Double Frequency Sweep Research Articles

Operando 17o NMR Studies of Degradation in Li-Oxygen Batteries

Lithium-oxygen batteries are a promising next-generation battery technology, offering energy densities more than double that of the current state-of-the-art lithium-ion technology while not using transition metals in their cathodes. However, Li-oxygen battery commercialisation is hampered by short lifetimes caused by reactive oxygen species, such as singlet oxygen, that degrade the electrodes and electrolyte, resulting in a build-up of breakdown products. Even studying this breakdown is challenging as no technique can simultaneously detect and quantify all of the breakdown products, particularly in a non-destructive way. 17O NMR is ideally suited to this study as all common breakdown and discharge products form from a reaction involving oxygen gas or its derivatives. Thus, using 17O2 enriched gas leads to all the species of interest becoming enriched1 and hence detectable by NMR.Operando NMR, conducted as the cell cycles, is a powerful analysis technique offering non-invasive, quantitative, real-time measurements, often without heavy modification to the system of interest. Operando 17O NMR is particularly challenging due to 17O’s low sensitivity, broad signals and low natural abundance. We demonstrate how to overcome these challenges using sample enrichment, experimental setup and data post-processing. Specifically, we employ a double frequency sweep (DFS), Carr-Purcell-Meiboom-Gill (qCPMG) pulse sequence, a custom cell design and Gaussian processes (GP) to fit the data. These methods made monitoring degradation on the tens of minute timescales with the cell using 8mL (ca. $20) of 70% 17O2 possible. These methods can be applied to enable other 17O NMR studies, for example, of CO2 capture2, to be done in an operando manner and more broadly to other nuclei with similar NMR properties, such as sulphur in lithium sulphur batteries.We utilise these methods to separate out the chemical and electrochemical degradation occurring in the lithium-air cell by comparing a cell continuously discharged to one with “rest” periods in the discharge. Additionally, we can observe the onset of degradation mechanisms, be it at certain voltages or depths of discharge as well as species with limited lifetimes, such as H2O and CO2. This, along with ex-situ NMR measurements of electrolyte degradation caused by singlet oxygen has shed light on the fraction of degradation caused by singlet oxygen. In addition to highlighting the effect of high cell voltages on the breakdown and subsequent rapid reformation of solid breakdown products.Additives previously suggested to prevent this breakdown (LiI, dimethyl anthracene and triethylenediamine), by suppressing singlet oxygen, were tested in the cell. It was shown that while these almost entirely suppressed breakdown leading to water formation, and eventually to LiOH, they only had minor effects on the solid degradation products.It is hoped these insights can lead to the development of new and refined strategies to prevent breakdown in future cells.References1) Berge, A.H. et al. (2022) Revealing carbon capture chemistry with 17-oxygen NMR spectroscopy. Nat Commun 13, 77632) Leskes M. et al. (2013) Monitoring the Electrochemical Processes in the Lithium-Air Battery by Solid State NMR Spectroscopy J. Phys. Chem. C 117, 51, 26929–26939FigureA - In-situ cell mounted in NMR probe containing cell assemble and 17O2 gasB - Top quantification of common breakdown species, regression and error bars generated using gaussian processes. Highlighted is the breakdown of Li2CO3 at the end of the charge to produce CO2, which rapidly reacts as the start of discharge to reform Li2CO3 C - Schematic of breakdown mechanisms observed and their estimated contributions to breakdown Figure 1

On the use of single-frequency versus double-frequency satellite-transition pulses for MQMAS

