Selective Detection and Quantitation of Organic Molecule

Jun 1, 2010 - Duangporn Wanapun,† Umesh S. Kestur,‡ David J. Kissick,† Garth J. Simpson,*,† and Lynne S. Taylor*,‡. Departments of Chemistry...
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Anal. Chem. 2010, 82, 5425–5432

Selective Detection and Quantitation of Organic Molecule Crystallization by Second Harmonic Generation Microscopy Duangporn Wanapun,† Umesh S. Kestur,‡ David J. Kissick,† Garth J. Simpson,*,† and Lynne S. Taylor*,‡ Departments of Chemistry and Industrial and Physical Pharmacy, Purdue University, West Lafayette, Indiana 47907 Second order nonlinear optical imaging of chiral crystals (SONICC) was applied to selectively detect crystal formation at early stages and characterize the kinetics of nucleation and growth. SONICC relies on second harmonic generation (SHG), a nonlinear optical effect that only arises from noncentosymmetric ordered domain structures, which include crystals of chiral molecules. The model systems studied include pharmaceutically relevant compounds: griseofulvin and chlorpropamide. SONICC demonstrates low detection limits producing an 8 order of magnitude improvement relative to macroscopic average techniques and 5 order of magnitude improvement relative to optical microscopy. SONICC was also applied to examine the kinetics of crystallization in amorphous griseofulvin. The results show that SONICC enables simultaneous monitoring of individual crystal growth, nucleation rate, and macroscopic crystallization kinetics. The ability to characterize and control crystal formation is critical for many technological applications and is of fundamental importance. The solid state properties of active pharmaceutical ingredients (APIs) are of critical importance to their processability, stability, safety, and efficacy, and thus, these properties must be carefully controlled and subject to regulatory scrutiny. APIs can potentially exist in numerous solid state forms including polymorphs, hydrates, cocrystals, salts, and amorphous materials.1 The free energy of the solid form varies with the solid state structure, with subsequent implications for important physicochemical properties such as apparent solubility and chemical stability. A large percentage of pharmacologically active compounds suffer from poor aqueous solubility and consequently bioavailability, which in turn has provided the motivation for the development of formulations containing high energy solid state forms. Amorphous solids are an attractive option for increasing the bioavailability of APIs. As a result of the absence of long-range, three-dimensional order, amorphous systems have a higher free energy than the corresponding crystalline phase(s), and, due to the absence of the crystal lattice, typically have a faster dissolution rate. However, as a consequence of their higher free energy, amorphous APIs * Corresponding authors. E-mail: [email protected] (G.J.S.); lstaylor@ purdue.edu (L.S.T.). † Department of Chemistry. ‡ Department of Industrial and Physical Pharmacy. (1) Byrn, S.; Pfeiffer, R.; Stephenson, G.; Grant, D. J. W.; Gleason, W. B. Solid State Chemistry of Drugs; 2nd ed.; SSCI Inc.: West Lafayette, 1999. 10.1021/ac100564f  2010 American Chemical Society Published on Web 06/01/2010

