Spinning Sideband Manifolds Research Articles

17O NMR Spectroscopy in Lithium-Ion Battery Cathode Materials: Challenges and Interpretation.

Modern studies of lithium-ion battery (LIB) cathode materials employ a large range of experimental and theoretical techniques to understand the changes in bulk and local chemical and electronic structures during electrochemical cycling (charge and discharge). Despite its being rich in useful chemical information, few studies to date have used 17O NMR spectroscopy. Many LIB cathode materials contain paramagnetic ions, and their NMR spectra are dominated by hyperfine and quadrupolar interactions, giving rise to broad resonances with extensive spinning sideband manifolds. In principle, careful analysis of these spectra can reveal information about local structural distortions, magnetic exchange interactions, structural inhomogeneities (Li+ concentration gradients), and even the presence of redox-active O anions. In this Perspective, we examine the primary interactions governing 17O NMR spectroscopy of LIB cathodes and outline how 17O NMR may be used to elucidate the structure of pristine cathodes and their structural evolution on cycling, providing insight into the challenges in obtaining and interpreting the spectra. We also discuss the use of 17O NMR in the context of anionic redox and the role this technique may play in understanding the charge compensation mechanisms in high-capacity cathodes, and we provide suggestions for employing 17O NMR in future avenues of research.

High resolution solid state NMR in paramagnetic metal-organic frameworks

We study the metal-organic framework (MOF) ZIF-67 with 1H and 13C nuclear magnetic resonance (NMR). In addition to the usual orbital chemical shifts, we observe spinning sideband manifolds in the NMR spectrum due to hyperfine interactions of the paramagnetic cobalt with 1H and 13C. Both orbital and paramagnetic chemical shifts are in good agreement with values calculated from first principles, allowing high-confidence assignment of the observed peaks to specific sites within the MOF. Our measured resonance shifts, line shapes, and spin lattice relaxation rates are also consistent with calculated values. We show that molecules in the pores of the MOF can exhibit high-resolution NMR spectra with fast spin lattice relaxation rates due to dipole-dipole couplings to the Co2+ nodes in the ZIF-67 lattice, showcasing NMR spectroscopy as a powerful tool for identification and characterization of “guests” that may be hosted by the MOF in electrochemical and catalytic applications.

Synthesis, crystal structure, and magnetic properties of a one-dimensional chain antiferromagnet NiC2O4·2NH3

NiC2O4·2NH3 was synthesized hydrothermally, and its structure was solved by single-crystal X-ray diffraction. Accordingly, NiC2O4·2NH3 crystallizes in the centrosymmetric monoclinic space group C2/m (no. 12) with lattice parameters of a ​= ​10.767(5) Å, b ​= ​5.414(2) Å, c ​= ​5.005(2) Å and β ​= ​96.3(4)°. The NiO4N2 octahedra align in a parallel pattern through shared C2O42− units and thus form linear one-dimensional (1D) chains extending along the b-axis. These linear chains are separated along the a-axis by NH3 molecules and weakly coupled with each other through hydrogen bonding. 1H and 13C solid-state NMR revealed isotropic resonances at −115(3) ppm and −312(5) ppm, respectively, for NiC2O4·2NH3, the ammonia protons and oxalate carbons being paramagnetically shifted via the Fermi contact interaction from d8 Ni(II). Room-temperature paramagnetic shift anisotropies of 400(30) ppm for 1H and 780(40) ppm for 13C were determined from simulations of the spinning sideband manifolds. Magnetic susceptibility shows a broad maximum around T(χmax) ​= ​35 ​K, suggesting well-developed spin–spin correlations along the Ni–C2O4–Ni chains. No long-range order is observed down to 2 ​K, which is further confirmed by heat capacity results. The intrachain interaction J/k of −31.0 ​K is estimated by fitting the data with a 1D spin chain model. The isothermal magnetization curve at 2 ​K shows a field-induced phase transition around 5 ​T. The magnetization value at 9 ​T is only 0.087 μB, which is far from saturation. All magnetic results indicate NiC2O4·2NH3 is a good 1D chain quantum antiferromagnet.

Off-resonance 13C-2H REDOR NMR for site-resolved studies of molecular motion.

