Quadrupolar Echo Research Articles

Glass transition of polydimethylsiloxane–vanadate hybrid materials studied through [formula omitted] and [formula omitted] NMR

Nuclear magnetic resonance (NMR) analysis of quadrupolar nuclei is shown to be a robust and powerful tool for studying glass transition of elastomeric nano-composites. In the case of polydimethylsiloxane–vanadate (PDMSV) materials, single pulses on 17 O and 51 V nuclei allow an observation of the effect on the quadrupolar splitting of motional changes above the calorimetric glass transition ( 177±1 K ). Moreover, intensities of quadrupolar echoes are found sensitive to changes of motional correlation times occurring at the glass transition. Their variations give rise to consistent values of T g (=184±5 K for 17 O , =178±2 K for 51 V ). These results obtained through twin probing NMR analysis of half integer quadrupolar nuclei unambiguously confirm previous assumptions on chemical homogeneity and co-polymer effects.

Theoretical and experimental study of quadrupolar echoes for half-integer spins in static solid-state NMR

Numerical simulations of powder spectra produced by a two-pulse sequence applied to a quadrupolar nuclei system of half-integer spin number make it possible to propose simple experimental instructions to record static echo spectra with minimum lineshape distortion. Calculations take into account quadrupolar (first and second orders), shielding, scalar and inhomogeneous dipolar interactions as well as the radiofrequency pulse specifications (strength, duration, phase). The suggested instructions have been checked experimentally in different cases: for a large spin number system with Li93NbO3, when two interactions are present with a 63/65Cu complex, and in the two-site system of 87Rb2SO4.

Solid State Deuteron NMR Studies of Polyamidoamine Dendrimer Salts. 2. Relaxation and Molecular Motion

Nonexponential recovery curves have been obtained for anisotropic deuteron spin lattice relaxation of deuterated polyamidoammonium chloride salts for integer generations G = 1, 2, 3, 5, 7, and 9, at room temperature. The temperature dependence of the relaxation of generations 2, 3, and 9 is reported. Multiple exponential relaxation behavior is ascribed to a sum of single exponential, anisotropic contributions from overlapping quadrupole echo powder patterns. These are assigned to interior secondary amide, R2ND, deuterated tertiary amine, R3ND+, and terminal ammonium, RND3+, deuterons in the glassy polymer. Additional temperature dependent features in the middle of the spectra arise from mobile phases. For each type of deuteron the best fit of the relaxation data is achieved by numerically solving the stochastic Liouville equation for the relevant motional model. Planar libration of R2ND and R3ND+ deuterons is simulated by jumps along an arc. Motion of RND3+ groups is modeled as a two-frame process in whic...

Solid-State QCPMG NMR of Low-γ Quadrupolar Metal Nuclei in Natural Abundance

Taking advantage of an order of magnitude in sensitivity enhancement obtained by sampling of quadrupolar-echo (QE) solid-state NMR spectra during a quadrupolar Carr−Purcell−Meiboom−Gill (QCPMG) pulse sequence, we demonstrate that the coordination environment of low-γ quadrupolar metal nuclei can be studied routinely for powders with these nuclei in natural abundance. The general applicability of the method is demonstrated by 39K, 25Mg, 67Zn, and 87Sr QCPMG solid-state NMR experiments for K2MoO4, KVO3, Mg(VO3)2, Zn(CH3COO)2·2H2O, Zn(Ala)2·H2O, Sr(NO3)2, and SrMoO4. For all samples the quadrupolar coupling parameters and the isotropic chemical shifts are extracted by numerical simulation and iterative fitting of the spin−echo sideband spectra observed in the experimental QCPMG NMR spectra. These parameters are discussed in light of the crystal structures for the compounds.

Solid State Deuteron NMR Studies of Polyamidoamine Dendrimer Salts. 1. Structure and Hydrogen Bonding

