Multiple-quantum NMR Research Articles

Intermolecular multiple-quantum coherence NMR signals modulated by double distant dipolar fields

A modified CRAZED pulse sequence was applied to obtain the intermolecular multiple-quantum coherence NMR signals from double distant dipolar fields in highly polarized spin systems. Complete theoretical analyses were explicitly derived from the dipolar field treatment combined with product operator formalism. Two typical samples containing several different components were chosen for the experimental verifications. The computer simulations and experimental observations are consistent with the theoretical predictions. The results presented herein provide a convenient way to understand the combined effects of multiple distant dipolar fields from the different components in complicated chemical or biological solutions. When experimental conditions such as selective radio-frequency pulses are not optimal, it may be helpful to identify possible unexpected signals or artefacts of high-resolution NMR spectroscopy in inhomogeneous fields.

Separating Chemical Shift and Quadrupolar Anisotropies via Multiple-Quantum NMR Spectroscopy

Chemical shift anisotropy (CSA) has been an invaluable probe of structure and dynamics for a variety of systems in NMR spectroscopy. Unfortunately, the presence of strong quadrupolar couplings has severely limited the ability to measure CSA in nuclei with spins I > 1/2. Here we show that these two interactions can be refocused at different times in a 2D multiple-quantum NMR experiment on polycrystalline samples. Combining this experiment with appropriate affine transformations allows these interactions to be cleanly separated into orthogonal dimensions. The 1D projection onto each axis can be fit to extract the respective principal tensor components. These components can then be used to fit the 2D spectrum for the relative orientation between the CSA and quadrupolar-coupling tensors. The necessary affine transformation parameters are given for all possible I values. Illustrative examples of spectra and analyses are given for 63Cu in K3[Cu(CN)4], 59Co in K3[Co(CN)6], and 87Rb in RbCrO4.

Uncertainties in the Determination of Cross-Link Density by Equilibrium Swelling Experiments in Natural Rubber

Equilibrium swelling is a feasible and simple experiment to determine the cross-link density of networks. It is the most popular and useful approach; however, in most of the cases, the given values are highly uncertain if not erroneous. The description of the complex thermodynamics of swollen polymer networks is usually based on the Flory−Rehner model. However, experimental evidence has shown that both the mixing term described by the Flory−Huggins expression and the elastic component derived from the affine model are only approximations that fail in the description and prediction of the rubber network behavior. This means that the Flory−Rehner treatment can only give a qualitative evaluation of cross-link density because of its strong dependence on the thermodynamic model. In this work, the uncertainties in the determination of the cross-link density in rubber materials by swelling experiments based on this model are reviewed. The implications and the validity of some of the used approximations as well as their influence in the relationship of the cross-link densities derived from swelling experiments are discussed. Importantly, swelling results are compared with results of a completely independent determination of the cross-link density by proton multiple-quantum NMR, and the correlation observed between the two methods can help to validate the thermodynamic model.

The generation of intense radiofrequency fields in μcoils

Large amplitude radiofrequency (rf) fields hold great promise in wide line NMR where it becomes possible to excite the full breadth of the line in a quantitative fashion. Applications in quadrupole NMR and in NMR of paramagnetic systems benefit greatly from intense fields. Spin manipulations in multiple quantum NMR experiments, specifically, the generation of multiple quantum coherence in MQ NMR, are more efficiently produced using intense rf fields. In this work we describe a μcoil probe that produces an rf field of 25 MHz, more than five times larger than the greatest rf field reported in the literature. We accomplish this in a robust, 127 μm diameter solenoid coil using 1 kW of rf power.

Spin selective multiple quantum NMR for spectral simplification, determination of relative signs, and magnitudes of scalar couplings by spin state selection

In the present work we demonstrate a novel method for spectral simplification and determination of the relative signs of the scalar couplings using a spin selective multiple quantum NMR experiment. A spin selective excitation of double quantum coherence of A and M spins in a weakly coupled three spin system of the type AMX, results in a doublet in the double quantum dimension whose separation corresponds to the sum of couplings of the active spins to the passive spin X. One component of the doublet has the passive spin X in mid R:alpha state while the other component has the passive spin X in mid R:beta state. The spin selective conversion of double quantum coherence to single quantum coherence does not disturb the spin states of the passive spin thereby providing the spin state selection. There will be two domains of single quantum transitions in single quantum dimension at the chemical shift positions of A and M spins. The mid R:alpha domain of A spin is a doublet because of mid R:alpha and mid R:beta states of M spin only, while that of mid R:beta domain is another doublet in a different cross section of the spectra. The scalar coupling J(AM) can be extracted from any of the mid R:alpha and mid R:beta domain transitions while the relative displacements of the two doublets between the two domains at the two chemical shifts provides the magnitude and sign of the scalar coupling J(AX) relative to the coupling J(MX). Similar result is obtained for zero quantum studies on AMX spin system. The proposed technique is discussed theoretically using product operator approach. The new spin state selective double quantum J-resolved sequence has also been developed. The methodology is confirmed experimentally on a homonuclear weakly coupled three spin system and applied to two different heteronuclear five spin systems.