We introduce a 13C-2H Rotational Echo DOuble Resonance (REDOR) technique that uses the difference between on-resonance and off-resonance 2H irradiation to detect dynamic segments in deuterated molecules. By selectively inverting specific regions of the 2H magic-angle spinning (MAS) sideband manifold to recouple some of the deuterons to nearby carbons, we distinguish dynamic and rigid residues in 1D and 2D 13C spectra. We demonstrate this approach on deuterated GB1, H/D exchanged GB1, and perdeuterated bacterial cellulose. Numerical simulations reproduce the measured mixing-time and 2H carrier-frequency dependence of the REDOR dephasing of bacterial cellulose. Combining numerical simulations with experiments thus allow the extraction of motionally averaged quadrupolar couplings from REDOR dephasing values.

An investigation of the phosphate removal mechanism by MgFe layered double hydroxides

The phosphate adsorption properties including kinetics and uptake pathway of MgxFe layered double hydroxides (LDH) with targeted x values of 2 and 3 and intercalated with nitrate (NO3−) and chloride (Cl−) anions were investigated at a phosphate concentration of 16.31 mgP·L−1 and pH (pH = 5, 7, and 9) similar to wastewater conditions. The synthesized MgxFe-LDH show fast adsorption (90–98%) of the final phosphate removal within 3 h and remove 68–73% of the total phosphate content after 24 h. The pristine MgxFe-LDH and solid products after phosphate exposure were characterized by PXRD, FT-IR, zeta-potential, SEM, and solid-state 31P MAS NMR spectroscopy to investigate the phosphate removal pathway. Interestingly, the four MgxFe-LDH phase had similar Mg:Fe ratios irrespective of the Mg:Fe ratio of the reactants based on PXRD. The MgxFe-LDH plate-like morphology was preserved after phosphate exposure and no sign of phosphate intercalation were evident by PXRD, FT-IR, and SEM albeit a small amount of the MgxFe LDH was dissolved based on ICP-OES, PXRD and the final pH. Partial dissolution of the LDH was clearly evident by SEM for Mg2Fe-LDH exposed to 200% theoretical P capacity. The FT-IR spectra and zeta-potential values indicated that the phosphate ions are adsorbed by surface complexation. The 31P MAS NMR spectra of MgxFe-LDH exposed to phosphate has an intense spinning sideband manifold and only minor paramagnetic shifts (<30 ppm) are observed. Thus, phosphate is in the proximity of iron, but not directly bound to the paramagnetic iron via Fe-O-P bond (inner-sphere complexation or mineralization). Thus, the dominating phosphate uptake pathway by MgxFe-LDH is surface complexation similar to MgAl-LDH and possible the formation of ill-defined magnesium phosphate due to partial dissolution of the MgFe-LDH, especially at high P loading.

Fast electron paramagnetic resonance magic angle spinning simulations using analytical powder averaging techniques.

Simulations describing the spin physics underpinning nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) spectroscopy play an important role in the design of new experiments. When experiments are performed in the solid state, samples are commonly composed of powders or glasses, with molecules oriented at a large number of angles with respect to the laboratory frame. These powder angles must be represented in simulations to account for anisotropic interactions. Numerical techniques are typically used to accurately compute such powder averages. A large number of Euler angles are usually required, leading to lengthy simulation times. This is particularly true in broad spectra, such as those observed in EPR. The combination of the traditionally separate techniques of EPR and magic angle spinning (MAS) NMR could play an important role in future electron detected experiments, combined with dynamic nuclear polarization, which will allow for exceptional detection sensitivity of NMR spin coherences. Here, we present a method of reducing the required number of Euler angles in magnetic resonance simulations by analytically performing the powder average over one of the Euler angles in the static and MAS cases for the TEMPO nitroxide radical in a 7 T field. In the static case, this leads to a 97.5% reduction in simulation time over the fully numerical case and reproduces the expected spinning sideband manifold when simulated with a MAS frequency of 150 kHz. This technique is applicable to more traditional NMR experiments as well, such as those involving quadrupolar nuclei or multiple dimensions.