It has been shown recently that a rotor-period long pulse applied at a frequency selective to the satellite-transitions of half-integer quadrupole nuclei can efficiently interconvert central-transition (CT) and triple-quantum (TQ) coherences for the acquisition of MQMAS spectra [I. Hung, Z. Gan, J. Magn. Reson. 324 (2021) 106913; doi: https://doi.org/10.1016/j.jmr.2021.106913]. By using a pair of such pulses and selecting opposite changes in coherence order, the anisotropic phase of the effective rf field can be refocused. Efficient multiple-quantum interconversion has led to low-power MQMAS pulse sequences capable of obtaining isotropic NMR spectra for the largest quadrupolar couplings to date. In this work, we extend the satellite-transition selective pulses from single- to double-frequency (or cosine) irradiation. By applying average Hamiltonian theory in the quadrupolar jolting frame, it is shown that the phase for TQ/CT conversion converges when the double-frequency irradiation matches the mirror-image symmetry of the satellite-transitions. The coherent conversion explains the mechanism behind the double-frequency sweep (DFS) and fast amplitude modulation (FAM) methods used for MQMAS. However, the strict matching condition limits the bandwidth of such double-frequency pulses to less than one spinning frequency. The use of a pair of identical cosine satellite-transition pulses is proposed to refocus the residual anisotropic phase spread. The refocusing leads to a more efficient MQMAS pulse sequence with a broader bandwidth suitable for large quadrupolar couplings and chemical shift ranges. Comparisons with the recently presented single-frequency lpMQMAS and other MQMAS pulse schemes show that cos-lpMQMAS is more efficient, less susceptible to fluctuations in spinning frequency, and suffers from less distortion in quadrupolar line shapes, as demonstrated with model compounds of moderate and large quadrupolar couplings, 87RbNO3 and β-71Ga2O3. In particular, the results for β-71Ga2O3 show an order of magnitude increase in MQMAS efficiency.

A novel pulse scheme for multiple quantum excitation, SFAM to enhance the sensitivity of MQMAS experiments

The basic MQMAS sequence consists of two hard pulses, one excites the equilibrium population to MQ (Multiple Quantum) coherence, and the other converts back to detectable coherence after some evolution time t1 (Medek et al., 1995 [1]). Unfortunately the MQ excitation and conversion processes are very inefficient due to the nonlinear nature of MQ processes. MQ conversion (converting MQ back to detectable coherence) efficiency can significantly be enhanced with DFS (Double Frequency Sweep) or FAM (Fast Amplitude Modulation) type pulses instead of rectangular pulse irradiation (Goldbourt and Madhu, 2002 [2]). In contrary to conversion, it is more challenging to enhance MQ excitation in MQMAS experiments, since most methods result in distorted lineshapes (Goldbourt and Madhu, 2002 [2]; Lim and Grey, 1998 [3]). In the present work MQ excitation of single crystals was studied, and the understanding of the process led to a principle, which was extended to the excitation of powder samples as well. The resulting method was implemented into the MQMAS sequence to enhance MQ excitation of powder samples under MAS condition. The new sequence called SFAM (Shifted Fast Amplitude Modulation) can provide high enhancements at low RF powers (ϵ>4 at νrf=40kHz) compared to rectangular pulses. Although simulated lineshapes of SFAM predict only minor deviations from ideal lineshapes, experimentally obtained lineshapes along the anisotropic dimension show rather strong distortions. SFAM is relatively simple to optimize, and shows robustness with respect to the miscalibration or inhomogeneity of the RF power as well as to other parameters of the pulse scheme. A good agreement was found between numerically and experimentally optimized parameters.

High sensitivity and resolution in 43Ca solid-state NMR experiments

A thorough investigation of solid-state NMR signal enhancement schemes and high-resolution techniques for application to the spin-7/2 43Ca nuclide are presented. Signal enhancement experiments employing double frequency sweeps, hyperbolic secant pulses, and rotor-assisted population transfer, which manipulate the satellite transitions of half-integer quadrupolar nuclei to polarize the central transition (m = + 1/2 ↔ –1/2), are carried out on four well-characterized 43Ca isotopically enriched calcium salts: Ca(NO3)2, Ca(OD)2, CaSO4·2H2O, and Ca(OAc)2·H2O. These results, in conjunction with numerical simulations of 43Ca NMR spectra under magic-angle spinning conditions, are used to identify the technique that provides the most uniform (or quantitative) polarization enhancement as well as the largest signal enhancement factors independent of size of the 43Ca quadrupolar coupling constant, which is the most significant source of resonance broadening in 43Ca NMR spectra. These samples are further investigated using 43Ca double-rotation NMR spectroscopy to yield isotropic, or solution-like, NMR spectra with exquisite resolution. In addition, three unique calcium sites are resolved for the hemihydrated form of calcium acetate (unknown structure), Ca(OAc)2·0.5H2O, with double-rotation NMR, whereas the more common, but more time-consuming, multiple quantum magic-angle spinning technique only clearly resolves two calcium sites. The results shown herein will be useful for other NMR spectroscopists attempting to acquire 43Ca solid-state NMR data for unknown and more complex materials with a higher degree of both sensitivity and resolution.

