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[Xue Han](https://orcid.org/0000-0003-4812-1410), Kexin Dai, [Kohsaku Kawakami](https://orcid.org/0000-0002-3466-9365)

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This document is the Accepted Manuscript version of a Published Work that appeared in final form in Molecular Pharmaceutics, copyright ©  2024 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/acs.molpharmaceut.3c01116[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Influence of Nucleation on Relaxation, Molecular Cooperativity, and Physical Stability of Celecoxib Glass](https://mdr.nims.go.jp/datasets/2aea965a-d1d4-4ba8-89ad-87db986936d5)

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Influence of Nucleation on Relaxation, Molecular Cooperativity, and Physical Stability of Celecoxib GlassXue Han1,2, Kexin, Dai1,3,4, Kohsaku Kawakami1,2,*1 Research Center for Macromolecules and Biomaterials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan2 Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan3 Department of Chemical Engineering, University of California, Santa Barbara, CA 93106, United States4 Present address: Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States* Corresponding authorE-mail: kawakami.kohsaku@nims.go.jp, Tel. +81-29-860-4424Manuscript pages: 27Figures: 11Tables: 2Submitted to Molecular PharmaceuticsAbstractAlthough nucleation is considered as the first step in the crystallization of glass materials, the structure and properties of the nuclei are not understood well. Influence of nucleation on the structure and dynamics of celecoxib glass was evaluated in this study. The nuclei for Form III were induced by annealing the glass at freezing temperature, and their impact on the relaxation behavior was investigated using thermal analysis and broadband dielectric spectroscopy to find accelerated α relaxation and suppressed β relaxation. Also observed after nucleation was decrease in cooperativity of the molecular motion, presumably because of appearance of void spaces in the glass structure. During long-term isothermal crystallization studies, crystal growth to Form III was accelerated in the presence of the nuclei, whereas this effect was less remarkable when a different crystal form dominated the crystallization behavior. These observations should provide more detailed insights into the nucleation mechanism and impact of nucleation on molecular dynamics including physical stability of pharmaceutical glasses. Also discussed is remarkable acceleration of the crystallization rate of the celecoxib glass just below its Tg, which could be understood by diffusionless crystal growth.Keywords: Glass, Nucleation, Crystallization, Relaxation, Cooperative rearranging region1 IntroductionAlthough amorphous solid dispersion is now one of the most important options for developing poorly soluble candidates1-3, glass theory still involves many unsolved issues. As glasses are thermodynamically unstable, they may eventually be transformed to more stable crystalline forms. Crystallization kinetics are closely related to molecular mobility4,5. However, many other physicochemical and practical factors, including mechanical stress4,6,7, thermal history8, surface area9,10, and sample size11 can also influence behavior of glasses, which must be clarified to precisely control glass stability.The modes of molecular mobility can be divided into primary relaxation (i.e., α relaxation), in which the glass structure is rearranged mainly by molecular diffusion to achieve a more energetically favored state, and secondary relaxation (β, g, and d relaxation), which is more local and fast movement. Generally, an amorphous solid is physically stable below Tg 50 °C12 because of disappearance of the excess entropy, where proceeding of a relaxation is not expected. However, the contribution of the secondary relaxation to glass stability requires further investigation. Secondary relaxation occurs over shorter time scales at lower temperature ranges relative to α relaxation to enable intermolecular movement within restricted domains13. Furthermore, secondary relaxation can in turn initiate primary relaxation, which may influence glass stability14. Paladi et al. proposed that the relatively fast nucleation of the o-benzylphenol system is induced by βrelaxation, even at low temperatures15, whereas Okamoto et al. indicated that