CRYSTAL GROWTH & DESIGN
Growth Rings in D-Sorbitol Spherulites: Connection to Concomitant Polymorphs and Growth Kinetics
2003 VOL. 3, NO. 6 967-971
Lian Yu* Lilly Research Laboratories, Eli Lilly and Company, Indianapolis, Indiana 46285 Received April 18, 2003;
Revised Manuscript Received July 8, 2003
ABSTRACT: D-Sorbitol spherulites developed concentric rings in response to changes of crystallization temperature. Unlike extinction rings of polymer spherulites, these growth rings were linked to the concomitant crystallization of polymorphs (E and E′) in temperature-dependent ratios. The growth rings provided a convenient way to measure the kinetics of crystal growth, similar to the use of tree rings in dendrochronology to determine the climatic effect on a tree’s growth. The observed growth kinetics spanned 4 orders of magnitude and conformed approximately to the theory of interface-controlled growth parametrized with a viscosity-derived diffusion coefficient and thermodynamic driving force of crystallization. Near the glass transition temperature, however, the observed growth rate was faster than predicted, a discrepancy observed previously with other materials and attributed to the breakdown of the Stokes-Einstein relation between diffusion coefficient and viscosity. The same theory predicted a faster growth rate of the commercial γ polymorph than polymorphs E and E′; however, the opposite was observed. This discrepancy may arise from conformational barriers to crystallization. Introduction Understanding and controlling polymorphism, the ability of a molecule to crystallize in different lattices, remains a subject of broad interest and active research. The polymorphism of D-sorbitol (D-glucitol), an important material in pharmaceutical and nutritional sciences, is rich and still poorly understood. The current confusion is illustrated by the names of the D-sorbitol polymorphs: A, B, C, E, SM1, SM2, R, β, γ, ∆, etc., some of which apparently overlap.1 Powder X-ray diffraction data suggest at least five polymorphs1,2, and the Cambridge Structural Database (v.5.24, Nov. 2002) contains two crystal structures (A3 and 4). Hydrate formation has been reported for D-sorbitol,1,4 as has conformational polymorphism,4 which constitutes a rare exception to Jeffrey and Kim’s rule of alditol conformations.5 The liquid of D-sorbitol spontaneously crystallizes near room temperature as low-melting crystals (mp 80 °C, termed E by Du Ross2), even when seeded with the high-melting commercial polymorph γ (mp 100 °C).6 Consequently, the γ polymorph is crystallized commercially at high temperature with extensive seeding.2 The viscosity of D-sorbitol as a function of temperature, required for kinetic analysis of crystallization, has been determined.7,8 Spherulitic crystallization is frequently observed in the melt crystallization of polymers and is less common among nonpolymers.9 A spherulite consists of an array of crystal fibrils that have grown radially outward from a central nucleus. The fibrils branch as they grow in a tree-like manner. Periodic extinction rings are sometimes observed by light microscopy because of concerted twisting of crystal fibrils during growth. Reported here is a hitherto unknown phenomenon revealed by the spherulitic crystallization of D-sorbitol: growth rings developed in response to changes of crystallization temperature. The growth rings were linked to the * Corresponding author. Tel. (317) 276-1448. E-mail: yu_lian@ lilly.com.
concomitant crystallization of polymorphs10 and used to study the kinetics of crystal growth, as tree rings are used to study the climatic effect on a tree’s growth. Experimental Procedures D-sorbitol (99+%, γ polymorph) was purchased from Aldrich and used as received. To study its crystallization, ca. 3 mg of the γ crystals was placed on a 15 mm cover glass and heated to 130 °C on a hot stage to melt the crystals. The melt was initially cloudy because of the presence of air bubbles but clarified in 2 h at 130 °C under vacuum (5” Hg). This property of the commercial d-sorbitol was reported previously.7 The clear melt was covered by another 15 mm cover glass and cooled to desired temperatures to observe crystallization. The thickness of the liquid sample thus produced was 10-20 µm, which was estimated from its weight, density, and area. For measurements at subambient temperatures, the cover glass assembly was placed in a DSC cell (see later), and the temperature and duration of crystallization were programmed via the DSC control software. Polarized light microscopy (PLM) was performed with a Nikon Optiphot Pol 2 microscope. Hot-stage measurements were carried out with a Linkam THMS 600. Differential scanning calorimetry (DSC) was conducted at 5 °C/min in crimped Al pans using a TA Q1000 DSC under nitrogen purge (50 mL/min). The temperature and heat flow were calibrated using indium. A sample for DSC analysis was accurately weighed into an Al pan, clarified (degassed) at 130 °C under vacuum (5” Hg), and hermetically sealed. X-ray diffraction (XRD) was performed with a Siemens D5000 X-ray diffractomenter, which was equipped with a CuKR source (λ ) 1.54056 Å) operating at a tube load of 50 kV and 40 mA. The divergence slit size was 1 mm, the receiving slit was 1 mm, and the detector slit was 0.1 mm. Data were collected by a Kevex solid-state (SiLi) detector. Each sample was scanned between 4 and 35° (2θ) with a step size of 0.02° and a maximum scan rate of 3 s/step.