have the potential to crystallize over time scales that vary considerably from compound to compound and also with external conditions such as temperature and relative humidity.2-5 Crystallization will profoundly influence the bioavailability of the API and, therefore, must be understood at a fundamental level, detected at an early stage, and where possible, completely inhibited over the lifetime of the product. Several formulation strategies have been utilized to stabilize amorphous formulations, most notably the use of polymeric crystallization inhibitors.6-9 Clearly, in order to understand and control the crystallization behavior of amorphous systems, analytical methods that enable the detection and quantification of crystals are essential. A major challenge in assessing the long-term stability of amorphous materials is the long times required for stability studies, which are dictated by the earliest time point at which crystal formation can be definitively detected. Currently, thermal, optical, X-ray diffraction, and spectrochemical techniques10-18 are typically used to detect and characterize crystal formation. Each of these routine methods has its own strengths and limitations. Most importantly, detection of crystallinity below 1% is a challenging limit for existing analytical techniques, particularly in the complex matrixes that are charac(2) Morris, K. R.; Newman, A. W.; Bugay, D. E.; Ranadive, S. A.; Singh, A. K.; Szyper, M.; Varia, S. A.; Brittain, H. G.; Serajuddin, A. T. M. Int. J. Pharm. 1994, 108 (3), 195–206. (3) Konno, H.; Taylor, L. S. Pharm. Res. 2008, 25 (4), 969–978. (4) Rumondor, A. C. F.; Stanford, L. A.; Taylor, L. S. Pharm. Res. 2009, 26 (12), 2599–2606. (5) Qi, S.; Weuts, I.; De Cort, S.; Stokbroekx, S.; Leemans, R.; Reading, M.; Belton, P.; Craig, D. Q. M. J. Pharm. Sci. , 99 (1), 196–208. (6) Simonelli, A. P.; Mehta, S. C.; Higuchi, W. I. J. Pharm. Sci. 1969, 58 (5), 538–549. (7) Yoshioka, M.; Hancock, B. C.; Zografi, G. J. Pharm. Sci. 1995, 84 (8), 983–986. (8) Serajuddin, A. T. M. J. Pharm. Sci. 1999, 88 (10), 1058–1066. (9) Leuner, C.; Dressman, J. Eur. J. Pharm. Biopharm. 2000, 50 (1), 47–60. (10) Erdemir, D.; Lee, A. Y.; Myerson, A. S. Curr. Opin. Drug Discovery Dev. 2007, 10, 746–755. (11) Gobey, J.; Cole, M.; Janiszewski, J.; Covey, T.; Chau, T.; Kovarik, P.; Corr, J. Anal. Chem. 2005, 77 (17), 5643–5654. (12) Yoshioka, M.; Hancock, B. C.; Zografi, G. J. Pharm. Sci. 1994, 83 (12), 1700–1705. (13) Miller, J. M.; Collman, B. M.; Greene, L. R.; Grant, D. J. W.; Blackburn, A. C. Pharm. Dev. Technol. 2005, 10 (2), 291–297. (14) Berry, D. J.; Seaton, C. C.; Clegg, W.; Harrington, R. W.; Coles, S. J.; Horton, P. N.; Hursthouse, M. B.; Storey, R.; Jones, W.; Friscic, T.; Blagden, N. Cryst. Growth Des. 2008, 8 (5), 1697–1712. (15) Abu Bakar, M. R.; Nagy, Z. K.; Saleemi, A. N.; Rielly, C. D. Cryst. Growth Des. 2009, 9 (3), 1378–1384. (16) Harris, R. K. Analyst 2006, 131 (3), 351–373. (17) Bugay, D. E. Adv. Drug Delivery Rev. 2001, 48 (1), 43–65. (18) Newman, A. W.; Byrn, S. R. Drug Discovery Today 2003, 8 (19), 898–905.

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teristic of formulated products. Early crystal detection would be extremely beneficial, enabling a rapid assessment of the crystallization tendency of a given compound and allowing for efficient screening of crystallization inhibitors. Furthermore, sensitive detection of crystal formation could provide insights into fundamental factors governing nucleation and crystal growth in highly viscous organic systems such as glasses and supercooled liquids. Early detection of crystallization in amorphous systems is important to enable a complete description of crystallization kinetics. Crystallization is a two stage process consisting of nucleation followed by growth of viable nuclei. Typically, when crystallization is experimentally monitored, a lag period occurs, before crystals can be detected. This lag period is usually ascribed to nucleation, and it is clear that the length of this lag period will be dependent on the sensitivity of the analytical method to the relative fraction and/or size of the crystallites. Several methods are commonly used to study crystallization kinetics;3,19-22 however, the information provided by these tools is usually incomplete. For example, isothermal calorimetry can effectively monitor the enthalpy of crystallization and allow an estimation of overall rate of crystallization, but it does not directly allow for the independent assessment of the crystal nucleation and growth rates. X-ray powder diffraction and spectroscopic techniques can measure the lag time before crystallization events can be detected and then be used to monitor the overall crystallization rate but are only sensitive to about 1% crystallinity.23,24 Conventional optical microscopy (OM) enables monitoring of both crystal nucleation and growth but still suffers from fundamental limitations associated with incoherent optical techniques and is only easily applicable for optically transparent materials. OM represents a reasonable compromise between sensitivity and ease of use. However, OM still requires a detectable crystal size of several micrometers in order to definitively distinguish organic crystals (e.g., by detection of crystal birefringence) from noncrystalline particles or other scattering centers. As a result, OM can be difficult to reliably use for quantitative analysis of early stage crystal growth. More importantly, simple OM methods are currently limited to characterization of transparent media, as scattering in complex matrixes and powders complicate definitive crystal detection. In this study, second order nonlinear optical imaging of chiral crystal (SONICC)25 is explored as a possible sensitive and selective alternative for the detection of crystallization from model amorphous systems. In the presence of intense optical fields (e.g., such as those arising within the focal volume of a pulsed laser), interactions between light and matter that scale nonlinearly with peak intensity start to become significant. Multiphoton absorption and second harmonic generation (i.e., the frequency doubling of light) have been increasingly explored and utilized in several fields (19) Hancock, B. C.; Shamblin, S. L.; Zografi, G. Pharm. Res. 1995, 12 (6), 799–806. (20) Aso, Y.; Yoshioka, S.; Kojima, S. J. Pharm. Sci. 2000, 89 (3), 408–416. (21) Alie, J.; Menegotto, J.; Cardon, P.; Duplaa, H.; Caron, A.; Lacabanne, C.; Bauer, M. J. Pharm. Sci. 2004, 93 (1), 218–233. (22) Zhou, D.; Zhang, G. G. Z.; Law, D.; Grant, D. J. W.; Schmitt, E. A. Mol. Pharm. 2008, 5 (6), 927–936. (23) Taylor, L. S.; Zografi, G. Pharm. Res. 1998, 15 (5), 755–761. (24) Forster, A.; Hempenstall, J.; Rades, T. J. Pharm. Pharmacol. 2001, 53 (3), 303–315. (25) Wampler, R. D.; Kissick, D. J.; Dehen, C. J.; Gualtieri, E. J.; Grey, J. L.; Wang, H. F.; Thompson, D. H.; Cheng, J. X.; Simpson, G. J. J. Am. Chem. Soc. 2008, 130 (43), 14076–14077.

