Spin Diffusion Rate Research Articles

Maximizing Relayed 1H Hyperpolarization Transfer by Slow-Fast MAS NMR Spectroscopy.

1H-detected dynamic nuclear polarization (DNP)-enhanced fast magic angle spinning (MAS) NMR experiments provide unprecedented sensitivity to study the structure and dynamics in advanced materials and biomolecules. However, in relayed DNP experiments, DNP enhancements decrease with faster MAS rates, which is detrimental for sensitivity. The decrease is because 1H-1H spin diffusion rates are significantly reduced at fast MAS frequencies. To improve sensitivity at these fast MAS rates, here, we propose to combine fast polarization build-up by relay at slow MAS rate with high-resolution 1H NMR at fast MAS for acquisition. We perform experiments on l-histidine·HCl·H2O with MAS rates of up to 65 kHz using a 0.7 mm DNP probe at 18.8 T and 100 K. We obtain a 35% improvement in sensitivity in experiments where the sample is polarized at 20 kHz MAS and where the signal is acquired at 60 kHz MAS.

Low perturbation limit decoherence analyzed by scaling the Double Quantum Hamiltonian

By varying the magnitude of the effective interaction between spins in relation to the perturbations, we study the decoherence behavior in a connected proton system. Making use of the Magnus expansion, we introduce a NMR pulse sequence that generates an average Hamiltonian with Double Quantum terms multiplied by a scaling factor, δ, with the possibility to take positive and negative values. The performance of the pulse sequence for different values of the scaling factors was validated in polycrystalline adamantane, by observing the evolution of the polarization. A time reversal procedure, accessible through the change of sign in the controlled Hamiltonian, was necessary to observe multiple quantum coherences. The spin counting develops a characteristic growth in two species of clusters for the scaled time. The influence of the scaling factor on the reversibility was observed through the behavior of the Loschmidt echoes, which decayed faster as the scaling factor increases. From the analysis of dynamics and its reversibility, we extracted characteristic times for the spin diffusion, T2δ and the intrinsic decoherence decay, T3δ for each scaling factor δ, and perturbation time scale, TΣ. Observing the dependence of reversibility vs. perturbation rates, both normalized with the spin diffusion rate, we find that in the limit of low perturbations, T2δ/T3δ deviates from the linear dependence on T2δ/TΣ that corresponds to strong perturbation. The asymptotic value T2/T3≈0.15 as T2δ/TΣ vanishes, gives evidence that the main source of irreversibility is the intrinsic decoherence associated to the chaotic many-body dynamics of the system.

Spin dynamics, entanglement, and the nature of the spin liquid state in YbZnGaO4

Electron spin dynamics was studied down to 80 mK in the triangular-lattice quantum spin-liquid candidate ${\mathrm{YbZnGaO}}_{4}$ using muon spin relaxation, finding no evidence for freezing or ordering of the Yb spins. The muon spin relaxation rate can be represented by the sum of two contributions, one dependent on longitudinal magnetic field and the other independent of field. The field-dependent term follows the form expected for two-dimensional diffusion of mobile spin excitations. The spin-diffusion rate obtained for these excitations in the high temperature paramagnetic regime is comparable with the exchange coupling frequency $J/h$, reducing significantly in the low temperature quantum regime. This slowdown is assigned to the effect of quantum entanglement. The exchange coupling $J$ is estimated to be 2.0(2) K from the crossover between the two regimes. The field-independent term is only weakly dependent on temperature, and at 15 K its absolute value is consistent with dipolar coupling of the muon to the three Yb moments closest to the muon site, where the spin dynamics of these moments is determined by exchange fluctuations. The temperature-dependent properties in the quantum regime are compared against the three possible U(1) spin-liquid models that have been obtained for the strongly spin-orbit coupled triangular lattice by Y.-D. Li, Y.-M. Lu, and G. Chen [Phys. Rev. B 96, 054445 (2017)]. The comparison with theory takes published specific heat and thermal conductivity data into account, along with the spin-diffusion rate obtained from the muons. It is found that the nodal spin-liquid model U1A11 containing both linear and quadratic nodes provides better agreement with experiment than either the U1A00 spinon Fermi surface (FS) model or the U1A01 model that contains only linear nodes.

