Factors Influencing Crystal Growth Rates from Undercooled Liquids of

Article pubs.acs.org/JPCB

Factors Influencing Crystal Growth Rates from Undercooled Liquids of Pharmaceutical Compounds Niraj S. Trasi, Jared A. Baird,† Umesh S. Kestur,‡ and Lynne S. Taylor* Department of Industrial and Physical Pharmacy, Purdue University, 575 Stadium Mall Drive, West Lafayette, Indiana 47907, United States ABSTRACT: Amorphous forms of drugs are increasingly being used to deliver poorly water-soluble compounds. Therefore, understanding the magnitude and origin of differences in crystallization kinetics is highly important. The goal of this study was to better understand the factors that influence crystal growth rates from pharmaceutically relevant undercooled liquids and to evaluate the range of growth rates observed. The crystal growth rates of 31 drugs were determined using an optical microscope in the temperature region between the glass transition temperature (Tg) and the melting temperature (Tm). Thermodynamic parameters such as Tm, melting enthalpy, and Tg were determined using a differential scanning calorimeter (DSC). Selected viscosity values for the undercooled liquid were taken from the literature. The growth rates of the different compounds were found to be very different from each other with a variation of about 5 orders of magnitude between the fastest growing compounds and the slowest growing compounds. A comparison of the physicochemical properties showed that compounds that had fast crystal growth rates had smaller molecular weights, higher melting temperatures, lower melt entropies, lower melt viscosities, and higher crystal densities. Variations in the growth rates of the compounds could be rationalized to a large extent by considering the thermodynamic driving force for crystallization, the viscosity, and the entropy difference between the melt and undercooled liquid. This study therefore provides important insight into factors that may compromise the stability of amorphous pharmaceuticals.

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INTRODUCTION Low molecular weight organic glasses are important for a number of diverse areas of technology including drug delivery, biomolecule preservation, and electronics. It is thus important to understand the molecular and thermodynamic factors that impact the rate of phase transformation to the lower energy crystalline state. In the context of using glasses for delivery of poorly water-soluble drugs, the molecular structure is determined by the therapeutic activity, and cannot be changed to enhance glass forming ability per se. Therefore, it is important to establish the range of glass stability for drug-like organic compounds in order to establish when the glass is a feasible drug delivery strategy. The underlying reason for the current interest in the formulation of noncrystalline drug forms stems from a dramatic increase in the number of newly discovered drug candidates that have extremely low aqueous solubility. It has been demonstrated for several molecules that the therapeutic impact of the drug can be improved by delivering an amorphous form of the drug.1,2 In order to utilize an amorphous drug delivery strategy, it is essential that the glassy form of the drug is maintained for the lifetime of the product, which is typically in the range of 2−3 years. Since it is not feasible to wait for this length of time to determine if crystallization will occur or at least not for every candidate drug, it is essential to develop a fundamental understanding of crystallization tendency. This © 2014 American Chemical Society

will enable discrimination of compounds that are at higher risk of crystallization from those which can be successful delivered in the glassy form. In a recent study, the crystallization tendency of approximately 50 organic compounds (mostly pharmaceuticals) was studied by evaluating the glass forming ability (GFA) and glass stability (GS) of the compounds during melt quenching and subsequent reheating.3 Dramatic differences in crystallization tendency were observed leading to the classification of the various compounds into three groups based on whether they crystallized during the cooling stage (class I, rapid crystallizers, poor GFA), crystallized during the reheating stage (class II, intermediate crystallizers, good GFA but poor GS), or showed no crystallization during either cooling or reheating (class III, slow crystallizers, good GFA and GS). This experimental method represents a simple and rapid way to evaluate the inherent crystallization tendency of a compound and its potential to be formulated as a glass. The crystallization behavior observed during melt quenching and subsequent reheating depends on the experimental conditions (cooling, heating rate) as well as the temperature dependence and rates of the crystal nucleation and growth processes, both of which Received: May 6, 2014 Revised: July 28, 2014 Published: July 30, 2014 9974

