Enhanced Crystal Nucleation in Glass-Forming Liquids by Tensile

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Enhanced Crystal Nucleation in Glass-Forming Liquids by Tensile Fracture in the Glassy State Yuan Su,† Lian Yu,‡ and Ting Cai*,† †

State Key Laboratory of Natural Medicines, Department of Pharmaceutics, School of Pharmacy, China Pharmaceutical University, Nanjing 210009, China ‡ School of Pharmacy and Department of Chemistry, University of Wisconsin, Madison, 53705, United States

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S Supporting Information *

ABSTRACT: Crystal nucleation in a supercooled liquid typically attains its maximal rate near the glass transition temperature Tg and slows down with further cooling, becoming exceedingly slow in the glassy state. We report that cooling a liquid well below its Tg can actually increase the rate of nucleation because of tensile fracture. Cooling liquid griseofulvin (an antifungal drug) approximately 80 K below its Tg induces extensive network fracture due to tensile stress from a thermally less expansive container, and reheating the sample above Tg leads to crystallization that otherwise would not occur. An extensive statistical study revealed a direct connection between fracture and crystal nucleation. This phenomenon explains puzzling results in the literature concerning anomalous nucleation in deeply supercooled liquids and is relevant for selecting storage conditions to ensure the physical stability of amorphous drugs. drug, see the inset of Figure 2 for its structure) to Tg − 80 K induces extensive network fracture because of tensile stress from a thermally less expansive container. Reheating the sample above Tg leads to crystallization that otherwise would not occur. An important element of this work is to rely on the stochastic nature of fracture to compare samples that are cooled to the same temperature, some fractured and others not. This provides a direct test of the link between fracture and crystal nucleation. Although the literature contains scattered reports on fracture-induced nucleation,7,16−18 this direct test is missing. Without this test, the seeming enhancement of nucleation could simply be a result of the temperature effect on nucleation (slow at high temperatures, fast at low temperatures), having nothing to do with fracture. Our finding explains puzzling results in the literature concerning the anomalous “generation and extinction” of crystal nuclei in deeply supercooled liquids.19−23 It is also relevant for selecting storage conditions to ensure the physical stability of amorphous drugs. Figure 1 shows the differential scanning calorimetry (DSC) traces of GSF that indicate cooling-induced fracture and crystal nucleation. In Run 1, the crystals of GSF (Form I) are heated at 10 K min−1, showing melting at 492 K with a heat of fusion of 116 J g−1, consistent with the literature values.24,25 In Run 2, the GSF melt is cooled at 15 K min−1. The melt first undergoes a glass transition (361 K), and then shows an abrupt release of

G

lasses are amorphous solids that combine the mechanical strength of crystals and the spatial uniformity of liquids, making them useful for many applications.1 In pharmaceutics, amorphous solids are used for their increased solubility in the delivery of poorly soluble drugs.2,3 A central requirement in developing any amorphous material is its stability against crystallization since crystallization eliminates all its advantages over crystals.2,4,5 This motivates a fundamental understanding of crystallization in deeply supercooled liquids and glasses. Crystallization is a complex process of nucleation and crystal growth. In the nucleation step, a viable nucleus is born that can grow to macroscopic size. Nucleation has very different kinetics from crystal growth.6,7 Typically, the temperature at which nucleation is the fastest is below that for crystal growth.7−9 For glass-forming liquids, nucleation usually reaches its maximal rate near the glass transition temperature (Tg) and slows down with further cooling.7,10,11 This temperature dependence is consistent with the classical nucleation theory (CNT).12,13 According to the CNT, the nucleation rate is limited at high temperatures by the thermodynamic barrier for creating a nucleus and at low temperatures by the molecular mobility available. The CNT predicts an exceedingly slow nucleation rate below Tg.6,13 This view is widely accepted in the field of amorphous materials. In fact, the so-called “Tg − 50 K rule” states that amorphous solids are stable against crystallization if stored at temperatures 50 K or more below Tg.2,14,15 We report here that crystal nucleation can be significantly enhanced if a molecular liquid is cooled below Tg to cause fracture. Cooling the liquid griseofulvin (GSF, an antifungal © XXXX American Chemical Society

Received: September 22, 2018 Revised: November 7, 2018 Published: December 3, 2018 A

