A Metastable Polymorph of Metformin Hydrochloride: Isolation and

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A Metastable Polymorph of Metformin Hydrochloride: Isolation and Characterization Using Capillary Crystallization and Thermal Microscopy Techniques Scott L. Childs,*,§ Leonard J. Chyall,‡ Jeanette T. Dunlap,‡ David A. Coates,‡ Barbara C. Stahly,‡ and G. Patrick Stahly‡

CRYSTAL GROWTH & DESIGN 2004 VOL. 4, NO. 3 441-449

SSCI, Inc., 3065 Kent Avenue, West Lafayette, Indiana, 47906 USA, and Design Science Research, LLC, 1256 Briarcliff Road NE, Atlanta, Georgia 30306 USA Received December 3, 2003;

Revised Manuscript Received March 12, 2004

ABSTRACT: Capillary crystallization techniques and thermal microscopy have been used to identify and characterize a metastable polymorph of metformin hydrochloride. The single crystal structure of the metastable polymorph (Form B) is reported and compared to the known thermodynamically stable form (Form A). There is a 5.8% density difference between Form A and Form B. N-H‚‚‚N hydrogen bonds form a 1D rod motif in Form A as opposed to a 0D dimer in Form B, while the charge-assisted N-H‚‚‚Cl hydrogen bonds maintain a layered motif in both Forms A and B. The preferential generation of metastable solid phases is discussed in the context of classical nucleation theory. Introduction Compounds used as active pharmaceutical ingredients (APIs) must be screened for polymorphism according to ICH guidelines.1 The goal of the screen is to determine if an API can exist in multiple solid forms, not only polymorphs but also hydrates, solvates, and amorphous forms. If so, the solid form of the API to be used in the drug product must be selected rationally and manufactured consistently. Screening methods are as varied as those who carry them out, but all involve the generation and analysis of multiple solid samples of the compound under scrutiny. What varies is the number of samples that are generated, the conditions under which the solids are produced, and the methods by which they are analyzed. At present, polymorph screening is an empirical process in which solids are generated under various conditions and analyzed to determine the solid form. The concept that different solid forms arise from different experimental conditions compels the use of a variety of crystallization methods in a polymorph screen. Traditional approaches to polymorph generation are described by Guillory in a recent review.2 These procedures include crystallization from single solvents or solvent mixtures, and nonsolvent methods such as sublimation, thermal treatment, and crystallization from the melt. From solution, crystallization can be induced by any of a number of methods that increase the concentration of the solute to a level above the equilibrium solubility value. As examples, solvent evaporation, cooling, or addition of an antisolvent to a solution of the compound are common crystallization techniques. As pointed out by Guillory, factors that may affect the polymorphic form that crystallizes from solution include, among others, the solvent polarity, degree of supersaturation, temperature (including the cooling profile), ad* Corresponding author. Design Science Research, LLC, 1256 Briarcliff Rd NE, Atlanta, GA 30306 USA. Tel. 404.377.4324. FAX 404.712.9357. E-mail [email protected]. ‡ SSCI, Inc. § Design Science Research, LLC.

ditives, seeds, pH, and agitation rate. Thus, the number of conditional variations necessary to cover all conceivable experiments in an empirical study is enormous. It is essential to identify the most stable solid phase early in the development of the drug product. The goal is to avoid problems such as those exhibited by ritonavir, in which a new, more thermodynamically stable polymorph arose after 240 lots of the commercial drug product had been produced.3 It is also necessary to conduct crystallization procedures that provide highenergy forms. While generally not used as the commercial form, metastable phases of APIs can often be present during the manufacturing process. By identifying, isolating, and characterizing metastable solid forms, potential problems in large-scale processes are easier to avoid. We are developing polymorph screening techniques with the goal of identifying polymorphs that would otherwise be missed using traditional methods. As part of this program, we developed a new screening technique that makes use of capillary tubes as the crystallization vessels.4,5 It is postulated that the very slow evaporation rate in a capillary allows for an increase in the metastable zone width, where the concentration is high enough for the solution to become supersaturated relative to the metastable phases. Because of this, crystallizations by solution evaporation in capillary spaces may afford both stable and metastable forms, thus providing an operationally simple method to explore all energetic space. A new polymorph of nabumetone was recently identified using this technique.4 The application of counter-diffusion in capillary spaces is a technique that has been used to grow high-quality single crystals of proteins.6 Another advantage of the capillary method is that polymorph screens can be conducted on compounds that are available in limited supply. An overview of the polymorphic complexity of a substance can be obtained with less than 50 mg of material. Another technique that we use to encourage formation of metastable solid phases is adapted from melt crystal-