dx.doi.org/10.1021/jp504450h | J. Phys. Chem. B 2014, 118, 9974−9982

The Journal of Physical Chemistry B

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The goals of the current study were threefold. First, to evaluate the range in crystal growth rates for a group of pharmaceutically relevant compounds, second, to evaluate how well the observed growth rates correlate with various molecular, thermodynamic, and kinetic properties of the compounds, and third, to determine the extent to which the growth rate can be modified through the addition of a polymer for compounds with a range of growth rates. To achieve these goals, the growth rates of a group of 31 pharmaceutically relevant compounds were studied as a function of temperature. The majority of these compounds have previously been evaluated in terms of their GFA and GS upon cooling from the undercooled melt state.3 The impact of molecularly dispersed polyvinylpyrrolidone (PVP) on the growth rates of a subset of these compounds was also determined.

are complex in nature. Both crystal growth and nucleation processes show a bell-shaped dependence with temperature, with the maximum in the growth rate occurring at a higher temperature than the maximum in the nucleation rate.4 Thus, rapidly crystallizing compounds have significant growth velocities in a temperature region where nucleation is thermodynamically and kinetically favorable, leading to crystallization. In contrast, compounds which are good glass formers but readily crystallize upon reheating are thought to form nuclei during cooling in a temperature region where the crystal growth is slower, and hence only crystallize during heating when a favorable temperature zone for growth is encountered. For compounds that do not crystallize during cooling and heating, more than one explanation is possible. The nucleation and growth rates could be both inherently low, or the compounds could have a rapid growth rate but a low nucleation rate. Simple cooling and heating studies of crystallization tendency thus do not necessarily provide fundamental insights into the key phenomena controlling devitrification. Amorphous solids are normally kinetically stabilized against crystallization by the addition of polymers which are thought to impact the molecular mobility of the drug, in particular if specific drug−polymer interactions are formed.5,6 One requirement is that the polymer has to be miscible with the drug to exhibit the stabilizing effect. Also, the amount of polymer needed to stabilize the amorphous solid for a certain period of time (e.g., to have a shelf life of 2 years) will depend on the inherent crystallization tendency of the drug itself. A compound that has a rapid crystallization rate will require more polymer to prevent its crystallization during a given experiment than a compound that has a slower crystallization rate. Again, in this case, it is important to determine if the effect is due to inhibition of nucleation during the experiment or whether it was due to a decrease in crystal growth rate. In one study investigating the effect of polymers on acetaminophen (APAP) crystallization, it was observed that the cellulose derivative, hydroxypropyl methyl cellulose acetate succinate (HPMCAS), inhibited nucleation significantly while having little effect on crystal growth, while poly(acrylic acid) (PAA) increased the nucleation rate but substantially delayed the crystal growth rates.7 Both polymers at 15% w/w converted APAP from a compound with inherently good GFA but poor GS (class II) to a system whereby APAP exhibited good GFA and GS (class III) based on the classification system described above. Thus, it is important to independently study the two phenomena of nucleation and growth, and to understand the key parameters impacting these rate processes. Nucleation is the first step in crystallization, since growth only occurs from nuclei. However, it is a difficult phenomenon to study, since nuclei are too small to be studied directly. Crystal growth of organic compounds, on the other hand, has been more extensively studied.8−16 In one study of a number of organic compounds, it was proposed that the maximum crystal-growth velocity (MCV) showed a simple dependence on the sum of the enthalpies of all phase transitions between the glass transition temperature and the melting point and the number of atoms (excluding hydrogens) in the molecule. In other words, the authors proposed that the maximum rate of crystal growth depended on simple molecular and thermodynamic properties.17 For the group of compounds studied, the MCV varied by about 5 decades.

