Multiple-quantum NMR Research Articles

Statistical tensor analysis of the MQ MR signals generated by weak quadrupole interactions

Multiple quantum NMR signals that appear in the presence of weak quadrupole interactions were formulated using statistical tensors (Fano, 1957). The approach aimed to present a concise and a computer-based tool for a detailed analysis and modification of the MQ pulse sequences. The calculation avoids a lengthy procedure of utilizing exponential operators and, moreover, the same formulae are applicable for any interval in the TQ pulse sequence, as well as any spin value. The quantum operator algebra was implemented using “Mathematica” software (Wolfram Inc.). The results of tensor's evolutions in the TQ pulse sequence were graphically illustrated using corresponding spherical harmonics. The visualization takes into consideration the parity properties of irreducible tensors and the corresponding spherical harmonics.

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.

Crystallization in PEG networks: The importance of network topology and chain tilt in crystals

We synthesized poly(ethylene glycol) (PEG) networks by Cu(I) catalyzed azide-alkyne cycloaddition (CuAAC) using three-arm star-PEG with azide end groups and linear PEG oligomers of different molar masses with alkyne end groups. After extensive characterization of the networks by 13C MAS and 1H multiple-quantum (MQ) NMR spectroscopy, their crystallization behavior is studied by differential scanning calorimetry (DSC), temperature dependent small and wide angle X-ray scattering (SAXS, WAXS) as well as 1H FID NMR. Since CuAAC introduces 1,4-disubstituted 1,2,3-triazole (TR) rings as chain defects into the network, we compare our results with those obtained from linear PEG which contained a purposely introduced TR ring in the middle of the polymer chain. PEG network chains are able to form the characteristic 72 helices upon cooling to −20 °C and crystallize into the monoclinic unit cell in complete analogy to the homopolymer. The crystallinity of the networks, though it is lower as compared to the linear samples, reached values of about 30–50%. Given the fact that the network chains are highly constrained in their configurational freedom, this is very surprising. However, cross-links and the TR defects have only a minor effect on the molecular dynamics of the PEG chains in the crystals since the characteristic αc-relaxation process (helix jumps) is also detected in the PEG networks by analysis of the 1H FIDs. The SAXS data reveal that randomly arranged stacks of lamellae are formed upon crystallization and the chains are tilted in the crystals at large angles of about 40°–55°. Supported by all experimental data, we propose a model to explain the formation of polymer crystals in the networks and concluded that primary and secondary loops which extent the network chains beyond the length of the linear precursors play an essential role for the crystallization.

Strain-induced structural and dynamic changes in segmented polyurethane elastomers

Polyurethane elastomers have been widely used in the industry and daily life due to their versatile physical and chemical properties. Therefore, a fundamental understanding of the structures and dynamics at a molecular level will provide piercing insights into the precise design and application of new polyurethane materials. In this study, we mainly focused on investigating the strain-induced structural and dynamic changes in a typical polyurethane elastomer composed of poly(ε-caprolactone) (PCL) and 4,4′-diphenylmethylene diisocyanate (MDI) as the soft and hard segments, respectively. Obvious strain-hardening phenomenon was observed during the mechanical tensile test, and a systematic comparison was performed on the fractured and pristine samples. DSC results revealed that the crystallization of PCL chains was still going on after the sample was fractured, and the crystallite structures became stable after physical aging at 25 °C for two days. 1H solid-state nuclear magnetic resonance (NMR) experiment was further employed to determine the fraction of mobile PCL chains that were converted to crystallites during stretching. Besides, the microphase separation was also significantly enhanced in the fractured sample. The mobility of amorphous PCL chains was largely reduced due to the strain-induced crystallization of nearby PCL segments, as revealed by the 1H magic-sandwich echo (MSE) NMR experiments. 1H multiple quantum (MQ) NMR experiments also quantitatively revealed the strain-induced orientation of amorphous PCL chains in the fractured sample, indicating that the PCL crystallites were acting as the physical cross-linkages to prevent the contraction of the elongated PCL chains when the sample is fractured.

Contributions of different parts of dipole-dipole interactions to relaxation of multiple quantum NMR coherences in a single crystal of calcium fluorapatite

Contributions of different parts of dipole-dipole interactions to relaxation of multiple quantum NMR coherences in a single crystal of calcium fluorapatite

Combinatorial Enumeration of Isomers of Superaromatic Polysubstituted Cycloarenes and Coronoid Hydrocarbons with Applications to NMR.