Temperature dependent deuteron quadrupole echo line shapes are reported for integer generations, G = 1, 2, 3, 5, 7, 9, of polyamidoammonium chloride salts. The spectra are characteristic of amorphous materials undergoing broad glass transitions between 25 and 65 °C. Adequate fits of room-temperature line shapes were obtained by assuming Gaussian distributions of hydrogen bond lengths for interior R2ND···O and R3ND+···Cl- deuterons in the dendrimer spacers and Gaussian distributions of librational cone angles for motion of the C3v axes of terminal RND3+ groups. The estimated average hydrogen bond lengths at both types of interior site are 2.2 ± 0.15 Å, independent of generation number. For G = 2 the spectra obtained upon anion substitution of Cl- by Br- demonstrate that both types of hydrogen bonding are counterion dependent. In the temperature range from −30 to 60 °C the decreases in quadrupole coupling constants and increases in observed asymmetry parameters at the interior sites are ascribed to effects of planar libration. In the dendrimer interior the average amplitude of planar libration increases with temperature and decreases with increasing generation. Thermal energy is dissipated in counterion mobility for low generations and in mobility of the dendrimer spacers for high generations. In addition to 3-fold rotation, asymmetric cone libration is required to explain the observed temperature dependent asymmetry parameters of terminal ND3+ groups. For both low- and high-generation dendrimers the terminal groups buried in the interior exhibit smaller average librational amplitudes than those of generation 3.

Models for molecular motions within polymer chains. Part 1. A solid-state NMR study of hexane-1,6-diyl bis( p-nitrobenzoate)

Solid-state NMR experiments on hexane-1,6-diyl bis(p-nitrobenzoate) and its 1,1,6,6- and 2,2,5,5-deuteriated derivatives present a coherent view of the molecular dynamics of the central alkyl chain. The techniques used include 13C CP/MAS spectra, 2H quadrupole echo spectra, associated with measurements of 13C T1ρ relaxation times, 2H and 13C T1 relaxation times and quadrupole echo reduction factors. Molecular dynamics in the central chain are dominated by librational motions at the CH2 groups that can best be approximated by a six-site conical model. The activation energies for these librations are ca. 35 kJ mol−1. gauche–trans flips in the chain can be ruled out as the origin of the effects observed.

NMR study of chain dynamics in the hexagonal high-pressure phase of polyethylene

At high pressure (>3300 bar) polyethylene shows a hexagonal phase between the orthorhombic phase and the liquid phase. This first NMR investigation of polyethylene in its hexagonal phase shows that the mobility of the molecular chains is very high. Deuteron quadrupole echo spectra have been used to determine the character and rate of local reorientations of the molecular chains. The chains perform rapid axial reorientations, similar to those observed in the rotator phases occurring in the long normal alkanes. From proton rotating frame relaxation data we derive a high rate of translational diffusion in the chain direction. These observations contribute to the understanding of the important role of the hexagonal phase in the growth of chain-extended polyethylene crystals.

Deuterium NMR Studies of Local Motions of Benzene Adsorbed on Ca-Montmorillonite

2H NMR spectra and interpretations are presented on two samples of deuterium-labeled benzene that have been adsorbed on a major soil component, Ca-montmorillonite clay. Spectra were obtained on the samples with two different benzene loading levels over a wide temperature range and using two values of the quadrupolar echo delay period. Computer simulations of line shapes resulting from various forms of local motion of C−2H moieties provide useful guidelines for interpreting the experimental results. The results suggest that absorbed benzene molecules first form π-complexes with Ca2+ in the interlayer space of the clay with an adsorption enthalpy of 42 ± 4 kJ/mol at temperatures at or below −75 °C. The adsorbed molecules undergo small-angle wobbling of the C6 axis accompanied by rapid discrete jumps about the C6 axis. At higher temperatures, benzene molecules start to perform large-angle wobbling of the C6 axis with extremely fast jumps around the axis, and eventually desorb from Ca2+ to tumble freely in the interlayer space of the clay. The enthalpy and entropy changes between different motional states were obtained from the variable temperature studies. The activation energies of relevant molecular motions were also estimated. This approach is attractive for elucidation of the detailed motional behaviors of organic pollutants adsorbed in soil.

Local Motions of Organic Pollutants in Soil Components, as Studied by 2H NMR

2H NMR spectra and interpretations are presented on a series of samples, each consisting of a deuterium-labeled organic pollutant (trichloroethylene, acetone, pyridine, benzene, or ethylene glycol) adsorbed on a soil component (montmorillonite clay or humic acid). Spectra were obtained over a wide temperature range and using two values of the quadrupolar echo delay period. Computer simulations of line shapes resulting from various forms of local motion of C−2H moieties provide useful guidelines for interpreting the experimental results. In a few cases, detailed line shape simulations are given. This approach is attractive for elucidation of the detailed motional behaviors of organic pollutants adsorbed in soil.