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EXPERIMENTAL METHODS Materials. D-Salicin, carbamazepine, cinnarizine, dibucaine, griseofulvin, piroxicam, flurbiprofen, tolazamide, acetaminophen, flutamide, nilutamide, ketoprofen, probucol, pimozide, clotrimazole, nimesulide, warfarin, droperidol, and nimesulide were purchased from Sigma-Aldrich (Missouri, USA). Indomethacin was purchased from Hawkins Inc. (Minnesota, USA). Tolbutamide, miconazole, and bifonazole were obtained from Spectrum Chemicals (New Jersey, USA). Celecoxib, aceclofenac, loratadine, carvedilol, efavirenz, mevastatin, and felodipine were purchased from Attix Pharmaceuticals (Ontario, Canada). Clozapine was purchased from Euroasia Chemicals Pvt. Ltd. (Mumbai, India). Poly(vinylpyrrolidone) K-12 (PVP, Mw 2−3000 g/mol) was obtained from BASF Chemicals (New Jersey, USA). Determination of Crystal Growth. Determination of isothermal growth rates was performed by hot stage microscopy. A 3−5 mg portion of the powder was placed between two coverslips and heated to above the melting point of the compound and subsequently quenched to room temperature by placing the sample on an aluminum block. The samples were seeded with the starting crystalline material at the edge and heated to ensure sufficient growth had occurred into the bulk. Seeding of crystals was performed for bulk crystal growth rate measurements in order to monitor the growth of the polymorph of interest. The samples were then examined using a polarizing microscope (Nikon Eclipse E600 POL microscope, Nikon Corp, Tokyo, Japan). The temperature of the sample was controlled by a hot stage (Linkam THMS 600, Surrey, U.K.), and pictures of the growth front were taken at regular intervals using time lapse photography. The increase in the growth front was plotted against time, and the slope represented the growth rate. The growth rates were determined for each sample in a temperature range of 30−90 °C above the compound’s glass transition temperature. Growth rate determination at lower temperatures was possible for compounds with slightly faster growth rates. To measure surface growth, the same procedure was followed, but the top coverslip was removed. Surface growth rates can be determined only at temperatures close to Tg, and in many cases, the crystal growth front was quite irregular. For these compounds, an equivalent radius was calculated by measuring the total area crystallized using ImageJ software (v 1.45, National Institute of Health, Bethesda, MD) as described in a previous publication.18 Crystal growth rate determinations for drug and polymer mixtures were performed by first preparing powder mixtures of selected drug compounds and 10 molar percent of PVP. The 9975



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Figure 1. Growth rates of the various compounds plotted after (a) normalizing to the glass transition temperature (Tg) and (b) normalizing to the melting temperature (Tm). Growth rates of the different compounds are color coded on the basis of whether they are class I and II (red symbols) or class III (blue symbols). Classification is based on the crystallization behavior during cooling of the melt and subsequent heating using the method described previously.3

Figure 2. (a) Surface growth rates of selected compounds normalized to Tg. (b) Bulk growth rates of the same compounds. It can be seen that the order of growth rates changes between surface and bulk crystal growth rates.

the normalization based on the extent of undercooling. It can be seen that when normalized to Tg the growth rates of the fastest and slowest growing compounds vary by about 4 orders of magnitude, while the variation is about 5 orders of magnitude difference when normalized with respect to ΔT. It can also be observed that the relative order of the compounds changes when normalized to different temperature scales. For example, when normalized to Tg, the compound with the fastest crystal growth rate is griseofulvin, closely followed by nilutamide, celecoxib, and tolbutamide, while using the undercooling yields acetaminophen and pimozide as the fasted growing compounds. Surface Growth Rate. The crystal growth at the surface has been shown to be generally faster than that from the bulk, in particular at lower temperatures where the material does not flow.13 The faster surface growth rate is thought to be due to the higher molecular mobility at the surface at temperatures below or close to Tg.19 However, the relationship between surface and bulk growth rates has not been widely explored. In other words, if a compound has a high bulk growth rate relative to other compounds, will it also have a high surface growth rate relative to the same compounds? To study this, surface crystallization experiments were performed for selected compounds to see if the order of surface growth rates matches that observed in bulk and the data is shown in Figure 2. We note that the order of growth rates does not necessarily match that observed in the bulk. Felodipine, for example, has a surface