Cross-term Splittings Due to the Orientational Inequivalence of Proton Magnetic Shielding Tensors: Do Water Molecules Trapped in Crystals Hop or Tunnel?

Water molecules trapped in crystals of barium chlorate monohydrate have been investigated by magic-angle spinning (MAS) proton NMR spectroscopy in the temperature range 110-300 K. At high temperatures, a single spinning sideband pattern is observed. Below 150 K, however, two interleaved spinning sideband manifolds appear, with distinct centerbands that do not coincide with the average isotropic chemical shift seen at high temperatures. This hitherto unknown "cross-term splitting" results from the interplay of the homonuclear dipole-dipole coupling and two anisotropic proton shielding tensors that have identical principal components but nonequivalent orientations. The resulting cross terms cannot be averaged out by rotation about the magic angle. The analysis of the exchange-induced broadening, coalescence, and narrowing of the cross-term splitting in MAS spectra allows one to estimate the rate of exchange of the two protons between 140 and 190 K. The experimental data is compared with 2H and 1H NMR studies of the same sample reported in the literature. Density functional theory methods are utilized to estimate the thermal activation energy for a 2-fold hopping process of proton exchange about the H-O-H bisector. The Bell-Limbach model allows one to take into account contributions due to incoherent quantum tunneling in the low-temperature regime.

Measuring 13C/15N chemical shift anisotropy in [13C,15N] uniformly enriched proteins using CSA amplification

Extended chemical shift anisotropy amplification (xCSA) is applied for measuring 13C/15N chemical shift anisotropy (CSA) of uniformly labeled proteins under magic-angle spinning (MAS). The amplification sequence consists of a sequence of π-pulses that repetitively interrupt MAS averaging of the CSA interaction. The timing of the pulses is designed to generate amplified spinning sideband manifolds which can be fitted to extract CSA parameters. The 13C/13C homonuclear dipolar interactions are not affected by the π-pulses due to the bilinear nature of the spin operators and are averaged by MAS in the xCSA experiment. These features make the constant evolution-time experiment suitable for measuring CSA of uniformly labeled samples. The incorporation of xCSA with multi-dimensional 13C/15N correlation is demonstrated with a GB1 protein sample as a model system for measuring 13C/15N CSA of all backbone 15NH, 13CA and 13CO sites.

Supramolecular self-organisation and conformational isomerism of a binuclear O,O′-dipropyl dithiophosphate gold(I) complex, [Au2{S2P(OC3H7)2}2]: Synthesis, 13C and 31P CP/MAS NMR spectroscopy, single-crystal X-ray diffraction study and thermal behaviour

Crystalline one-dimensional polymeric catena-poly[bis(μ2-O,O′-dipropyldithiophosphato-S,S′)digold(I)] (Au–Au) (1) was prepared and studied using 13C and 31P CP/MAS NMR spectroscopy and single-crystal X-ray diffraction. To elucidate the structural function of Dtph ligands in crystalline gold(I) O,O′-dipropyl dithiophosphate, the chemical shift anisotropy parameters (δaniso and η) were calculated from spinning sideband manifolds in 31P MAS NMR spectra. A novel structure of the gold(I) compound comprises two isomeric, non-centrosymmetric binuclear molecules of [Au2{S2P(OC3H7)2}2] (isomers ‘A’ and ‘B’), whose four Dtph groups display structural inequivalence. In each isomeric binuclear molecule of 1, a pair of μ2-bridging dipropyl Dtph ligands almost symmetrically links two neighbouring gold atoms, forming an extensive eight-membered metallocycle [Au2S4P2], while the intramolecular aurophilic Au⋯Au bond additionally stabilises this central cyclic moiety. At the supramolecular level of complex 1, intermolecular aurophilic Au⋯Au bonds yield almost linear infinite polymeric chains (⋯‘A’⋯‘B’⋯‘A’⋯‘B’⋯)n. The thermal behaviour of this compound was studied by the simultaneous thermal analysis (STA) technique (a combination of TG and DSC) under an argon atmosphere.

