Molecular dynamics of half-integer quadrupolar nuclei studied by QCPMG solid-state NMR experiments on static and rotating samples. Theory and simulations

Simulations of QCPMG NMR type experiments have been used to explore dynamic processes of half-integer quadrupolar nuclei in solids. By setting up a theoretical approach that is well suited for efficient numerical simulations the QCPMG type experiments have been analyzed regarding the effect of the magnitude of the EFG- and CSA-tensors, the spin-quantum number, different dynamical processes and MAS. Compared to the QE experiment the QCPMG experiment offers not only intensity gain by an order of magnitude and changes in overall lineshape as a function of the kinetic rate constant but the lineshape of the individual spin-echo sidebands is also very sensitive towards dynamics. Hereby a visual identification of the dynamics is obtained. In common for all the simulations the spin-echo sidebands are narrow in the slow (k< or =10(2) Hz) and the fast (k> or =10(7) Hz) dynamic regime whereas they are broadened in the intermediate regime 10(3)< or =k< or =10(7) Hz. The maximum intensity of the spin-echo sidebands for two-site jumps is highly dependent on the type of anisotropic interactions involved and the type of QCPMG experiment. Hence, in the fast limit the maximum intensity was 140% of the initial intensity when significant CSA was present or under the QCPMG-MAS experiment compared to 89 or 71% for the static experiment influenced by the quadrupolar interaction only. For 3-, 4-, and 6-site jumps the maximum intensity in the fast limit reached up to 339% of the intensity in the static limit.     

Adsorption of Na onto γ-alumina studied by solid-state Na and Al nuclear magnetic resonance spectroscopy

The adsorption of Na⁺ on γ-alumina surfaces at four coverages of Na₂CO₃ [5, 10, 15 and 20% (w/w)] was characterized by solid-state ²³Na and ²⁷Al nuclear magnetic resonance (NMR) spectroscopy. The experimental results suggest that two distinct adsorbed species are present on the alumina surface: surface species and surface salts. At the lower coverages of Na₂CO₃ (5 and 10%), the surface species is predominant, in which the Na⁺ cations are associated with the oxygen atoms of γ-alumina. Increasing the loading level to 15% results in the appearance of a second adsorbed species that is attributed to the surface salt, Na₂CO₃, deposited on the solid surface. Further adsorption of Na₂CO₃ leads to an increase in the amount of surface salt while the amount of surface species remains unchanged. ¹H---²⁷Al Cross-polarization magic angle spinning (CP-MAS) experiments give the evidence that some Na⁺ cations in the form of surface species are coordinated with the Brönsted acid sites of γ-alumina. This may be the main driving force that improves appreciably the catalytic efficiency of an Na₂CO₃---Al₂O₃ catalyst.     

Al nuclear magnetic resonance study of synthetic and natural corundum (α-Al2O3) Some experimental aspects of quantitative Al nuclear magnetic resonance spectroscopy

The ²⁷Al nuclear magnetic resonance (NMR) response of a series of natural and synthetic corundum (α-Al₂O₃) samples is studied quantitatively by short-pulse excitation and frequency-stepped adiabatic half-passage (FSAHP). Using on- and off-resonance nutation NMR, it was established that the quadrupole coupling parameters of visible Al is identical in all samples. Remarkably, the relaxation behavior for the aluminum is very different in the various samples and has a marked effect on the quantitative response. In natural corundum samples the ²⁷Al spin-lattice relaxation is very efficient as these samples contain paramagnetic impurities. As a result, however, the full signal could not be recovered, which is attributed to relaxation broadening of spins in the vicinity of these impurities. In synthetic samples, containing no impurities, the full signal could be recovered, although the relaxation behaviour appeared to depend strongly on the preparation method. We observed differences in the spin-lattice relaxation by a factor 20; the longest T₁ was observed in a crushed single crystal. This implies that α-Al₂O₃ can only be used as a standard in quantitative analyses if it has been characterized thoroughly. Furthermore, the effective relaxation behaviour for different types of excitation is studied. Finally, a method to measure the spin-lattice relaxation of half-integer quadrupole nuclei is introduced, using a frequency-stepped adiabatic passage (FSAP) to invert the spin system.     

Derivation of extended boundary condition method from general definition of -matrix elements and Lippman–Schwinger equation for transition operator

Waterman's surface-integral expressions for the T-matrix elements are derived on the basis of the quantum-mechanical potential scattering approach in electromagnetic scattering problem. We use general definition of the elements of the T-matrix as the matrix elements of the dyadic transition operator and Lippman–Schwinger volume integral equation for the dyadic transition operator. The interrelations of the Q- and Waterman's T-matrix with the transition operator are shown.