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including surface characterization, analysis of pharmaceutical crystalline powders,26-28 and deep tissue imaging.29-33 Second harmonic generation (SHG), the nonlinear optical effect underlying SONICC, describes the up-conversion to generate light at twice the energy (half the wavelength). As a result of symmetry properties underpinning second order nonlinear optical interactions, SHG is allowed only from noncentosymmetric systems (i.e., those exhibiting an absence of inversion symmetry), which includes surfaces and interfaces, as well as all homochiral crystals (i.e., crystals comprised of unit cells with nonsuperimposable mirror images).However, isotropic and centosymmetric systems, including liquids, glasses, and other amorphous materials lacking long-range order (relative to the wavelength of light) generate no coherent SHG and negligible background due to nearly perfect cancellation. Furthermore, SONICC shares the same high penetration depths of multiphoton excited fluorescence in turbid media, as the focal volume is generally the only location with sufficient intensity to produce significant SHG. Initial investigations with well-characterized pharmaceutical systems are described in the present work to assess the potential utility of SONICC for characterization of API crystallization at the nanoand microscales. MATERIALS AND METHODS Amorphous API Preparation. Griseofulvin ((2S,6′R)-7-chloro2′,4,6-trimethoxy-6′-methyl-3H,4′H-spiro[1-benzofuran-2,1′cyclohex[2]ene]-3,4′-dione) was purchased from Hawkins Inc., Minneapolis, MN, and chlorpropamide (4-chloro-N-(propylcarbamoyl)benzenesulfonamide) was purchased from Sigma-Aldrich Co, St Louis, MO. About 1-3 mg of the drug was melted onto a precleaned microscopic cover glass. The samples were held in the molten state for a period of 2-4 min and were rapidly quenched by placing them on a cold surface. The effect of moisture was minimized by a constant nitrogen purge throughout the experiment. Formation of an amorphous material was confirmed by the absence of birefringence using polarization light microscopy (Nikon Eclipse E600 POL microscope, Nikon Corp Tokyo, Japan). Monitoring API Crystallization. Amorphous griseofulvin and chlorpropamide were maintained above their glass transition temperatures (Tg of griseofulvin is 88.9 °C,22 Tg of chlorpropamide is 15.1 °C34) at 120 and 30 °C during image acquisition, respectively. Isothermal crystallization was monitored by multimodal SHG and conventional optical microscopy. Since the efficiency of coherent SHG depends on the peak power of the photon energy source, an ultrafast laser with high (26) Strachan, C. J.; Rades, T.; Lee, C. J. Opt. Lasers Eng. 2005, 43 (2), 209– 220. (27) Strachan, C. J.; Lee, C. J.; Rades, T. J. Pharm. Sci. 2004, 93 (3), 733–742. (28) Lee, C. J.; Strachan, C. J.; Manson, P. J.; Rades, T. J. Pharm. Pharmacol. 2007, 59 (2), 241–250. (29) Zipfel, W. R.; Williams, R. M.; Christie, R.; Nikitin, A. Y.; Hyman, B. T.; Webb, W. W. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 7075–7080. (30) Campagnola, P. J.; Loew, L. M. Nat. Biotechnol. 2003, 21 (11), 1356–1360. (31) Campagnola, P. J.; Millard, A. C.; Terasaki, M.; Hoppe, P. E.; Malone, C. J.; Mohler, W. A. Biophys. J. 2002, 82 (1), 493–508. (32) Millard, A. C.; Campagnola, P. J.; Mohler, W.; Lewis, A.; Loew, L. M. Second harmonic imaging microscopy. In Biophotonics, Pt B; Academic Press Inc: San Diego, 2003; Vol. 361, pp 47-69. (33) Zoumi, A.; Yeh, A.; Tromberg, B. J. Proc. Natl. Acad. Sci. U.S.A. 2002, 99 (17), 11014–11019. (34) Wildfong, P. L. D.; Morley, N. A.; Moore, M. D.; Morris, K. R. J. Pharm. Biomed. Anal. 2005, 39 (1-2), 1–7.

