Broadband MAS NMR spectroscopy in the low-power limit
Graphical abstract
Introduction
Nuclear magnetic resonance spectroscopy (NMR) is an important technique used for structural characterization in materials science, chemistry, and biology. However, NMR studies suffer from low sensitivity due primarily to the inherently low nuclear spin polarization. This effect is particularly troublesome for nuclei with low gyromagnetic ratio and low natural abundance, such as Li, C, N, or Si, as the sensitivity scales with the electromotive force induced in the NMR coil, , which itself is proportional to :where is the gyromagnetic ratio and is the number of spins in the system. Before taking into account the number of spins present, this means that the sensitivity relative to H for Li is 5.9, and only a miniscule 0.3 for Li! Add to this the low natural abundance of Li (7.59) and considering that the signal-to-noise ratio grows only by the square root of the number of co-added transients, we see that it is obviously crucial to maximize the strength of the signal in each scan in order to collect a spectrum in a reasonable amount of time for low-abundance, low-gamma nuclei.
Furthermore, in solid-state NMR measurements, poor sensitivity and resolution are often observed due to large anisotropic interactions that severely broaden signals [1], [2]. Broadening caused by the shift anisotropy (SA) often is of the order of 10s of kHz for diamagnetic samples and 100s of kHz in the case of paramagnetic samples, while broadening due to quadrupolar interactions can be many MHz [2]. Magic-angle spinning (MAS) [3], [4] is ubiquitously used to improve sensitivity and resolution in solid-state NMR experiments by turning a broad static powder pattern into a series of narrower bands separated by the rotational frequency with intensities that are characteristic of the anisotropy experienced by the nucleus. The maximum sensitivity and resolution is achieved using the highest possible MAS rotation rate available, and in the infinite speed limit, all of the signal collapses to a single narrow band centered about the isotropic resonance frequency.
The acquisition of MAS spectra of nuclei exhibiting very broad anisotropic spinning sideband patterns is inherently challenging due primarily to limitations in the bandwidth of the pulse used and the detection bandwidth of the probe. A spin echo experiment, --, must typically be used to acquire a flat baseline, however, conventional RF pulses often have bandwidths limited to around 100 kHz using typical maximum pulse powers available in MAS probes. It is possible to overcome bandwidth issues by using a shorter refocusing pulse, for instance a or even a pulse, but this approach results in severe sensitivity losses as or pulses do not efficiently refocus coherences. Another approach to solve this issue could be the use of frequency stepping [5], [6], [7], [8] to collect multiple spectra at different frequency offsets and sum them to yield a spectrum without truncation due to pulse imperfections or limited probe bandwidth. This technique is suitable for highly abundant and sensitive spins such as H and P, however in practice it is time consuming for sensitive studies of low-, low-abundant nuclei.
A more sensitive alternative is to use broadband swept-frequency pulses for refocusing coherences exhibiting broad anisotropic spinning sideband manifolds. Many pulse shapes have been introduced to solve this problem, such as the hyperbolic secant pulse [9], the Wide, Uniform-Rate Smooth-Truncation (WURST) pulse [10], and the tanh/tan pulse [11]. These broadband pulses have many uses in a variety of magnetic resonance applications and in the case of solid-state studies, WURST pulses have been used to great effect in ultra-wideline spectroscopy [12] of static powders [13], [14], [15], and have also been used in broadband adiabatic inversion cross polarization (BRAIN-CP) experiments of static powders [16], [17].
Broadband swept-frequency pulses were not robustly applied to fast MAS ( kHz) studies of samples with very large shift anisotropies until the introduction of short high-powered adiabatic pulses (SHAPs) [18], which typically utilize the tanh/tan pulse shape with very broad frequency sweeps ( MHz, Fig. 1 left panel) and short pulse times (50 s) and RF field strengths several times the MAS rotation frequency. These pulses have been particularly successful primarily in the application to paramagnetic samples [18], [19], [20], [21], [22], [23], [24], [25] and have been incorporated into conventional MAS NMR experiments such as the spin echo [18], the Carr-Purcell-Meiboom-Gill echo train acquisition technique [26], a heteronuclear correlation variant of the transferred-echo double resonance experiment [19], and the magic angle turning experiment [20]. Indeed, these pulses have proven quite useful in broadband MAS NMR measurements, however it must be stressed that SHAPs demand very high RF fields, , falling in the so-called high-power regime, , and this relationship between MAS rate and the required RF field seems to grow at a rate that is more than linear [27]. This is due to the fact that the increased rate of modulation of the anisotropic shift during higher MAS rates necessarily cause SHAPs to require increasing RF field strengths at increasing MAS rates to maintain the adiabatic condition, and thus keep the magnetization sufficiently locked to the effective field [18]. The use of SHAPs are therefore limited to studies where suitably high RF fields can be achieved [27].