29Si, 27Al, 1H and 23Na MAS NMR Study of the Bonding Character in Aluminosilicate Inorganic Polymers

Si-29, Al-27, H-1 and Na-23 solid-state magic-angle spinning (MAS) nuclear magnetic resonance (NMR) has been used to relate nominal composition, bonding character and compressive strength properties in aluminosilicate inorganic polymers (AIPs). The Si-29 chemical shift varies systematically with Si-to-Al ratio, indicating that the immediate structural environment of Si is altering with nominal composition. Fast H-1 MAS and Si-29 T (SiH)/T-1 rho relaxation measurements demonstrated that occluded pore H2O mobility within the disordered cavities is slow in comparison with H2O mobility characteristics observed within the ordered channel structures of zeolites. The Al-27 MAS NMR data show that the Al coordination remains predominantly 4-coordinate. In comparison with the Si-29 MAS data, the corresponding Al-27 MAS line shapes are relatively narrow, suggesting that the AlO4 tetrahedral geometry is largely unperturbed and the dominant source of structural disorder is propagated by large distributions of Si-O bond angles and bond lengths. Corresponding Na-23 MAS and multiple-quantum MAS NMR data indicate that Na speciation is dominated by distributions of hydration states; however, more highly resolved Na-23 resonances observed in some preparations supported the existence of short-range order. New structural elements are proposed to account for the existence of these Na resonances and an improved model for the structure of AIPs has also been proposed.

Crystalline Aluminium Borates with the Mullite Structure: A 11B and 27Al Solid-State NMR Study

Al-27 magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectra were acquired at 8.45, 14.1 and 16.45 T for a series of aluminium borates with the mullite structure (Al6-x B (x) O-9, where x has nominal values of 1 to 4) augmented with Al-27 multiple-quantum MAS NMR spectra at 8.45 T. Even though the Al-27 NMR spectra are complex, simulation of the combined set of data produced a relatively well-defined set of parameters (e.g., quadrupolar interaction, isotropic chemical shift, etc.) for each site. The B-11 MAS NMR spectra of the same compounds were also acquired at 14.1 T. Linear changes in the X-ray a-, b- and c-cell parameters with composition suggest that these compounds constitute a continuous series. Based on a Rietveld structural refinement of the compound synthesized as Al4B2O9, the resulting site occupancies and relative site distortions allow the identification of particular sites with specific NM resonances. Changes in the Al-27 and B-11 MAS NMR spectra of the related compounds with x = 1-4 show at the lowest Al contents a greater degree of asymmetry in the Al sites of the octahedral chains. A fairly distorted cross-linking tetrahedral site, which persists throughout the composition range, is accompanied in the lower Al compositions by two 5-fold coordinated Al-O units which are replaced by two more-regular tetrahedral Al-O sites as the Al content increases. In the compounds of lowest Al composition (i.e., highest B content) both the tetrahedral and trigonal cross-linking sites are distinguishable, but as the Al content increases, the BO4 units progressively disappear.

Thermal Degradation in a Trimodal Poly(dimethylsiloxane) Network Studied by 1H Multiple Quantum NMR

Thermal degradation of a filled, cross-linked siloxane material synthesized from poly(dimethylsiloxane) chains of three different average molecular weights and with two different cross-linking species has been studied by (1)H multiple quantum (MQ) NMR methods. Multiple domains of polymer chains were detected by MQ NMR exhibiting residual dipolar coupling (<Omega(d)>) values of 200 and 600 Hz, corresponding to chains with high average molecular weight between cross-links and chains with low average molecular weight between cross-links or near the multifunctional cross-linking sites. Characterization of the <Omega(d)> values and changes in <Omega(d)> distributions present in the material were studied as a function of time at 250 degrees C and indicate significant time-dependent degradation. For the domains with low <Omega(d)>, a broadening in the distribution was observed with aging time. For the domain with high <Omega(d)>, increases in both the mean <Omega(d)> and the width in <Omega(d)> were observed with increasing aging time. Isothermal thermal gravimetric analysis reveals a 3% decrease in weight over 20 h of aging at 250 degrees C. Degraded samples also were analyzed by traditional solid-state (1)H NMR techniques, and off-gassing products were identified by solid-phase microextraction followed by gas chromatography-mass spectrometry. The results, which will be discussed here, suggest that thermal degradation proceeds by complex competition between oxidative chain scissioning and postcuring cross-linking that both contribute to embrittlement.

