Article pubs.acs.org/JPCB

Low-Concentration Polymers Inhibit and Accelerate Crystal Growth in Organic Glasses in Correlation with Segmental Mobility C. Travis Powell,† Ting Cai,† Mariko Hasebe,† Erica M. Gunn,† Ping Gao,‡ Geoff Zhang,‡ Yuchuan Gong,‡ and Lian Yu*,† †

School of Pharmacy and Department of Chemistry, University of WisconsinMadison, Madison, Wisconsin 53705, United States Global Pharmaceutical R & D, Abbott Laboratories, North Chicago, Illinois 60064, United States

‡

ABSTRACT: Crystal growth in organic glasses has been studied in the presence of low-concentration polymers. Doping the organic glass nifedipine (NIF) with 1 wt % polymer has no measurable effect on the glass transition temperature Tg of host molecules, but substantially alters the rate of crystal growth, from a 10-fold reduction to a 30% increase at 12 °C below the host Tg. Among the polymers tested, all but polyethylene oxide (PEO) inhibit growth. The inhibitory effects greatly diminish in the liquid state (at Tg + 38 °C), but PEO persists to speed crystal growth. The crystal growth rate varies exponentially with polymer concentration, in analogy with the polymer effect on solvent mobility, though the effect on crystal growth can be much stronger. The ability to inhibit crystal growth is not well ordered by the strength of host−polymer hydrogen bonds, but correlates remarkably well with the neat polymer’s Tg, suggesting that the mobility of polymer chains is an important factor in inhibiting crystal growth in organic glasses. The polymer dopants also affect crystal growth at the free surface of NIF glasses, but the effect is attenuated according to the power law us ∝ ub0.35, where us and ub are the surface and bulk growth rates.

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INTRODUCTION

elucidate the modification of solvent properties by polymer solutes25 to technological advantages. There have been few studies that compare different polymers as inhibitors of crystallization in organic glasses. Such comparison has been made in the liquid state (above the glass transition temperature Tg),22,23 but it is unclear whether the conclusions are readily applied to glasses, since the latter can crystallize by different mechanisms.6,7,9−11 Furthermore, polymer inhibitors can be much more effective in glasses than in liquids,21,23 requiring direct tests of their performance in the glassy state. Such studies will help assess the ability to transfer the conclusions from liquid-state investigations to glasses; for example, the importance of polymer-host hydrogen bonds in inhibiting crystal growth.22,23 This study compared six polymer additives (Figure 1, Table 1) as inhibitors of crystal growth in the glass of nifedipine (NIF), a poorly water-soluble drug and a model system for studying the stability of amorphous drugs.26−28 We compared the polymers at a low concentration of 1 wt % so that they generally exist in dilute solutions (no overlap on average between polymer chains) and have little effect on the dynamics of host molecules.25,29 The low concentration simplifies the interpretation of polymer effects on crystallization and helps prepare for further studies at higher concentrations. The polymers tested were polyvinyl pyrrolidone (PVP), polyvinyl acetate (PVAc), 60:40 vinyl pyrrolidone−vinyl acetate

Glasses can form upon cooling liquids, condensing vapors, and evaporating solutions while avoiding crystallization. For many applications, glasses are advantageous over crystals.1 While familiar glasses are inorganic and polymeric, organic glasses of relatively low molecular weights have received attention for applications in electronics, biopreservation, and drug delivery.2−5 In these applications, glasses must be stable against crystallization. Recent work has discovered, however, that organic liquids can develop fast modes of crystal growth as they are cooled to become glasses, in the bulk6,7 and at the free surface,8−11 leading to crystal growth much faster than predicted by standard models. For such systems, effective methods are needed to inhibit crystallization. This study is concerned with stabilizing organic glasses against crystallization with polymer additives. The ready solubility of polymers in organic solvents makes them a viable general strategy to engineer organic glasses for improved properties. Macromolecules are known to inhibit crystallization: antifreeze proteins suppress ice formation in arctic fish to enable their survival in subzero waters;12,13 polymer additives prevent the crystallization of fuels and crude oils in cold climates14,15 and the formation of gas hydrates in pipelines;16 amorphous calcium carbonate is stabilized against crystallization by macromolecules.17−20 Polymers can inhibit crystallization in organic liquids and glasses,21−24 enabling their use as vehicles for drug delivery. At present, the understanding is still lacking of the mechanism by which polymer inhibitors function. Work in this area continues the long-standing efforts to © 2013 American Chemical Society