nucleation proceeds even at a temperature 186 °C below the Tg16. It is frequently reported that secondary relaxation may be related to the nucleation and crystal growth of glasses17,18.In our previous study8, the nucleation of celecoxib (CEL) glass was found to proceed at the freezing temperature. The maximum nucleation rate was found to exist at -50 °C, which is below its Tg by 108 °C. As nuclei are difficult to detect directly, nucleation may not be recognized unless crystal growth follows. It can happen if the temperatures for nucleation and crystal growth are sufficiently separated. Glasses with or without nuclei may exhibit different performances, even though they are characterized the same using conventional evaluation methods including x-ray powder diffraction and differential scanning calorimetry. In fact, the nucleated CEL glass failed to form a supersaturated state after suspension of the glass in aqueous media, although it was observed for the non-nucleated glass19. In this study, we evaluated the influence of nucleation on glass dynamics in comparison with the non-nucleated glass with emphasis on their relaxation, molecular cooperativity, and crystallization behaviors.2 Experimental2.1 Materials CEL (Fig. 1) was purchased from Tokyo Kasei (Tokyo, Japan) and used without further purification. Four crystal forms, form I to IV, have been identified so far, where form III is the most stable form at room temperature. Form I is the stable form at higher temperature, which has thermodynamically enantiotropic relationship with form III. The transition temperature between form I and III has not been identified but expected to exist at slightly higher than room temperature. Tg of CEL glass is 58 °C4,8.Fig. 1 Chemical structure of CEL.2.2 Preparation of Glass SamplesDifferential scanning calorimetry (DSC) (Q2000, TA Instruments, New Castle, DE, USA) was used to prepare the glass samples. The instrument was calibrated using indium and sapphire, and dry nitrogen was used as the inert gas during the measurements at a flow rate of 50 mL/min. Approximately 5 mg of the crystalline CEL was heated to 180 °C for melting in a crimped aluminum pan. The sample was then cooled to 25 °C at a rate of 20 °C/min to obtain “intact glass.” The “nucleated glass” was prepared by cooling the melt to −20 °C at a rate of 20 °C/min, followed by storage in a freezer in which the temperature was maintained at −20 °C for 16 h.2.3 Annealing StudyBoth types of glasses were annealed in DSC or temperature-controlled ovens for predetermined periods. DSC was used when the annealing time was shorter than 2 h, whereas ovens were used for longer annealing times. For the oven-storage, the samples (in the DSC pans) were enclosed in air-tight boxes with silica-gel. The difference in annealing procedure was confirmed to have a negligible influence by applying both protocols for some studies. To observe the impact of nucleation and subsequent annealing on cold crystallization behavior, the samples were subjected to DSC measurements at a heating rate of 10 °C /min. All measurements were at least triplicated.Relaxation experiments were performed using the modulated mode, in which a 0.5 °C amplitude and 60 s period were applied at a heating rate of 2 °C /min. A nonreversing heat flow was used to evaluate the relaxation behavior. To offset the frequency effect, the recovery enthalpy values for the non-annealed glass were subtracted from the enthalpy of the annealed glass. The relaxation function, Φ, is expressed as follows:                      Φ = 1 − () ,                  (2)where Ht is the enthalpy recovery measured under the given conditions and H is the maximum enthalpy recovery calculated using the following equation:                         =  ,                 (3)where Tg and Ta are the glass transition temperature and annealing temperature, respectively, and Cp is the change in heat capacity at Tg. The mean relaxation time, τ, was calculated by fitting the relaxation enthalpy data to the Kohlrausch-Williams-Watts (KWW) equation20,21:                        Φ =  ,                   (4)where β (0  β≤ 1) is a fitting parameter, generally believed to describe the distribution of relaxation time.2.4 Broadband Dielectric Spectroscopy (BDS)BDS measurements were performed on a Novocontrol Alpha dielectric spectrometer (Montabaur, Germany) in the frequency range of 10-2 to 107 Hz under