10.1021/cg034243p CCC: $27.50 © 2004 American Chemical Society Published on Web 04/10/2004

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Figure 1. Structure of metformin hydrochloride.

lization and involves the use of very small amounts of high boiling organic liquids as the crystallization medium. This technique requires that the compound be saturated in a minimum amount of a suitable liquid at high temperatures. The use of a liquid additive and nonisothermal crystallization conditions is intended to increase the molecular mobility and thus lower the entropic barriers that hinder nucleation and crystallization from the melt.7 The intent is to generate the highest supersaturation that is feasible at elevated temperatures. Screening experiments that vary the amount of the liquid additive, the solubility of the solute in the additive liquid, the saturation temperature, the supersaturation achieved, and the subsequent thermal profile will often lead to the precipitation of a metastable solid, if one exists. In this paper, we report the identification and characterization of a new polymorph of metformin hydrochloride (Figure 1). This compound is the API in an antihyperglycemic drug marketed by Bristol-Myers Squibb under the trade name Glucophage, and is also currently available from generic suppliers. The properties of metformin hydrochloride have been summarized in a review article.8 The new metastable form presented here was initially identified using capillary crystallization techniques and further characterized by thermal microscopy and single-crystal X-ray analysis. Experimental Procedures and Results General Methods. Metformin hydrochloride (1,1dimethylbiguanide hydrochloride) was purchased from Sigma Chemical (St. Louis, MO) and used as received. Solvents and other reagents were purchased from commercial suppliers and used as received. Capillary tubes were purchased from Charles Supper Co. (Natick, MA). Solutions of metformin hydrochloride were prepared in various solvents at two different initial concentrations and added to X-ray quality capillary tubes. The solvent was allowed to evaporate at various temperatures and pressures to provide a solid residue. The resulting solids were then analyzed by XRPD. XRPD analyses were performed on an Inel diffractometer, which has been previously described.4 Ambient temperature and hot stage microscopy experiments were performed using a custom built aluminum hot-stage. A temperature controller was used to regulate the temperature of the aluminum block (( 1 °C). The temperature range of the device is ambient to 320 °C with heating and cooling rates of ∼3 °C/min. Polarized transmitted light was used to illuminate the sample, and observations were made with a Baush & Lomb Stereozoom 4 microscope. Images were acquired using an Olympus SZX9 microscope using an Olympus C-750 digital camera. Raman analyses were performed on a Nicolet FT-Raman 960 spectrometer. This spectrometer uses an excitation wavelength of 1064 nm. Approximately 0.5 W (variable) of Nd:YVO4 laser power was

Childs et al.

used to irradiate the samples. Each spectrum is the result of 256 co-added scans acquired at 4 cm-1 resolution. Form A of metformin hydrochloride was analyzed as received from the commercial supplier by packing the material in a 1.0-mm diameter capillary. A sample of Form B used for Raman analysis was prepared by allowing a solution of metformin hydrochloride in 3:1 acetone/water at an initial concentration of ∼200 mg/ mL to evaporate to dryness at 60 °C in a 0.7-mm diameter capillary tube. For single-crystal data collection, suitable crystals of Form A and Form B were coated with Paratone-N oil, suspended in a small fiber loop, and placed in a cooled nitrogen gas stream at 100 K on a Bruker D8 SMART APEX CCD sealed tube diffractometer with graphite monochromated Mo KR (0.71073 Å) radiation. Data were measured using a series of combinations of phi and omega scans with 10 s frame exposures and 0.3° frame widths. Data collection, indexing, and initial cell refinements were all carried out using SMART9 software. Frame integration and final cell refinements were done using SAINT10 software. The SADABS11 program was used to carry out the absorption correction on Form B. The structures were solved using direct methods and difference Fourier techniques (SHELXTL, V5.10).12 All the hydrogen atoms were located from difference Fouriers and included in the final cycles of least squares with isotropic Uij’s. All non-hydrogen atoms were refined anisotropically. Scattering factors and anomalous dispersion corrections are taken from the International Tables for X-ray Crystallography.13 Structure solution, refinement, and generation of publication tables were performed by using SHELXTL, V5.10 software. Powder patterns were calculated from the single-crystal data using PowderCell 2.3.14 Additional details of data collection and structure refinement are given in Table 2. More details can be found in the corresponding CIF files, which are included as Supporting Information. Polymorph Screen in Capillary Tubes. For the capillary polymorph screen of metformin hydrochloride, 28 different solvents and 8 different evaporation conditions were used to provide close to 500 separate experiments. The poor solubility of metformin hydrochloride in most organic solvents limited the screen to solutions of the compound in alcohols and mixtures of miscible organic solvents with water. The results from these experiments organized by evaporation technique are summarized in Table 1. The majority of the crystallizations provided the known crystal form, which we designated Form A. This was evident by comparison of the corresponding XRPD patterns with a simulated powder pattern for the published X-ray structure.15 In addition to Form A, numerous crystallizations provided a different crystalline phase, which was designated Form B. As shown in Figure 2, the XRPD patterns for Forms A and B are easily distinguished from each other. These two polymorphs could also be distinguished by their Raman spectra (Figure 3). For all experiments and all techniques, 45% of the capillary experiments yielded an XRPD pattern that corresponded to Form B. Approximately 16% of the attempted crystallizations provided samples that were unsuitable for XRPD analysis, or the analysis provided

