scholarly journals A Practical Review of NMR Lineshapes for Spin-1/2 and Quadrupolar Nuclei in Disordered Materials

2020 ◽  
Vol 21 (16) ◽  
pp. 5666 ◽  
Author(s):  
Kuizhi Chen
Keyword(s):  
Chemical Shift ◽  
Structural Disorder ◽  
Magic Angle Spinning ◽  
Second Order ◽  
Double Quantum ◽  
Magic Angle ◽  
Quadrupolar Nuclei ◽  
Isotropic Chemical Shift ◽  
Quadrupolar Coupling ◽  
Angle Spinning

NMR is a powerful spectroscopic method that can provide information on the structural disorder in solids, complementing scattering and diffraction techniques. The structural disorder in solids can generate a dispersion of local magnetic and electric fields, resulting in a distribution of isotropic chemical shift δiso and quadrupolar coupling CQ. For spin-1/2 nuclei, the NMR linewidth and shape under high-resolution magic-angle spinning (MAS) reflects the distributions of isotropic chemical shift, providing a rich source of disorder information. For quadrupolar nuclei, the second-order quadrupolar broadening remains present even under MAS. In addition to isotropic chemical shift, structural disorder can impact the electric field gradient (EFG) and consequently the quadrupolar NMR parameters. The distributions of quadrupolar coupling and isotropic chemical shift are superimposed with the second-order quadrupolar broadening, but can be potentially characterized by MQMAS (multiple-quantum magic-angle spinning) spectroscopy. We review analyses of NMR lineshapes in 2D DQ–SQ (double-quantum single-quantum) and MQMAS spectroscopies, to provide a guide for more general lineshape analysis. In addition, methods to enhance the spectral resolution and sensitivity for quadrupolar nuclei are discussed, including NMR pulse techniques and the application of high magnetic fields. The role of magnetic field strength and its impact on the strategy of determining optimum NMR methods for disorder characterization are also discussed.

scholarly journals Residual dipolar line width in magic-angle spinning proton solid-state NMR

2021 ◽  
Vol 2 (1) ◽  
pp. 499-509
Author(s):  
Matías Chávez ◽  
Thomas Wiegand ◽  
Alexander A. Malär ◽  
Beat H. Meier ◽  
Matthias Ernst
Keyword(s):  
Chemical Shift ◽  
Line Width ◽  
Magic Angle Spinning ◽  
Spin Systems ◽  
Second Order ◽  
Magic Angle ◽  
Line Broadening ◽  
Third Order ◽  
Angle Spinning ◽  
Effective Hamiltonians

Abstract. Magic-angle spinning is routinely used to average anisotropic interactions in solid-state nuclear magnetic resonance (NMR). Due to the fact that the homonuclear dipolar Hamiltonian of a strongly coupled spin system does not commute with itself at different time points during the rotation, second-order and higher-order terms lead to a residual dipolar line broadening in the observed resonances. Additional truncation of the residual broadening due to isotropic chemical-shift differences can be observed. We analyze the residual line broadening in coupled proton spin systems based on theoretical calculations of effective Hamiltonians up to third order using Floquet theory and compare these results to numerically obtained effective Hamiltonians in small spin systems. We show that at spinning frequencies beyond 75 kHz, second-order terms dominate the residual line width, leading to a 1/ωr dependence of the second moment which we use to characterize the line width. However, chemical-shift truncation leads to a partial ωr-2 dependence of the line width which looks as if third-order effective Hamiltonian terms are contributing significantly. At slower spinning frequencies, cross terms between the chemical shift and the dipolar coupling can contribute in third-order effective Hamiltonians. We show that second-order contributions not only broaden the line, but also lead to a shift of the center of gravity of the line. Experimental data reveal such spinning-frequency-dependent line shifts in proton spectra in model substances that can be explained by line shifts induced by the second-order dipolar Hamiltonian.

scholarly journals Determination of the Full 207Pb Chemical Shift Tensor of Anglesite, PbSO4, and Correlation of the Isotropic Shift to Lead–Oxygen Distance in Natural Minerals

Crystals ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 43 ◽  
Author(s):  
Otto Zeman ◽  
Jennifer Steinadler ◽  
Rupert Hochleitner ◽  
Thomas Bräuniger
Keyword(s):  
Chemical Shift ◽  
Single Crystal ◽  
Polycrystalline Sample ◽  
Magic Angle Spinning ◽  
Magic Angle ◽  
Isotropic Chemical Shift ◽  
Natural Minerals ◽  
Angle Spinning ◽  
Data Acquisition And Processing

The full 207 Pb chemical shift (CS) tensor of lead in the mineral anglesite, PbSO 4 , was determined from orientation-dependent nuclear magnetic resonance (NMR) spectra of a large natural single crystal, using a global fit over two rotation patterns. The resulting tensor is characterised by the reduced anisotropy Δ δ = ( - 327 ± 4 ) ppm, asymmetry η C S = 0 . 529 ± 0 . 002 , and δ i s o = ( - 3615 ± 3 ) ppm, with the isotropic chemical shift δ i s o also verified by magic-angle spinning NMR on a polycrystalline sample. The initially unknown orientation of the mounted single crystal was included in the global data fit as well, thus obtaining it from NMR data only. By use of internal crystal symmetries, the amount of data acquisition and processing for determination of the CS tensor and crystal orientation was reduced. Furthermore, a linear correlation between the 207 Pb isotropic chemical shift and the shortest Pb–O distance in the co-ordination sphere of Pb 2 + solely surrounded by oxygen has been established for a large database of lead-bearing natural minerals.

scholarly journals Efficient polynomial analysis of magic-angle spinning sidebands and application to order parameter determination in anisotropic samples

2021 ◽  
Vol 2 (2) ◽  
pp. 589-606
Author(s):  
Günter Hempel ◽  
Paul Sotta ◽  
Didier R. Long ◽  
Kay Saalwächter
Keyword(s):  
Chemical Shift ◽  
Magic Angle Spinning ◽  
Parameter Determination ◽  
Magic Angle ◽  
Chemical Shift Tensors ◽  
Line Shapes ◽  
Fitting Procedure ◽  
The Common ◽  
Angle Spinning

Abstract. Chemical shift tensors in 13C solid-state NMR provide valuable localized information on the chemical bonding environment in organic matter, and deviations from isotropic static-limit powder line shapes sensitively encode dynamic-averaging or orientation effects. Studies in 13C natural abundance require magic-angle spinning (MAS), where the analysis must thus focus on spinning sidebands. We propose an alternative fitting procedure for spinning sidebands based upon a polynomial expansion that is more efficient than the common numerical solution of the powder average. The approach plays out its advantages in the determination of CST (chemical-shift tensor) principal values from spinning-sideband intensities and order parameters in non-isotropic samples, which is here illustrated with the example of stretched glassy polycarbonate.

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