ambient pressure. The glass samples were prepared by melting CEL crystal on a stainless-steel sample stage using a hot plate heated to 200 °C. The prepared samples were transferred to the dielectric spectrometer after cooling down to the room temperature, and then heating up to 220 °C and quench again in spectrometer for completely removing water. The nucleated glass was prepared by cooling the sample for 60 min at −50 °C in the equipment. The measurement temperatures ranged from −120 °C to 120 °C, which was controlled by the Quatro system using nitrogen gas generated from liquid nitrogen. When the nucleated glass was investigated, the temperature was raised from the lowest temperature with intervals of 4 °C (below 0 °C), and 2 °C (above 0 °C). The intact glass was investigated with the same intervals for those for the nucleated glass without pre-annealing, and all the measurements are triplicated for confirming reproducibility. Temperature stability was ensured to be within  0.2 °C of the designated temperature.The relaxation curves were fitted using the Havriliak-Negami (HN) function as shown below to obtain the average relaxation time22:            (5)where *() is the complex permittivity, '() and "() are the real and imaginary parts of the complex dielectric permittivity, ∞ is the high-frequency limit permittivity, k denotes either the primary or secondary process, ∆k is the relaxation strength, and a and b are exponents of the relaxation processes. The relaxation map (the relaxation times as a function of temperature) was drawn by analyzing the dielectric spectra acquired at various temperatures. As determination of the a relaxation time was difficult in experimental timeframes especially below Tg, the structural relaxation peak was horizontally shifted to the lower frequencies side for the deconvolution based on the master plot as generally accepted. 2.5 X-ray Powder DiffractionX-ray powder diffraction (XRPD) data were obtained on a Rigaku RINT Ultima X-ray Diffraction System (Rigaku Denki, Tokyo, Japan) with Cu K-α radiation. The samples for the measurements were prepared in DSC pans. Approximately 5 mg of crystalline CEL was subjected to the DSC heating/cooling/annealing treatments as described previously. The samples were subsequently heated at a rate of 10 °C /min until cold crystallization was completed. Then, heating was terminated to collect the samples for the XRPD measurements. The voltage and current were set to 40 kV and 40 mA, respectively. Data were acquired at a scan rate of 2 °C /min with 0.02° intervals (2θ).2.6 Density Measurement  The true density of the CEL glass was measured on an AccuPyc II gas pycnometer (Micromeritics, Norcross, GA, USA) using helium gas. Approximately 0.5 g of crystalline CEL was melted on a hot plate and then cooled under ambient atmosphere. Subsequently, the obtained glass pellets were ground using a mortar and pestle. The powder was confirmed to be completely amorphous by XRPD and DSC. The measurement was repeated ten times to obtain the mean value.3 Results3.1 Effect of Nucleation on DSC CurvesFigure 2 shows the DSC curves of the intact and nucleated glasses after annealing at various temperatures. The recovery enthalpy grew for both glasses with increasing annealing time due to the proceeding relaxation. Meanwhile, for the intact glass, the temperature of the recovery peaks shifted to higher temperature with increasing annealing time at all annealing temperature conditions, which is a typical phenomenon after annealing21. For the nucleated glasses, a small endothermic pre-Tg peak appeared after short-term annealing (indicated by arrows in the figure), which shifted to higher temperature and merged with the recovery peak with increasing annealing time. The pre-Tg peak was observed relatively clearly for the glasses annealed at 30 °C, whereas it was only found occasionally at 35 and 40 °C, and never at 45 °C. As a result, the recovery enthalpy temperature was lowered after long-term annealing, particularly at 30 and 35 °C. Another important finding was broadening of the DSC curves in the glass transition region after nucleation, which was most likely because of increase in size of cooperative rearranging region (CRR)23,24. Fig. 2 Change in the total heat flow curves after annealing of intact and nucleated CEL glasses. The nucleated glass was prepared by storing the intact one at −20 °C for 16 