Multiple-quantum NMR Experiments Research Articles

Dissipative dynamics of multiple-quantum NMR coherences in two-spin systems

Multiple-quantum (MQ) NMR experiments were performed at a special orientation of a hambergite (Be2BO3OH) single crystal, which consists of alternating zigzag proton chains. At the chosen orientation, one of the dipolar coupling constants in the chain becomes zero and the system becomes a set of well-isolated dipolar coupled spin pairs. The relaxation of the spin pairs in the MQ NMR experiment was studied on the basis of the Lindblad equation. Fermi’s golden rule was used to investigate the relaxation mechanism. The agreement of the calculated relaxation time with the experimental value (125 μs) suggests that the dipole–dipole interactions with protons surrounding the pair are responsible for the relaxation of MQ coherences.

1H multiple quantum NMR in alternating quasi-one-dimensional spin chains of hambergite

Multiple quantum (MQ) dynamics was investigated in quasi-one-dimensional 1H zigzag spin chains in hambergite (Be2BO3OH) single crystals. Due to the non-linear arrangement of the spins, dipolar coupling strengths alternate along the chain. To solve the problem of MQ NMR experiments taking too much time due to extremely long 1H spin–lattice relaxation times, the samples were exposed to gamma irradiation to produce the defects accelerating the relaxation. The influence of the radiation dose was investigated. The experimental dependencies of MQ coherence intensities on the MQ excitation time in alternating spin chains were obtained and compared with the theory for inhomogeneous spin chains with nearest neighbor interactions developed earlier. The correspondence of the observed MQ dynamics to the alternating spin chain was demonstrated.

Revealing impacts of electrolyte speciation on ionic charge storage in aluminum-quinone batteries by NMR spectroscopy

Rechargeable aluminum-organic batteries are composed of earth-abundant, sustainable electrode materials while the molecular structures of the organic molecules can be controlled to tune their electrochemical properties. Aluminum metal batteries typically use electrolytes based on chloroaluminate ionic liquids or deep eutectic solvents that are comprised of polyatomic aluminum-containing species. Quinone-based organic electrodes store charge when chloroaluminous cations (AlCl2+) charge compensate their electrochemically reduced carbonyl groups, even when such cations are not natively present in the electrolyte. However, how ion speciation in the electrolyte affects the ion charge storage mechanism, and resultant battery performance, is not well understood. Here, we couple solid-state NMR spectroscopy with electrochemical and computational methods to show for the first time that electrolyte-dependent ion speciation significantly alters the molecular-level environments of the charge-compensating cations, which in turn influences battery properties. Using 1,5-dichloroanthraquinone (DCQ) for the first time as an organic electrode material, we utilize solid-state dipolar-mediated and multiple-quantum NMR experiments to elucidate distinct aluminum coordination environments upon discharge that depend significantly on electrolyte speciation. We relate DFT-calculated NMR parameters to experimentally determined quantities, revealing insights into their origins. The results establish that electrolyte ion speciation impacts the local environments of charge-compensating chloroaluminous cations and is a crucial design parameter for rechargeable aluminum-quinone batteries.

Simulation of Multiple-Quantum NMR Dynamics of Spin Dimer on Quantum Computer

Dynamics of spin dimers in multiple quantum NMR experiment is studied on the 5-qubit superconducting quantum processor of IBM Quantum Experience for the both pure ground and thermodynamic equilibrium (mixed) initial states. The work can be considered as a first step towards an application of quantum computers to solving problems of magnetic resonance. This article is dedicated to Prof. Klaus Möbius and Prof. Kev Salikhov on the occasion of their 85th birthdays.

Multiple quantum NMR in solids as a method of determination of Wigner–Yanase skew information

A connection of the Wigner–Yanase skew information and multiple quantum (MQ) NMR coherences is considered at different temperatures and evolution times of nuclear spins with dipole–dipole interactions in MQ NMR experiments in solids. It is shown that the Wigner–Yanase skew information at temperature T is equal to the double second moment of the MQ NMR spectrum at the double temperature for any evolution times. A comparison of the many-spin entanglement obtained with the Wigner–Yanase information and the Fisher information is conducted.

Orientational dependencies of dynamics and relaxation of multiple quantum NMR coherences in one-dimensional systems.

Dynamics and relaxation, or decoherence, of multiple quantum (MQ) coherences are investigated experimentally and theoretically for different orientations of a single crystal of fluorapatite with respect to the external magnetic field. Dynamics of MQ coherences is studied as a function of the preparation period of the MQ NMR experiment. Their relaxation, or decoherence, during the evolution period is also investigated. Universal curves for dynamics and relaxation are obtained and describe the experimental data for different orientations of the investigated sample. Those curves prove the dipolar nature of the observed relaxation process. The contribution of the heteronuclear interactions to the dipolar relaxation is also investigated. The source of discrepancies between experimental data and theoretical results in the experiments with a large angle between the nuclear spin chains and the external magnetic field are discussed.