Figure 1. Crystallization of two similarly prepared amorphous griseofulvin thin films at 120 °C monitored by SONICC and OM. Griseofulvin appeared amorphous at 0 min when inspected by both SONICC and OM in (a) whereas the sample contained small crystalline domains only observed by SONICC in (b).

repetition rate is required in order to improve signal-to-noise of the measurement. Since no net energy is deposited in the system during the process of second harmonic generation, SHG itself is a nondestructive probe. Since both griseofulvin and chlorpropamide are transparent at both 800 and 400 nm, heating from onephoton or two-photon absorption can be assumed to be negligible. Although high power (µJ) ultrafast pulses have been shown to influence crystal nucleation,35 no such effects are expected using the ∼0.5 nJ/pulse powers in these experiments. In addition, the use of a rapid-scanning mirror during imaging distributes any local heating that might result over a relatively large distance, further reducing the potential for sample perturbation. SONICC images were acquired using a custom system performing beam scanning with a resonant vibrating mirror (∼8 kHz) to direct the beam along the fast-axis scan, and a Cambridge galvanometer for slow-axis scanning. A single image frame scanning was completed in 45 s for griseofulvin. Since amorphous chlorpropamide crystallizes relatively fast, an image acquisition time of 25 s was performed in order to obtain high time-resolution crystallization kinetics. The incident beam was generated from an ultrafast Spectra-Physics Mai Tai, 100 fs, 80 MHz, 40 mW average power at 800 nm during imaging, focused onto the sample using a 10× objective (N.A. ) 0.3). The depth-of-field and spot size were measured to be ∼60 µm and ∼2 µm, respectively. The (35) Nakamura, K.; Hosokawa, Y.; Masuhara, H. Cryst. Growth Des. 2007, 7 (5), 885–889.

use of relatively low magnification allowed measurements over a large field of view, while the low laser power of 40 mW was selected to avoid saturating the detectors during the crystallization experiments. The SHG was collected in both epi and transmission, with dichroic mirrors and narrow band-pass filters (Chroma HQ400/20 m-2p) centered around 400 nm used to reject the incident beam. The SHG signals in both transmission and epi were detected by photomultiplier tubes (Burke, XP 2920PC) with photon counting electronics (Becker-Hickl PMS 400A), with the relative collection efficiencies of the transmission and epi detectors calibrated using the two-photon excited fluorescence from Chroma standard slides. OM images were taken using a CCD camera (SPOT Insight, Diagnositc Instruments). SHG images were analyzed by ImageJ software. SHG signals were normalized against the corresponding two-photon fluorescence. RESULTS AND DISCUSSION Detection of Nascent Nanoscopic Crystals by SONICC. Isothermal crystallization of amorphous griseofulvin was monitored by SONICC and conventional optical microscopy (OM) at 120 °C as shown in Figure 1, where threshold images were set to a signal-to-background of 3. At 120 °C, griseofulvin is above its Tg (i.e., it is a supercooled liquid), and therefore, crystallization is expected to be rapid since there is both a thermodynamic driving force for conversion to the lower free energy crystalline state and sufficient molecular mobility for self-assembly to Analytical Chemistry, Vol. 82, No. 13, July 1, 2010