h. The annealing temperature and time are indicated in the figure. The vertical lines in the figures show the peak-top temperature of the recovery peak of the non-annealed glasses. Arrows indicate pre-Tg peaks. An example of the separation into reversing and nonreversing heat flows is supplied in the supporting information.3.2 Effect of Nucleation on a RelaxationFigure 3 (a) and (b) show the fraction of remaining excess enthalpy, Φ, as function of annealing time at various temperatures. The obtained KWW parameters are listed in Table 1. The nucleated CEL glass exhibited a faster relaxation over the entire temperature range compared with the intact glass. The distribution of the relaxation time was almost the same for both glasses below 35 °C, as judged from their similar β values; however, the distribution was likely to be wider for the nucleated glass above 40 °C. Figure 3(c) shows Arrhenius plots of the relaxation time, where  was employed for comparison to take the distribution of the relaxation time into consideration21. The activation energy for the nucleated glass was larger (126 kJ/mol) than that of the intact glass (86.7 kJ/mol).Fig. 3 The fraction of remaining excess enthalpy  of (a) intact and (b) nucleated CEL glasses after annealing for a series of temperatures (shown in the figures) fitted by the KWW equation; (c) Arrhenius plot for the relaxation times. Table 1 KWW Parameters of CEL glass annealing at different temperatures. Temperature   (min)   (°C) Nucleated Intact Nucleated Intact Nucleated Intact 30 4910 27200 0.50 0.50 67.9 158 35 2160 4870 0.51 0.48 48.5 58.9 40 559 647 0.44 0.57 15.7 40.5 45 266 315 0.35 0.59 7.15 29.83.3 Deactivation or Formation of Nuclei during AnnealingAssumption of nuclei formation during annealing at the freezing temperature is supported by the fact that the probability of cold crystallization occurring during DSC heating dramatically increases after the freezing temperature annealing8. However, subsequent annealing at higher temperatures decreased the probability of crystallization and/or changed the form of the obtained crystal. Thus, annealing at higher temperatures was likely to deactivate the nuclei at certain conditions.Figure 4 (a) shows the typical heating curves of the nucleated CEL glasses after subsequent annealing at 30 °C for 60 or 240 min. After annealing for 60 min, cold crystallization and melting were observed at approximately 120 and 162 °C, respectively, in most cases. This observation can be interpreted as the crystallization and melting of Form III25-27. However, after annealing for 240 min, cold crystallization and melting were observed occasionally at approximately 110 and 164 °C, respectively, which can be considered as behaviors of Form I25-27. Figure 4 (b) shows the XRPD patterns of the corresponding samples collected after the cold crystallization during the DSC measurements. The sample annealed at 30 °C for 60 min produced diffraction peaks for Form III as represented by those at 14.4, 15.7, 19.2, 21.1 degrees25-27, for which lattice parameters were reported as a = 10.136, b = 16.778, c = 5.066, a = 97.62, b = 100.65, g = 95.95 (triclinic)28. The diffraction peaks for the 240-min annealed sample were represented by those at 5.5, 5.7, 7.2, 16.6 degrees, which can be assigned as those for Form I25-27.Fig. 4 (a) Typical DSC heating curves of the nucleated glass after subsequent annealing at 30 °C for 60 or 240 min. (b) XRPD patterns of the nucleated glass after the annealing at 30 °C for 60 and 240 min and DSC heating up to 150 °C.Figure 5 shows the probability of crystallization to each form after subsequent annealing of the nucleated glass at 30, 35, and 40 °C. Unless annealing was applied, crystallization resulted in the development of Form III. However, it was not always to obtain pure Form III after annealing. For example, when annealed at 30 °C for 30 min, a mixture of Form I and III was obtained more frequently than pure Form III. The probability of crystallization to such mixture or to Form I increased with increasing annealing time. Interestingly, this trend was intensified with increasing annealing temperature. Thus, Form I nuclei were more likely to be obtained during annealing.Fig. 5 Probability of crystallization to Form III, Form I, and their mixture after the annealing at the indicated temperature (n = 12).3.4 Impact of Nucleation on Secondary RelaxationFigure 