On the other hand, low-power pulses have been long used for a variety of applications, notably selective saturation [28], [29]. In order to achieve excitation, inversion, or refocusing of broad spinning sideband manifolds with low RF fields, one approach is to use DANTE pulse trains [30]; however, although this method can be used to excite broad spinning sideband manifolds, one must sacrifice bandwidth over the isotropic range of frequencies [27]. Spectra containing multiple isotropic environments are incompletely excited as a result, but it is nevertheless useful to accurately measure SA tensor information for isotropically resolved sites [30]. An alternative type of pulse that falls in the low-power regime, , and which suffers significantly less than DANTE with respect to limited isotropic bandwidth, was recently proposed for MAS measurements of spectra with broad sideband manifolds and was dubbed the single-sideband-selective adiabatic pulse (S3AP)[31]. S3APs sweep slowly through only a single sideband (. , Fig. 1 right panel) and rely on rotary resonance to invert or refocus the entire spinning sideband manifold during a long pulse (). This means that over the course of the pulse the instantaneous resonance frequency of the magnetization vector of each crystallite sweeps through the excitation window multiple times, eventually leading to inversion if the adiabatic condition is met. In this way S3APs have very low RF field requirements, and indeed have been shown in silico to demand decreasing RF fields at increasing MAS rates [27]. Using a similar principle, hyperbolic secant pulses and WURST pulses have been used to increase sensitivity for half-integer spin quadrupolar nuclei [32], [33], [34]. S3APs have been used recently in BRAIN-CP measurements under MAS conditions for integer spin [35] and half-integer spin quadrupolar nuclei [36], and were also recently used to achieve efficient population inversion of the N resonances with large quadrupolar couplings in glycine at an MAS rate of 111 kHz [37].
Here we explore the advantages of using high-power tanh/tan SHAPs versus low-power WURST S3APs for population inversion in broadband NMR experiments for the case of the paramagnetic lithium ion battery cathode material LiFe0.25Mn0.75PO4 [38]. This material exhibits a large SA due to coupling between Li spins and unpaired electrons in the and metal centers. We use both the Li ( = 6.27 MHz/T) and Li ( = 16.55 MHz/T) nuclei in order to examine the effect of on the pulse performance at MAS rates ranging from 40 kHz to 111 kHz.
Section snippets
Inversion pulses in the high-power and low-power limits
We start by discussing the use of high-power SHAPs and low-power S3APs for population inversion. We note in passing that despite the fact that swept-frequency pulses are most routinely used as refocusing pulses (in magnetic resonance imaging, solution-state NMR, and static solid-state NMR studies in particular), the pulse performance under MAS conditions is much more readily examined in the case of inversion. Therefore the remainder of this manuscript will focus solely on the inversion
Simultaneous irradiation over multiple sidebands
A possible solution to this problem could be to sweep over multiple sidebands simultaneously. The concept of simultaneous irradiation is itself not new [40] but has not yet been applied to spin inversion using broadband sweeps. We begin by recalling the form of a constant amplitude, constant phase pulse:where is the RF field strength and is the phase of the RF pulse. This equation can be readily adapted for time-dependent amplitudes and phases:
Conclusions
We have examined the benefits and limitations of both high-power SHAPs and low-power S3APs and their application to broadband MAS studies of a sample with large shift anisotropy. Using a MAS rotation rate of 111.111 kHz, we found that in the case of Li, where the anisotropy is large but is low, the high-power SHAP performs poorly due primarily to sufficiently large RF fields being unavailable, whereas the low-power S3AP provided the maximum achieved sensitivity of all Li experiments owing
Experimental
Li and Li MAS experiments were carried out on the olivine structure lithium-ion battery cathode material LiFe0.25Mn0.75PO4 using a Bruker Avance III NMR spectrometer operating at an external field strength of 11.74 T corresponding to Larmor frequences of 73.603 MHz and 194.391 MHz for Li and Li, respectively. The sample was packed in a 0.7 mm rotor and spun at the magic angle, 54.736 relative to the external magnetic field. The magic angle was calibrated by measuring the STMAS [43], [44]
Acknowledgements
This work was financially supported by the People Program of the European Union’s FP7 (FP7-PEOPLE-2012-ITN No. 317127 “pNMR”), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant No. 648974 “P-MEM-NMR”), and the Agence Nationale de la Recherche (Grant No. ANR-15-CE29-0025-01). KJS would like to thank Prof. Philip J. Grandinetti for fruitful discussions about adiabatic pulses.
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