DOI: 10.1021/acs.cgd.8b01427 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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elastic solid (approximately the end point of the glass transition during cooling). As T decreases, σ increases and may eventually exceed the critical value for fracture. The condition for this is G > Gc, where G is the energy release rate as a crack extends and Gc is a material property (fracture toughness). For our supported film, G is given by26,29 ψ 2σ 2h (2) E̅ where ψ2 is a geometric factor (1.2 for our open-surface sample) and E̅ = E/(1 − ν2). Together, eqs 1 and 2 predict a well-defined temperature at which fracture occurs in the glass film. This prediction is verified by our experiments. Figure 2 shows the probability of G=

Figure 1. DSC traces of GSF. Run 1: Heating GSF crystals (Form I) at 10 K min−1 from 313 to 503 K. The endotherm labeled “Form I” corresponds to crystal melting. Run 2: Cooling the melt of GSF at 15 K min−1 to Tc,1 = 243 K. The glass transition (Tg) occurs at 361 K and fracture occurs at 280 K (sharp exotherm labeled Tfrac). The photograph shows the fractured glass in a DSC pan. Run 3: Reheating the fractured glass at 10 K min−1 to 503 K. The exotherm is due to crystallization. Further heating detects the melting of crystals (Forms II and III). Run 4: Cooling a GSF melt at 15 K min−1 to Tc,2 = 323 K without fracture. Run 5: Reheating the unfractured glass formed in Run 4 at 10 K min−1 to 503 K. No crystallization is detected.

Figure 2. Probability of fracture plotted against the temperature to which the system is cooled (Tc). Thirty samples were measured for each Tc. The structure of GSF is shown in the inset.

heat at ∼80 K below Tg. This is a consequence of fracture, as observed in other molecular glasses26 and discussed below. In essence, as a molecular liquid is cooled while adhering to a less thermally expansive container (aluminum DSC pan), tensile stress builds up below Tg and accumulates to exceed the fracture toughness of the material. The exothermal peak at Tfrac represents the release of the excess enthalpy stored as the glass sample is cooled under stress relative to a free-standing film.26 In Run 3, the fractured GSF glass is reheated. The glass-toliquid transition is observed at 361 K, in agreement with the literature value.24,25,27 At higher temperatures, a broad exothermic peak is observed corresponding to crystallization, followed by two melting peaks at 477 K (Form III) and 486 K (Form II). (Form II spontaneously nucleates and because of slow growth rate, Form III cross-nucleates on Form II.25) It is significant that the crystallization event just described does not occur if the sample had not been cooled so deeply as to cause fracture (see Runs 4 and 5 in Figure 1). This suggests that fracture is responsible for the creation of crystal nuclei which grow upon reheating, a hypothesis to be evaluated below. For a glass-forming liquid film cooled on a substrate of lower thermal expansion coefficient, tensile stress builds up in the glassy state according to28 σ=

E Δα(Tset − T ) 1−ν

fracture for samples cooled to a chosen temperature Tc. For each Tc, a total of 30 independent samples were analyzed. Notice that no or few samples fractured at high Tc, while nearly all fractured at low Tc. The probability of fracture increases sharply with cooling near 278 K, consistent with the prediction of fracture mechanics. The fact that the rise is not infinitely sharp reflects the stochastic nature of the fracture. From the average fracture temperature 278 K, we obtain Gc = 3.4 J/m2 for GSF, in reasonable agreement with the values for molecular glasses (∼1 J/m2);29 the discrepancy might arise from the nonuniformity of sample thickness and errors in estimated physical constants (see Supporting Information). To test our hypothesis of fracture-induced nucleation, a statistical study was performed where a large number of samples were cooled to various target temperatures Tc, and their behaviors upon heating were recorded. Table 1 shows the results of this study. For each Tc, a total of 30 samples were analyzed. For each sample, we record whether fracture occurs and whether it crystallizes during heating. This yields a total of four categories of behaviors: (A) fractured and crystallized, (B) not fractured and not crystallized, (C) fractured and not crystallized, and (D) not fractured and crystallized. The typical DSC curves for different categories are shown in Figure S1. If fracture causes crystal nucleation, then all the samples should fall in the first two categories in Table 1. We see that this is indeed the case. If Tc is high, no fracture occurs and the sample does not crystallize upon heating. But if Tc is low, every sample fractures and crystallizes upon reheating. For samples cooled to an intermediate Tc (e.g., 278 K), fracture occurs in

(1)

where Δα is the difference in linear thermal expansion coefficients between the film and the substrate, E is Young’s modulus of the film, ν is its Poisson’s ratio, and Tset is the temperature at which the liquid begins to respond like an B