mixtures were prepared by cryomilling in a Spex 6750 freezer mill (Spex Sampleprep, Metuchen, NJ, USA) and then allowed to return to room temperature before removing the contents. These samples were then melted between two coverslips and nucleated with the starting crystal form and the growth rate determined as for the pure compounds. Thermal Analysis. Glass transition temperatures, melting temperatures, and enthalpy were evaluated using a TA Instruments Q2000 (New Castle, DE) differential scanning calorimeter (DSC). The instrument was calibrated for temperature using indium and tin and for enthalpy using indium. Dry nitrogen at 50 mL/min was used as the purge gas.

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RESULTS Growth Rate of Compounds. The growth rates of the various compounds are shown in Figure 1. Since the different compounds studied all have different glass transition and melting temperatures, it is necessary to normalize the temperature scale to allow an appropriate comparison of the growth rates. The normalization can be done either with respect to the Tg (normalizing for molecular mobility and assuming that all compounds have the same mobility at Tg) or with respect to the Tm (normalizing for differences in the extent of undercooling which influences the thermodynamic driving force). T/Tg and ΔT, i.e., (Tm − T), were used as the two temperature normalization approaches. Figure 1a shows the data which has been normalized to Tg, while Figure 1b shows 9976



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and heating method described previously.3 Interestingly, several of the compounds which show good glass forming ability and stability (i.e., resistance to devitrification, “class III” compounds) actually had very high crystal growth rates. In fact, the growth rates of the class III compounds span the entire range of growth rates observed and class III compounds had both among the fastest and slowest growth rates for the group of compounds examined. In contrast, those compounds with poor glass stability (class II or I-b compounds whereby class II compounds readily form glasses at moderate cooling rates but class I-b compounds require rapid quenching) had moderate to fast growth rates, tending to populate the upper half of the growth rate plot. From a risk assessment perspective, the data shown in Figure 1 is very revealing, assuming that the relative magnitude of growth rates translates reasonably well to the lower temperatures where products are stored. Hence, class III compounds that have very high growth rates (Figure 1, compounds with blue symbols that populate the upper half of the figure) clearly have good glass forming ability because of a low tendency to form nuclei under the conditions of the experiment. However, it should be noted that, during the processing operations used to make amorphous formulations, residual or process-induced nuclei may be present in the system. In this instance, the system may have a high probability of undergoing crystallization over the shelf life of the product, since the crystal growth rate is relatively high. In contrast, class III compounds with inherently low growth rates (Figure 1, compounds with blue symbols that populate the lower half of the figure) will exhibit much slower crystallization kinetics, even if nuclei are present. Clearly, compounds with poor glass stability (class II and class I-b, compounds with red symbols) are already in the higher risk category with fast growth rates. Therefore, we can generate an extended classification that provides an improved picture of the crystallization tendency of a compound, taking into account both the nucleation and growth behavior. By combining the crystallization behavior in the DSC3 with the growth rate data obtained herein, a revised classification that takes into account both nucleation behavior and growth rate can be proposed. In Figure 4, we depict class I-a

growth rate higher than that of carbamazepine and nilutamide, yet it grows more slowly than nilutamide at all temperatures and carbamazepine at higher temperatures in the bulk. However, the compound with the slowest surface growth, loratadine, also has a slow bulk growth rate, while the faster surface growing compounds, piroxicam and acetaminophen, also have fast bulk growth rates. Extent of Growth Rate Modification by PVP. The impact of adding 10 molar % of the well-known polymeric crystal growth inhibitor, PVP, to undercooled melts of acetaminophen, flutamide, nilutamide, aceclofenac, and indomethacin was evaluated. These compounds have quite different bulk growth rates, but all contain good hydrogen bond donor groups and therefore would be expected to interact similarly with the hydrogen bond acceptor group present in PVP. For all of these mixtures, the increase in Tg compared to the parent compound was around 2−3 °C. The objective of these experiments was to determine if PVP would be a relatively less effective inhibitor for a fast growing compound compared to a slowly growing compound, evaluating systems with a similar potential to hydrogen bond with the polymer. As can be seen from Figure 3,