Received: June 28, 2013 Revised: August 1, 2013 Published: August 2, 2013 10334

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inhibit crystal growth is not accurately ordered by the strength of the polymer-host hydrogen bonds, but correlates remarkably well with the Tg of the neat polymer. This correlation suggests the importance of the mobility of polymer chains in inhibiting crystallization. The polymer dopants also alter the rate of crystal growth at the free surface of NIF glasses, but the effect is attenuated according to the power law us ∝ ub0.35, where us and ub are the surface and bulk growth rates.

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MATERIALS AND METHODS Nifedipine (1,4-dihydro-2,6-dimetyl-4-(2-nitrophenyl)-3,5-pyridinedicarboxylate; NIF) was obtained from Sigma-Aldrich (St. Louis, MO); PVP-K15 (M w ≈ 8 kg/mol) from ISP Technologies (Texas City, TX); PVP-K12 (Kollidon 12PF, 2−3 kg/mol), PVP-K30 (Kollidon 30, 44−54 kg/mol), and PVP/VA (Kollidone VA64, 45−70 kg/mol) from BASF; PVPK90 (1000−2000 kg/mol) from GAF Chemicals; the dimer of vinyl pyrrolidone (“VP dimer”, (1,3-bis(2-pyrrolidione-1-yl)butane, 224 g/mol) from Abbott Laboratories; poly(vinyl acetate) (PVAc, 83 kg/mol) and poly(ethylene oxide) (PEO, 8, 100, and 8000 kg/mol) from Sigma-Aldrich (St Louis, MO); poly(vinyl acetate) (PVAc, 15 kg/mol) and polystyrene (Mw = 1.78, 8.4, 16.6 g/mol, Mw/Mn = 1.05) from Scientific Polymer Products Inc.; and HPMCAS (18 kg/mol, Shin-Etsu AQOAT Type AS-MF) from Shin-Etsu Chemicals (Nigita, Japan). Except for PS, no polydispersity data were provided by the supplier. Polymer-doped NIF glasses were prepared by cryomilling followed by melting and cooling. A total of 1 g of a 9:1 NIF/ polymer mixture was milled at 10 Hz (SPEX CertiPrep model 6750 with liquid nitrogen as coolant) for five 2-min cycles, each followed by a 2-min cool down, to yield a 10 wt % polymer in NIF mixture. This mixture was diluted with NIF 9:1 in the same procedure of cryomilling to yield a 1 wt % polymer mixture. A glass sample for studying crystal growth was prepared by melting 2−3 mg of NIF (pure or doped) at 183 °C on a coverslip. After 1 min, the liquid was covered with another coverslip, held for an additional 2 min, and cooled to room temperature by contact with an aluminum block. The resulting NIF glass film was 12−15 μm thick. Given the photosensitivity of NIF, the samples were always shielded from light. For crystal growth at 30 °C, the samples resided in a desiccator placed in an incubator (Isotemp Incubator Model 146E, Fisher Scientific) with temperature stability better than ±0.1°. Crystal growth at 80 ± 0.1 °C was monitored on a Linkam THMS 600 hot stage. Crystal growth was observed with an Olympus BH2UMA polarized light microscope. Bulk crystal growth was measured with a sample sandwiched between two microscope coverslips. For growth at 30 °C, we tracked crystals growing from seeds previously formed by storage at 60 °C. There was no difference between growth rates observed at 30 °C of crystals spontaneously nucleated at 30 °C and previously formed at 60 °C. The procedure of forming crystals first at 60 °C saved time, especially with slowcrystallizing samples, and ensured observation of crystal growth in a freshly made glass. Bulk crystal growth at 30 °C yielded spherulites and the advancing velocity of the growth front was measured. Each reported growth rate was the average value for two or three independently prepared samples in each of which two or three crystal patches were tracked. To observe crystal growth at a free surface, one of two coverslips that confined an NIF glass film was removed by gently bending the assembly. The sample was allowed to crystallize partially at 40 °C and

Figure 1. Molecular structures referred to in this paper. NIF: nifedipine. FEL: felodipine. IMC: indomethacin.

