Dynamic Angle Spinning Research Articles

Construction of a quantum Stirling engine cycle tuned by dynamic-angle spinning

In this contribution, we investigate two coupled spins as a working substance of the quantum Stirling heat engine cycle. We propose an experimentally implementable scheme in which the cycle is driven by tuning the dipole-dipole interaction angle via a dynamic-angle spinning technique under a magnetic field. Realistic parameters are chosen for the proposed heat engine cycle. In addition, our goal is to calculate the power of the engine. To this end, we focus on the microdynamics of the quantum isothermal process to predict the required-time per engine cycle. The obtained results show that the engine has high efficiency. Furthermore, the engine attains maximum power at the same point where the maximum efficiency is satisfied.

Pneumatic angle adjustment for magic angle spinning spherical rotors

Precise alignment of the sample's spinning axis is vital for many magic angle spinning solid state NMR experiments. Spherical rotors are a new paradigm for magic angle spinning NMR, having been demonstrated to spin stably with little risk of rotor crash, but like cylindrical rotors, they have previously only utilized a mechanical adjustment method to set the sample's rotation axis to the magic angle. Here we show that by using a second gas aperture within the stator, a spherical rotor's axis of rotation may be precisely pitched about the magic angle without mechanical adjustment or motion of the stator. The 2H MAS sideband lineshape of the carboxylic acid deuteron resonance in d4-malonic acid is used as a measure of the rotor's absolute deviation above or below the magic angle by comparing the experimental data to simulated lineshapes. We observe a linear, monotonic relationship between the angle adjustment gas flow rate and the rotor's pitch angle, which is also accompanied by an increase in spinning rate. Precise and in operando control of the spinning axis angle is expected to have considerable advantages to future implementation of MAS within narrow-bore magnets, and for variable angle spinning (VAS) and dynamic angle spinning (DAS) experiments.

Correction to “Directly vs Indirectly Enhanced 13C in Dynamic Nuclear Polarization Magic Angle Spinning NMR Experiments of Nonionic Surfactant Systems”

Correction to “Directly vs Indirectly Enhanced ¹³C in Dynamic Nuclear Polarization Magic Angle Spinning NMR Experiments of Nonionic Surfactant Systems”

ChemInform Abstract: Spatial Reorientation Experiments for NMR of Solids and Partially Oriented Liquids

AbstractReview: 290 refs.

Dynamic-angle spinning of quadrupolar nuclei

In dynamic-angle spinning (DAS), a sample spins around an axis inclined at an angle θ ( t ) with respect to the magnetic field such that the averages of P n ( cos θ ) are zero. The simplest case is where θ ( t ) assumes two discrete values θ 1 and θ 2 (complementary DAS angles) such that the averages of P 2 ( cos θ ) and P 4 ( cos θ ) are zero, thereby removing second-order quadrupolar (and dipolar) broadening. Examples of DAS complementary angles are θ 1 = 37.38 ° and θ 2 = 79.18 ° . Experimental details for DAS experiments are provided and applications to sodium-23 and oxygen-17 NMR illustrate the enhanced resolution achieved by removing the second-order broadening inherent in magic-angle spinning.

Homonuclear correlation experiments for quadrupolar nuclei, spinning away from the magic angle

We present a set of homonuclear correlation experiments for half-integer quadrupolar spins in solids. In all these exchange-type experiments, the dipolar interaction is retained during the mixing time by spinning the sample at angles other than the “regular magic angle” (54.7°). The second-order quadrupolar interaction is averaged by different strategies for the different experiments. The multiple-quantum off magic angle spinning (MQOMAS) exchange experiment is essentially a regular MQMAS experiment where the quadrupolar interaction is averaged by combining magic angle spinning with a multiple- to single-quantum correlation scheme. The sample is spun at the magic angle at all times except during the mixing time which is added to establish homonuclear correlation. In the multiple-quantum P 4 magic angle spinning (MQ P 4MAS) exchange experiment, the sample is spun at one of the angles at which the fourth-order Legendre polynomial vanishes ( P 4 magic angle), the remaining second-order quadrupolar interaction now governed by a second-rank tensor is refocussed by the multiple to single-quantum correlation scheme. In the dynamic angle spinning (DAS) exchange experiment, the second-order quadrupolar interaction is averaged by correlating the evolution from two complementary angles. These experiments are demonstrated and compared, in view of their specific advantages and disadvantages, for 23 Na in the model compound Na 2SO 3.