Revisiting Segmental Order: A Simplified Approach for Sulfur-Cured Rubbers Considering Junction Fluctuations and Entanglements

The use of modern multiple-quantum proton NMR experiments for the determination of cross-link density requires precise knowledge of several model-dependent physical and structural quantities, like the dipolar static frequency or the definition of vector segmental order. In this paper, different models for describing segmental order of the polymer backbone, based on different assumptions about the contribution of cross-links and entanglements, are critically reviewed and applied for the analysis of unfilled natural rubber samples with average mass between cross-links and entanglements determined from network tube model fittings of stress–strain data. A recent theoretical model developed by Lang and Sommer, which allows for the consideration of junction fluctuations, is adapted for the analysis of NMR experimental results. After having verified the correlation between the calculations with this enhanced theoretical treatment and the residual dipolar coupling from multiple-quantum NMR experiments carried out...

NEW INSIGHTS INTO RUBBER NETWORK STRUCTURE BY A COMBINATION OF EXPERIMENTAL TECHNIQUES

ABSTRACTRobust quantitative cross-link density characterization becomes necessary for the complete understanding of the structure and optimization of final properties of rubber compounds for industrial applications. A combination of different experimental techniques have been used to establish the quantitative consistency on the correlations between the results obtained by the individual methods within a reliable unique (physically based) platform reclined on the concept of rubber elasticity that considers the impact of entanglements in technical rubbers. The contribution of cross-links and elastically active entanglements to mechanical properties has been quantified by the analysis of uniaxial stress–strain measurements by means of the extended tube model of rubber elasticity. In a complementary manner, rubber network structure has also been investigated by state-of-the-art multiple-quantum low-field NMR experiments and classical T1 and T2 relaxation measurements. In addition, equilibrium swelling data were analyzed by the classical phantom and Flory–Rehner limits as well as by applying the theoretical approach proposed by Helmis, Heinrich, and Straube that takes into account topological constraints during swelling. Correlations among these complementary techniques have been reported, and the interpretation of the obtained differences is addressed. The baseline study focuses on unfilled NR, setting the basis for the investigation of unfilled SBR matrices and filled rubbers.

Dipolar relaxation of multiple quantum NMR coherences in one-dimensional systems

Dipolar relaxation of multiple quantum (MQ) NMR coherences is investigated theoretically on the evolution period of the MQ NMR experiment in chains with an arbitrary number of spins. The dependencies of the intensities of these coherences on the lengths of the evolution and preparation periods are obtained. It is shown that the intensity of the MQ NMR coherence of the zeroth order does not decay completely in the relaxation process. The experimental results obtained for a quasi-one-dimensional chain of 19F nuclear spins in calcium fluorapatite qualitatively agree with the results of the developed theory.

Relaxation of Multiple Quantum NMR Coherences in Quasi-One-Dimensional Spin Systems

Abstract Dynamics and relaxation of the multiple quantum (MQ) NMR coherences of the zeroth and second orders are studied experimentally and theoretically in a quasi-one-dimensional chain of nuclear spins 19F in calcium fluorapatite. The dependencies of the intensities of those coherences on the time of the preparation period of the MQ NMR experiment is obtained. A good agreement of the experiment with theoretical predictions is demonstrated. Dipolar relaxation of the MQ NMR coherences is investigated on the evolution period of the MQ NMR experiment. A theory of dipolar relaxation of the MQ NMR coherences is developed for the model in which only the ZZ part of the secular dipole–dipole interactions is taken into account (ZZ model). It is shown that the MQ NMR coherence of the zeroth order is not subject to dipolar relaxation in the ZZ model. The experimental data qualitatively agree with the results of the developed theory for the MQ NMR coherence of the second order.

Dynamics and relaxation of multiple quantum NMR coherences in a quasi-one-dimensional chain of nuclear spins 19F in calcium fluorapatite

Multiple quantum experiments on nuclear magnetic resonance on spins of 19F in calcium fluorapatite have been performed. It has been shown that more than 97% of the observed signal refers to the multiple quantum coherences of the zeroth and plus/minus second orders. The dependences of the intensities of these coherences on the time of the preparation period of the multiple quantum NMR experiment have been obtained. The dipole relaxation of multiple quantum coherences on the evolution period of the multiple quantum nuclear magnetic resonance experiment has been studied. A probe providing short radio-frequency pulses with the duration up to 0.3 μs has been developed for experiments. The experimental results show that the studied system can be used for the transmission of quantum information and the study of the decoherence process in strongly correlated multispin clusters.