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.

Solid-State NMR and Impedance Spectroscopy Study of Spin Dynamics in Proton-Conducting Polymers: An Application of Anisotropic Relaxing Model.

The 1H–13C cross-polarization (CP) kinetics in poly[2-(methacryloyloxy)ethyltrimethylammonium chloride] (PMETAC) was studied under moderate (10 kHz) magic-angle spinning (MAS). To elucidate the role of adsorbed water in spin diffusion and proton conductivity, PMETAC was degassed under vacuum. The CP MAS results were processed by applying the anisotropic Naito and McDowell spin dynamics model, which includes the complete scheme of the rotating frame spin–lattice relaxation pathways. Some earlier studied proton-conducting and nonconducting polymers were added to the analysis in order to prove the capability of the used approach and to get more general conclusions. The spin-diffusion rate constant, which describes the damping of the coherences, was found to be strongly depending on the dipolar I–S coupling constant (DIS). The spin diffusion, associated with the incoherent thermal equilibration with the bath, was found to be most probably independent of DIS. It was deduced that the drying scarcely influences the spin-diffusion rates; however, it significantly (1 order of magnitude) reduces the rotating frame spin–lattice relaxation times. The drying causes the polymer hardening that reflects the changes of the local order parameters. The impedance spectroscopy was applied to study proton conductivity. The activation energies for dielectric relaxation and proton conductivity were determined, and the vehicle-type conductivity mechanism was accepted. The spin-diffusion processes occur on the microsecond scale and are one order faster than the dielectric relaxation. The possibility to determine the proton location in the H-bonded structures in powders using CP MAS technique is discussed.

Secular and semi-nonsecular models of cross-polarization kinetics for remote spins: an application for nano-structured calcium hydroxyapatite

The 1H → 31P cross-polarization (CP) kinetics in the nanostructured calcium hydroxyapatite (nano-CaHA) was measured under moderate (5 kHz) magic-angle spinning (MAS) rate. This material was chosen as it contains the distanced 1H–31P spin pairs and the interactions between them are characterized by a relatively low dipolar coupling (b) that could be comparable with the spin-diffusion rates (R). Therefore, the physical legitimacy to use the secular solution of the quantum Liouville–von Neumann equation is doubtful. The semi-nonsecular model of spin dynamics was applied, and the results were compared with those obtained by the secular approach. The comparable results obtained by both models show that the secular model is applicable, with certain reservation, also in the case of |b| ≈ R. The extremely high anisotropy of spin diffusion in the nano-CaHA was deduced. This can be a matter of the applied approach, as the interactions of the 31P spins with the proton bath were neglected in both models. The high anisotropy could also be caused by the physical reasons that stem from the structural and proton diffusion features of CaHA. This material belongs to low-dimensional proton conductors possessing a large motional freedom for protons along OH– chains.

Spin diffusion transfer difference (SDTD) NMR: An advanced method for the characterisation of water structuration within particle networks

HypothesisThe classical STD NMR protocol to monitor solvent interactions in gels is strongly dependent on gelator and solvent concentrations and does not report on the degree of structuration of the solvent at the particle/solvent interface. We hypothesised that, for suspensions of large gelator particles, solvent structuration could be characterised by STD NMR when taking into account the particle-to-solvent 1H–1H spin diffusion transfer using the 1D diffusion equation. ExperimentsWe have carried out a systematic study on effect of gelator and solvent concentrations, and gelator surface charge, affecting the behaviour of the classical STD NMR build-up curves. To do so, we have characterised solvent interactions in dispersions of starch and cellulose-like particles prepared in deuterated water and alcohol/D2O mixtures. FindingsThe Spin Diffusion Transfer Difference (SDTD) NMR protocol is independent of the gelator and solvent concentrations, hence allowing the estimation of the degree of solvent structuration within different particle networks. In addition, the simulation of SDTD build-up curves using the general one–dimensional diffusion equation allows the determination of minimum distances (r) and spin diffusion rates (D) at the particle/solvent interface. This novel NMR protocol can be readily extended to characterise the solvent(s) organisation in any type of colloidal systems constituted by large particles.

