Triple-Quantum 23Na MAS NMR Spectroscopy as a Technique for

Jan 2, 2008 - Growth Des. , 2008, 8 (1), pp 6–10 ... Triple-quantum 23Na MAS NMR spectroscopy has been applied to characterize the three polymorphs ...
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CRYSTAL GROWTH & DESIGN 2008 VOL. 8, NO. 1 6–10

Communications Part of the Special Issue: Facets of Polymorphism in Crystals

Triple-Quantum 23Na MAS NMR Spectroscopy as a Technique for Probing Polymorphism in Sodium Salts Mingcan Xu and Kenneth D. M. Harris* School of Chemistry, Cardiff UniVersity, Park Place, Cardiff CF10 3AT, Wales, United Kingdom ReceiVed October 31, 2007; ReVised Manuscript ReceiVed December 4, 2007

ABSTRACT: Triple-quantum 23Na MAS NMR spectroscopy has been applied to characterize the three polymorphs of sodium acetate. The crystallographically distinct sodium sites in each of these polymorphs are uniquely identified from the triple-quantum 23Na MAS NMR spectra. These data provide access to the 23Na quadrupole interaction parameters (quadrupole coupling constant and asymmetry parameter) for each sodium site, which provide a quantitative measure of the local structural properties of the sodium cations in each polymorphic form. Polymorphism1 arises when a given type of molecule can form different crystal structures or, as in the present case, when a salt of a given composition can form different crystal structures. Although different polymorphs have the same chemical composition, their solid state properties are generally different as a consequence of their different crystal structures. In recent years, there has been substantial research activity in this field, driven both by fundamental scientific curiosity and by industrial necessity. The physical and chemical properties of polymorphs (such as chemical reactivity, solubility, melting point, and dynamics) depend strongly on crystal structure, and polymorphic systems therefore provide an ideal opportunity to study relationships between crystal structure and physical properties of solids. Although crystal structures can generally be determined straightforwardly by single-crystal X-ray diffraction2 (or, particularly if single crystals of suitable size and quality are not available, by powder X-ray diffraction techniques3), solid-state NMR spectroscopy is a valuable complementary technique to X-ray diffraction, particularly as it can provide detailed information on local structural properties, disorder, and dynamic properties. There have been many applications of solid state NMR techniques in polymorphism research, reviewed elsewhere,4 including studies relating to chemical reactivity,5a disorder,5b and functional group dynamics5c in polymorphic systems. In different polymorphic forms of a given molecule, the different spatial arrangements of the molecules can lead to significant differences in the local environment for each atom within the molecule, leading to different values of the NMR parameters that characterize a given nucleus in the different polymorphs. In * Corresponding author. E-mail: [email protected].

principle, such information can be extracted from the NMR spectrum for each crystallographically distinct site for the nucleus of interest. For nuclei with spin I ) 1/2 (such as 13C), magic angle sample spinning (MAS) can remove most anisotropic interactions, allowing high-resolution solid-state NMR spectra to be recorded readily6 (sometimes, as in the case of high-resolution 13C NMR of organic materials, high-power 1H decoupling is also required in conjunction with MAS). Such studies have been exploited widely in polymorphism research, on the basis of the fact that each crystallographically distinct site in the asymmetric unit corresponds, in principle, to an individual peak in the high-resolution NMR spectrum. In the case of organic materials, most solid-state NMR studies of polymorphism have focused on high-resolution solid state 13C NMR, for which the main property of interest has been the isotropic 13C NMR chemical shift, and the fact that the set of isotropic chemical shifts observed in the high-resolution solid state 13C NMR spectrum provides a basis for distinguishing the different polymorphic forms. A large number of NMR-active nuclei, on the other hand, have I g 1, and are termed quadrupolar nuclei. For such nuclei, quadrupolar interactions (see Section 2), which are not present in the case of spin I ) 1/2 nuclei, can give rise to significant line broadening. Thus, for example, the second-order quadrupolar interaction can be very large, and is not removed by MAS. As a consequence, for such nuclei, it can be substantially more difficult to record high-resolution solid-state NMR spectra (of the type recorded routinely for 13C NMR) that enable different polymorphs to be distinguished. Thus, although solid-state NMR studies of spin I ) 1/2 nuclei such as 13C are applied routinely to characterize polymorphic systems, there have been far fewer solid-state NMR studies of quadrupolar nuclei for polymorphic systems. Neverthe-