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occur. At 0 min, no detectable crystals were observed in either the OM or SONICC channels, consistent with expectations for a supercooled liquid. After 7.5 min, a single crystalline domain was detected by SONICC (highlighted region), although no crystals were observed by OM until after 39 min and then with low contrast. Similar trends were observed for additional crystals initiated at later times as shown in Figure 1a, with SONICC always providing much earlier detection than OM. Figure 1b demonstrates crystal detection as a function of time for another melt-quenched griseofulvin sample prepared and monitored under comparable conditions. At 0 min, the meltquenched griseofulvin showed no presence of crystals under OM, similar to Figure 1a. However, several submicrometer crystals were readily observed by SONICC, which subsequently grew to macroscopic crystals observable by conventional OM. The SONICC images suggest the presence of residual nanocrystalline material in the griseofulvin melt prior to analysis. It is widely known that the crystallization rates of amorphous APIs can be greatly influenced by the conditions of preparation and crystallization.36,37 The presence of crystal seeds is one of the major factors that will affect the observed crystallization rate, especially at early stages of crystallization. Therefore, SONICC provides a selective way to verify that the preparation method has destroyed all the crystalline structure in a sample. This is obviously important not only for subsequent analysis and understanding of the crystallization behavior but also for ensuring that samples that are intended to be amorphous are not loaded with undetectable (by conventional techniques) quenched in nanoscopic crystals which will reduce the subsequent physical stability. Such subtle differences in sample structure can profoundly influence crystallization kinetics, especially when crystallization rates are relatively slow with long lag times to reach detectable crystal sizes. Crystallization of chlorpropamide at 30 °C was similarly monitored as shown in Figure 2. Since amorphous chlorpropamide forms crystals relatively quickly (∼30 min), the image acquisition time was reduced to approximately 25 s per frame to gain a higher time resolution. A SHG signal from several crystal centers (Figure 2) arises after 125 s, followed by their subsequent growth. The corresponding crystals only become visible for the first time by OM after 500 s. Estimated Detection Limit of SONICC. The number of analytical techniques that are suitable for the routine detection of nanometric sized organic crystallites is limited. It is, therefore, of interest to determine the lower limit of detection of crystals using the SONICC technique. The smallest crystal size detectable by SONICC can be estimated by taking advantage of the coherent nature of SHG. Directionality dictates the signal strength of SHG as a result of constructive/destructive interference of fundamental F

(ω) and second harmonic (2ω) wave vectors (k ) associated with wavelength of light and the optical constants of the material. Neglecting the effects of scattering, the SHG generated within the medium will propagate coherently in either the forward (parallel) or backward (antiparallel) direction relative to the wave vector of the fundamental beam. The forward and backward (36) Bhugra, C.; Shmeis, R.; Pikal, M. J. J. Pharm. Sci. 2008, 97 (10), 4446– 4458. (37) Bhugra, C.; Pikal, M. J. J. Pharm. Sci. 2008, 97 (4), 1329–1349.

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Figure 2. Crystallization of amorphous chlorpropamide at 30 °C monitored by (left) SONICC and (right) OM with a 10× objective.

coherence lengths, LCf and LCb, respectively, can be estimated by the relations in eqs 1 and 2.38 LCf )

2π |F k 2ω - 2F k ω|

(1)

LCb )

2π 2ω F | k + 2F k ω|

(2)

F

Where |k ω,2ω | )(2π · n)/(λ), λ is the wavelength of the fundamental (800 nm) and SHG (400 nm), respectively, and n is the refractive index of the medium. SHG coherence lengths of griseofulvin (n ) 1.65)39,40 can be estimated from eq 1 as LCf) 4.8 µm and LCb)120 nm, using an assumed refractive index mismatch of the fundamental (800 nm) and SHG (400 nm) light due to dispersion of 5%. A significant difference in LCfand LCb is (38) LaComb, R.; Nadiarnykh, O.; Townsend, S. S.; Campagnola, P. J. Opt. Commun. 2008, 281 (7), 1823–1832. (39) Cao, X. P.; Hancock, B. C.; Leyva, N.; Becker, J.; Yu, W. L.; Masterson, V. M. Int. J. Pharm. 2009, 368 (1-2), 16–23. (40) Watanabe, A.; Yamaoka, Y.; Kuroda, K.; Yokoyama, T.; Umeda, T. Yakugaku Zasshi-J. Pharm. Soc. Jpn. 1985, 105 (5), 481–490.

