CP/MAS of quadrupolar S = 3/2 nuclei.

The spin dynamics of Hartmann-Hahn cross-polarization from I = 1/2 to quadrupolar S = 3/2 nuclei is investigated. A density-matrix model applicable to cases where the quadrupole frequency vQ is much larger than the rf amplitude v1S of the S spins, predicts the time development of the spin state of an isolated I, S spin pair in static situations and in three distinct cases of magic-angle-spinning speed vR. These cases are characterized as slow, intermediate, and fast, depending on the magnitude of the parameter alpha = v1S2/vQvR relative to the intermediate value of 0.4. The model predictions are supported by numerical simulations. The polarization transfer from I to S is efficient in the limits of slow and fast sample spinning. When alpha < 1, the Hartmann-Hahn condition is shifted over once or twice vR. When the spinning rate is intermediate, poor spin-locking of the quadrupolar spins prevents the accumulation of a cross-polarization signal and, in addition, depletes the spin-locked I magnetization. Experimental CP/MAS data obtained in NaOH show that the concepts developed for isolated spin pairs are also applicable to cross-polarization in a strongly coupled multi-spin system.     

Pulse FT NMR of non-equilibrium states of half-integer spin quadrupolar nuclei in single crystals

For quadrupolar nuclei with spin quantum numbers equal to 3/2, 5/2 and 7/2, the intensities of the NMR transitions in a single crystal are examined as a function of the rf excitation flip angle. Single-quantum NMR intensities are calculated using density matrix theory beginning under various non-equilibrium conditions and are compared with those determined experimentally. As a representative spin-3/2 system, the flip-angle dependence of the ²³Na NMR intensities of a single crystal of NaNO₃ was investigated beginning with the inversion of the populations associated with one of the satellite transitions. Subsequently, the populations of both satellite transitions were inverted using highly frequency-selective hyperbolic secant pulses. Calculated and experimental intensities are in good agreement. As an example of a spin-5/2 system, the flip-angle dependence of the ²⁷Al NMR transition intensities was determined using a single crystal of sapphire, Al₂O₃, starting under different nuclear spin population conditions. The experimental trends mimicked those predicted by the density matrix calculations but the agreement was not as good as for the spin-3/2 case. Some SIMPSON simulations were also carried out to confirm the results generated by our density matrix calculations. The theoretical flip-angle behavior of the NMR transition intensities obtained from a spin-7/2 spin system is also discussed.     

Critical factors in obtaining meaningful fast MAS NMR spectra of non-integral spin quadrupolar nuclei. A review with particular emphasis on27Al MAS NMR of catalysts and minerals

In the last decade, magic angle spinning (MAS) NMR has become an extremely important method for studying the structure of inorganic solids. Advances in NMR technology have greatly aided in understanding the structure of catalysts, minerals, clays, ceramics, glasses, etc. Obtaining meaningful MAS spectra of spin-1/2 nuclei such as²⁹Si and³¹P is relatively straightforward and well understood. In contrast, obtaining meaningful MAS spectra is far from simple with non-integral spin quadrupolar nuclei such as¹¹B (I=3/2),¹⁷O (I=5/2),²³Na (I=3/2),²⁷Al (I=5/2),⁶⁹Ga (I=3/2), and⁷¹Ga (I=3/2)?to name some of the most commonly studied nuclei. Many additional factors have to be considered. This paper will deal with these factors and the utility of very fast MAS for studying non-integral spin quadrupolar nuclei in inorganic solids.     

Geometry of kinked protein helices from NMR data

Residual dipolar couplings between spin-1/2 and quadrupolar nuclei are often observed and exploited in the magic-angle spinning (MAS) NMR spectra of spin-1/2 nuclei. These orientation-dependent splittings contain information on the dipolar interaction, which can be translated into structural information. The same type of splittings may also be observed for pairs of quadrupolar nuclei, although information is often difficult to extract from the quadrupolar-broadened lineshapes. Here, the complete theory for describing the dipolar coupling between two quadrupolar nuclei in the frequency domain by Hamiltonian diagonalization is given. The theory is developed under MAS and double-rotation (DOR) conditions, and is valid for any spin quantum numbers, quadrupolar coupling constants, asymmetry parameters, and tensor orientations at both nuclei. All terms in the dipolar Hamiltonian become partially secular and contribute to the NMR spectrum. The theory is validated using experimental 11B and 35/37Cl NMR experiments carried out on powdered B-chlorocatecholborane, where both MAS and DOR are used to help separate effects of the quadrupolar interaction from those of the dipolar interaction. It is shown that the lineshapes are sensitive to the quadrupolar coupling constant of both nuclei and to the J coupling (including its sign). From these experiments, the dipolar coupling constant for a heteronuclear spin pair of quadrupolar nuclei may be obtained as well as the sign of the quadrupolar coupling constant of the perturbing nucleus; these are two parameters that are difficult to obtain experimentally otherwise.     