Enhancing the central-transition NMR signal of quadrupolar nuclei by spin population transfer using SW-FAM pulse trains with a tangent-shaped sweep profile

Solid-state NMR of quadrupolar nuclei with half-integer spin, such as 25Mg (I=5/2) or 43Ca (I=7/2), suffers from low sensitivity, which may be improved using spin population transfer (SPT) from the satellite transitions. Effecting SPT with good efficiency is especially challenging under static conditions, and several techniques such as double-frequency sweeps (DFS), hyperbolic secant pulses (HS) and frequency-swept fast-amplitude modulated pulses (SW-FAM) have been suggested for achieving the necessary manipulations of the satellite transitions. We here investigate the SPT properties of an SW-FAM sequence with a tangent-shaped profile. The new SW(tan)-FAM pulse train is shown to possess superior SPT performance to the SW(1/τ)-FAM sequence, which hitherto has been considered to be the best FAM method for signal enhancement of static spectra, by both numerical simulations on a 27Al model system, and experimental results on aluminium acetyl acetonate, Al(acac)3. In addition, the CT enhancement of individual crystallites from the polycrystalline sample with a defined angle between principal z-axis of the diagonal Q-tensor and the external field was considered by numerical simulations. In the vicinity of the magic angle θm=54.7°, a region of zero enhancement exists. Use of the SW(tan)-FAM sequence allows extending the frequency sweep further into this region, with beneficial effects for the overall enhancement and the faithfulness of the line shape. In agreement with previously published studies, our numerical simulations on SPT for single crystals again evidence that the enhancement factors for a polycrystalline sample range from zero enhancement to the maximum gain of 2I, with the total enhancement factor of the full powder pattern being the summation of these strongly varying individual factors. This variation is the cause for line shape distortions in SPT-enhanced spectra. At the same time, these findings prove the capability of frequency sweeps (i.e., DFS and SW-FAM) to fully invert the satellite transitions under certain conditions.

Sensitivity enhancement in MAS NMR of half-integer quadrupolar nuclei using sideband selective double-frequency sweeps

Sensitivity enhancement of the NMR signal of the half-integer spin quadrupolar nuclei under magic angle spinning (MAS) conditions is demonstrated using the DFS (Double Frequency Sweep) enhancement scheme. It has been shown, both through numerical simulations and by experiments, that with a sinusoidal amplitude profile a narrow band DFS scheme performs much better than a DFS scheme with a large bandwidth. The total enhancement compares favorably to the hyperbolic secant (HS) pulse scheme under MAS. Finally, we report the robustness of this DFS scheme with respect to variation of different experimental parameters, making it a very attractive choice for acquiring sensitivity-enhanced NMR experiments of half-integer quadrupolar nuclei.

A natural abundance solid-state 25Mg NMR study of layered magnesium phosphates

Natural abundance 25Mg solid-state magic-angle spinning and static NMR spectra of several representative layered magnesium phosphates were acquired at 21.1 and 9.4 T by using quadrupolar echo and double-frequency sweep quadrupolar Carr–Purcell–Meiboom–Gill pulse sequences. The spectra were dominated by the second-order quadrupolar interaction. The electric field gradient tensor parameters were extracted from the spectra via spectral simulations. These parameters, such as the quadrupolar coupling constant (CQ), appear to be sensitive to some parameters describing the distortion of the MgO6 octahedron in the layer. The empirical relationships between CQ and several structural parameters were established and used to obtain partial information on the Mg environment in a layered material (MgHPO4·1.2H2O) with unknown structure. Theoretical calculations suggest that the CQ values of the Mg sites are affected not only by the oxygen atoms in the first coordination sphere, but also by the spatial arrangements of the atoms in the second and third coordination spheres and beyond.

