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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- particles (dimers) and (ii) the large system of equivalent spin- 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.

Highly controlled polymers and nanostructures are increasingly translated from the lab to the industry. Together with the industrialization of complex systems from renewable sources, a paradigm change in the processing of plastics and rubbers is underway, requiring a new generation of analytical tools. Here, we present the recent developments in time domain NMR (TD-NMR), starting with an introduction of the methods. Several examples illustrate the new take on traditional issues like the measurement of crosslink density in vulcanized rubber or the monitoring of crystallization kinetics, as well as the unique information that can be extracted from multiphase, nanophase and composite materials. Generally, TD-NMR is capable of determining structural parameters that are in agreement with other techniques and with the final macroscopic properties of industrial interest, as well as reveal details on the local homogeneity that are difficult to obtain otherwise. Considering its moderate technical and space requirements of performing, TD-NMR is a good candidate for assisting product and process development in several applications throughout the rubber, plastics, composites and adhesives industry.

The importance of sustainable polymers has increased greatly in the last years since most polymers are derived from non-renewable sources. Sustainable polymers (i.e., biopolymers) such as natural rubber (NR) are proposed as a solution for this concern. A comparative study between NR and deproteinized NR (DPNR) was carried out to elucidate the role of proteins on the network formation and degradation of peroxide cross-linked NR using time-domain NMR experiments. The 1H multiple-quantum (MQ) NMR experiments provided information on the cross-link density and its spatial distribution, while the actual fraction of non-coupled network defects was obtained by exploiting the Hahn echo approach measured on swollen samples. The results showed that proteins influenced the network formation during the vulcanization process of NR, leading to a higher number of non-elastic network defects and promoting the creation of additional cross-links with a broader spatial distribution. The formation of network heterogeneities in different length scales deeply influences the mechanical properties of NR samples. On the other hand, the proteins showed a pro-oxidant activity on the degradation behavior by accelerating the degradation process of peroxide cross-linked NR.

The statistical model developed in this study allows us to calculate the shape of multiple quantum (MQ) NMR spectra (the dependence of the amplitudes of the corresponding MQ coherences on their orders) by decomposing the desired time-correlation functions (TCFs) over an infinite set of orthogonal operators and by using some well-known facts from the physics of traditional model systems. The resulting expression contains series of gradually increasing numbers of spins in clusters of correlated spins depending on time. The influence of the possible degradation of these clusters on the shape of the spectra is taken into account. Analytical and numerical calculations are performed for various parameter values included in the final expressions. The developed theory adequately describes the results of the numerical calculations of the MQ spectra performed by us and experiments: the transformation of the Gaussian profile into an exponential one, the asymptotics (wings) of the spectrum depending on the coherence order M , and the dependence of the relaxation rate of the MQ spectrum on M , as well as the narrowing and stabilization of the MQ spectrum under the influence of a perturbation.

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 F 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.

Multiple quantum (MQ) nuclear magnetic resonance (NMR) experiment is considered on chains of fluorine atoms in calcium fluorapatite. The second moments of the line shapes of the MQ coherences on the evolution period of the MQ NMR experiment are calculated analytically in the approximation of nearest neighbor interactions. The calculated values are used for a description of the experimental data with semi-phenomenological formulas assuming that the relaxation of the MQ coherences follows the Gaussian law on the evolution period. A satisfactory agreement with the experimental data is demonstrated.

A new strategy is demonstrated that simultaneously enhances sensitivity and resolution in three- or higher-dimensional heteronuclear multiple quantum NMR experiments. The approach, referred to as mixed-time parallel evolution (MT-PARE), utilizes evolution of chemical shifts of the spins participating in the multiple quantum coherence in parallel, thereby reducing signal losses relative to sequential evolution. The signal in a given PARE dimension, t ₁, is of a non-decaying constant-time nature for a duration that depends on the length of t ₂, and vice versa, prior to the onset of conventional exponential decay. Line shape simulations for the ¹H-¹⁵N PARE indicate that this strategy significantly enhances both sensitivity and resolution in the indirect ¹H dimension, and that the unusual signal decay profile results in acceptable line shapes. Incorporation of the MT-PARE approach into a 3D HMQC-NOESY experiment for measurement of HN-HN NOEs in KcsA in SDS micelles at 50°C was found to increase the experimental sensitivity by a factor of 1.7±0.3 with a concomitant resolution increase in the indirectly detected ¹H dimension. The method is also demonstrated for a situation in which homonuclear ¹³C-¹³C decoupling is required while measuring weak H3'-2'OH NOEs in an RNA oligomer.

This chapter contains sections titled: Introduction Applications of NMR for Characterizing Silicones Highlights of Recent Advances in NMR Methodology Conclusions and Outlook Acknowledgements

NMR spectroscopy provides a powerful approach for the characterisation of chemical exchange and molecular interactions by analysis of series of experiments acquired over the course of a titration measurement. The appearance of NMR resonances undergoing chemical exchange depends on the frequency difference relative to the rate of exchange, and in the case of one-dimensional experiments chemical exchange regimes are well established and well known. However, two-dimensional experiments present additional complexity, as at least one additional frequency difference must be considered. Here we provide a systematic classification of chemical exchange regimes in two-dimensional NMR spectra. We highlight important differences between exchange in HSQC and HMQC experiments, that on a practical level result in more severe exchange broadening in HMQC spectra, but show that complementary alternatives to the HMQC are available in the form of HZQC and HDQC experiments. We present the longitudinal relaxation optimised SOFAST-H(Z/D)QC experiment for the simultaneous acquisition of sensitivity-enhanced HZQC and HDQC spectra, and the longitudinal and transverse relaxation optimised BEST-ZQ-TROSY for analysis of large molecular weight systems. We describe the application of these experiments to the characterisation of the interaction between the Hsp90 N-terminal domain and a small molecule ligand, and show that the independent analysis of HSQC, HMQC, HZQC and HDQC experiments provides improved confidence in the fitted dissociation constant and dissociation rate. Joint analysis of such data may provide improved sensitivity to detect and analyse more complex multi-state interaction mechanisms such as induced fit or conformational selection.

Carr–Purcell–Meiboom–Gill (CPMG) relaxation dispersion NMR experiments are invaluable for probing sparsely and transiently populated biomolecular states that cannot be directly detected by traditional NMR experiments and that are invisible by other biophysical approaches. A notable gap for RNA is the absence of CPMG experiments for measurement of methine base 1H and methylene C5′ chemical shifts of ribose moieties in the excited state, partly because of complications from homonuclear 13C–13C scalar couplings. Here we present site-specific 13C labeling that makes possible the design of pulse sequences for recording accurate 1H–13C MQ and SQ CPMG experiments for ribose methine H1′–C1′ and H2′–C2′, base and ribose 1H CPMG, as well as a new 1H–13C TROSY-detected methylene (CH2) C5′ CPMG relaxation pulse schemes. We demonstrate the utility of these experiments for two RNAs, the A-Site RNA known to undergo exchange and the IRE RNA suspected of undergoing exchange on microseconds to millisecond time-scale. We anticipate the new labeling approaches will facilitate obtaining structures of invisible states and provide insights into the relevance of such states for RNA-drug interactions.