provide a measurement of crystal nucleation, as the critical nucleus is not related physically to the backward coherence length. However, it does provide a calibration point for assessing crystal size with subdiffraction limited precision. Griseofulvin. A representative F/B ratio of a single pixel in the griseofulvin image stack (Figure 3a) remains close to unity until 20 min, after which forward-generated SHG is favored. At this point, an upper limit on the crystal detection limit can be calculated using the measured signal-to-background ratio of 30; when the crystals become thicker than LCb, they will transition to strongly favoring forward-generated SHG. On the basis of the measured signal-to-background at that transition point, back-calculation to the smallest detectable crystalline domain, giving rise to a signal-to-background of 3, is estimated to be 90 nm in thickness, assuming for simplicity that the crystal thickness is comparable in all dimensions. The ability to detect a single crystallite of 90 nm far exceeds the detection capability of other common techniques. A useful parameter for quantifying the relative amount of crystalline material in a sample is percent crystallinity, which is defined here as the volume of crystalline material relative to the total volume of material. detectable smallest crystalline volume × 100% FOV volume

Figure 3. Forward and backward SHG of a single-pixel and the corresponding forward-to-backward ratio (F/B) of crystallization of (a) griseofulvin and (b) chlorpropamide. Predicted relationship of forward and backward SHG is demonstrated in (c).

a result of constructive and destructive interference as dominant factors for forward and backward propagation, respectively. The uncertainty in the refractive index mismatch in griseofulvin material only minimally affects the estimate of LCb, which is a key parameter to estimate the smallest size of crystalline domain detectable by SHG. Within the slowly varying field approximation (valid for these measurements obtained using low N.A. objectives),38 the relative SHG intensity in the forward and backward directions can be predicted as a function of wave propagating distance as demonstrated in Figure 3c. In the figure, intensity is normalized to SHG in the forward direction, and the crystalline domain length is normalized to LfC. At an early stage of crystal formation, when the crystalline domain is much less than LCb, the ratio of forward SHG (F) and backward SHG (B) denoted F/B is predicted and observed to be close to unity (i.e., the efficiency of SHG to propagate in both directions is equivalent). Once the crystalline domain exceeds the size of LbC, forward SHG (F) increases much faster than backward SHG (B). Therefore, the ratio of F/B can be used as an internal “ruler” to estimate the size of the crystalline domain relative to LCb. From the signal-to-noise measured at the point at which the ratio transitions away from unity to favoring forward propagation (i.e., for a crystal thickness no greater than ∼120 nm), the crystalline size corresponding to a S/N of 3 can be back-calculated. This analysis was applied for the forward and backward SHG analysis of single pixels, with representative results shown in Figure 3 for griseofulvin and chlorpropamide. The F/B measurement does not directly

(3)

In eq 3, the FOV volume is the probed volume within the fieldof-view. For these experiments, the depth of field defining the focal volume was measured to be 60 µm, such that the FOV volume ) 600 × 600 × 60 µm3. Therefore, the detection limit of percent crystallinity in amorphous griseofulvin is ≈3.4 × 10-9 %v/v. For comparison, typical detection limits using conventional methods (e.g., Raman spectroscopy, differential scanning calorimetry (DSC), X-ray diffraction analysis (XRD)) are routinely in the 0.1-10% crystallinity range. Thus, the SONICC measurement represents an approximate 2.9 × 107 to 2.9 × 108fold increase in sensitivity. For pristine samples such as those characterized here, optical microscopy can definitively distinguish between a likely crystal and a scattering center for crystals >5 µm, corresponding to a % crystallinity of >6 × 10-4%, such that SONICC still represents an improvement by at least 5 orders of magnitude. Chlorpropamide. Complementary studies with chlorpropamide were particularly interesting. Unlike griseofulvin, which strongly favors crystallization into an SHG-active space group by nature of the intrinsic chirality, chlorpropamide is not intrinsically chiral and, therefore, can form both SHG-active and SHG-inactive crystal polymorphs.41-43 Estimates of the smallest crystalline domain detectable were performed from analysis of the timedependent SHG depicted in Figures 2 and 3b. Similar to griseofulvin crystallization, the F/B is approximately one at early stages of crystallization, followed by a F/B of greater than one corresponding to the growth of the crystal. However, the chlorpropamide SHG response does not increase steadily, as in the case of (41) Drebushchak, T. N.; Chukanov, N. V.; Boldyreva, E. V. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 2007, 63, O355–O357. (42) Drebushchak, T. N.; Chukanov, N. V.; Boldyreva, E. V. Acta Crystallogr., Sect. E: Struct. Rep. Online 2006, 62, O4393–O4395. (43) Simmons, D. L.; Ranz, R. J. Can. J. Pharm. Sci. 1973, 8 (4), 125–127.