DOI: 10.1021/acs.cgd.8b01427 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Table 1. Results of a Statistical Study of the Link between Fracture and Crystal Nucleationa Tc, K

fractured and crystallized

not fractured and not crystallized

fractured and not crystallized

not fractured and crystallized

total

243 263 268 273 278 283 293 303 313 323

30 28 23 21 14 4 0 0 0 0

0 1 4 8 13 24 27 28 28 30

0 0 2 1 2 0 0 0 1 0

0 1 1 0 1 2 3 2 1 0

30 30 30 30 30 30 30 30 30 30

a

Of 30 sample cooled to a chosen temperature Tc, the different categories of behaviors are reported in terms of fracture and crystallization upon heating.

some of the samples, while the others remain intact. We find that nearly all fractured samples crystallize, and nearly all unfractured samples do not. This latter result is a strong indication of fracture-induced crystal nucleation since the two groups of samples have exactly the same thermal history except for the occurrence of fracture. The direct comparison just described is absent in the previous reports of fracture-induced nucleation,7,16−18 which weakens the claims. In the absence of fracture, the nucleation rate is known to have a strong temperature dependence, making the different crystallization probabilities after cooling to different lower temperatures not cleanly linked to fracture. But this connection is readily made for two groups of samples cooled to an identical Tc, with one group fractured and the other not. Thus, low-temperature tensile fracture is directly responsible for the creation of crystal nuclei which grow at elevated temperatures. The few samples that fall in the latter two categories in Table 1 (fractured & not crystallized, and not fractured & crystallized) are likely results of failure of DSC to detect fracture events and/or random nucleation events. Additional experiments were performed to determine whether crystal nuclei were formed at the fracture temperature or during the subsequent heating of a fractured glass. In the first scenario, we imagine that nucleation occurs in the glassy state, shortly after fracture; this could occur by the sudden release of strain energy near fracture sites and by the higher molecular mobility now available at the free surfaces that are created. Crystal nucleation is known to be accelerated by interfaces (heterogeneous nucleation).30−32 In the second scenario, we imagine that fracture creates free surfaces and voids inside a glass, and upon heating above Tg, there is active liquid flow around the cracks to minimize surface area. This motion and the available free surfaces might combine to cause crystal nucleation. To distinguish the two scenarios above, the fractured glasses of GSF with Tc = 243 K were heated at different rates (10, 20, and 50 K min−1). At this Tc, all the samples fractured (see Table S1). If crystal nuclei form immediately or shortly after fracture, the subsequent heating should show crystallization in all samples, regardless of heating rate. However, we observed a strong dependence of the crystallization probability on the heating rate. As shown in Figure 3b, at 10 K min−1, all samples crystallized; at 50 K min−1, only 6.7% samples crystallized. This large difference in crystallization during heating indicates that

Figure 3. (a) Temperature programs to investigate the conditions under which nuclei form. In Run 1, GSF crystals were heated to 503 K and held for 10 min. The melt was cooled to 243 K (Run 2), and heated to 453 K (Run 3a) at the three different heating rates (10, 20, or 50 K min−1). Samples were annealed at 453 K (where GSF exhibits the fastest growth rate23,25) for 10 min to allow crystal growth, and heated at 10 K min−1 to 503 K (Run 3b). (b) Probability of crystallization of GSF glasses that were heated at different rates (10, 20, and 50 K min−1). Each column represents the probability calculated from a total of 30 independent samples.

the nuclei were not directly generated by the fracture event, but instead, they formed during the heating process, perhaps a result of liquid flow around the healing cracks and perhaps just above the glass transition temperature at which the bulk nucleation rate is expected to be maximal.11 In summary, we report that crystal nucleation can be greatly enhanced if a glass-forming liquid is cooled to well below Tg because of tensile fracture. We find that fracture is directly responsible for the subsequent crystallization of GSF glasses during heating. Fracture creates free surfaces and voids inside a glass which can provide sites for heterogeneous nucleation7,30,33,34 through enhanced molecular mobility.35 In our systems, nuclei are not formed immediately after fracture, but during the subsequent heating and the re-equilibration of the fractured glass in the liquid state. In other systems, it is possible that storage of a fracture glass below Tg might lead to crystal nucleation and growth near fracture sites. The finding of this work has significant implications for predicting and controlling the physical stability of amorphous materials. It is generally accepted that crystal nucleation is exceedingly slow far below Tg, leading to the “Tg − 50 K rule” for the safe storage of amorphous pharmaceuticals.2,14,15 We have shown, however, that deep cooling can be detrimental to C