~(13)C CP/MAS OF MOTIONS IN SOLID POLYMERS

High-resolution 13C spectra of solid polymers are often acquired with cross polarization with magic angle spinning (CP/MAS) to take advantage of the abunda ntly available protons in the polymer chains. The sequence for transferring mag netization from 1H to13C using Hartmann-Hahn spin locking in the rotating frame is now a standard in commercial solidstate NMR spectrometers.     

PRISE THE SECRET OF HETEROGENEITY OUT OF BIOPOLYMER SYSTEMS

High-resolution 13C spectra of solid polymers are often acquired with cross polarization with magic angle spinning (CP/MAS) to take advantage of the abunda ntly available protons in the polymer chains. The sequence for transferring mag netization from 1H to13C using Hartmann-Hahn spin locking in the rotating frame is now a standard in commercial solidstate NMR spectrometers.     

Single- and multiple-quantum cross-polarization in NMR of quadrupolar nuclei in static samples

Cross-polarization from a spin I=1/2 nucleus (e.g., ¹H) to a spin S = 3/2 nucleus (e.g., ²³Na) or a spin S = 5/2 nucleus (e.g., ²⁷A1 or ⁿO) in static powder samples is investigated. The results of conventional (single-quantum), three-quantum, and five-quantum cross-polarization experiments are presented and discussed. Based on a generalization of an existing theory of cross-polarization to quadrupolar nuclei, computer simulations are used to model the intensity and lineshape variations observed in cross-polarized NMR spectra as a function of the radio-frequency field strengths of the two simultaneous spin-locking pulses. These intensity and lineshape variations can also be understood in terms of the spin S = 3/2 or 5/2 nutation rates determined from experimental quadrupolar nutation spectra. The results of this study are intended as a preliminary step towards understanding single- and multiple-quantum cross-polarization to quadrupolar nuclei under MAS conditions and the application of these techniques to the MQMAS NMR experiment.     

Electron-nuclear cross polarization

We describe the coherent polarization transfer from an unpaired electron to neighboring nuclei via electron-nuclear cross polarization (eNCP) in a doubly, tilted rotating frame. Although the experiment superficially resembles the well-known Hartmann-Hahn cross polarization (CP) process introduced by Pines et al., that is widely used in solid-state nuclear magnetic resonance (SSNMR), it differs in significant respects. In particular, eNCP requires an alternative treatment due to the very different sizes of the specific terms in the spin Hamiltonian. We derive analytical expressions for the matching condition for optimal polarization transfer and verify their correctness with experimental results obtained with electron detected CP experiments performed on powder samples of BDPA radical dispersed in a protonated polystyrene matrix and with numerical simulations. We use fully protonated BDPA as an example of polarization transfer to strongly coupled nuclei. In contrast, perdeuterated BDPA serves as an example of the transfer of polarization from electrons to weakly coupled nuclei. In addition, we performed CP on a paramagnetic crystal to determine the influence of resolved hyperfine structure on the CP process. It is shown that almost no structure is observed in the corresponding electron-(1)H CP matching curve. It appears that only a restricted number of hyperfine coupled (1)H's contribute to the observed signal intensities in the CP experiment.     

CP MAS Kinetics Study of Ionic Liquids Confined in Mesoporous Silica: Convergence of Non-Classical and Classical Spin Coupling Models

The high data point density measurements of ¹H→¹¹B cross-polarization (CP) kinetics upon magic-angle spinning (MAS) of [bmim][BF₄] confined in mesoporous SBA-15 and MCM-41 were carried out. The complex shaped ¹¹B CP MAS signals were observed in both silica and decomposed into two Lorentz components. This points towards the possibility of bimodal distribution of [bmim][BF₄] in the studied confinements. The convergence of classical and non-classical spin coupling models was deduced processing CP kinetic curves. A good fit of the theoretical curves to the experimental data was achieved using both models without any non-random deviations between theory and experiment to appear. The convergence of spin coupling models was discussed in terms of relatively high mobility of BF₄ ^? anion respect to the cation and the dynamics of anions in pores. These factors delete the borders between spin clusters. The spin diffusion along the pore surfaces in MCM-41 is more than twice faster than in SBA-15.     