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griseofulvin, but rather levels off or even decreases in some cases, in both the forward and backward directions prior to increasing again. Chlorpropamide can exist in four known polymorphs under common experimental conditions, where the R and γ chlorpropamide polymorphs belong to the P212121 and P21 crystal space groups, respectively, and are SHG active while the β and δ polymorphs belong to Pbcn and Pbca space groups, respectively, and are SHG inactive. In chlorpropamide, the chirality within the R and γ lattices is conformational rather than structural and the chiral center within the crystal arises from the specific orientation of the molecules in the unit cell. The nontrivial trends in SHG during crystallogenesis cannot be easily explained by nucleation and growth of a single crystal polymorph and are tentatively attributed to conversion between multiple polymorphic forms during crystal formation and growth. The calculation of the coherence length of chlorpropamide was performed in a similar manner. The refractive index of chlorpropamide was estimated according to the Vogel method39,44-46 to be 1.51 which results in LCf ) 5.3 µm and LCb ) 136 nm, giving rise to a measured signal-to-background of 5. As a result, the detection limit is estimated to be 125 nm in crystal length corresponding to 9 × 10-9 % crystallinity or one part in 10 billion by volume. These results collectively suggest that SHG enables the detection of crystal formation with a vastly lower detection limit than conventional routine methods. It is worth noting that refractive indices of most APIs lie in between 1.4 and 1.8 such that the smallest detectable size of crystalline domains of APIs, detected by SONICC, should routinely be in the submicrometer range, providing a considerable advantage over other techniques. Application of SONICC to Study the Kinetics of Crystallization. A three-dimensional growth map depicting the evolution of crystal size is shown in Figure 4. The map was generated from the stack of time dependent SHG images using a particle counting algorithm built in ImageJ. For each SHG image frame (corresponding to the time axis), the particle size distribution was determined (inset of Figure 4), which represents the area of the individual crystals formed. The average intensity of each crystal is represented by the height in the inset figure and by the gray scale in the growth map. For example, at 210 min, crystal site I has an area of 1400 µm2 with an average SHG intensity of 421, while crystal sites II and III have areas of 5300 and 109 × 103 µm2 with an average SHG intensity of 829 and 1685 counts, respectively. This representation of the growth map concisely contains much of the information needed to describe the kinetics of crystal nucleation and growth (vide infra). Quantitative real-time monitoring of crystal nucleation and growth kinetics is readily achievable as a result of the low background and high contrast in the SONICC images. Using a standard threshold-based particle counting algorithm, crystal nucleation rates (number of particles per unit time and volume), growth rates (area of particles per unit time), and overall (44) Vogel, A. I. J. Chem. Soc. 1948, (Nov), 1833–1855. (45) Vogel, A. I.; Cresswell, W. T.; Jeffery, G. H.; Leicester, J. J. Chem. Soc. 1952, (Feb), 514–549. (46) Nelken, L. H. Index of Refraction. In Handbook of Chemical Property Estimation Methods: Environmental Behavior of Organic Compounds Lyman, W. J., Reehl, W. F., Rosenblatt, D. H., Eds. Ametican Chemical Society: Washington DC, 1990.

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Figure 4. (a) Evolution of the crystal size distribution from the stack of time dependent SHG image frames. The y-axis corresponds to the area of contiguous pixels above the threshold, with the average SHG intensity proportional to the darkness of the line. The discontinuities in the sizes (red arrow in the short-time inset) correspond to coalescence of multiple crystals within the images, as illustrated in (b). As growing crystals overlap within the field of view (red arrow in the image at 138 min), the counting algorithm records them as one large crystal rather than two small ones, leading to abrupt discontinuous changes in the size distribution.

crystallization kinetics (relative integrated SHG intensity per unit time) can be obtained from a single set of measurements as shown in Figures 4 and 5. The growth map shown in Figure 4a is derived from the SHG image stack of griseofulvin crystallized at 125 °C. The y-axis of the growth map indicates the area of each contiguous SHG-active particle with a signal exceeding a threshold 3 times the noise. Each trace in the growth map represents the growth of an individual crystallite. In the limit of well-separated crystallites, this map also corresponds to the number of nuclei and size of the corresponding crystallites. Crystal growth rates were determined prior to coalescence of crystallites. Coalescence of multiple crystallites in the images appears as discontinuous jumps in the traces as two crystallites overlap to form a single contiguous SHGactive area. The gray scale of each trend is weighted by the mean SHG intensity, which is proportional to the growth of each crystallite in a vertical direction for dendritic crystallites. The growth rates of three individual crystallites, labeled a, b, and c in Figure 5a, are calculated from the square root of the area to be 1.54 ± 0.02, 1.173 ± 0.005, and 1.16 ± 0.02 µm · min-1, respectively, and are obtained from the growth in area as a function of time for the individual crystallites in temporal windows absent of coalescence. (Uncertainties are determined from the standard errors of the fits.) Crystalline region a represents the growth of a single crystallite prior to coalescence whereas crystalline region b, demonstrating a smaller growth rate, results from the coalescence of crystalline a and independently growing crystallite. The reduction of growth rate upon coalescence may be described by the reduction of total surface, where crystal growth occurs. The quantitative differences between the measured growth rates between crystallites may arise from