Optimized excitation pulses for the acquisition of static NMR powder patterns from half-integer quadrupolar nuclei

Various amplitude- and phase-modulated excitation pulses for the observation of static NMR powder patterns from half-integer quadrupolar nuclei have been generated using the optimal control routines implemented in SIMPSON 2.0. Such pulses are capable of both excitation of the central transition and signal enhancement by population transfer from the satellites. Enhancements in excess of 100% have been achieved for the central transition of the spin-3/2 87Rb nucleus compared with a selective π/2 pulse. These pulses are shown to be relatively insensitive to changes in RF power and transmitter offsets, and can achieve a more uniform signal enhancement than double-frequency sweeps (DFS), resulting in more accurate spectral lineshapes. We also investigate the possibility of “calibration-free” optimized pulses for general use on half-integer quadrupoles with unknown interaction parameters. Such pulses could prove extremely useful for studying low abundance or insensitive nuclei for which experimental optimization of the DFS scheme may be difficult. We demonstrate that a pulse optimized for an arbitrary spin-3/2 system can function well on multiple samples, and can also excite the central transition of higher spin numbers, albeit with a smaller enhancement. The mechanism by which these optimized pulses achieve the signal enhancement is highly complex and, unlike DFS, involves a non-linear excitation of the satellite transition manifold, as well as the generation and manipulation of significant multiple-quantum coherences.

Incomplete double frequency sweeps to select small quadrupolar coupling static powder patterns

Difference spectra based on the magnitude of the quadrupolar coupling of a site has been observed under static conditions utilizing a double frequency sweep pulse sequence to enhance the central transition of a small electric field gradient (EFG) environment. Through the use of convergent sweeps that only cover the inner satellite transitions of the smaller EFG site, an echo spectrum results that favors the smaller site, which can then be used in conjunction with normal echo spectra to create a difference spectrum that consists primarily of the smaller site. The simplification of the static lineshape data permits simulation for the extraction of chemical shift anisotropy (CSA) information for the site. The method is demonstrated using 93Nb NMR for samples with multiple niobium environments due to mixtures of compounds, MgNb 2O 6/LiNbO 3, or due to crystallographic structure, KCa 2Nb 3O 10.

Natural Abundance 43Ca NMR Spectroscopy of Tobermorite and Jennite: Model Compounds for C–S–H

There are few effective methods for characterizing the molecular scale structural environments of Ca2+ in hydrated cements, which has limited our ability to understand the structure of, for example, Ca–silicate hydrate (C–S–H). 43Ca nuclear magnetic resonance (NMR) spectroscopy has long been considered too insensitive to provide useful data in this regard, but 43Ca magic angle spinning (MAS) NMR spectra reported here for synthetic tobermorite and jennite with naturally abundant levels of 43Ca demonstrate that this is a viable approach. We show that spectra with useful signal/noise ratios can be obtained in a reasonable acquisition period (∼2 days) using an H0 field strength of 21.1 T, 5 mm rotors spinning at a frequency of 5 kHz, and a double frequency sweep preparatory pulse sequence. Tobermorite and jennite produce relatively broad resonances due to their complex structures and structural disorder, however, the chemical shift differences between six‐coordinate 43Ca in jennite and seven‐coordinate 43Ca in 11 Å tobermorite are large enough that the signals are entirely resolved at this field. These data suggest that signal from ideal tobermorite‐like and jennite‐like sites in cement C–S–H can most likely be distinguished by 43Ca NMR and that this method will be a powerful approach for studying cement‐based ceramic materials in the coming decade.

Solid‐state natural abundance 25Mg NMR studies of Na2MgEDTA·4H2O—a possible new reference compound for 25Mg NMR spectroscopy

Natural abundance solid-state (25)Mg NMR measurements were made of the disodium salt of magnesium ethylenediaminetetraacetate tetrahydrate (Na(2)MgEDTA x 4 H(2)O). Both magic angle spinning (MAS) and static experiments were employed to determine the quadrupole coupling constant (C(q)) and the asymmetry parameter (eta(q)) of the electric field gradient (EFG) tensor associated with (25)Mg in this compound, giving the values C(q) = 1.675(5) MHz and eta(q) = 0.15(1). The isotropic chemical shift was determined to be delta(iso) = 0.25(10) ppm (relative to 11 M MgCl(2) aqueous solution) and a small chemical shift anisotropy (CSA) contribution (approximately -13 ppm) was detected, one of the first CSA reports in (25)Mg NMR. This compound exhibited remarkably good (25)Mg NMR sensitivity, due to its fast spin-lattice relaxation and modest quadrupole coupling, which allowed its use as a secondary shift reference and as a test sample for the implementation and optimisation of signal-enhancement methods in (25)Mg NMR spectroscopy, such as double frequency sweeps (DFS) and the use of adiabatic hyperbolic secant (HS) and WURST pulses.