Table 1. Polymers Used in This Worka substance

Mw, kg/mol

Tg (°C)

NIF PEO 8k PEO 100k PEO 8000k PVAc 15k PVAc 83k PS 1.8k PS 8.4k PS 17k HPMCAS-MF PVPVA 64 PVP K12 PVP K15 PVP K30 PVP K90

0.346 8 100 (Mv) 8000 (Mv) 15 83 1.78 8.4 16.6 18 45−70 2−3 8 44−54 1000−2000

42 −19 −47 −53 30 36 53 91 93 114 102 102 120 164 176

a Molecular weights are from the suppliers. Tgs are our DSC data and from ref 30 (for PEO). Tg values from this work are onset temperatures on second heating. Reference 31 gives Tg = −62 °C for a PEO with Mw = 118 kg/mol and Mw/Mn = 1.18.

copolymer (PVP/VA), hydroxypropyl methylcellulose acetate succinate (HPMCAS), polystyrene (PS), and polyethylene oxide (PEO). Most are useful in pharmaceutical formulations. These polymers have different abilities to hydrogen bond with NIF, enabling a study of the suspected role of this interaction in crystallization inhibition.22,23 The polymers differ substantially in Tg30,31 and provide an opportunity to test the effect of segmental mobility on crystal growth. The trio PVP, PVP/VA, and PVAc have related structures (two homopolymers and their copolymer) with different strengths of interaction with NIF,32 and may be especially useful for identifying polymer properties correlated with inhibitory performance. We report that at a low concentration of 1 wt %, polymer additives have strong and different effects on the rate of crystal growth in NIF glasses, from a 10-fold reduction to a 30% increase at 12 °C below the host Tg. Among the polymers tested, all but PEO are growth inhibitors. The inhibitory effect greatly diminishes in the liquid state (at Tg + 38 °C), but PEO persists to be a growth promoter. We found that the ability to 10335

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transferred to 30 °C to observe further crystal growth. This procedure was used again to save time and to measure the growth from seed crystals in a freshly made glass. Differential scanning calorimetry (DSC) was performed with a TA Instruments DSC Q2000. A total of 4−6 mg of material was loaded in a crimped aluminum pan and scanned at 10 °C/ min. Polymorph identification was made by X-ray powder diffraction using a Bruker D8 Advance diffractometer, and by Raman microscopy (Thermo DXR equipped with a 780 nm laser).

Another test for miscibility relied on the Tg of the NIF− polymer mixtures, where miscibility is signaled by a single Tg and its variation with concentration. Although none of the polymers tested changes the Tg of NIF significantly at 1 wt %, increasing its concentration leads to observable effects. By this test, NIF is found miscible with PVP, PVP/VA, and PVAc at any ratio,32 and with PEO and HPMCAS at 1 wt % or higher. The test was inconclusive, however, for the pair NIF-PS and we base its miscibility on the Tm test only. In summary, all our observations are consistent with the miscibility of NIF and 1 wt % polymer. At present, there is no data on the solvent quality for the polymers dissolved in NIF and their radii of gyration. Many polymers used in this work had relatively broad distributions of molecular weights as supplied. It is therefore difficult to precisely evaluate the critical concentration c* above which polymer chains overlap. Nevertheless, judging from the literature data on common polymers in other solvents,34 our concentration of 1 wt % is likely below c* for all polymers below ca. 1000 kg/mol in molecular weight. Effect of Polymer Dopants on Bulk Crystal Growth in NIF Glasses. Table 2 shows the effect of 1 wt % polymer on

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RESULTS State of Mixing between NIF and Polymer Dopants. To understand the effect of polymer additives on crystal growth, it is relevant to learn whether the polymer is miscible with NIF at the concentration used (1 wt %). We observed that (1) polymer-doped liquid NIF is optically clear, showing no evidence of heterogeneity, and (2) crystal growth rate is altered by the polymer additive and the effect is spatially uniform and varies smoothly with concentration. These observations suggest a uniform dispersion of polymer chains in liquid NIF. A further test of the polymer-host miscibility examined the polymer’s effect on the melting point, Tm, of NIF crystals. We observed that (1) the polymer depresses the Tm and (2) the Tm depression increases upon increasing the polymer concentration from 1 to 10 wt %. Figure 2 shows the typical DSC data