Figure 5. Analysis of the (a) rate of crystal growth (subset of the data in Figure 4a), (b) rate of crystal nucleation, and (c) overall crystallinity relative to the complete crystallization at the end of the experiment of amorphous griseofulvin at 125 °C.

several effects including: (i) intrinsic variability in crystal growth rates and (ii) differences in crystallite orientation. The rate of nucleation can be obtained from particle counting with a correction for coalescence being applied as shown in Figure 5b. Here, it is assumed that each particle detected arises from a single nucleation site. The number density of crystallites per unit volume was calculated from the number density per unit area and the depth of field of 60 µm (experimentally measured). The coalescence was corrected when the number of particles counted at each time point was less than the number of counted particles at the previous time point. Although this simple correction approach will undercount nucleation if coalescence and the detection of a new crystallite occur in precisely the same frame (corresponding to no net change in the number of SHG-active particles), the frame rate of acquisition (45 s) was sufficiently fast relative to the nucleation rate to make such a simultaneous event unlikely. The coalescence results when two crystals overlap and the particle counting algorithm counts them as one large crystal. The steady state nucleation rate is estimated to be 2.85 ± 0.03 mm-3

min-1 at 125 °C. The overall rate of crystal formation and fraction crystallized (R) also can be determined by integration of the SHG intensity over the FOV as shown in Figure 5c.The rate of crystallization of an amorphous material can be estimated from the Johnson-Mehl-Avrami (JMA) equation; R ) 1 n e[-(k(t-t0)) ], where k is an apparent rate of crystallization, t0 is an induction time, and n is the order of reaction associated with the mechanism of nucleation.22,47-49 With an order of reaction (n) of 2, the rate of crystallization of amorphous griseofulvin at 125 °C (Figure 5b) is calculated to be 3.35(±0.01) × 10-3 min-1. The temperature-dependent apparent rates of crystallizations (k) were determined at five different temperatures, the results of which are summarized in an Arrhenius plot (Figure 6). From the plot, the activation energy for isothermal crystallization of griseof(47) Avrami, M. J. Chem. Phys. 1941, 9 (2), 177–184. (48) Avrami, M. J. Chem. Phys. 1939, 7 (12), 1103–1112. (49) Johnson, W. A.; Mehl, R. F. Trans. Am. Inst. Min. Metall. Eng. 1939, 135, 416–442.

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Figure 6. Arrhenius plot for isothermal crystallization of griseofulvin measured by SONICC. The apparent rate constants were determined from the JMA equation with the order of two. The uncertainty in the activation error is reported as one standard deviation of the slope from a linear curve fit.

ulvin was determined by SONICC analysis to be 140 ± 20 kJ/ mol. A previous study by Zhou22 reported an activation energy for the isothermal crystallization of griseofulvin determined by DSC to be 167 kJ/mol. The comparable activation energy independently determined by SONICC and DSC suggests both measurements are reliably probing similar ensemble-averaged phenomena. However, SONICC also has the advantage of concurrently providing complementary microscopic information on nucleation and growth of individual crystallites. CONCLUSIONS Early detection of crystallization of amorphous griseofulvin and chlorpropamide was performed by SONICC. The results of the current study provide evidence that SONICC can be used to sensitively and selectively detect the existence and formation of crystalline APIs. The detection limit of SONICC for crystallinity is measured to be approximately 1 part in 10 billion by volume, which is ∼8 orders of magnitude better than that of common macroscopic average methods and ∼5 orders of magnitude of

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improvement relative to OM. Consistent with these expectations, amorphous samples that appeared crystal free under OM were found to contain submicrometer crystal seeds, presumably due to incomplete melting during preparation or entrainment of nuclei during cooling. Crystallization in the presence of crystal seeds were faster than in samples where seeds could not be detected. The smallest detectable crystalline domain was estimated by SONICC to be