Article pubs.acs.org/ac
Quantitative Analysis of Hydration Using Nitrogen-14 Nuclear Quadrupole Resonance Alan Gregorovič* Institute “Jožef Stefan”, Jamova 39, 1000 Ljubljana, Slovenia
ABSTRACT: Hydration is a quite common process in pharmaceutical solids. Sometimes it is desirable, as it stabilizes the crystal structure; in other cases it is unwanted, as it changes the physical and chemical properties of drugs. We here use 14N NQR spectroscopy to quantitatively analyze hydration of a model compound, 5-aminotetrazole. 14N NQR has some great advantages compared to other routinely used techniques to study hydration, like a very simple spectrum, single point calibration, and no need for special sample preparation, but the method’s great disadvantage is a rather small sensitivity. Nevertheless, here we demonstrate that 14N NQR, although being significantly less sensitive than XRD, NIR, and also 35Cl NQR, is still capable of providing excellent quantitative accuracies. We can achieve errors 99%, while the standard errors of regression are 16.3 mV for ATZ and 11.0 mV for ATZMH. These errors are only slightly larger than the probe noise which is measured to be vprobe = 10 ± 1 mV (empty probe). From this comparison we conclude that probe noise, which is mainly thermal noise, is the dominant source of uncertainty in our measurements. The accuracies of nATZ and nATZMH as determined from IATZ and IATZMH during a quantitative analysis (using eq 1 and eq 2) are defined by probe noise and are ΔnATZ = vprobe/i0ATZ = ± 0.60 mmol for ATZ and ΔnATZMH= ± 0.56 mmol for ATZMH or ±50 mg for ATZ and ±57 mg for ATZMH expressed for the respective masses (MATZ and MATZMH was taken into account). These values could be halved with a 4 fold increase of the D
DOI: 10.1021/acs.analchem.5b01492 Anal. Chem. XXXX, XXX, XXX−XXX
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Analytical Chemistry experimental time, i.e. to 64 h for ATZ and 16 h for ATZMH. In the case of ATZMH, we could do another 4-fold increase of the experimental time, to 64 h, but this is the maximum time we currently use for simple averaging. The results we found are extremely promising for 14N NQR based quantitative analysis. Part of the merit for good accuracies is in a very good thermal stabilization of the sample, which allows for very long measuring times. As is well-known, the NQR frequencies are very temperature dependent, with typical values of 1 kHz/K for 14N NQR.22 A poorly temperature stabilized measurement leads to a shift and broadening of the line shape which are proportional to the temperature swing. This introduces errors in coherent averaging. In addition, the probe sensitivity decreases when the signal frequency moves away from the tuning frequency ν0 as 1 − 2QΔν/ν0, where Δν is the frequency offset while Q is the probe quality factor. Special attention was also taken to position all the samples exactly in the middle of the coil, as the coil itself is also less sensitive toward the edges.23 Both factors were estimated to comprise up to 5% in our previous measurements, where we did not pay attention to these details. SLSE Measurements. When long experimental times cannot be used, for example real-time monitoring of hydration, one can use faster methods of detection. In 14N NQR, several pulse sequences can be used to achieve this, falling into two categories: (i) the “spin-lock” pulse sequences and (ii) the steady state pulse sequences. ATZ and ATZMH are suitable for the “spin-lock” sequences, where the most popular one is the SLSE sequence16 exciting a train of echoes and is shown in Figure 3a. This pulse sequence is very often used when searching for a resonance, since the average echo has a high S/N, but is less appropriate for quantitative analysis. The reason is relaxation. The echoes in the SLSE are not all of the same amplitude but slowly decay;16 the decay time is usually denoted by T2eff. The amplitude of the average echo is still proportional to the amount of sample but now also influenced by T2eff. In principle, there is no guarantee that T2eff will be the same in all samples, especially for those originating from different sources. We do often observe variations up to 20% for such samples. When planning these measurements, the variation of T2eff was our biggest concern, especially for the partially hydrated samples, due to a possibility of a random distribution of water molecules. To check the T2eff decays in our samples, we first obtained a thoroughly averaged SLSE signal and compared the T2eff decays for different samples. The results are shown in Figure 3b for the ATZ peak and in Figure 3c for the ATZMH peak. To our surprise, all the decays are practically identical. Nevertheless, these results do not mean that material prepared with different methods or under different conditions would not have a larger T2eff variability. Knowing precisely the T 2eff decay allows also the determination of the optimal number of echoes in a SLSE sequence. Namely, the S/N of the average echo depends on the number of averaged echoes. At smaller numbers, the S/N increases with each additional echo, then reaches a maximum (nmax averaged echoes) and then slowly fades away as the number of echoes further increases, because the echoes in the tail of the decay curve contain very little signal. From the measured decay curves, we find that for the ATZ peak nmax = 675, and the S/N of the average echo is 10.3 times larger than the S/N of the spin−echo. For the ATZMH peak nmax = 690, and the S/N factor here is 7.0. It should be stressed, however, that the S/N is not too sensitive on the number of echoes
Figure 3. (a) The SLSE pulse sequence, which consists of a preparatory pulse (usually 90°) and a train of equally spaced refocusing pulses (usually 90° or 180°). The echo is formed between the refocusing pulses (dashed line) with a maximum in the middle (empty square). (b) The normalized decay of the echo amplitudes at the ATZ frequency is shown for samples 1−5. The signal of sample 1 (blue line) has here the highest S/N. (c) The normalized echo amplitudes at the ATZMH frequency are shown. Now, sample 10 has the highest S/N. It is clear here that the decays are practically the same for all samples at a respective frequency.