Evidence for phase separation during the crystallization of hyperquenched glassy clathrate hydrate forming solutions

Tetrahydrofuran, a water-soluble cyclic ether molecule, is well known for its ability to form clathrate hydrates (cubic structure II, melting point 277.5 K). An aqueous solution of THF (17:1 molecular ratio) was hyperquenched (cooled at a rate of 106 Ks−1) to 77 K to give recoverable samples of ∼1 g of metastable amorphous material. The crystallization process was studied on three complementary length scales by x-ray powder diffraction, quadrupole echo double resonance (QEDOR) NMR spectroscopy, and Raman spectroscopy as the amorphous material was annealed at temperatures between 80 and 190 K. Results show that phase separation of the two components occurred predominantly during the annealing process, resulting in clusters of crystalline THF and ice Ic before clathrate hydrate crystallization was initiated. During the hyperquenching process, the decreasing molecular mobility of water molecules between room temperature and the fictive temperature (the temperature below which the solution becomes structurally immobilized upon hyperquenching) inhibits growth of the crystal nuclei that normally would result in crystalline clathrate hydrate formation. Annealing the samples between 110–140 K showed that the local hydrogen bonded O–H--O structure of the water molecules changed toward the arrangement characteristic of crystalline ice Ic. We propose that this process forces the THF out of the glassy solution, thus increasing the THF cluster size in the deposit so that these become visible to diffraction. Further annealing, above 150–160 K caused large-scale growth of crystalline clathrate hydrate material, which then could be associated with a reduction in the THF cluster size, and ice Ic.

Quadrupolar echo double resonance (QEDOR) and solid echo double resonance (SOLEDOR) NMR

We propose two new double resonance experiments that are sensitive to internuclear dipolar couplings, namely Quadrupolar Echo DOuble Resonance (QEDOR) and SOLid Echo DOuble Resonance (SOLEDOR). The experiments are explained by analysis of the spin evolution during the pulse sequences, and are demonstrated for deuterium–proton double resonance experiments with partially deuterated polycrystalline glycine. In addition to molecular dynamics information normally obtained from the standard quadrupolar echo experiment, the QEDOR experiment is able to provide information about the local molecular surroundings by probing heteronuclear dipolar interactions. We have illustrated this with experiments on single-phase and phase-separated samples of tetrahydrofuran clathrate hydrate.

2H NMR lineshape analysis using automated fitting procedures based on local and quasi-global optimization techniques

A new approach is presented for the analysis of wideline H-2 NMR lineshapes, based on automated fitting of simulated spectra to experimental spectra using either 'downhill simplex' or simulated annealing algorithms. This approach provides an objective assessment of the level of agreement between experimental and simulated H-2 NMR spectra, and removes much of the subjectivity that is characteristic of the traditional approach involving trial-and-error variation of the parameters used in the simulation, followed by visual comparison between experimental and simulated H-2 NMR spectra to assess the quality of fit. Applications of our new approach are reported for the analysis of (i) static H-2 NMR powder patterns, (ii) the temperature dependence of H-2 NMR powder patterns in the intermediate motion regime (including the case of fitting experimental spectra with poor signal-to-noise ratio) and (iii) the dependence of quadrupole echo 2H NMR spectra on the echo delay. Quantitative details relating to the dynamic properties of thiourea-d(4) in its pure crystalline phase and in the chlorocyclohexane-thiourea-d(4) inclusion compound are presented, in addition to the motion of the guest molecules iri the benzenetricarbonylchromium-d(6)-thiourea inclusion compound and the pyrazine-d(4)-alpha-zirconium phosphate intercalation material. (C) 1998 John Wiley & Sons, Ltd.

Investigation of multiaxial molecular dynamics by [formula omitted] MAS NMR spectroscopy

The technique of 2 H MAS NMR spectroscopy is presented for the investigation of multiaxial molecular dynamics. To evaluate the effects of discrete random reorientation a Lie algebraic formalism based on the stochastic Liouville–von Neumann equation is developed. The solution to the stochastic Liouville–von Neumann equation is obtained both in the presence and absence of rf irradiation. This allows effects of molecular dynamics to be evaluated during rf pulses and extends the applicability of the formalism to arbitrary multiple pulse experiments. Theoretical methods are presented for the description of multiaxial dynamics with particular emphasis on the application of vector parameters to represent molecular rotations. Numerical time and powder integration algorithms are presented that are both efficient and easy to implement computationally. The applicability of 2 H MAS NMR spectroscopy for investigating molecular dynamics is evaluated from theoretical spectra. To demonstrate the potential of the technique the dynamics of thiourea– 2 H 4 is investigated experimentally. From a series of variable temperature MAS and quadrupole echo spectra it has been found that the dynamics can be described by composite rotation about the CS and CN bonds. Both experiments are sensitive to the fast CS rotation which is shown to be described by the Arrhenius parameters E CS=46.4±2.3 kJ mol −1 and ln( A CS)=32.6±0.9. The MAS experiment represents a significant improvement by simultaneously allowing the dynamics of the slow CN rotation to be fully characterized in terms of E CN=56.3±3.4 kJ mol −1 and ln( A CN)=25.3±1.1.