Results Growth Rings in D-Sorbitol Spherulites. The liquid of D-sorbitol crystallized near room temperature as spherulites (Figure 1a). If the temperature was varied during crystallization, concentric rings developed
10.1021/cg034062n CCC: $25.00 © 2003 American Chemical Society Published on Web 07/29/2003
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Figure 1. D-sorbitol spherulites viewed between crossed polars. (a) Grown at constant temperature (22 °C). (b) Grown at different temperatures. Crystallization at each temperature yielded a distinct growth ring.
in the spherulites; for example, Figure 1b shows a set of growth rings formed at 40 °C in 1.5 h, 25 °C in 10 h, and 35 °C in 3 h. The growth rings differed from each other in birefringence (brightness between crossed polars); a lower temperature of crystallization led to a more birefringent growth ring (brighter between crossed polars). The growth rings were stable indefinitely at room temperature if protected from moisture. At high humidity, the spherulites deliquesced in days, with the transformation beginning at the edges. On heating, the spherulites in Figure 1a (grown at 22 °C) became less birefringent but retained their spherical morphology until melting at 80 °C. When the growth rings in Figure 1b were heated, the more birefringent rings became less birefringent, and all rings approached the same brightness between crossed polars, making them less easily distinguished. All the rings melted simultaneously at 80 °C. The growth rings observed here differ from the extinction rings that sometimes appear on polymer spherulites (termed banded or ringed spherulites).9 The extinction rings arise from concerted and periodic twisting of crystal fibrils; when twisted to orientations of extinction, the fibrils appear dark between crossed polars. The contrast between the D-sorbitol growth rings, however, arose from their different birefringence and texture as a result of crystal growth at different temperatures. The remainder of this work investigated the connection of the growth rings to the concomitant crystallization of D-sorbitol polymorphs and the use of the growth rings in kinetic studies of crystal growth. Concomitant Polymorphs. Quinquenet et al.1 sug-
Yu
Figure 2. DSC of D-sorbitol. (a) Solid line: crystallized at 22 °C. Short dash: crystallized at 42 °C. Long dash: no crystallization. ∆Tgrowth: temperature range of kinetic study. (b) Solid line: crystallized at 22 °C, heated to 60 °C [to the circle in panel a], and cooled. Long dash: no crystallization.
gested on the basis of DSC data that melt-crystallized D-sorbitol (Du Ross’ polymorph E2) comprises two polymorphs. As Figure 2a shows, melt-crystallized Dsorbitol displayed two endotherms: a major one (E) at 80 °C and a minor one (E′) at 55 °C. Being germane to the interpretation of the growth rings, the assignment was verified in this study. That the E endotherm corresponded to melting was confirmed by hot-stage microscopy, but several possibilities exist for E′ and its relation to E: (1) E′ is a polymorphic transition without melting. E is the melting of the transformed polymorph. (2) E′ is the melting of one polymorph and the simultaneous crystallization of the melt to another polymorph. E is the melting of the resulting polymorph. (3) E′ is the melting of one polymorph without significant recrystallization of the melt. E is the melting of a preexisting polymorph and has minimal contribution from the recrystallized melt. These possibilities were evaluated against a DSC experiment in which a 22 °C crystallized sample was heated just past E′ (to the circle in Figure 2a) and cooled. Subsequent heating (Figure 2b, solid curve) revealed a glass transition at -3 °C whose intensity was approximately 1/3 that of the D-sorbitol liquid (long-dashed curve). Further heating showed that the E′ endotherm was eliminated by the preheating, but the E endotherm was intact. Thus, heating past E′ melted a crystalline phase and generated a liquid phase that was approximately 1/3 of the total mass. This result contradicts
Growth Rings in Spherulites and Concomitant Polymorphs
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Figure 3. XRD of D-sorbitol. (a) As purchased (the γ polymorph). (b) Recrystallized from a melt at 22 °C.