around nmax, so that our choice of 512 echoes still provides a large S/N. For comparison, if one would average nmax equal echoes (no T2eff relaxation), the S/N of the averaged echo would be (nmax)1/2 times larger than the S/N of an individual echo, i.e. 26.0 times for ATZ and 26.3 times for ATZMH. The results presented here are valid for the SLSE sequence with a 2 × “90°” refocusing pulse; for the variant with a “90°” refocusing pulse we observe an almost identical behavior. Fast SLSE. The quantitative results obtained with the fast SLSE measurement are shown in Figure 4. Here, we show nATZ and nATZMH, which have been determined from the magnitude of the averaged SLSE echo using eq 1 and eq 2. The scaling constants i0ATZ and i0ATZMH have been determined from two separately measured SLSE responses with a large number of scans: sample no. 1 was used to determine i0ATZ and sample no. 10 for i0ATZMH. Note, the values for i0ATZ and i0ATZMH found here (not reported) are smaller than the one found previously for the spin−echo experiments, as the averaged echo is smaller than the spin−echo due to the T2eff decay. The solid lines in Figure 4 represent the expected amounts of nATZ and nATZMH based on nwater; i.e. n0ATZ − nwater and nwater, respectively. All the experimentally determined quantities nATZ and nATZMH are very close to their expected values. The standard error is 1.7 mmol for ATZ and 2.0 mmol for ATZMH. Thus, the quantitative accuracy of the fast SLSE method dropped 3−4 times E
DOI: 10.1021/acs.analchem.5b01492 Anal. Chem. XXXX, XXX, XXX−XXX
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estimates on the size of r0, but several DFT calculations suggests that r0 should be around several lattice constants. Now, we can look at few scenarios of water distribution in a partially hydrated crystal and inspect their influence on the peak area and line width. We use the ATZMH resonance as an example. In the first scenario, we consider water protruding in the crystallite as a single cluster, which grows as the hydration level increases until the crystallite absorbs the maximum amount of water. In such a scenario, the NQR resonance would always be relatively narrow and of a constant width. Its area would linearly increase with the amount of water at all hydration levels. In a second scenario, the water molecules form a layer just beneath the surface, which gets thicker as the hydration level increases. The resonance for a very thin layer should be broad, but probably observable, due to the anisotropic shape of the cluster (in one dimension, the cluster would be much larger than r0). The resonance in a thicker layer (>r0) should be narrow. A liner relationship between the peak area and water content should be here observed at all hydration levels, except perhaps at very small ones. In a third scenario, water molecules occupy random positions inside the crystallite then, as the hydration level increases, form very small clusters which eventually merge into intermediate clusters, until a fully ordered crystallite is obtained at 100% hydration. Here, we would observe a considerable departure from the linear dependence of the peak area on water content, as at smaller to intermediate hydration levels, the very small clusters would not produce observable resonance. In addition, when the resonance would appear, it should be broad, getting quickly narrower as the clusters progressively merge at higher hydration levels. Our measurements definitively support a scenario where at least intermediate clusters form because the dependence of IATZ and IATZMH on nwater is linear and apparently the sum of nATZ and nATZMH is constant, equal to the initial amount, n0ATZ. The line width of the ATZMH resonance is constant at all hydration levels, which would suggest the first or second scenario. The line width of the ATZ resonance however shows some variations, which would suggest the existence of many intermediate clusters. However, since these variations mainly occur at small water contents, it is difficult to imagine the large amounts of anhydrate material broken down into intermediate clusters by a rather small amount of water, as this should then be distributed in a thin framework, most probably making the ATZMH resonance unobservable. Given that this is not the case (the ATZMH resonance is nicely observed even at low water content), we conclude that the variations of ATZ line width is probably due to crystal structure defects. This could be checked by measuring the ATZ resonance very accurately before hydration and will certainly be the subject of our future investigations.