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Table 1. Metformin Hydrochloride Capillary Crystallizations Arranged by Technique evaporation method

tube diam (mm)

initial conc

XRPD pattern

all techn

vacuum (RT)

cold

room temp

heat

0.7

1.0

1X

2X

Form A Form B undetermined unknown A+B total B/(A+B) (%)

224 180 81 4 1 490 45

66 32 9

77 11 27 1

28 63 24

98 95 32 3

116 13

115 69

228 49

126 85 49 1 1 262 40

86 76 51 3

107 33

53 74 21 3 1 152 58

138 104 30 1 1 274 43

Figure 2. Representative XRPD patterns for metformin hydrochloride polymorphs.

Figure 3. The fingerprint region of the Raman spectra for metformin hydrochloride polymorphs.

inconclusive results. In addition to these results, four experiments provided XRPD patterns that could not be matched to either Form A or Form B, and one experiment provided an XRPD pattern corresponding to a

216 47

mixture of both forms. The samples that gave rise to unique XRPD patterns were not characterized further; however, these samples may constitute other new solid phases of this compound. The XPRD patterns for these four samples are provided as Supporting Information. We found no apparent trend in the bias toward the crystallization of Form B based on solvent identity. However, the temperature of the capillary evaporation had a significant effect on the identity of the polymorph generated (Table 1). Crystallizations performed at elevated temperatures resulted in preferential crystallization to Form B (69% Form B), while crystallizations performed below room temperature provided predominantly Form A (13% Form B). The preference can be attributed to a temperature effect rather than the increased evaporation rate that occurs at higher temperatures. Crystallizations performed at room temperature with vacuum-assisted evaporation resulted in predominantly Form A (33% Form B), while the slower evaporation rates provided from ambient pressure evaporations resulted in 58% of Form B (Table 1). Capillary tubes of 0.7 mm and 1.0 mm diameter were used in the evaporation experiments. Form B was detected in the 0.7-mm capillaries in 49% of the experiments. In 1.0-mm capillaries Form B was detected in 40% of the experiments. It is known that the equilibrium and diffusion properties of a constrained fluid are related to the capillary width,16 and our results suggest that using capillaries with a smaller diameter may generate a slightly more favorable environment for isolating the high-energy polymorph of metformin hydrochloride. Samples of Form B are stable for several weeks when left undisturbed in the capillary tubes. However, grinding Form B or simply attempting to remove the solids from the capillaries resulted in a phase transformation to Form A. Identification of Form A and Form B with Thermal Microscopy Techniques. When we began our studies of metformin hydrochloride, we found a report by Kuhnert-Brandstatter et al. in which thermal microscopy was used to generate a new polymorph of this compound by tempering the melt at 50 to 60 °C.17 Our attempts to reproduce this observation failed, even after considerable effort. We observed that metformin hydrochloride decomposes upon melting at 232 °C, and the decomposition products interfered with the recrystallization of the material. Since gas evolution was also observed by Kuhnert-Brandstatter et al. upon melting the compound, it is possible that the crystalline material that they observed corresponded to a decomposition product. The thermal microscopy techniques that we are developing are intended to address this kind of difficulty with crystallization from the melt. The thermal microscopy technique creates conditions that are similar to,