Table 2. Growth Rates of NIF Crystals in the Presence of 1 wt % Polymera polymer (1 wt %) pure NIF PEO 8k PEO 100k PEO 8000k PVAc 15k PVAc 83k PS 1.8k PS 8k PS 17k HPMCAS-MF PVPVA 64 VP dimer PVP K12 PVP K15 PVP K30 PVP K90

Figure 2. Melting endotherms of NIF crystals measured at a slow rate of 0.2 °C/min in the presence of 1 and 10 wt % PEO. The melting point decreases with the polymer concentration, indicating the two components are fully miscible at 1 wt % (concentration of our crystal growth measurements).

log ub (m/s) 30 °C

log ub (m/s) 80 °C

log us (m/s) 30 °C

−9.44 −9.29 −9.36 −9.39 −9.89 −9.94 −9.94 −10.06 −10.19 −10.12 −10.35 −9.64 −10.30 −10.42 −10.61 −10.34

−6.78 −6.38 −6.40 −6.26 −6.93 −6.84 −7.11 −7.09 −7.19 −6.82 −6.93 −6.92 −7.00 −6.85 −6.96 −6.84

−8.46 −8.39 −8.42 −8.46 −8.58 −8.65 −8.55 −8.81 −8.88 −8.78 −8.78 −8.55 −8.86 −8.88 −8.72 −8.64

(0.11) (0.05) (0.05) (0.09) (0.02) (0.09) (0.07) (0.07) (0.02) (0.06) (0.16) (0.06) (0.09) (0.06) (0.15) (0.06)

(0.08) (0.09) (0.07) (0.09) (0.16) (0.07) (0.07) (0.05) (0.02) (0.07) (0.04) (0.04) (0.12) (0.09) (0.15) (0.10)

(0.03) (0.04) (0.02) (0.08) (0.08) (0.04) (0.09) (0.04) (0.08) (0.04) (0.05) (0.06) (0.02) (0.09) (0.04) (0.08)

a

ub: bulk crystal growth rate. us: surface crystal growth rate. Standard deviations are in parentheses.

the rate of bulk crystal growth, ub, in an NIF glass at 30 °C (Tg − 12 °C) and, for comparison, in an NIF liquid at 80 °C (Tg + 38 °C). Figure 3 shows the morphologies of the crystals grown under these conditions. The crystals were polycrystalline spherulites, whose texture became finer with cooling; they were identified by Raman microscopy and X-ray diffraction to be the β polymorph.35 The grain size of crystals grown from glasses is estimated to be 102−103 nm, a conclusion reached from the inability to resolve them by light microscopy and the lack of significant broadening of X-ray diffraction peaks. The presence of 1 wt % polymer did not significantly change the crystal morphology. It is noteworthy that at 30 °C, NIF crystals grow in the so-called “glass-to-crystal” or GC mode,6,7,21 which emerges as an organic liquid is cooled near Tg and is characterized by crystal growth orders of magnitude faster relative to diffusion or structural relaxation in the liquid state.

on which this conclusion is based, for PEO. According to thermodynamic principles, Result (1) indicates that the polymer is fully or partially soluble in NIF at the concentration tested, and result (2) rules out the possibility that at 1 wt % polymer, the components are only partially miscible, for if so, increasing the concentration to 10 wt % should not further increase the Tm depression. The results of the Tm test thus support the NIF-polymer miscibility at 1 wt % polymer. Although the focus here is the miscibility at 1 wt % (the concentration of our crystallization studies), miscibility likely exists at much higher polymer concentrations. For PVP, PVP/ VA, or PVAc, the depression of the NIF Tm continues with increasing polymer concentration to at least 70 wt %.32,33 10336

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Figure 3. Morphologies of crystals grown in amorphous NIF. The linear velocity of the advancing growth front was measured (arrows).