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Communications less, it is important to emphasize that studies of quadrupolar nuclei allow access to information on the quadrupole interaction tensor for the nucleus under investigation, which contains valuable information on properties such as the local structure and symmetry of the site occupied by the nucleus and the dynamic properties of the site (as widely exploited, for example, in 2H NMR studies of the dynamics of organic solids5c). Indeed, the quadrupole interaction tensor can be particularly sensitive to changes in such properties, and thus solid-state NMR studies of quadrupolar nuclei are potentially a very informative approach in the investigation of polymorphic systems. A breakthrough in the study of quadrupolar nuclei was the development of the multiple-quantum (MQ) MAS NMR technique.7 As discussed below, this two-dimensional technique allows substantially more detailed information to be obtained concerning the quadrupolar nucleus of interest, than would be possible from the standard one-dimensional MAS NMR spectrum of the same material. To date, however, only very few studies of polymorphic materials using MQ-MAS NMR spectroscopy have been published and have focused only on inorganic materials such as P2O5, Na5P3O10 and NaNbO3.8–10 So far, the advantages of using MQMAS NMR spectroscopy have not been exploited to investigate polymorphism in organic materials. In the present paper, we address this issue by reporting 23Na MQ-MAS NMR studies of the three polymorphs of sodium acetate. Quadrupolar nuclei possess an electric quadrupole moment eQ, which interacts with the electric field gradient (EFG) at the site of the nucleus, giving rise to the quadrupolar interaction. In the principal axis system, the EFG tensor is described by three components Vxx () ∂2V/∂x2), Vyy () ∂2V/∂y2), and Vzz () ∂2V/∂z2), where V is the electric potential and by convention |Vzz| g |Vyy| g |Vxx|. As the EFG tensor is traceless, Vzz ) –(Vxx + Vyy). It is conventional to describe the quadrupole interaction using two parameters (corresponding to the fact that there are two independent principal components of the EFG tensor): the static quadrupole coupling constant, defined as χ ) eQVzz/h, and the static asymmetry parameter η, defined as η ) (|Vyy| – |Vxx|)/|Vzz|. Note that the value of η is in the range 0 e η e 1. MQ-MAS NMR spectroscopy is a two-dimensional technique that allows high-resolution solid-state NMR spectra to be recorded for half-integer quadrupolar nuclei (i.e., with spin I ) 3/2, 5/2, 7/2, etc). In the present case, we focus on the 23Na nucleus, which has I ) 3/2 and 100% natural abundance. The basic idea of the MQ-MAS technique is to obtain high-resolution solid-state NMR spectra by manipulating spin coherences. At first, a symmetric multiple-quantum coherence is excited. Multiple-quantum coherences are allowed to evolve for a time t1, and after an intermediate stage, the multiple-quantum coherences are finally transferred into observable single-quantum coherences. An echo forms at time t2 ) f(t1). After Fourier transformation and proper shearing, an isotropic spectrum is obtained along the F1 dimension; this spectrum depends on the isotropic chemical shift and the isotropic component of the second-order quadrupolar interaction11 In the original experiments, a simple two-pulse sequence was used, which led to poor sensitivity and “phase twisted” twodimensional lineshapes.7 New pulse schemes were devised, such as z-filter,12 shifted-echo,13 fast-amplitude modulation,14 and double-frequency sweeping.15 In the three-pulse z-filter scheme, a symmetric coherence-transfer pathway is selected: (0, ( p, 0, –1). The first pulse creates the maximum ( p coherences, which after an evolution time t1, are transferred along z by the second pulse to remove any phase memory from all crystallites. The third pulse is a selective low-power π/2 pulse transforming zero-order coherences to an observable signal. As the signal is amplitude-modulated, it is easiest to optimize the lengths of the three pulses independently.12,16 Sodium acetate is known to exist in three polymorphic forms, denoted polymorphs I, II, and β.17,18 Polymorph β was obtained by dehydration of sodium acetate trihydrate under a vacuum (the sample of sodium acetate trihydrate used in this work was purchased

Crystal Growth & Design, Vol. 8, No. 1, 2008 7

Figure 1. High-resolution solid state 13C NMR spectra recorded for polymorphs of sodium acetate: (a) polymorph I, (b) polymorph II, and (c) polymorph β. Note that the sample of polymorph II used in this study contains a small impurity amount of polymorph β.