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(4) Laitinen, R.; Lobmann, K.; Strachan, C. J.; Grohganz, H.; Rades, T. Emerging trends in the stabilization of amorphous drugs. Int. J. Pharm. 2013, 453, 65−79. (5) Qi, S.; McAuley, W. J.; Yang, Z.; Tipduangta, P. Physical stabilization of low-molecular-weight amorphous drugs in the solid state: a material science approach. Ther. Delivery 2014, 5, 817−841. (6) Fokin, V. M.; Schmelzer, J. W.; Nascimento, M. L.; Zanotto, E. D. Diffusion coefficients for crystal nucleation and growth in deeply undercooled glass-forming liquids. J. Chem. Phys. 2007, 126, 234507. (7) Descamps, M.; Dudognon, E. Crystallization from the amorphous state: nucleation-growth decoupling, polymorphism interplay, and the role of interfaces. J. Pharm. Sci. 2014, 103, 2615− 28. (8) Jenniskens, P.; Blake, D. F. Crystallization of Amorphous Water Ice in the Solar System. Astrophys. J. 1996, 473, 1104−1113. (9) Schmelzer, J. W. P.; Abyzov, A. S.; Fokin, V. M.; Schick, C.; Zanotto, E. D. Crystallization of glass-forming liquids: Maxima of nucleation, growth, and overall crystallization rates. J. Non-Cryst. Solids 2015, 429, 24−32. (10) Laksmono, H.; McQueen, T. A.; Sellberg, J. A.; Loh, N. D.; Huang, C.; Schlesinger, D.; Sierra, R. G.; Hampton, C. Y.; Nordlund, D.; Beye, M.; Martin, A. V.; Barty, A.; Seibert, M. M.; Messerschmidt, M.; Williams, G. J.; Boutet, S.; Amann-Winkel, K.; Loerting, T.; Pettersson, L. G.; Bogan, M. J.; Nilsson, A. Anomalous Behavior of the Homogeneous Ice Nucleation Rate in ″No-Man’s Land″. J. Phys. Chem. Lett. 2015, 6, 2826−2832. (11) Fokin, V. M.; Zanotto, E. D.; Schmelzer, J. W. P. Homogeneous nucleation versus glass transition temperature of silicate glasses. J. Non-Cryst. Solids 2003, 321, 52−65. (12) Turnbull, D.; Fisher, J. C. Rate of Nucleation in Condensed Systems. J. Chem. Phys. 1949, 17, 71−73. (13) Sosso, G. C.; Chen, J.; Cox, S. J.; Fitzner, M.; Pedevilla, P.; Zen, A.; Michaelides, A. Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations. Chem. Rev. 2016, 116, 7078−116. (14) Hancock, B. C.; Zografi, G. Characteristics and Significance of the Amorphous State in Pharmaceutical. J. Pharm. Sci. 1997, 86, 1− 12. (15) Hatley, R. H. M. Glass Fragility and the Stability of Pharmaceutical Preparations-Excipient Section. Pharm. Dev. Technol. 1997, 2, 257−264. (16) Legrand, V.; Descamps, M.; Alba-Simionesco, C. Glass-forming meta-toluidine: A thermal and structural analysis of its crystalline polymorphism and devitrification. Thermochim. Acta 1997, 307, 77− 83. (17) Dudognon, E.; Danede, F.; Descamps, M.; Correia, N. T. Evidence for a new crystalline phase of racemic Ibuprofen. Pharm. Res. 2008, 25, 2853−8. (18) Ayenew, Z.; Paudel, A.; Rombaut, P.; Van den Mooter, G. Effect of Compression on Non-isothermal Crystallization Behaviour of Amorphous Indomethacin. Pharm. Res. 2012, 29, 2489−2498. (19) Okamoto, N.; Oguni, M. Discover of crystal nucleation proceeding much below the glass transition temperature in a supercooled liquid. Solid State Commun. 1996, 99, 53−56. (20) Okamoto, N.; Oguni, M.; Sagawa, Y. Generation and extinction of a crystal nucleus below the glass transition temperature. J. Phys.: Condens. Matter 1997, 9, 9187−9198. (21) Paladi, F.; Gamurari, V. G.; Oguni, M. Effect of annealing in glass-transition region on anomalous generation and extinction of crystal nuclei at very low temperatures in o-benzylphenol and salol. Moldavian J. Phys. Sci. 2002, 1, 64−67. (22) Paladi, F.; Oguni, M. Anomalous generation and extinction of crystal nuclei in nonequilibrium supercooled liquid o-benzylphenol. Phys. Rev. B: Condens. Matter Mater. Phys. 2002, 65, 144202. (23) Paladi, F.; Oguni, M. Generation and extinction of crystal nuclei in an extremely non-equilibrium glassy state of salol. J. Phys.: Condens. Matter 2003, 15, 3909−3017. (24) Mahieu, A.; Willart, J. F.; Dudognon, E.; Eddleston, M. D.; Jones, W.; Danede, F.; Descamps, M. On the polymorphism of