Selective observation of a spinning-sideband manifold of paramagnetic solids by rotation-synchronized DANTE

We examine applicability of rotation-synchronized Delays Alternating with Nutation for Tailored Excitation (rs-DANTE) to a crowded sideband spectrum spreading over a few 100kHz by the paramagnetic interaction. It is shown that rs-DANTE can be used to excite 6Li spinning sideband manifolds of the three crystallographic Li sites (2b, 4h, and 2c) in a magic-angle spinning (MAS) spectrum of 6Li-enriched Li2MnO3. The observed lineshape is insensitive to rf inhomogeneiety, thus indicating practical applicability of rs-DANTE to a paramagnetic system. Each sideband pattern can be described by the paramagnetic anisotropies evaluated by taking the electron–6Li dipolar interactions into account. The isotropic chemical shift for each site can thus be obtained by comparing the experimental sideband pattern to the calculated one. It is therefore possible by this approach to obtain both isotropic and anisotropic shift information. Further effects of structural disorder in Li2MnO3 on the isotropic shift and the sideband pattern are discussed.

A fixation mode of gold from solutions using heterogeneous reaction of cadmium dicyclohexyl dithiophosphate with H[AuCl4]. Structural and (13C, 31P) CP/MAS NMR studies and thermal behaviour of crystalline polymeric gold(I) dicyclohexyl dithiophosphate and bis(dicyclohexylthiophosphoryl) disulphide

Two novel compounds: polynuclear catena-poly[bis(μ3-O,O′-di-cyclo-hexyldithiophosphato-S,S,S′)digold(I)] (AuAu) (1) and crystalline bis(O,O′-di-cyclo-hexylthiophosphoryl)disulphide, (cyclo-C6H11O)2P(S)SS(S)P(O-cyclo-C6H11)2 (2) were prepared using heterogeneous reaction between freshly precipitated binuclear cadmium(II) dithiophosphate (Dtph), [Cd2{S2P(O-cyclo-C6H11}4] and H[AuCl4] in 2M hydrochloric acid. The isolated compounds 1 and 2 (the fixation mode of gold from the solution and the oxidised form of Dtph groups, respectively) have been studied by means of single-crystal X-ray diffraction, 13C and 31P cross-polarisation/magic-angle-spinning (CP/MAS) NMR spectroscopy and simultaneous thermal analysis (STA). Centrosymmetric binuclear molecule of 1, [Au2{S2P(O-cyclo-C6H11)2}2] comprises a pair of μ-bridging di-cyclo-hexyl Dtph ligands, linking two neighbouring gold atoms, and displays additional intramolecular aurophilic bond Au⋯Au. At the supramolecular level of structural self-organisation of complex 1, infinite polymeric zigzag chains arise due to pairs of the secondary bonds Au···S between neighbouring binuclear molecules. Centrosymmetric molecule of 2 displays two O,O′-di-cyclo-hexythiophosphoryl fragments, which are connected by the chemical bond S(1)S(1)a, and a planar zigzag array [SPSSPS] passing through the central part of the molecule. To characterise additionally the Dtph groups in both compounds 1 and 2, chemical shift anisotropy (CSA) parameters (δaniso and η) were calculated from spinning sideband manifolds in experimental 31P MAS NMR spectra. The thermal behaviour of complex 1 was studied using simultaneous thermal analysis (a combination of TG and DSC) under an argon atmosphere. The thermal behaviour displays stepwise mass loss, comprising thermal decompositions of the organic and inorganic parts of 1 with gold(I) dithio-meta-phosphate and reduced metallic gold as the intermediate and the final products, respectively.

Ultrasonic mediated synthesis of hexagonal benzene-bridged periodic mesoporous organosilicas

A rapid synthesis route to synthesize highly ordered benzene-bridged periodic mesoporous organosilicas (PMOs) with the hexagonal mesostructures in a short time via the aid of ultrasonic irradiation is reported. By varying the time periods for the ultrasonic irradiation and hydrothermal treatment, the structural and textural properties of the resultant materials can be finely tuned. The resultant materials exhibited well ordered hexagonal mesostrucutres with surface areas in the range of 653–1097m2/g, pore volumes of 0.52–1.26cm3/g, and pore diameters in the range of 3.9–6.4nm, which are comparable to the conventional analogs. Different synthesis procedures, namely ultrasonic irradiation and hydrothermal treatment, have significant influence on the particle morphology and the change in morphology was evident from SEM analysis. It is of great interest that 13C solid-state NMR can reveal subtle changes in the overall arrangements of the carbon atoms in the phenylene rings embedded in the silica framework due to different synthesis procedures by simulating the 13C NMR spinning sideband manifolds. This study shows that the ultrasonic mediated synthesis route is an easy and effective way not only to significantly reduce the total synthesis time of PMOs from days to a few hours, but also to easily screen a wide range of synthesis conditions in order to optimize and scale-up their production.