We have employed combinatorial techniques based on character cycle indices, Pólya's theory, and Euler totem function to enumerate isomers of polysubstituted cycloarenes and coronoid hydrocarbons which have been receiving considerable attention because of their superaromaticity, ring currents, and interesting magnetic properties. Systematic enumeration and construction of tables of polysubstituted isomers such as fluoro-chloro superaromatic hydrocarbons are considered as they are of interest in the study of environmental pollutants and toxicity. Isomers of fluoro-chloro polysubstituted donut shaped circumkekulenes, circumseptulenes, circumoctulenes, etc., are enumerated in addition to other cycloarenes, polycyclic circumcoronaphenes and coronoids. Applications to 13C NMR, proton NMR and multiple quantum NMR spectroscopies of these superaromatic species are considered.

Imine Metathesis Catalyzed by a Silica-Supported Hafnium Imido Complex

The well-defined single-site silica-supported hafniaaziridine complex [(≡Si–O−)Hf(η2,π-MeNCH2)(η1-NMe2)(η1-HNMe2)] was prepared using surface organometallic chemistry. Upon thermal treatment under high vacuum, the grafted species was converted into the unprecedented hafnium imido bis-amido complex [(≡Si–O−)Hf(═NMe)(η1-NMe2)]. The surface complexes were characterized by elemental analysis and the following spectroscopic techniques: infrared, solid-state single and multiple quantum NMR, advanced DNP-SENS, and extended X-ray absorption fine structure. [(≡Si–O−)Hf(═NMe)(η1-NMe2)] catalyzed imine metathesis under mild conditions, and characterization of the reactivity showed that the imido exchange with N-(4-phenylbenzylidene)benzylamine yielded [(≡Si–O−)Hf (═NCH2Ar)(η1-NMe2)], demonstrating a kind of 2 + 2 mechanism involving the imine and the imido groups; the proposed reaction mechanism is also supported by DFT calculations.

The Second Moments of the Line Shapes of Multiple Quantum NMR Coherences in One-Dimensional Systems

The second moments of the line shapes of the zeroth- and second-order multiple quantum NMR coherences determined by the dipole–dipole interactions of nuclear spins in crystals have been calculated. The second moments determined by the zz part of the dipole–dipole interaction have been derived both by a direct calculation and based on the exact solution (in terms of the zz model) for the decay of the multiple quantum coherence intensities on the evolution period of a multi-quantum NMR experiment. The decay of the multiple quantum NMR coherence intensities in a single crystal of calcium fluorapatite is well described by the Gaussian curves with the calculated second moments.

Interplay between Crystallization and Entanglements in the Amorphous Phase of the Crystal-Fixed Polymer Poly(ϵ-caprolactone)

This work focuses on the influence of amorphous-phase entanglements on the semicrystalline morphology of poly(ϵ-caprolactone). This polyester is classified as crystal-fixed; i.e., it displays no translational chain dynamics in the crystals. We study a wide range of well-entangled samples with molecular weights up to several million using polarization microscopy to assess the lamellar growth rate, small-angle X-ray scattering and proton time-domain NMR to characterize the morphology, and proton multiple-quantum NMR, auxiliary carbon-13 NMR, rheology, and tensile deformation to assess the entangled chain dynamics in the melt and semicrystalline states. We demonstrate a significant increase in the density of entanglements in the amorphous phase relative to the melt. The dependencies of our observables on crystallization temperature and molecular weight suggest that entanglements control the thickness of the amorphous layers. This is rationalized by an only slowly relaxing exclusion zone with enhanced entangl...

Transfer of scaled multiple-quantum coherence matrices

Multiple quantum (MQ) NMR coherence spectra, which can be obtained experimentally in MQ NMR, can be transferred from the sender to the remote receiver without mixing the MQ coherences of different orders and distortions. The only effect of such transfer is scaling of the certain blocks of sender’s density matrix (matrices of MQ coherences of different orders). Such a block-scaled transfer is an alternative to the perfect state transfer. In particular, equal scaling of higher-order MQ coherences matrices is possible. Moreover, there are states which can be transferred to the receiver preserving their zero-order coherence matrix. The examples of block-scaled transfer in spin-1/2 communication lines of 6 and 42 nodes with two-qubit sender and receiver are presented.

High-performance recyclable cross-linked polyurethane with orthogonal dynamic bonds: The molecular design, microstructures, and macroscopic properties