Molecular dynamics from 2H Quadrupolar Carr–Purcell–Meiboom–Gill solid-state NMR spectroscopy

The 2H quadrupolar Carr–Purcell–Meiboom–Gill (QCPMG) NMR experiment is proposed as a convenient method to obtain detailed information about molecular dynamics in solids. Compared to the quadrupolar-echo (QE) experiment QCPMG offers two advantages. First, a sensitivity enhancement by about an order of magnitude is achieved by splitting the QE spectrum into spin-echo sidebands. Second, the lineshape of the individual sidebands provides detailed information about the molecular dynamics and increases the dynamic range by two orders of magnitude. The 2H QCPMG method is demonstrated experimentally and numerically using the two-fold flip process in dimethyl sulfone.

What's water got to do with it? A nuclear magnetic resonance study of molecular motion in pig stratum corneum.

The 1H and 2H magnetic resonance signals from pig stratum corneum were measured as a function of hydration. The 1H free induction decay contained two components, one motionally restricted and the other isotropically mobile on the timescale of 10(-5) s. From its T2 decay, the mobile signal was further subdivided into two components; one, which was 11% of the signal and 5.5% of the mass of the dehydrated stratum corneum, was assigned to nonaqueous tissue (likely hydrocarbons) and the other to water. As water content increased from 0 to 0.25 gH2O/gSC, the second moment of the motionally restricted signal decreased from 5.4 x 10(9) to 3.6 x 10(9) s(-2), whereas the water T2 time increased from less than 0.3 ms to 3.3 ms. The 2H quadrupolar echo from stratum corneum hydrated in 2H2O had a signal from motionally restricted deuterons, attributed to deuterons exchanged onto O-H and N-H groups, and a mobile signal from 2H2O. The amount of exchange, 9.5% of the hydrogen sites in the motionally restricted fraction, was close to the number of exchangeable sites on keratin, the most abundant protein in stratum corneum. Our results are consistent with a model in which the bulk of the water interacts closely with the corneocytes in stratum corneum.

Temporal Characteristics of NMR Signals from Spin 3/2 Nuclei of Incompletely Disordered Systems

Anisotropic nuclear quadrupole interactions can produce residual quadrupole splitting in the NMR spectra of rapidly moving quadrupolar nuclei in incompletely disordered aqueous heterogeneous systems. Such systems may include hydrated sodium nuclei in biological tissue and biopolymer gels. To describe the NMR signals from such samples, we use a domain model in which each domain is characterized by a quadrupole frequency and a residence time of the nucleus. We show that the signals from each domain after one pulse, the quadrupole echo sequence, and the various multiple quantum filters (MQFs) can be expressed as a linear combination of five different phase coherences. To simulate the effect of various distributions (Pake powder pattern, Gaussian, etc.) of quadrupole frequencies for different domains on the NMR signal, we have written the computer program CORVUS. CORVUS also includes the effects of exchange between different domains using diffusion and random jump models. The results of computer simulations show that the Gaussian and Pake powder pattern quadrupole frequency distributions produce very different phase coherences and observable NMR signals when the exchange rate (1/taue) between different domains is slow. When 1/taue is similar to the root mean square quadrupole frequency (final sigma), the signals from the two distributions are similar. When 1/taue is an order of magnitude greater than final sigma, there is no apparent evidence of quadrupole splitting in the shape of the signal following one pulse, but the residual effects of the quadrupole splitting make a significant contribution to the fast transverse relaxation rate. Therefore, in this case, it is inappropriate to use the observed biexponential relaxation rates to obtain a single correlation time. The quadrupole echo and the various MQF signals contain an echo from the satellite transitions in the presence of quadrupole splitting. The peak of this echo is very sensitive to 1/taue. The time domain analysis of these signals is more direct and less ambiguous than the frequency domain analysis because the echo does not occur at the beginning of data acquisition. The quadrupole echo pulse sequence is the most sensitive detector of residual quadrupole splitting and exchange of sodium ions between different domains. However, if the sample is compartmentalized so that only a fraction of the nuclei have quadrupole splitting, the double quantum magic angle filter (DQ-MA) is more suitable. This is because the DQ-MA signal contains only the contributions from satellite transitions. Use of simulations to analyze signals from various one-pulse, quadrupole echo, and multiple quantum filter pulse sequences can yield information on substrate order and aid in quantitation of multiple quantum filter signals.