from ACROS). Polymorph I was obtained by crystallization from an aqueous solution of sodium acetate at 373 K, by evaporation of solvent. Polymorph II was obtained by crystallization from a solution of sodium acetate in methanol by slow evaporation in a glovebox under a flow of nitrogen gas at ambient temperature. Two-dimensional triple-quantum (3Q) 23Na MAS NMR spectra were recorded at 79.39 MHz on a Chemagnetics Infinity 300 spectrometer using the three-pulse z-filter sequence.12,16 The mutation rates of the hard pulses P1 and P2 were 100 kHz, with optimized pulse durations of 7.9 and 1.7 µs, respectively. For the third pulse P3, the mutation rate was set to 20 kHz with pulse duration 12 µs. The z-filter delay ∆t was 10 µs. The hyper complex approach was applied to obtain a pure absorption mode of the twodimensional line shape.16 All samples were packed into 4 mm rotors in a glovebox under flowing nitrogen. The 23Na 3Q-MAS NMR spectra were recorded using an HXY triple-resonance probe with a MAS frequency of 12 kHz. For each spectrum, 120 scans were accumulated with a recycle delay of 1 s. The 23Na chemical shifts are referenced to an aqueous solution of sodium chloride (1.0 mol dm–3). High-resolution solid state 13C NMR spectra were recorded at 75.48 MHz on a Chemagnetics Infinity 300 spectrometer (7.5 mm HX probe) under conditions of 13C r 1H cross-polarization (contact time, 1 ms), high-power 1H decoupling, and MAS (3 kHz). The recycle delay was 30 s. The crystal structures of the three polymorphs of sodium acetate have been determined previously17,18 from single-crystal or powder X-ray diffraction techniques. Details of the crystal structures are discussed below. High-resolution solid-state 13C NMR19 highlights the differences in the local structures of the acetate anions in the different polymorphic forms, and the carbon signal for the carboxylate group in particular provides clear discrimination between the different polymorphic forms (see Figure 1). The present paper demonstrates that 23Na 3Q-MAS NMR is a powerful technique for characterization of the sites occupied by the sodium cations in the different polymorphic forms, particularly as it provides quantitative information on the quadrupole interaction parameters (i.e., χ and η) that characterize each sodium site. The 23Na 3Q-MAS NMR spectrum of polymorph I of sodium acetate is shown in Figure 2a, and clearly demonstrates the existence of two crystallographically distinct sodium sites in this polymorph. We emphasize that this fact would not be readily apparent from

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Figure 2. Solid-state 23Na 3Q-MAS NMR spectra recorded for polymorphs of sodium acetate: (a) polymorph I, (b) polymorph II, and (c) polymorph β. Table 1. Quadrupole Interaction Parameters and Isotropic Shifts for the Polymorphs of Sodium Acetate Determined from the 23Na 3Q-MAS NMR Spectra Discussed in the Texta polymorph I χ (MHz) η δ

Na(I-1) site

Na(I-2) site

polymorph II Na(II) site

polymorph β Na(β) site

1.14 ( 0.09 0.71 ( 0.14 1.64

1.42 ( 0.11 0.69 ( 0.14 4.74

1.35 ( 0.11 0.78 ( 0.16 4.10

1.22 ( 0.10 0.16 ( 0.03 1.38

a The estimated errors in the extraction of χ and η from the 23Na 3Q-MAS NMR spectra are indicated. The maximum estimated error in the determination of δ is (0.01 ppm.

inspection of the standard one-dimensional 23Na MAS NMR spectrum, given the substantial overlap of the broad signals from the two sodium sites. On projection of the two-dimensional 23Na 3Q-MAS NMR spectrum on to the isotropic dimension, two wellseparated signals are observed. The measured intensity ratio of these signals is close to 2:1, consistent with the known crystal structure17 of polymorph I (orthorhombic, space group Pcca) in which there are two sodium cations in the asymmetric unit, one on a general position and the other on a special position of multiplicity 2 (a 2-fold rotation axis). These two sites are denoted Na(I-1) and Na(I2), respectively. The high-resolution 13C NMR spectrum of polymorph I (Figure 1a) shows two signals for the carboxylate group of the acetate anion; again, one of the acetate anions in the asymmetric unit occupies a general position, whereas the other is located on a 2-fold rotation axis, and the intensity ratio of these signals is again close to 2:1. The cross-sections of the 23Na NMR signals for both sodium sites are shown on the left side of Figure 2a, and each exhibits a characteristic quadrupolar line shape, from which the quadrupole interaction parameters have been derived according to the method of Engelhardt20 (Table 1). The values of η for the two sites are close to each other (0.71 and 0.69), whereas there is a more significant difference between the values of χ for the two sites (1.14 and 1.42 MHz). Polymorph II has a layered structure,16 which is characterized by stacking defects of the layers that give rise to two alternative domains described by the orthorhombic space groups Pcca and Icab.