6(a) and 6(d) show the dielectric loss spectra of the intact and nucleated CEL glasses below Tg under ambient pressure, where contributions of the secondary relaxation processes (β,  and ) could be observed. Figure 6(b) and 6(e) are examples of the spectra obtained at -120 °C deconvoluted by the CC functions for g and d relaxations. These processes were not affected by the nucleation. However, nucleation was found to influence the b relaxation. Figure 6(c) and 6(f) show the spectra obtained at 36 °C for both glasses. The maxima of the peak (vp) obtained after the deconvolution shifted to the lower frequency after the nucleation, which suggested suppression of the b relaxation by the nucleation. According to previous literature29, the β process was considered to reflect the small-angle reorientations of intermolecular origin of the entire drug molecule; the  process represents the rotation of the phenyl ring with respect to the sulfonamide group (Ph−SO2NH2), which enables H-bond formation; and the  process is associated with rotations of the phenyl ring with respect to the methyl group (Ph−CH3), which does not form hydrogen bonds with other molecules. The temperature dependencies of the relaxation times for both glasses are presented in Figure 7. The activation energies for the three secondary relaxation processes of the intact CEL glass are as follows: ∆Eβ = 79.1 kJ/mol for β relaxation, ∆E = 33.9 kJ/mol for  relaxation, ∆E = 23.9 kJ/mol for  relaxation, which agree with the values reported by Grzybowska et al30. The nucleated CEL glass exhibited similar  (∆E = 40.8 kJ/mol) and   (∆E = 22.1 kJ/mol) processes but larger β relaxation time than that of the intact one with larger activation energy (∆Eβ = 94.9 kJ/mol). This presumably means nucleation partially suppressed local molecular mobility.Fig. 6 Dielectric loss spectra of (a) intact CEL glass at different temperatures; Examples of dielectric loss spectra of intact CEL obtained at (b) -120 °C (deconvoluted into g and d relaxations using CC functions as presented by blue and red dashed lines, respectively) and (c) 36 °C (deconvoluted into , β, and g relaxations using HN function (for ) and CC function (for β and g) as presented by green, magenta, and blue lines, respectively.) Dielectric loss spectra of (d) nucleated CEL glass at different temperatures; Examples of dielectric loss spectra of nucleated CEL obtained at (e) -120 °C and (f) 36 °C deconvoluted as same as for the intact glasses.Fig. 7 The temperature dependencies of secondary relaxation times of intact (open symbols) and nucleated (closed symbols) CEL glass. Activation energies were determined by the Arrhenius equation and presented in the figure (Underlined: Nucleated CEL; No line: Intact CEL). (a) The entire relaxation map for all secondary relaxations. (b) Expanded map for b-relaxation.3.5 Isothermal Crystallization of CEL GlassFigure 8 shows the evolution of the crystallinity of the intact and the nucleated CEL glasses at 35 and 40 °C as a function of the storage period. The crystallinity of CEL was calculated by using ΔCp under the assumption that it was proportional to the amorphous fraction. The data were fitted using the Avrami–Erofeev equation, as shown below5,10:   100[1 exp {k (t  d)n }]           (7)where k is the crystallization rate, d corresponds to the induction time, and n is the Avrami parameter, which is related to both the nucleation mechanism and crystal growth dimensions. Despite the absence of a statistically meaningful difference, the nucleated glass appeared to exhibit faster crystallization compared to the intact one at 35 °C, whereas no difference in the crystallization rate was observed at a 40 °C storage. The kinetic parameters for crystallization are summarized in Table 2. At 35 °C, the faster crystallization of the nucleated glass was revealed to be because of faster initiation of the crystal growth (i.e., smaller t10). No obvious difference was found for the crystallization rates of both glasses. Unusual small Avrami constants, small t10, and fast crystallization rates were obtained for storage at 40 and 45 °C for both glasses and at 50 °C for the nucleated glass; this was likely to be explained by the simultaneous crystallization of two types of crystals, Form I and III. Thus, a comparison of the crystallization parameters to evaluate effect of the nucleation is only meaningful for data at 35 and 60 °C. The nucleated glass exhibited smaller t10 at 60 °C than that for the intact one, suggesting that initiation of the crystal growth was enhanced by the preformed nuclei. However, the faster the crystallization rate was found for the intact glass. Thus, it is difficult to evaluate whether the preformed nuclei accelerated the crystallization.    