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

Abstract

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 δ_iso and quadrupolar coupling C_Q. 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.

Keywords: DQ–SQ; MQMAS; amorphous material; disorder; high-field NMR; inhomogeneous broadening; lineshape; quadrupolar nuclei; solid-state NMR.

Figure 1

(a–c) Simulated powder lineshapes of static spectra (¹³C at 9.4 T) with 3 kHz chemical shift anisotropy (CSA) and 5 kHz dipolar coupling interactions introduced separately or together as indicated in the figures. With 5 kHz magic-angle spinning, all inhomogeneous patterns in (a–c) break up to an isotropic peak and spinning sidebands, as shown in (d). (e,f) show the suppression of dipolar coupling and CSA for a dehydrated zeolite HZSM-5 catalyst in ¹H NMR by magic-angle spinning (MAS). The spectra of (e,f) were acquired at 9.4 T, where (f) was acquired at spinning frequency of 10 kHz. Spinning sidebands are denoted in “*”.

Figure 2

¹³C CP-MAS spectra and XRD patterns showing a drug material I prepared with different degrees of disorder. A and B are both base molecules that can affect the formation of crystallinity for I. The material in crystalline (a), crystalline with site disorder (b) and amorphous (c) forms were prepared by mixing I with A or B at ratios indicated in each figure. Reprinted from Ref. [12], Copyright (2011), with permission from Elsevier.

Figure 3

The line-shape of cross peaks in 2D spectroscopy in (a) Lorentzian, (b) Gaussian and (c) mixed shapes. The spectrum in (a,b) are simulated and in (c) is a ²³Na NOESY spectrum acquired on 2 M NaCl in D₂O. (d) is acquired on the same sample as of (c) but with a shim gradient applied during the experiment. The schematic in (e) illustrates three spins located at different positions of the sample and their frequencies in the spectrum. (a–d) are reprinted from Ref. [50], Copyright (1995), with permission from Elsevier.

Figure 4

Typical types of disorder patterns illustrated by 1D MAS and 2D MAS DQ-SQ spectra in three materials, which are 1D (a) and 2D INADEQUATE (b) ³¹P NMR for N,N-bis(diphenylphosphino)-N-((S)-R-methylbenzyl)amine; 1D (c) and 2D INADEQUATE (d) ¹³C NMR for 10% carbon-13 labeled cellulose; 1D (e) and 2D dipolar-based DQ-SQ (f) ¹H NMR for dehydrated zeolite catalyst HZSM-5. (e) was acquired at 9.4 T, at 10 kHz spinning frequency. (a–d) are reprinted (adapted) with permission from Ref. [13]. Copyright (2020) American Chemical Society. (f) is reprinted (adapted) with permission from Ref. [8]. Copyright (2020) American Chemical Society.

Figure 5

Simulated powder lineshapes in spectroscopy of spin-1/2 nuclei with only CSA (left) and spin-n/2 nuclei with only quadrupolar interaction (right) at static, finite MAS and infinite MAS conditions as denoted in the figure. With infinite MAS, CSA is completely removed in the left bottom figure, however a broad quadrupolar lineshape presents in the bottom right figure due the remaining second-order quadrupolar broadening. Adapted with permission from Ref. [55]. Copyright 2002, Wiley.

Figure 6

²⁷Al MAS NMR of A9B2 (9Al₂O₃·2B₂O₃) acquired at 17.6 T showing the deconvolution of four sites (a) and, at four different fields 14, 19.6, 25 and 40 T showing field-dependent resolution enhancement (b). All four sites are completely resolved at 40 T where quadrupolar broadening is majorly removed. The peaks are also resolved in the 2D MQMAS spectrum at 19.6 T as shown in (c). (a,b) are reprinted (adapted) with permission from Ref. [22]. Copyright (2002) American Chemical Society. (c) was acquired at 19.6 T at National High Magnetic Field Laboratory (NHMFL).

Figure 7

Experimental spectra showing sheared MQMAS spectra of the six scenario lineshapes described in Table 1, with the indication of chemical shift (CS) and/or quadrupole induced shift (QIS) lines. Projections are not shown as the focus is on the lineshape analysis. The detailed information of all figures are: (a) ²⁷Al MQMAS for hydrated zeolite HZSM-5 at 14.1 T; (b) ²⁷Al MQMAS of zeolite HUSY; (c) ²⁷Al MQMAS for the same hydrated zeolite HZSM-5 in (a) but at 35.2 T; (d) ¹⁷O MQMAS for hydrated zeolite HZSM-5 at 18.8 T and (e) ²⁷Al MQMAS of CaO-Al₂O₃-SiO₂ glass at 17.6 T. (a) and (c) are reprinted (adapted) with permission from Ref. [8]. Copyright (2020) American Chemical Society. (b) is reprinted from Ref. [59], Copyright (2010), with permission from Elsevier. (d) was acquired at 18.8 T at National High Magnetic Field Laboratory. (e) is reprinted from Ref. [2], Copyright (2004), with permission from Elsevier.

Figure 8

Fittings of ⁶⁷Zn 1D MAS NMR acquired for a metal-organic framework material ZIF-62 in its crystalline (a,b) and glass (c,d) forms, at two different fields 19.6 and 35.2 T as indicated in the figure. Blue dashed lines in (a,b) are quadrupolar fitted crystalline sites and red dashed lines are the sum of the fittings. Red dashed lines in (c,d) are disorder fittings resulted from Czjzek model. (e) shows a representative Czjzek fitting for 2D MQMAS spectrum acquired for ²³Na of a disordered sodium silicate glass material. (a–d) are adapted from Ref. [1]. Reprinted with permission from AAAS. (e) is reprinted from Ref. [66], Copyright (2011), with permission from Elsevier.