A practical comparison of MQMAS techniques

A systematic experimental evaluation of several approaches to multiple-quantum MAS NMR was performed for spin-5/2 nuclei using 27Al NMR of the aluminosilicate andalusite and the porous aluminum phosphate AlPO 4-14 as model. Experiments were conducted in the fields of 9.4 and 17.6 T using magic-angle spinning frequencies up to 30 kHz and rf-field strengths of 250 and 120 kHz. Numerical SIMPSON optimizations of the NMR parameters were performed alongside the experimental evaluations. Both theory and experiment show that the optimization is most critical for the species in the sample that have the largest quadrupolar coupling constant. For 5QMAS experiments it could be confirmed that the highest available rf-field strength and rotation frequency are favorable for the efficiency of the experiments. For 3QMAS experiments of sites with moderate quadrupolar coupling constants optimum results were obtained at less stringent conditions. The comparison of a FAM II-modification and DFS gave the expected improvement by a factor of about two with respect to a rectangular pulse. No significant difference between these techniques concerning the signal-to-noise ratios was obtained. An actual improvement of the isotropic resolution by a factor of about two was obtained going from 3QMAS to 5QMAS. In addition the resolution of the spectra increases by a factor of about two going from 9.4 to 17.6 T.

Multiple quantum NMR dynamics in dipolar ordered spin systems

We investigate analytically and numerically the multiple-quantum (MQ) NMR dynamics in systems of nuclear spins $1∕2$ coupled by the dipole-dipole interactions in the case of the dipolar ordered initial state. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar temperature in the quasiequilibrium state which is established after the time of order ${\ensuremath{\omega}}_{\mathit{loc}}^{\ensuremath{-}1}$ (${\ensuremath{\omega}}_{\mathit{loc}}$ is the dipolar local field) after the MQ NMR experiment. The other method uses an additional resonance ${(\ensuremath{\pi}∕4)}_{y}$ pulse after the preparation period of the standard MQ NMR experiment in solids. Many-spin clusters and correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids.

Dipolar temperature and multiple-quantum NMR dynamics in dipolar ordered-spin systems

We investigate analytically and numerically the multiple-quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by dipole-dipole interactions in the case of the dipolar-ordered initial state. We suggest a new method of MQ NMR based on the measurement of the dipolar temperature in the quasi-equilibrium state, which establishes after the time of order ωloc−1 (ωloc is the dipolar local field) after the MQ NMR experiment. Manyspin clusters and correlations are created faster in such an experiment than in usual MQ NMR experiments and can be used for the investigation of the many-spin dynamics of nuclear spins in solids.

Hydrogel formation by photocrosslinking of dimethylmaleimide functionalized polyacrylamide

Polyacrylamide (PAAm) hydrogels are obtained in an efficient and controlled manner by means of photocrosslinking of linear PAAm chains which are functionalized with dimethylmaleimide (DMMI) groups. The reaction is conveniently performed in the presence of thioxanthone disulfonate as a triplet sensitizer.The fundamental investigation of the photoreaction on the basis of model compounds shows that the dimerization of DMMI groups in aqueous solution leads to asymmetric products instead of the expected cyclobutane derivatives. Nevertheless, crosslinking occurs in a well controlled manner without perceptible side reactions. The systematic analysis of the progress of the reaction by means of UV–vis spectroscopy indicates that the rate of dimerization is simply proportional to the concentration of sensitizer and the intensity of irradiation. The dimerization reaction can be interrupted at any intermediate stage by discontinuing the UV irradiation in order to study the system as it changes from a semi-dilute polymer solution to a fully crosslinked gel.The network formation was investigated macroscopically by rheology and microscopically by multiple-quantum NMR experiments. The results clearly indicate that the formation of active network strands occurs in proportion with DMMI conversion. The crosslinking efficiency varies markedly with concentration, but is surprisingly high (>60% at 80gL−1), while the length of the network chains seems to be independent of concentration.