(1) and (2) because both require that the system comprise only crystals when heated past E′ and thus display no glass transition. This result, however, agrees with (3), which requires that the system contain a liquid phase after being heated past E′. (3) is therefore adopted over (1) and (2). With this assignment, the small exotherm circled in Figure 2a is attributed to the crystallization of a small amount of the liquid to the higher-melting E when heating continued. The small exotherm was not detected at faster heating rate (e.g., 20 °C/min). From (3), it follows that melt-crystallized D-sorbitol contained two polymorphs: a main polymorph (E) melting at 80 °C and a minor polymorph (E′) melting at 55 °C. Thus, Quinquenet et al.’s suggestion of concomitant crystallization of D-sorbitol polymorphs has been confirmed. The concomitant crystallization of polymorphs has been observed with other molecules.10 This study found in addition that the ratio of the two DSC endotherms (E′/E) changed with the temperature of crystallization (Tc), with a lower Tc leading to a higher E′/E ratio. Figure 2a illustrates this trend for Tc ) 22 °C (solid curve) and 42 °C (short-dashed curve). Because E and E′ were the independent melting of two polymorphs (or nearly so), D-sorbitol that crystallized at lower Tc was richer in E′. Such an effect of crystallization temperature on polymorphic composition has been observed with fats and fatty acids11 and polymers.12 The concomitant crystallization of D-sorbitol polymorphs suggests an explanation for the temperaturedependent growth rings. Because the spherulite that crystallized at lower temperature was richer in E′ (by DSC) and more birefringent (by light microscopy), the E′ phase should be more birefringent than the E phase. Thus, the different E′/E ratios obtained at different temperatures of crystallization should lead to growth rings of different birefringence. The nature of melt-crystallized D-sorbitol that gives rise to the growth rings remains poorly understood. On one hand, the birefringence and energy of melting of this material demonstrate its crystalline order, and the lack of glass transition (Figure 2a, solid and shortdashed curves) indicates the absence of a liquid component. On the other hand, the XRD data (Figure 3)
Figure 4. (a) Observed (circles) and predicted growth rates. The (D/λ) curve shows the diffusion term in eq 1. The E/E′ and γ are predicted growth rates for respective polymorphs. (b) The ∆Gx term in eq 1 (calculated by integrating heat capacities). The arrow from Tl to T shows the path of integration.
suggest that the material was less crystalline than the purchased γ polymorph and probably disordered (see its broad and weak diffractions peaks). With the low resolution available, XRD revealed no gross differences between samples with different E′/E ratios as determined by DSC. It is possible that the facile concomitant crystallization of E and E′ stems from their similar crystal structures, which enable cross nucleation between polymorphs.6 Additional data from high-resolution diffractometry, spectroscopy, and microscopy should yield a better understanding of these phases and the formation of growth rings. Kinetic Studies via Growth Rings. The temperature-dependent growth rings of D-sorbitol spherulites are reminiscent of tree rings formed in response to climatic changes. As trees in tropical regions do not develop annual rings because of less distinct climatic changes, D-sorbitol spherulites showed no growth rings when they crystallized at a constant temperature. The widths of D-sorbitol growth rings formed at different temperatures in known durations (Figure 1b) were measured to obtain the radial growth rate from 7 to 65 °C, which spanned 4 orders of magnitude (Figure 4a). The absolute growth rate varied slightly from sample to sample, principally a result of sample thickness. For samples 10-20 µm thick, the growth rate was 69.4 ( 2.8 µm/h (n ) 15) at 40.5 °C. If the growth rates of different samples were scaled at one temperature (40.5 °C), their curves of growth kinetics overlap, as shown in Figure 4a.