Dynamic Nuclear Polarization with Vanadium(IV) Metal Centers

Summary Dynamic nuclear polarization (DNP) harnesses the large polarization of electron spins to dramatically increase nuclear magnetic resonance (NMR) sensitivity. This study expands the scope of DNP beyond its traditional focus on hyperpolarizing the solvent network using exogenous polarizing agents (PAs). We introduce 1H DNP with endogenous V4+ centers positioned in a set of vanadyl complexes with tunable V4+-1H distances. We traced the polarization transfer from V4+ to 1H spins, specifically differentiating between direct V4+-1Hs polarization transfer and the 1H spin-diffusion-mediated bulk solvent 1H polarization buildup and illuminated the effect of the V4+-1H distance on these processes. These results deepen our understanding of polarization pathways and expand the catalog of PAs to broad-line transition metals. This study establishes crucial first steps toward employing strategically positioned endogenous paramagnetic metal centers for DNP and the conceptual framework of hyperfine DNP spectroscopy that merges both spatial and chemical diagnosis of target nuclear spins.

Structural Analyses of Alanine Trimer and Tetramer Crystals with Antiparallel and Parallel β-Sheet Structures Using Solid-State 1H Spin-Diffusion 2D Correlation NMR Spectroscopy.

Poly-l-alanine (PLA) sequences are key elements of the crystalline domains of spider dragline and wild silkworm silks. In the present work, 1H spin-diffusion two-dimensional (2D) correlation NMR spectra were observed for selectively deuterated (Ala)3 and (Ala)4 crystals to develop the analytical method for the structure of PLA sequences. The build-up curves of the cross peaks for three kinds of 1H pairs in selectively deuterated (Ala)3 and (Ala)4 crystals were observed to obtain spin-diffusion rate constant k j, k from relaxation master equations P i, j(τm). The k j, k values subsequently lead to effective interproton distance r j, keff (obs) values for individual proton-proton pairs, which include intra- and intermolecular contributions. The r j, keff (obs) values were compared to r j, keff (calc) values obtained from the experimentally determined atomic coordinates of antiparallel (AP) β-sheet (Ala)3 and (Ala)4 and parallel (P) β-sheet of (Ala)3 and (Ala)4 crystals. The agreement between the r j, keff (obs) and r j, keff (calc) values was good for AP β-sheet (Ala)3 and (Ala)4 crystals but poor for P β-sheet (Ala)3 and (Ala)4 crystals. These deviations were obtained from the interproton distances of the interchain contributions due to different packing arrangements. The packing arrangements of the PLA region are important when considering the relevant structure and the mechanical properties of silks.

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

Dynamic nuclear polarization (DNP) can be applied to enhance the sensitivity of solid-state NMR experiments by several orders of magnitude due to microwave-driven transfer of spin polarization from unpaired electrons to nuclei. While the underlying quantum mechanical aspects are sufficiently well understood on a microscopic level, the exact description of the large-scale spin dynamics, usually involving hundreds to thousands of nuclear spins per electron, is still lacking consensus. Generally, it is assumed that nuclear hyperpolarization can only be observed on nuclei which do not experience strong influence of the unpaired electrons and thus being significantly removed from the paramagnetic polarizing agents. At the same time, sufficiently strong hyperfine interaction is required for DNP transfer. Therefore, efficient nuclear spin diffusion from the strongly-interacting nuclei to the NMR-observable bulk is considered to be essential for efficient nuclear hyperpolarization. Based on experimental results obtained on the endohedral fullerene N@C60 as a polarizing agent sparsely diluted in C60, we discuss the effect of the spin-diffusion barrier. We introduce electron-driven spin diffusion (EDSD) as a novel mechanism for nuclear polarization transfer in the proximity of an electron spin which is particularly relevant under magic-angle spinning (MAS) DNP conditions.