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Figure 4. Form B of metformin hydrochloride generated from thermal microscopy experiments.

but distinctly different than, a pure melt with the addition of a small amount of a high boiling additive. The additive is used to avoid the difficulty that is often associated with crystallization of an API from a pure melt. Schmitt7 found that, from the melt, “crystallization studies under nonisothermal conditions revealed that compounds with the highest entropic barriers and lowest mobilities were most difficult to crystallize, regardless of the thermodynamic driving forces.” The mobility necessary to achieve the proper orientation and configuration can be supplied to a poorly behaving melt with the addition of very small amounts of an organic liquid that essentially acts as a solvent, but does not evaporate easily at elevated temperatures. Experiments were conducted in which metformin hydrochloride was melted in the presence of a small amount (approximately equal wt:wt ratio) of an organic liquid with a high boiling point between a microscope slide and coverslip. For this compound, we found that the addition of ethylene glycol dramatically affects the crystallization behavior of the resulting solution. Melting metformin hydrochloride in the presence of ethylene glycol not only lowered the temperature of the melting point, but it also prevented thermal decomposition of the API. It was possible to crystallize Form A from the melt by slowly cooling this mixture. However, rapid cooling of an extremely concentrated mixture would produce a solid phase that grew quickly and exhibited a different morphology (Figure 4). An XRPD pattern of the material obtained by rapidly cooling the melt matched the pattern for Form B obtained in capillary experiments. Isolation of Single Crystals of Form A and Form B. The more stable form of metformin hydrochloride (Form A) is the preferred product from crystallization experiments performed in vials using slow evaporation at room temperature to generate supersaturated conditions. Crystals of Form A suitable for single-crystal X-ray diffraction were generated by slow evaporation of a 2:1 methanol/water solution at ambient temperature in a 20-mL scintillation vial. It was found that single crystals of Form B could be grown by manipulating the temperature of the hot-stage during the crystal growth process. Form B was prepared by allowing a hot melt of a mixture of metformin hydrochloride and ethylene glycol to cool rapidly on a benchtop or a cold metal plate. The cylindrical disk morphology characteristic of Form B began growing rapidly (radially at ∼5 mm/min). The slide was incubated at 40 °C, and

Figure 5. Form A growing at the expense of Form B. The large blades on the left are Form A.

these disks grew until they covered a significant portion of the slide. The temperature was then raised 80 °C, and the radial growth rate decreased in response to the changing temperature and supersaturation level. At 80 °C, an equilibrium was established in which the radial growth of Form B stops and the individual nucleated crystals at the boundary of the radially growing metastable Form B begin growing as single crystals (Figure 4) with a hexagonal habit. These hexagonal tablets were incubated at 80 °C for several hours to grow crystals large enough for single-crystal analysis. Form A was also observed to nucleate under these conditions as needles, but the growth rate of Form A was much slower and could be localized on the time-scale of the experiment (Figure 5). Form A appears to be more thermodynamically stable as all experiments showed complete conversion of Form B into Form A over a 24 to 36 h period at temperatures between 0 °C and 140 °C. The metastable nature of Form B and the rapid crystal growth in the constrained environment between the slide and coverslip resulted in the growth of very thin plates (ca. 0.1 to 0.2 mm thickness). Despite this, the crystals displayed well-defined morphology and uniform extinction under crossed polarized light. The effort required to isolate and mount one of these crystals for single-crystal X-ray diffraction analysis before it converted into Form A was not trivial. Once the coverslip was removed, the single crystals of Form B would transform into Form A within minutes. The successful attempt at isolating a single crystal of Form B involved selecting a promising specimen on a slide, removing the coverslip, rapidly isolating the crystal in a drop of Paratone-N, quickly lifting it from the oil with a mounting

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Table 2. Crystal Data and Structure Refinement Details for Metformin Hydrochloride Polymorphs empirical formula formula weight temperature (K) wavelength (Å) crystal system space group a (Å) b (Å) c (Å) R (°) β (°) γ (°) volume (Å3) Z density (calculated) (mg/m3) absorption coefficient (mm-1) F(000) crystal size (mm) theta range for data collection index ranges reflections collected independent reflections completeness to theta ) 32.97° absorption correction refinement method data/restraints/parameters goodness-of-fit on F2 final R indices [I > 2sigma(I)] R indices (all data) largest diff peak and hole (eÅ-3)