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The theory of interface-controlled growth13 applies to crystallization without compositional change and thus to the crystallization studied here. This theory treats crystallizations that do not involve molecular diffusion against concentration gradients, which exist during crystallization in multicomponent systems. This theory postulates that the crystal growth rate depends on the rate of molecular diffusion to the growth interface and the rate of molecular integration to the crystal lattice. The rate equation is given by
r ) (D/λ) [1 - exp(-∆Gx/RT)]
(1)
where D is the diffusion coefficient of the liquid, λ the jump distance across the growth interface, ∆Gx the thermodynamic driving force of crystallization, T the temperature in K, and R the ideal gas constant. D was obtained from the viscosity η via the Stokes-Einstein relation
D ) kT/(6πηa)
(2)
where k is the Boltzmann constant and a the molecular radius. The viscosity η of the D-sorbitol liquid is given by7 log η ) -4.4321 + 682.08/(T - 221), where η is in the SI unit (kg s-1 m-1 ) 10 poise), and T is in K. The molecular radius a was estimated using the VOLUME function in Gaussian98,14 which returns the radius of the solvent cavity around a molecule, a parameter recommended for self-consistent reaction field (SCRF) calculations. For the conformers of D-sorbitol in various crystal structures3,4 (retrievable from the Cambridge Structural Database), the value of a in Å was calculated to be 4.40 (CSD ref. code: GLUCIT01), 4.28 (GLUCIT02_a), 4.49 (GLUCIT02_b), 4.37 (HIPKAS_a), 4.14 (HIPKAS_b), and 4.21 (HIPKAS_c). The average value of a ) 4.3 Å was used in eq 2. The term ∆Gx was previously calculated from the temperature and heat of melting.15 In this study, however, ∆Gx was obtained directly from the heat capacities available from the TA Q1000 DSC. The ∆Gx was calculated with the following equations:
∆Gx ) ∆Hx - T∆Sx ∆Hx ) ∆Sx )
∫TT(CpL - Cpc)dτ 1
∫TT(CpL - Cpc)d ln τ 1
where CpL is the heat capacity of the liquid phase, Cpc the heat capacity of the crystalline phase (including the latent heat of melting), Tl a temperature above the crystalline melting point, and T the temperature of crystallization. Cpc was obtained from a DSC scan of the crystalline D-sorbitol and CpL from a rescan of the melt produced by the first heating without removing the sample from the DSC cell. Because they always crystallized together, E and E′ were treated as a single growing phase, and the integrations were performed through both endotherms. Figure 4b shows the result of this calculation. The E/E′ curve in Figure 4b was obtained by integrating the data corresponding to the solid curve in Figure 2a (crystals obtained at 22 °C). The result changed slightly if the DSC data corresponding to
crystals obtained at a different temperature was used. This variation, however, did not significantly influence the predicted growth rate because the diffusion term (D/λ) dominates the temperature dependence of the function in eq 1 unless the temperature approaches the melting point. The only unknown parameter in eq 1, λ (the distance of molecular jump across the growth interface), was adjusted until the predicted growth rates best matched those observed. This adjustment was equivalent to shifting the r versus T curves vertically in Figure 4a without changing its curvature. The optimal value of λ thus found was 135 Å. Figure 4a shows the growth kinetics predicted by eq 1 for different polymorphs. The predicted growth rates converge to the term (D/λ) at large undercoolings (Tm - T) because the term [1 - exp(-∆Gx/RT)] approaches unity. At small undercoolings, the term [1 - exp(-∆Gx/ RT)] becomes more important. Over 4 orders of magnitude, the predicted growth kinetics for the E and E′ polymorphs (curve E/E′) agrees reasonably well with the experimental data. Figure 4a also reveals a systematic disagreement between observed and predicted growth rates: at lower temperatures (near Tg), the observed growth rate was significantly faster than the predicted. Because the (D/ λ) term dominates the temperature dependence of r at large undercoolings and D was calculated from viscosity η via eq 2, this disagreement suggests that r has a weaker temperature dependence than η. This conclusion can be seen also from the log(r/r0) - log η plot, where r/r0 is the crystal growth rate normalized to the growth rate at a reference temperature. The theory