Investigation of Network Heterogeneities in Filled, Trimodal, Highly Functional PDMS Networks by 1H Multiple Quantum NMR

The segmental order and dynamics of polymer network chains in a filled, tri-modal silicone foam network have been studied by static 1H Multiple Quantum (MQ) NMR methods to gain insight into the structure property relationships. The foam materials were synthesized with two different types of crosslinks, with functionalities, {phi}, of 4 and near 60. The network chains were composed of distributions of high, low, and medium molecular weight chains. Crosslinking was accomplished by standard acid catalyzed reactions. MQ NMR methods have detected domains with residual dipolar couplings ( ) of near 4 kRad/s and 1 kRad/s assigned to (a) the shorter polymer chains and chains near the multifunctional (f=60) crosslinking sites and to (b) the longer polymer chains far from these sites. Three structural variables were systematically varied and the mechanical properties via compression and distributions of residual dipolar couplings measured in order to gain insight in to the network structural motifs that contribute significantly to the composite properties. The partitioning of and the average values of the residual dipolar couplings for the two domains were observed to be dependent on formulation variable and provided increased insight into the network structure of these materials which are unavailable from swelling and spin-echo methods. The results of this study suggest that the domains with high crosslink density contribute significantly to the high strain modulus, while the low crosslink density domains do not. This is in agreement with theories and experimental studies on silicone bimodal networks over the last 20 years. In-situ MQ-NMR of swollen sample suggests that the networks deform heterogeneously and non-affinely. The heterogeneity of the deformation process was observed to depend on the amount of the high functionality crosslinking site PMHS. The NMR experiments shown here provide increased ability to characterize multimodal networks of typical engineering silicone foam materials and to gain significant insight into structure-property relationships.

Time evolution of multiple quantum coherences in NMR

In multiple quantum NMR, individual spins become correlated with one another over time through their dipolar couplings. In this way, the usual Zeeman selection rule can be overcome and forbidden transitions can be excited. Experimentally, these multiple quantum coherences (MQC) are formed by the application of appropriate sequences of radio frequency pulses that force the spins to act collectively. 1H spin coherences of even order up to 16 were excited in a polycrystalline sample of ferrocene (C 5H 5) 2Fe and up to 32 in adamantane (C 10H 16) and their evolutions studied in different conditions: (a) under the natural dipolar Hamiltonian, H ZZ (free evolution) and with H ZZ canceled out by (b) time reversion or (c) with the MREV8 sequence. The results show that when canceling H ZZ the coherences decay with characteristic times ( τ c≈200 μs), which are more than one order of magnitude longer than those under free evolution ( τ c≈10 μs). In addition, it is observed that with both MREV8 and time reversion sequences, the higher the order of the coherence (larger number of correlated spins) the faster the speed of degradation, as it happens during the evolution with H ZZ . In both systems, it is observed that the sequence of time reversion of the dipolar Hamiltonian preserves coherences for longer times than MREV8.

Gelation as Studied by Proton Multiple-Quantum NMR

A novel NMR approach for the study of gelation in flexible polymer systems is presented, and the data are compared to results from rheological and light scattering experiments. Proton multiple-quantum NMR, also applicable at low field and amenable to high-throughput experimentation, represents a simple and robust yet powerful method that allows one to detect the topological gel point, quantify the gelation kinetics, and characterize composition, microstructure, and dynamics of the forming and the final gel. Applications to end-linked and statistically cross-linked poly(dimethylsiloxane) chains in the bulk, as well as statistically cross-linked poly- (styrene) chains in solution are presented, and good agreement as well as complementarity between the results from the different methods is found.

Mixed-time parallel evolution in multiple quantum NMR experiments: sensitivity and resolution enhancement in heteronuclear NMR

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, t1, is of a non-decaying constant-time nature for a duration that depends on the length of t2, 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 (1)H 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 degrees 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.

Second moment of multiple-quantum NMR and a time-dependent growth of the number of multispin correlations in solids

The time evolution of multispin correlations (the growth of the number of correlated spins as a function of time) can be observed directly using the multiple-quantum nuclear magnetic resonance spectroscopy of solids. A quantity related to this number, namely, the second moment 〈n 2(t)〉 of the intensity distribution of coherences of different orders in the multiple-quantum spectrum can be calculated using the theory proposed in this work. An approach to the calculation of the four-spin time correlation function through which this moment is expressed is developed. The main sequences of contributions in the expansion of this function into a time power series are summed using the approximation of a large number of neighbors both for systems with a secular dipole-dipole interaction and for systems with a nonsecular effective interaction. An exponential dependence of 〈n 2(t)〉 is obtained. The value of 〈n 2(t)〉 is additionally calculated using an expansion in terms of orthogonal operators for three model examples corresponding to different limiting realizations of spin systems. It is shown that the results of the microscopic theory at least qualitatively agree with both the results obtained for model examples and experimental results obtained recently for adamantane.