Polyurethane materials (PUs) have been widely used in industry and daily life due to the versatile chemistry. However, despite the rapid advance in synthetic chemistry, it still remains a significant challenge for the facile fabrication of PUs with a single cross-linked network embedded with excellent mechanical properties and recyclability. Herein, in this study, we proposed a simple strategy to fabricate a high-performance recyclable cross-linked PU and revealed the relationship between microscopic structure and macroscopic properties. The UPy (2-ureido-4-[1H]-pyrimidione) motifs were incorporated into the backbone chains of PUs, where the quadruple hydrogen bonding interactions between UPy dimers can significantly enhance the mechanical strength and toughness. Furthermore, a single small molecular Diels-Alder adduct was utilized as the chemical crosslinker, rendering the final cross-linked PUs healable and recyclable. The thermal reversibility of the Diels-Alder reaction was well verified by DSC and solid-state NMR spectroscopy. Notably, it was found that the incorporation of UPy motifs could enhance the strain-induced crystallization (SIC), leading to a large stress at break. The structural and dynamic changes induced by SIC were quantitatively addressed by proton multiple-quantum NMR spectroscopy and SAXS experiments, where SIC further imposed restrictions on the mobility of surrounding polymer chains in the soft domain and led to the change of microphase separated nanostructures. Overall, a simple strategy is proposed here for the facile fabrication of high performance recyclable PUs, and the detailed investigation here on the structure-property relationship may further provide insights into developing high performance polymeric materials.

Time-Domain NMR Observation of Entangled Polymer Dynamics: Focus on All Tube-Model Regimes, Chain Center, and Matrix Effects

Proton multiple-quantum time-domain NMR combined with time–temperature superposition is a powerful method to study entangled chain dynamics. Overcoming the previous limitation to regimes II–IV of the tube model, this study extends the method to regime I (localized Rouse motions) by use of a pulse sequence adapted to shorter times, thus covering all relevant regimes for the model case of poly(butadiene) with molecular weights (M) between 10 and 200 kDa. We determine a value for the entanglement time that is consistent with current rheological results and confirm a value below 1 for the time scaling exponent of the segmental orientation autocorrelation function (OACF) in regime I previously observed by other NMR techniques. The origins of deviations from tube-model predictions are assessed by focusing on the dynamics of the chain centers in end-chain deuterated triblock samples and by dilution of probe chains to 15% in a deuterated matrix with M of 2 MDa. The study is complemented by self-diffusion coeffici...

Accurate Measurement of Residual Dipolar Couplings in Large RNAs by Variable Flip Angle NMR.

NMR approaches using nucleotide-specific deuterium labeling schemes have enabled structural studies of biologically relevant RNAs of increasing size and complexity. Although local structure is well-determined using these methods, definition of global structural features, including relative orientations of independent helices, remains a challenge. Residual dipolar couplings, a potential source of orientation information, have not been obtainable for large RNAs due to poor sensitivity resulting from rapid heteronuclear signal decay. Here we report a novel multiple quantum NMR method for RDC determination that employs flip angle variation rather than a coupling evolution period. The accuracy of the method and its utility for establishing interhelical orientations are demonstrated for a 36-nucleotide RNA, for which comparative data could be obtained. Applied to a 78 kDa Rev response element from the HIV-1 virus, which has an effective rotational correlation time of ca. 160 ns, the method yields sensitivity gains of an order of magnitude or greater over existing approaches. Solution-state access to structural organization in RNAs of at least 230 nucleotides is now possible.

Structural Investigation of Ye’elimite, Ca4Al6O12SO4, by 27Al MAS and MQMAS NMR at Different Magnetic Fields

Ye’elimite is the principal component in calcium sulfoaluminate cement, which currently attracts significant attention, since it can be produced with lower CO2 emissions compared to conventional portland cement. The crystal structure of ye’elimite is not well-established, and it has been proposed to exhibit cubic, tetragonal, and orthorhombic structures. The present work reports a comprehensive 27Al magic-angle spinning (MAS) and multiple-quantum (MQ) MAS NMR study of ye’elimite, utilizing six magnetic fields from 4.7 to 22.3 T. These spectra are only compatible with the orthorhombic Pcc2 structure of ye’elimite, implying the presence of eight distinct AlO4 sites. The 27Al NMR spectra are convincingly simulated by eight distinct sites, and 27Al quadrupole coupling parameters and isotropic chemical shifts are reported for the first time for ye’elimite. These parameters are a prerequisite for a reliable interpretation and quantification of ye’elimite in 27Al NMR spectra of ye’elimite-based cements. Density functional theory (DFT) calculations are used in the assignment of the specific Al sites in ye’elimite. Structural relaxations by DFT, using two proposed Pcc2 structures as starting points, result virtually in the same set of optimized fractional atomic coordinates, which is proposed as a new refined structure for ye’elimite. The refined structure gives the best agreement between experimental and calculated 27Al quadrupole tensor elements for the eight Al sites. Finally, the 33S MAS NMR spectra for ye’elimite, monosulfate, and anhydrite are reported.