Characterization of Network Structure and Chain Dynamics of Elastomeric Ionomers by Means of 1H Low-Field NMR

The network structure and chain dynamics of ionic elastomers based on carboxylated nitrile rubber (XNBR) cross-linked with different content of magnesium oxide (MgO) have been studied by different low-field time-domain NMR experiments. Ionic contacts created during the vulcanization tend to aggregate trapping some polymer segments that show restricted mobility as it was quantified by analyses of refocused free induction decays. Increasing the MgO content above the stoichiometric fraction has no effect on the amount of trapped polymer segments, but it increases the network cross-link density as measured by multiple-quantum (MQ) NMR experiments. The central finding of this work is that MgO addition above the stoichiometric content enhances the mechanical properties by creating a larger number of smaller ionic clusters, which act as dynamic cross-links, but are not readily seen by other techniques. Changes in the network structure and morphology of segregated thermolabile ionic domains have an impact on the ...

MQ NMR dynamics in dipolar ordered state at negative temperature

We investigate theoretically the Multiple Quantum (MQ) NMR dynamics at negative absolute temperatures in systems of nuclear spins 1/2 coupled by the dipole–dipole interactions and with the initial conditions determined by the dipolar ordered state. Two different methods of MQ NMR are used. One of them is based on the measurement of the dipolar energy. The other method uses an additional resonance (π/4)y-pulse after the preparation period of the standard MQ NMR experiment. It is shown that at negative temperatures many-spin clusters and spin correlations are created faster, and the intensities of MQ coherences are higher than in the usual MQ NMR experiments. So, the eighth-order MQ coherence in 10-spin system of the cyclopentane molecule appears to be 1.5 times faster and its intensity is four orders higher than at positive temperatures. The proposed MQ NMR methods at negative absolute temperatures can be used for the investigation of many-spin dynamics of nuclear spins in solids.

Reversible Cross-Linking, Microdomain Structure, and Heterogeneous Dynamics in Thermally Reversible Cross-Linked Polyurethane as Revealed by Solid-State NMR

Polyurethane material is widely utilized in industry and daily life due to its versatile chemistry and relatively easy handling. Here, we focused on a novel thermally reversible cross-linked polyurethane with comprehensive remarkable mechanical properties as reported in our recent work (Adv. Mater. 2013, 25, 4912). The microphase-separated structure and heterogeneous segmental dynamics were well revealed by T2 relaxometry experiments, which was also first utilized to in situ monitor the reversible cross-linking associated with Diels-Alder (DA) and retro-Diels-Alder (RDA) reactions. On the basis of T2 relaxometry results, we determined the actual temperature of the (R)DA reaction as well as the corresponding activation energies of the motion of soft segments. Besides, the roles of the temperature and cross-linker contents on the microdomain structure and dynamics are discussed in detail. It is found that the microphase separation is enhanced by the increase of temperature as well as the incorporation of cross-linkers. Also, the polyurethane samples are still thermal-stable even at a high temperature beyond the disassociation of the cross-linkages. Furthermore, Baum-Pines and three-pulse multiple-quantum NMR experiments are utilized to investigate the heterogeneous structures and dynamics of the mobile and rigid segments, respectively. Both the results obtained from the T2 relaxometry and multiple-quantum NMR experiments are in good agreement with the macroscopic mechanical properties of the polyurethane. Finally, it is also well demonstrated that proton T2 relaxometry combined with multiple-quantum NMR is a powerful method to study the heterogeneous structures and dynamics of a multiphase polymer system.

Low temperature MQ NMR dynamics in dipolar ordered state

We investigate analytically and numerically the Multiple Quantum (MQ) NMR dynamics in dipolar ordered spin systems of nuclear spins 1/2 at low temperatures. We consider two different methods of MQ NMR. One of them is based on the measurement of the dipolar energy. The other method uses an additional resonance (π/4)y-pulse after the preparation period of the standard MQ NMR experiment in solids and allows one to measure the Zeeman energy. Both considered methods are sensitive to the contribution of remote spins in the interaction and to the spin system structure. The QS method is sensitive to the spin number in the molecule while the PS method gives very similar time dependencies of the intensities of MQ coherences for different spin numbers. It is shown that the use of the dipolar ordered initial state has the advantage of exciting the highest order MQ coherences in clusters of 4m identical spins, where m=1,2,3,…, that is impossible to do with the standard MQ method. MQ NMR methods based on the dipolar ordered initial states at low temperatures complement the standard NMR spectroscopy for better studying structures and dynamic processes in solids.