Figure 4. Amount of ATZ (nATZ) and ATZMH (nATZMH) in samples 1−10 estimated from the fast 14N NQR SLSE measurement shown as a function of the amount of absorbed water (nwater).
compared to the spin−echo method but is still good and might be acceptable for some applications, e.g. real-time monitoring of hydration or dehydration. We should note here that the SLSE signal obtained with four scans does not allow determination of T2eff due to the insufficient S/N. Discussion. The samples for this analysis could have been prepared also by mixing appropriate amounts of anhydrous ATZ and ATZMH instead of partially hydrating the samples, but we intentionally used the hydration method. The reason is related to the distribution of crystalline water in the samples. The mixed samples would consist of some completely anhydrous crystallites and some fully hydrated crystallites. Both types of crystallites would be ordered from the crystallographic point of view. This would then be reflected in the NQR parameters, which are well-defined in ordered environments, while being poorly defined in disordered environments. Contrary to the mixed samples, the partially hydrated samples contain partially hydrated crystallites with a difficult to predict distribution of crystalline water. The influence of crystalline water distribution on the ATZMH resonance is best understood by considering the 1/ r3 dependence of the NQR frequency on charges located a distance r from the nucleus.19 At some point, when r becomes sufficiently large r > r0, the charge influence on the NQR frequency becomes vanishingly small so that all charges located farther away than r0 can be ignored. Then we can define three classes of water clusters based on their size l: (i) very large clusters, where l ≫ r0, (ii) very small clusters, where l < r0, and (iii) intermediate clusters, where l ∼ 5r0. The NQR resonance pertaining to very large clusters is equal to the resonance in bulk and for well ordered crystallites also very narrow. The contribution of the surface layer (∼r0-thick), where the crystal is not completely ordered from the NQR point of view, is here negligible due a very small surface to volume ratio. The NQR resonance of very small clusters will be too broad to be observed, as all the nuclei would belong to the cluster surface layer, each nucleus having a different local environment, depending on how close to the edge of the cluster it is located. This will cause large variations in NQR frequency. In intermediate clusters, where the volume of the surface layer is of the same order as the volume of the cluster central region, the resonance will be broad, but observable. In addition, the line width should depend on l. So far, there are no experimental
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CONCLUSIONS We have used 14N NQR spectroscopy to quantify the amount of aminotetrazole and aminotetrazole monohydrate in several partially hydrated samples using two pulse sequences: (i) a spin−echo pulse sequence, which is very reliable but slowly accumulates signal, and (ii) a SLSE pulse sequence, which allows for much faster acquisitions, but is less accurate due to the signal dependence on some relaxation parameters. There are two key findings of these studies. First, the 14N NQR spectroscopy can provide very accurate quantitative information even though its intrinsic sensitivity is very small, all F
DOI: 10.1021/acs.analchem.5b01492 Anal. Chem. XXXX, XXX, XXX−XXX
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(17) Obata, S.; Takeya, S.; Fujihisa, H.; Honda, K.; Gotoh, Y. J. Phys. Chem. B 2010, 114, 12572. (18) Pirnat, J.; Lužnik, J.; Jazbinšek, V.; Ž agar, V.; Seliger, J.; Klapotke, T. M.; Trontelj, Z. Chem. Phys. 2009, 364, 98. (19) Slichter, C. P. Principle of Magnetic Resonance, 3rd ed.; Springer: Berlin, 1996. (20) Kyriakidou, G.; Jakobsson, A.; Althoefer, K.; Barras, J. Anal. Chem. 2015, 87, 3806. (21) Lužnik, J.; Pirnat, J.; Jazbinšek, V.; Lavrič, Z.; Srčič, S.; Trontelj, Z. Appl. Magn. Reson. 2013, 44, 735. (22) Seliger, J.; Ž agar, V.; Zidanšek, A.; Blinc, R. Chem. Phys. 2006, 331, 131. (23) Barras, J.; Katsura, S.; Sato-Akaba, H.; Itozaki, H.; Kyriakidou, G.; Rowe, M. D.; Althoefer, K. A.; Smith, J. A. S. Anal. Chem. 2012, 84, 8970.
provided that good temperature control of the sample is implemented, which allows long experimental times with a large amount of averages. The accuracy of a quantitative analysis at frequencies around 3.7−3.8 MHz is ∼1 mmol, when the spin− echo pulse sequence is used with 1024 repetitions. This estimate is not limited to aminotetrazole but can be used also for other molecular crystals having similar 14N NQR frequencies. And second, we have shown that the T2eff decay during the SLSE sequence is rather independent of the level of hydration, which allows the use of the echo train to increase the S/N and quantify hydration even faster, for aminotetrazole on the order of minutes, perhaps even faster with a single scan. This approach could be used for real-time monitoring of hydration and dehydration. We expect these findings to have important implications for the future of 14N NQR quantitative analysis in a variety of pharmaceutical applications, as quantitative 14N NQR is a robust and model-free technique which does not need special sample preparation.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The author thanks the student B. Ferjanc who helped with some measurements.
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REFERENCES
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