Processing of CP MAS kinetics: Towards NMR crystallography for complex solids

Variable temperature and high data point density measurements of 1H–31P cross-polarization kinetics in the powdered ammonium dihydrogen phosphate (ADP) have been carried out in the range of −40 °C to +90 °C upon 7 and 10 kHz MAS. The advanced route of processing CP MAS kinetic data has been developed. It is based on reducing the incoherent far range order spin couplings and extracting the CP oscillatory term with the sequent mathematical treatment. The proper replica has been found, which allowed to reduce the Fourier-Bessel (Hankel) transform calculating the angularly averaged and purely distance-depending spin distribution profile to the routine Fourier transform. The shortest 31P–1H distances determined by CP MAS kinetics get between the values obtained by neutron and X-ray diffraction, whereas those for more remote protons are slightly larger. The changes in P⋯H distances are hardly noticeable, though a certain trend to increase upon the heating can be deduced. The clearly pronounced effect was the increase of the spin-diffusion rate constant upon heating. It allows to state that the communication between interacting spins is the process extremely easy to activate.

Chain Dynamics, Relaxation Times, and Conductivities of Bithiophene--Acene Copolymers Measured Using High Frequency Saturation Transfer EPR.

We present a study to probe the formation of localized aromatic sextets and their effects on the charge transport properties in polymers with acene cores. Bithiophene-acene copolymers containing benzene, naphthalene, or anthracene as acene cores were synthesized using Yamamoto polymerization. Drop-casted polymer films were chemically doped and analyzed using high frequency saturation transfer EPR (HF ST-EPR), a method which has proven useful in the study of conducting polymers. The spin-spin and spin-lattice relaxation times were determined for these polymers at low temperatures (4 to 20 K) and used to obtain inter- and intrachain spin diffusion rates and conductivities. Similar interchain spin diffusion rates were seen across all polymer systems; however, anthracene containing polymer poly(hexylTTATT) was found to have the largest intrachain spin diffusion rate. The poly(hexylTTATT) intrachain spin diffusion rate may be artificially high if the anthracene ring restricts the diffusion of spin to the hexylated quaterthiophene segment in poly(hexylTTATT) whereas the spins diffuse through the acene cores in the benzene and naphthalene derivatives. Alternatively, as both the spin diffusion rates and conductivities vary unpredictably with temperature, it is possible that the π-electron localization previously seen in the anthracene core could be relieved at lower temperatures.

Analytical descriptions of cross-polarisation dynamics: relaxing the secular approximations

In this work, analytical expressions of the cross-polarisation (CP) dynamics under both static and magic-angle spinning (MAS) conditions are obtained by solving the generalised Liouville-von Neumann quantum mechanical equation beyond the standard approximations, i.e., reintroducing neglected non-secular terms in the system superoperator. Although the simple model of a two-spin system interacting with a spin bath gives a rather crude description of CP dynamics, it accounts well for the orientation dependence of CP in a static sample of ferrocene powder and permits to detect slight departures from the Hartmann–Hahn matching condition. This approach also has the advantage of yielding manageable analytical expressions that can be used even by less inclined or experienced workers to obtain results that are good enough in an operational sense. Moreover, the resulting spin diffusion rate constants containing different sources of anisotropy of the system–environment interaction as well as their dependence on the MAS frequency are related semi-quantitatively to the local network of dipolar interactions. Finally, it is shown that non-secular solutions improve significantly the analysis of CPMAS-based separated-local-field spectroscopy experimental data in the absence of homonuclear decoupling.