Table 2 (column 2) shows the effect of 1 wt % polymer on the rate of crystal growth in the bulk of an NIF glass at 30 °C. It is noteworthy that the polymer dopants do not cause the growth rate to be time dependent, as might be expected for crystal growth in a two-component system. At 1 wt %, PVP and PVP/VA slow the growth by 1 order of magnitude, while the other polymers are less effective, their performance decreasing in the order HPMCAS, PS, and PVAc. PEO is exceptional in that it accelerates crystal growth, in agreement with Miyazaki et al.,36 who report faster crystal growth in NIF glasses containing 5 wt % PEO (300 g/mol) at room temperature. With the limited data collected, the polymer effect on crystal growth is insensitive to molecular weight, and Figure 4 compares the inhibitory performance of polymers in which the data for different molecular weights are averaged. Table 2 and Figure 4 show that, on going from 30 to 80 °C, the effect of 1 wt % polymer on crystal growth generally vanishes, with the exception of PEO. In Figure 5, we highlight the weakening of polymer effect upon heating for PVP, a good growth inhibitor at 30 °C. With increasing PVP concentration, crystal growth at 30 °C slows more quickly than at 80 °C. At the range of concentration studied, log ub decreases linearly with polymer concentration, validating the exponential law ub = ub0 exp(−kw), where ub0 is the growth rate in pure NIF, w is the weight fraction of polymer, and k is an efficiency index for the polymer. For PVP-doped NIF, k = 204 and 47 for T = 30 and 80 °C, respectively. The exponential dependence of ub on w has also been observed for PVP-doped Felodipine (FEL),22 and Figure 5 includes the data at 80 °C on that system, for which the exponential law holds up to at least 4.5 wt %, with a k value similar to that for PVP-NIF. FEL has a similar structure as NIF (Figure 1), and similar Tg (43 °C) and crystal melting points. It is not surprising that PVP similarly influences crystal growth in the two liquids. Note in Figure 5 the smooth decrease of crystal growth rates with polymer concentration, which is consistent with the miscibility of the polymer with host molecules in this range of concentration. The exponential law ub = ub0 exp(−kw) recalls the concentration dependence for the polymer modification of solvent mobility. Lodge and co-workers have observed that “the addition of polymer modifies the mean rotational relaxation

Figure 4. Effects of 1 wt % polymer on NIF bulk crystal growth at 80 °C (Tg + 38 °C) and 30 °C (Tg − 12 °C). For each growth rate, the top half of the error bar is shown. Note the different units for crystal growth rates (μm/s and nm/s).

Figure 5. Exponential dependence of bulk crystal growth rate ub in amorphous NIF on PVP concentration at 30 °C (Tg − 12 °C)21 and 80 °C (Tg + 38 °C). The PVP grade is K15. For comparison, the data on FEL at 80 °C (Tg + 37 °C) are also shown, for which the PVP used is K29/32.22

time of the solvent molecules, following an approximately exponential dependence on polymer concentration”,25 τ = τ0 exp(−Ac), where τ0 is the relaxation time of the pure solvent, c is the polymer concentration, and A is an efficiency index for the polymer. The similar concentration dependence might suggest similar polymer-host interactions underlying the two phenomena. In this comparison, note that the polymer effect on crystal growth rate can be much larger than that on solvent mobility; for example, k = 204 for the inhibition of NIF crystal growth by PVP and |A| < 10 for the modification of Aroclor mobility by polymers.25 Concerning the ranking of the polymer effects on crystal growth at 30 °C (Figure 4), Kestur and Taylor reported a 10337