Probing the 1H spin distribution in hybrid organic-inorganic gels by multiple-quantum NMR spectroscopy

Multiple-quantum (MQ) NMR was used to characterize the organic phase distribution in a series of hybrid organic-inorganic gels namely methyltrimethoxysilane aerogel and QM resins (trimethylsiloxysilicate polymers) with different composition. The Gaussian model of distribution of MQ coherence intensities was used to determine the effective 1H spin cluster size (N). The growth of the effective cluster size with the time of excitation of MQ NMR coherences τ indicates the uniform distribution of organic moieties in the studied gels, but the growth rate is significantly slower than that of adamantane which was used for comparison as an example of the systems with uniform distribution of 1H spins. The growth rate was described by the exponents α in the scaling law of the form N~τα. The obtained values of α were 3.07 for adamantane, 1.27 for aerogel and 1.8 for QM resins. This difference was attributed to the surface distribution of the 1H spins in the studied gels. The growth rate of spin clusters in aerogel is slower in comparison with QM resins with different content of 1H spins which show similar growth rate among each other. This result was explained by the higher local concentration of 1H spins on the surfaces of silica regions in QM resins.

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...

Viscoelasticity and Structures in Chemically and Physically Dual-Cross-Linked Hydrogels: Insights from Rheology and Proton Multiple-Quantum NMR Spectroscopy

Hydrogels have received considerable attention as an innovative material due to their widespread applications in various fields. As a soft and wet material, its mechanical behavior is best understood in terms of the viscoelastic response to the periodic deformation, which is closely related to the microscopic chemically/physically cross-linked structures. Herein, a dual-cross-linked (DC) hydrogel, where a physically cross-linked network by ionic coordination (Fe3+) is imposed on a chemically cross-linked poly(acrylamide-co-acrylic acid) network, was studied in detail by rheology and proton multiple-quantum (MQ) NMR spectroscopy. Rheology experiments revealed the diverse temperature- and strain-frequency-dependent viscoelastic behaviors for DC hydrogels induced by the dynamic Fe3+ coordination interactions, in contrast to the single chemically cross-linked (SC) hydrogels. During the shear experiment, the trivalent Fe3+ complex with moderate/weak binding strength might transform to those with strong binding...

Synthesis and Structural NMR Characterization of Novel PPG/PCL Conetworks Based upon Heterocomplementary Coupling Reactions

AbstractA new approach to hybrid model network formation based upon heterocomplementary end‐linking of four‐arm star poly‐ε‐caprolactone (PCL) and linear polypropylene glycol (PPG) precursors is demonstrated. Specifically, hydroxy‐terminated PCL(OH)4 and an amino‐terminated linear PPG(NH2)2 are reacted with a bifunctional coupling agent containing one carboxylic acid chloride group and one oxazinone group. PCL(OH)4 is first reacted with the former in a solution, and the so‐obtained oxazinone‐terminated intermediate is then reacted with PPG(NH2)2 to form a network both in the solution and in the melt. A strong effect of electron‐withdrawing groups on the reactivity of the oxazinone group, and thus on the network formation, is evidenced. Network structure and properties are studied by swelling experiments and low‐field multiple‐quantum (MQ) NMR, which confirm the successful formation of hybrid networks and provide information on the significant network inhomogeneities. On the methodological side, a reliable approach to MQ NMR data analysis for networks of variable degree of inhomogeneity is discussed.

Effective Floquet Hamiltonian theory of multiple-quantum NMR in anisotropic solids involving quadrupolar spins: Challenges and Perspectives.

The response of a quadrupolar nucleus (nuclear spin with I >12) to an oscillating radio-frequency pulse/field is delicately dependent on the ratio of the quadrupolar coupling constant to the amplitude of the pulse in addition to its duration and oscillating frequency. Consequently, analytic description of the excitation process in the density operator formalism has remained less transparent within existing theoretical frameworks. As an alternative, the utility of the "concept of effective Floquet Hamiltonians" is explored in the present study to explicate the nuances of the excitation process in multilevel systems. Employing spin I =32 as a case study, a unified theoretical framework for describing the excitation of multiple-quantum transitions in static isotropic and anisotropic solids is proposed within the framework of perturbation theory. The challenges resulting from the anisotropic nature of the quadrupolar interactions are addressed within the effective Hamiltonian framework. The possible role of the various interaction frames on the convergence of the perturbation corrections is discussed along with a proposal for a "hybrid method" for describing the excitation process in anisotropic solids. Employing suitable model systems, the validity of the proposed hybrid method is substantiated through a rigorous comparison between simulations emerging from exact numerical and analytic methods.

Dipolar Relaxation of Multiple Quantum NMR Coherences as a Model of Decoherence of Many-Qubit Coherent Clusters

Dipolar relaxation of multiple quantum (MQ) nuclear magnetic resonance (NMR) coherence is investigated on the evolution period of the MQ NMR experiment in chains of 19F nuclei in a single crystal of calcium fluorapatite. The dependence of the relaxation time of the MQ coherence of the second order on the size of the coherent spin cluster formed on the preparation period is obtained. The dipolar relaxation of MQ NMR coherences is considered as a model for the investigation of decoherence of quantum states of many-qubit spin clusters.