Form A

Form B

C4H13ClN5 165.64 100(2) 0.71073 monoclinic P2(1)/c 7.9231(12) 13.894(2) 7.9231(12) 90 114.48 90 793.8(2) 4 1.386 0.418 352 0.30 × 0.14 × 0.07 2.82 to 33.04° -11 e h e 11 -21 e k e 21 -11 e l e 11 10423 2836 [R(int) ) 0.0480] 94.3% none full-matrix least-squares on F2 2836/0/139 1.078 R1 ) 0.0354, wR2 ) 0.0763 R1 ) 0.0445, wR2 ) 0.0781 0.438 and -0.307 eÅ-3

C4H13ClN5 165.64 100(2) 0.71073 monoclinic P2(1)/c 7.6261(7) 6.1684(6) 18.1508(16) 90 99.447(2) 90 842.25(13) 4 1.306 0.394 352 0.24 × 0.21 × 0.04 2.27 to 32.97° -11 e h e 11 -9 e k e 9 -26 e l e 27 10438 2982 [R(int) ) 0.0504] 94.0% semiempirical from equivalents full-matrix least-squares on F2 2982/0/139 1.173 R1 ) 0.0597, wR2 ) 0.1321 R1 ) 0.0745, wR2 ) 0.1390 0.936 and -0.289 e Å-3

loop, and freezing the crystal at 100 K in the diffractometer cold stream. The entire isolation and mounting process had to be completed in less than two minutes. After this, most of the exposed plates of Form B had already begun the transformation into Form A. However, once the crystal of Form B was placed in the cold stream on the diffractometer at 100 K, it was stabilized and did not convert to Form A during data collection. Structural Analysis of Form A and Form B. The X-ray structure of Form A of metformin hydrochloride has been previously reported.15 We redetermined this crystal structure to make more accurate comparisons between the two polymorphs based on data collected under identical conditions (Table 2). Specifically, we are interested in the relative density difference between the two polymorphs. There is a 5.8% difference in density between the single-crystal structures of Forms A and B (both collected at 100 K). Gavezzotti and Filippini18 published an analysis of densities of polymorphs contained in the Cambridge Structural Database (CSD) and found that 93% of the polymorphic pairs in the CSD had a density difference of less than 5%. The density difference for the two forms of metformin hydrochloride suggests that Form B is a highly metastable structure, which correlates with the difficulty in handling this polymorph. Both structures are monoclinic (P21/c) with one complete metformin cation and one chloride anion in the asymmetric unit (Figure 6 and Figure 7). The organization of the two forms is similar in that the N-H‚‚‚N hydrogen bonds form substructures that are linked by N-H‚‚‚Cl charge assisted hydrogen bonds. The chloride ions and the associated N-H‚‚‚Cl charge-assisted hydrogen bonds are confined to a layer in both structures (Figure 8 and Figure 9). These hydrogen bonds are in

Figure 6. Metformin hydrochloride Form A shown at 50% probability ellipsoids.

the bc plane in Form B and the ac plane in Form A. The aggregates created by the neutral N-H‚‚‚N hydrogen bonds form two very different motifs. In Form A, the N-H‚‚‚N hydrogen bonds create a one-dimensional (1D) rod motif, while in Form B, a centrosymmetric 0D dimer is generated by the hydrogen bonds between cations (Figure 10). The conformations of the metformin cations in Forms A and B are different with respect to the N5-C2-N1C1 dihedral angle. For Form A this angle is -53.7°, while the dihedral angle is 129.1° in Form B. The asymmetric unit for Form A and Form B are shown in Figures 6 and 7, respectively. The different dihedral angles place the -C(NH2)2 group of the molecule in approximately opposite directions when the two polymorphs are compared. For Form A, the -C(NH2)2 group is near to the -N(CH3)2 group, providing a more compact asymmetric unit when compared to Form B, which has a more ex-

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Figure 7. Metformin hydrochloride Form B shown at 50% probability ellipsoids. Figure 10. Aggregation of metformin cations based on neutral N-H‚‚‚N hydrogen bonds. Form A is a 1D chain, while Form B is a centrosymmetric dimer.