Water–Polysaccharide Interactions in the Primary Cell Wall of Arabidopsis thaliana from Polarization Transfer Solid-State NMR

Polysaccharide-rich plant cell walls are hydrated under functional conditions, but the molecular interactions between water and polysaccharides in the wall have not been investigated. In this work, we employ polarization transfer solid-state NMR techniques to study the hydration of primary-wall polysaccharides of the model plant, Arabidopsis thaliana. By transferring water (1)H polarization to polysaccharides through distance- and mobility-dependent (1)H-(1)H dipolar couplings and detecting it through polysaccharide (13)C signals, we obtain information about water proximity to cellulose, hemicellulose, and pectins as well as water mobility. Both intact and partially extracted cell wall samples are studied. Our results show that water-pectin polarization transfer is much faster than water-cellulose polarization transfer in all samples, but the extent of extraction has a profound impact on the water-polysaccharide spin diffusion. Removal of calcium ions and the consequent extraction of homogalacturonan (HG) significantly slowed down spin diffusion, while further extraction of matrix polysaccharides restored the spin diffusion rate. These trends are observed in cell walls with similar water content, thus they reflect inherent differences in the mobility and spatial distribution of water. Combined with quantitative analysis of the polysaccharide contents, our results indicate that calcium ions and HG gelation increase the amount of bound water, which facilitates spin diffusion, while calcium removal disrupts the gel and gives rise to highly dynamic water, which slows down spin diffusion. The recovery of spin diffusion rates after more extensive extraction is attributed to increased water-exposed surface areas of the polysaccharides. Water-pectin spin diffusion precedes water-cellulose spin diffusion, lending support to the single-network model of plant primary walls in which a substantial fraction of the cellulose surface is surrounded by pectins.

Inhomogeneous Spin Diffusion in Traps with Cold Atoms

The spin diffusion and damped oscillations are studied in the collision of two spin polarized clouds of cold atoms with resonant interactions. The strong density dependence of the diffusion coefficient leads to inhomogeneous spin diffusion that changes from central to surface spin flow as the temperature increases. The inhomogeneity and the smaller finite trap size significantly reduce the spin diffusion rate at low temperatures. The resulting spin diffusion rates and spin drag at longer time scales are compatible with measurements at low to high temperatures for resonant attractive interactions but are incompatible with a metastable ferromagnetic phase. This does not exclude that the colliding clouds can evolve into a repulsive initial state which subsequently decays during the bounce and the initial damped oscillations.

The influence of the molecular system on the performance of heteronuclear decoupling in solid-state NMR

The intensity of the carbon signal in a CPMAS experiment has been measured for two CH and three CH 2 moieties in four test molecules under different phase-modulated proton decoupling conditions and as a function of the spinning rate. The proton decoupling schemes investigated were the golden standard TPPM and three of the GTn family. Aim of this analysis was to better describe experimentally the impact and limitations of phase-modulated decoupling. Sizeable differences in the response to decoupling were observed in otherwise chemically identical molecular fragments, such as the CHCH 2 found in tyrosine, phenyl-succinic acid or 9-Anthrylmethyl-malonate, probably due to differences in spin-diffusion rates. In keeping with known facts, the efficiency of the decoupling was observed to decrease with the MAS rate, but with somewhat different trends for the tested systems.

H 2 -decoupling-accelerated H1 spin diffusion in dynamic nuclear polarization with photoexcited triplet electrons

In dynamic nuclear polarization (DNP) experiments applied to organic solids for creating nonequilibrium, high (1)H spin polarization, an efficient buildup of (1)H polarization is attained by partially deuterating the material of interest with an appropriate (1)H concentration. In such a dilute (1)H spin system, it is shown that the (1)H spin diffusion rate and thereby the buildup efficiency of (1)H polarization can further be enhanced by continually applying radiofrequency irradiation for deuterium decoupling during the DNP process. As experimentally confirmed in this work, the electron spin polarization of the photoexcited triplet state is mainly transferred only to those (1)H spins, which are in the vicinity of the electron spins, and (1)H spin diffusion transports the localized (1)H polarization over the whole sample volume. The (1)H spin diffusion coefficients are estimated from DNP repetition interval dependence of the initial buildup rate of (1)H polarization, and the result indicates that the spin diffusion coefficient is enhanced by a factor of 2 compared to that without (2)H decoupling.