Figure 9 shows the DSC curves of the stored CEL glasses. The glasses stored at 35 °C primarily crystallized into Form III, whereas those stored at 60 °C crystallized into Form I, as could be judged from the melting behaviors. The glasses stored at a temperature range of 40-50 °C crystallized into both forms as revealed by double melting peaks, which was likely the reason of the low apparent values of the Avrami constants. Fig. 8 Evolution of crystallinity of intact (black circles and lines) and nucleated glasses (red circles and lines) stored at (a) 35 °C and (b) 40 °C. The fitting lines are drawn by the Avrami-Erofeev equation.Table 2. Kinetic Parameters for Isothermal Crystallization of CEL Glasses  Intact   Nucleated   Temperature (°C) k (h-1) t10 (h) n k (h-1) t10 (h) n 35 9.36×10-16 1930 3.1 9.51×10-16 1590 3.2 40 (1.17×10-5) (285) (1.4) (5.55×10-11) (538) (2.5) 45 (3.59×10-8) (391) (1.9) (1.34×10-7) (301) (1.8) 50 9.10×10-17 1130 3.5 (9.88×10-10) (696) (2.1) 60 4.57×10-18 2830 3.5 1.34×10-18 2340 3.7The values in parenthesis are apparent ones obtained for simultaneous crystallization to multiple crystal forms. t10: Time to reach 10% crystallinity calculated by the Avrami-Erofeev equation.Fig. 9 DSC curves of the intact (black) and nucleated (red) CEL glasses after isothermal storage. The storage temperature and periods are indicated in the figure.   Figure 10 shows evolution of crystallinity of intact CEL glass as functions of storage temperature and time. Although investigation was also made at 30 °C, no crystallization was found for 150 days. The crystallization was obviously the fastest at 40 and 45 °C, which could be elucidated by diffusionless crystal growth31-34. The same trend was confirmed for the nucleated glass.Fig. 10 Evolution of crystallinity of intact CEL glass as functions of storage temperature and time. The data was fitted with Avrami-Erofeev equation. Storage temperatures are indicated in the figure. All data were at least triplicated but only mean values are presented without error bars for clarity.4 Discussion4.1 Impact of Nucleation on Glass Structure and DynamicsNucleation is the initial step in crystallization. If the difference between the optimum temperatures for nucleation and crystal growth is sufficiently large, the nucleated state may be retained without proceeding of crystal growth. Further crystallization proceeds easily once the nucleated glass is exposed to an appropriate temperature condition for crystal growth.During nucleation, structural ordering is expected to accompany local densification. Thus, spatial heterogeneity should be induced by nucleation, which seems to significantly impact relaxation dynamics; α relaxation of the high- and low-density regions is expected to be suppressed and accelerated, respectively. Based on the relaxation study performed by DSC, the fast dynamics originating from the low-density region appear to have a greater impact than the slow dynamics of the high-density region. Echeverría et al. made a similar speculation when comparing enthalpy and creep relaxation; enthalpy relaxation was assumed to depend sensitively on the high molecular mobility region when structural heterogeneity exists35. Spatial heterogeneity was also suggested by small β values in the KWW equation. BDS provided larger relaxation time and larger activation energies for β relaxation of the nucleated CEL, indicating that the local motion of the molecule was also influenced. This observation agrees with previous findings, where nucleation was observed to have relevance to the β relaxation17,18.Figure 11 shows a schematic representation of the possible impact of nucleation on the glass structure. As nuclei are expected to have higher density than non-nucleated glass, local condensation should occur after nucleation. It may leave void spaces in the glass structure if molecular diffusion is not sufficiently fast. It is likely for the CEL glass, as the nucleation temperature is much lower than Tg. Two notable differences were observed for the DSC curves of the nucleated