Solid‐State NMR Spectroscopic Methods in Chemistry.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Relative Orientation of Quadrupole Tensors from High-Resolution NMR of Powdered Solids

Techniques such as dynamic-angle spinning (DAS), double rotation (DOR), multiple-quantum MAS (MQMAS), and satellite-transition MAS (STMAS) may be used to obtain high-resolution NMR spectra of half-integer quadrupolar nuclei in powdered solids. These methods enable resolution of crystallographically inequivalent nuclei and also yield the quadrupolar coupling constant CQ, quadrupolar asymmetry η, and isotropic chemical shift δCS of each crystallographic site. However, no information is obtained that relates one quadrupole tensor to another, such as internuclear distances or relative orientations. Here, we discuss a recently developed modification of the MQMAS NMR experiment that utilizes two-dimensional correlation of second-order (rank l = 4) broadened MAS line shapes to obtain the relative orientation of quadrupole tensors. This new method involves the insertion of a “mixing time”, τm, into the MQMAS experiment such that magnetization transfer between two distinct nuclei within a crystallite during this period will result in a two-dimensional “cross-peak” correlating the two line shapes. The shapes of these cross-peaks are characteristic of the three Euler angles, α‘, β‘, and γ‘, that describe the relative orientation of the two quadrupole tensors. In this work we use the example of 23Na (I = 3/2) NMR of borax (Na2B4O7·10H2O) to discuss in more detail the nature of the magnetization transfer. We also derive an analytical expression for the rank l = 4 orientational dependence of the second-order quadrupolar interaction in terms of the relative orientation of two quadrupole tensors and simulate the effect upon the shape of the cross-peak when the angles α‘, β‘, and γ‘ are changed. Finally, the use of this novel technique is demonstrated in a 23Na NMR study of sodium metasilicate pentahydrate (Na2SiO3·5H2O) and in a comparative 23Na NMR study of sodium tungstate dihydrate (Na2WO4·2H2O) and sodium molybdate dihydrate (Na2MoO4·2H2O).

Solid-state NMR spectroscopic methods in chemistry.

Over the last decades, NMR spectroscopy has grown into an indispensable tool for chemical analysis, structure determination, and the study of dynamics in organic, inorganic, and biological systems. It is commonly used for a wide range of applications from the characterization of synthetic products to the study of molecular structures of systems such as catalysts, polymers, and proteins. Although most NMR experiments are performed on liquid-state samples, solid-state NMR is rapidly emerging as a powerful method for the study of solid samples and materials. This Review outlines some of the developments of solid-state NMR spectroscopy, including techniques such as cross-polarization, magic-angle spinning, multiple-pulse sequences, homo- and heteronuclear decoupling and recoupling techniques, multiple-quantum spectroscopy, and dynamic angle spinning, as well as their applications to structure determination. Modern solid-state NMR spectroscopic techniques not only produce spectra with a resolution close to that of liquid-state spectra, but also capitalize on anisotropic interactions, which are often unavailable for liquid samples. With this background, the future of solid-state NMR spectroscopy in chemistry appears to be promising, indeed.

Satellite-Transition MAS NMR of Spin I=3/2, 5/2, 7/2, and 9/2 Nuclei: Sensitivity, Resolution, and Practical Implementation

The satellite-transition MAS (STMAS) experiment offers an alternative approach to established methods such as dynamic angle spinning (DAS), double rotation (DOR), and multiple-quantum MAS (MQMAS) for obtaining high-resolution NMR spectra of half-integer quadrupolar nuclei. Unlike the multiple-quantum experiment, STMAS involves two-dimensional correlation of purely single-quantum coherences; satellite transitions in t 1 (or F 1) and the central transition in t 2 (or F 2). To date, STMAS has primarily been demonstrated for nuclei with spin quantum numbers I=3/2 and, to a lesser extent, I>5/2. However, many chemically relevant nuclei possess I>3/2, such as 17O and 27Al (both I=5/2), 59Co ( I=7/2), and 93Nb ( I=9/2). Here, we discuss the application of STMAS to nuclei with spin quantum numbers from I=3/2 to 9/2. First, we consider the practical implementation of the STMAS experiment using 87Rb ( I=3/2) NMR as an example. We then extend the discussion to include nuclei with higher spin quantum numbers, demonstrating 27Al, 45Sc ( I=7/2), 59Co, and 93Nb STMAS experiments on both crystalline and amorphous samples. We also consider the possibility of experiments involving satellite transitions other than m I =±1/2↔±3/2 and, using 93Nb NMR, demonstrate the correlation of all single-quantum satellite transitions up to and including m I =±7/2↔±9/2. The absolute chemical shift scaling factors in these experiments are discussed, as are the implications for isotropic resolution.