Figure 3. Crystal growth rates of aceclofenac, acetaminophen (APAP), flutamide, nilutamide, and indomethacin (IMC) in the presence and absence of 10 molar % PVP.

the initial crystal growth rate of a compound did not appear to influence the extent of polymer impact on growth rate reduction, since the polymer reduced growth for all the compounds by around the same extent. This observation suggests that compounds having faster crystal growth rates will require a significantly larger amount of polymer to stabilize their amorphous form than those with a slower growth rate.

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DISCUSSION Crystallization from undercooled melts is governed by two processes, nucleation and growth, whereby the overall crystallization kinetics depends on the magnitude of these two processes and their temperature dependencies. Thus, when a compound can readily form a glass, for example, by cooling from the melt, this could occur from a variety of factors including low nucleation rate, low growth rate, a combination of these factors, or poor overlap between the temperature regions where nucleation and growth are favorable. In an effort to deconvolute some of these effects, the bulk growth rates of the various compounds can be compared to their glass forming ability upon cooling of the melt and the glass stability following reheating. Parts a and b of Figure 1 show a plot of growth rates versus temperature whereby the compounds have been color coded on the basis of their GFA/GS assessed using the cooling

Figure 4. An extended classification system for compounds based on their nucleation and crystal growth rate behavior.

compounds as having high nucleation and growth rates with substantial overlap between nucleation and growth zones and hence a high tendency to crystallize during cooling from the melt. Class I-b compounds also have high nucleation and growth rates, but the overlap between the two zones is minimal. Hence, class I-b compounds have good glass forming ability, but once nuclei are formed, there is a high probability of 9977



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combined effect of these two factors leads to a maximum in the crystal growth rate as a function of temperature, as shown in Figure 5.

crystallization due to rapid growth rates, and these compounds have poor GS. Class II compounds have rapid growth rates but have a lower tendency to form nuclei. Again, they will show good GFA but will show poor GS if nuclei are present. Class III encompasses compounds which readily nucleate but have a slow growth rate, while class IV compounds have both slow nucleation and growth rates. Thus, the highest risk compounds for formulation as amorphous drug delivery systems are class I compounds followed by class II. Class III compounds have an intermediate risk level, while class IV compounds are likely to be the most robust compounds, highly suited for an amorphous formulation. It is of interest to better understand the origin of the diversity in growth rates seen between the various compounds. The three most common models applied to describe the growth of crystals from the melt are (1) normal or continuous growth, (2) screw-dislocation, and (3) two-dimensional or surface nucleation growth.20−22 These models differ in terms of the structure of the growing interface. Thus, the normal growth model assumes that the interface is rough on an atomic/ molecular scale and that there is a high population of equivalent growth sites on the interface. In contrast, the screw-dislocation approach models the interface as smooth with imperfections whereby growth occurs only on steps provided by screwdislocations. The 2-D nucleation model postulates growth by the formation and lateral growth of two-dimensional nuclei at the interface. Regardless of the proposed growth mechanism, all crystal growth models incorporate a term to describe molecular mobility, since molecules need to diffuse across the interface and attach to the growth site, and a term to describe the thermodynamic driving force which determines the probability that the molecules remain attached to the crystal face rather than moving back into the undercooled liquid. Using the model developed by Jackson, the growth rate (U) is given by23 U=

⎛ ΔH ΔT ⎞⎤ ⎛ ΔS ⎞ 2kBT ⎡ f ⎢1 − exp⎜ − ⎟ ⎟⎥ exp⎜ − 2 πλ η ⎢⎣ ⎝ kBTTm ⎠⎥⎦ ⎝ kB ⎠

Figure 5. Schematic showing the effect of the thermodynamic driving force and molecular mobility on the crystal growth rate and the maximum crystal velocity (MCV).