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similar order for a smaller number of polymers doped in liquid FEL.23 Working in the liquid state (70−110 °C) and with a higher polymer concentration of 3 wt %, they observed that the inhibitory effects of polymers on crystal growth follow the order: PVP (most retarding) > PVP/VA > HPMCAS > PVAc (least retarding). In addition to the qualitative agreement, several points are worth noting. First, our working at a lower temperature (in the glassy state) is perhaps responsible for the ability to distinguish the effects of different polymers at a lower concentration (1 wt %). Second, Kestur and Taylor prepared polymer−FEL mixtures differently: they prepared a 10 wt % polymer mixture by evaporating a solution and diluted it with crystalline FEL in a cryo-mill, whereas in our procedure both steps were performed solvent-free in a cryo-mill. The similar polymer effects observed in the two studies argue that the two methods achieved similar uniformity of mixing. It is remarkable that PEO accelerates crystal growth in amorphous NIF at both 30 and 80 °C, while the other polymers have the opposite or no effect. To understand this finding, we tested the effect of PEO on a similar liquid, indomethacin (IMC, Figure 1). IMC has similar Tg and crystal melting points as NIF, and its crystal growth from supercooled liquids has been studied.37 With IMC, we observed a similar accelerating effect of PEO on crystal growth; in the presence of 1 wt % PEO 8k and at 80 °C, the growth of the α and γ polymorphs is approximately 3 times faster. While this result suggests the generality of the PEO effect, further work is needed to test it fully. To understand the growth-promoting effect of PEO, we ruled out its connection with PEO’s ability to crystallize. The melting point of PEO crystals is below 80 °C, and yet at this temperature it accelerates the crystal growth of host molecules. To test PEO’s ability to crystallize at 30 °C, we annealed an NIF glass containing 1 wt % PEO 1000k for 4 days and analyzed the sample by DSC for PEO crystals, conditions under which their melting endotherms would be visible. No such evidence was detected, however. In this context, it is noteworthy that should PEO crystallize, liquid NIF would become purer, and its crystal growth rate should approach that in pure NIF, not faster. As discussed later, we speculate that the PEO effect results from its high mobility. Effects of Polymer Dopants on Surface Crystal Growth of NIF Glasses. NIF glasses can grow crystals faster at the free surface than in the interior,10 a phenomenon also known for other organic glasses.8,9,11 While this work concerned mainly with bulk crystal growth in the presence of polymer dopants, we also examined the faster surface process. The last column in Table 2 gives the rates of crystal growth at the surface us at 30 °C (faster surface growth is not observed at 80 °C). As reported previously, the rate of surface crystal growth at 30 °C slows slightly over time,24 and the rates reported are for approximately the first day. These data show that the polymer dopants have a significantly weaker effect on us than on ub. This conclusion was already drawn for PVP dopants24 but is now substantiated with additional polymers. The plot of log us vs log ub (Figure 6) shows that all data points are above the line us = ub, meaning crystal growth is faster at the surface than in the bulk. Figure 6 also shows that us and ub are correlated, with a 10-fold change in ub being associated with a 2-fold change in us. The relation is approximately described by the power law us ∝ ub0.35, which holds for two decades of change in ub. This finding is relevant for evaluating the various explanations for the weaker effect of

Figure 6. Correlation between surface and bulk crystal growth rates (us and ub) of NIF glasses doped with polymers. For comparison, data points are also shown for pure NIF (open circle), NIF containing 1 wt % VP dimer (open square), and NIF containing PVP K15 at 0.5 and 2 wt %.24 The power law us ∝ ub0.35 approximately describes the correlation between us and ub.

polymer dopants on surface crystal growth than on bulk crystal growth.24 For example, one explanation attributes the effect to the surface depletion of polymer molecules. This explanation seems implausible because the different polymers used in this study are unlikely to share the same tendency of surface enrichment or depletion.

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DISCUSSION The key finding of this work is that low-concentration polymers can substantially influence crystal growth in organic glasses. At 30 °C (Tg − 12 °C) and 1 wt % polymer, PVP and PVP/VA can slow bulk crystal growth in nifedipine 10-fold, while the other polymers are less effective, with their effectiveness decreasing in the order HPMCAS ≥ PS ≥ PVAc (Figure 4). The inhibitory effect of 1 wt % polymers greatly diminishes in the liquid state (at 80 °C or Tg + 38 °C). Of the polymers tested, PEO is exceptional in that it accelerates growth at both 30 and 80 °C. We now use these results to assess which polymer property is connected with its ability to inhibit crystal growth. We first consider the proposal that a polymer’s ability to inhibit crystal growth is controlled by its ability to hydrogen bond with host molecules.23 In forming hydrogen bonds, NIF is a donor and acceptor. Among the polymers tested, PVP, PVP/ VA, PVAc, and PEO are acceptors, HPMCAS both acceptor and donor, and PS is neither. Setting HPMCAS aside, the strength of polymer−NIF hydrogen bonding is expected to follow the order:23 PVP (strong) > PVP/VA > PVAc ∼ PEO > PS (none). This order agrees with the ranking proposed for polymers interacting with FEL, which has similar hydrogenbonding groups as NIF (Figure 1).23,38 On the basis of hydrogen bonding, the effectiveness of polymers as crystal growth inhibiters of NIF should be PVP (most effective) > PVP/VA > HPMCAS ≥ PVAc ∼ PEO > PS (least effective). This prediction agrees to some extent with experiment (e.g., PVP > PVAc), but major discrepancies are obvious. For example, PS forms no hydrogen bond with NIF, but has an inhibiting effect between those of PVAc and HPMCAS, which 10338