The different domains correspond to a translation of the layers within the structure relative to each other, but the local environment of the sodium cation within each layer is the same in each domain, and thus there is only one type of local structure for the sodium cations in this polymorph. This sodium site, which lies on a 2-fold rotation axis, is here denoted Na(II). Correspondingly, the 23Na 3Q-MAS NMR spectrum (Figure 2b) shows only one signal. The measured quadrupole interaction parameters are χ ) 1.35 MHz and η ) 0.78, which are relatively close to the values for the Na(I-2) site of polymorph I. Polymorph β of sodium acetate is prepared by dehydration of sodium acetate trihydrate under a vacuum, and the reported crystal structure is orthorhombic with space group Pmn21.18 There is one sodium site (here denoted Na(β)) in the asymmetric unit, which lies on a crystallographic mirror plane. Correspondingly, the 23Na 3Q-MAS NMR spectrum exhibits one signal, with χ ) 1.22 MHz and η ) 0.16. It is noteworthy that this value of η is substantially lower than that for any of the sodium sites in polymorphs I and II. As a consequence of the low value of η, polymorph β would represent an ideal sample to use for setting up 23Na 3Q-MAS NMR experiments. In summary, the main features from the 23Na 3Q-MAS NMR results (Table 1) are: (i) the values of χ and η are very similar for the Na(I-2) and Na(II) sites; (ii) the values of χ are higher for the Na(I-2) and Na(II) sites than for the Na(I-1) and Na(β) sites; and (iii) the value of η for the Na(β) site is significantly lower than for the sodium sites in the other polymorphs. Clearly, the values of the 23Na quadrupole interaction parameters depend on the details of the crystal structures of the different polymorphic forms, and in particular on the details of the structure in the local vicinity of the sodium cations. Given that the 23Na quadrupole interaction parameters depend directly on the electric field gradient (EFG) tensor at the site of the 23Na nucleus, it is not straightforward to rationalize differences in the 23Na quadrupole interaction parameters directly from differences in local structure, as it is not straightforward to deduce, even in qualitative terms, how a given change in local structure (e.g., slight differences in Na · · · O distances or slight differences in the spatial arrangement

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Figure 3. Local structure of the sodium sites in the three polymorphs of sodium acetate, viewed in different directions in (a) and (b).

of the set of oxygen atoms in the first coordination shell around the sodium cation) will influence the EFG tensor at the site of the nucleus and hence influence the 23Na quadrupole interaction parameters. To assess such issues rigorously, it is necessary to carry out periodic electronic structure calculations for the different structures in order to compute the EFG tensors within the crystal structures (as carried out previously to assess differences in quadrupolar interaction parameters between polymorphs in the case of the 2H nucleus21). Such calculations are currently in progress for the polymorphs of sodium acetate.22 Nevertheless, it is instructive to highlight the key differences (and similarities) in the local structural properties of the sodium sites in the three polymorphs of sodium acetate, as such differences undoubtedly contribute to the observed differences in the quadrupole interaction parameters. First, we note that for all polymorphs (and for both sodium sites of polymorph I), the sodium cation is surrounded by six oxygen atoms from acetate anions, and here we consider only this first coordination shell. The spatial arrangement of these six oxygen atoms is remarkably similar for all the sodium sites and is summarized in Figure 3a. Thus, there are four oxygen atoms (termed “basal” oxygen atoms) lying in an approximately square arrangement in a plane, with the sodium cation lying just above this plane. On the other side of the sodium cation, there are two other oxygen atoms (termed “nonbasal” oxygen atoms). Clearly the geometry of this arrangement reflects the symmetry of the sodium site, and thus for the cases with 2-fold symmetry (i.e., Na(I-2) and Na(II)), we have r1 ) r2, r3 ) r6, and r4 ) r5, whereas for the case with mirror symmetry (i.e., Na(β)), we have r1 * r2, r3 ) r5, and r4 ) r6 (note that the two nonbasal oxygen atoms and the sodium cation lie within the mirror plane). For all sodium sites, the Na · · · O distances for the basal oxygen atoms are all relatively short and lie in the range 2.31–2.47 Å, and all O · · · Na · · · O angles involving the basal oxygen atoms lie in the range 80–100°. As a consequence, the four basal oxygen atoms form an approximately square arrangement. The main differences in local structure for the different sodium sites concern the positions of the nonbasal oxygen atoms. The Na · · · O distances for the nonbasal oxygen atoms are typically longer than for the basal oxygen atoms, and are all in the range 2.56–2.80 Å with the exception of the Na(I-1) and Na(β) sites for which one of these Na · · · O distances is reasonably short (2.47 and 2.48 Å, respectively). The fact that both of these Na · · · O distances are long for the Na(I-2) and Na(II) sites, whereas one of these Na · · · O distances is long and the other relatively short for the Na(I-1) and Na(β) sites, is the main difference between the local structures of the Na(I1) and Na(β) sites in comparison with the Na(I-2) and Na(II) sites, and may be a factor contributing to the higher values of χ observed for the Na(I-2) and Na(II) sites. We also note that the set of Na · · · O