Figure 8. Packing diagram of metformin hydrochloride Form B. All N-H‚‚‚Cl interactions (yellow) are confined to a layer and metformin hydrochloride dimers are joined with N-H‚‚‚ N (dashed blue) interactions. Hydrogen atoms are omitted for clarity, metformin molecules are displayed in blue, and Cl ions are green.

Discussion The preferential formation of the metastable Form B in capillary experiments prompted us to conduct a theoretical investigation into the effects of highly supersaturated conditions on the nucleation of polymorphic phases. Classical nucleation theory (CNT) can be used to calculate the rate of nucleation for a particular form under specific conditions. The results of these calculations are compared to the results in this study, but also comment on the preparation of metastable forms in general. According to CNT, the following rate equation predicts the number of nuclei formed per unit time per unit volume:20

(

J ) A exp -

where A )

Figure 9. Packing diagram of metformin hydrochloride Form A. Hydrogen atoms are omitted for clarity, metformin molecules are displayed in blue, and Cl ions are green. The page is approximately orthogonal to the ac bisector.

tended molecular backbone. There is possibly a link between the crystal growth unit that exists in solution and the resulting aggregates observed in the structures. The structure of the metastable Form B may comment on current theory concerning the relationship between the organization in a supersaturated solution and the addition of units to the growing structure.19 If the conformation associated with the 0D dimer aggregate in Form B is similar to the conformation present in the highly supersaturated solution, then it would be energetically favorable to add these preorganized growth units to the growing crystal faces rather than require a substantial conformational change at the liquid-to-solid interface.

)

B ln S2

( ) kT vo2γ

1/2

DCe ln S and B )

16π vo2γ3 3k3T3 (1)

where J, nucleation rate (m-3 s-1); A, kinetic preexponential factor (m-3s-1); γ, interfacial tension (J/m2); vo, molecular volume (m3); k, Boltzmann constant (1.38 × 10-23 J/K); T, temperature (K); Ce, equilibrium concentration or solubility as a molecular concentration (m-3); D, diffusion coefficient in volume-diffusion controlled systems (m2/s); S, supersaturation ratio (S ) Csol/Cequil where C ) concentration). Values for interfacial tension (γ) can be calculated using the equation provided by Mersmann:21

( )

( )

F CS M kT and CS ) γ ) 0.414 2/3 ln L where vo ) N F M vo C a (2) where γ, interfacial tension (J/m2); CS, concentration of solute in the solid (mol/m3); CL, concentration of solute in the liquid (mol/m3); F, crystal density (g/m3); M, molecular weight (g/mol); Na, Avogadro’s number (6.022 × 1023/mol).

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When considering the probability of nucleation for one of two possible polymorphs, it is not the absolute value of the nucleation rate, but rather the relative nucleation rates of two polymorphs that is of interest. Nucleation is the first step in the selection of a polymorphic phase, and the first polymorph to nucleate will have the best chance of relieving the supersaturated condition through crystal growth. To quantify the competition between nucleation of polymorphic phases, it is helpful to generate an expression that reflects the fraction of nucleation of one form relative to the total number of nucleation events:22

R)

[

(

J1 A2 B1 B2 ) 1 + exp 2 J1 + J2 A1 ln S1 ln S22

)]

-1

(3)

Values of R will be between 0 and 1. If R ) 1.0, it is predicted that only Form A will nucleate; R ) 0.5 means that there is an equal probability for the nucleation of Form A or Form B. To determine the value of R across a range of supersaturation values, the molecular weight of the solute, density of each polymorph, equilibrium concentration of each polymorph in the crystallization solvent, and temperature must be known. In the course of a polymorph screen, the molecular weight, density, and equilibrium concentration (solubility) of the known phase is typically readily available. To use eq 1 to approximate experimental conditions that would favor the formation of a new polymorph, values for the density and relative solubility of a possible metastable phase must be estimated. On the basis of these assumptions, reasonable estimates for the conditions necessary for preferentially nucleating a metastable phase can be determined. The density difference between polymorphs is typically within a few percent and rarely extends past 5-7%.18 A review of the literature indicates that relative solubility values for pharmaceutical polymorphs are typically within a defined rangesthe solubility of the metastable form is usually less than twice that of the more stable form.3,23 Although exceptions to these assumptions exist, these values for relative density and solubility differences limit the parameter space for the unknown values needed to calculate the relative nucleation rates a pair of dimorphs. In the present case of metformin hydrochloride, the density difference between the two polymorphs is known, and illustrating the relative nucleation rates of the metformin hydrochloride polymorphs only requires that the solubility of the metastable phase relative to the stable phase be estimated. We were not able to measure the solubility of Form B because of the sensitivity of this form to handling. In addition to choosing a range of possible solubility values for Form B, we have calculated the relative nucleation rate at three different equilibrium concentrations to demonstrate the effect that the equilibrium solubility has on the nucleation competition. The equilibrium solubility can be manipulated experimentally through solvent selection, but the relative solubility of the metastable phase will remain the same regardless of the equilibrium solubility of the stable phase.24 By estimating and plotting three different values for the metastable form relative solubility and a separate plot for each estimated equilibrium solubility value (Figure 11), several trends appear. The plots