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do hydrogen bond with NIF; PEO can hydrogen bond with NIF, but accelerates crystal growth; PVP forms stronger hydrogen bonds with NIF than PVP/VA, but the two polymers have comparable inhibitory performance. For this system, hydrogen bonding does not accurately rank the effectiveness of crystal growth inhibitors. For the polymers tested in this work, there is a significant correlation between the polymer’s Tg and its ability to inhibit crystal growth in NIF glasses. As Figure 7 shows, the growth

Figure 7. Bulk growth rate of NIF crystals at 30 °C (Tg − 12 °C) and 80 °C (Tg + 38 °C) in the presence of 1 wt % polymer vs the Tg of the neat polymer. Circled points are for pure NIF.

rate of NIF crystals at 30 °C in the presence of 1 wt % polymer generally decreases with the increase of the polymer Tg in the neat state (R2 = 0.89 for linear correlation). This trend largely vanishes at 80 °C, except for the persistent effect of PEO. Why is a polymer’s Tg linked to its ability to inhibit crystal growth? One answer is that the mobility of polymer chains influences the process of crystal growth in the host matrix. A low-Tg polymer is expected to have high segmental mobility, and a high-Tg polymer should have low mobility. In dilute solutions, the mobility of polymer chains is altered by solvent molecules, but retains some “memory” of its neat state.39−41 One explanation for this effect is the connectivity and “selfconcentration” of polymer segments.39 We sketch this effect for our system in Figure 8 on the basis of literature data. Figure 8a shows the structural relaxation time τα of liquid NIF42,43 and IMC.44,45 The two liquids have similar molecular structures and nearly identical dynamics. We have extended the τα of IMC to higher temperatures with the aid of viscosity data,46 assuming τα ∝ η. Figure 8a also shows the dynamics of two dilute polymer solutes, PS and PEO, to illustrate the situations in which polymer chains are less and more mobile than the host molecules. For PEO, we use the NMR data on 1 wt % PEO in IMC (determined to 67 °C and extrapolated to 40 °C),41 and assume the dynamics of dilute PEO in NIF is the same as in IMC. For PS, we begin with the τα of pure PS47 and correct it for the solvation effect using the self-concentration model.39 For this purpose, we calculate the effective Tg of dilute PS in the NIF host:40 1/Tg,eff = ϕself /Tg,PS + (1 − ϕself)/Tg,NIF, where Tg,PS is the Tg of pure PS (373 K), Tg,NIF is the Tg of pure NIF (315 K), and ϕself = 0.35 is a typical value for the selfconcentration of dilute PS in many hosts. The resulting value,

Figure 8. (a) Mobility of liquid NIF and IMC and dilute polymers solutes. (b) Mobility of dilute polymers relative to host molecules.

Tg,eff = 333 K, is used to shift the τα of pure PS to obtain the τα of dilute PS in NIF, a procedure known to reproduce the observed dynamics of dilute PS in many hosts.40 Figure 8b shows the ratio τpoly/τsolvent, where poly = PS or PEO and solvent = NIF or IMC, as a function of temperature. Figure 8 shows that the lower-Tg PEO is more mobile than the host molecules, whereas the higher-Tg PS less mobile. Furthermore, with cooling, PEO becomes even more mobile relative to the host molecules, and PS, even less mobile. Understanding the effect of polymer additives on crystal growth requires knowing the movements of host and polymer molecules during the process. This information, unfortunately, is limited. Crystallization can reject impurities, but it is unlikely that polymer molecules are pushed forward by the growing polycrystalline spherulite over long distances, because the enrichment of polymer molecules would alter the linear growth rate, in conflict with our observation of nearly constant growth rates over hundreds of micrometers. A more likely scenario involves local adjustments of host and polymer molecules to allow the development of coherent crystalline domains that comprise the spherulite. Entrapment of polymer chains in crystal lattices is also possible.48 The mobility of polymer chains could affect the rate of crystal growth if (1) the chains must move out of the way for solvent molecules to crystallize and (2) the chains slow down or speed up neighboring solvent molecules and their rate to join the growing crystals. At 1 wt 10339