Oxygen sites in silicate glasses: a new view from oxygen-17 NMR

Nuclear Magnetic Resonance (NMR) studies of 17O in silicate glasses is beginning to provide new information on structure from an “anionic” viewpoint, which is an important complement to more traditional discussions of cation coordination and connectivities. A variety of techniques are discussed here, but the most important recent advances have used the new, two-dimensional, high resolution techniques of Dynamic Angle Spinning (DAS) and Triple Quantum Magic Angle Spinning (3QMAS), which have resolved and distinguished peaks for bridging oxygens linking Si, Al and B cations, as well as non-bridging oxygens. These approaches have provided some of the first quantitative constraints on the extent of ordering, both among network modifier cations and among network former cations.

Niobium-93 MQMAS NMR Spectroscopic Study of Alkali and Lead Niobates

93Nb (I=9/2) multiple-quantum magic-angle spinning (MQMAS) NMR spectra of a series of inorganic niobates have been measured. 93Nb MQMAS spectroscopy yields spectra with typically an order of magnitude higher resolution than that obtainable with 93Nb MAS spectroscopy and 93Nb dynamic-angle spinning (DAS) spectroscopy. For example, the full-width at half-maximums of the 93Nb resonances of LiNbO3 were 9 (MAS), 5.8 (DAS), and 0.7 kHz (MQMAS). Broadening of the 93Nb MAS and DAS spectra is due to the second-order quadrupolar and homonuclear dipolar interactions, respectively. The quadrupolar products (PQ) and isotropic chemical shifts (δiso) of the 93Nb resonances of LiNbO3, NaNbO3, PbNb2O6, Pb2Nb2O7, Pb3Nb2O8, Pb5Nb4O15, Pb3Nb4O13, and Pb1.83Nb1.71Mg0.29O6.39 were determined from MQMAS spectra and range from 13.6 to 26.8 MHz and from −951 to −1113 ppm, respectively. Resonances with relatively large quadrupolar coupling constants (>30 MHz) were not observed using MQMAS spectroscopy, but were detected using nutation spectroscopy. The applicability and limitations of MQMAS spectroscopy in studying inorganic niobates containing multiple 93Nb resonances are addressed and compared with those of MAS, nutation, and DAS spectroscopies.

Three- and five-quantum17O MAS NMR of forsterite Mg2SiO4

Three- and five-quantum 17 O MAS NMR experiments are used to resolve fully the three crystallographically distinct oxygen species in forsterite (Mg 2 SiO 4 ). The chemical shift and quadrupolar parameters extracted from these spectra are compared with the literature values obtained using conventional 17 O MAS and dynamic-angle-spinning (DAS) NMR.

A density matrix description of 14N overtone nuclear magnetic resonance in static and spinning solids

Overtone NMR is an experiment introduced by LeGros, Bloom, Tycko, and Opella, capable of providing 14N powder spectra devoid of first-order quadrupole broadenings by irradiation and observation of the nuclear spins at twice their Larmor frequency. This technique constitutes one of the most promising alternatives for the acquisition of high resolution solid 14N NMR spectra from random powders, particularly if it can be combined with strategies capable of removing the substantial second-order quadrupole broadenings remaining in the overtone line shapes. In order to facilitate the search for these averaging manipulations, we present here a theoretical description of the overtone experiment based on the time-domain propagation of density matrices. It is shown that by combining perturbation methods with appropriate rotating-frame transformations and diagonalizations, overtone spin-1 phenomena can be described using a single set of fictitious spin-1/2 operators. By contrast to conventional spin-1/2 irradiation and detection processes, however, overtone manipulations involve an unusual angular dependence on the azimuthal angle defining rotations about the main Zeeman magnetic field. This behavior introduces unexpected complications toward the narrowing of overtone resonances by conventional sample spinning techniques. Nevertheless, it can still be shown that the removal of all spin-1 anisotropies by certain forms of dynamic-angle spinning overtone NMR remains feasible.

Pictorial Representation of Anisotropy and Macroscopic Reorientations of Samples in Solid-State NMR: Second-Order Interactions

The representation of second-order broadening effects in solid-state NMR by general fourth-degree surfaces is presented. Static second-order quadrupolar and “dipolar−quadrupolar” interactions are treated in a unified way. Most experiments involving the fast reorientation of samples such as magic-angle spinning, variable-angle spinning, dynamic-angle spinning, and double-rotation and multiple-quantum magic-angle spinning are also illustrated by using averaged fourth-degree surfaces. The equations of the surfaces are derived analytically and allow the derivation of most results concerning these experiments. This article is an extension of the representation of the first-order effects by quadrics to more complex broadening effects. Multidimensional experiments will also be discussed in this frame. It can be noted that this approach is essentially Cartesian. P2(cos θ) and P4(cos θ) Legendre polynomials are not explicitly used in this work.

