhancement factors. This new software is employed to investigate the MAS speed dependence of the enhancement factors in large spin systems where spin diffusion is of importance, as well as to investigate the impacts of solvent and polarizing agent deuteration on the performance of MAS DNP.

Efficient cross-effect dynamic nuclear polarization without depolarization in high-resolution MAS NMR

Dynamic nuclear polarization (DNP) has the potential to enhance the sensitivity of magic-angle spinning (MAS) NMR by many orders of magnitude and therefore to revolutionize atomic resolution structural analysis. Currently, the most widely used approach to DNP for studies of chemical, material, and biological systems involves the cross-effect (CE) mechanism, which relies on biradicals as polarizing agents. However, at high magnetic fields (≥5 T), the best biradicals used for CE MAS-DNP are still far from optimal, primarily because of the nuclear depolarization effects they induce. In the presence of bisnitroxide biradicals, magic-angle rotation results in a reverse CE that can deplete the initial proton Boltzmann polarization by more than a factor of 2. In this paper we show that these depolarization losses can be avoided by using a polarizing agent composed of a narrow-line trityl radical tethered to a broad-line TEMPO. Consequently, we show that a biocompatible trityl-nitroxide biradical, TEMTriPol-1, provides the highest MAS NMR sensitivity at ≥10 T, and its relative efficiency increases with the magnetic field strength. We use numerical simulations to explain the absence of depolarization for TEMTriPol-1 and its high efficiency, paving the way for the next generation of polarizing agents for DNP. We demonstrate the superior sensitivity enhancement using TEMTriPol-1 by recording the first solid-state 2D 13C-13C correlation spectrum at natural isotopic abundance at a magnetic field of 18.8 T.

1 H-19 F REDOR-filtered NMR spin diffusion measurements of domain size in heterogeneous polymers

Solid state NMR spectroscopy is inherently sensitive to chemical structure and composition and thus makes an ideal method to probe the heterogeneity of multicomponent polymers. Specifically, NMR spin diffusion experiments can be used to extract reliable information about spatial domain sizes on multiple length scales, provided that magnetization selection of one domain can be achieved. In this paper, we demonstrate the preferential filtering of protons in fluorinated domains during NMR spin diffusion experiments using ¹ H-¹⁹ F heteronuclear dipolar dephasing based on rotational echo double resonance (REDOR) MAS NMR techniques. Three pulse sequence variations are demonstrated based on the different nuclei detected: direct ¹ H detection, plus both ¹ H➔¹³ C cross polarization and ¹ H➔¹⁹ F cross polarization detection schemes. This ¹ H-¹⁹ F REDOR-filtered spin diffusion method was used to measure fluorinated domain sizes for a complex polymer blend. The efficacy of the REDOR-based spin filter does not rely on spin relaxation behavior or chemical shift differences and thus is applicable for performing NMR spin diffusion experiments in samples where traditional magnetization filters may prove unsuccessful. This REDOR-filtered NMR spin diffusion method can also be extended to other samples where a heteronuclear spin pair exists that is unique to the domain of interest.

Basic principles of static proton low-resolution spin diffusion NMR in nanophase-separated materials with mobility contrast

We review basic principles of low-resolution proton NMR spin diffusion experiments, relying on mobility differences in nm-sized phases of inhomogeneous organic materials such as block-co- or semicrystalline polymers. They are of use for estimates of domain sizes and insights into nanometric dynamic inhomogeneities. Experimental procedures and limitations of mobility-based signal decomposition/filtering prior to spin diffusion are addressed on the example of as yet unpublished data on semicrystalline poly(ϵ-caprolactone), PCL. Specifically, we discuss technical aspects of the quantitative, dead-time free detection of rigid-domain signals by aid of the magic-sandwich echo (MSE), and magic-and-polarization-echo (MAPE) and double-quantum (DQ) magnetization filters to select rigid and mobile components, respectively. Such filters are of general use in reliable fitting approaches for phase composition determinations. Spin diffusion studies at low field using benchtop instruments are challenged by rather short (1)H T1 relaxation times, which calls for simulation-based analyses. Applying these, in combination with domain sizes as determined by small-angle X-ray scattering, we have determined spin diffusion coefficients D for PCL (0.34, 0.19 and 0.032nm(2)/ms for crystalline, interphase and amorphous parts, respectively). We further address thermal-history effects related to secondary crystallization. Finally, the state of knowledge concerning the connection between D values determined locally at the atomic level, using (13)C detection and CP- or REDOR-based "(1)H hole burning" procedures, and those obtained by calibration experiments, is summarized. Specifically, the non-trivial dependence of D on the magic-angle spinning (MAS) frequency, with a minimum under static and a local maximum under moderate-MAS conditions, is highlighted.

Moderate MAS enhances local (1)H spin exchange and spin diffusion

Proton NMR spin-diffusion experiments are often combined with magic-angle spinning (MAS) to achieve higher spectral resolution of solid samples. Here we show that local proton spin diffusion can indeed become faster at low (<10 kHz) spinning rates as compared to static conditions. Spin diffusion under static conditions can thus be slower than the often referred value of 0.8 nm(2)/ms, which was determined using slow MAS (Clauss et al., 1993). The enhancement of spin diffusion by slow MAS relies on the modulation of the orientation-dependent dipolar couplings during sample rotation and goes along with transient level crossings in combination with dipolar truncation. The experimental finding and its explanation is supported by density matrix simulations, and also emphasizes the sensitivity of spin diffusion to the local coupling topology. The amplification of spin diffusion by slow MAS cannot be explained by any model based on independent spin pairs; at least three spins have to be considered.