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be informative to systematically vary its molecular weights, from oligomers to polymers, to learn the relative importance of polymer−host interactions and chain mobility. Also valuable would be the use of small-molecule additives as modifiers of crystal growth, with which the control of purity and functional groups is more straightforward than for polymers. The role of polymer segmental mobility in crystallization inhibition can be tested by molecular simulations and with the aid of directly measured mobility data for organic glasses and better knowledge on the displacement of polymer chains during the crystallization of host molecules.

% polymer, the average mobility of host molecules does not change significantly as indicated by no measurable change in the Tg and in agreement with the literature data on other polymer−solvent systems.25,29 Nevertheless, a fraction of host molecules are in contact with the polymer chains and their mobility could be modified as a result; in this process, strong polymer−host interactions would enforce the dynamic coupling of solvent and solute molecules. In the polymer modification of solvent mobility, the effectiveness of a polymer has been observed to depend on the dif ference between the mobility of polymer and host molecules.49 If the same holds for our system, the greater polymer effect on NIF crystal growth at 30 °C than at 80 °C (Figure 4) could reflect the greater difference between τpoly and τsolvent at 30 °C. The ability of PEO to accelerate crystal growth at both 80 and 30 °C might result from its high mobility relative to host molecules at both temperatures. In this context, it is noteworthy that a polymer’s effects on solvent dynamics and crystal growth both depend exponentially on its concentration (ref 25 and Figure 5). Further work is needed to test these ideas with the aid of directly measured mobility data for relevant organic glasses and better knowledge of the displacement of polymer chains in order to accommodate crystal growth. A connection between the mobility of polymer chains and their ability to inhibit the crystallization is consistent with the very different inhibitory performance of the dimer and the polymers of vinyl pyrrolidone for crystal growth in NIF glasses.24 Here, the polymers can effectively inhibit crystal growth, but the dimer has virtually no effect. While the dimer and the polymer have the same ability to hydrogen bond with NIF, the polymer chains have much lower mobility than the dimer molecules (their Tgs differ by 160−240 °C). Thus, the dimer molecules are expected to reorganize more rapidly than the polymer chains to accommodate the growing crystal and to increase the mobility of neighboring molecules as they join the crystal. We also note that the two factors considered that may influence inhibitory performance, direct polymer−host interactions and the polymer’s segmental mobility, need not be in conflict and could work synergistically. It is possible that effective inhibitors of crystal growth optimize both factors.

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AUTHOR INFORMATION

Corresponding Author

*(L.Y.) E-mail: [email protected]. Phone: (608) 263 2263. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Abbott Laboratories and the NSF (DMR-1234320) for supporting this work and M. D. Ediger for helpful discussions. C.T.P. thanks the NSF for a graduate research fellowship.

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REFERENCES

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CONCLUSION Doping the organic glass nifedipine (NIF) with 1 wt % polymer has substantially different effects on the rate of crystal growth, from 10-fold reduction to 30% increase. Polyethylene oxide (PEO) is exceptional in that it speeds crystal growth. The inhibitory effects of polymer dopants largely vanish in the liquid state (at Tg + 38 °C), but PEO persists as growth promoter. A polymer’s ability to inhibit crystal growth is not accurately ordered by its hydrogen bonding with NIF, but correlates remarkably well with the Tg of the neat polymer. The result argues that the mobility of polymer chains plays an important role in inhibiting crystal growth. This work also measured the faster crystal growth at the free surface of NIF glasses. The latter is similarly affected as the bulk process, but to a smaller extent according to the power law us ∝ ub0.35, where us and ub are the surface and bulk growth rates, respectively. These findings are relevant for the selection of polymer additives to stabilize organic glasses against crystallization and for understanding the mechanism by which polymers inhibit crystallization. In future studies, it would be valuable to test the generality of our finding with other systems. For a given polymer, it would 10340

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