Cation sites in mixed-alkali phosphate glasses

Two lithium/sodium mixed-alkali phosphate glasses were investigated with solid-state two-dimensional heteronuclear correlation NMR. The systems represent two distinct families of mixed-alkali glasses, as they contain a fixed sodium-to-lithium ratio of 1:3, but different overall concentrations of cations. In both glasses, direct NMR evidence is found for the presence of multiple sodium cation environments using frequency-selective editing of two-dimensional correlation spectra. Frequency-specific subspectra were obtained by projection of 23Na resonances correlated to distinct phosphate tetrahedral environments. Dynamic-angle-spinning (DAS) NMR provides for high-resolution subspectra of quadrupolar 23Na nuclei allowing spectral separation of multiple distinct sodium environments. Identification of distinct cation sites is important for understanding the physical origin of the `mixed-alkali effect', where non-linear behavior of physical properties is observed in glasses as a function of relative cation populations.

Oxygen sites in the zeolite stilbite: a comparison of static, MAS, VAS, DAS and triple quantum MAS NMR techniques

Static, magic angle spinning (MAS), variable angle spinning (VAS), dynamic angle spinning (DAS) and triple quantum magic angle spinning (3QMAS) NMR techniques were applied to separate and quantify oxygen signals from Al–O–Si and Si–O–Si sites of 17O-enriched samples of the mineral stilbite, a natural zeolite. DAS experiments showed that there was a distribution of quadrupolar coupling constants, asymmetry parameters and isotropic chemical shifts. Two methods were used to study the quantification problem of DAS and 3QMAS. Our results showed that DAS was quantitative. In 3QMAS, signal intensity from sites with larger quadrupolar coupling constants was reduced because of less efficient excitation. All techniques have shown a clear difference in rates of exchange between the two types of sites with interchannel H 2O molecules.

Pictorial Representation of Anisotropy and Macroscopic Reorientations of Samples in Solid-State NMR: First-Order Interactions

The representation of second-order broadening effects in solid-state NMR by general fourth-degree surfaces is presented. Static second-order quadrupolar and “dipolar−quadrupolar” interactions are treated in a unified way. Most experiments involving the fast reorientation of samples such as magic-angle spinning, variable-angle spinning, dynamic-angle spinning, and double-rotation and multiple-quantum magic-angle spinning are also illustrated by using averaged fourth-degree surfaces. The equations of the surfaces are derived analytically and allow the derivation of most results concerning these experiments. This article is an extension of the representation of the first-order effects by quadrics to more complex broadening effects. Multidimensional experiments will also be discussed in this frame. It can be noted that this approach is essentially Cartesian. P2(cos θ) and P4(cos θ) Legendre polynomials are not explicitly used in this work.

Multiple-quantum magic-angle spinning and dynamic-angle spinning NMR spectroscopy of quadrupolar nuclei

Several aspects of the Multiple-Quantum Magic-Angle Spinning (MQMAS) technique (L. Frydman and J.S. Harwood, J. Am. Chem. Soc., 117 (1995) 5367) are compared with Dynamic-Angle Spinning (DAS). Examples of MQMAS spectra are shown for I = 3 2 nuclei with C Q up to 3.6 MHz, and for 27Al ( I = 5 2 ) with C Q up to 10 MHz. The MQMAS linewidth is largely independent of the magnitude of the homonuclear dipolar interaction, while the spinning sideband manifold is similar to that observed in DAS experiments. MQMAS is technically simple and routinely useful for studying nuclei with short spin-lattice relaxation times, but care must be taken in its use for quantitative studies as the excitation of the triple-quantum coherence is not uniform. In this regard, MQMAS is most useful for samples with small quadrupolar coupling constants. In the specific case of 17O, DAS would give spectra with excellent resolution in comparison to MQMAS. The different advantages of DAS and MQMAS make them useful complementary techniques in many cases. Two additional methods are also presented for extracting the chemical shift anisotropy (CSA) directly for quadrupolar nuclei using the multiple-quantum scheme.

A Comparison of Strategies for Obtaining High-Resolution NMR Spectra of Quadrupolar Nuclei

Abstract A comparison of high-resolution NMR methods for quadrupolar nuclei is presented. The samples studied are pure and modified boron oxide glasses, and the boron NMR spectra are recorded using three different experiments capable of high resolution: Double Rotation, Dynamic Angle Spinning, and Multiple-Quantum Magic Angle Spinning. Resolution of the similar ring and nonring boron sites in these glasses, in the presence of disorder, provides a realistic study of the strengths and limitations of these experiments. Conclusions about the relative applicability of these experiments in different situations are presented.