Figure 11. The three plots represent varying levels of hypothetical solubility. (a) 10 mg/mL, (b) 50 mg/mL, and (c) 200 mg/mL. The three lines in each plot represent a range for the solubility difference between the two polymorphs at 293 K. SB ) solubility of Form B, SA ) solubility of Form A; SB is represented as 1.1, 1.6, or 2.5 times the value of SA.

indicate that at low supersaturation, the more stable form dominates the nucleation competition; however, as supersaturation is increased the nucleation of the metastable phase becomes more probable and eventually dominates. The supersaturation level required for the nucleation of the metastable phase to dominate the system decreases as the equilibrium solubility of the API in the crystallization solvent is increased. CNT predicts that higher temperatures will favor the formation of a metastable phase, which generally agrees with our experimental observations. However, the large difference in polymorph fraction observed experimentally is not reflected as dramatically by the calculations (Figure 13). The effect of temperature observed experimentally is presumably due to influences in addition to the increased probability for nucleation of Form B that theory predicts will accompany an increase in temperature. The free energy difference between polymorphs will also change as a function of temperature,25 and this is not taken into account in these calculations. Figure 12 shows that as the theoretical equilibrium solubility of the API is increased, the supersaturation level required to achieve equal probability for nucleating either polymorph is decreased. When the solubility of Form A is low, it requires much higher supersaturation ratios to achieve nucleation of Form B. As the solubility of Form A is increased, the supersaturation level

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Acknowledgment. We thank Ken Hardcastle and Karl Hagen at the Emory University X-ray diffraction center for collecting the single crystal diffraction data. Supporting Information Available: X-ray crystallographic information files (CIF) for metformin hydrochloride Forms A and B. Raman spectra for these two forms and four XRPD patterns obtained from the capillary screen that were not further characterized are also included. This information is available free of charge via the Internet at http://pubs.acs.org.

References Figure 12. The plotted lines represent the point where nucleation of either polymorph has equal probability (where R ) 0.5). The area above a line represents a greater probability that the metastable form will nucleate, while in the area below the line the more stable form will be favored. Three possible degrees of solubility of Form B relative to Form A are plotted (Form B is 1.1, 1.6, or 2.5 times more soluble than Form A).

Figure 13. The effect of temperature on the calculated polymorph fraction (R) of metformin hydrochloride for a crystallization experiment in which the metastable form (Form B) is 1.6 times more soluble than the stable form (Form A) and the equilibrium solubility of Form A in the crystallization solvent is 50 mg/mL.

required to achieve predominant nucleation of Form B is lowered. As the difference in solubility is increased, the supersaturation levels required for equal nucleation probability are dramatically increased at lower solubility values, while at higher solubility values the effect is less significant. Conclusions To obtain metastable phases of active pharmaceutical ingredients, the results from calculations based on classical nucleation theory suggest that achieving very high supersaturation in a solution in which the API is reasonably soluble should be achieved before nucleation occurs, and under these conditions the nucleation of the metastable phase is a more probable event. After nucleation, the crystallization environment must be able to sustain growth of the metastable phase. Both capillary crystallization experiments and our thermal microscopy techniques have been designed to achieve these requirements. Slow evaporation experiments in capillaries have been shown to provide the necessary conditions for generating metastable forms under thermodynamic conditions, and our thermal microscopy method provides identical results under kinetic conditions. Both methods have been shown to readily produce the metastable Form B of metformin hydrochloride, and we continue to develop and use these methods to identify and characterize new solid forms of pharmaceuticals.

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