An efficient amplification pulse sequence for measuring chemical shift anisotropy under fast magic-angle spinning

A two-dimensional experiment for measuring chemical shift anisotropy (CSA) under fast magic-angle spinning (MAS) is presented. The chemical shift anisotropy evolution is amplified by a sequence of π-pulses that repetitively interrupt MAS averaging. The amplification generates spinning sideband manifolds in the indirect dimension separated by the isotropic shift along the direct dimension. The basic unit of the pulse sequence is designed based on the magic-angle turning experiment and can be concatenated for larger amplification factors.

A magic-angle turning NMR experiment for separating spinning sidebands of half-integer quadrupolar nuclei

A two-dimensional magic-angle turning NMR experiment is described for separating spinning sidebands of half-integer quadrupolar nuclei. The experiment is an alternative to quadrupolar phase-adjusted sideband separation (QPASS) [Chem. Phys. Lett. 272 (1997) 295] that yields infinite speed spectra in one dimension and spinning sideband manifolds in the other dimension. A shear transformation is introduced for processing of quadrupolar magic-angle turning (QMAT) data with time evolution of only one rotor period. The QMAT experiment has the advantages of averaging the first-order modulation of the pulse sequence efficiencies giving smaller residual spinning sidebands, linearly incrementing pulse timings for convenient practical implementation, and easily adjustable pulse spacings suitable for higher spinning frequencies.

Magnetization transfer magic-angle-spinning z-spectroscopy of excised tissues

NMR experiments devised to aid in analyses of tissues include magnetization transfer (MT), which can highlight the signals of biological macromolecules through cross-relaxation and/or chemical exchange processes with the bulk 1H water resonance, and high-resolution magic-angle-spinning (HRMAS) methods, akin to those used in solid-state NMR to introduce additional spectral resolution via the averaging of spin anisotropies. This paper explores the result of combining these methodologies, and reports on MT “z-spectroscopy” between water and cell components in excised tissues under a variety of HRMAS conditions. Main features arising from the resulting 1H “MTMAS” experiments include strong spinning sideband manifolds centered at the liquid water shift, high-resolution isotropic features coinciding with aliphatic and amide proton resonances, and a second sideband manifold arising as spinning speeds are increased. Interpretations are given for the origin of these various features, including simulations shedding further light onto the nature of MT NMR signals observed for tissue samples. Concurrently, histological examinations are reported validating the limits of HRMAS NMR procedures to the analysis of tissue samples preserved in a number of different ways.

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.

Preparation and structural organisation of heteroleptic tetraphenylantimony(V) complexes comprising unidentately and bidentately coordinated O, O′-dialkyldithiophosphate groups: Multinuclear ( 13C, 31P) CP/MAS NMR and single-crystal X-ray diffraction studies

O, O′-dipropyldithiophosphate and O, O′-di- iso-butyldithiophosphate (Dtph) tetraphenylantimony(V) complexes of the general formula [Sb(C 6H 5) 4{S 2P(OR) 2}] (R = C 3H 7, i-C 4H 9) were prepared and studied by means of 13C, 31P CP/MAS NMR spectroscopy and single-crystal X-ray diffraction. Distorted octahedral and trigonal bipyramidal molecular structures have been established for prepared complexes. These unexpected structural distinctions between chemically related compounds are defined by the principally different coordination modes of O, O′-dipropyldithiophosphate and O, O′-di- iso-butyldithiophosphate ligands in their molecular structures (i.e., S, S′-bidentate chelating and S-unidentately coordinated, respectively). To characterise quantitatively phosphorus sites in both species of dithiophosphate ligands, 31P chemical shift anisotropy parameters ( δ aniso and η) were calculated from spinning sideband manifolds in MAS NMR spectra. The 31P chemical shift tensors for the bidentate chelating and unidentately coordinated dithiophosphate ligands display a profoundly rhombic and nearly axially symmetric characters, respectively.