Sensitivity enhancement of solid-state NMR spectra of half-integer spin quadrupolar nuclei: Double- or single-frequency sweeps? Insights from the hyperbolic secant experiment

Improved sensitivity enhancements of the central NMR transition of non-integer spin quadrupolar nuclei in MAS powder samples are realized when only a single satellite transition spinning side band is irradiated using a conventional double-frequency sweep experiment compared to irradiation of the entire spinning side band manifold. For example, for 87Rb in RbClO 4, enhancement factors of 2.2 versus 1.9 are observed when only one satellite transition spinning side band is targeted versus the entire spinning side band manifold. Similarly, for 27Al in Al(acac) 3, the corresponding enhancement was 3.4 compared to 2.6.

Multinuclear MRI of Solids: from Structure to Transport

Direct multinuclear imaging of rigid solids has been performed using the conventional two-pulse spin-echo pulse sequence and liquids magnetic resonance imaging (MRI) hardware. Two-dimensional 27Al and 51V images of an Al2O3-V2O5-glass composite sample and 11B, 23Na, 27Al and 29Si images of glass have been detected, extending the range of nuclei and solid materials that can be studied by this approach. For a spinning cylinder packed with Al2O3 powder, quantitative velocity maps have been obtained by directly detecting the 27Al nuclear magnetic resonance signal of the solid phase. The two velocity components in the imaging plane transverse to the rotation axis have been mapped using the three-pulse stimulated echo sequence. Some possibilities to improve sensitivity in the MRI experiments on rigid solids have been considered. In particular, inversion of the satellite transitions by a double frequency sweep adiabatic passage has led to a signal enhancement by a factor of two in 27Al MRI of a glass sample despite a short repetition time (0.5 s) of the imaging pulse sequence.

Sensitivity enhancement of solid-state NMR spectra of half-integer spin quadrupolar nuclei using hyperbolic secant pulses: Applications to spin-5/2 nuclei

The use of hyperbolic secant, HS, pulses to obtain NMR signal enhancements for the central transition of spin-5/2 quadrupolar nuclei in solids is explored. By inverting the populations of nuclear-spin energy levels prior to applying a selective-observe pulse, enhancements near the theoretical maximum are obtained for the central 27Al NMR transition in a single crystal of α-Al 2O 3. The experimental enhancements obtained using HS inversion pulses for powder samples are compared to those obtained using the double-frequency sweep method. For every sample investigated, the HS enhancement factors are equal to or superior to those previously reported using other enhancement techniques.

New opportunities for double rotation NMR of half-integer quadrupolar nuclei

A combined approach is presented which expands the applicability of double rotation (DOR) by overcoming its most prominent disadvantages: spinning stability and sensitivity. A new design using air-bearings for the inner rotor and a computer-assisted start-up procedure allows DOR operation over in principle unlimited time at outer rotor speeds of up to 2000 Hz. Sensitivity enhancement of the DOR experiment is achieved by applying amplitude-modulated adiabatic pulses such as the double frequency sweep (DFS) before pulse excitation. Repeating the DFS enhancement and signal readout several times without allowing for spin–lattice relaxation leads to sensitivity enhancements of a factor 3 for 27Al in various minerals. As a result, it becomes possible to study low sensitivity quadrupolar nuclei and various long duration 2D measurements can be performed routinely. Spinning is adequate to suppress residual homonuclear dipolar couplings in the spectral dimension of typical quadrupolar spin systems. In 2D-exchange spectroscopy, however, homonuclear correlation can still be established through dipolar–quadrupolar cross-terms.