This peak represents the maximum crystal velocity (MCV) for that particular compound, and the temperature at which it is observed is Tcryst,max. Below Tcryst,max, bulk growth is dominated by the viscosity term, while, above Tcryst,max, crystal growth is under thermodynamic control. The MCV thus provides a reference point to compare the various compounds. Table 1 ranks the compounds in terms of their MCV from the highest to lowest values. It can be seen that there are 4 orders of magnitude difference between the MCV of the fastest growing compound (nimesulide) and the slowest (clotrimazole). On the basis of the range of MCV values, it is convenient to divide the compounds into three groups to aid with further analysis. Thus, the fastest growing compounds, group 1, are designated as those compounds having maximum growth rates between 10 and 100 μm/s, the intermediate growing compounds, group 2, have maximum growth rates of 1−10 μm/s, while the slow growing compounds, group 3, have maximum growth rates of 0.01−1 μm/s. Various physicochemical parameters can then be averaged for each group and deviations from the global average evaluated to determine trends between the properties and crystal growth rates. Figure 6 shows the outcome of this analysis. The three groups are color coded as red (fast), green (intermediate), and blue (slow). We can see that properties such as molecular size, melting temperature, melting entropy, free energy difference between the melt and the crystal, Tm − Tg, and viscosity all vary from the global average for the various groups, suggesting that they are important factors contributing to the observed differences in crystal growth rates. Of these various factors, viscosity stands out as the parameter where the different group averages deviate most from the global average whereby group 3 has a much higher than average melt viscosity. The parameter Tm − Tg also varies considerably among the three groups, while crystal density seems to vary greatly between group 1 and 2. Figure 7 provides a more detailed look at the relationship between the melt viscosity and Tm − Tg for compounds where melt viscosity information is available.25 From Figure 7, it is apparent that there is a trend between the melt viscosity and the value, Tm − Tg, although there is considerable scatter in the data, particularly for the higher viscosity values. Thus, for those compounds with a high melt viscosity, the value Tm − Tg is smaller, while, for compounds with a low melt viscosity, the

(1)

where λ is the average diffusion jump distance, η is the viscosity, kB is the Boltzmann constant, ΔS and ΔH are the entropy and enthalpy difference, respectively, between the liquid and the crystal, T is the temperature, Tm is the melting temperature, and f is the fraction of interface sites which are active growth sites. Here it is assumed that the Stokes−Einstein equation holds and that the viscosity is an adequate descriptor for the diffusion coefficient for molecular transport across the crystal− liquid interface. This is a reasonable assumption for the temperature range where growth rates were determined in this study. However, it should be noted that, as the temperature approaches Tg, decoupling of diffusion and viscosity occurs, resulting in a breakdown of the Stokes−Einstein relationship, and the growth rate is no longer proportional to the experimentally determined viscosity.24 In addition, at temperatures close to Tg, the growth mechanism for some crystals changes from being diffusion controlled to a diffusionless mechanism.12 Equation 1 shows that two of the main factors influencing crystal growth rate are the thermodynamic driving force and the viscosity which reflects the molecular mobility. At temperatures close to the melting point, the mobility is very high while the thermodynamic driving force is very low. At lower temperatures, the molecular mobility decreases while the thermodynamic driving force increases, since ΔG ∝ Tm − T. The 9978