General formulae for $f_1 \to f_2 \gamma$

At one-loop level the decay , where f₁ and f₂ are two spin-1/2 particles with the same electric charge, is mediated by a boson B and a spin-1/2 fermion F. The boson B may have either spin - interacting with the fermions through the Dirac matrices 1 and - or spin 1 - with V+A and V-A couplings to the fermions. I give general formulae for the one-loop electroweak amplitude of in all these cases. Received: 24 February 2003 / Revised version: 26 March 2003 / Published online: 2 June 2003     

Efficient Time Propagation Technique for MAS NMR Simulation: Application to Quadrupolar Nuclei

The quantum mechanical Floquet theory is investigated in order to derive an efficient way of performing numerical calculations of the dynamics of nuclear spin systems in MAS NMR experiments. Here, we take advantage of time domain integration of the quantum evolution over one period as proposed by Edenet al.(1). But a full investigation of the propagatorU(t,t₀), and especially its dependence with respect totandt₀within a formalized approach, leads to further simplifications and to a substantial reduction in computation time when performing powder averaging for any complex sequence. Such an approximation is suitable for quadrupolar nuclei (I> 1/2) and can be applied to the simulation of the RIACT (rotational induced adiabatic coherence transfer) phenomenon that occurs under special experimental conditions in spin locking experiments (2–4). The present method is also compared to the usual infinite dimensional Floquet space approach (5, 6), which is shown to be rather inefficient. As far as we know, it has never been reported for quadrupolar nuclei withI≥ 3/2 in spin locking experiments. The method can also be easily extended to other areas of spectroscopy.     

<Emphasis Type="Italic">CPT</Emphasis> Groups of Higher Spin Fields

CPT groups of higher spin fields are defined in the framework of automorphism groups of Clifford algebras associated with the complex representations of the proper orthochronous Lorentz group. Higher spin fields are understood as the fields on the Poincaré group which describe orientable (extended) objects. A general method for construction of CPT groups of the fields of any spin is given. CPT groups of the fields of spin-1/2, spin-1 and spin-3/2 are considered in detail. CPT groups of the fields of tensor type are discussed. It is shown that tensor fields correspond to particles of the same spin with different masses.     

Technical aspects of fast magic-angle turning NMR for dilute spin-1/2 nuclei with broad spectra

For obtaining sideband-free spectra of high-Z spin-1/2 nuclei with large (>1000 ppm) chemical-shift anisotropies and broad isotropic-shift dispersion, we recently identified Gan's modified five-pulse magic-angle turning (MAT) experiment as the best available broadband pulse sequence, and adapted it to fast magic-angle spinning. Here, we discuss technical aspects such as pulse timings that compensate for off-resonance effects and are suitable for large CSAs over a range of 1.8γB₁; methods to minimize the duration of z-periods by cyclic decrementation; shearing without digitization artifacts, by sharing between channels (points); and maximizing the sensitivity by echo-matched full-Gaussian filtering. The method is demonstrated on a model sample of mixed amino acids and its large bandwidth is highlighted by comparison with the multiple-π-pulse PASS technique. Applications to various tellurides are shown; these include GeTe, Sb₂Te₃ and Ag_0.53Pb₁₈Sb_1.2Te₂₀, with spectra spanning up to 190 kHz, at 22 kHz MAS. We have also determined the ¹²⁵Te chemical shift anisotropies from the intensities of the spinning sidebands resolved by isotropic-shift separation.     

Nuclear magnetic double resonance for a spin system subject to scalar relaxation of the second kind