and intact glasses: the nucleated glass had a wide glass transition region and a pre-Tg peak (Figures 2 and 3). The wide glass transition region of the nucleated glasses reflects the low cooperative molecular motion of the CEL molecules, which might be produced by the disruption of the glass structure caused the presence of void spaces. The size of CRR was determined to be 2.7 and 2.2 nm for intact and nucleated glass, respectively. Its typical value for organic glasses are approximately 2 nm23 if it is determined by width of the glass transition region; thus, these values appeared to be general. Using the true density value of 1.41 g/cm3, the number of the CEL molecules can be calculated as 28 and 15 for intact and nucleated glass, respectively, per the region. The number of 15 may be regarded as the number of molecules per nuclei. In the supporting information, change in the CRR size during the annealing is presented. Although the deviation of the data was large, the CRR size of the nucleated glass was likely to increase during the annealing at 40 and 45 °C. It may be connected to deactivation of nuclei, which can be a partial reason for absence of efficacy of nuclei for the stability at 40 °C (Figure 8b). As for the pre-Tg peak, similar peaks were previously reported for indomethacin glass, which was obtained by annealing it at temperatures much lower than its Tg36. It was explained by the nucleation of Form α. As the pre-Tg peak shifted to a higher temperature and merged with the enthalpy recovery peak at Tg, it was observed only during the short annealing periods. The molecules in the low-density region may be responsible for the pre-Tg peak. Because molecules in that region are expected to exhibit higher mobility, it may be reasonable to assume that their enthalpy recovery could be observed at temperatures lower than the Tg.Fig. 11 Schematic representation of the nucleation process. Nucleation causes local densification, by which void space is formed. The CRR becomes smaller after nucleation because of disruption by the void spaces.4.2 Effect of Preformed Nuclei on Glass StabilityThe nuclei formed at the freezing temperature were expected to crystallize into Form III. However, annealing temperatures higher than room temperature revealed that Form I could also be obtained. With increase in the annealing temperature, the probability of crystallization into Form I and Form III increased and decreased, respectively. Thermodynamic stability of Form I and III have an enantiotropic relationship, and Form III is the stable form at ambient temperature. One possible reason of appearance of Form I is that Form I may have higher thermodynamic stability above 30 °C, that is, spontaneous transformation from Form III to From I might proceed. Another simple assumption is that the nucleation temperature of Form I may exist above the ambient temperature. In fact, nucleation temperatures are frequently found near Tg37-39.The crystallization proceeded into Form I at 60 °C (Figure 9). Although the nuclei formed at the freezing temperature were those for Form III, initiation of the crystal growth into Form I at 60 °C was a little faster for the nucleated glass (Table 2). Thus, formation of the Form III nuclei seems to assist nucleation/crystal growth of Form I by any means. The presence of the low-density region may assist in the formation of nuclei of Form I. Promotion of formation of different crystal form is a known phenomenon called as cross-nucleation40, in which the original crystal appears to work as a template for the new crystal form. The intact glass exhibited faster crystal growth relative to the nucleated one, which may be related to formation of the void spaces. The long-term storage stability is anticipated to be poor if nuclei exist. It was true to some extent if Form III was the dominant form after the crystallization (35 °C). The effect was unclear when two crystal forms grew together (40-50 °C) or a different crystal form dominated the crystallization behavior (60 °C). Impact of the preformed nuclei on the glass stability was demonstrated to depend on the following storage condition.4.3 Diffusionless Crystal Growth below TgThe isothermal crystallization behavior was observed in the temperature range from 30 °C to 60 °C to find the fastest crystallization at 40 and 45 °C, which can be understood by the frequently reported phenomenon of accelerated