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Table 1. Compounds Showing Various Physicochemical Parameters in Descending Order of Their Maximum Crystal Velocity (MCV)a

a

The compounds were separated into three groups based on their MCV (maximum crystal velocity) with growth rates between 10 and 100, 1 and 10, and 0.01 and 1 μm/s being used to delineate groups 1, 2, and 3, respectively.

temperature range between Tm and Tg is higher. Moreover, the more slowly growing compounds (as indicated by the blue color) tend to have a high melt viscosity and low Tm − Tg values, while the converse is true for the more rapidly crystallizing compounds. If it is assumed that the viscosity is a constant value at Tg for all the compounds analyzed, then this indicates that compounds with lower melting points relative to their Tg values will have a lower MCV than compounds with higher melting points relative to the Tg values. This makes sense given the observation that the MCV tends to occur at temperatures around 0.94 Tm;26 thus, compounds that have relatively high viscosities at the melting point and a smaller temperature range to traverse to reach T g will have correspondingly higher viscosities at the temperature of the MCV. The importance of the viscosity at the melting temperature has been highlighted by Angell who studied the glass forming ability of isomers of xylene and found that the lowest melting point isomer had the best GFA.27 The fragility of the compounds also needs to be taken into account. Thus,

there are three compounds with group 2 MCVs (tolazamide, aceclofenac, and bifonazole) that fall among the group 1 compounds, indicating that they have similar melt viscosities. The most likely reason why aceclofenac and bifonazole do not fall into the category of fast growers is that their viscosity increases more dramatically with temperature than for the group 1 compounds, i.e., they appear to be more fragile,25 while tolazamide could be a slower than expected grower due to its complex molecular structure. The importance of viscosity in dictating the magnitude of the observed growth rate was further evaluated by comparing crystal growth rates for several compounds as a function of the viscosity in the form of a log−log plot (Figure 8). The growth rate was first normalized to account for differences in the thermodynamic driving force, yielding the corrected growth rate, Ukin, using eq 2 Ukin = 9979

U (−ΔG / RT )

(1 − e

)

(2)



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Figure 6. Histogram illustrating how the group average of a given physicochemical parameter varies from the global average for compounds in each of the three groups. The compounds were segregated into three different groups based on their growth rates using MCV values (see Table 1).

where U is the experimentally determined growth rate and ΔG (the free energy between the melt and the crystalline state) can be approximated by ΔSmΔT. ΔSm is the entropy difference between the melt and crystalline state at the melting temperature, while ΔT is the extent of undercooling. For a given compound, the growth rate is highly dependent on the viscosity. However, interestingly, the compounds appear to fall into two groups whereby, at a similar viscosity, one set of compounds has growth rates around 2−3 orders of magnitude higher than the other group. Clearly, there are other parameters that contribute to the crystal growth rate of a compound at a certain viscosity and thermodynamic driving force. An additional factor identified by Jackson as being of importance (shown in eq 1) in impacting the growth rate is the entropy difference between the melt and the liquid.23 The molecule needs to have the correct orientation to join the crystal, and only a certain fraction of molecules in the melt (reflected by the entropy difference) will have the correct orientation. To evaluate the importance of the entropy difference between the crystal and the liquid, a plot of the normalized growth rate versus melt entropy (Sm) was constructed for compounds where viscosity data was available.28 This crystal growth rate, Ukin, was normalized for viscosity differences by multiplying Ukin by τα/a, where the structural relaxation time, τα, is given by Cη/G, assuming that C and G are constants with values of 4 and 2, respectively.28 “a” is the molecular diameter and was determined from the molecular structure of the various compounds using the crystal conformation as found from the Cambridge Structural Database (ConQuest version 1.15). A plot of Ukinτα/a versus the configurational entropy is shown in Figure 9, from which it can be seen that the compounds follow the expected trend but with considerable scatter, resulting in a correlation coefficient of 0.61; a similar extent of scatter was observed by Ediger and co-workers when they compared the growth rates of inorganic and organic compounds using this approach.28 These results indicate that entropy certainly plays a role in impacting the crystal growth rate but that there are additional factors that are not accounted

Figure 7. Plot of the melt viscosity versus the parameter Tm − Tg showing a somewhat linear trend whereby the faster growing compounds (red symbols) have lower viscosity and a higher melting point relative to the glass transition temperature. Groups 2 and 3 are colored green and blue, respectively. Bifonazole (*), aceclofenac (**), and tolazamide (***) are group 2 compounds that appear with group 1 compounds.