The equation of motion of a reduced spin density operator characterizing the state of a group of spins scalar coupled to a second group of spins which are either relaxing rapidly and/or irradiated with a strong radiofrequency field is derived within the framework of the non-viscous liquid approximation. An analytic expression for the spectral densities entering this equation is derived within the extreme narrowing approximation for the case in which the relaxation rates of the nuclei in the second group of spins are much greater than any scalar couplings between them. The resultant equation is used to discuss the conditions needed in a high resolution nuclear magnetic double resonance experiment to decouple a spin-½ nucleus (A) from a rapidly relaxing quadrupolar nucleus (X) in the fast relaxation limit, defined by |2πJ_AX T _1X | ? 1, in which the A resonance consists of a single broadened line. It is found that, if (ω _A - ω _X )² ? T _1X ^-2 so that the x and y components of the J_AX coupling can be neglected, decoupling, in the sense that all broadening of the A resonance is removed, occurs only when the strength of the B ₂ field be such that γ _X ² B ₂ ² ? T _1X ^-2 and that the conventional decoupling criterion γ _X ² B ₂ ² ? 4π² J_AX ² is not applicable. However, if the x and y components of the A-X scalar coupling cannot be neglected because the condition (ω _A - ω _X )² ? T _1X ^-2 is not satisfied, it is found that the X spin can never be entirely decoupled. It is shown that such double resonance experiments enable both the coupling constants between spin-½ and quadrupolar nuclei and the relaxation times of the latter nuclei to be extracted in situations in which measurement of the half-widths of spin-1/2 transitions can only yield the product J_AX ² T _1X in the absence of irradiation of the quadrupolar nuclei.     

Sensitivity enhancement of the central-transition signal of half-integer spin quadrupolar nuclei in solid-state NMR: features of multiple fast amplitude-modulated pulse transfer

Sensitivity enhancement of solid-state NMR spectrum of half-integer spin quadrupolar nuclei under both magic-angle spinning (MAS) and static cases has been demonstrated by transferring polarisation associated with satellite transitions to the central m=-1/2-->1/2 transition with suitably modulated radio-frequency pulse schemes. It has been shown that after the application of such enhancement schemes, there still remains polarisation in the satellite transitions that can be transferred to the central transition. This polarisation is available without having to wait for the spin system to return to thermal equilibrium. We demonstrate here the additional sensitivity enhancement obtained by making use of this remaining polarisation with fast amplitude-modulated (FAM) pulse schemes under both MAS and static conditions on a spin-3/2 and a spin-5/2 system. Considerable signal enhancement is obtained with the application of the multiple FAM sequence, denoted as m-FAM. We also report here some of the salient features of these multiple FAM sequences with respect to the nutation frequency of the pulses and the spinning frequency.     

Study on ethyl groups with two different orientations in [N(C2H5)4]2CuBr4

The crystal structure and phase transition temperature of [N(C₂H₅)₄]₂CuBr₄ are studied using X-ray diffraction and differential scanning calorimetry (DSC); measurements revealed a tetragonal structure and the two phase transition temperatures T_C of 204 K and 255.5 K. The structural geometry near T_C is discussed in terms of the chemical shifts for ¹H magic angle spinning (MAS) nuclear magnetic resonance (NMR) and ¹³C cross-polarization (CP)/MAS NMR. The two inequivalent ethyl groups are distinguishable by the ¹³C NMR spectrum. The molecular motions are discussed in terms of the spin–lattice relaxation times T_1ρ in the rotating frame for ¹H MAS NMR and ¹³C CP/MAS NMR. The T_1ρ results reveal that the ethyl groups undergo tumbling motion, and furthermore that the ethyl groups are highly mobile.     

An experimental study of cross polarization from1H to27Al in crystalline and amorphous materials

The conditions for successful¹H?²⁷Al cross polarization experiments have been investigated. It was found that boehmite was a good material for setting up the Hartmann-Hahn match condition, and both tetrahedral and octahedral aluminium was observed in a variety of environments. The contact time dependence of the CP signal was studied for several samples and simulations showed thatT _IS could be estimated and hence information on mean¹H?²⁷Al distances in glasses deduced. CP signals could be obtained even ifT _1? ^Al is much less thanT _IS, contrary to some previous suggestions. MAS reduces both the size of the CP signal and the optimum contact time and to maintain signal strength spinning should be as slow as possible.     

Mixed spin transverse Ising model with longitudinal random crystal field interactions

The effect of a longitudinal random crystal field interaction on the phase diagrams of the mixed spin transverse Ising model consisting of spin-1/2 and spin-1 is investigated within the finite cluster approximation based on a single-site cluster theory. In order to expand a cluster identity of spin-1, we transform the spin-1 to spin-1/2 representation containing Pauli operators. We derive the state equations applicable to structures with arbitrary coordination number N. The phase diagrams obtained in the case of a honeycomb lattice (N=3) and a simple-cubic lattice (N=6), are qualitatively different and examined in detail. We find that both systems exhibit a variety of interesting features resulting from the fluctuation of the crystal field interactions. Received: 13 February 1998 / Accepted: 17 March 1998