Crystal Growth & Design, Vol. 8, No. 1, 2008 9 distances (and the local symmetry (2-fold axis)) at the Na(I-2) and Na(II) sites are very similar, which is undoubtedly related to the fact that the values of χ and η are very similar for these sites. Another structural difference concerns the orientation of the plane formed by the sodium cation and the two nonbasal oxygen atoms relative to the “square” formed by the basal oxygen atoms (see Figure 3b). The angle ω, defined in Figure 3b, is exactly 90° for the Na(β) site, as a consequence of the mirror symmetry of this site, whereas for all other sodium sites, the value of ω differs from 90° (Na(I-1), ω ≈ 81°; Na(I-2), ω ≈ 84°; Na(II), ω ≈ 70°). This is the main structural feature that distinguishes the local structure of the Na(β) site in comparison with the Na(I-1), Na(I-2), and Na(II) sites, and may be a factor contributing to the substantially lower value of η observed for the Na(β) site. As discussed above, we do not imply that the structural differences highlighted here are solely responsible for the differences in quadrupole interaction parameters observed for the different sodium sites in the three polymorphs, and we emphasize that much more detailed insights will be generated from periodic electronic structure calculations that are currently in progress.22 As discussed above, however, the local structures of all the sodium sites in the three polymorphs are actually remarkably similar, and the small structural differences highlighted above point toward the fact that the 23Na quadrupole interaction parameters are sensitive to even small differences in local structural features. Finally, we note that projection of the two-dimensional 23Na 3QMAS NMR spectra onto the isotropic dimension (F1) yields a parameter (denoted δ in Table 1) that depends on the isotropic 23Na chemical shift and the isotropic component of the second-order 23Na quadrupolar interaction. These values again (as with χ) provide a clear discrimination between the Na(I-2) and Na(II) sites on the one hand, and the Na(I-1) and Na(β) sites on the other (with a higher value of δ in the former case). However, given that δ subsumes the effects of both the isotropic chemical shift and the isotropic component of the second-order quadrupolar interaction, a qualitative interpretation of the observed values of δ on the basis of the comparison of structural properties of the different polymorphs is not readily justified. In summary, the 23Na 3Q-MAS NMR experiments reported here have yielded clear differences in the 23Na quadrupole interaction parameters for the sodium sites in the three polymorphs of sodium acetate. It is clear from the results presented here that 23Na 3QMAS NMR spectroscopy is a sensitive technique to distinguish different polymorphic forms in the present case, and we anticipate that this will prove to be an equally powerful approach to distinguish different polymorphic forms of other sodium salts. Although, in the present case, the crystal structures of the three polymorphs of sodium acetate are already known and the results of the 23Na 3QMAS NMR studies are interpreted in the knowledge of these crystal structures, other applications of the MQ-MAS technique can be clearly envisaged in which the aim is to yield structural insights for polymorphic systems in cases for which the crystal structures are not known. Finally, we note that the local structural information discussed in the present paper assumes averaging over the rapid smallamplitude motions (e.g., librational motions) that inevitably occur in the structures of the three polymorphs investigated, an issue that may be investigated directly by other NMR techniques involving variabletemperature studies (see, for example, refs 23–25).

Acknowledgment. We are grateful for financial support from Cardiff University and the Basic Technology Program of the U.K. Research Councils (Project entitled Control and Prediction of the Organic Solid State).

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