physical stability because of fracture and creation of free surfaces. Given free surfaces provide sites for heterogeneous nucleation and molecular mobility, fractured glasses can be substantially less stable on storage than their unfractured counterparts. Storage conditions must be chosen carefully to avoid fracture. Easy-to-fracture molecular glasses may be stabilized by incorporating polymer additives to increase resistance against fracture.29 The finding of this work also provides an explanation for some puzzling results in the literature. Oguni et al. have reported “anomalous” nucleation in molecular glasses at low temperatures. For salol, o-benzylphenol, and other systems, nucleation is slow in the liquid state, but is enhanced upon cooling to temperatures far below Tg (Tg − 100 K or lower).19−23 They proposed that the enhanced nucleation is facilitated by the β relaxation that remains active even at such low temperatures.19−23 More puzzling, they report that crystal nuclei formed at low temperatures disappear over time as the glass ages.21−23 Our results suggest that fracture could be responsible for the crystal nuclei formed at low temperatures but do not offer an immediate explanation for the extinction of crystal nuclei upon aging.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.8b01427.

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Details of the experimental methods, calculation of the critical energy release rate, number and probability of samples fractured in Run 2 and crystallized in Run 3 at different cooling temperature and heating rate, typical DSC curves for four categories of crystallization behaviors (PDF)

AUTHOR INFORMATION

Corresponding Author

*Tel: 86-025-83271123. E-mail: [email protected]. ORCID

Ting Cai: 0000-0001-7510-9295 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful for financial support of this work by the National Natural Science Foundation of China (No. 81872813), the State Project for Essential Drug Research and Development (No. 2017ZX09301075), the Program of State Key Laboratory of Natural Medicines-China Pharmaceutical University (No. SKLNMZZCX201826), the 111 project (B16046), and the Program for Jiangsu Province Innovative Research Team.

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REFERENCES

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griseofulvin: identification of two additional polymorphs. J. Pharm. Sci. 2013, 102, 462−468. (25) Su, Y.; Xu, J.; Shi, Q.; Yu, L.; Cai, T. Polymorphism of Griseofulvin: Concomitant Crystallization from the Melt and Single Crystal Structure of a Metastable Polymorph with Anomalously Large Thermal Expansion. Chem. Commun. 2018, 54, 358−361. (26) Chen, Y.; Powell, C. T.; Yu, L. Tensile Fracture of Molecular Glasses Studied by Differential Scanning Calorimetry: Reduction of Heat Capacity by Lateral Constraint. J. Phys. Chem. B 2017, 121, 444−449. (27) Shi, Q.; Cai, T. Fast Crystal Growth of Amorphous Griseofulvin: Relations between Bulk and Surface Growth Modes. Cryst. Growth Des. 2016, 16, 3279−3286. (28) Hutchinson, J. W.; Suo, Z. Mixed Mode Cracking in Layered Materials. Adv. Appl. Mech. 1991, 29, 63−187. (29) Powell, C. T.; Chen, Y.; Yu, L. Fracture of molecular glasses under tension and increasing their fracture resistance with polymer additives. J. Non-Cryst. Solids 2015, 429, 122−128. (30) Müller, R.; Zanotto, E. D.; Fokin, V. M. Surface Crystallization of Silicate Glasses. J. Non-Cryst. Solids 2000, 274, 208−231. (31) Š pillar, V.; Dolejš, D. Heterogeneous nucleation as the predominant mode of crystallization in natural magmas-numerical model and implications for crystal−melt interaction. Contrib. Mineral. Petrol. 2015, 169, 1−16. (32) Liu, X. Y. Heterogeneous nucleation or homogeneous nucleation? J. Chem. Phys. 2000, 112, 9949−9955. (33) Zanotto, E. D. Experimental studies of surface nucleation and crystallization of glasses. Ceram. Trans. 1993, 30, 65−74. (34) Zanotto, E. D.; Fokin, V. M. Recent studies of internal and surface nucleation in silicate glasses. Philos. Trans. R. Soc., A 2003, 361, 591−613. (35) Huang, C.; Ruan, S.; Cai, T.; Yu, L. Fast Surface Diffusion and Crystallization of Amorphous Griseofulvin. J. Phys. Chem. B 2017, 121, 9463−9468.

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DOI: 10.1021/acs.cgd.8b01427 Cryst. Growth Des. XXXX, XXX, XXX−XXX