Conformational Changes of an Ion Channel Detected Through Water−Protein Interactions Using Solid-State NMR Spectroscopy

The influenza A virus M2 protein is a pH-gated and amantadine-inhibited proton channel important for the virus life cycle. Proton conduction by M2 is known to involve water; however direct experimental evidence of M2-water interaction is scarce. Using (1)H spin diffusion solid-state NMR, we have now determined the water accessibility of the M2 transmembrane domain (M2-TM) in virus-envelope-mimetic lipid membranes and its changes with environment. Site-specific water-protein magnetization transfer indicates that, in the absence of amantadine, the initial spin diffusion rate mainly depends on the radial position of the residues from the pore: pore-lining residues along the helix have similarly high water accessibilities compared to lipid-facing residues. Upon drug binding, the spin diffusion rates become much slower for Gly(34) in the middle of the helix than for the N-terminal residues, indicating that amantadine is bound to the pore lumen between Gly(34) and Val(27). Water-protein spin diffusion buildup curves indicate that spin diffusion is the fastest in the low-pH open state, slower in the high-pH closed state, and the slowest in the high-pH amantadine-bound state. Simulations of the buildup curves using a 3D lattice model yielded quantitative values of the water-accessible surface area and its changes by pH and drug binding. These data provide direct experimental evidence of the pH-induced change of the pore size and the drug-induced dehydration of the pore. This study demonstrates the capability of (1)H spin diffusion NMR for elucidating water interactions with ion channels, water pores, and proton pumps and for probing membrane protein conformational changes that involve significant changes of water-accessible surface areas.

High-Resolution Solid-State NMR Investigation of the Phase Transition in Decamethylferrocene−Acenaphthenequinone Charge-Transfer Complex

A charge-transfer complex composed of decamethylferrocene (D) and acenaphthenequinone (A) was prepared. The material was a 1:1 neutral complex with a mixed-stack structure and exhibited a phase transition at -16 degrees C. High-resolution (13)C and (1)H NMR spectroscopy revealed that an inclination of A with respect to D occurs below the phase-transition temperature. The (1)H spin-diffusion rates of the complex undergoing high-speed magic-angle spinning (MAS) were measured to determine the shortest (1)H-(1)H distance r between D and A. To analyze the experimental results, we derived the analytical expression of the spin-diffusion rate W(z) for a homonuclear multispin system undergoing MAS. It was found that W(z) for the complex is proportional only to 1/r(6) under high-speed MAS conditions. On the basis of this relationship and the crystal structure at 20 degrees C, it was determined that the shortest (1)H-(1)H distance r at -27.7 degrees C (below the phase transition temperature) is 0.4 A shorter than that at 20 degrees C. Given this information, a plausible model of the low-temperature structure is discussed.

Staphylococcus aureus Peptidoglycan Tertiary Structure from Carbon-13 Spin Diffusion

The cell-wall peptidoglycan of Staphylococcus aureus is a heterogeneous, highly cross-linked polymer of unknown tertiary structure. We have partially characterized this structure by measuring spin diffusion from (13)C labels in pentaglycyl cross-linking segments to natural-abundance (13)C in the surrounding intact cell walls. The measurements were performed using a version of centerband-only detection of exchange (CODEX). The cell walls were isolated from S. aureus grown in media containing [1-(13)C]glycine. The CODEX spin diffusion rates established that the pentaglycyl bridge of one peptidoglycan repeat unit of S. aureus is within 5 A of the glycan chain of another repeat unit. This surprising proximity is interpreted in terms of a model for the peptidoglycan lattice in which all peptide stems in a plane perpendicular to the glycan mainchain are parallel to one another.