A Solid-State 39K and 13C NMR Study of Polymeric Potassium Metallocenes

The quadrupolar Carr-Purcell Meiboom-Gill (QCPMG) and double frequency sweep (DFS)/QCPMG pulse sequences are applied in order to acquire the first solid-state 39K NMR spectra of organometallic complexes, the polymeric main group metallocenes cyclopentadienyl potassium (CpK) and pentamethylcyclopentadienyl potassium (Cp*K). Piecewise QCPMG NMR techniques are used to acquire a high S/N 39K spectrum of the broad central transition of Cp*K, which is ca. 200 kHz in breadth. Analytical and numerical simulations indicate that there is a significant quadrupolar interaction present at both potassium nuclei (C(Q)(39K) = 2.55(6)/2.67(8) MHz and 4.69(8) MHz for CpK (static/MAS) and Cp*K, respectively). Experimental quadrupolar asymmetry parameters suggest that both structures are bent about the potassium atoms (eta(Q)(39K) = 0.28(3)/0.29(3) for CpK (static/MAS) and eta(Q)(39K) = 0.30(3) for Cp*K). Variable-temperature (VT) 39K NMR experiments on CpK elucidate temperature-dependent changes in quadrupolar parameters which can be rationalized in terms of alterations of bond distances and angles with temperature. 13C CP/MAS NMR experiments are conducted upon both samples to quantify the carbon chemical shielding anisotropy (CSA) at the Cp' ring carbon atoms. Ab initio carbon CSA and 39K electric-field gradient (EFG) and CSA calculations are conducted and discussed for the CpK complex, in order to correlate the experimental NMR parameters with molecular structure in CpK and Cp*K. 39K DFS/QCPMG and 13C CP/MAS experiments prove invaluable for probing molecular structure, temperature-dependent structural changes, and the presence of impurities in these systems.

Sensitivity enhancement of MQMAS NMR spectra of spin 3/2 nuclei using hyperbolic secant pulses

The use of hyperbolic secant (HS) pulses to enhance the intensity of the central transition in MQMAS experiments for spin 3/2 quadrupolar nuclei is investigated by examining 87Rb NMR spectra of a powder sample of RbNO 3. The application of HS pulses prior to the triple-quantum (3Q) excitation provides sensitivity enhancements in MQMAS spectra that are superior to those previously reported. For the conversion of 3Q to single-quantum (1Q) observables, the HS pulses have an efficiency similar to that reported for double frequency sweeps (DFS) but greater than that of the fast amplitude modulation (FAM) technique.

Sensitivity enhancement of NMR spectra of half-integer quadrupolar nuclei in the solid state via population transfer

Three population transfer techniques for improving the sensitivity of the central transition of NMR spectra from half-integer quadrupolar nuclei in the solid state are described. Two of the methods attempt to invert the populations of energy levels associated with the satellite transitions either by employing double frequency sweeps (DFS) or hyperbolic secant (HS) pulses. The third method, rotor-assisted population transfer (RAPT), is designed to saturate the satellite transitions. The effect of various experimental parameters on the resulting sensitivity enhancement is discussed. We trust that novice solid-state NMR spectroscopists interested in acquiring NMR spectra of half-integer spin quadrupolar nuclei will find these notes helpful. © 2005 Wiley Periodicals, Inc. Concepts Magn Reson Part A 26A: 47–61, 2005

Signal enhancement of NMR spectra of half-integer quadrupolar nuclei in solids using hyperbolic secant pulses

Signal enhancement of the central NMR transition of quadrupolar nuclei with half-integer spin is achieved by applying a hyperbolic-secant π-inversion (sechinv) pulse to the satellite transitions. In combination with the quadrupolar Carr–Purcell Meiboom–Gill (QCPMG) pulse train, the sechinv pulse provides an additional signal enhancement of up to 2.7 for spin 3/2 nuclei in powdered solids. The 87Rb NMR enhancements realized using this experiment are compared to those obtained employing rotor-assisted population transfer (RAPT) and double frequency sweep (DFS) pulse experiments on magic angle spinning (MAS) powdered samples. In every case, the sequence employing sechinv pulses gives greater enhancements than the previously reported methods.

Signal enhancement in NMR spectra of half-integer quadrupolar nuclei via DFS–QCPMG and RAPT–QCPMG pulse sequences

Two signal enhancement schemes capable of providing large signal-to-noise gains in static and magic-angle spinning NMR spectra of the central transition of half-integer quadrupolar nuclei are presented. Amplitude-modulated double-frequency sweeps (AM-DFS) and rotor-assisted population transfer (RAPT) pulse sequences are used as preparatory sequences in combination with the quadrupolar Carr–Purcell Meiboom–Gill (QCPMG) pulse sequence to obtain large signal enhancements ranging from one to two orders of magnitude. Specific applications to two spin-3/2 nuclei ( 87Rb and 39K) and one spin-5/2 nucleus ( 85Rb) are presented.