Figure 8. Crystal growth rate corrected for thermodynamic driving force, plotted against the undercooled melt viscosity in a log−log format for a subset of the compounds.

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growth velocity which occurred at a temperature of approximately 0.94Tm. While differences in melt viscosity (molecular mobility) and configurational entropy could explain much of the observed variation in growth rates, additional factors that have not yet been elucidated clearly play a role. For compounds with a hydrogen bond donor group, a small amount of the polymer, PVP, was found to reduce the growth rate by the same extent irrespective of the growth rate of the pure compounds, indicating that more rapidly growing compounds will require more polymer to form amorphous systems that are resistant to crystallization.

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AUTHOR INFORMATION

Corresponding Author

Figure 9. Crystal growth rates (corrected for thermodynamic driving force and normalized to the structural relaxation time) as a function of melting entropy (ΔSm).

*E-mail: [email protected]. Fax: +1 (765) 494-6545. Phone: +1 (765) 496-6614. Present Addresses †

Oral Drug Products, Manufacturing Science and Technology, AbbVie Inc., 1401 Sheridan Road, North Chicago, Illinois 60064, United States. ‡ Drug Product Science and Technology, Bristol-Myers Squibb Company, New Brunswick, New Jersey 08903, United States.

for which could include molecular level interactions in the melt and at the interface. Polymers are typically used in the formulation of amorphous materials for drug delivery applications, with one key role being to retard crystallization. Formation of specific interactions such as H-bonding between the drug and polymer are thought to be important in impacting the extent of growth rate inhibition,5,29 and above a certain concentration, high Tg polymers will also increase the viscosity of the system and reduce growth rates through reducing the mobility in the system. Interestingly, our data suggest that, for a given polymer and for a drug that contains a good hydrogen bond donor group that is available to participate in an intermolecular interaction (OH or NH), the relative reduction in growth rate is very similar between different compounds. In other words, no matter what the initial growth rate is, addition of 10 mol % of PVP reduces the growth rate of the studied compounds by a factor of around 5−10. Therefore, if it is desirable to reduce the growth rate to a given value, compounds with faster growth rates will clearly require more polymer than compounds that grow more slowly. Finally, we note that our study on growth rates was conducted at temperatures above the glass transition temperature. Therefore, the observations are directly pertinent to understand the tendency for crystal growth during high temperature processing such as melt extrusion. This is of particular importance, since most postextrusion cooling processes are slow in nature (i.e., the extruded material is not quench cooled); thus, the product may spend sufficient time in the compound’s undercooled temperature region where nucleation and crystal growth processes may be favorable. Amorphous products are typically stored at lower temperatures, and it is well accepted that growth rate trends cannot readily be extrapolated from high to low temperatures. However, it is likely that compounds with high growth rates in the undercooled liquid relative to other compounds will also be fast growers relative to other compounds in the glassy region, in particular for compounds where faster growth is driven by small melt entropy values.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the National Science Foundation Engineering Research Center for Structured Organic Particulate Systems (NSF ERC-SOPS) (EEC-0540855) for financial support.

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REFERENCES

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CONCLUSIONS Crystal growth rates from undercooled melts of low molecular weight organic compounds of pharmaceutical relevance were observed to vary by up to 5 orders of magnitude. The various compounds could be grouped into fast, intermediate, and slow growers on the basis of the magnitude of the maximum crystal 9981



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Factors Influencing Crystal Growth Rates from Undercooled Liquids of

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