Sensitivity-Enhanced Quadrupolar-Echo NMR of Half-Integer Quadrupolar Nuclei. Magnitudes and Relative Orientation of Chemical Shielding and Quadrupolar Coupling Tensors

A novel approach to quadrupolar-echo (QE) NMR of half-integer quadrupolar nuclei in static powders is analyzed. By acquisition of the QE spectrum during a Carr−Purcell−Meiboom−Gill (CPMG) train of selective π pulses, the second-order quadrupolar line shape for the central transition is split into a comb of sidebands leading to a considerable increase in the sensitivity compared to a conventional QE spectrum. The applicability of the method for determination of magnitudes and relative orientation of chemical shielding and quadrupolar coupling tensors is examined. Through numerical simulation and iterative fitting of experimental 87Rb (RbClO4 and RbVO3) and 59Co spectra (Co(NH3)5 Cl3), it is demonstrated that the quadrupolar CPMG experiment represents a useful method for studying half-integer quadrupolar nuclei exhibiting large quadrupolar coupling combined with anisotropic chemical shielding interactions. Sensitivity enhancements by a factor of up to about 30 are observed for the samples studied.

Detection of Second-Order Director Fluctuations by Deuteron Spin-Spin Relaxation at a Standard High Field

We report on the measurements of deuteron spin-spin relaxation time T 2 in the nematic phase of MBBA and 5CB using the quadrupolar echo pulse train in a magnetic field of 7 T. The spectral densities J 0 (i) (0) at different carbon sites were derived from the T 2 and T 1 measurements. Using a model that combined rotational diffusion motion of individual molecules and their internal bond rotations, the spectral densities J 1 (i)(ω0) and J 2 (i)(2ω0) could be interpreted, while the measured J 0 (i)(0) were too large. It is argued that second-order director fluctuations contribute in part to the J 0 (i)(0) spectral densities. Thus T 2 measurements at a standard high magnetic field can be used to gain insights on director fluctuations.

Dynamic Properties of Cyclohexane Guest Molecules Constrained within the Zeolite H-ZSM-5 Host Structure: A Wide-Line Solid State 2H NMR Investigation

Dynamic properties of perdeuterated cyclohexane (C6D12) molecules included within the zeolite H-ZSM-5 host structure have been studied by variable-temperature wide-line solid-state 2H NMR spectroscopy. Three types of rapid motion have been identified for the C6D12 molecules in the temperature range 93−233 K as follows: motion A, rapid reorientation about the C3 symmetry axis of the C6D12 molecule; motion B, rapid restricted wobbling of the C3 symmetry axis, described as precession of the C3 symmetry axis on the surface of a cone (the half angle of which increases with increasing temperature); motion C, a rapid four-site jump motion, the geometry of which is dictated by the orientations of the tunnel axes at the intersection between the zigzag and straight tunnels of the H-ZSM-5 host structure. The temperature dependence of the quadrupole echo 2H NMR line shape in the temperature range 263−368 K is interpreted in terms of cyclohexane ring inversion occurring in the intermediate motion regime, in addition to motions A−C, which are in the rapid motion regime. From the 2H NMR line shape analysis, the activation energy for the cyclohexane ring inversion process is estimated to be ca. 48 kJ mol-1. The dynamic properties are compared with those of cyclohexane in other solid host structures, and the constraints imposed by the H-ZSM-5 host structure on the dynamic properties of the cyclohexane guest molecules are assessed.

Theoretical and experimental study of quadrupolar echoes in solid state NMR

Theoretical explanations are offered for the creation of echo, anti-echo and transient signals observed in solid state NMR of quadrupolar nuclei, based on density matrix calculations and using concepts in agreement with the definition of coherence transfer pathways. From these calculations, taking into account all interactions (except homogeneous dipolar) the correct experimental conditions are deduced for the avoidance of spectral distortions. This theory and the experimental requirements have been verified on a test compound (Na2SO4) which yields echo spectra similar to idealized ‘perfect’ pulse spectra.