Site-specific NMR mapping and time-resolved monitoring of serine and threonine phosphorylation in reconstituted kinase reactions and mammalian cell extracts

We outline NMR protocols for site-specific mapping and time-resolved monitoring of protein phosphorylation reactions using purified kinases and mammalian cell extracts. These approaches are particularly amenable to intrinsically disordered proteins and unfolded, regulatory protein domains. We present examples for the ¹⁵N isotope-labeled N-terminal transactivation domain of human p53, which is either sequentially reacted with recombinant enzymes or directly added to mammalian cell extracts and phosphorylated by endogenous kinases. Phosphorylation reactions with purified enzymes are set up in minutes, whereas NMR samples in cell extracts are prepared within 1 h. Time-resolved NMR measurements are performed over minutes to hours depending on the activities of the probed kinases. Phosphorylation is quantitatively monitored with consecutive 2D ¹H-¹⁵N band-selective optimized-flip-angle short-transient (SOFAST)-heteronuclear multiple-quantum (HMQC) NMR experiments, which provide atomic-resolution insights into the phosphorylation levels of individual substrate residues and time-dependent changes thereof, thereby offering unique advantages over western blotting and mass spectrometry.

Solid-state multiple quantum NMR in quantum information processing: exactly solvable models

Multiple quantum (MQ) NMR is an effective tool for the generation of a large cluster of correlated particles, which, in turn, represent a basis for quantum information processing devices. Studying the available exactly solvable models clarifies many aspects of the quantum information. In this study, we consider two exactly solvable models in the MQ NMR experiment: (i) the isolated system of two spin-1/2 particles (dimers) and (ii) the large system of equivalent spin-1/2 particles in a nanopore. The former model is used to describe the quantum correlations and their relations with the MQ NMR coherences, whereas the latter helps one to model the creation and decay of large clusters of correlated particles.

Time-Domain NMR Observation of Entangled Polymer Dynamics: Universal Behavior of Flexible Homopolymers and Applicability of the Tube Model

Using a benchtop NMR spectrometer, we performed proton multiple-quantum NMR experiments to study the dynamics of well-entangled linear poly(butadiene), poly(isoprene), and poly(dimethylsiloxane) in a broad molecular weight range. The method provides a direct time-domain measurement of the segmental orientation autocorrelation function over many decades, based on time−temperature superposition. The function can be directly compared to theoretical predictions based on the tube model, and the Rouse and the disentanglement times can be evaluated relative to the known entanglement time. We obtain universal results for all three polymers when plotted against the molecular weight normalized by the entanglement molecular weight, with the familiar mass scaling exponents of 2.0 ± 0.2 and 3.2 ± 0.2, respectively. However, the time scaling exponent derived for motions in the constrained-Rouse regime II is not constant at the predicted value of −1/4 but is always larger and also a universal function of molecular weigh...

Numerical analysis of relaxation times of multiple quantum coherences in the system with a large number of spins

We study the decay of multiple quantum (MQ) NMR coherences in systems with the large number of equivalent spins. As being created on the preparation period of the MQ NMR experiment, they decay due to the dipole-dipole interactions (DDI) on the evolution period of this experiment. It is shown that the relaxation time decreases with the increase in MQ coherence order (according to the known results) and in the number of spins. We also consider the modified preparation period of the MQ NMR experiment [G. A. Alvarez and D. Suter, Phys. Rev. Lett. 104, 230403 (2010)] concatenating the short evolution periods under the secular DDI Hamiltonian (the perturbation) with the evolution period under the nonsecular averaged two-spin/two-quantum Hamiltonian. The influence of the perturbation on the decoherence rate is investigated for the systems consisting of 200-600 equivalent spins.

Ultra-high resolution 17O solid-state NMR spectroscopy of biomolecules: A comprehensive spectral analysis of monosodium L-glutamate·monohydrate

Monosodium L-glutamate monohydrate, a multiple oxygen site (eight) compound, is used to demonstrate that a combination of high-resolution solid-state NMR spectroscopic techniques opens up new possibilities for (17)O as a nuclear probe of biomolecules. Eight oxygen sites have been resolved by double rotation (DOR) and multiple quantum (MQ) NMR experiments, despite the (17)O chemical shifts lying within a narrow shift range of <50 ppm. (17)O DOR NMR not only provides high sensitivity and spectral resolution, but also allows a complete set of the NMR parameters (chemical shift anisotropy and electric-field gradient) to be determined from the DOR spinning-sideband manifold. These (17)O NMR parameters provide an important multi-parameter comparison with the results from the quantum chemical NMR calculations, and enable unambiguous oxygen-site assignment and allow the hydrogen positions to be refined in the crystal lattice. The difference in sensitivity between DOR and MQ NMR experiments of oxygen in bio/organic molecules is also discussed. The data presented here clearly illustrates that a high resolution (17)O solid-state NMR methodology is now available for the study of biomolecules, offering new opportunities for resolving structural information and hence new molecular insights.