crystallization just below Tg, called diffusionless crystal growth or GC mode31-34. Its mechanism has been interpreted as the possible formation of embryos and the decrease in interfacial energy between the crystal/glass interface. Since acceleration of the crystallization was observed for both the intact and nucleated glasses, this observation is not necessarily related to the presence of the preformed nuclei. Moreover, the observation did not have relevance to the resultant crystal form.In the series of our studies, initiation time for crystallization, t10, was shown to depend only on temperature for compounds with high crystallization tendency4,5,10,41. This conclusion was made by mainly observing the crystallization kinetics above Tg. However, the t10 values obtained in this study for the CEL glass cannot be explained by this general rule due to significant effect of the diffusionless crystal growth. Although remarkable enhancement of the crystallization rate based on this mechanism has been observed for small molecules such as toluene31, degree of the enhancement has been marginal for larger compounds. For example, the crystal growth rate for ROY (5-methyl-2-[(2-nitrophyenyl)amino]-3-thiophenecarbonitrile, molecular weight: 259 Da) just below Tg was shown to be larger only by an order of magnitude than that just above Tg34. However, this study revealed that the crystallization rate of the CEL glass at 40 °C was faster than that at 60 °C by more than eleven orders of magnitude. Hatase et al. suggested that the phenyl ring might play an important role for the diffusionless crystal growth32. Based on this assumption, two benzene rings in CEL might have some contribution. Relationship between chemical structure of organic compounds and appearance of the diffusionless crystal growth is of great importance to understand crystallization mechanism of small organic compounds.5 ConclusionThe properties of nucleated CEL glass were investigated and compared with those of the intact one to understand how the presence of nuclei influences the structure and dynamics of organic glasses. The nucleated glass exhibited faster structural relaxation and a wider distribution of relaxation times than the intact one, presumably because of the spatial heterogeneity of its glass structure, which included condensed and void portions. The concept of void formation also explains the smaller CRR of the nucleated glass. BDS measurements revealed that β relaxation was suppressed by nucleation. In the long-term isothermal crystallization study, the crystal growth of Form III was accelerated in the presence of the nuclei at 35 °C. However, the nuclei for Form I also appeared at higher temperatures, diminishing the influential role of the preformed nuclei. Nevertheless, presence of form III nuclei and/or the formation of the void space after nucleation appeared to assist the formation of nuclei for form I. The crystallization rates just below Tg (40 °C) were faster than that just above Tg (60 °C) by more than eleven orders of magnitude, which could be explained by diffusionless crystal growth. These observations provide a better insight into the crystallization mechanism of small organic glasses.Supporting InformationThe supporting Information is available free of charge athttps://pubs.acs.org/doi/XXXXXXThe Supporting Information includes an example of the separation of the DSC heat flow curve into reversing and nonreversing heat flows, where presence of pre-Tg peak in the reversing heat flow and widening of the glass transition region found in the nonreversing heat flow are presented. Also included is quantitative analysis on change in the size of the CRR after nucleation and during the annealing.Conflict of InterestThe authors declare no conflict of interest.References1. Murdande, S. B.; Pikal, M. J.; Shanker, R. M.; Bogner, R. H. Solubility Advantage of Amorphous Pharmaceuticals: I. 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In Handbook of Thermal Analysis and Calorimetry, 2nd Ed.; Vyazovkin, S., Koga, N., Schick, C., Eds.; Elsevier: Amsterdam, 2018; 6, pp 613-641.1image2.pngimage3.pngimage4.pngimage5.pngimage6.pngimage7.emf(a)(b)image8.pngimage9.pngimage10.emf0204060801000 20 40 60 80 100 120 140 160Crystallinity (%)Time (d)45℃ 40℃ 50℃35℃60℃image11.emfNucleationCRR : 2.7 nmvoidvoidnucleiCRR : 2.2 nmNucleationCRR : 2.7 nmvoidvoidnucleiCRR : 2.2 nmimage1.png