A Spectroscopic Study of Calcium Surface Sites and Adsorbed Iron Species at Aqueous Fluorapatite by Means of 1H and 31P MAS NMR

Assignments of the protolytic speciation at the calcium hydroxyl surface sites of synthetic fluorapatite and the chemical interactions between fluorapatite-maghemite and fluorapatite-Fe2+ ions have been studied by means of 1H and 31P single-pulse and 31P CP MAS NMR. Three possible forms of calcium hydroxyl surface sites have been suggested and assigned to [triple bond] CaOH, [triple bond]Ca(OH)2-, and [triple bond]CaOH2+, and their mutual ratios were found to vary as a function of pH. Due to their paramagnetic properties, iron species and Fe2+ ions adsorbed at the fluorapatite surface display a broad spinning sideband manifold in the single-pulse 31P MAS NMR spectra. The resonance lines in the 31P CP MAS NMR spectra originating from the bulk phosphate groups PO4(3-) and phosphorus surface sites [triple bond]POx and [triple bond]POxH decrease with increasing Fe2+ ion adsorption. When iron species originating from maghemite are adsorbed at the fluorapatite surface, no 31P NMR signal is detected, which supports the hypothesis that surface reactions occur between the phosphorus surface sites of fluorapatite and iron species.

Distinguishing Individual Lipid Headgroup Mobility and Phase Transitions in Raft-Forming Lipid Mixtures with 31P MAS NMR

A model membrane system composed of egg sphingomyelin (SM), 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC), and cholesterol was studied with static and magic angle spinning 31P NMR spectroscopy. This model membrane system is of significant biological relevance since it is known to form lipid rafts. 31P NMR under magic angle spinning conditions resolves the SM and DOPC headgroup resonances allowing for extraction of the 31P NMR parameters for the individual lipid components. The isotropic chemical shift, chemical shift anisotropy, and asymmetry parameter can be extracted from the spinning side band manifold of the individual components that form liquid-ordered and liquid-disordered domains. The magnitude of the 31P chemical shift anisotropy and the line width is used to determine headgroup mobility and monitor the gel-to-gel and gel-to-liquid crystalline phase transitions of SM as a function of temperature in these mixtures. Spin-spin relaxation measurements are in agreement with the line width results, reflecting mobility differences and some heterogeneities. It will be shown that the presence of DOPC and/or cholesterol greatly impacts the headgroup mobility of SM both above and below the liquid crystalline phase transition temperature, whereas DOPC displays only minor variations in these lipid mixtures.

51V Solid-State Magic Angle Spinning NMR Spectroscopy of Vanadium Chloroperoxidase

We report 51V solid-state NMR spectroscopy of the 67.5-kDa vanadium chloroperoxidase, at 14.1 T. We demonstrate that, despite the low concentration of vanadium sites in the protein (one per molecule, 1 mumol of vanadium spins in the entire sample), the spinning sideband manifold spanning the central and the satellite transitions is readily detectable. The quadrupolar and chemical shift anisotropy tensors have been determined by numerical simulations of the spinning sideband envelopes and the line shapes of the individual spinning sidebands corresponding to the central transition. The observed quadrupolar coupling constant C(Q) of 10.5 +/- 1.5 MHz and chemical shift anisotropy delta(sigma) of -520 +/- 13 ppm are sensitive reporters of the geometric and electronic structure of the vanadium center. Density functional theory calculations of the NMR spectroscopic observables for an extensive series of active site models indicate that the vanadate cofactor is most likely anionic with one axial hydroxo- group and an equatorial plane consisting of one hydroxo- and two oxo- groups. The work reported in this manuscript is the first example of 51V solid-state NMR spectroscopy applied to probe the vanadium center in a protein directly. This approach yields the detailed coordination environment of the metal unavailable from other experimental measurements and is expected to be generally applicable for studies of diamagnetic vanadium sites in metalloproteins.