Slow Backbone Dynamics of the C-Terminal Fragment of Human Centrin 2 in Complex with a Target Peptide Probed by Cross-Correlated Relaxation in Multiple-Quantum NMR Spectroscopy

The C-terminal domain of human centrin 2 (C-HsCen2) strongly binds to P1-XPC, a peptide comprising 17 amino acids with a NWKLLAKGLLIRERLKR sequence. This peptide corresponds to residues N847-R863 of XPC, a protein involved in the recognition of damaged DNA during the initial step of the nucleotide excision repair pathway. The slow internal dynamics of the protein backbone in the C-HsCen-P1-XPC complex was studied by measuring the relaxation rates of zero- and double-quantum coherences involving neighboring pairs of carbonyl 13C and amide 15N nuclei. These relaxation rates, which reflect dynamics on time scales in the range of micro- to milliseconds, vary significantly along the protein backbone. Analysis of the relaxation rates at different CaCl2 concentrations and ionic strengths shows that these slow motions are mainly affected by the binding of a Ca2+ ion to the lower-affinity EF-hand III. Moreover, we discuss the possible functional role of residues that undergo differential exchange in the formation of HsCen homodimers.

19F Single-Quantum and 19F−33S Heteronuclear Multiple-Quantum Coherence NMR of SF6 in Thermotropic Nematogens and in the Gas Phase

(19)F single-quantum (SQC) and (19)F-(33)S heteronuclear multiple-quantum coherence (HMQC) NMR spectroscopy of sulfur hexafluoride (SF(6)) dissolved in thermotropic liquid crystals (TLCs) were used to investigate the properties of TLCs. On one hand, environmental effects on the NMR parameters of SF(6), (19)F nuclear shielding, (19)F-(33)S spin-spin coupling, secondary isotope effects of sulfur on (19)F shielding, and the self-diffusion coefficient in the direction of the external magnetic field were studied as well. The temperature dependence of the (19)F shielding of SF(6) in TLCs was modeled with a function that takes into account the properties of both TLC and SF(6). It appears that the TLC environment deforms the electronic system of SF(6) so that the (19)F shielding tensor becomes slightly anisotropic, with the anisotropy being from -0.5 to -1.4 ppm, depending upon the TLC solvent. On the contrary, no sign of residual dipolar coupling between (19)F and (33)S was found, meaning that the so-called deformational effects, which arise from the interaction between vibrational and reorientational motions of the molecule, on the geometry of the molecule are insignificant. Diffusion activation energies, E(a), were determined from the temperature dependence of the self-diffusion coefficients. In each TLC, E(a) increases when moving from an isotropic phase to a nematic phase. The spin-spin coupling constant, J((19)F,(33)S), increases by ca. 10 Hz when moving from the gas phase to TLC solutions. The secondary isotope shifts of (19)F shielding are practically independent of TLC solvent and temperature. For the first time, (19)F-(33)S heteronuclear multiple-quantum NMR spectra were recorded for SF(6) in the gas phase and in a liquid-crystalline solution.

Chain Dynamics in Elastomers As Investigated by Proton Multiple-Quantum NMR

The influence of segmental and cooperative dynamics in elastomers on the time evolution in NMR experiments is considered using static proton multiple-quantum experiments. A novel experimental strategy as well as Monte Carlo simulations of a simple rotational diffusion model is used to investigate the applicability of the Andersen−Weiss approximation, upon which our analytical solutions are based. On the basis of temperature-dependent experiments, the validity of one of the most popular models used so far for the interpretation of NMR experiments is disproved. This model, which is based on slow rotational diffusion of a preaveraged residual coupling tensor, is refined by explicit consideration of the time scale of fast segmental processes which average the intrasegmental dipolar coupling toward a plateau value that is related to the chain order parameter associated with topological restrictions by chemical and physical cross-links. Models based on exponential or power-law loss of correlation are shown to provide physically reasonable representations of the data. As opposed to various earlier approaches, multiple-quantum NMR is unique in that it can be used to verify or falsify the different models. Data measured on permanently cross-linked systems are only weakly influenced by slow, cooperative processes, while reptation dynamics in corresponding linear-chain melts effectively prevents the observation of a well-defined order parameter.