of interfacecontrolled growth (or any theory assuming r ∝ D ∝ η-1) implies a straight line of slope -1 for this plot.16 The log(r/r0) - log η plot for D-sorbitol, however, is a straight line (corr. coeff. ) 0.996) with a slope of -0.76. This again demonstrates that r is a weaker function of temperature than η. The D-sorbitol result described above is consistent with the results reported for 1,3bis(1-naphthyl)-5-(2-naphthyl)benzene (TNB) and 1,2diphynylbenzene (OTP), for which the slopes of the log(r/ r0) - log η plots are -0.74 and -0.72, respectively. The TNB and OTP results have been attributed to faster molecular diffusion near Tg than predicted from viscosity via eq 2 or the breakdown of the Stokes-Einstein relation.16 Because of the greater driving force of crystallization (Figure 4b), the γ polymorph is predicted to grow faster than the E and E′ polymorphs (curve γ in Figure 4a). The opposite, however, was observed. As reported previously,6 γ seeds introduced to the D-sorbitol melt did not grow but instead caused the crystallization of the E and E′ phases. Because the theory of interfacecontrolled growth reasonably accounted for the growth kinetics of the E and E′ polymorphs, the discrepancy may stem from activation barriers that are not included in the theory. One such activation barrier may be the conformational change necessary for crystallization. Being conformationally flexible, D-sorbitol and other alditols are likely to undergo conformational changes upon crystallization.5
Growth Rings in Spherulites and Concomitant Polymorphs
Conclusion The spherulites of D-sorbitol developed growth rings of different birefringence in response to temperature changes during crystallization. The growth rings have been linked to the concomitant crystallization of two polymorphs (E and E′) in temperature-dependent ratios. As tree rings reflect a tree’s growth rate in changing climatic conditions, the growth rings of D-sorbitol were useful for studying the kinetics of crystal growth. Measuring the widths of the growth rings formed at different temperatures in known durations yielded the growth rate of D-sorbitol spherulites over 4 orders of magnitude. The observed growth kinetics conformed approximately to the theory of interface-controlled growth. The theory under-predicted the growth rate near Tg, a disagreement seen with other materials and attributed to the breakdown of the Stokes-Einstein relation between diffusion coefficient and viscosity. The same theory predicted that the commercial γ polymorph should grow faster than the E and E′ polymorphs, but the opposite was observed. This discrepancy may arise from additional activation barriers caused by the conformational change necessary for crystallization. References (1) Quinquenet, S.; Ollivon, M.; Grabielle-Madelmont; Serpelloni, M. Thermochim. Acta 1988, 125, 125. (2) Du Ross, J. W. Pharm. Technol. 1984, Sept., 42. (3) Park, Y. A.; Jeffrey, G. A.; Hamilton, W. C. Acta Crystallogr. 1971, B27, 2393. (4) Schouten, A.; Kanters, J. A.; Kroon, J.; Comini, S.; Looten, P.; Mathlouthi, M. Carbohydr. Res. 1998, 312, 131. (5) Jeffrey, G. A.; Kim, H. S. Carbohydr. Res. 1970, 14, 207. (6) Yu, L. J. Am. Chem. Soc. 2003, 125, 6380.
Crystal Growth & Design, Vol. 3, No. 6, 2003 971 (7) Angell, C. A.; Stell, R. C.; Sichina, W. J. Phys. Chem. 1982, 86, 1540. (8) Nakheli, A.; Eljazouli, A.; Elmorabit, M.; Ballouki, E.; Fornazero, J.; Huck, J. J. Phys.: Condens. Matter 1999, 11, 7977. (9) Keith, H. D. in Physics and Chemistry of the Organic Solid State; Fox, D., Labes, M. M., Weissberger, A., Eds.; Interscience: New York, 1963. (10) Bernstein, J.; Davey, R. J.; Henck, J.-O. Angew. Chem., Int. Ed. Engl. 1999, 38, 3441. (11) Garti, N.; Sato, K., Eds. Crystallization and Polymorphism of Fats and Fatty Acids; Marcel Dekker: New York, 1988. (12) Gan, Z.; Abe, H.; Doi, Y. Macromol. Chem. Phys. 2002, 203, 2369-2374. (13) Raghavan, V.; Cohen, M. In Treatise on Solid State Chemistry, Vol. 5; Hannay, N. B., Ed.; Plenum Press: New York, 1975. (14) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98; Gaussian, Inc.: Pittsburgh, PA, 1998. (15) Yu, L. J. Pharm. Sci. 1995, 84, 966. Yu, L.; Stephenson, G. A.; Mitchell, C. A.; Bunnell, C. A.; Snorek, S. V.; Bowyer, J. J.; Borchardt, T. B.; Stowell, J. G.; Byrn, S. R. J. Am. Chem. Soc. 2000, 122, 585. (16) Ngai, K. L.; Magill, J. H.; Plazek, D. J. J. Chem. Phys. 2000, 112, 1887.
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